Non-crimp fabric composites
© Woodhead Publishing Limited, 2011
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© Woodhead Publishing Limited, 2011
Non-crimp fabric composites Manufacturing, properties and applications Edited by Stepan V. Lomov
Oxford
Cambridge
Philadelphia
New Delhi
© Woodhead Publishing Limited, 2011
Published by Woodhead Publishing Limited, 80 High Street, Sawston, Cambridge CB22 3HJ, UK www.woodheadpublishing.com Woodhead Publishing, 1518 Walnut Street, Suite 1100, Philadelphia, PA 19102–3406, USA Woodhead Publishing India Private Limited, G-2, Vardaan House, 7/28 Ansari Road, Daryaganj, New Delhi – 110002, India www.woodheadpublishingindia.com First published 2011, Woodhead Publishing Limited © Woodhead Publishing Limited, 2011 The authors have asserted their moral rights. This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. Reasonable efforts have been made to publish reliable data and information, but the authors and the publisher cannot assume responsibility for the validity of all materials. Neither the authors nor the publisher, nor anyone else associated with this publication, shall be liable for any loss, damage or liability directly or indirectly caused or alleged to be caused by this book. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming and recording, or by any information storage or retrieval system, without permission in writing from Woodhead Publishing Limited. The consent of Woodhead Publishing Limited does not extend to copying for general distribution, for promotion, for creating new works, or for resale. Specific permission must be obtained in writing from Woodhead Publishing Limited for such copying. Trademark notice: product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation, without intent to infringe. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library. ISBN 978-1-84569-762-4 (print) ISBN 978-0-85709-253-3 (e-book) The publisher’s policy is to use permanent paper from mills that operate a sustainable forestry policy, and which has been manufactured from pulp which is processed using acid-free and elemental chlorine-free practices. Furthermore, the publisher ensures that the text paper and cover board used have met acceptable environmental accreditation standards. Typeset by RefineCatch Limited, Bungay, Suffolk Printed by TJI Digital, Padstow, Cornwall, UK
© Woodhead Publishing Limited, 2011
Contents
Contributor contact details Introduction
xiii xvi
Part I
Manufacturing of non-crimp fabrics
1
1
Production of non-crimp fabrics for composites
3
A. SCHNABEL and T. GRIES, Institut für Textiltechnik (ITA) of RWTH Aachen University, Germany
1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10
Introduction Warp-knitted non-crimp fabric (NCF) Weft-knitted NCF Non-crimp woven fabrics 3D woven and non-interlaced NCF Fixation by adhesion Comparison of production technologies Future trends Acknowledgements References
3 5 22 23 27 30 33 35 37 37
2
Standardisation of production technologies for non-crimp fabric composites
42
F. KRUSE and T. GRIES, Institut für Textiltechnik (ITA) of RWTH Aachen University, Germany
2.1 2.2 2.3 2.4 2.5
Introduction Classification and standardisation of non-crimp fabric (NCF) production methods Outstanding patents of existing machines for the production of NCFs The ‘Hexcel patent’ – EP 0972102 B1 Product patents in the production of NCFs
42 42 47 59 61
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Contents
2.6
Immobilisation of adhesive on the surface of semi-finished textile products (DE 102008004112 A1) References
64 65
Structural stitching of non-crimp fabric preforms for composites
67
2.7 3
P. MITSCHANG, Institut für Verbundwerkstoffe GmbH, Germany
3.1 3.2 3.3 3.4 3.5 3.6
Introduction Threads for structural stitching technology Stitching technology and sewing machines Quality aspects for structural stitching Applications and future trends References
67 68 70 74 81 82
4
Understanding and modelling the effect of stitching on the geometry of non-crimp fabrics
84
S. V. LOMOV, Katholieke Universiteit Leuven, Belgium
4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8
Introduction General parameters of the fibrous plies Geometry of the stitching Distortions of fibres in the plies Change of the geometry after shear A geometrical model of NCF Conclusion References
84 85 86 92 98 100 100 102
5
Automated analysis of defects in non-crimp fabrics for composites
103
M. SCHNEIDER, Toho Tenax Europe GmbH, Germany
5.1 5.2 5.3 5.4 5.5
Motivation Quality characteristics of non-crimp fabric (NCF) Quality analysis of NCF by digital image analysis Future trends References
Part II Manufacturing of non-crimp fabric composites 6
Deformability of textile preforms in the manufacture of non-crimp fabric composites
103 104 106 111 114 115
117
S. V. LOMOV, Katholieke Universiteit Leuven, Belgium
6.1
Introduction
117
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6.2 6.3 6.4 6.5 6.6 6.7
Shear Biaxial tension Compression Bending Conclusion References
118 128 132 136 139 141
7
Modelling the deformability of biaxial non-crimp fabric composites
144
P. HARRISON, University of Glasgow, UK, W-R. YU, Seoul National University, Korea and A. C. LONG, University of Nottingham, UK
7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8
Introduction Behaviour of fabric architecture on the shear and draping behaviour of non-crimp fabrics (NCFs) Modelling strategies for NCF forming Energy-based kinematic mapping Finite element modelling of forming for NCFs Future trends Further information and advice References
144 145 148 149 156 161 162 162
8
Permeability of non-crimp fabric preforms
166
R. LOENDERSLOOT, University of Twente, The Netherlands
8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8
Introduction Experimental permeability results Geometric effects Deformation and permeability Conclusions Acknowledgements References Appendix: nomenclature
166 168 187 196 208 209 210 214
9
Understanding variability in the permeability of non-crimp fabric composite reinforcements
216
A. ENDRUWEIT and A. C. LONG, University of Nottingham, UK
9.1 9.2 9.3 9.4 9.5 9.6
Introduction Material characterisation Permeability measurement Modelling and simulation Future trends References
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216 217 222 233 239 239
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10
Modelling of the permeability of non-crimp fabrics for composites
242
B. VERLEYE, S. V. LOMOV and D. ROOSE, Katholieke Universiteit Leuven, Belgium
10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8
Introduction Numerical simulation Experimental validation Parametric study Influence of shear Conclusion Acknowledgements References
Part III Properties of non-crimp fabric composites 11
Mechanical properties of non-crimp fabric (NCF) based composites: stiffness and strength
242 246 251 253 256 257 257 258 261
263
S. V. LOMOV, T. TRUONG CHI and I. VERPOEST, Katholieke Universiteit Leuven, Belgium
11.1 11.2 11.3 11.4
11.6 11.7 11.8 11.9 11.10
Introduction Materials and composite production Test procedures Mechanical properties of non-crimp fabric (NCF) composites Mechanical properties of composites based on sheared MMCF Damage development in B2 (0°/90°) laminates X-ray radiography Damage initiation in non-sheared and sheared materials Conclusions References
274 279 283 285 286 287
12
Damage progression in non-crimp fabric composites
289
11.5
263 264 265 266
L. E. ASP, J. VARNA and E. MARKLUND, Swerea SICOMP and Luleå University of Technology, Sweden
12.1 12.2 12.3 12.4 12.5
Introduction Damage progression in non-crimp fabric (NCF) composites due to in-plane loading Damage progression in impacted NCF composites Conclusions References
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289 290 300 308 308
Contents
13
Fatigue in non-crimp fabric composites
ix
310
K. VALLONS, Katholieke Universiteit Leuven, Belgium
13.1 13.2 13.3 13.4 13.5 13.6
Introduction Fatigue in non-crimp fabric (NCF) composites Post-fatigue residual properties Conclusions and open questions References Appendix
310 311 330 332 332 333
14
Mechanical properties of structurally stitched non-crimp fabric composites
335
N. HIMMEL, Institut für Verbundwerkstoffe GmbH, Germany and H. HEß, BASF Engineering Plastics Europe, Germany
14.1 14.2 14.3 14.4 14.5 14.6 15
Introduction Materials and stitching configurations Characterisation of structurally stitched NCF laminates Simulation of mechanical behaviour of structurally stitched laminates Conclusions and future trends References Predicting the effect of stitching on the mechanical properties and damage of non-crimp fabric composites: finite element analysis
335 337 341 348 354 355
360
D. S. IVANOV, S. V. LOMOV and I. VERPOEST, Katholieke Universiteit Leuven, Belgium
15.1 15.2 15.3 15.4 15.5 15.6 16
Introduction Representative volume element (RVE) of non-crimp fabric (NCF) composites Elastic analysis Damage accumulation in NCF composites Conclusions References
360 363 369 372 383 384
Modelling drape, stress and impact behaviour of non-crimp fabric composites
386
A. K. PICKETT, University of Stuttgart, Germany
16.1 16.2 16.3 16.4
Finite element (FE) methods for drape, stress and impact analysis Laminate analysis and FE stiffness for non-crimp fabric (NCF) FE methods for infusion analysis Draping and FE simulation
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386 387 389 390
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Contents
16.5 16.6 16.7 16.8
Infusion simulation Stiffness and failure Impact and failure References
394 394 396 400
17
Modelling stiffness and strength of non-crimp fabric composites: semi-laminar analysis
402
E. MARKLUND, J. VARNA and L. E. ASP, Swerea SICOMP and Luleå University of Technology, Sweden
17.1 17.2 17.3 17.4 17.5
Introduction Stiffness models Strength models for non-crimp fabric (NCF) composites Conclusions References
402 405 420 435 436
Part IV Applications of non-crimp fabric composites
439
18
441
Aerospace applications of non-crimp fabric composites P. MIDDENDORF and C. METZNER, EADS Innovation Works, Germany
18.1 18.2 18.3 18.4 18.5
Introduction Aeronautic requirements Application examples Future trends References
441 443 445 447 448
19
Non-crimp fabric: preforming analysis for helicopter applications
449
F. DUMONT and C. WEIMER, Eurocopter Deutschland GmbH, Germany
19.1 19.2 19.3 19.4 19.5 19.6 20
Introduction Preform techniques for non-crimp fabrics (NCFs) Main NCF deformation mechanism observed during preforming Preforming defect analysis Conclusion and future trends References
449 449 454 456 458 460
Automotive applications of non-crimp fabric composites
461
B. SKÖCK-HARTMANN and T. GRIES, Institut für Textiltechnik (ITA) of RWTH Aachen University, Germany
20.1 20.2
Introduction Applications of non-crimp fabrics (NCF) in the automotive industry
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461 466
Contents
20.3
xi
20.4 20.5 20.6
Research and development for the use of NCF in automotive applications Future trends Conclusion References
469 476 478 479
21
Non-crimp fabric composites in wind turbines
481
G. ADOLPHS and C. SKINNER, OCV Technical Fabrics, Belgium
21.1 21.2 21.3 21.4 21.5 22
Introduction Development of non-crimp fabric (NCF) composites in wind energy NCF materials used in nacelle construction Future trends References
481 483 491 492 493
Cost analysis in using non-crimp fabric composites in engineering applications
494
P. SCHUBEL, University of Nottingham, UK
22.1 22.2 22.3 22.4 22.5 22.6
Introduction Costing methodologies: current approaches Technical cost modelling Case study: 40 m wind turbine blade shell Acknowledgements References
494 495 496 504 509 509
Index
511
© Woodhead Publishing Limited, 2011
Contributor contact details
(* = main contact)
Chapter 1
Chapters 4, 6 and 11
A. Schnabel* and T. Gries Institut für Textiltechnik (ITA) of RWTH Aachen University Otto-Blumenthal-Strasse 1 52074 Aachen Germany
S. V. Lomov Department of Metallurgy and Materials Engineering Katholieke Universiteit Leuven Kasteelpark Arenberg 44 bus 2450 B-3001 Heverlee (Leuven) Belgium
e-mail:
[email protected]; thomas.gries@ita. rwth-aachen.de
e-mail:
[email protected]
Chapter 5 Chapter 2 F. Kruse* and T. Gries Institut für Textiltechnik (ITA) of RWTH Aachen University Otto-Blumenthal-Strasse 1 52074 Aachen Germany e-mail:
[email protected];
[email protected]
Chapter 3 P. Mitschang Manufacturing Science Institut für Verbundwerkstoffe GmbH Erwin-Schroedinger-Strasse 58 67663 Kaiserslautern Germany
M. Schneider Toho Tenax Europe GmbH Kasinostrasse 19–21 42103 Wuppertal Germany e-mail:
[email protected]
Chapter 7 P. Harrison* University of Glasgow School of Engineering University Avenue Glasgow G12 8QQ UK e-mail:
[email protected]
e-mail:
[email protected]
xiii © Woodhead Publishing Limited, 2011
xiv
Contributor contact details
W-R. Yu Seoul National University Department of Materials Science and Engineering Gwanak _ 599 Gwanak-ro Gwanak-gu Seoul 151–742 Korea A. C. Long University of Nottingham Faculty of Engineering University Park Nottingham NG7 2RD UK
Chapter 8 R. Loendersloot University of Twente Faculty of Engineering Technology – Applied Mechanics & Production Technology P.O. Box 217 7500 AE Enschede The Netherlands e-mail:
[email protected]
Chapter 9 A. Endruweit and A. C. Long* Faculty of Engineering (M3) – Division of Materials, Mechanics and Structures University of Nottingham University Park Nottingham NG7 2RD UK e-mail:
[email protected]
Chapter 10 B. Verleye*, S. V. Lomov and D. Roose
Katholieke Universiteit Leuven Celestijnenlaan 200A B-3001 Leuven Belgium e-mail:
[email protected]
Chapter 12 L. E. Asp* and E. Marklund Swerea SICOMP AB Box 104 SE-43122 Mölndal Sweden e-mail:
[email protected]; erik.
[email protected]
J. Varna Div. Polymer Engineering Luleå University of Technology SE-97187 Luleå Sweden e-mail:
[email protected]
Chapter 13 K. Vallons Department of Metallurgy and Materials Engineering Katholieke Universiteit Leuven Kasteelpark Arenberg 44 bus 2450 B-3001 Heverlee Belgium e-mail:
[email protected]
Chapter 14 N. Himmel* Institut für Verbundwerkstoffe GmbH (Institute of Composite Materials) University of Kaiserlautern Erwin-Schrödinger-Strasse 67663 Kaiserlautern Germany e-mail:
[email protected]
© Woodhead Publishing Limited, 2011
Contributor contact details
H. Hess BASF Engineering Plastics Europe 67056 Ludwigshafen Germany
xv
D-81663 Munich Germany e-mail:
[email protected]
Chapter 19 Chapter 15 D. S. Ivanov, S. Lomov and I. Verpoest Department of Metallurgy and Materials Engineering Katholieke Universiteit Leuven Kasteelpark Arenberg 44 bus 2450 B-3001 Heverlee Belgium e-mail:
[email protected]
Chapter 16 A. K. Pickett Institute for Aircraft Design University of Stuttgart Germany e-mail:
[email protected]
Chapter 17 E. Marklund* and L. E. Asp Swerea SICOMP AB Box 104 SE-43122 Mölndal Sweden e-mail:
[email protected]; erik.
[email protected]
J. Varna Div. Polymer Engineering Luleå University of Technology SE-97187 Luleå Sweden e-mail:
[email protected]
Chapter 18 P. Middendorf* and C. Metzner EADS Deutschland GmbH Innovation Works
F. Dumont* and C. Weimer Production Techologies and Projects Laboratories, Materials and Processes Eurocopter Deutschland GmbH D-81663 Munich Germany e-mail:
[email protected];
[email protected]
Chapter 20 B. Sköck-Hartmann* and T. Gries Institut für Textiltechnik (ITA) of RWTH Aachen University Otto-Blumenthal-Strasse 1 52074 Aachen Germany e-mail: Britta.Skoeck-Hartmann@ita. rwth-aachen.de; thomas.gries@ita. rwth-aachen.de.
Chapter 21 G. Adolphs and C. Skinner* OCV Technical Fabrics Chaussée de la Hulpe 166 1170 Brussels Belgium e-mail: Christopher.Skinner@ owenscorning.com; Georg.adolphs@ owenscorning.com
Chapter 22 P. J. Schubel University of Nottingham Faculty of Engineering University Park Nottingham NG7 2RD UK e-mail:
[email protected]
© Woodhead Publishing Limited, 2011
Introduction
The subject of this book, non-crimp fabrics (NCF), is a textile engineer’s answer to a long-standing challenge faced by designers of composite parts: to combine a perfect placement of the reinforcing fibres with easy, inexpensive, automated manufacturing of the part. A part made using unidirectional (UD) tapes, placed by hand or by robot and consolidated in an autoclave, has ideal fibre placement and the best local mechanical properties due to the UD microstructure of the reinforcement. However, the manufacture of such parts is cumbersome and costly. On the other hand, an out-of-autoclave manufacturing process, for example vacuum-assisted resin transfer moulding (RTM) which uses woven laminates, is relatively cheap and takes advantage of easy handling of large sheets of the fabric. In this case, however, the local mechanical properties are affected, because the fibres deviate from their ideal directions due to the crimp (inherent to the woven fabric) and because of the necessary presence of the second fibre system, lying transverse to the direction of the design loads. Hence the challenge to create a reinforcement which would combine UD fibres with integrity, ease of handling and drape of textile fabrics. There are different ways to create such a non-crimp textile structure, which are reviewed in Chapter 1 of this book. These include quasi-UD woven fabrics, noncrimp and non-interlaced three-dimensional weaving, weft- and warp-knitting of UD plies and adhesive bonding of the plies. However, the rest of the book is dedicated to the most widely used type of NCF – multiaxial multiply warp knitted fabrics. The impressive examples of applications of composites reinforced by such NCFs include: a floor pan of a car, which weighs half was much as its steel prototype (carbon fibre NCF); a six-metre diameter pressure bulkhead of an A380 aircraft (also carbon fibre NCF) and a sixty-metre-long blade of a wind turbine (glass fibre NCF). This book presents a comprehensive overview of all the aspects of NCF usage as composite reinforcement – manufacturing of NCF in the textile industry, manufacturing of composites with NCF reinforcements and the mechanical properties of NCF composites and their applications. The chapters are rich in factual material, including test results for the most popular types of carbon and xvi © Woodhead Publishing Limited, 2011
Introduction
xvii
glass NCF and their composites, which makes the book a useful reference source. The book can also serve as a textbook for courses on NCF composites in an advanced study programme. Part I, ‘Manufacturing of non-crimp fabrics’ starts with an overview of types of NCF and production methods (Chapter 1, A. Schnabel and T. Gries), which is supported by the discussion of available standardisation of NCF in Chapter 2 (F. Kruse and T. Gries). NCF laminates, with plies in NCF layers stitched (warpknitted) with a thin polyester yarn with linear density of few tex, can be further stitched together with a thick strong glass, aramid or carbon thread, which will provide delamination resistance for the composite. The technology of such ‘structural stitching’ is described in Chapter 3 (P. Mitschang). The ideal UD placement of fibres in the plies of NCF is distorted by the needles and yarns during warp-knitting process. These distortions create an intricate pattern in the internal geometry of fibre placement and free spaces (which become resin-rich zones in the composite), as described in Chapter 4 (S. V. Lomov). As the fibre distortions define the significance of knock-down factors of the mechanical properties of NCF composites in comparison with their UD laminate counterparts, the characterisation and control of these defects is of paramount importance for quality control. An automated system for quality control is described in Chapter 5 (M. Schneider). Part II, ‘Manufacturing of non-crimp fabric composites’ focuses on two crucial phenomena: deformability of NCF during draping on a three-dimensional (3D) mould and resin flow through the fabric. Chapter 6 (S. V. Lomov) describes the resistance of NCF to shear, bi-axial tension and compression, as measured in laboratory tests. This knowledge is further advanced in Chapter 7 (P. Harrison, W-R. Yu and A. C. Long), which describes the behaviour of NCF during draping on a mould, based on mathematical models of the behaviour of a unit cell of NCF and the drape of NCF cloth. Discussion of resin flow through NCF starts with an overview of permeability measurements in Chapter 8 (R. Loendersloot), which also includes measurements of sheared and compressed laminates. Variability issues surrounding the permeability of NCF are covered in Chapter 9 (A. Endruweit and A. C. Long). The models of resin flow of NCF at unit cell level are introduced in Chapter 10 (B. Verleye, S. V. Lomov and D. Roose). These models allow prediction of the permeability of NCF, including sheared configurations, which can be used in macro-models of the part impregnation. Part III, ‘Properties of non-crimp fabric composites’ discusses the mechanical behaviour of NCF composites under different loading types and methods to model this behaviour and predict the mechanical properties. Chapter 11 (S. V. Lomov, T. Truong Chi and I. Verpoest) summarises the results of measurements of mechanical properties of NCF composites in tension and shear, and describes damage progression during a tensile test based on acoustic emission registration and X-ray post-mortem examination. Chapter 12 (L. E. Asp, J. Varna and
© Woodhead Publishing Limited, 2011
xviii
Introduction
E. Marklund) continues with a detailed microscopy examination of damage to NCF composites under tension, compression and impact loading. Fatigue behaviour of NCF composites is studied in Chapter 13 (K. Vallons), and mechanical properties of structurally stitched NCF composites in Chapter 14 (N. Himmel). All these studies have a common focus: to reveal and understand how distortions of the UD fibrous plies, introduced by the non-structural and structural stitching, influence the mechanical behaviour of the composite. This understanding helps to establish design limits for NCF composite part and to determine the knock-down factors for the mechanical properties in comparison with the properties of UD laminates, which can be predicted with well-known methods. Because of the complex internal geometry of NCF, predicting the mechanical behaviour of its composites is not that straightforward. Chapter 15 (D. S. Ivanov, S. V. Lomov and I. Verpoest) introduces meso-level (unit cell) finite element (FE) models which allow prediction of elastic response, damage initiation and progression and strength of NCF composites. Chapter 16 (A. Pickett) describes FE modelling of NCF composite parts on macro-scale, which integrates models of forming and infusion during manufacturing and structural analysis of the consolidated part. More engineering-type models (semi-laminar analysis) are described in Chapter 17 (E. Marklund, J. Varna and L. E. Asp). Part IV, ‘Applications of non-crimp fabric composites’ describes the existing and prospective use of NCF composites in aeronautics (Chapter 18, P. Middendorf and C. Metzner, and Chapter 19, F. Dumont and C. Weimer), automotive (Chapter 20, B. Sköck-Hartmann and T. Gries) and wind energy (Chapter 21, G. Adolphs and C. Skinner) industries. The authors do not limit themselves to success stories, but also describe the requirements and limitations for using NCF composites in their respective fields. This part finishes with the important issue of cost analysis of using NCF composites in engineering applications, in Chapter 22 (P. Schubel). The book summarises the results of research and developments performed mainly in the last ten years. During this time, I have worked in the Composite Materials Group (CMG) (Department MTM, Katholieke Universiteit Leuven). The leader of CMG, Professor Ignaas Verpoest, introduced me more than ten years ago to a fascinating world of textile composites. I acknowledge with gratitude his influence, leadership, scientific inspiration and – most of all – friendship. In wider terms, the research in the field of NCF was for myself an interesting and inspiring experience of being a part of a Europe-wide ‘NCF composites community’, spanning different ‘walks’ of science and engineering – textile and composites engineers and manufacturers, designers, experimentalists, university professors, software developers – and combining so many different application fields at the cutting edge of development of modern technologies such as aeronautic, automotive and energy. Woodhead Publishing undertakes continuous efforts in creating a comprehensive library of books on textile and composites science and technology. The present book is a part of this library, and I am grateful to the publisher for the opportunity
© Woodhead Publishing Limited, 2011
Introduction
xix
to edit it and to gather together a group of distinguished authors – experts in the field. Special thanks are due to Professor. Andrew Long, who has taken the role of editor for the chapters written by myself, and to the Woodhead staff – Adam Hooper, Bonnie Drury and Nell Holden, who helped in putting the book together. Stepan Lomov Leuven
© Woodhead Publishing Limited, 2011
1 Production of non-crimp fabrics for composites A. SCHNABEL and T. GRIES, Institut für Textiltechnik (ITA) of RWTH Aachen University, Germany
Abstract: For the manufacturing of non-crimp fabrics there is a wide range of production technologies. The focus in this chapter is on the production of warp-knitted non-crimp fabrics. The production process of coursewise and non-coursewise biaxial and multiaxial warp-knitted NCF is described in detail and the production of non-crimp fabrics by means of weft knitting with weft insertion and specially adapted weaving processes is explained. Other processes are shown to produce non-crimp fabrics made of tapes and threads by means of resins or adhesives. The different technologies are compared and evaluated. An outlook on actual and future research topics and developments concludes this chapter. Key words: production of non-crimp fabric (NCF), warp-knitted NCF, weft-knitted NCF, non-crimp woven fabric, fixation by adhesion.
1.1
Introduction
The chapter ‘Production of non-crimp fabrics, for composites’ comprises a short introduction to non-crimp fabric (NCF), an overview of production technologies and the produced fabrics, a comparison of production technologies, current trends and an outlook on the future. Non-crimp fabrics are defined as drawn parallel oriented layers of reinforcing threads or tows, which are positioned by means of an additional fixation material. Figure 1.1 gives an overview of different NCF structures. In technical literature, there is a wide range of terms for the production technologies for different kinds of fabrics. Furthermore, no uniform designation of thread systems is used. Therefore, at the beginning of each section, the terms used are introduced and, for clarity, throughout the chapter the terms ‘thread’ and ‘fibre’ will be used for reinforcement systems and ‘yarn’ for auxiliary systems. The definition of Roye et al. (2005), is used for the expressions two-dimensional (2D) textile and three-dimensional (3D) textile. • •
A textile is defined as a 2D structure if it does not extend in more than two directions, neither in yarn architecture nor in textile architecture. A textile is defined as a 3D structure if its yarn architecture and/or its textile architecture extends in three directions, regardless of whether it is made in one step or in a multiple-step process.
A cornerstone for the production of NCF was set in 1949 with patent number DD000000008194A, granted to Heinrich Mauersberger. The patent describes a 3 © Woodhead Publishing Limited, 2011
4
Non-crimp fabric composites
1.1 Overview of different non-crimp fabrics (ITA).
novel textile material and the associated production method. The basic idea is that chain-stitch seams are used for the production of textile fabrics by interlinking loose filling threads or drawn parallel weft threads. Intersecting weft threads are routed with a guide rail and connected with chain-stitch seams. Threads that are fed in process direction to the stitching unit can be fixed via a ‘zig-zag’ chain stitch. The position of the needle puncture should be between two weft threads (Mauersberger, 1954). NCF can also be produced with coursewise warp-knitting technology, weftknitting technology and specially adapted weaving processes. Besides the above-
© Woodhead Publishing Limited, 2011
Production of non-crimp fabrics for composites
5
mentioned methods, incoherent reinforcing fibre layers are joined and positioned by being pre-impregnated with resin or by fixation with adhesives. Adhesives for the joining of non-crimp fabrics are used in the form of fluid, powder, granulate or non-woven hotmelt.
1.2
Warp-knitted non-crimp fabric (NCF)
Knitting processes with loop formation in production direction are called warpknitted fabrics. The compound needles are assembled on a continuous needle bar and moved together during the loop formation. Due to the production process, warp-knitted fabrics are created with several yarn systems (Anon., 1969). In warp-knitted NCFs the loop formation is used to bind reinforcing layers together. The machine technology is very productive compared to other technologies. Warp-knitted NCFs are very flexible in respect to layer setup and fibre orientation, but they are limited to a constant width and area weight. There is coursewise and non-coursewise fixation of the reinforcing threads. In a machine with coursewise weft insertion, every warp and weft thread is bound with a single knitting loop. Compared to other technologies, the threads remain undisturbed. The stitch length can be defined in the machine settings. The technology for coursewise biaxial and multiaxial NCF is called warp-knitting. In machines with a non-coursewise weft insertion, the stitch length is independent to the position of the thread. Therefore, threads can be damaged or deflected. There exist non-coursewise biaxial and multiaxial NCF. Non-coursewise multiaxial NCFs are called warp-knitted multiaxial layers (Verwirkte multiaxiale Gelege; WIMAG) or stitch-bonded fabrics (Nähgewirkte variable Gelege; NVG). These phrases were coined in the Federal Republic of Germany and in the former German Democratic Republic, respectively. The term ‘stitch-bonding’ is more appropriate to describe non-coursewise weft insertion technology. Nevertheless, in the following, the more common term ‘warp-knitting’ will be used for noncoursewise biaxial and multiaxial NCF (Weber and Weber, 2004; Wulfhorst, 1998). Table 1.1 shows the important properties of coursewise and non-coursewise fabrics and the relating production technologies. Table 1.1 Characteristics of coursewise and non-coursewise non-crimp fabric and the relating production technologies
Fibre damage Dislocation of the reinforcing threads Variability of the stitch length Complexity of the machine technology
Coursewise weft insertion
Non-coursewise weft insertion
− − + +
+ + + −
+ Higher/− Lower
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1.2.1 Biaxial warp-knitted NCF Fabric set-up Biaxial warp-knitted NCFs are made out of at least three thread systems. • • •
Pillar threads (0°). Weft threads (90°). Warp-knitting yarns.
The reinforcing threads are fed parallel (pillar threads) and perpendicular – respectively diagonal – (weft threads) to the process direction. Warp-knitting yarns are often manufactured from a thermoplastic, such as polyethylene or polyamide, and are used for the fixation of the intersection points of the pillar and weft threads. The yarn spacing between the pillar and weft threads can be adjusted depending on the application. Figure 1.2 shows a scheme of biaxial warp-knitted fabrics with coursewise (a) and non-coursewise (b) weft insertion and different yarn spacings. Unidirectional warp-knitted fabrics can be produced in principle with biaxial warp-knitting machines with weft insertion. Thereby, only weft threads are processed and positioned with warp-knitting yarns.
1.2 Biaxial warp-knitted non-crimp fabrics with coursewise (a) and non-coursewise (b) weft insertion (ITA).
Working principle The warp-knitting machine with biaxial weft insertion can be divided into three machine modules. • • •
Feeding module. Warp-knitting module. Take-up module.
The feeding module consists of a weft insertion system, which is continuously filling weft threads into the hooks or needles of two transport systems. There is one transport system on each side of the machine. The distance between the transport systems defines the width of the fabric. The transport system continuously supplies the loose fibre layers to the warp-knitting module. The pillar threads are
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1.3 Warp-knitting machine with biaxial weft insertion (ITA).
guided by the pillar thread sinkers and fed directly between the compound needles. The weft and pillar threads are fixed in the warp-knitting unit together, by means of warp-knitting yarns. Afterwards, the NCF is cut out of the transport chain and is wound onto the take-up module. Figure 1.3 shows the working principle and the essential functional features of a warp-knitting machine with biaxial weft insertion. Feeding module Weft carriage system Weft carriage systems are mounted on a portal, which is positioned above the transport systems of a warp-knitting machine with weft insertion (Fig. 1.4). The weft carriage system swings permanently between the two transport systems. Thus the weft carriage system take-off takes threads out of a stationary creel and supplies these threads to the transport systems. In the reversal points of the insertion device, the weft threads are pressed down mechanically. Subsequently, the threads lay between the hooks of a shogging rake and at the same time at the back of the weft lay-in units of the transport system. The shogging rake shifts laterally and the weft insertion starts to move in the other direction, whereby the threads are fixed in the weft lay-in units. As soon as the weft threads are fixed, the weft-insertion device moves to the other side of the machine and continues with the same procedure (Wunner, 1987). Parallel and cross-weft insertion can be realised with computer-controlled weft carriage systems (Mayer, 2007).
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1.4 Weft carriage system (ITA).
Weft thread transport system Transport chains are widely used as weft-thread transport systems in weft insertion machines. The ratio of the speed of the transport chain to the number of revolutions of the knitting elements determines the stitch length of the warp-knitting yarns. Weft thread transport chains of warp-knitting machines with biaxial weft insertion can be equipped with a wide range of different weft lay-in units. The weft lay-in units can be divided into hook and needle systems (Fig. 1.5), which are used for coursewise and non-coursewise weft insertion (LIBA, 2007c).
1.5 Hook (left), needle (middle) and pin-hook system (right) (ITA).
Hook systems are applied generally for coursewise weft insertion. Weft threads are endlessly filled into open transport hooks, which are closed by weft clamps automatically. The clamps fix the weft threads with an optimum tension and in their exact position during the warp-knitting process. Therefore, the weft threads are drawn parallel and no thread tension difference can occur (LIBA, 2007e). The thread density in the transport system is unequal to the thread density in the fabric. Open, as well as closed, structures can be produced. Closed structures are produced with a fully threaded hook system and an adapted ratio of the speed of the transport chain to the number of revolutions of the knitting elements. Open structures can be manufactured with partly and fully threaded hook systems and a corresponding speed of transport chain. In needle systems, the transport chain segments are equipped with needle hook leads (LIBA, 2007c). When the weft threads are laid down into the weft lay-in units, the needle hooks can penetrate and split the weft threads. Due to this system, the exact position of the threads cannot be guaranteed. Needle systems are used,
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therefore, for non-coursewise weft insertion. If many threads are supplied to the needle hooks, closed fabrics with a high density and an even distribution of weft threads can be produced. The pin-hook system is a further development of the needle system. Pins and hooks are arranged in two separate rows. The vertical pin row defines the gauge of the weft layers, whereas the horizontal hooks take up the tensile force of the threads. Therefore, the weft threads can be filled directly – without a shogging rake system – into the weft lay-in units (Wiedenhöft and Vettermann, 1999; Zeidler et al., 2005). The pin-hook system promises a higher quality (e.g. a reduced number of gaps between the weft threads) of the finished textile, but also a higher percentage of blends. Creel Rovings – endless, drawn, twist-free filament bundles – from cheeses and bobbins are fed from creels. These creels are equipped with thread brakes or compensation thread tensioners to regulate the thread tension. Integrated thread breakage and tensioned thread inspection displays show fractured and tensioned threads optically. Bobbin creels for weft insertion have to be adapted, because of the intermittent thread consumption and the brittle fibre material. Bobbin creels are equipped with individual bobbin drives and buffer storages to achieve a constant tension and take-off speed (Fig. 1.6). These creels can also be used to spread fibre tows with up to 48 000 filaments in warp-knitting machines with multiaxial weft insertion. There are also cheese creels with compensating thread tensioners, which are used for biaxial and multiaxial weft insertion (Hoersting and Wienands, 1999; LIBA, 2004; Mayer, 2009c).
1.6 Bobbin creels (left and middle) and cheese creel (right) with compensating thread tensioner (ITA).
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Machine equipment Additional equipment for warp-knitting machines with biaxial weft insertion are conveyors, fibre choppers and fleece devices. The conveyor transports chopped fibres to the knitting elements, where fibre layers and chopped fibres are fixed together. Fleece devices are used for feeding of fleece rolls above or underneath the weft threads. Warp-knitting module In the warp-knitting module, the loose fibre layers are fixed together with knitting loops. The motions of the knitting elements (Fig. 1.7) are generated with eccentric gears and corresponding actuating levers. Each knitting element has its own gear. The eccentric gears are driven by a three-phase asynchronous motor with servo converter, which is controlled electronically (LIBA, 2007e).
1.7 Knitting elements (coursewise weft insertion) and walking needle concept (LIBA, 2007e).
Warp-knitting machines with biaxial weft insertion are produced mainly with working widths from 102 to 245 inches and gauges from 3.5 to 24. A gauge is defined as the number of needles per inch (25.4 mm). Loop formation process The loop formation process is divided into seven steps (Fig. 1.8), which are carried out continuously and represent one revolution of the main shaft (Mayer, 2009e; Weber and Weber, 2004). 1. In the first step of the loop formation process, the compound needles and closures, respectively slides, are in their lowest position. The heads of the compound needles are covered from the closures, the guide bars are in their foremost position and the underlapping of the guide bars is carried out.
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1.8 Loop formation process (ITA). See text for further explanation.
2. In the second step, the compound needles stroke upward, whereas the closures stay in their lowest position and the pillar thread sinkers fix the vertical position of the fabric. The knit loops slide out of the needle heads onto the needle shafts and the guide bars complete the underlapping motion. 3. In the third step, the compound needles reach their topmost position, the closures start to stroke upwards and the guide bars begin to swing past the compound needles. 4. In the fourth step, the compound needles and closures stay in their topmost position. The closures are still inside the grooves of the compound needles. The guide bars reach their sternmost position, begin to overlap and start to swing backwards. 5. In the fifth step, the guide bars swing past the compound needles and closures, which are still in their topmost position. The guide bars lay the warp-knitting yarns into the hooks of the compound needles. 6. In step six, the guide bars swing into their foremost position. The compound needles stroke faster downwards than the closures. The closures emerge out of the grooves and begin to cover the heads of the needles. The previous knit loops start to slide upwards from the needle shafts. 7. In the seventh step, the compound needles and the closures emerge between the knock-over sinker. The knit loop slides over the covert compound needles and is cast off. Thereby the warp-knitting yarns in the needle heads are pulled through the casted loops and complete the loop formation process. Walking needle The puncture of the fabric through the compound needles and the simultaneous movement of the fabric can lead to damage and deflection of the reinforcing threads. In the walking needle system, an additional horizontal movement – in the direction of production – during the vertical stroke, is carried out in order to reduce the negative influence of the needles. The degree of horizontal needle movement can be adjusted manually with an adapted actuating lever (LIBA, 2007c).
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Weft thread sinkers Weft thread sinkers as well as weft inserters allow a precise positioning and fixation of weft threads in coursewise weft insertion systems. The weft thread sinkers place the weft thread closest to the knitting elements on the back of the compound needles. The weft threads are kept in this position until they are fixed with warp-knitting yarns. One of the limiting factors for the working speed of biaxial warp-knitting machines is the weft insertion frequency. Therefore, special thread-forward devices were developed. They accelerate the weft thread next to the warp-knitting elements and therefore increase the distance to the following weft thread. The accelerated weft thread can then be fixed without being constrained by the previous, or the following, weft thread. Thereby a reduced gauge of the weft lay-in units can be realised. Hence, more weft threads can be fed at any one time and, furthermore, the amount of the weft threads in the transport chain is reduced (Wunner, 1974; Wunner, 2009; Weiland, 1988). Yarn let-off Yarn let-off systems are generally classified in positive and negative systems. In negative systems, the needles pull the required amount of yarn from warp beams, section warp beams or bobbins. The yarn tension is controlled with yarn-tension devices or yarn brakes, which limit the maximum working speed. In positive systems, the required yarn length is provided from usually electromechanically driven warp beams. Furthermore, electronically controlled yarn let-off systems with a constant or a variable yarn intake are used. For the adjusted supply of the pillar threads, electromechanically driven delivery rolls are used (Wuensch, 2008). Stitch types There exist different stitch types in knitting patterns to join the loose fibre layers together. The stitch types are predetermined by the scaling of the underlap of the guide bar, which is driven mainly by pattern discs. The most common stitch types are pillar, tricot and plain (Fig. 1.9). The stitch type and the stitch length affect the drapability of the fabric. The drapability is defined as the spherical deformability of flat textile material without structural folds, which is equivalent to the adaptation of flat textile material onto curved 3D surfaces. A larger underlap and a greater stitch length of the warp-knitting yarn increase the formability and at the same time complicate the handling of the material (Hanisch et al., 2007; Hufenbach, 2007). Take-up module The take-up module is located towards the warp-knitting module and consists of a weft thread cutting device, a suction device, a fabric take-off and a fabric wind-up.
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1.9 Stitch types – pillar (left), tricot (middle) and plain (right) (ProCad Warpknit 3D ITA).
The cutting device and vacuum cleaner The weft thread cutting device detaches the weft thread ends from the transport chain after the warp-knitting elements. Common cutting devices are thermal systems, hard metal scissors and motor-driven diamond-disc blades. The weft thread blend in the transport chain is brushed out and removed with a vacuum cleaner. Fabric take-off For the fabric take-off, mechanically or electronically controlled systems with two to three rollers are used, which provide an appropriate tension in the fabric. In mechanical roller systems, the take-up speed can be adapted by changing the transmission ratio of the gearbox. Electronically controlled roller systems offer the possibility to adapt the take-up speed as input into the machine’s operation (Wuensch, 2008). Fabric wind-up Two different kinds of batching devices – radially or axially driven – are applied in warp-knitting machines with biaxial weft insertion. They are selected depending on the material. Axially driven wind-up systems have a centre drive with a slipclutch. The wind-up speed can be controlled with skipping rollers. Radially driven wind-up systems are constantly driven at the circumference by friction rollers. They have two operating modes: speed and instantaneously regulated (LIBA, 2005; Mayer, 2007, 2009a). Machine operation The machine operating system is housed in a dust-resistant and air-conditioned control cabinet to protect it from fluff and mechanical damage. The central machine operating system controls all functions of the machine, such as production
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speed and fabric take-off speed. The operating system is equipped with a counterlayer calculation including automatic optimizing and a printer to keep records of product and fault protocols. The operating panel shows production parameters, malfunctions and indicates necessary maintenance work. Furthermore, the operating system is linked to an external customer network by an ethernet interface. External remote diagnostics via modem allow machine diagnostic and customer support for rapid problem-solving through the machine manufacturer (Petrenz, 2009; Mayer, 2009b; Anon, 2010a).
1.2.2 Multiaxial warp-knitted NCF Multiaxial warp-knitting technologies for coursewise and non-coursewise weft insertion (Fig. 1.10) have been developed (Arnold et al., 2000; LIBA, 2007d; Parekh, 1989). Multiaxial warp-knitted NCF with coursewise weft insertion has not yet become generally accepted in practice. Therefore, only the most important characteristics of the fabric and the production technology are given in this chapter. Multiaxial warp-knitted NCF with non-coursewise weft insertion is produced with a machine technology that is similar to the warp-knitting technology with biaxial weft insertion and therefore only the main differences are explained in this chapter. The productivity of the machine depends mainly on the number of stitches per minute and on the stitch length of the warp-knitting module as well as the frequency and the width of the weft insertion (Petrenz, 2009). Warp-knitting with multiaxial weft insertion is one of the most commonly used production technologies for the manufacturing of multiaxial NCF. Fabric set-up Multiaxial warp-knitted NCF with coursewise weft insertion is made of up to four reinforcing fibre layers consisting of diagonal weft threads (e.g. 45°), weft threads (90°) and warp threads (0°). They are fixed using warp-knitting yarns (Anon, 1986).
1.10 Multiaxial warp-knitted non-crimp fabric with coursewise (a) and non-coursewise (b) weft insertion (ITA).
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Multiaxial warp-knitted NCF with non-coursewise weft insertion consist of a current maximum of seven parallel layers of rovings or spread fibre tows. The orientation of the single fibre layers can be freely adjusted to between −20° and +20° relative to the production direction (angle specification analogous to EN13473-1). On the top side of the fabric, an additional layer at 0° can be attached. The introduction of two surface fabrics, for example non-wovens, is also possible (Fig. 1.11). The mass per unit area, the structure – closed or open – of the fabric, the material as well as the thread count of each layer can be varied individually for each layer. The single fibre layers are fixed together with a warp yarn (LIBA, 2007d; Mayer, 2009d).
1.11 Schematic set-up of a multiaxial warp-knitted non-crimp fabric with non-coursewise weft insertion (LIBA, 2007d).
Working principle In coursewise weft insertion machines, the knitting unit, a beam with multiple pillar threads (0°), a transport system for weft insertion (90°) and a take-up unit are mounted on a large turntable, which rotates around its own vertical axis. Stationary beams or creels supply reinforcing threads for the diagonal weft insertion to the rotating knitting machine (Fig. 1.12). Up to two diagonal thread systems can be fed. Because of the superposition of the stationary and the rotating systems, the threads are laid diagonally across the width of the fabric (Parekh, 1989). The working principle of non-coursewise weft insertion machines is comparable to that of biaxial warp-knitting machines. The standard machine configuration consists of three weft carriage systems, which are adjustable in small ranges or between −45° and +45°. The single fibre layers are filled in consecutive steps into the weft lay-in units of the transport system. The pillar threads made out of rovings have to be supplied directly between the compound needles to avoid shifting after deposition (Fig. 1.13). Fibre deflections (undulations) can lead to fabrics with lower quality and, therefore, to fabrics with reduced mechanical properties. Therefore, the pillar threads are fixed immediately together in the warp-knitting module by at least two knitting heads (Wienands et al., 2004).
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1.12 Coursewise multiaxial warp-knitting machine (top, ITA; bottom, Anon, 1986).
Several other approaches to producing multiaxial warp-knitted NCF with 0° layers at any position – between or on top of the other fibre layers – have been developed. In one process, a conventional fabric with a 0° layer on top is manufactured and afterwards merged with another fabric on a separate machine. To get a symmetrical NCF, the upper fabric has to be turned over. Threads in the production direction can also be fixed on any layer by coating them with glue or heating them up to their melting point. A fixation by means of adhesive is not necessary when spread and torsion-free fibre tows are fed (Friedrich, 2002; Wagner and Palmer, 1998; Anon, 2005).
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1.13 Non-coursewise multiaxial warp-knitting machine (top, LIBA, 2007d; bottom, Karl Mayer Textilmaschinenfabrik GmbH, 2010).
Feeding module Weft carriage system There exist two substantial weft insertion technologies in non-coursewise multiaxial warp-knitting machines. • •
Insertion of endless weft threads. Insertion of finite weft threads.
Weft carriage systems for the insertion of endless weft threads manipulate roving and small spread fibre tows (<12k) from bobbins and cheeses. A fibre tow with 12k consists of 12 000 single filaments. The insertion of finite weft threads was developed for the precise and distortion-free placing of discontinuously and continuously spread fibre tows (>12k) made of carbon. These tows are less expensive than conventional carbon fibre rovings. A weft carriage system with a clamping and cutting device is used for the placement of the fibre tows.
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1.14 Stationary (left) and mobile (right) weft insertion portal (ITA).
Closed NCF with an areal weight of at least 75 g/m2 can be produced (Bompard et al., 2005; Bittmann, 2006; Anon, 2002, 20056; LIBA, 2007b; Mayer, 2009f). There are stationary and mobile weft insertion portals (Fig. 1.14). In stationary systems, only the weft carriage systems are moveable. They are positioned on a linear guide of the weft insertion portals. In stationary systems, the orientation of the fibre layers is predetermined by the position and accordingly the angle of the weft insertion portal in respect to the direction of the process. The angle has to be adjusted to the ratio of working speed and weft insertion speed. The fibre angle can be changed mechanically within a predefined range (Naumann and Wilkens, 1986). In machines with mobile weft insertion portals, the weft carriage systems can move independently parallel and lateral to the process direction of the warpknitting machine. The orientation of the fibre layers result from the superposition of the transport system motion and the portal movement (Wunner, 1987; Hoersting et al., 2002). In stationary systems, the moving mass is lower and the carriage system can be guided more accurately, but they are less flexible compared to mobile systems. Weft thread transport system Transport chains with needle, pin-hook (q.v. 1.2.1 Biaxial warp-knitted NCF) and pin-pin systems are used for the production of multiaxial warp-knitted NCF, which are made out of endless weft threads. Finite weft threads are fixed and transported with needle fields or clamping systems in warp-knitting machines with multiaxial weft insertion (Fig. 1.15).
1.15 Pin-pin (left), needle-field (middle) and clamping system (right) (ITA).
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The pin-pin system was developed for the processing of small fibre tows (<12k). Small mass per unit areas of the fabric can be produced (150 g/m2). The pins are arranged in two separate rows. The upright pin row fixes the position of the weft layers, whereas the horizontal pins take up the tensile force of the weft threads. The weft threads are filled directly into the weft lay-in units with the corresponding weft carriage system (Anon, 2005). Needle-field systems consist of upright needles, which are arranged in several shifted rows. In these systems, the fibre tows are fed above the needles from a weft carriage system. Afterwards the fibre tows are kneeled down to the transport chain, by means of insertion profiles. Due to the needle field, the fibre tows are divided into strand-shaped sections and clamped between the needles. An additional magnetic tape can clamp the weft threads (Erth et al., 2005). In clamping systems, spring devices bear a versatile weft clamp against a steady clamping plate. The weft carriage system conveys spread fibre tows to the insertion position. The current as well as the previously inserted fibre tows are fixed with a supporting clamping unit. Afterwards, the self-locking clamping system on the transport chain is opened with a rocker. The new fibre tows are pressed into the open clamping unit on the transport chain. After closing the clamping system, the support clamping unit releases the fibre tows (Anon, 2002; Volbers, 2005; Munzert and Unglaub, 2008). Creel For the insertion of endless weft threads, similar creels to those in warp-knitting machines with biaxial weft insertion are used. The insertion of finite weft threads can be performed from pre-spread pancake coils and creels with an online spreading device. Carbon fibres are often provided in form of carbon fibre hanks (heavy tows) by the manufacturer, which can consist of over 46 000 filaments. The fibre tows are wound on bobbins or placed in containers. They are too thick as textile reinforcement materials, where small mass per unit areas are desired. For the subsequent treatment, the filament bundles have to be spread to achieve a constant areal weight. The spreading of the filament bundles is more even if the filaments are heated during the process. The filament bundles can be heated with hot air, heated rollers, heat radiators and electrodes (Fig. 1.16). A spreading device consists, for example, of three staggered electrodes so that the filaments rest on the electrodes. The heated filament bundle runs through a spreading device. The filaments are deflected at the run-in and at the run-out. The width of the opening determines the width of the spread fibre tow (Nestler et al., 2009).
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1.16 Spreading device with electrodes (Nestler et al., 2009).
Machine equipment The warp-knitting machine with multiaxial weft insertion can be equipped with conveyors, fibre choppers and fleece devices. A conveyer supports the fibre layers during the transport in the warp-knitting machine. It is especially used for the production of heavy fabrics with a large working width. Another application is the transport of chopped fibres. Fleece devices are used to feed additional material above or under the weft threads. Warp-knitting module The warp-knitting module is nearly identical in construction and equipment with the biaxial warp-knitting module (q.v. 1.2.1 Biaxial warp-knitted NCF). There are warp-knitting machines with gauges from 3.5 to 14 needles per inch and working widths between 50 and 152 inches. The machines have up to three guide bars and one pillar thread bar, which are manipulated with patterns discs. The pattern is selected depending on the layer setup and the desired drapability. Take-up module The take-up module is similar to the one in the warp-knitting machine with biaxial weft insertion (q.v. 1.2.1 Biaxial warp-knitted NCF) and is located towards the warp-knitting unit. It consists of the weft thread cutting device, the suction device, the fabric take-off and the fabric wind-up. Weft thread cutting devices can additionally be used to cut a fabric into two. Therefore, two 635 mm (25 inch) fabrics can be produced on a 1270 mm (100 inch) production machine. This leads to a reduction of blend and an increase of productivity.
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1.2.3 Spacer warp-knitted NCF Fabric set-up Spacer warp-knitted NCF consists of two top surfaces out of weft threads, pillar threads and warp-knitting yarns, which are connected with pile threads (Fig. 1.17). The warp-knitting yarns thereby fix the weft and pillar threads together. Pile threads from monofilaments can be used for a statically effective reinforcement in through-thickness direction. Spacer warp-knitted NCF can be used for integral systems, such as an integrated engine hood system for higher pedestrian safety. Depending on the the number and the type of the pile threads, the absorption characteristics can be adjusted (Skoeck-Hartmann et al., 2008).
1.17 Spacer warp-knitted non-crimp fabric (ProCad Warpknit 3D – ITA).
Working principle Spacer warp-knitted NCF is produced with double needle bar raschel machines. The machine has symmetric build-up warp-knitting elements (Fig. 1.18). The spacer distance of the fabric can be adjusted continuiously by means of changing the distance of the trickplate. The machine is equipped with two 90° weft thread transport systems. They supply the weft threads to the knitting elements. Horizontal magazine weft insertion systems feed the weft threads into weft lay-in units (hook system) of the transport system. A shogging rake system enables regular and non-regular repetition of weft threads without material waste. The pillar threads are fed at the front and at the back of the knitting elements. Warpknitting yarns as well as pile threads are supplied with guide bars. A high pattern flexibility can be achieved with up to six computer-controlled guide bars (Roye, 2007; LIBA, 2007a; Janetzko and Maier, 2007).
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1.18 Double needle bar raschel machine (ITA).
1.3
Weft-knitted NCF
The weft-knitting process has a loop formation perpendicular to the production direction. Therefore, one yarn system is already sufficient for the manufacturing of weft-knitted fabrics (Anon, 1969). In weft-knitted NCF, reinforcing threads are fixed within the loops (Fig. 1.19) (Binh, 2005).
1.19 Biaxial (left) and multiaxial (right) weft-knitted non-crimp fabric (ITA).
Fabric set-up Weft-knitted NCF can be produced as biaxial and multiaxial fabrics or as two- and three-dimensional near net-shape textile structures. Warp and weft threads out of rovings are superposed and fixed together with loop systems. Due to the coursewise weft insertion, the reinforcing threads remain non-crimped (Table 1.2). Through the combination of weft insertion over the entire width or part of the width with or without the support of a stitch-transferring device and by changing loop sizes on individual needles, 3D near net-shape preforms can be produced (Binh, 2005; Hufenbach, 2007; Anon, 2009b).
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Table 1.2 Multilayer weft-knitted non-crimp fabric structures
Adapted from Hufenbach, 2007.
Working principle On the basis of multiaxial five-ply weft-knitted NCF (Table 1.2), the typical production process is described. The reinforcing threads are merged coursewise in multilayer weft-knitted NCF. The warp threads are positioned in the centre of the needle bed. They are supplied by means of guide bars, which are equipped with thread guides. Weft threads are fed during the lateral carriage movement underneath the needle-backs of the driven-out needles. The reinforcing threads are fixed through the subsequent knitting row. The manufacturing of a knitting row is carried out in two steps. In the first step, four layers are fixed from the right knitting yarn (3) by means of an R–L standard knitting pattern. The retained layers are right weft thread (2), right diagonal thread (5), vertical warp thread (1) and left diagonal thread (5). In the second step the last left weft thread (2) in a knitting row is attached to the already fixed layers by the left knitting yarn (3) through the R–L knitting pattern. The left knitting yarn (3) likewise fixes only four layers (right weft thread (2), vertical warp thread (1), left diagonal thread (5) and left weft thread (2)) (Binh, 2005; Hufenbach, 2007).
1.4
Non-crimp woven fabrics
Woven fabrics consist of two interlacing thread systems: warp and weft. The wavelike yarn crimp of conventional woven fabrics leads to a structural elongation of the fabrics (approximately 1–3%). The elongation reduces the Young’s modulus of composites reinforced with woven fabrics. Therefore, special non-crimp woven fabrics have been developed. These woven fabrics use thin auxiliary yarns or suitable patterns like Atlas to avoid bending of the reinforcing threads. Thin fibre tows made out of spread filament bundles can also reduce the yarn crimp.
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1.4.1 Advanced synchron weave Fabric set-up Advanced synchron weave combines a multilayered NCF and a weave. The fabric consists of drawn reinforcing threads, which are retained by thin auxiliary yarns. The reinforcing warp and weft threads are crossed perpendicularly. Bending, which is caused by the weaving process, is only induced in the auxiliary yarn. Figure 1.20 shows a three-layered NCF, with two layers in a warp and one in a weft direction. The fabric is built up by intermittent reinforcing threads and auxiliary yarns (Cramer, 1989, 1991). Working principle The working principle is based on conventional weaving technologies and can be divided into the following steps. • • • •
Shed formation. Feeding of reinforcing warp threads. Weft insertion. Take-up.
A shed must be formed to be able to insert a weft thread. To form the shed, the warp yarns (auxiliary yarns) are raised or lowered individually or in groups. Reinforcing warp threads are fed between the auxiliary yarns without shed formation. A weft insertion system supplies reinforcement threads and auxiliary yarns. Common weft insertion systems for reinforcement threads use rigid rapiers or flexible band rapiers (Cramer, 1989, 1991).
1.20 Advanced synchron weave (left, ITA; right, Cramer, 1991).
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1.4.2 Leno weave Fabric set-up A leno weave consists of two perpendicularly crossed thread systems: weft threads and leno threads. In uniaxial reinforced leno weaves, the reinforcing threads are fed as weft threads and interlinked with leno threads with auxiliary yarns. In biaxial reinforced leno weaves, reinforcing threads and auxiliary yarns are used as leno threads. The auxiliary yarns interlink the reinforcing threads in warp and weft. Due to different tensions and diameters, the reinforcing threads remain uncrimped. Uniaxial and biaxial grid-like, as well as closed, fabrics can be produced (Fig. 1.21).
1.21 Leno weave with uniaxial (left) and biaxial (right) reinforcement (ITA).
Working principle The production principle of leno fabrics has been known for a long time, e.g. for the selvedge formation of woven fabrics on shuttleless looms. To build the selvedge, leno heddles and disc lenos are used to enlace neighbouring warp threads. Based on this principle, a technology was developed to produce leno weaves, where leno threads are used to fix reinforcing threads. The tensions of the leno threads are conventionally controlled with one warpthread system and one warp let-off motion. For the production of closed fabrics with reinforcing threads in warp and weft, machines with at least two warp-thread systems and warp let-off motions are deployed. The auxiliary yarns and the reinforcing threads are supplied from two separate warp beams. This system permits the separate adjusting of the tension for reinforcing threads and auxiliary yarns. Due to the lower tension of the auxiliary yarns the reinforcing threads are non-crimped. The auxiliary yarns are twisted around the reinforcing threads (Fig. 1.22) (Wahhoud, 2005; Dornier, 2007; Kleicke et al., 2007).
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1.22 Leno weave technique (Dornier, 2007).
1.4.3 Tape weave Fabric set-up Tape weaves are made of spread fibre tows in warp and weft direction (Fig. 1.23). With the fibre tows, more fibres can be inserted into a given volume and undulations can be reduced compared to conventional weaves. This leads to lower areal weights with similar mechanical properties.
1.23 Weave made of rovings (top) and tape weave (bottom) adapted from (Anon, 2010b).
Working principle The working principle (Fig. 1.24) is based on a conventional weaving machine. Significant modifications for the processing of spread fibre tows in warp and weft direction are necessary. The warp tapes are supplied vertically from cylindrical double-flanged packages which are divided into two groups. Each group feeds material for the top and bottom layer. The particular fibre tows are deflected by an
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1.24 Tape weave working principle (top, ITA; bottom, Khokar, 2006).
adapted shedding system. A gripper inserts the weft fibre tow in the shed between the upper and lower warp fibre tows (Khokar, 1998, 2006).
1.5
3D woven and non-interlaced NCF
There are several technologies for manufacturing 3D woven fabrics with different complexity and productivity (Fig. 1.25). These technologies can be classified according to Khokar (2001) into two processes: 2D and 3D weaving. Non-interlaced NCF can be produced with a non-interlacing process called noobing by
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1.25 Categorisation of production technologies for 3D woven and non-interlaced NCF (ITA).
Khokar (2001) and a non-interlacing weaving process called non-crimp 3D orthogonal weaving by Mohamed and Bogdanovich (2009), Khokar (2001), Chen (2005), Behera and Mishra (2007), Stig (2009), and Mohamed and Bogdanovich (2009).
1.5.1 Fabric set-up A 3D weave made from conventional 2D weaving looms consists of either singleor multilayer warp and weft. The different layers of the warp can be interconnected. In 3D weaves, produced with the 3D weaving process, a grid-like multilayer warp is interlaced with vertical and horizontal weft threads. In the 2D and 3D weaving process, reinforcing threads can be integrated in warp and weft direction. In the non-interlacing processes, three mutually perpendicular sets of threads are assembled without interlacing, interloping or intertwining. The following figure depicts a selection of common fabric structures: orthogonal (Fig. 1.26, left), multilayer (Fig. 1.26, middle), angle-interlock (Fig. 1.26, right) and spacer. Multilayer and angle-interlock fabric structures will lead to low-crimped yarns. Based on the existing production technologies solid, shell, hollow, nodal and
1.26 Fabric structures – orthogonal (left), multilayer (middle) and angleinterlock (right) (ITA).
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spatial fabrics can be manufactured (Khokar, 2001; Chen, 2005; Behera and Mishra, 2007; Gokarneshan and Dhanapal, 2007; Bogdanovich and Mohamed, 2009; McHugh, 2009; Stig, 2009).
1.5.2 Working principle The 2D weaving process is designed to place two orthogonal sets (single or multilayer) of threads: warp and weft. Through interlacing of multilayer warp and weft threads, a 3D fabric can be produced. Therefore, the multilayer warp threads are manipulated in the 2D weaving loom by means of a mono-directional shedding operation in the fabric width direction. Weft threads are inserted in the formed sheds with weft insertion systems (Fig. 1.27, top left) (Khokar, 2001; Mohamed and Salama, 2001; Behera and Mishra, 2007). Due to the production process a substantial level of crimp and fibre damage can occur in the fabric induced by interlacing and moving machine parts (e.g. heddles) (Mohamed and Bogdanovich, 2009).
1.27 2D weaving, adapted from Khokar (2001) (top left), 3D weaving (top right) (ITA), non-interlacing weaving, adapted from Mohamed and Zhang (1992) (bottom left) and uniaxial non-interlacing process (bottom right) (ITA).
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The 3D weaving process works with bidirectional shedding. This means that, contrary to the 2D weaving process, the shed formation takes place in the fabricthickness and fabric-width directions. Vertical and horizontal weft threads are interlaced with the warp threads. The 3D shed formation takes place successively in a given circle (Fig. 1.27, top right) (Khokar, 2001; Behera and Mishra, 2007). Due to the interlacing the reinforcing threads are crimped in the resulting structure (Mohamed and Bogdanovich, 2009). In the non-interlacing weaving process (Fig. 1.27, bottom left) multiple weft threads are inserted simultaneously into the shed and subsequent beat-up by the reed. Only the z-directional (through-thickness) yarns are drawn through heddles of the shedding formation and moved up and down. Since there is no interlacing between the warp and weft layers no crimp occurs (Mohamed and Zhang, 1992; Mohamed and Bogdanovich, 2009; Bogdanovich and Mohamed, 2009). Two types of non-interlacing processes exist: uniaxial (Fig. 1.27, bottom right) and multiaxial. In the uniaxial non-interlacing process, two sets of auxiliary yarns are traversed with carriers vertical and horizontal between uniaxial reinforcing threads that are arranged in a grid. The axial threads are bound in the width and thickness directions by the auxiliary yarns without crimp. In the multiaxial noninterlacing process, four sets of threads are interconnected by stitching in the fabric thickness direction (Khokar, 2001; Gokarneshan and Dhanapal, 2007).
1.6
Fixation by adhesion
Besides the knitting and weaving technology, biaxial as well as multiaxial NCF can be produced through fixation of the reinforcing layers by alternative methods such as chemical, thermal or mechanical consolidation. Ideally the consolidation technologies do not negatively influence the properties of the NCF and the subsequent treatment (Bompard et al., 2008; Cooper, 1989; Friedrich, 2002; Hoersting, 1997).
1.6.1 Bonded tape NCF Fabric set-up Multiaxial bonded tape NCF consist of a plurality of parallel-oriented fibre layers. At least one of the fibre layers is made of spread fibre tows. The 0° unidirectional sheet (in the production direction) can lie between or on top of the transversal layers (Bompard et al., 2008). Working principle Endless and finite unidirectional fibre tows are superposed in different directions and fixed together. A chemical bonding agent can be deposited by spraying a
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1.28 Working principle for a multiaxial bonded tape NCF (ITA).
liquid compound onto the fibres or if the fibres are pulled through a bath with a chemical bonding agent. Another option is to dust a heat-fusible or thermoadhesive polymer onto the fibres. If a removable bonding agent is used, an additional consolidation by needling, stitching or a jet of water under pressure is applied (Fig. 1.28) (Bompard et al., 2008).
1.6.2 Bonded thread NCF Fabric set-up Biaxial and multiaxial bonded thread NCF consists of warp and weft threads, which are combined without interlacing to an open scrim by means of a substrate. In the former fabric the weft threads are orthogonal to the warp threads and lay between an upper and lower layer of warp threads. The latter fabric has warp threads and diagonal weft threads lying upon another. The fabric has an open, net-like structure (Fig. 1.29) (Cooper, 1989; Anon, 2009a).
1.29 Biaxial (left) and multiaxial (right) bonded thread NCF (ITA).
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Working principle A weft carrier inserts an array of weft threads in two axially aligned weft retainer wheels. The distance between the wheels defines the width of the later fabric. Warp threads are fed continuously from above and below the machine into the gap between two feed rollers. The distance between the feed rollers coincides with the effective diameter of the weft retainer wheels. The weft threads are cut at their ends, fixed temporarily with a clamping device and inserted between the warp threads. An additional pair of weft retainer wheels can increase the working speed (Fig. 1.30). Subsequently, the warp and weft threads are coated with a binder substrate and dried. In a further development of the system, diagonal weft threads can also be brought in (Cooper, 1989; Anon, 2009a).
1.30 Production process of biaxial bonded thread non-crimp fabric (Cooper, 1989).
1.6.3 Fold-wound NCF Fabric set-up Fold-wound NCF is characterised by a symmetrical layer set-up and a centric 0° fibre layer. Each layer is made of spread fibre tows (Gruenert, 2007; Heinrich et al., 2009).
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Working principle One or more diagonally approaching webs (α-layers) are wound around a second fibre layer system (0° layer). A guiding system continuously transports the 0° layer in direction of production and turns it around the rotational axis of the system. The α-layer systems are folded before being placed on the edge of the 0° layer. The α-layers are fixed together by means of binding systems (e.g. adhesives). A subsequent calender consolidates the manufactured multiaxial NCF (Fig. 1.31) (Gruenert, 2007; Heinrich et al., 2009).
1.31 Fold-winding system (Gruenert, 2007).
1.7
Comparison of production technologies
A classification of the production technologies with regard to the productivity of the process and the complexity of the NCF is difficult without considering the whole production process and the quality as well as the geometry of the final FRP component. In addition, the productivity of the individual manufacturing machines in the literature is described only insufficiently. Therefore, Fig. 1.32 can only give a coarse estimation of the mass throughput and the complexity of the semifinished NCF for the most important NCF production technologies. Warp-knitting with biaxial weft insertion was selected as the reference for the highest productivity, and the multilayer weft-knitting for the highest complexity of semi-finished NCF. In Fig. 1.33, the production technologies are arranged regarding their application in the NCF production industry and the quantity of produced NCF. The industrial application is classified as ‘low’ when they are used predominantly in research facilities and as ‘high’ when they are widespread and commonly used standard applications. Apart from these essential criteria, the permeability, the deformability (drapability) and the mechanical performance of the NCF can also be taken into account for an evaluation. These characteristics will be described in subsequent sections of this book.
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1.32 Realizable productivity and complexity of important non-crimp fabric production technologies (ITA).
1.33 Classification of non-crimp fabric production technologies regarding produced amount and industrial application (ITA).
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Future trends
For the determination of future trends in the production of NCF, the integrated production process – from the fibre to the fibre-reinforced plastic component – has to be considered. Composite parts are currently manufactured using manual and semiautomated processes. These are time- and cost-consuming and cause an inefficient use of cost-intensive tool forms. Furthermore, manual operations can lead to problems with regard to reproducibility and the complex subsequent finishing steps. On the one hand, the aerospace and wind energy industries demand large-scale fibre-reinforced plastic (FRP) components. The challenges in the production of these parts are the handling of large textile semi-finished fabrics and their storage management. Moreover, sections with large numbers of layers have to be realised and handled using stacking and joining technologies. On the other hand, the automotive industry requires mass-produced FRP components with a wide range of properties. Among these are metallic inserts, reinforcement structures, apertures and 3D curved surfaces with small radii. One possible process chain for the mass production of FRP components is the manufacturing of dry textile preforms and the impregnation and consolidation by resin injection moulding processes. A key challenge for the realisation of this process chain is the economic production of dry textile preforms that fulfill the requirements of the impregnation process. One requirement is the fixation of the reinforcement fibres to avoid disorientations caused by impregnation pressure. Another key challenge is the production of textile preforms with a high level of quality and reproducibility with short cycle times. Future developments are aimed therefore at the production of near net-shape textile preforms in short cycle times and unit costs. Near net-shape preforms are textile fabrics, with dimensions close to the final product’s shape (Grundmann, 2009). There are two strategies to achieve these goals. One approach is to increase the complexity of the semi-finished fabrics e.g. multiaxial warp-knitted NCF, which can also be referred to as tailored NCF. Using complex semi-finished fabrics, handling and further processing steps in a subsequent preforming process can be reduced (Fig. 1.34). Furthermore, expensive material can be saved. Preforming is thereby defined as the production of the textile preforms in a sequence of automated process steps (Grundmann, 2009). The other approach is to enhance the productivity of already near-net shape technologies like multilayer weft-knitting or 3D weaving. Multiaxial warp-knitted NCF with non-coursewise weft insertion can be produced with high production rates. They have good mechanical properties and are flexible in respect to their layer set-up and fibre orientation. Therefore, they are already an important raw material for the production of fibre-reinforced composites and they are widely used in many applications such as wind turbine blades and aerospace. Current drawbacks are the constant width and thickness of these fabrics as well as the constant stitching type. Further development of the production
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1.34 Preforming technologies (ITA).
technology provides complex semi-finished fabrics. The research goals are the manufacture of multiaxial warp-knitted NCF with local reinforcements (braided structures, NCF, tapes and rovings), a locally adjusted drapability and a large number of layers (Hufenbach, 2007; Grundmann et al., 2009; Heinrich and Vettermann, 2009). In order to produce locally reinforced NCF, a warp-knitting machine with multiaxial weft insertion is supplemented with a feeding module. Focus during the development was set on depositing large textile structures, because of their difficult handling. The feeding module consists of a storage unit with an endless web on a shaft, an integrated cutter and a buffer storage. Several modules can be staggered in a row to produce multilayer textile structures. The warp-knitting module and the take-up module have to be adapted for a continuous process (Schnabel et al., 2009). Local reinforcements, especially bionic structures, can be realized by variable filament or tape placement on NCF. Therefore, racking devices are positioned directly in front of the warp-knitting elements. The racking devices are manipulated with servo drives and can move in opposite directions. Crossbreed structures with and without changes in density are possible (Heinrich and Vettermann, 2009).
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Adhesives for the fixation of loose fibre layers provide a high potential for the economic production of near net-shape textile preforms. On the one hand, a certain amount of adhesive is necessary to fix the filaments. On the other, the adhesives can build a barrier and reduce the permeability, enhancing the impregnability as well as the drapability of the fabric. Future research must focus on solving these problems. There are several approaches to adjust the drapability locally. The stitch type has the biggest influence on drapability. To modify the knitting stitch type during the process, an electromechanically driven guide bar will be integrated into the warpknitting machine (Grundmann et al., 2009). Another approach to influence the local drapability is the use of laser transmission welding. The laser unseams partial warp thread loops without damaging the reinforcement fibre and the finish (Falk, 2005). For the design of FRP components out of complex semi-finished NCF new component design methods are necessary, which consider the above-listed material characteristics. Furthermore, advanced drape simulation tools are necessary, with which the deformation of the semi-finished NCF during a preforming process can be determined and also predict the effects of defects (e.g. the effect of fibre angle deviation on strength). Highly efficient planning tools are needed to develop economically viable and cost-effective fibre-reinforced composite parts. These tools have to be specifically designed to allow the representation of preforming process chains – which include the production of semi-finished NCF – and their assessment under the perspectives of technical feasibility and cost-effectiveness. The development of virtual process chains has to be combined with adapted fabric planning to pave the way for massproduced fibre-reinforced composite parts.
1.9
Acknowledgments
We would like to thank the Deutsche Forschungsgemeinschaft (DFG) for supporting and funding the FOR860 working group of researchers.
1.10
References
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LIBA Maschinenfabrik GmbH (2007), Tricot Machine with Multiaxial Weft Insertion: COPCENTRA MAX3 CNC, Naila: LIBA Maschinenfabrik GmbH, 08/2007 [corporate literature]. LIBA Maschinenfabrik GmbH (2007), Tricot machine with weft insertion: COPCENTRA HS-2-ST, Naila: LIBA Maschinenfabrik GmbH, 07/2007 [corporate literature]. Mauersberger H (1954), Verfahren zur Herstellung von Kettenstichware, DD000000008194A, 06.09.1954. KARL MAYER Textilmaschinenfabrik GmbH (2007), Biaxial: Warp knitting machines with parallel weft insertion, Obertshausen; KARL MAYER Textilmaschinenfabrik GmbH, 08/2007 [corporate literature]. KARL MAYER Textilmaschinenfabrik GmbH (2009), HKS 2 | HKS 2–3 | HKS 2–3 E: Tricot Machines, Obertshausen; KARL MAYER Textilmaschinenfabrik GmbH,08/2009 [corporate literature]. KARL MAYER Textilmaschinenfabrik GmbH (2009), Kamcos® Karl Mayer Command System, Obertshausen; KARL MAYER Textilmaschinenfabrik GmbH, 09/2008 [corporate literature]. KARL MAYER Textilmaschinenfabrik GmbH (2009), Malitronic® Multiaxial Special, Obertshausen; KARL MAYER Textilmaschinenfabrik GmbH, 10/2009 [corporate literature]. KARL MAYER Textilmaschinenfabrik GmbH (2009), Multiaxial Warp knitting machines with multiaxial weft insertion, Obertshausen; KARL MAYER Textilmaschinenfabrik GmbH, 08/2009 [corporate literature]. KARL MAYER Textilmaschinenfabrik GmbH (2009), Technical Textiles, Obertshausen; KARL MAYER Textilmaschinenfabrik GmbH, 04/2009 [corporate literature]. KARL MAYER Textilmaschinenfabrik GmbH (2009), MULTIAXIAL ‘Cut & Lay’ Carbon, Obertshausen; KARL MAYER Textilmaschinenfabrik GmbH, 08/2009 [corporate literature]. McHugh C (2009), Creating 3-D, One Piece, Woven Carbon Preforms using Conventional Weaving and shedding, Sampe Journal, No. 6, Vol. 45, 8–28. Mohamed M and Bogdanovich A (2009), Comparative Analysis of Different 3D Weaving Processes, Machines and Products, Proceedings of 17th International Conference on Composite Materials (ICCM-17), Edinburgh, UK, July 27–31, 2009. Mohamed M and Salama M (2001), High speed three-dimensional weaving method and machine, US000006315007B1, 13.11.2001 Mohamed M and Zhang Z (1992), Method of forming variable cross-sectional shaped three-dimensional fabrics, US000005085252A, 04.02.1992 Munzert H and Unglaub M (2009), Haltevorrichtung an den Transportketten einer Maschine zum Vorlegen von Fadengelegen, Verfahren zum Vorlegen und Fixieren von Filamentscharen zu einem Fadengelege und Multiaxialmaschine zur Durchführung des Verfahrens mit einer Haltevorrichtung, DE000010214140B4, 20.03.2008. Naumann R and Wilkens C (1986), Kettenwirkmaschine mit Magazinschußvorrichtung und auf dieser hergestellte Kettenwirkware, DE3447643C1, 07.08.1986. Nestler J, Vettermann F and Reuchsel D (2009), Device and method for spreading a carbon fibre hank, US000007536761B2, 26.05.2009. Parekh D (1989), Reinforcing fabric for power transmission belts, hoses and the like, US000004845963A, 11.07.1989. Petrenz S (2009), Malitronic® – eine neue Maschinengeneration zur Herstellung von Hochleistungsgelegen, Chemitzer Textiltechnik Tagung, 12, 129–141.
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Roye A, Stüve J and Gries T (2005), Definition for the differentiation of 2D – and 3D – textiles. Part 1: production in one – stepprocesses, Technical Textiles, 48, 212–214. Roye A (2007), Hochleistungsdoppelraschelprozess für Textilbetonanwendungen, Textiltechnik/Textile Technology, 1–175. Schierz M, Waldmann M, Franzke G and Offermann P (2003), Direction-dependent yarn tensioning regulation for the production of multi-axial reinforcement structures – Richtungsabhängige Regulierung der Garnspannung für die Herstellung von multiaxialen Verstärkungsstrukturen Techtextil, Techtextil-Symposium, 10, 1–9. Schnabel A, Kruse F F, Behling T and Gries T (2009), Automated Textile Preforming of Semi-Finished Fabrics for the Mass Production of Fibre-Reinforced Plastic Components, Intelligent Textiles and Mass Customisation International Conference, Marocco Casablanca, 12.11.2009. Skoeck-Hartmann B, Diesel O, Cherif C and Gries T (2008), Integrated bonnet systems for pedestrian safety in Dörfel, A. Proceedings of the 2nd Aachen-Dresden International Textile Conference, Dresden, Dresden : Institute of Textile and Clothing Technology. Stig F (2009), An Introduction to the Mechanics of 3D-Woven Fibre Reinforced Composites, Licentiate degree; Stockholm. Volbers J (2005), Breitenverstellbare multiaxiale Kettenwirkmaschine zur anwendungsspezifischen Verarbeitung von Carbonfasern, Abschlussbericht über ein Entwicklungsprojekt, AZ: 22075, Deutsche Bundesstiftung Umwelt. Wagner G and Palmer R J (1998), Improved warp/knit reinforced structural fabric, WO001998010128A1, 12.03.1998. Wahhoud A (2005), Neue Gestaltungskonzepte zur Gewebeherstellung, WebereiKolloquium Denkendorf, 10, Denkendorf, 26–27 Apr, 2005. Weber K and Weber M (2004), Wirkerei und Strickerei – Technologische und bindungstechnische Grundlagen, Frankfurt am Main, Deutscher Fachverlag. Weiland J (1988), Kettenwirkmaschine mit Magazinschusseinrichtung, DE3720348C1, 29.09.1988. Wiedenhöft K and Vettermann F (1999), Die neue Malimo-Multiaxial als Beispiel für mechatronische Lösungen im Textilmaschinenbau, Chemnitzer TextilmaschinenTagung, 7, 179–186. Wienands C, Unglaub M and Maier S (2004), Verfahren und Vorrichtung zum kontinuierlichen Herstellen von verwirkten/vernähten multi-axialen Gelegen aus mehreren Lagen von Fäden, DE19913647B4, 01.04.2004. Wuensch I (2008), Lexikon Wirkerei und Strickerei, Frankfurt am Main, Deutscher Fachverlag. Wulfhorst B (1998), Textile Fertigungsverfahren – Eine Einführung, München, Wien, Carl Hanser Verlag. Wunner R, 1974. Kettenwirk- und Raschelmaschine mit vorbereitetem Eintrag mehrerer Schußfäden. DE000002244096C3. 08.09.1974. Wunner R (1987), Verfahren und Vorrichtung zum Legen von Querschußfäden für eine Kettenwirkmaschine, DE000003343048C2, 14.05.1987. Wunner R (2009) Kettenwirkmaschine nach Art einer Raschelmaschine, DE102007004315B4, 20.05.2009. Zeidler G, Reuchsel D and Vettermann F (2005), Verbesserung der Gelegequalität durch ein neues Verfahren zum Schusseintrag auf Karl Mayer Multiaxialmaschinen, Chemnitzer Textilmaschinen-Tagung, 10, 263–268.
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2 Standardisation of production technologies for non-crimp fabric composites F. KRUSE and T. GRIES, Institut für Textiltechnik (ITA) of RWTH Aachen University, Germany
Abstract: This chapter reviews the standardisation of the production of non-crimp fabrics (NCFs), as well as the patents protecting these methods. The first part discusses some common considerations in the production and use of NCFs, such as layer orientation, areal weight and bonding patterns. The second part focuses on some of the most important inventions and patents in this area: the computer-controlled weft insertion system (DE 19726831 C2), the LIBA type weft thread transport system (MAX5), the online tow-spreading system, and the ‘Hexcel patent’ (EP 0972102 B1). Key words: production of non-crimp fabric (NCF), warp-knitted NCF, weft-knitted NCF, non-crimp woven fabric, fixation by cohesion.
2.1
Introduction
This chapter gives an overview of the standardisation of the production of noncrimp fabrics (NCFs) and the patent situation. The first part refers to some of the typical questions asked about the production and use of NCFs. For example, it is concerned with topics such as the reference coordinate system of the orientation of single layers, and the estimation of areal weights. The second part is dedicated to selected important patents. It has not been easy to limit the extent of this chapter as the patent situation changes daily and the number of interesting patents is very high. In many conversations with European machine producers, the authors tried to determine those inventions which have had a major influence on the machine technology. These achievements can be read about in the second part of the chapter, which also offers an overview of the famous ‘Hexcel patent’.
2.2
Classification and standardisation of non-crimp fabric (NCF) production methods
Standards are very helpful in terms of allowing for successful communication between customers and textile producers. Terms and units must be defined, as well as a unified designation system for textile construction. Furthermore, important process parameters such as the layer orientation or testing procedures for the areal weight, fabric thickness, moisture, length and width should also be standardised. A very comprehensive standard in respect to the aspects quoted above is the European standard EN 13473, Parts 1, 2 and 3. In the following 42 © Woodhead Publishing Limited, 2011
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section, parts of this standard and references to other standards, which are linked to EN 13427, are described.
2.2.1 Classification Non-crimp fabrics (NCF) are officially defined and standardised as multiaxial multi-ply fabrics. Contrary to other production technologies for textile fabrics, the fibres of each layer are orientated straight, and are only laid upon each other during the production process. Finally, the fixation of the single layers to a useable fabric is done by warp-knitting or by binder application. The fibre materials and the orientation, as well as the areal weight, of each layer can be chosen in a very flexible manner. Furthermore, fibre mats or short fibres can be inserted between each layer, as is shown in Fig. 2.1. Chopped strand mat
Auxilary material (Non-woven)
0º
+45º
90º
–45º
Stitching pattern
2.1 Classification of a non-crimp fabric.
2.2.2 Important terms and definitions A standard for the designation of a multiaxial NCF is given in EN 13473, Part 1. It consists of three data blocks, which are shown in Table 2.1. The three data blocks provide the following information: • • •
Data block 1: identification of the layer stacking sequence and textile construction Data block 2: identification of the binding system Data block 3: identification of the fabric manufacturer
In general, the individual item block shall be separated from the identity block by a comma (,). The three data blocks of the individual item block are framed by © Woodhead Publishing Limited, 2011
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Table 2.1 Designation system for multiaxial non-crimp fabrics according to EN 13473-1 Designation Identity block
Individual item block
International standard
Data block 1 Example [. . .]
EN 13473-1
Data block 2
Data block 3
[. . .]
[. . .]
rectangular brackets ([. . .]). If a data block is not used, this shall be indicated by empty rectangular brackets ([]). Data block 1 The descriptions of the single layers in data block 1 are separated by a double slash (//), starting with the first layer due to the production succession, see Fig. 2.2. In position 1 of each layer description, the material types and grades used in the layer are identified by code letters according to Table 2.2. In position 2 of the layer description, the areal weight is identified in the unit grams per square metre. Position 3 indicates the orientation of the layers. Data block 2 In this block, the binding system is defined and described by three values, which are separated from each other by a comma (,). In position 1 of the binding description, the used materials are identified by abbreviations according to Table 2.2.
Table 2.2 Abbreviations for material type from EN 13473-1 Code letter
Material type
A C G K PA PE PES PET PP
Aramide Carbon Glass Ceramic Polyamide Polyethylen Polyester Polyethylenterephthalate Polypropylene
NOTE: Supplements of further material types are possible. The material grades have to be additionally specified in each case.
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Table 2.3 Code letter for the type of binding system from EN 13473-1 Code letter
Type of binding system
L C
Loop system Chemical binding system
In position 2, the areal weight or the mass per unit area is identified [g/m2]. In data block 3, the binding type is identified according to Table 2.3. Data block 3 Data block 3 can be used as a code for the NCF’s producer. An example of the use of the designation system is shown below. The NCF has the following characteristics. • • • • • • •
E-glass reinforcement yarn. Three layers in the sequence −45°//+45°//0°. Parallel weft. Areal weight of the 45° plys: 235 g/m2. Areal weight of the 0° layer: 425 g/m2. Joined by a loop system using PES, 12 g/m2. The manufacture’s code is ITA-FOR860-TP1 (in this example).
The correct designation for this NCF is therefore: EN 13473,[G, 235, −45°//G, 235, +45°//G, 425, 0°][PES, 12, L][ITA-FOR860-TP1] Following this introduction to the designation of an NCF, this chapter will now provide some important definitions of the layer orientation and the estimation of the areal weight.
2.2.3 Definition of the layer orientation One very important standard used to define the layer orientation is the reference coordinate system. According to the ISO/DIS 1268-1 the 0° direction is parallel to the direction of production, e.g. the movement of the transport chains. The ‘1’ axis in Fig. 2.2 represents the y axis and, therefore, the 90° direction. Layer orientations within the positive quadrant from 0° to 90° are defined as positive. The ‘2’ axis or the z axis indicates the direction of the stacking sequence.
2.2.4 Estimation of the areal weight The estimation of the areal weight, or the mass per unit area, is a common procedure carried out when setting up a new product, or in order to control the
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2.2 Definition of the layer orientations according to ISO/DIS 1268-1/EN 13473-1.
areal weight randomly during production. A normative definition for textiles made with glass, carbon or aramid yarns is given in ISO 3374. To perform the tests, the specimen must be cut out of the textile in a specific manner, which is shown in Fig. 2.3. Each specimen must have a square or circular shape and an area of 100 cm2. The permissible error in the area of the resulting specimens should be 1% or less. In practice, this value can only be achieved through the use of a computer-controlled cutter or a stamping device. The use of handheld cutting disks or knives would result in a more or less pronounced shape distortion. Once it has been cut out, the specimen must be handled with great care, as otherwise some fibres may be lost. Before it is weighed, the specimen must be dried in a ventilated oven at 105°C±3°C for one hour. The specimen is cooled down to room temperature in a desiccator in order to keep the moisture as low as possible.
2.3 Suggested method for cutting out fabric specimens. Useable for fabrics wider than 50 cm. 1 = width of textile; 2 = warp direction.
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Table 2.4 Necessary characteristics and resolution of the used balance according to ISO 3374 Material
Measuring capability
Limit of permissible error
Resolution
Mats, all weights Fabrics ≥ 200 g/m2 Fabrics < 200 g/m2
0 to 150 g 0 to 150 g 0 to 150 g
0.5 g 10 mg 1 mg
0.1 g 1 mg 0,1 mg
The process of weighing must immediately follow the removal of the specimen from the desiccator. The necessary characteristics of the balance are given in Table 2.4. For a specimen area of 100 cm2, the resulting areal weight in grams per square metre is then:
[ g] PA = 10 000 + m A m2
[2.1]
Where m is the mass of the specimen in grams, and A the area of the specimen in cm2.
2.2.5 Bonding patterns In contrast with other warp-knitted fabrics, the loops in NCFs are only used for fixation. Therefore, the complexity of the bonding patterns used is relatively low. Nevertheless, a standardisation of the different and possible bonding patterns, as well as the basic concepts and the vocabulary which underpin them, is necessary and exists in the form of the international standard ISO 4921. One technique that is very common in biaxial or triaxial NCFs without any 0° layers is the simple pillar stitch, which is described under paragraph 3.2.37 of the ISO 4921 standard and sketched in Fig. 2.4. If 0° layers are applied, a weft insertion is necessary to prevent the 0° rovings from being lost. This can be achieved through the use of the tricot or the satin stitch, as shown in Fig. 2.4 centre and right.
2.3
Outstanding patents of existing machines for the production of NCFs
2.3.1 Computer-controlled weft insertion system (DE 19726831 C2) One very practical invention is the computer-controlled weft insertion system, which was patented on 10 Jan 2002 by the LIBA Maschinenfabrik GmbH, Naila. It was first used in the LIBA MAX 3 CNC, as can be seen in Fig. 2.5. In contrast to the parent machines produced by the LIBA company and its competitors, which
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2.4 Four commonly used bonding patterns in non-crimp fabrics: pillar stitch (top left), tricot stitch (top right), cord stitch (bottom left) and satin stitch (bottom right), according to ISO 4921.
2.5 New, computer-controlled weft insertion system of the LIBA MAX 3 CNC (left) and the old, fixed weft insertion system (right). (Source: LIBA GmbH).
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2.6 Computer-controlled weft insertion system, patented in DE 19726831 C2.
have fixed weft insertion systems, the new system facilitates a much higher rate of efficiency and flexibility. Figure 2.6 provides an overview of the new machine architecture. The universal weft layer (5) consists of one or more servomotor driven portal system (9), which moves in parallel with the direction of production (x-direction) on a gear rack (9) which is mounted on the modular machine frame (4). The fibers (3) are deposited by a layer carriage (2), which runs transversely to the direction of production (y and z-direction). With the degree of freedom offered by the portal system and the layer carriage, it is possible to realise every desired layer angle between −20° and +20° relative to the x-direction. The single layers are fixed up to the warping unit (8) by two chains (11) equipped with hooks on both sides of the machine, as shown in Fig. 2.7. This item is important insofar as it allows for the use of the full anisotropic potential of fibre-reinforced materials. Furthermore, the invention has led to a considerable reduction in the level of effort required to change the layer set-up. The desired angle of each ply is set in the computer via an interactive user interface. There is no mechanical work required, with the exception of some reed changes, if the areal weight is to be modified. Due to the lightweight portals and powerful servo motors, this invention made possible a much higher machine speed.
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2.7 Transport chain and layer carriage of DE 19726831 C2.
2.3.2 New weft thread transport systems (DE 10214140 B4) Despite all the advantages of the aforementioned invention, there are still some requirements regarding the production of textiles made from carbon fibres which remain unsatisfied. Carbon fibres are brittle and tend to break if they are bent around a small radius. So with the hook chains, which were the state-of-the-art technology until the patents dealt with in the following were published, there were some types of carbon fibres that could not be processed. Furthermore, there is a strong and economically driven demand for high-quality NCFs made from cheaper ‘heavy tow’ carbon rovings with up to 50k filaments. With the classical method of producing an NCF, which involves placing tows directly from the creels into the hook chain, it is not possible to realise low areal weights by using heavy tows with 24k filaments and above. The solution to this problem was found in a new process step prior to the placement. Before being placed, the carbon tows are spread into unidirectional (UD) tapes with a maximum areal weight of 300 g/m2. The spreading process can be done either online (see Section 2.3.3) or offline using a special machine. A special mechanism pulls out the tapes from the spreading unit or coils, then cuts them to a predefined length and places them into the transport chain with the clamping device. Despite the spreading process, the above-mentioned transport chain is one very important and critical item while producing NCFs out of spread tapes. © Woodhead Publishing Limited, 2011
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One invention of the Karl Mayer Textilmaschinenfabrik GmbH was a combination of a hook chain with a clamping mechanism. The relating patent was granted on 11 November 2006. The invention refers to a process and device to lay and fix band-shaped filament yarn sheets onto two transport devices arranged in parallel to one another to produce a uni-, bi- or multiaxial multi-ply fabric that is comprised of at least one layer of band-shaped filament sheets drawn in one direction, arranged side by side in one plane and separated from one another. The filament sheet is held on pin rows, as shown in Fig. 2.8.
2.8 Karl Mayer type clamping system for spreading tapes (patent claim EP 1512784 B1).
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2.9 Tape layer system of the LIBA MAX 5 CNC carbon with the clamping head (22), the sword (29) and the pressure pad (14). The numbers refers to the numeration in DE 10214140 B3 (Source: LIBA).
2.10 Transport chain of the LIBA MAX 5 CNC Carbon. As in Fig. 2.9, the numbers refer to the numeration in the text of the patent DE 10214140 B4 (Source: LIBA).
Another invention of the LIBA Maschinenfabrik GmbH was patented on 20 March 2008, patent number DE 10214140 B4. Before being placed, the carbon tows are spread into unidirectional (UD) tapes with a maximum areal weight of 300 g/m2. The spreading process can be done either online (see section 2.3.3) or offline using a special machine. A special mechanism pulls out the tapes from the spreading unit or coils, then cuts them to a predefined length and places them into the transport chain with the clamping device.
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The mechanism of clamping and transporting the UD tape is very simple, but also very effective. A sequence of clamping consists of eight phases, which are shown in Fig. 2.11. Note that the direction of production is perpendicular to the plane of the picture. Furthermore, only the left transport chain with the clamping device is shown.
2.11 Clamping sequence of an LIBA MAX 5 transport chain (patent claim DE 10214140 B4).
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In the first step, the UD tape (2) is pulled out from the coil or the online creel (see 2.3.3) and gripped by the clamping head (22). In step 2, the pressure pad (14) fixes the tape on the lower clamping plate (26) and a row of hooks (13). All parts of the clamping mechanism are mounted on the chain links of the transport chain (3), which moves steadily downwards to the warp-knitting unit (not shown). In the third step, the upper clamping plate (27) opens. Its movement is governed by a guide rail (30), which has a curvature at this point to generate the stroke of the clamping plate (27). In the fourth step, the clamping head (22) opens. Now, the part of the UD tape that is outside of the pressure pad is released. Thereafter, a sword (29) bends this free end of the tape down to an elastic profile (28). In step 6 the sword moves upwards, while the free end of the UD tape is fixed by the backwards-moving clamping plate (27) shortly afterwards (step 7). In the last step, the hub with the clamping head (22), the pressure pad (14) and the sword (29) moves up and against the direction of production. The process then repeats itself with the next tape. Another critical point while producing NCFs is the warping unit. Within this unit, the single layers are only fixed in the clamping or hook chains. Thus, only the parts of the layers that are beneath the clamping chains are stabilised while the rest is only kept in a straight orientation due to a certain pre-tension. An invention of the Karl Mayer Textilmaschinenfabrik GmbH refers to a device where a continuous converser belt running synchronously to the transport chains supports the weft layers up to the knitting area of the multiaxial machine. As a consequence thereof, a significantly higher process stability and fabric quality can be achieved. The principle is shown in Fig. 2.12, where the converser belt is designated with the number 6.
2.3.3 Online tow spreading and feeding systems (EP 2003232 A1) This invention, which uses spread tows or UD tapes in the production of multiaxial NCFs was a major step forward. But in practice it has been found that it is necessary to establish a very homogeneous state of stress within the UD tapes when placing them into the transport chains. Furthermore, there is a strong customer demand to spread the tows directly in the machine, rather than using a separate spreading unit. For these reasons, the coils used to store and transport the UD tapes once spread, which are a potential origin of failures, are now obsolete. The solution that has been found for both requirements is the use of online tow spreading systems. An example for such a complex online spreading system is given in Fig. 2.13 and 2.14. In order to achieve a constant state of stress, a combination of the creels (5) and the spreading unit (6) in one moveable frame called a carriage (3) was created. The carriage itself is supported via rollers (4) in the machine frame (1), which is aligned with the tape-laying system and fixed to the ground.
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2.12 Principle for the use of transport belts between the warping needles (patent claim DE 19852281 C2).
The single tows run from the bobbin (7) via the guide pulleys (9) into the spreading unit (6) as is shown in Fig. 2.14. The major advantage of this combined creel and spreading unit consists of the simple fact that the tows are pulled from the bobbins and spread by the spreading unit at a constant speed and without any interruptions. This leads to there being a very high and uniform quality amongst the produced tapes and the carriage (3) is able to deliver the tapes discontinuously to the gripper (15) due to its own movement (Fig. 2.15).
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2.13 Online tow spreading system according to EP 2003232 A1 (Source: LIBA).
2.14 Principle of the combined creel and spreading unit according to EP 2003232 A1.
The sequence of pulling out a spread tape and placing it into the clamping chain is illustrated in Fig. 2.16. In the first step, the carriage (3) runs into its endpoint (Lmax) while permanently spreading a tape, which is held at its free end by the gripper (15). The restraint (11) remains open. In step 2, the carriage (3)
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2.15 Movements of the tape (a), the gripper (b) and the carriage (c) during a lay-up sequence (EP 2003232 A1).
reaches its aft position and the gripper begins to pull out the tape. While pulling out the tape in step 3, the carriage moves forward in the same direction, but with a different speed, as shown in Fig. 2.16. At step 4, the carriage (3) reverses its movement while the gripper 15 slows down. In step 5, the tape is fully pulled out and the restraint (11) closes. At this point, the carriage (3) is on its way to its endpoint and constantly produces a tape reservoir. The tape-laying system (16, see section 2.3.2) is now moving against the direction of production to overtake the tape. In step 6, a cutter separates the tape, the gripper (15) opens and the tapelayer (16) puts the tape into the transport chains (12a and 12b) in the manner described in section 2.3.2. In step 7, the gripper (15) moves into its starting position while the carriage (3) or the spreading unit produces the tape reservoir. In step 8, the tape is clamped into the transport chains (12a and 12b respectively), the gripper (15) is in its starting position, and the carriage (3) is only a short distance away from its end position. Now everything is ready for the next sequence. On 17 December 2008 the patent EP 1512784 B1 was granted to the company Karl Mayer Textilmaschinenfabrik GmbH, which protects an alternative invention to feed spread carbon fibres tapes continuously into a knitting machine. The carbon fibres are unwound from a creel with carbon band bobbins by means of delivery rolls and led to a weft-laying device provided on the knitting machine. To do so, a band accumulator has been provided in between the creel and the weft laying device, the accumulating length of which can be varied. A control unit affects both delivery rolls and accumulator so that, notwithstanding an idle return motion of the weft laying device, the bobbins are unwound continuously and start-up tension and slow-down motion of bobbins will not adversely affect band tension in the multi-ply fabric. Further, a spreading device has been installed to ensure uniform width and thickness of carbon band before the weft laying device. The principle is shown in Fig. 2.17.
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2.16 Sequence of the placing of an offline spread tape into the transport chains according to EP 2003232 A1.
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2.17 Principle of a device to feed fibrous bands into a knitting machine (patent claim DE 102005008705 B3).
2.4
The ‘Hexcel patent’ – EP 0972102 B1
On 20 November 2003, a very famous and comprehensive patent was awarded to the French companies Société National d’Étude et de Construction de Moteures d’Aviation (National Company for the Design and Construction of Aviation Engines, SNECMA) and Hexcel Fabrics. In the preamble of the patent, it was stated that in a common production of NCFs, a certain amount of fibre undulation is unavoidable due to the warping loops in the fabric. In consequence of this fact, reduced mechanical properties are to be expected. One goal of the patent is therefore to avoid undulations and improve the mechanical properties by using alternative methods to fix the single layers of an NCF. Another goal of this patent also had a great influence on the development of production technologies for NCFs. The primary goal of the invention was to create a reduced-cost production method for NCFs, especially for those which are made from carbon fibres. As stated above, the production cost can be lowered by using tows with a very high number of filaments, e.g. heavy tows. The inventors of the Hexcel patent were among the first to identify the huge potential of using spread heavy tows, especially those made of carbon fibres. Following this, a wide range of methods of producing multiaxial NCFs out of heavy tows by spreading them to very low areal weights are given in the patent. An overview of the range of the patent is shown in Fig. 2.18.
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2.18 Figure from EP 0972102 B1, which is an indicator of the wide scope of this patent claim.
In patent claims 1 and 2, a maximum areal weight of 300 g/m2 and a minimum of 5 cm are protected. The used materials include every useable continuous and discontinuous high-performance fibre, including both carbon, ceramics and blends of the two, as well as glass and aramid fibres. Up to patent claim 9, further material properties, such as the use of use of carbon fibre tows with a minimum number of filaments of 12k, are also protected. In the sub-claims 10 to 22, different methods of applying a transversal cohesion to the fibres and the single UD layers are discussed. In the sub-claims 23–43, different methods of handling and fixing the different layers are protected. These refer particularly to methods which use all kinds of binders to prevent undulations, but also to those which function by warpknitting. In the claims 44–56, many of the above-named properties are protected for UD layers made from discontinuous fibres with a filament number higher than 12k, a width of more than 5 cm and an areal weight of a maximum of 300 g/m2. In claims 57 and above, the same is valid for spread cracked, and therefore also discontinuous, tows. In summary, the Hexcel patent was a highly visionary patent at the date of its announcement. However, the transfer of the patent claims to a commercially available machine has not taken place up to now. The use of carbon fibre heavy tows and the spreading of these into UD tapes to produce multiaxial NCFs is meanwhile the standard process of the companies LIBA and Karl Mayer Malimo. But the basic architecture of these modern machines is very similar to the Hexcel concept. Figure 2.19 shows this clearly.
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2.19 Figure 6a from EP 0972102 B1 – the basic architecture of all modern machines like the LIBA Max 5 or the Karl Meyer Multiaxial ‘cut and lay’ Carbon.
2.5
Product patents in the production of NCFs
2.5.1 Integrated manufacturing process for stringerstiffened panels (DE 10 2005 052573 A1) Thin-walled and stiffened-shell structures are very common in lightweight applications. A dry textile preform of a stringer-stiffened panel structure can be produced in various different ways. Reinforcement textiles for the panel of the structure are usually woven fabrics and/or multiaxial multi-ply fabrics. Stringers e.g. those in the form of hat or double-T profiles, are attached to these reinforcement textiles. The production of the hat or double-T profiles can be achieved through the forming, draping and fixing of plane reinforcement textiles to 3D textiles. However, hat or double-T profiles can also be manufactured through braiding, as this production process makes it possible to manufacture 3D structures in one step. The joining of both components, panel and stringer, can take place in a separate processing step before or after the consolidation of the construction units. In DE 10 2005 052573 A1, invented by the Institute of Textile Technology of RWTH, Aachen University and released on 3 May 2007, an integrated manufacturing process is described. During the multiaxial multi-ply fabric production of the basic textile, the prefabricated hat profiles are directly joined with the basic textile using warp-knitting.
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In order to allow for the implementation of an integrated manufacturing process, the multiaxial warp-knitting machine (Copcentra MAX 3 CNC from LIBA Maschinenfabrik GmbH, Naila) that is used at ITA was modified so that the multiaxial multi-ply warp-knitted fabrics and hat profile could be joined in one production step (Fig. 2.20 Integrated production process). The modification now permits a variable supply of stringer elements with a height of 50 mm, depending on position and number. The modification was achieved through the construction of a split piercing compound needle bar, a split closure bar and a split knock-over sinker, as well as split good rollers and a special device construction for hat profiles. A comparison of the joining technologies used in the project, ‘sewing with lockstitch’ and the ‘integrated manufacturing process’, is made according to the standard DIN 65148 ‘determination of the interlaminate shear strength in the tensile test’. The connection of the stringer to the panel is examined herewith. The test specimens are loaded in such a way that a shearing stress works in the connecting level between panel and stringer. The laminated sample test specimens are prepared with two milled grooves at a distance of 12.5 mm (Fig. 2.21) apart. During the tensile test, shear stress arises in the area between these grooves. This stress leads to material failure. The test specimens are stressed up to break. According to the standard, the constant test speed was selected in such a way that
2.20 Integrated production process.
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2.21 Preparation of test specimen (measurements in millimetres).
material failure takes place after approximately 60 seconds. In preliminary tests, an optimal test speed of 2 mm/min was determined. For the evaluation of the breaking tension, the ratio between the maximum strength and the shear crosssection is calculated. This is the interlaminate shear strength. The test series consisted of four different test specimens. The reference sample is a stringer-reinforced panel, which was added by one lockstitch seam per flange. Three further test specimens were manufactured in the integrated warp-knitting process, each with a different number of seams per flange. In order to eliminate discrepancies arising as a result of using different sewing threads, the same sewing thread material that was used by the lockstitch is used again in the integrated warp-knitting process in the area of joining the flanges. The evaluation of the test shows that the samples of the sewn textile preforms do not reach the values of the samples that were manufactured using the integrated process. The value of the breaking tension lies approximately 25% below the value of the test specimens of the integrated process. There is a difference in breaking tension between the sample test specimens from the integrated manufacturing process with a different number of seams per flange, but it is not significant.
2.5.2 NCFs stitched together using a fusible thread (EP 1 352 118 B1) Either stitching or the application of a binder is essential to allow for the handling of NCFs, but both serve to decrease the drape properties. In order to solve this problem, a fusible thread is used. Therefore, the stitched plies can be tailored and handled in the same way as common NCFs, and can also be heated in order to soften or melt the fusible thread, and hence to improve the drape of the fabric. The patent EP 1 352 118 B1 covers the draping of such an NCF over a forming tool within the steps of placing the NCF and heating it to soften the fusible thread to reduce the restriction of the drape by the stitching. It was published on 15 October 2003 by Airbus UK and Devold AMT.
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Claims 2–4 comprise different settings of the processing temperature, for example, to heat the NCF no higher than the fusion temperature of the thread, in order that a part of the thread remains. Claims 5–10 are about creating resin channels in the NCF by increasing the tension in the unfused stitching, and infusing the NCF with different types of matrix resin through those channels. Claims 11–18 concern manufacturing parameters such as the mass ratio of fusible thread to NCF, the melting temperature, or the material of the thread. The claims cover all possible NCF settings as known from the EN 13473, including different stitching patterns, such as tricot closed, and different yarn directions, from ±20° to 90°.
2.6
Immobilisation of adhesive on the surface of semifinished textile products (DE 102008004112 A1)
On 16 July 2009, a patent application from the company SAERTEX Wagner GmbH & Co. KG was published. It presupposes a semi-finished textile product with at least one surface provided with adhesive exhibits. It is a fact, particularly in the range of the rotors of wind power plants and also in boat building, that an adjustment of the textile single layers is welcome, especially when trying to fix them to vertical surfaces (Fig. 2.22). In order to achieve this, the composites are often implemented with selfadhesive. For example, a special thermoplastic adhesive based up on epoxy resins is applied to the surface of the textile. That is why the textiles can be fixed in a form, or on a pre-fixed layer. Furthermore, it is especially important in the group of sandwich components that the adhesions to the core material, e.g. balsa wood or various types of plastics, such as PVC or PE, are guaranteed. The problem with the special thermoplastic adhesives used is that the stickiness of the textiles is
2.22 Adjustment of textiles at the vertical surfaces of a rotor blade mold (source SGL Rotec).
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already beginning to decrease after only a short time. The capillary effect of the filaments, together with the affinity that the adhesives have to the size of the used fibres, leads to the adhesive migrating to the inside of the textile after a short time. Therefore, such textiles cannot be stored for long periods of time. Another possible means of increasing the adhesiveness of the surfaces is to apply natural rubber emulsions to the textiles. Unfortunately, natural rubber is barely soluble, so it tends to remain as a foreign particle in the fibre-reinforced construction unit and the strength of the NCF is reduced tremendously. The goal of this invention is to propose a textile with a sticky surface that is capable of being stored for a longer time with a normal strength. The solution is the immobilisation of the adhesive on the surface of the textile by the partial networking of at least one component of the glue, most commonly a monomer with double bonds, e.g. acrylic resin or vinyl ester. A preferred compound for the adhesive (related to its weight) is 25–40% natural rubber, 5–10% epoxide resin and 40–60% partial ester. In addition, the adhesive can contain an initiator, additives such as colourants or processing aids. It is also advantageous if the adhesive is capable of being swelled, because this facilitates a thorough mixture of the glue with the resin matrix. The adhesive can be sprayed onto the surface of the textiles in a quantity between two and 50 g/m2. In such a way, treated half-finished products exhibit a stable surface adhesiveness at ambient temperature which is consistent for a period of more than four months, and up to several years, so they are able to be positioned. Examples of such an adhesive include the self-adherent fabrics SAERfix® EP and SAERfix® UP from the company SAERTEX. The adhesive material is compatible with epoxy resins and is chemically incorporated into the matrix during the course of curing. There is no need to spray an additional adhesive and one can remove and reapply the fabric as necessary, as SAERTEX assures on its website: http://www.saertex .de/produkt_technik/produkte/saerfixR/ (15th June 2010).
2.7
References
Ref.No. DIN EN 13473–1 : 2001–11 Reinforcement – Specifications for multi axial multi-ply fabrics Part 1: Description Ref.No. DIN EN 13473–2 : 2001–11 Reinforcement – Specifications for multi axial multi-ply fabrics Part 2: Methods of test and general requirements Ref.No. DIN EN 13473–3 : 2001–11 Reinforcement – Specifications for multi axial multi-ply fabrics Part 3: Specific requirements Ref.No. ISO/DIS 1268–1 ISO Standard BS ISO 1268–1:2001 Fibre-reinforced plastics. Methods of producing test plates. General conditions Owner: BSI filed: 2002–01
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Ref.No. ISO 3374 : 2000(E) Reinforcement products – Mats and fabrics – Determination of mass per unit area Ref.No. ISO 4921 : 2000(E/F) DIN EN ISO 4921 Knitting – Basic concepts – Vocabulary (ISO 4921:2000); German version EN ISO 4921:2001 Owner: filed: 2002–04 Ref.No. DE 19726831 C2 Patent DE 19726831 C2 Owner: LIBA Maschinenfabrik GmbH Multi axial-Maschine mit Portalaufbau filed: 2002–10 Ref.No. EP 1512784 B1 Patent EP000001512784B1 Owner: MAYER Malimo Textilmaschinenfabrik GmbH, 09117 Chemnitz, DE filed: 2006–11 Ref.No. DE 10214140 B4 Patent DE 10214140 B4 Owner: LIBA Maschinenfabrik GmbH filed: 2008–03 Ref.No. DE 19852281 C2 Patent DE 000019852281 C2 Owner: KARL MAYER Malimo Textilmaschinenfabrik GmbH, 09117 Chemnitz, DE filed: 2003–04 European Patent Ref.No. EP 2003232 A1 Owner: LIBA Maschinenfabrik GmbH filed: 2007–06 Ref.No. DE 102005008705 B3 Patent DE 102005008705 B3 Owner: KARL MAYER Malimo Textilmaschinenfabrik GmbH, 09117 Chemnitz, DE filed: 2006–09 Ref.No. EP 0972102 B1 European Patent Method for producing multiaxial fibrous webs Owner: Hexcel Fabrics, 69608 Villeurbanne Cedex, FR filed: 2003–11 Ref.No. DIN 65148 DIN Standard Aerospace; testing of fibre-reinforced plastics; determination of interlaminar shear strength by tenside test Owner: filed: 1986–11 European Patent Ref.No. EP 1 352 118 B1 Owner: Airbus UK Limited Devold AMT AS filed: 2001–12 Publication of the invention Ref.No. DE 102008004112 A1 Owner: SAERTEX GmbH & Co. KG filed: 2009–07 SGL Rotec http://www.sgl-rotec.com Owner: SGL Rotec GmbH & Co. KG, 27809 Lemwerder, DE
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3 Structural stitching of non-crimp fabric preforms for composites P. MITSCHANG, Institut für Verbundwerkstoffe GmbH, Germany
Abstract: This chapter contains a short introduction on preform technology and answers the question of why stitching technology should be used. Different types of threads are described, followed by a short discussion about the advantages and disadvantages of each, which will help the reader to select the right type for a specific application. Quality aspects of sewn preforms are evaluated. Information is given about stitching technology, based on the requirements of composites. A description of the main technologies and a short overview of different stitching machines and their capabilities for structural stitching are also given. Finally, quality aspects of manufacturing structural stitched non-crimp fabrics (NCFs) are addressed. Special focus is given to machine parameters and their influence on compaction behaviour, permeability and laminate quality. Key words: stitching technology, thread selection, stitch hole ellipse, stitching parameters, stitched preform.
3.1
Introduction
The processing of non-crimp fabric (NCF) composites is generally carried out using a liquid moulding process like Resin Transfer Moulding (RTM) or Vacuumassisted Resin Infusion (VARI). During the manufacturing of structural components, the main focus is on maintaining the necessary fibre orientation in the component. This is the reason why, during the processing of NCFs in liquid moulding processes, a preforming process is established before the actual infusion process can be carried out. In addition to the use of a moulding process with thermoplastic binders, the stitching technique can be offered as preform technology to strengthen the fibres. Due to its development and broad application in the clothing industry, stitching technology offers a considerable range of advantages, such as the variable selection of stitch types and sewing threads. The potential applications of NCF composites, as well as the RTM process, can place demands on their structural seams. Therefore, it is necessary to differentiate between stitching for fixation or positioning, stitching for assembly reasons, and structural stitching (Mitschang et al., 2003). Table 3.1 shows the advantages as well as the challenges of structural stitching. Aside from the quality of the basic textile product (in this case, a non-crimp fabric) and the injection or infusion process (including the hardening of the resin), the quality of a laminate or component is decisively defined by the quality of the preform. Figure 3.1 shows how the quality of the component depends on the materials and processing steps used to produce it. 67 © Woodhead Publishing Limited, 2011
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Table 3.1 Advantages and challenges of structurally stitched non-crimp fabric preforms Advantages
Challenges
Easy handling of complex textile structures Manufacturing of semi-finished products Assembly for 3D geometries Waste reduction Pre-compaction of preforms Complex component Efficient injection or infusion processes Elimination of post-processing (net-shape) Improved 3D properties
3D and surface quality of laminate Thread material as a third component Thread impregnation Prevention of void formation Fibre separation Fibre deflection Prevention of resin-rich zones Reduction of in-plane properties Surface appearance and resin shrinkage
3.1 Factors influencing laminate and part quality.
The following sections describe the selection of sewing threads, an estimation of the available stitching technologies, the applicable machine technology, and the parameters that have to be taken into account in the construction of structural seams for NCFs.
3.2
Threads for structural stitching technology
According to the role of the individual seam, there are different sewing threads available (Ogale et al., 2004). In the first instance, these seams are to be differentiated according to the materials used in their construction. While thermoplastic sewing threads are primarily used for positioning, fixing, and as
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Table 3.2 Classification for yarn types to be used for stitching Thread type
Description
Mechanical properties
Spun yarn
Fibres with twist level, ∼ 400 turns/m 10–50 filaments, twisted ∼150 turns/m Bulky, looped filament orientation Filament core, staple fibre sheath
Medium strength and elongation Good strength and high elongation Inherent high elongation
Twisted multi filaments Textured yarn Core spun yarn
High performance thread
assembly seams, due to their high elongation at break, materials with high strength or stiffness are preferred for structural seams. These materials are mainly glass, aramid and carbon. As a second characteristic, the thread type is crucial in terms of determining the behaviour of the sewing thread. Table 3.2 shows a comparison of different types of sewing thread. The various types of sewing thread are generally all suitable to be used as needle threads as well as bobbin threads. In most cases, textured threads made of very fine polyester filaments (<15 tex) are used as bobbin threads. In the selection of a needle thread, it is important to consider the fact that the thread will have to pass through the needle eye several times and must therefore be able to withstand looping with the bobbin thread (knot formation). It is especially important to take account of this aspect when using carbon sewing threads. Core spun yarns and twisted multifilament yarns are suitable for structural sewing. Some commercially available threads include glass fibre sewing threads from Culimeta (Culimeta, 2010), PPG (PPG Fiber Glass, 2010) and Vetrotex (SaintGobain Vetrotex International, 2010) and carbon fibre sewing threads from Schappe Techniques and Toray. Typical here is the use of relatively thick sewing threads (70–150 tex) with medium to low twist. The low knot strength is a considerable problem in the manufacture of carbon fibre sewing threads, but it can be considerably increased through the use of core spun technology with a hybrid solution. Figure 3.2 shows the different sewing threads based on carbon fibre rovings. Type CF-1, CF-2, and CF-3 are hybrid threads manufactured using a crochet technology (Weimer, 1999), a wrapping technology, or a braiding technology (Schappe, 2004). An advantage of these technologies is that the carbon filaments are placed straight in the core of the sewing thread, which serves to optimise their load-bearing ability. A disadvantage is the cover of the used polyester thread, which is an additional component and an unwanted material in the composite. Alternatively, it also is possible for a carbon fibre roving to be turned or twisted, as shown in Fig. 3.2 by type CF-4, CF-5, and CF-6.
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3.2 Different types of carbon fibre sewing threads (IVW GmbH).
The process of turning and twisting carries a risk of causing pre-damages and leads to the suboptimal placement of fibres in the composite, as wells as inadequate load-carrying ability, due to the twists it creates in the filaments. Another important parameter for the selection of fibres is fibre sizing. The impregnation properties of the thread and the chemical compatibility between the sewing thread and the resin during the curing process is defined by the fibre design and the fibre sizing used. In addition to the requirement to be compatible with the resin system, a further function of fibre sizing is to reduce the sliding friction between the thread and the needle, as well as between the thread and the stitched textile structure. If there is too much friction, abrasive thread wear can occur and lead to thread breakage. Thus, not only will the efficiency and economic performance of the process be endangered, but the structural properties of the stitching will also be considerably reduced. The properties of strength, stiffness, elongation, and friction are all important for the complete performance of a chosen thread.
3.3
Stitching technology and sewing machines
Almost all stitching technologies are applicable in the manufacturing of preforms for NCFs (Poe et al., 2002). The specific selection has to be carried out according to the demands of its respective application. The modified lock stitch, chain stitch, blind stitch, one-side stitch and tufting are particularly suitable for structural stitched laminates (Ogale and Mitschang, 2004; Herkt et al., 2006; Drechsler,
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3.3 Schematic diagram of stitch formation using lock stitch and micrograph of a non-crimp fabric laminate stitched with a modified lock stitch.
2000). Figure 3.3 shows the lock stitch formation, as well as a NCF laminate stitched with a modified lock stitch using a glass fibre sewing thread. The modified lock stitch differs from the deployed standard lock stitch used in the apparel industry in terms of the interlace position of the needle and bobbin thread. While in the apparel industry, the interlace is positioned within the work piece, for structural stitching the interlace must be positioned on the rear side of the laminate due to there being minimal fibre undulation inside the laminate. This can be achieved through the adjustment of the tensile forces between the needle and bobbin thread during stitch formation. Aside from the lock stitch, which is well known and used in the apparel industry, there have been other seams established for structural stitching. These include one-side stitching techniques (such as KSL blind stitch RS 510, KSL double needle RS 530, and ITA sewing head) and tufting (KSL Tufting RS 522). Table 3.3 summarises the most commonly used stitch types in relation to their influence on the quality and properties of the preform. The one-side stitching heads (Fig. 3.4 and Fig. 3.5) are characterised by the fact that they form a chain stitch with one or two threads and that access to the textile (NCF) is granted only from one side. The blind stitch RS 510 can be performed while the textile is held in a tool because the curved blind stitch needle need not necessarily penetrate the textile material. Compared to stitch types such as the lock stitch, one-side stitch and blind stitch, no interlacing of the needle thread occurs during tufting (Fig. 3.6). The needle thread is inserted into the textile material by use of a hollow needle and forms a loop in the reinforcing material due to the difference in friction forces between the needle and thread, and the textile and thread. Typical of this stitch are the visible loops on the rear side of the laminates. Theoretically, it would also be possible for the loops to end in the material without penetrating it, but this cannot be realised in practice because the interior friction forces between the reinforcing textile and the sewing thread cannot be reproduced. Automation is a major aspect of structural stitching during the preforming process. Two different types can be distinguished. The first type consists of 2D
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Table 3.3 Stitch type and related influence on preform characteristics Stitch type (IAW DIN 61400)
Thread consumption
Handling
Lock stitch (Kl. 301)
– Hybridisation and high efficiency possible – High thread tensile forces
– Good shear – Different fibre – Exactly strength of displacement on adjustable layer package the upper or – Low fibre – Low tendency lower surface of material to warp the material content in the – High thread laminate tensile forces
Blind stitch – No bobbin – Possible (Kl. 103) thread stitching in a necessary solid tool – Large thread – Lower layers demand are not fixed – Low efficiency
One side stitch
– No bobbin thread necessary – High fibre consumption
Tufting
– Very high – No efficiency with interlacing, optimal thus no placement in joining the laminate between the (no loops) single layers
Fibre disorientation
– Lower single layers are not influenced by the stitching process – Local thread concentration, therefore, high shear
Compression
– Compaction of the layers not adjustable – Due to precompaction slight deviation of needle possible
– Good shear – Material – Seam width strength of penetration with influences the layer package 2 needles material in a – Different larger area orientation of 3D-reinforcement – Low thread strength – Thick needle necessary, thus movement in the laminate
– Thread strength (joining) insufficient for insertion of compaction force – Low fibre material content in the laminate
automatic sewing machines, which are generally equipped with the lock stitch. Figure 3.7 shows a two-dimensional (2D) plant for the manufacture of plane preforms, so-called textile reinforcements. The second type consists of the so-called sewing robots, which can be flexibly equipped with different stitching heads. These sewing robots have been developed especially for structural stitching in the spatial (3D) direction. Figure 3.8 shows the use of a flexible robot system for structural stitching as a gantry system with a suspended sewing robot.
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3.4 Stitching heads and schematic diagram of stitch formation using blind stitch (KSL, Lorsch; left: blind stitch RS 510, right: double needle RS 530).
3.5 Schematic diagram of stitch formation using one-side stitch and micrograph (ITA, RWTH Aachen).
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3.6 Tufting head and schematic diagram of stitch formation during tufting (KSL, Lorsch; tufting RS 522).
Table 3.4 shows more clearly the selection of the particular stitch types and sewing threads which have to be used, depending on the required seam type and task (Ogale, 2007).
3.4
Quality aspects for structural stitching
The sewing thread is inserted into the laminate oriented widthways, so positioned vertically to the in-plane reinforcement fibres. In order for the sewing thread to
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3.7 2D sewing plant for manufacturing of plane preforms (IVW, Kaiserslautern).
3.8 Flexible robot systems for structural stitching (KSL, Lorsch).
achieve the required effect of structural stitching, it is necessary to insert into the textile structure an adequate filament diameter in the form of bundled single filaments, which should be reinforced. Thicker sewing threads (filament bundles, as shown in Fig. 3.2) are normally used to keep the number of stitches per unit area low. When the needle penetrates the textile (NCF) the in-plane filaments are moved aside and the sewing thread is inserted. An ellipse is formed around the stitch hole due to the movement of the in-plane fibres. The dimensions of the ellipse depend upon the set-up of the layer orientation, the sewing thread, the stitching direction, and the machine parameters. It is possible to characterise the ellipse by measuring its half-axis. The real ellipse area has approximately 65%
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Table 3.4 Seam type related applicability of stitch types and threads Seam type
Stitch type
Thread applicable
Fixing and positioning
Modified lock stitch
Thin, flexible, high elongation, polyester Medium thick, less elongation, polyester Medium thicker, polyester Thicker polyester, Nomex®, or Kevlar® Thick, less elongation, polyester, Kevlar® Thick, polyester Polyester, Nomex®, or Kevlar® Polyester, Kevlar®, glass Carbon, glass, Kevlar® Carbon, glass, Kevlar® Carbon, glass, Kevlar®
Chain stitch
Assembling
Blind stitch Modified lock stitch Chain stitch One-side stitch Blind stitch
Structural
Tufting Modified lock stitch One-side stitch Tufting
of the area of an ideal ellipse, as calculated from the minor and major ellipse axis values measured from the laminate (Ogale, 2007). For the purpose of analysis, the stitch hole can also be modelled as a diamond shape of which the longer axis is oriented in parallel with the fibre direction of the individual layer (Roth, 2005; Heß et al., 2007). Figure 3.9 shows the top view of a stitched structure with the specification of the minor and major half axis. The set-up of the laminate has a major influence on the formation of the ellipse. The longer (major) half-axis of the ellipse is always positioned in the direction of the fibre orientation. If the stitching direction is running vertically to the fibre direction, a maximum expansion can be observed. The closer the stitching direction is to the fibre orientation, the lower the in-plane fibre undulation will be. This means that, in the case of a real laminate, each layer has a different orientation in fibre undulation, due to the variable laminate set-up. Figure 3.10 shows a fourply set-up, as well as a micrograph of the respective laminate. The fact that the fibre undulation is different in each laminate layer results in there being a loss of the in-plane mechanical properties, which should not be neglected. The formation of the stitch hole expansion depends directly on the type of sewing thread used. Figure 3.11 shows the ellipse formation (top view) and the stitch hole expansion in the cross-section of the laminate. A comparison between a flexible polyester thread and a very rigid carbon fibre sewing thread is shown in Fig. 3.11. The larger stitch expansion and, thus, the ellipse enlargement for the rigid carbon fibre thread is clearly visible. The optimised adjustment of the sewing machine parameters, especially the balance
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3.9 Ellipse formation in the laminate (top view) with half axis.
3.10 Influence of the layer set-up on ellipse formation in the laminate.
between needle and bobbin thread tension, also have a major influence on the quality of the seam. Figure 3.12 shows the impact of thread tension being too high, and compares this to an optimised machine parameter. The stitch hole expansion increases and the knot placement of the needle and bobbin thread moves into the laminate and generates additional fibre undulations in the intermediate layers. A further aspect that is directly influenced by ellipse formation is the surface quality of the laminate. A local compaction of the reinforcement fibres and visible fibre undulations in the upper laminate layer (Figure 3.13) occurs due to the penetration of the needle and the insertion of the needle threads. This leads to matrix-rich areas at the surface and the formation of sink marks due to the hardening of the used matrix macroscopic. After the preform has been placed in
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3.11 Influence of the thread material on ellipse formation.
3.12 Influence of the machine parameters on ellipse formation.
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3.13 Surface characteristic due to fibre concentration (left) and matrix shrinkage (right).
3.14 Reduction in ellipse size by preform compaction.
the injection mould, the preform is normally compacted to the final height required to reach the necessary fibre volume content. Figure 3.14 demonstrates the influence of preform compaction on ellipse formation, based on textured and twisted multifilament threads. It is possible to reduce the ellipse area by a factor of three to five depending on the sewing thread used. The compression force that is necessary in order to reach the required fibre volume content depends on the sewing thread used and the sewing machine parameters selected. Figure 3.15 clarifies this by using a
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3.15 Influence of stitch density on compaction pressure to reach a defined fibre volume content.
four-layer NCF [0/90]4. The layer set-up was stitched at three different stitch densities (13.33 and 3.33 stitches per cm2 and unstitched) with a twisted multifilament thread and high thread tension. Up to a fibre volume content of approximately 55%, no significant influence was recognised. A reduction in the compaction force necessary to reach a high-fibre compaction can be seen when using a very high stitch density and a high thread tension. An increase in the compaction force must be accepted when using lower stitch densities or low thread tension. This results from the fibre nesting being hindered by the inserted needle thread during compaction. This behaviour is unique to an NCF under the conditions described, and cannot be directly transferred to other lay-ups or other textiles, such as woven fabrics. A very high pre-compaction of the layer set-up during the stitching of structural seams can create flow channels at the surfaces of the preform due to insufficient compaction behaviour in the mould. These influence the injection flow in such a manner that the injected resin runs first of all along the seams and from there impregnates the reinforcing fibre structure. Figure 3.16 shows the change in flow front geometry in a biaxial NCF lay-up influenced by a stitch density of 3.33 stitches per cm2. Due to the fact that structural stitching is only used locally within a complete structure, this effect must be classified as negative. Flow channels are hardly used in the form of desired flow assistance due to their inadequate reproducibility.
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3.16 Influence of stitching on the flow front of a biaxial NCF (left: unstitched; right: stitch density 3.33 stitches per cm2; fibre volume content 50%).
3.5
Applications and future trends
At present, the use of structural sewing of NCFs is not widespread. The first applications of this technology can be found in aviation (Weimer, 2003), e.g. in the Airbus A380 pressure bulkhead or very fast rotating fan wheels. Structural sewing is used in these applications to improve the assembly properties of preforms, as well as the material properties of the component. From the component perspective, the essential motivation is the improvement of the impact behaviour and, consequently, the reduction of a delamination risk in the laminates. Therefore, it is the structural components with impact hazard in particular, such as the bottom of fuselages, rail vehicles and automobiles, or structures in airflows, such as turbine blades, the wing-leading edges of aeroplanes, or the blades of wind energy plants, that are predestined for future areas of application. The further development of stitching technology for the structural stitching of NCFs depends greatly on the complete development of stitching technology as the preform technology for liquid composite moulding processes. The machine technology is sufficiently developed. Specific adjustments are expected in the area of sewing thread development. The development of carbon fibre sewing threads, especially if achieved in combination with CFRPC compatible sizings, will serve to increase the effectiveness of NCFs. A further area of minor investigation is the influence of stitching on the actual impregnation process. Until now, there have been only publications on the influence of stitching on the flow of resin in fabrics (Rieber and Mitschang, 2010) but in principle these results should be transferable. By discovering new knowledge in the area of the structural effects of stitched NCFs, conclusions can be drawn about the optimal specifications such as stitch density, fibre diameter and others. General information for the use of the stitching technology in the preforming and structural application of NCFs is published in Long (2005), Beier et al.
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(2006) and Weimer and Mitschang (2001). Direct textile technologies for the manufacturing of 3D reinforcement structures are investigated by Tong et al. (2002). An excellent summary of the state of the art of structural stitching can be found in Ogale (2007).
3.6
References
Beier U, Fischer F, Sandler J K W, Altstadt V, Weimer C and Buchs W (2007), Mechanical Performance of Carbon Fibre-Reinforced Composites Based on Stitched Preforms, Composites Part A, 38, 1655–1663. Culimeta (2010), Technical yarns. Available from http://www.culimeta.de/technical-yarns. php (Accessed 26 January 2010). Drechsler K (2000), Advanced textile structural composite – needs and current developments, The Fifth International Conference on Textile Composites. 18–20 September, 2000, Leuven, Belgium. Herkt M, Middendorf P, Less C, Riedel W, Schouten M and Drechsler K (2006), 3-D reinforcement of composite T-joints by means of robot-assisted stitching technology, SAMPE April 30 May 2006, Long Beach, CA, USA. Heß H, Roth Y C and Himmel N (2007), Elastic Constants Estimation of Stitched NCF CFRP Laminates Based on a Finite Element Unit-Cell Model, Composites Science and Technology, 67, 1081–1095. Long A C (2005), Design and manufacture of textile composites, Cambridge, Woodhead Publishing Limited. Mitschang P, Ogale A, Schlimbach J, Weyrauch F and Weimer C (2003), Preform technology: a necessary requirement for quality controlled LCM processes, Polymer and Polymer Composites, 8, 605–622. Ogale A, Weimer C and Mitschang P (2004), Selection of sewing threads for preform manufacturing, Advanced Composite Letters, 13, 145–153. Ogale A, and Mitschang P (2004), Tailoring of Textile Preforms for Fiber-reinforced Polymer Composites, Journal of Industrial Textiles, 34, 77–96. Ogale A (2007), Investigations of sewn preform characteristics and quality aspects for the manufacturing of fiber reinforced polymer composites, IVW-Schriftenreihe, 70. Poe Jr C C, Dexter H B and Raju I S (2002), A review of the NASA textile composite research. Available from http://techreports.larc.nasa.gov/ltrs/PDF/1997/aiaa/NASAaiaa-97-1321.pdf (Accessed 7 October 2002). PPG Fiber Glass (2010), Bobin and texturized yarns. Available from http://www.ppg.com/ glass/fiberglass/products/pages/default.aspx (Accessed 26 January 2010). Rieber G, and Mitschang P (2010), 2D Permeability changes due to stitching seams, Composites Part A, 41, 2–7. Roth Y C (2005), Beitrag zur rechnerischen Abschätzung des Scheibenelastizitätsverhaltens in Dickenrichtung vernähter Faser-Kunststoff-Verbund-Laminate, IVW-Schriftenreihe, 55. Saint-Gobain Vetrotex International (2010), Glass filament yarns. Available from http:// www.vetrotexeurope.com/yarns.html (Accessed 26 January 2010). Schappe (2004), Carbon thread for composite industry by Schappe Techniques. Available from http://www.schappe.com (Accessed 12 December 2009). Tong L, Mouritz A P and Bannister M K (2002), 3D fibre reinforced polymer composites, Oxford, Elsevier.
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Weimer C (1999), Carbon fiber sewing thread for compound fiber and plastics materials, German Patent DE19932842. Weimer C and Mitschang P (2001), Aspects of the Stitch Formation Process on the Quality of Sewn Multi-Textile-Preforms, Composites Part A, 32, 1477–1484. Weimer C (2003), Preform-Engineering: Applied Technologies to Incorporate Part and Process Functions into Dry Textile Reinforcements, Composites Science and Technology, 63, 2089–2098.
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4 Understanding and modelling the effect of stitching on the geometry of non-crimp fabrics S.V. LOMOV, Katholieke Universiteit Leuven, Belgium
Abstract: Internal geometry of multiaxial multi-ply warp-knitted non-crimp fabrics (NCFs) and their composites is described in this chapter, based on the understanding of the production process of NCF, experimental studies of the internal structure of NCF composites and models of the same. The internal geometry of NCF is treated as geometry of cross-ply laminate of unidirectional fibrous plies, with fibres in the plies distorted due to interaction with the knitting needles and the stitching thread. The positions and dimensions of the distortions are characterised for different types of NCF in their relaxed state and after consolidation into composite material. This characterisation includes changes of NCF geometry due to shearing of the reinforcement during composite forming. A ‘virtual NCF’ model implemented in a software tool is described. Key words: internal geometry, warp-knitting, fibre distortions, shear, geometrical model.
4.1
Introduction
The production process (explained in Chapter 1) of specific types of non-crimp fabric (NCF) – produced by knitting together unidirectional plies of fibres – results in the fibrous structure of the fabric, which is very close to a laminate of unidirectional (UD) plies, the difference being distortions of the fibre placement given by the stitching. The plies of the fabric are formed as continuous layers of parallel fibres, placed as uniformly as the technology allows. These plies are formed by placement of thick tows, but the tows are spread as finely as possible before placement and are positioned as close together as possible. As the technology allows usage of tows of a variety of thickness and width (which can be larger than the spacing of knitting needles), and as the tows can be placed with any chosen orientation, it is impossible to ensure that the knitting needles go through the plies at positions in between the tows. The needles will penetrate the spread fibre bundles and the production parameters of the machine are set in such a way as to minimise possible fibre damage (e.g. ‘walking needle’, etc). The description given in the previous paragraph is idealised. The process of the piercing of the fibrous ply by the needle and forming of the stitching (warpknitted) loop results in a certain disturbance of the uniform placement of the fibres. These disturbances can cause resin-rich regions in the impregnated 84 © Woodhead Publishing Limited, 2011
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composite, affecting the mechanical performance of it. They can also change the permeability of the fabric, affecting the processability of it in liquid composite moulding. Another source of deviation of the behaviour from an ideal pile of multi-axial plies are the stitching loops, whose three-dimensional (3D) geometry can cause different geometrical features of the preform, which may affect processing and/or performance in a positive or a negative way. This chapter starts with a description of the idealised geometry of fibres in the plies and the stitching loops and proceeds to a discussion of distortions of the fibres due to stitching, including the transformation of the geometrical features of the fabric caused by shear deformation during draping of the preform. Finally, a model (with software implementation) of the internal geometry of NCF is introduced. The geometry description of NCF given in this chapter has been initially introduced in (Lomov et al., 2002).
4.2
General parameters of the fibrous plies
European standard EN 13473 defines a multiaxial multi-ply (non-woven) fabric (which is synonymous to the term ‘non-crimp fabric’ in the language of composite community) as follows. A textile structure constructed out of one or more laid parallel non-crimped nonwoven thread plies with the possibility of different orientations, different thread densities of the single thread plies and possible integration of the fibre fleeces, films, foams or other materials, fixed by loop systems or by chemical binding systems. The threads can be oriented parallel or alternating crosswise. These products can be produced on machines with insertion devices (parallel-weft or cross-weft) and warp-knitting machines or chemical binding systems.
In this book the NCF created by chemical binding systems will not be considered. The definition stresses the fact that the fibrous plies are laid up with threads. Binding the plies together by warp-knitting can be deliberately made in such a way that the stitching yarn pierces the plies in between the laid threads. This would result in open preform architecture. However, in NCF used in high-end composite production (which is the subject of this book), wide threads (flat tows) are laid very close together, forming continuous fibrous plies. The plies are bound by warp-knitting, with piercing sites positioned on the surface of the preform according to the needles’ spacing, without any connection to the tow positioning. Needles pierce the fibrous plies (probably in the middle of the laid-up tows), distorting them locally. This results in a preform construction close to an ideal laminate composed of unidirectional uniform plies. According to the standard, a fabric is characterised by the following parameters: • •
Fibrous nature of the plies – glass (G), carbon (C), aramid (A), etc. Areal density of the plies (g/m2). It is not necessarily the same for all the plies.
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• • •
Non-crimp fabric composites Direction of fibres in the plies, given by an angle with the machine direction (0°). The angles lie in the range [−90°, 90°], positive sign corresponds to x0y quadrant of a right-hand Cartesian co-ordinate system xyz, x going in the machine direction and z in the vertical direction of the successive layout of the plies. Nature of the binding – polyamide (PA), polyethylene (PE), polyester (PES/ PET), polypropylene (PP). This may refer to a stitching yarn or to a chemical binder. Areal density of the binding. Type of the binding agent – stitching or loop (L), chemical (C)
For example, the designation stipulated by the standard for three-ply glass fabric +45/−45/0, stitched by polyester yarn is [G, 235, +45° // G, 235, −45° // G, 425, 0°][PES, 12, L] The total areal density of the fabric is 235 + 235 + 425 + 12 = 907 g/m2. The weight of each single ply depends on the yarn weight and the yarn placement density. In general, the yarn weight is characterised by the number of filaments, which ranges from 3k up to 80k in the case of carbon tows. The areal density usually ranges from 100 g/m2 upwards. The higher the yarn weight, the higher is the minimum ply areal density to be reached with a closely covered surface. To reach low ply areal density using thick tows, the latter are spread with the special unit. Yarns with higher fibre count present economical advantages: the raw material is cheaper and the production can be faster (as more fibres are laid in one weft placement). Low ply areal weight is desirable as lighter fabrics have better drapability. The current technology allows achieving 150 g/m2 with a 12k yarn in the weft or 24k in 0° layer. The aim of ongoing development work is to reach the same 150 g/m2 with 40k to 80k yarns for all orientations.
4.3
Geometry of the stitching
4.3.1 Knitting pattern To understand the patterns of stitching seen on the surface of a non-crimp fabric (NCF), it is necessary to understand the principle of warp knitting. Here, a brief explanation is given; more detail can be found in (Spencer, 1997). The principle of warp knitting is illustrated in Fig. 4.1. A knitted fabric (in a warp-knitting process as such), or a knitted web (when warp-knitting is used to stitch fibrous plies) is an assembly of loops formed by the interaction between knitting needles and guides. Yarns are fed through the guides simultaneously on all the knitting needles, which are fixed on a needle bar and move together. Loop-forming action also
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4.1 Principle of warp-knitting: interaction of the knitting needles and guides.
occurs simultaneously at every needle in the needle bar during the same knitting cycle. Consider one warp yarn (‘new yarn’, a yarn which is about to make a new loop), going through the guide in the beginning of the knitting cycle (Fig. 4.1a). Knitting needles are in the high position. Old loops at the edge of the previously formed fabric are on the stems of the needles. The guide, carrying the new yarn, moves around a knitting needle, forming new loop (b, c). The knitting needle moves down, connecting the new loop with the old one, sitting on its stem (d, e). In the case of stitching of fibrous plies, the needles pull the new loop through the plies. Finally, the guide moves to another needle to start the next knitting cycle (f). The knitting action of the needles creates connection of the loops in the machine (‘wale’) direction (Fig. 4.2a). Movement of the guides across the needle bed creates the connection in the cross (‘course’) direction, forming a warp-knit pattern. The
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4.2 Principle of warp-knitting: pattern formation (a), coding (b) and examples of knitting patterns (c).
positions of the gaps between the needles, where the guides pass in the subsequent knitting cycles, can be used to code the pattern (so-called Leicester notation). Consider a diagram of the guide’s movement, a so-called lapping diagram (Fig. 4.2b). Rows of dots represent needles in plane view. The numbering of needles assumes the pattern mechanism to be on the right side. As the guides position themselves in the spaces between needles, the positions between the vertical columns of dots represent shift of the guides. The pattern is coded by the sequence of these numbers: s1 − S1/s2 − S2/ . . . /sN − SN where si and Si are the positions of the guides forming the i-th loop, N is the number of knitting cycles in the pattern. The positions of the guides si and Si refer to gaps between needles, where the elementary movement of the guide starts. A pair si – Si represents an overlap movement of the guides (the guides move behind the needles), Si/si+1 represents underlap movement (the guides move in front of the needles). We consider only the patterns with one-needle overlap, which means that /si − Si / = 1. Figure 4.2c presents examples of warp-knitting patterns, used for NCF reinforcements.
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When fibrous plies are stitched, the pattern is seen on the face of the fabric (see Fig. 4.2a). These yarns are laid on the face of the fabric by the guides. On the back of the fabric, chains of loops are seen, going in the machine direction. These are the loops formed on separate needles and interconnected due to the knitting action of the needles.
4.3.2 Positions of the stitching sites The stitching yarn pierces the fibrous plies at the positions defined by the needle spacing in the needle bed (spacing in the cross-direction, A) and by the speed of the material feeding in the knitting device (spacing in the machine direction, B). Normally B < A. The value of A is also expressed by the machine gauge, which is the number of needles per inch. In the warp-knitted fabric without fibrous plies, the yarn tension during knitting leads to significant deviations of the actual spacing of loops in the relaxed fabric from these values. In the case of multiaxial multi-ply fabrics, the stitching yarn is fixed by the fibrous plies, and the loop spacing is fairly regular. Figure 4.3 gives an example of the variability of these parameters in a fabric. Deviations of the positions of the stitching lead also to deviation of the loops from the ideal machine direction orientation. The inclination of the loops relative to the machine direction can be as high as 15°.
4.3 Actual spacing of the stitching loops. Carbon fabric 0/−45/90/45: (a) definition of A and B; (b) values of A and B for adjacent wales; (c) actual positions of the stitching sites (the grid is A x B).
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4.3.3 Geometry of the stitching loop To describe the loop geometry one can select between a pure geometrical approach, in which certain assumptions about the shape of the loop are introduced, or a mechanical approach, in which the shape of the loop is computed based on equations of equilibrium for the curved yarns forming the loop. The latter, much more sophisticated treatment, is felt to be unnecessary in our case, as the positions of the loops are fixed by the stitching going through the mat, and experimentally observed uncertainties of the loop shape are too large to justify refinements offered by a mechanical treatment of the problem. Hence, the geometrical approach is adopted here. The stitching yarn (polyester, polyamide, aramid, etc.) has normally low linear density (ca 10 tex, number of filaments ca 15) and low twist (<100 1/m). Hence it is easily compressible, which explains large variations in its dimensions. Three characteristic states of the yarn in the loop are considered: 1. Free: diameter of the circular cross-section dinit. The value of dinit is measured on the relaxed stitching yarn (off the bobbin) and represents the packing of its fibres before any interaction with the knitting device. 2. Compacted: diameter of the circular cross-section. [4.1] where T is the linear density of the yarn, ρ is the density of the fibres and K is the packing coefficient. Experimentally observed values of K lie in the range 0.8–0.9. The value of d0 represents the ultimate compacted state of the yarn of the yarn and does not depend on dinit. 3. Extreme flattened: dimensions of the cross-section d1min and d2max. These values are measured in a compression test of the stitching yarn. Figure 4.4b provides typical values of these dimensions. The values dinit, d0, d1min, d2max characterise the relaxed state and the compression behaviour of the stitching yarn (measured on the standard textile equipment). They are not specific to the fabric architecture. Figure 4.4 shows regions of these characteristic states along the yarn in the loop. The dimensions of the yarn crosssections in the straight parts of the yarn are kept constant; circular arcs connecting the straight parts introduce a linear transition from one dimension of the cross-sections to another. The model depicted in Fig. 4.4a introduces several assumptions for the yarn dimensions. Most of them, e.g., the maximum flattened state of the yarn on the surface of the fabric, are supported by experimental observations. The dinit value for the yarn knee (place difficult to observe in a real material) is stated to ensure a smooth transition between flattened horizontal and compacted vertical parts of the yarn. The geometry of the centre line of the yarn is defined by identifying a set of ‘anchor points’ A–M (Fig. 4.5) along the loop, and approximating the loop centre
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4.4 Dimensions of the stitching yarn: (a) scheme; (b) compression diagram and typical yarn dimensions; (c) typical configuration in the head of the loop; (d) spread yarn on the face of the fabric, seen from the top, (e) same, in the gap between two layers in a composite. Examples: polyester stitching yarn 6 tex.
4.5 Shape of the stitching loops. Schemes of positions of anchor points and examples of loops produced under average (left) and high (right) knitting tension.
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line between the anchor points by straight lines or circular arcs. Positions of the anchor points on the centre line of the yarn are shown in Fig. 4.5, where h is the total thickness of the plies (accounting for possible sinking of the stitching, see below), and all the arcs of the centre line (AB, CD, EF, GH, IJ and KL) are circular arcs with the diameter d0. The width of the loop w depends on the knitting tension. Considerable tension produces longish loops with w = 3d0; lesser tension increases w to (4 . . . 5)d0.
4.4
Distortions of fibres in the plies
4.4.1 Classification of the distortions The stitching causes distortions of the fibre orientations in the fibrous mat. These distortions can be localised near the stitching sites, or collate into a linear channel Fig. 4.6. Different authors use different terminology to designate these distortions: ‘cracks’ and ‘channels’ (Lomov et al., 2002), ‘SYD, yarn-induced fibre distortion’ (Loendersloot et al., 2006), ‘fish eyes’ (Lekakou et al., 2004; Schneider et al., 2004), ‘openings’ (Truong Chi et al., 2008). In this book the term ‘fibre distortion’ will be used, with the term ‘openings’ applied to the localised distortion and ‘channels’ for long separations of the fibrous plies. When the preform is being impregnated, the distortions provide routes for the resin flow. In a consolidated composite they create resin-rich zones, which may play an important role in initiation of damage. A localised distortion has a rhomboidal shape, with width b and length l (Fig. 4.7). A channel is formed if localised distortions touch or overlap each other, and is more common for 0°/90° fabrics. Because the placement of the stitching sites has different spacing in the length and the width direction (B
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4.6 Examples of fibre distortions, face (left) and back (right) of carbon non-crimp fabric: (a) 0°/−45°/90°/+45°, channels on the face and openings on the back; (b) +45°/−45°, openings on both sides; (c) 0°/90°, openings on the face and channels on the back; (d) 0°/90°, openings on both sides. All the fabrics produced on machine gauge 5, different producers.
back plies creates a system of fibre bundles inside the fabric, held together by the stitching and separated by these straight channels. Dimensions of these fibre bundles are defined by the knitting parameters A and B. They are sometimes referred to as ‘tows’, which should not be mistaken as the tows used in the fabric production.
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4.7 Definition of the dimensions of an opening.
4.8 Openings and channels inside a composite plate. Carbon noncrimp fabric 0°/−45°/90°/45° (as in Figure 4.6a). Lines show average dimensions of the cracks/channels observed from the surface and width 2d0 for the inner layers. (a) A section in the machine direction, opening in the −45° inner ply; (b) a section in the cross-direction, channel in the 0° face ply and an opening in the −45° inner ply; (c) a section in the cross-direction, channels in the 45° back ply, 0° face ply and an opening in the −45° inner ply; (d) gaps between layers of the non-crimp fabric in a laminate.
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4.4.2 Dimensions of the distortions It can be expected that the width of fibre distortions is proportional to the thickness of the stitching yarn. Choosing the compacted diameter d0 as a representative parameter (see Eq. [4.1]), one can introduce empirical coefficients k = b/d0 to calculate width b = kd0. Table 4.1 shows results of the measurements of dimensions of the openings/channels in various fabrics. The length of the openings is related to the width by a coefficient λ = l/b. The variation of the values of k is quite large. It seems that the fibres in a powdered fabric are more difficult to push away by the stitching, which explains low values of k and λ for this fabric. In non-powdered fabrics, channels tend to be wider than cracks, with averages for k of about 4 (openings) and about 6 (channels), and λ for openings of about 21. The dimensions of the openings/ channels are also influenced by knitting tension. For a given fabric the distribution of the dimensions of the distortions can be quite wide (Fig. 4.9). The values in Table 4.1 refer to the dimensions of the fibre distortions on the back and face of the fabric, which is easier to measure than dimensions of the distortions in the inner plies of three- or four-axial NCF. Figure 4.8 shows that for the inner plies the opening width can be taken approximately as bin = 2d0. This estimation corresponds also to the detailed measurements of the distribution of the width of the distortions in the plies of structurally stitched NCF (Hess et al., 2007). After consolidation of a composite plate/part, dimensions of the fibre distortions can somehow change. The measurements in (Koissin et al., 2009) show the following changes after composite consolidation: the width of the openings in +45°/−45° carbon NCF has changed from 0.50 ± 0.09 mm in the dry fabric to 0.43 ± 0.08 mm after consolidation, and the length of the openings from 9.3 ± 3.5 mm to 4.1 ± 0.9 mm after consolidation.
4.9 Distribution of width of the fibre distortions in 0°/−45°/90°/45° carbon non-crimp fabric (same as in Figure 4.6a): (a) face, channels, (b) back, openings.
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Lomov et al., 2002
Loendersloot et al., 2006
Loendersloot et al., 2006
Koissin et al., 2009
Koissin et al., 2009
0°/−45°/90°/45°, 12K
0°/90°, 24K
45°/−45°, 12K
0°/90°, 12K
−45°/−45°, 12K
PA = polyamide; PES = polyester
0°/90°, 12K, powdered n/a
Lomov et al., 2002
Reference
−45°/−45°, 12K
Fabric construction and tows used in production
PA, 10 tex
PES, 7.4 tex
PES, 7.4 tex
PES, 6 tex
PES, 7.6 tex
PES, 7.6 tex
PES, 7.6 tex
Material, linear density
0.107
0.087
0.087
0.071
0.088
0.088
0.088
d0, mm
Stitching
Face openings Back openings Face channels Back openings Face channels Back channels Face openings Back openings Face openings Back openings Face openings Back openings Face channels Back openings
Opening/channel
Table 4.1 Dimensions of fibre distortions in different non-crimp fabrics, average values
0.276 0.434 0.658 0.483 0.62 0.36 0.28 0.27 0.33 0.26 0.50 0.49 0.18 0.53
b, mm
5.05 7.15 n/a 7.28 n/a n/a 7.43 7.85 7.3 3.4 9.3 9.2 n/a 3.46
l, mm
3.13 5.39 7.47 5.48 7.04 4.09 3.94 3.80 3.79 2.98 5.74 5.73 1.68 4.95
k = b/d0
18.3 16.5 n/a 15.0 n/a n/a 26.5 29.1 22.1 13.0 18.8 18.7 n/a 6.53
λ = l/b
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4.4.3 Gaps between the non-crimp fabric (NCF) layers in a laminate The stitching loops, lying on the surface of NCF, can create gaps between layers on NCF in a laminate. Such a gap is shown in Fig 4.4e. These gaps do not necessarily have a constant thickness, but may be concentrated near the stitching sites Fig. 4.8d. When a large channel is formed, which goes in the machine direction (direction of the production of the fabric, parallel to the stitching loops), a stitching yarn section on the face or a loop on the back of the fabric can sink inside this channel (as is the case in Fig. 4.6a). This so-called ‘nesting’ behaviour is less pronounced in NCF laminates than in woven or braided fabric laminates, which translates to less variability of the laminate structure. However, this phenomenon also exists for NCF laminates: in the presence of this sinking the layers can come closer, closing gaps between layers introduced by the stitching yarn laying on the surface of the fabric (Lomov et al., 2002).
4.4.4 Fibre volume in fraction in the plies and deviations of the fibre directions Overall fibre volume fraction in a composite is estimated using the formula: [4.2] where m is the areal density of all the layers of the fabric, h is the thickness of the composite, ρ is the fibre density. The value of the thickness in this formula includes the thickness of the stitching yarn on each surface of the fabric (d1min). An average fibre volume fraction in the plies is estimated as [4.3] where ms is the areal density of the stitching. Finally, the stitching pulls fibres in the plies aside, increasing the local fibre volume fraction, which is evaluated with the formula [4.4] where Svoid is the area of a crack or a channel per one knitting needle: [4.5] where the length of the channel l within the rectangle between the neighbouring needles is
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[4.6] For example, for a quadriaxial carbon fabric the following values have been found: Vf = 60%, Vfpl.ave = 64%, Vfpl.loc = 66 . . . 74% (this is different in the inner and outer plies due to the difference in the size of the channels/opening). The fibres around the openings deviate from their ideal positions in the plies. The deviation can be described with a linear (Truong Chi et al., 2008) or a cosine (Hess et al., 2007) function, which aligns the fibre direction with the direction of the opening boundaries close to it, and returns the fibre direction to the ideal direction in the ply far from the opening.
4.5
Change of the geometry after shear
When NCF is sheared during the forming of a 3D preform, the distances between the stitching sites and dimensions of the fibre distortions change. This change affects the permeability of the preform and positions and dimensions of resin-rich zones in the composite. The change of biaxial NCF geometry after shearing was studied by (Loendersloot et al., 2006) and used for modelling of mechanical properties of NCF composites in (Truong Chi et al., 2008). Shearing changes the fibre orientation, areal density and thickness of the fabric, and hence the fibre volume fraction of the composites. The shear deformation is shown in Fig. 4.10a. The ply angle α, representing fibre direction in the sheared fabrics, can be computed based on the initial ply angle α0 and shear angle γ using the formula
α = α0 − γ/2.
[4.7]
The average fibre volume fraction of the composite plates made from the sheared fabrics Vf(shear) can be predicted based on that of the same thickness plates made from non-sheared fabrics Vf(no_shear) by applying a formula: Vf(shear) = Vf(no_shear)/cosγ.
[4.8]
During shear the stitching sites retain the rectangular configuration but come closer, changing according to the formula: [4.9] When the fabric is sheared, the distortions in the fibrous plies change their dimensions, staying aligned with the direction of the fibres (which is changed as a result of the shear deformation of the fabric). Measurements in (Loendersloot et al., 2006) for three different carbon NCFs suggest the following scenario of the change in the dimensions of the distortions.
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4.10 Change of geometry of biaxial non-crimp fabric fabric after shear: (a) a scheme of shear deformation; (b) non-dimensional width of the openings k = w/d0 in a carbon +45°/−45° non-crimp fabric, face (kf) and back (kb) of the fabric, for different shear angle γ; (c) distribution of non-dimensional width of the openings in a carbon +45°/−45° NCF, before shear and (d) after shear with γ = 30°.
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For low shear angles, below 30°, the width of the distortions decreases as the result of in-plane compression of the ply, associated with the shear deformation. The non-dimensional width k = w/d0 decreases to the value of about kmin≈2, which also corresponds to the non-dimensional width of the openings in the inner, constrained plies of four-ply NCF (as mentioned in section 4.4.2). For the higher shear angles, the width of the opening does not change. Subsequent shear deformation results in lateral compaction of the fibrous plies rather than narrowing of the openings. The value of kmin≈2 can be explained by the fact that there are two stitching yarns, each with a diameter not smaller than d0, which go through the opening, and have to be accommodated within the width w = kmind0. This behaviour is illustrated in Fig. 4.10b, which shows a typical result of measurements of change of the opening width in a biaxual +45°/−45° NCF. The distribution of the width of the openings changes from symmetric (close to normal) in non-sheared fabric to asymmetric (close to log-normal), with more openings of smaller width in the sheared fabric (Fig. 4.10c). The length of the openings does not change significantly after shearing.
4.6
A geometrical model of NCF
The geometrical description of NCF described in this chapter is implemented as a module of the textile simulation software WiseTex (Lomov et al., 2002; Verpoest et al., 2005) (Fig. 4.11). The input data for the model comes from the manufacturer’s specification of NCF, fibre volume fraction of the preform, measured or estimated dimensions of cross-sections of the stitching yarn and parameters of the fibre distortions, measured on the composite or estimated by approximate values given above: k≈4 (openings) or 6 (channels), λ≈21. The model also allows compression and shear of the fabric. The same geometry described in this chapter can be easily transferred to models of the permeability of NCF (Chapter 10) and finite element models (Chapters 16–19).
4.7
Conclusion
An NCF composite can be considered as a cross-ply UD laminate with the ideal UD placement of the fibres in the plies distorted by the stitching. The internal geometry, described in detail in this chapter, defines the features of processing behaviour and performance of NCFs and their composites, and the advantages and limitations of their applications, which will be discussed in detail in the subsequent chapters of the book.
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4.11 Geometrical model of non-crimp fabric in WiseTex software: input data and 3D visualisation of the fabric.
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4.8
References
Hess, H., Y. C. Roth and N. Himmel (2007). Elastic constants estimation of stitched NCF CFRP laminates based on a finite element unit-cell model. Composites Science and Technology 67: 1081–1085. Koissin, V., J. Kustermans, S. V. Lomov, I. Verpoest, B. Van Den Broucke and V. Witzel (2009). Structurally stitched NCF preforms: quasi-static response. Composites Science and Technology 69 (15–16): 2701–2710. Lekakou, C., S. Edwards, G. Bell and S. Amico (2004). Computer modeling for the prediction of the in-plane permeability of non-crimp stitch bonded fabrics. Flow Modelling in Composite Materials (FPCM-4), Newark, Delaware. Loendersloot, R., S. V. Lomov, R. Akkerman and I. Verpoest (2006). Carbon composites based on multiaxial multiply stitched preforms. Part 5: Geometry of sheared biaxial fabrics. Composites Part A 37: 103–113. Lomov, S. V., E. B. Belov, T. Bischoff, S. B. Ghosh, T. Truong Chi and I. Verpoest (2002). Carbon composites based on multiaxial multiply stitched preforms. Part 1: Geometry of the preform. Composites Part A 33(9): 1171–1183. Lomov, S. V., I. Verpoest, T. Peeters, D. Roose and M. Zako (2002). Nesting in textile laminates: Geometrical modelling of the laminate. Composites Science and Technology 63(7): 993–1007. Schneider, M., K. Edelmann and U. Tiltmann (2004). Quality analysis of reinforcement structure for composites by digital image processing. Proceedings of the 25th International SAMPE-Europe Conference. Paris, France: 267–272. Spencer, D. J. ed. (1997). Knitting Technology. Cambridge, Woodhead Publishing. Truong Chi, T., D. S. Ivanov, D. V. Klimshin, S. V. Lomov and I. Verpoest (2008). Carbon composites based on multiaxial multiply stitched preforms. Part 7: Mechanical properties and damage observations in composite with sheared reinforcement. Composites Part A 39: 1380–1393. Verpoest, I. and S. V. Lomov (2005). Virtual textile composites software WiseTex: integration with micro-mechanical, permeability and structural analysis. Composites Science and Technology 65(15–16): 2563–2574.
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5 Automated analysis of defects in non-crimp fabrics for composites M. SCHNEIDER, Toho Tenax Europe GmbH, Germany
Abstract: In order to judge the textile quality of non-crimp fabric (NCF), a discontinuous laboratory testing method is developed, which is based on a digital image processing system. A flatbed scanner with an additional transmitted light device is used for the digital image acquisition of flat fabric reinforcement. In principle, the pixels of a digital image are similar to a map of numbers, which in this case range from 0 (i.e. black pixel) to 255 (i.e. white pixel). The user selects geometrical dimensions to be measured and the software analyses all pixels according to this selection. According to Airbus Industrie Material Specifications (AIMS), standard testing routines are developed in order to quantify the following parameters: regularity of knitting structure (distance between all adjacent knitting points), fish eye measurement in the layers, gap quantification, reinforcement fibre orientation and abrasion particles. Key words: carbon fibres, textile, non-crimp fabric, effect of defects, digital image processing, quality inspection, pixel.
5.1
Motivation
Textile reinforcements show a potential to decrease the overall production costs of composites. General process optimisation of standard textile machinery, which has been worked out since many decades for mass-production of standard textiles provides a very useful basis for composite production. These improved efficiencies and process robustness have to be transferred to the processing of highperformance materials, such as glass and carbon fibres. Moreover, new techniques, such as non-crimp fabric (NCF) production, are created, based on conventional knitting in combination with multiaxial placement of reinforcement fibres. But it is not only inexpensive production methods for reinforcement textiles that are required; moreover, high-quality textiles are needed. The mechanical performance of composites reinforced with textiles is not only determined by the type of textile and fibre as well as the resin to be used, but is also affected by the textile quality. In particular, the accuracy of the reinforcement fibre alignment affects the fibre-dependent properties of the final carbon fibre-reinforced polymer (CFRP). This fibre orientation is determined in the manufacturing method of the textile, but can also be modified during the manufacturing process and the post-processing (e.g. handling of the material). On the one hand, all defects within the textiles (gaps, misaligned fibres, etc.) lead directly to a drop in mechanical 103 © Woodhead Publishing Limited, 2011
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performance. All volumes which are not homogeneously covered by filaments will be filled by resin in the final component and thus provide resin-rich area with limited performance. On the other hand, the reinforcement fibre must be straight in the textiles. Carbon fibres only show excellent mechanical performance when all filaments perfectly follow the load paths. Any yarn undulations created, for instance, by textile patterning or harmful post-processing result in reduced performance. Besides the defect localisation in the material, the aerospace industry demands a total documentation of the material quality. It is an important task of the supplier to document and guarantee material properties to a given specification. In order to minimise this effort, any automatic system is welcomed. Therefore, it is important to characterise, and if necessary to optimise, the quality of textiles as soon as possible in the production process in order to meet high mechanical requirements. The quality (e.g. homogeneity and orientation of the reinforcement fibres, gaps between the fibres, etc.) of textile structures has to be judged either directly online during the production, by e.g. visual inspection, or indirectly with mechanical testing and quality control procedures on the final laminate composite. These latter procedures are time-consuming, expensive and generally unsuitable as techniques to improve production processes or material performance. This chapter describes the principal development of a tool to detect automatically and document fabric anomalies as described in typical fabric material specifications. The primary focus is on biaxial NCF, because these materials are standard in current Airbus material specifications.
5.2
Quality characteristics of non-crimp fabric (NCF)
Defects of NCF may occur in both production (i.e. placement of the reinforcement fibres or knitting of the total system) and subsequent manufacturing of the CFRP components (see Chapters 1 and 2). Any post-processing of NCF may produce additional effects which reduce the mechanical performance. Airbus Industrie Material Specifications (AIMS) define and quantify several defects of NCF, for example: 1. 2. 3. 4. 5. 6. 7. 8.
crease or wrinkle (break or line, usually caused by a sharp fold, Fig. 5.1); cut or tear (adjacent yarns are cut or broken, Fig. 5.1); yarn splice (broken or severed yarn, which is rejoined); fuzz ball (accumulation of loose or frayed fibres within the fabric or on the surface, Fig. 5.2); gap (open space between parallel fibres or even between filaments, Fig. 5.2); missing knitting loop (partly missing knitting row, Fig. 5.2); incorrect fibre orientation (fibre, which is not aligned or not along given orientation, Fig. 5.2); and missing reinforcement yarn (totally missing reinforcement fibre).
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5.1 Non-crimp fabric with exemplary defects (defects 1, 2).
5.2 Non-crimp fabric with exemplary defects (defects 4, 5, 6, 7).
Yarn splices (defect 3) cannot be illustrated since carbon fibres to be used for NCF are usually not spliced. Missing reinforcement yarns (defect 8) are almost impossible in NCF due to fibre detectors which stop the production when fibres are broken. Nevertheless, gaps between reinforcement fibres are sometimes regarded as missing
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fibres, although the fibres are only pushed away/together. Figure 5.2 shows additional parameters which give further indices of the NCF quality: A. angle between knitting yarn and carbon fibre and B. distance between knitting points. In order to limit the effects of these defects, the maximum number of their occurrences is regulated in material specification. Materials are usually checked by means of a visual inspection upon shipping by the material supplier and upon receipt by the customer. At the moment, automated tools of inspection to detect and quantify the number of defects are not available.
5.3
Quality analysis of NCF by digital image analysis
5.3.1 System The system consists of a flatbed scanner with an additional transmitted light device, a state-of-the-art powerful personal computer with an enlarged main memory and a standard digital imaging software package. Based on this equipment, a custom-made routine is developed in order to analyse and quantify the textile quality of NCF. The final efficiency of the systems is a result of the computer performance, calculation algorithms and image resolution. Since a general method for quality monitoring (QM) based on digital image processing is addressed and only a laboratory offline system is created, the analysis time is not that important. An overall analysis time of several minutes is realised at the moment. If the system is transferred to an online method and placed directly into an NCF machine, the efficiency has to be improved. In any case, reduced resolution of the scanned pictures decreases the analysis time dramatically. High-resolution flatbed scanners are capable of acquiring a digital picture of any flat textile; the transmitted light device in particular delivers further insights. Other reasons to choose a scanner instead of a microscope or a digital camera with additional illumination are the easily adjustable and reproducible light and scanning conditions. Any light reflections or optical phenomena are almost excluded by the linear movements of the illumination and scanning device. In order to find a compromise between all conflicting aspects, i.e. file size and processing speed as well as sampling size and resolution, a picture 10 cm by 10 cm is scanned with a resolution of 720 dpi. These parameters produce a manageable file with a size of around 8 MB which is finally saved in a grey value 8-bit TIF format. In principle, the pixels of a digital image are similar to a map of numbers, which in this case range from 0 (i.e. black pixels) to 255 (i.e. white pixels).
5.3.2 Working principle Figure 5.3 presents a scanned picture of the important elements of NCF in detail to explain the working principle. One may see two loops of the knitting yarn in the
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5.3 Detailed picture of non-crimp fabric. (Please note that the abovementioned scanning conditions are not kept.)
vertical direction and the carbon fibres under an angle of 45°. In the centre of the picture a so-called fish eye results from the penetration of a knitting yarn. Two disadvantages stem from fish eyes: the carbon fibres are no longer straight and the open volumes of the fish eyes will end up in the final laminate as unreinforced resin-rich areas. Fish eyes and wider gaps, which may extend over several knitting points or even over the total width of an NCF, are discontinuities in the laminate and may cause final failure of the laminate and, therefore, are important to analyse. The flexibility of the reinforcement fibre, the tension of the knitting yarn and the needle size, as well as the movement of the needle during the needle penetration in the moving NCF, influence the size of the gap eyes. Gap eyes are also responsible for the out-of-plane permeability of NCF (among others). It is worth correlating gap eye properties with impregnation properties (see Chapter 8). In Fig. 5.4 a graph is plotted of the grey values that generated the picture of the NCF in Fig. 5.3. The peak of the gradient is given by the majority of grey pixels coming from the wide area covered with carbon fibres. By means of the digital image software, all pixels in two user-defined ranges can be selected: In range 1, with a threshold from 0 to 29, all dark pixels are chosen. These pixels present fish eyes, but also gaps between the carbon fibres or even between single filaments. In range 2, all light pixels (threshold 174 to 255) build the knitting yarns. If these two ranges are applied to the pixels of Fig. 5.3, the interesting items of NCF are selected and highlighted (and marked in colour in the original software) (Fig. 5.5, light areas = range 1, dark areas = range 2). In the next step the digital software measures, based on implemented standard routines, selected geometrical
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5.4 Graph of the grey value distribution.
5.5 Detailed picture of a non-crimp fabric with selected pixels and geometrical dimensions.
dimensions on all particles, which are built from connected pixels of the same range. The following dimensions of NCF are measured in detail. • • •
Orientation, width and area of fish eyes and gaps (between single filaments as well as between whole carbon yarns). Width of knitting loops (i.e. knitting errors). Orientation and curvature of knitting yarns.
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These data are automatically displayed in tabular form and the measurements of all individual fish eyes, gaps, knitting yarns, etc., are collected and analysed statistically. By combining certain results further information is gathered. For example, the orientation of carbon fibres is calculated from the orientation of all small filament gaps as well as from the fish eye directions. The difference between the orientation of the knitting yarns and the carbon fibres indicates the accuracy of the production process.
5.3.3 Results In Fig. 5.6 the described working principle is applied to a 10 cm by 10 cm scan of NCF. One may easily see that the wide gap between the carbon fibres is detected (light area) as well as small fish eyes at all knitting points. Additionally, the knitting yarns are found and marked in a dark colour. A knitting error (detailed picture in Fig. 5.6) increases the measured width of the knitting row and thus will be detected. A short summary of the final results is shown in Table 5.1, which compares three different NCFs: NCF 1 in standard quality, NCF 2 with a wide gap over the whole NCF width, shown in Fig. 5.6, and NCF 3 with a strong curvature in the knitting rows (Fig. 5.7). For example, the gap in NCF 2 is detected via 14 particles as gap 2 (width >2 mm). The maximum width of these particles is 3.5 mm (light shaded area in Table 5.1). The knitting error in NCF 2 produces a maximum width of 3.2 mm in the local width of the knitting row (light shaded area in Table 5.1) compared to a standard level of 1.0 mm (dark shaded area in Table 5.1). Also, the curvature of the knitting rows in NCF 3 increases the width of the total knitting row to a value of 6.5 mm (standard mean value 1.4 mm).
5.6 Non-crimp fabric 2 with gap and knitting errors.
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© Woodhead Publishing Limited, 2011
Mean value Maximum Number of detected part Mean value Maximum Number of detected part Mean value Maximum
Number of detected part
NCF = non-crimp fabric
NCF 3 – curvature in knitting yarns
NCF 2 – gap and knitting error
NCF 1 – standard configuration
Area
0.0 0.4
0.0 0.3
0.0 0.3
Width 0.1 0.1
2899
0.1 0.1
1775
0.1 0.1
3659
Orientation 30.7
149.0
12.9
Area 0.4 3.4
1.4 3.3
0.4 1.7
Width 0.2 0.7
2139
0.5 0.7
1757
0.2 0.4
1894
37.4
163.4
14.1
Area 15.7 18.4
Width 0
2.9 3.5
14
0
27.3
Orientation
Gap (width >2 mm)
Knitting parameter
136.0
47.2
135.7
Orientation
Fish eyes
3.1 6.5
27
1.5 3.3
37
1.4 1.7
25
Curvature of knitting rows
Filament gaps
Orientation
Table 5.1 Summary of final results of three different non-crimp fabrics analysed by digital image processing
0.8 1.0
0.9 3.2
0.9 1.0
Local width of knitting row
44.5
47.2
47.8
Carbon fibre orientation vs. knitting yarn orientation
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5.7 Non-crimp fabric 3 with curvature in knitting rows.
The system is used at the moment in daily work to improve carbon fibres for their processing properties in NCF, to judge the NCF qualities from different origins and to document NCF within material specifications. All data are collected in an internal database, but they cannot be published. The current drawbacks of the described principles are that only visible layers may be scanned. The separation of multilayer NCF via melting the knitting thread may provide an interim solution. However, until now the system works only offline on a laboratory scale. In order to solve these drawbacks, it must be a main focus of future developments to install the system directly onto the NCF production machine and collect the digital pictures of individual layers online.
5.4
Future trends
In addition to the NCF discussed in this chapter, this technology can also be used on a number of other flat, semi-finished products employed to manufacture highperformance CFRP components. These semi-finished products include fabrics
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(used in various resin transfer mould [RTM] processes) and prepregs (usually processed in autoclaves). An example of a digitally processed image of a woven fabric is depicted in Fig. 5.8, where light reflections on the warp yarns are used to measure the yarn width behind every single weaving point. The numbers in Fig. 5.8 are the actual yarn widths in millimetres. Based on these figures, the yarn width variation may easily be determined. These details may help to localise process problems or select inhomogeneously spreading fibres.
5.8 Yarn width (in mm) of warp yarns in a woven fabric.
A further measurement of woven fabrics is shown in Fig. 5.9. By means of the transmitted light device a transparent projection is created. The small light marks in Fig. 5.9 result from fibre-uncovered areas in the immediate area of weaving points. If one subtracts the area of the detected marks from the total area of the analysed woven fabric, the area coverage is determined (e.g. 93.2% area coverage for the fabric in Fig. 5.9). This information also reflects the out-of-plane permeability of the fabric. Of course, other measurements based on the light marks are possible: yarn orientation in both horizontal and vertical directions, etc.
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5.9 Area coverage of woven fabric via transmitted light device.
In the case of prepregs, especially when laid on curved surfaces, so-called blisters may occur. Blisters are small areas lifting on the surface and appearing predominately as the prepreg is laid flat or draped on 3D surfaces. With the tool developed the amount of blistering can be characterised for different materials. The blistering varies both in the shape and number of blisters for different materials (Fig. 5.10, left and middle). An example of blisters detected by the software is shown in the right picture of Fig. 5.10.
5.10 Blisters on different prepreg materials.
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The procedure described above will allow automated inspection according to product specification of semi-finished products by both the supplier and user. Compared to the currently employed inspection methods, this will result in a significant reduction of cost and effort. Additionally, the developed tool can also be used for an in situ online quality monitoring tool. If this tool is integrated in the process control, process parameters may automatically be changed during the production cycle. Furthermore, quantified textile quality parameters will enable a reproducible comparison of the mechanical performance of such materials containing textiles with different defects. The effect of these defects will be correlated with the mechanical performance of these materials (see Chapter 3). Once the effects of certain fabric defects are known, the need to perform additional mechanical testing with fabrics can be eliminated. This will save the yarn and fabric manufacturer time and effort during the development process. Additionally, influences of noticed defects could be estimated at the shop-floor level. Any postprocessing of NCF to component reinforcements needs clear guidelines of tolerable, minor changes of NCF.
5.5
References
v. Diest, K., Entwicklung einer Bilderkennungssoftware zur Bestimmung der Faserorientierung von GMT-Bauteilen. IVW-Bericht 93–57. Fischer, G., Quantitative Ermittlung der Orientierung von Kurzglasfasern mit der Bildanalyse. Kunststoffe (1987) 77 (5): 509–512. Huber U., Maier, M., Optische Bestimmung der Faserorientierung in Verbundwerkstoffen. Nachr Chem Tech Lab (1997), 45: 134–136. Michaeli W., Heber M., Easy and quick method for the measurement of fibre orientation. ANTEC (1994), 1790–1793. Yaguchi H., Hojo H., Lee D.G., Kim E.G., Measurement of planar orientation of fibers for reinforced thermoplastics using image processing. International Polymer Processing (1995) 10 (3): 262–269.
© Woodhead Publishing Limited, 2011
6 Deformability of textile preforms in the manufacture of non-crimp fabric composites S. V. LOMOV, Katholieke Universiteit Leuven, Belgium
Abstract: Deformability of multiaxial multi-ply stitched preforms is studied in biaxial tension, shearing and compression. Biaxial tension tests reveal a strong interrelation between the two directions of tension in the case of tension in bias direction. The picture frame test is combined with full-field optical measurements of the shear strain, allowing true registration of the fabric shear angle. The difference between the shear behaviour in different directions relative to the stitching is shown. Thickness is measured for one of the sheared fabrics. Compression tests reveal a high compressibility of the preforms and a limited nesting effect in laminates. Key words: deformability, biaxial tension, shear, compression.
6.1
Introduction
Deformability of textile preforms plays a key role in the quality of a composite part formed into a three-dimensional (3D) shape. The deformation modes of primary importance are in-plain deformation (tension and shear) and compression of the preform. Resistance of dry preform to bending also plays a role in composite forming. This chapter, largely based on papers (Lomov et al., 2003a; 2005) with the addition of results of more recent research, describes resistance to these types of deformations of a set of typical non-crimp fabrics (NCF) (internal geometry of the same fabrics is described in Chapter 4). The most important deformation mode of a preform in forming is shear. Shear resistance of NCF is the subject of a number of publications (Long et al., 2002; Harrison et al., 2003; Yu et al., 2004; 2005; Lee et al., 2007). An important feature of NCF shear behaviour is the difference of shear resistance for different directions of the test vis-à-vis the stitching. The picture frame test, which is the main instrument of the published studies of shear resistance of NCF, is, as has been recently revealed by the international benchmarking round-robin exercise (Cao et al., 2008), a difficult test to standardise and interpret the results. In the study reported in this chapter, the picture frame test is accompanied by optical measurements of the strain field on the surface of the fabric (Lomov et al., 2008), which allows correct interpretation of the test results. The bias extension test, which is widely used for measurement of shear resistance of woven fabrics, is not applied to NCF because of asymmetry of the fabric 117 © Woodhead Publishing Limited, 2011
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deformation introduced by the stitching, which makes interpretation of the results of bias extension difficult. There are no publications on biaxial tension of NCF, apart from a qualitative discussion in (Hoersting, 1998). The tensile behaviour of a preform can seriously influence its drapability, as a tension may be introduced in the actual forming process by use of a blankholder. Apart from a quantitative characterisation of the preform behaviour, the biaxial tensile test must answer two qualitative questions, which are discussed in this chapter. •
•
When tested in the direction of fibres, how large is the initial non-linear region of the stress–strain diagram, caused by crimp of the fibres? The lesser this region, the more close to reality will be the assumption of linearity of the preform resistance (which would be advantageous to use to make the draping simulation less computationally demanding). Do tension deformations in two directions affect one another (as it is the case for woven fabrics)? If yes, then the independent description of the fabric tensile resistance in two directions, adopted in some draping codes, does not describe the real behaviour and the material models should be made more complex.
The compression behaviour of glass NCF is covered in the series of papers (Robitaille and Gauvin, 1998a; 1998b; 1999); carbon NCFs are studied in Endruweit (2003), Chen et al., (2001) and Hammani (2000). Knowledge of the compression diagrams is necessary to calculate the thickness of a preform in vacuum-assisted resin infusion (VARI) and similar processes, where it is not defined by the distance between rigid parts of the mould, but by the pressure involved in the process, acting on the flexible part of the mould. It is also interesting to observe and assess the degree of nesting in a NCF laminate (a model of the nesting is presented in (Lomov et al., 2002)). Apart from this, the compression behaviour determines normal forces acting on a preform during forming, hence friction between the preform and the tool and between the preform layers, which strongly affects preform formability. In an actual compositeforming process, a preform is under simultaneous action of compression and shear. This chapter reports the results of such a test. The work reported in this chapter was done in the Department of Metallurgy and Material Engineering (MTM), Katholieke Universiteit (KU) Leuven, Belgium, and in the Department of Mechanical Engineering, Universiteit Twente. Four fabrics are studied in this Chapter (Fig. 6.1). Their parameters are shown in Table 6.1. The terminology used for description of the defects in the fibrous layers, induced by the stitching, is explained in Chapter 4. Table 6.2 summarises the tests done for all the fabrics.
6.2
Shear
Only the biaxial fabrics (B1, B2 and B3) were tested in the picture frame test, as for a quadriaxial fabric the test is impossible because of tension applied to the
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© Woodhead Publishing Limited, 2011
Quadriaxial 4 carbon fabric
Q
2
0;−45;90; +45
+45;−45
0;90
2
Bidiagonal carbon fabric
B2
B3
+45;−45
Bidiagonal carbon fabric with glass stabilising yarns Biaxial carbon fabric
B1
2
629±31
541±12
329±14
322±16
Tricotchain
Chain
Tricotchain
Tricot
5
5
5
5
24K Toray T700 50E 12K Tenax HTS 5631 12K Toray T700 50E
Stitching
PES 7.6 tex
156± 8
5.09 2.58 6
PES 5.79 2.22 5 5 tex
260
Channel 0.66
Opening 0.28
Opening 0.18
5.03 2.64 6
PES 7.6 tex
Back
n/a
7.7
4.2
5.05
Opening 0.48
Opening 0.29
Channel 0.40
7.28
8.0
n/a
7.15
Width, Length, mm mm Opening 0.43
Width, Length, Type mm mm
Opening 0.28
Mass, Face g/sq Type m
Defect in fibrous plies
4.94 1.71 3
B, mm
150± 8
PES 7.6 tex
Mass, Yarn A, g/sq mm m
12K 156± Toray 8 T700 50E
Preform Description Number Orientation Mass of Stitching Gauge Plies ID of plies of plies, the pattern (needles degrees fabric, per inch) Tow g/sq m
Table 6.1 Parameters of non-crimp fabric
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6.1 Samples of non-crimp fabric, face (left) and back (right).
fibres oriented in the load direction. Shear tests were done in the laboratories of KU Leuven (fabrics B1 and B2) and Universiteit Twente (fabric B3) on the identical picture frames. Tests in Leuven were supported by full-field strain measurements; in the tests in Universiteit Twente, the thickness of the sheared fabric was measured with a special device under a pressure of 0.5 kPa. Table 6.2 Summary of the deformability tests performed for different types of NCFs Shear
B1 B2 B3 Q
Biaxial tension
Shear diagram
Strainmapping
Thickness
+ + + −
+ + − −
− − +
+ + − +
Compression Unsheared
Sheared
+ + + +
+ + + −
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6.2.1 Picture frame test Figure 6.2 depicts the picture frame of the Department MTM, KU Leuven, and shows the method of gripping the sample. Hinge 1 moves freely in groove 3. Hinge 2 is connected to the bottom grip of the machine. When the crosshead moves up, pulling at point A, the frame starts closing, its sides rotating in hinges; hinge 1 goes up inside groove 3. Note that the centres of the hinges are in line with the internal edges of the frame. The maximum stroke of the machine, allowed by groove 3, is 22 mm, which gives the maximum shear angle of the frame (50°). The picture frame of the Department of Mechanical Engineering, Universiteit Twente, has the same dimensions and gripping system. The loading arrangement is, however, different: the load is applied directly to hinges 1 and 2. Hence, the displacement of the hinges is not restricted and the test can go on to higher shear angles. The frame was mounted on a Zwick machine; the force is measured with a 1 kN force-cell and a 12-bit AD converter, which results in a step size of 0.2441 N in the force data. In KU Leuven, the frame was mounted on an Instron 4467 machine with a 1 kN load cell with the same precision parameters as in Twente. The shear angle of the
6.2 Picture frame (Department MTM, KU Leuven): (a) empty frame: 1, 2 – hinges, 3 – groove, 4 – lip, 5 – plate with screws; (b) grips; frame with samples of fabrics B1, SC test (c) and B2, SS test (d); (e) load-displacement diagram of the empty frame.
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frame γ is related to the displacement of the machine x via a solution of a trigonometrical equation describing the movement of the frame. A test speed of 20 mm/min was used in all the tests. First, the load-displacement diagram was registered with an empty frame (Fig. 6.2), to be subtracted from the load diagram in the test with the fabric, to produce the net force F, acting on the fabric. Lips 4 are pressed by screws in plates 5. The lips and the frame beneath them have a wavy surface, securely gripping a fabric sample (Fig. 6.2). When the sample is fixed in the frame, it is possible to feel that it is tensed. The deformation of the pre-tensed fabric cannot exceed a value of 2.8%, given by the geometry of the lips. In practice, the pre-tension is significantly smaller: a very rough estimation of the difference in the distance between the stitching before and after mounting of the fabric gives the range of the pre-tension as 0.5–1%. In the tests performed in the University of Twente, the mounting procedure was different, with the aim of minimising the fabric tension. The grips were loosened to the point where the tension in the fabric disappeared (felt by the operator). The effect of this is discussed in section 6.5. The fabric is firmly gripped in the frame, with the fibres parallel to the frame sides. During the test, the fibres near the grips are gradually bent and the shear angle in the central part of the sample is different from the shear angle of the frame. The lesser the bending resistance near the grips, the smaller this deviation. One of the ways to minimise it is to take out of the fabric the fibres parallel to the nearest frame side (Fig. 6.2). In the preliminary test it was found that without this measure the test is impossible to perform because of the extensive wrinkling of the material. Therefore, the fibres near the grips were taken out in all the experiments described in this chapter. The result of the test is the dependency of the shear force per unit width of the frame side T on the shear angle of the frame γ. The latter is easily calculated from the displacement on the testing machine (1); the former is calculated as
[6.1]
where F is the force applied by the loading machine, w is the width of the gripped side of the sample, α is the frame angle, γ is the shear angle. Three loading cycles were performed for each sample. Load diagrams and strain fields during unloading (return of the frame to initial rectangular configuration) were not registered. The normalisation issues are discussed in (Peng et al., 2004). In some regions of the shear diagrams, the force measurements were performed at the limit of the machine precision (the difference in tensile force of the frame with fabric and the empty frame was about 1 N, which corresponds to a shear force less than 0.01 N/mm). Another factor that may affect the precision of the measurements is friction in the hinges. In the presence of high fabric pre-tension
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this is an uncontrollable factor, which might lead to unsatisfactory results in the first shearing cycle. Fabrics B1 and B3 can be mounted in the picture frame with their fibres parallel to the frame sides in two ways: with the stitching parallel to the loading direction and across it. In the former case, the stitching, firmly clamped by the frame grips, is in tension, and one can expect high resistance to deformation. This test direction will be abbreviated as ST (stitching–tension). In the latter case the stitching is in compression, which should not affect the test result very much. This test direction will be abbreviated as SC (stitching–compression). These observations were also made in other studies of the deformability of NCF (Long et al., 2002; Harrison et al., 2003; Yu et al., 2004). The presence of the glass stabilising yarns in fabric B1 introduces another complication: they are oriented along the tension directions. Therefore, even in the SC tests some ‘parasitic’ tension may be present. To minimise it, the glass yarns were cut near the grips after mounting the sample. In spite of this, the glass yarns are firmly set inside the fabric by the stitching. This leads to irregularities of the fabric shear, shown in the next section. When fabric B2 is mounted with the fibres parallel to the frame sides, the stitching is also parallel to them. There should be no difference in the test direction. This case will be referred as SS (stitching–shear). To constitute a true characterisation of the fabric shear behaviour, the test must provide dependency of the shear force on the average shear angle of the fabric. Due to the complications of the gripping discussed above, one cannot be sure that it is the same as the shear angle of the frame. The shear angle of the fabric was measured using the ARAMIS strainmapping system. The reader is referred to (Lomov et al., 2006; 2008; Willems et al., 2008; 2009) for details of the measurement technique and data processing. Plate I (see colour section between pages 396 and 397) shows results of the full-field registration of the shear field in the example of fabric B2. The curves are the result of averaging data for three samples. There was no statistically significant difference in the average shear angle of the fabric in different shear cycles. Fabric B1 develops a lot of local wrinkling, which prevents resolving the deformation field after the frame shear angle reaches approximately 18°, hence results for it are not shown. Fabric B2, in the SS test, behaves in a more stable way, and the strain field can be resolved up to the maximum shear angle of the frame. The local shear angle of the fabric was determined by the angle between the diagonals of initially square facets visible in Plate I. The measurements show the following: • •
The average shear angle of the fabric is the same as the shear angle of the frame. The scatter of the local shear angle is about ±2°. The size of the facets is about 15 × 15 mm. The local shear angle in these measurements is the result of averaging over three unit cells of the fabric, hence local variations within unit cells do not cause the scatter value given above. This value (±2°) is quite low, allowing the conclusion that the shear field is fairly even.
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6.2.2 Shear diagrams Fabrics B1 and B2 were tested in laboratory of the Department MTM, KU Leuven. Figure 6.3 shows the results of the picture frame tests on fabrics B1 (SC and ST tests) and B2 (SS test): shear force as a function of the frame shear angle and average fabric shear angle. Three shear cycles are shown.
6.3 Shear diagrams of fabric B1, SC (a) and ST (inset) tests, and fabric B2, SS test (b). Error bars show standard deviation of five tests. Only loading diagrams were registered.
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The diagrams for the first shear cycle for both fabrics show extremely irregular behaviour and evidence of tension of the fibres in the frame. This type of behaviour was labelled in (Lomov et al., 2006) as ‘bad tests’, and normally such tests are discarded from the data processing. The cause of ‘bad’ behaviour of a woven fabric has been identified in (Lomov et al., 2006) as deviations of the yarns from directions parallel to the frame sides and variations of the pre-tension of the different yarns. The arrangement of an NCF sample in the frame is much more difficult than mounting of woven fabrics. Fibres, which have to be taken away near the grips, are firmly fixed in the fabric by stitching. Hence, the disturbances given to the fibres in the fabric by the process of taking these fibres away are more serious than in a woven fabric. These disturbances are larger for fabric B1, as in this case the fibres are inclined 45° to the stitching, and ‘cracks’ in the fibrous ply do not form continuous fibre bundles between the stitching sites (as ‘channels’ in fabric B2 do). We were not able to make a ‘good’ test (without evidence of the fibre tension) in the first shear cycle. After the first cycle the sample is ‘conditioned’ (Nguyen et al., 1999; Long, 2000; Mohammed et al., 2000; Lebrun et al., 2003; Sharma et al., 2003; Peng et al., 2004; Lomov et al., 2006) and its behaviour is much more stable. In our measurements the first cycle represented the experimental rig behaviour rather than the material itself and therefore it was not used for the material characterisation. In the second and the third shear cycles some tests also resulted in ‘bad’ diagrams. These were considered faults in mounting the sample and discarded from the data processing. For the ‘good’ tests the second and the third shear cycles produce very close diagrams for both fabrics. The differences lie well inside experimental scatter, but the third cycle gives shear resistance some 5% less than the second. The scatter is quite large for fabric B1 (up to 50%), and less for fabric B2 (about 20%). On closer inspection, the diagrams for fabric B2 bear evidence of the fibre tension even on the second and the third cycles. The difference in the shear diagrams of the two fabrics compared in Fig. 6.4 is not large, but the shear resistance of fabric B2 is definitely lower than that of the fabric B1 (the initial region of the B2 diagram, possibly influenced by the fibre tension, still present in the second cycle, should not be considered). The difference in the shear resistance has to be attributed to the differences in the stitching pattern and direction, since the fabrics have the same areal density. The fibres are tightly fixed by the tricot pattern in fabric B1; the 45° direction of the fibres does not connect diagonally the stitching sites (rectangular spacing 4.94 × 1.71 mm, Table 6.1). This produces ‘openings’ in the fibrous ply, without formation of continuous fibre bundles in the plies. The tight fixation of the fibres is evidenced by a significant resistance of the fibres to pulling them out of the fabric (as it was done along the grips). In fabric B2 the fibres are fixed by the tricot-chain stitching much more loosely. There are ‘openings’ on the face (0°) ply and ‘channels’ in the back (90°). The latter give fibres freedom to rotate during the shear deformation, behaving like a trellis up to a certain ‘locking’ shear angle, when the rotation
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6.4 Comparison of the shear diagrams of fabrics B1 and B2 (picture frame test, see Fig. 6.3 and KES-F) and fabric B3 (picture frame test, Fig. 6.5).
becomes impossible without lateral compaction of the fibres (about 23°, judging by a geometrical estimation of the locking angle γlock = arccos(w/p), where w is the bundle width and p is the bundle spacing). Finally, Fig. 6.3a (inset) shows results of ST tests of fabric B1, with the stitching in tension. The shear force (which actually represents the tensile resistance of the chain of the stitching loops) is five times higher than in SC tests, and the shear modulus is 20 times higher; the test had to be stopped at the shear angle of 1.7° because of the too-high load on the load cell of the machine. Fabric B3 was tested in the laboratory of the Department of Mechanical Engineering, Universiteit Twente. Figure 6.5 shows the results of the tests: shear force as a function of the frame shear angle. Three shear cycles are shown. The curves are an average of five experiments, which are quite reproducible: coefficient of variation in the range of 20%. To study the influence of the shear rate, the experiments were repeated at machine speeds from 10 to 1000 mm/min. No systematic variation of the shear resistance has been found; the curves changed within the experimental scatter range. The results demonstrate the same difference between the first shear cycle and the second and third shear cycles. In this test the full cycle has been registered, showing a hysteresis effect. Measurements up to higher shear angles show a
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6.5 Shear diagram of fabric B3 (picture frame test).
sharp increase of the fabric resistance, starting at the frame shear angle of around 45°, which is in accordance with the measurements for fabrics B1 and B2 (Fig. 6.3). When sheared in the ST direction (negative shear angles in Fig. 6.5), the same increase of the shear resistance is registered as for fabric B1 (Fig. 6.3b). In spite of the qualitative likeness, the quantitative results of the tests in Universiteit Twente (fabric B3) are quite different to those from KU Leuven (fabrics B1 and B2). The shear resistance of fabric B3 is about ten times lower than of fabrics B1 and B2 (Fig. 6.4), in spite of the fact that the areal density of the former is 50% higher than of the latter. This can be explained by the difference of the mounting procedure in two laboratories, which led to difference in the fabric pre-tension. Fabric B3, tested with deliberately loosened grips in Universiteit Twente, had much less pre-tension than fabrics B1 and B2, which were tested in KU Leuven without a special procedure to minimise the pre-tension and were subjected to a considerable pre-strain of about 0.5%. The reader is referred to the discussion and quantitative estimation of the influence of pre-tension on the results of picture frame test in (Lomov et al., 2004; 2006). When compared with measurements from the Kawabata Evaluation System (KES-F) (Lomov et al., 2003a), Fig. 6.4, the picture frame shear diagrams show close values of the diagram slope, i.e., shear modulus of the fabric. However, the values of the shear force in the KES-F measurement are significantly lower than in the picture frame test. This is explained by the difference in the level of the
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fabric pre-tension in the two tests. In the KES-F measurement (Lomov, Verpoest et al., 2003a), a controlled pre-tension of 0.01 N/mm is given to the fabric. In the picture frame test the pre-tension is not controlled, but by the values of the prestrain, given above as about 0.5%, and results of the tension tests, the pre-tension can be estimated as lying in the range 0.1–1 N/mm, which is by two orders of magnitude higher than in the KES-F test.
6.3
Biaxial tension
Biaxial tension tests were performed for fabrics B1, B2 and Q.
6.3.1 Equipment and samples The biaxial tester of the department of MTM, KU Leuven (Fig. 6.6) is a tensile machine equipped with four independently controlled axes, developed for the study of deformation of textiles, films and thin sheets. The clamping system consists of freely moveable clamping rigs (mechanical or pneumatic) mounted on each axis. The axes’ movements are fully computer-controlled; the output consists of force-displacement curves in the two principal directions. The apparatus can be used to investigate the constitutive behaviour, anisotropy and limits of deformation of the material. The types of tests that can be performed are: • • •
uniaxial stress tests with clamping in one single direction; biaxial tests with principal strain ratios varying between zero and infinity; and shear tests using a tensile bar clamped over the centreline of the material.
The biaxial tensile tester has four different axes, which can all be driven separately. The machine has two force transducers in total, one for each direction. They can register a maximum force of about 5 kN, with an accuracy of 0.1%. The axes can be moved at different speeds, ranging from 25 to 175 mm/min, in steps of 25 mm/min.
6.3.2 Tension diagrams The fabric behaviour in a biaxial tester is determined by the interaction between the yarns or fibres. The theory of the test is well developed for woven fabrics, where interference between warp and weft is determined by the crimp of the yarns (Kawabata, 1973a; 1973b; Boisse et al., 1999; Launay et al., 1999; Lomov et al., 2003b; 2008; Willems et al., 2008; 2009). In NCF, the fibres in plies are almost straight and are not interlaced one with another. They are, however, linked by the stitching. The extent of the link is different for different fabrics and the different directions of the test. The tests were performed with the following ratios of deformation on the machine axes: ‘1 : free’, meaning that only one pair of the clamps is used, ‘1 : 0’,
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6.6 Biaxial tensile tester (a), clamping of the sample (b).
when one set of the clamps is moving, the other staying fixed, ‘1 : 1’ (equal deformations in both directions), ‘1 : 2’ and ‘1 : 5’ (ratio of deformation in two directions). Different axis speeds were set, corresponding to the chosen ratio of deformations. The tests were performed in the 0°/90° and +45°/−45° directions relative to the production direction of a fabric. At the end of the diagrams, the apparent stiffness reduces because of the onset of slippage in the grips. In the case of 0°/90° test of the fabric B1 and the +45°/−45° test of fabric B2 (Fig. 6.8) the deformation goes in the direction in-between the fibres. Stitching serves as ‘hinges’ between the two fibre systems in the plies. This ensures a strong link between the two tension directions. The direction of the stitching in fabric B1
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6.7 Tension of fabrics B1 and B2: (a) biaxial and uniaxial in fibre direction (deformation ratios 1 : free, 1 : 0, 1 : 1, 1 : 2, 1 : 5 for each fabric); (b) uniaxial and (c) biaxial in the bias directions (ratio between deformations in two directions is shown on the curves, the first value being the direction of the strain and load shown by the curve). Five tests are averaged for each curve, Cv ≈ 5–10%.
is different in the tests in 0° and 90°. No statistically significant difference was found in these two cases. In the uniaxial tension test in the bias direction (Fig. 6.7a) the fabrics are highly extensible (‘bias extension test’). When deformation in the direction perpendicular to load is restricted (biaxial test, Fig. 6.8b), the stiffness of the fabric increases together with the decrease of the deformation ratio (loading : perpendicular), shown in Fig. 6.10b. This behaviour is
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6.8 Compression diagram, fabric B3: (a) Instron measurements, numbers refer to the compression cycles; (b) combination of Instron and KES-F measurements.
caused primarily by the test configuration: fibres gripped in the clamp in one direction are also gripped in the clamp in the other direction. The results of the tests should be considered as a qualitative indication of the fabric’s behaviour, as the quantitative results depend on the test configuration. The test reflects the combination of shear and tension, which may happen in the actual forming. Comparing the diagrams for fabrics B1 and B2 in Fig. 6.7, one notices that the diagrams are quite close. Fabric B2, however, offers higher load resistance, with identical areal density of the fabrics (see Table 6.1). This can be attributed to the straighter fibres in the fibre bundles of fabric B2 (to compare the width of the openings and channels in the two fabrics, see Table 6.1, which gives the degree of deviation of the fibres from straight lines). In the cases of +45°/−45° test for B1, 0°/90° for B2 (Fig. 6.7a) and both directions for fabric Q, fibres lie in the directions of applied tension. In this case, one may expect non-linearity in the initial stage of deformation, because of the
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waviness of the fibres in the plies. Fibres undergo straightening before taking up the full load of the tension. Tension diagrams of fabric Q in 0/90 and +45/−45 tests are quite similar to those of fabrics B1 and B2 and are not included in Fig. 6.7a. No link between the test directions is revealed by the tests of fabrics B1 and B2. The curves for the different deformation ratios are mixed and are not distinguishable statistically. Fabric B2 exhibits higher tension resistance because of the straighter fibres in it (see above). It is interesting to note that the non-linearity range in strain (about 0.1%) is of the same order as has been registered for woven fabrics (Lomov et al., 2003b).
6.3.3 Validity of simplified models In forming simulation software, fabric tension is normally characterised independently for two directions, and it is preferable to have a linear tension diagram of the fabric for the sake of computational effectiveness. Our observations lead to the following conclusions regarding these two assumptions. All the measured diagrams exhibit a nonlinear behaviour. The authors are not aware of studies where simulation with linear and nonlinear diagrams would be compared. Such a study is needed to conclude on the necessity of using true nonlinear diagrams instead of linear approximation. One may argue that, in the absence of comparative simulations, it is not clear if incorporation of tensile data is needed at all, and whether the assumption of inextensible fibres would not be enough for an acceptable simulation. Because of low deformations in the fibre direction this reasoning might be true, but one should take into account interdependence between tension and shear. Studies of shearing of woven fabrics show that calculation of the tension forces is of paramount importance for the correct calculation of the shear resistance, which can differ by orders of magnitude when coupled with tension (Lomov and Verpoest, 2006; Cao et al., 2008; Launay et al., 2008) which should also be the case for NCF. A model with inextensible fibres does not allow such a calculation. Our results show that there is no significant coupling between the tension directions if they coincide with the fibre directions in the fabric. Hence, for NCF this assumption in the material models of the existing simulation software can be retained.
6.4
Compression
Compression tests were performed in the laboratory of the department of MTM, KU Leuven on Instron and in the laboratory of Centexbel, Gent on KES-F. A flat cylindrical punch with a diameter of 50 mm is mounted in the Instron 4467. A load cell of 1 kN is used. The lowest pressure measured on Instron with sufficient accuracy is 1–5 kPa, which is the upper limit of the KES-F pressure range. To study the effect of nesting of the layers (Lomov et al., 2002), tests on one, two and four layers of each fabric were performed. In each test, three compression cycles
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were performed, up to a pressure of 200 kPa. For more detail on the experimental technique see (Lomov et al., 2003a; 2005).
6.4.1 Compression test results The behaviour of the NCF in compression exhibits common well-known features of compression (Gutowski et al., 1986; Lomov and Verpoest, 2000; Chen et al., 2001; 2006). The initial stiffness is low, fabrics are compressed to about 70–80% of the initial thickness at a pressure of 50 kPa. With the pressure increase to the maximum value of 200 kPa, the thickness of the fabric additionally decreases to about 60–70% of the initial thickness. Actual values depend on the number of layers and compression cycle. Figure 6.8 shows typical results of the Instron tests: one layer of fabric B3 for different compression cycles, measured on Instron and KES-F. One sees that the diagrams of the second and the third compression cycles are very close to one another. To make the data overview more brief, we do not discuss below the data on the third cycle. As mentioned above, the Instron diagrams do not provide reliable data for the low-load range, hence, they do not allow determination of the initial fabric thickness. These data are provided by the KES-F measurement. The Instron and KES-F measurements (fabric B3) are compared in Fig. 6.8, which shows typical features common for the fabric behaviour in all of the studied cases. For the first cycle, KES-F and Instron measurements fairly correspond to one another. A certain jump is evident when passing from KES-F to Instron results for the second cycle. This can be explained by the fact that in contrast with the KES-F measurements in the lower pressure range (up to 5 kPa), the first cycle up to 200 kPa cannot be treated as ‘conditioning’, as it gives permanent high deformation to the sample (note that the thickness at the start point of the second cycle of the Instron diagram in Fig. 6.8 almost coincides with the end-point of the first cycle). Based on this, the first cycle of the Instron tests is used below for discussions on the fabric behaviour. The ‘conditioning’ of the sample by a first cycle of compression is recommended for KES-F measurements at low loads (Lomov et al., 2003a). Hence, the second cycle of KES-F test is adopted as representing the fabric behaviour. To present the considerable amount of data in a concise form, the diagrams were approximated with a power law: [6.2] where T is the fabric thickness, mm; p is the pressure, kPa; p* is a parameter, kPa; T0 is a parameter, mm, corresponding to the fabric thickness in the relaxed state ( p = 0); Tmin is a parameter, mm, corresponding to the fabric thickness at p = ∝; a is a dimensionless power parameter.
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Approximation 6.2 was applied to the data set as follows. Consider a set of repetitive measurements for a given test parameters: type of fabric, number of layers, number of the compressive cycle. The set of measurements normally consists of five Instron diagrams. These diagrams are processed to produce an averaged diagram. The coefficient of variation of such a set lies within 5–10% for all the measured data. As discussed above, the averaged Instron diagram does not allow us to define T0. This is defined by the KES-F measurement in the second cycle, as the first KES-F cycle serves to condition the sample. Hence, the averaged KES-F second cycle diagram was added to the averaged Instron first cycle diagram for p < 5 kPa. The combined diagram was used via a least-square minimisation procedure to determine the best-fit parameters T0, Tmin, p0 and a in Equation 6.2. In this case T0 represents true initial fabric thickness, and the approximation 6.2 can be used in the pressure range 0–200 kPa. For the second compressive cycle, KES-F and Instron data do not correspond one to another. Therefore, only averaged Instron diagram was used to fit the Equation 6.2. Such an approximation is strictly usable only in the range 5–200 kPa, and in this case T0 value has to be considered as an extrapolative estimation of the fabric thickness at the beginning of the second compression cycle. The results of this processing are summarised in Table 6.3, which provides the results of the compression tests in full. For the discussion of characteristic features of the behaviour of the fabrics, the data on the first compressive cycle will be used.
6.4.2 Trends in the compressive behaviour The studied fabrics show quite similar compressive behaviour. Moreover, certain dependency can be established on the areal density of the fabrics. Consider the parameters of the compression diagrams for the first compressive cycle (one layer). Figure 6.9a shows the dependency of these parameters on the areal density of the fabric. Parameters T0 and Tmin increase with the increase of the fabric areal density, as may be expected. Parameters p* and a do not exhibit a trend – the shape of all the diagrams is very much the same. Hence, the compression diagrams of the studied fabrics can be approximated with Equation 6.2, where p* and a are the same for all the fabrics (average values, shown in Fig. 6.9a), and T0 and Tmin are calculated using the linear regression formulae, also shown in Fig. 6.9a. Figure 6.9b compares the results of such an approximation with the measurements. The fabrics in question are obtained from different producers and were manufactured using different heavy carbon tows. The similarities of the compression behaviour and the recognisable trend vs. areal density of the fabrics reflect similarities of the fibre bundle structure and of the textile manufacturing process. The approximations shown in Figure 6.9 could probably be applied to other NCFs.
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Table 6.3 Compression test. Parameters of Equation 6.2 Fabric
Layers
Cycle
T0, mm
Tmin, mm
p, kPa
a
B1
1
1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
1.153 0.957 2.082 1.541 4.268 2.972 0.829 0.835 1.425 1.718 2.673 3.203 0.945 0.870 1.517 1.540 3.499 3.291 1.360 1.046 2.410 2.310 4.868 3.972
0.324 0.251 0.635 0.547 1.245 0.979 0.309 0.246 0.593 0.527 1.135 1.050 0.396 0.485 0.850 0.834 1.805 1.669 0.601 0.515 1.054 0.961 2.072 2.005
1.343 1.097 1.901 4.824 1.490 4.952 2.660 0.953 3.845 0.802 6.368 1.346 6.932 3.691 15.231 1.926 6.309 1.577 2.652 8.742 5.707 5.297 4.719 14.450
0.631 0.339 0.624 0.438 0.620 0.393 0.709 0.372 0.546 0.360 0.476 0.330 0.382 1.013 0.535 0.335 0.578 0.326 0.637 0.448 0.484 0.367 0.476 0.452
2 4 B2
1 2 4
B3
1 2 4
Q
1 2 4
6.9 First compressive cycle, one layer: (a) parameters of the Equation 6.2 vs. areal density of the fabric; (b) compression diagrams, points – measured, lines – calculated using Equation 6.2 with averaged parameters.
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6.4.3 Nesting effect in the fabrics As is discussed in (Lomov et al., 2002; 2003a), nesting of the layers (decrease of the thickness per layer in a laminate) in NCF laminates is of minor importance, being caused by the thin stitching yarn lying on the surface of the fabric and creating the surface roughness of the fabric. Our current measurements show variable nesting for the studied unsheared fabrics. Table 6.4 gives nesting coefficients ζ, calculated as ,
[6.3]
where N is the number of layers in the laminate, T(N) – thickness of the laminate, T(1) – thickness of one layer. The initially significant nesting decreases with the increase of pressure (nesting coefficient increases), and for sheared fabric it even gives the opposite effect: increase of thickness per layer in a laminate. The latter phenomenon can be explained by the fact that when sheared, layers in a laminate tend to buckle because of irregularities of fibre placement in layers and unevenness of tension applied to different layers.
Table 6.4 Nesting coefficients in the compression tests Fabric
Shear angle, °
B1
0
B2
0
B3
0
Q
0
6.5
Number of layers
2 4 2 4 2 4 2 4
Nesting coefficient T0
T(10 kPa)
Tmin
0.90 0.93 0.86 0.81 0.80 0.93 0.89 0.89
1.00 0.97 0.99 1.00 0.94 0.97 0.99 0.97
0.98 0.96 0.96 0.92 1.07 1.14 0.88 0.86
Bending
Bending rigidity of NCF was measured on KES-F in Centexbel, Gent. Bending rigidity is expressed as the slope of the torque versus curvature between 0.5 and 1.5 cm−1. Bending hysteresis is expressed as the difference in momentum at a curvature of 1 cm−1. Figure 6.10 and Table 6.5 show the results of the measurements for fabrics B1, B2 and Q. To assess isotropy of the bending properties, let us consider a formula introduced in (Jiang and Hu, 1999), which accounts for difference of curvature of differently
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6.10 Typical bending diagrams on NCF. Two diagrams are registered on one graph, with an offset for clarity.
Table 6.5 Bending rigidity Fabric and test direction
B Bending rigidity, 10−4 Nm2/m
2HB Bending hysteresis 10−2Nm/m
B1, MD B1, CD B1, +45° B1, −45° B2, MD B2, CD B2, +45° B2, −45° Q, MD Q, CD Q, +45° Q, −45°
0.59 ± 0.18* 0.62 ± 0.15 0.63 ± 0.117 0.62 ± 0.132 2.48 ± 0.65 1.41 ± 0.38 2.07 ± 0.31 2.20 ± 0.14 1.90 ± 0.704 1.324 ± 0.57 1.27 ± 0.365 1.16 ± 0.22
2.08 ± 0.114 2.45 ± 0.316 2.01 ± 0.152 2.09 ± 0.138 5.03 ± 0.27 4.19 ± 0.262 3.88 ± 0.22 3.66 ± 0.25 8.88 ± 1.05 8.91 ± 0.716 7.56 ± 1.23 8.02 ± 1.11
oriented tows in the fabric under bending. They state that if the interaction between carbon fibre plies and influence of stitching could be neglected, then the bending rigidity of the multi-ply fabric Bfabric is given by [6.4]
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where Bi is the bending rigidity of the ply, αi is the angle between the direction of the ply fibres and the direction of bending. The difference between properties (both bending rigidity and hysteresis) in machine/cross and bias directions for the fabrics B1 and B2 is not statistically significant. This applies not only for values of bending rigidity, but also for the full shape of the diagrams (Fig. 6.10). This remarkable observation shows that the influence of stitching and frictional interaction of the plies is negligible for these fabrics. Indeed, Equation (6.1) gives for the machine or cross direction Bfabric = 2Bicos245 = Bi, and for bias direction also Bfabric = Bi. Fabric B2 demonstrates certain differences in bending rigidity in machine and cross directions. The fibrous structure of the plies in these directions is indeed different (Fig. 6.1). The stitching introduces relatively large gaps between fibres in machine and cross directions, forming fibre bundles between stitching yarns. The fibres in these bundles are tightened together, and the bending resistance of such a bundle must be larger than that of the loosely placed fibres in the ply, because intra-ply slippage of the fibres is prevented. The fibre bundles in the machine direction are more tightly packed than in the cross direction, which may explain the observed difference. Measurements show a significant difference in bending rigidity between fabrics B1 and B2, the latter being three times higher. Areal density of the fabrics B1 and B2 are same. As the bending rigidity of the fabric B2 is also higher than the bending rigidity of the fabric Q (which is twice as heavy), then the difference cannot be attributed to the different stitching pattern of the fabrics B1 and B2. A possible source of the difference is the difference in the raw material: carbon tows of 12 k and 24 k. For the fabric Q, the bending rigidity in machine/cross is about 25% larger than in the bias direction, and this difference is statistically significant. By the placement of the fibres in the fabric, the properties in machine/cross and bias directions should be identical. The observed difference may be attributed to the difference in influence of stitching and friction between plies. In the MD ply, the stitching introduces fibre bundles increasing the bending resistance, as discussed above. In the bias plies, the stitching produces smaller ‘cracks’ in the plies, which do not affect the bending resistance (in the same way as it is not affected for the fabric B). Hence, the plies in machine/cross directions are stiffer in bending than the bias direction plies. However, the difference in the global shape of the diagrams is not large (Fig. 6.10). The diagrams demonstrate large initial stiffness. When estimated by a secant to the curvature 0.5 cm−1, the initial bending rigidity for fabrics B1, B2 and Q is about 7.5, 20.1 and 18.0 Nmm, or more than ten times higher than the bending rigidity measured between 0.5 and 1.5 cm−1. To estimate the relationship between the bending properties of the fabrics and carbon tows, the ratios of the bending rigidity of the fabrics (units Nmm) to their areal density and the bending rigidity of the tows (units Nmm2) to their linear density
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can be estimated. The ratio, which can be called relative bending rigidity, is expressed then in Nmm2/Ktex both for fabrics and tows. The ratio for the fabrics B1, B2 and Q is 0.19 Nmm2/Ktex, 0.60 and 0.22 Nmm2/Ktex (machine direction), which is quite close. The measurements of the bending rigidity of the heavy carbon tows (Fig. 6.11) suggest a value of about 0.4 Nmm2/Ktex (calculated as the slope of the best fit straight line). The large scatter of the data is probably caused by the difference in sizing of the tows. The average value for our fabrics (0.33 Nmm2/Ktex) and the data for the yarns correspond to one another. The ratio of the bending rigidity to the linear density of individual carbon fibres themselves is about 0.3 Nmm2/Ktex, which is close to the quoted values. The values in the range of 0.2–0.6 Nmm2/Ktex can be proposed as rough estimations for similar fabrics.
6.11 Bending rigidity of heavy carbon tows. Line = simple sum of bending rigidity of the fibres; points = experimental (Lomov et al., 2003a).
6.6
Conclusion
Characterisation of the behaviour of NCF in tension, shear, compression and bending leads to the following conclusions.
6.6.1 Shear Shear of biaxial NCF is characterised by the same phenomena as other bi-directional textiles, when sheared in the direction of compression of the stitching: hysteresis of the diagram, leading to non-zero starting shear resistance, low shear modulus up to approximately 30°, when the main shear resistance mode is friction, and rapid increase of the shear modulus with the onset and intensification of the lateral
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compression of the fibre bundles. Shear in the direction of tension of the stitching produces high and rapidly increasing resistance in the picture frame test. Shear resistance depends strongly on pre-tension of the fabric. In the absence of the universally adopted procedure to control and measure the pre-tension, any reporting of picture frame tests should be supplemented with a thorough description of the gripping procedure and estimations of the pre-tension. The KES-F and picture frame shear tests coincide in shear modulus with a large difference in the absolute value of the shear resistance, caused by the difference in pre-tension. For the same pre-tension conditions, the shear resistance of the fabrics of 0°/90° and +45°/−45° construction of the same areal density is close. Average angle of shear of a fabric corresponds to the shear angle of the frame. Variations of the local shear angle of the fabric do not exceed 2°.
6.6.2 Tension Tension resistance in two test directions is strongly coupled for a test in a bias direction, and is not significantly coupled for a test in the fibre directions. When two directions are coupled, the resistance in direction X increases with the increase of deformation ratio Y : X. Tension diagrams exhibit a non-linear region. Biaxial tension resistance of fabrics with 0°/90° and +45°/−45° construction of the same areal density is close.
6.6.3 Compression The behaviour of NCF in compression exhibits common features, typical for compression of textile reinforcements in general. The initial stiffness is low, with reduction of thickness to 70–80% of the initial thickness at a pressure of 50 kPa. With the pressure increase to the maximum value of 200 kPa, the thickness of the fabric additionally decreases to about 60–70% of the initial thickness. The compressive resistance significantly increases after the first compressive cycle, becoming stable in the subsequent cycles. Instron compressive diagrams of the first cycle coincide with KES-F measurements. Compression diagrams of all the studied unsheared fabrics can be estimated by formula 6.2 with the shape parameters p* and a constant, and thickness parameters T0 and Tmin linearly depending on the areal density of the fabric. The limited nesting effect has been confirmed for NCF under different pressure levels.
6.6.4 Bending The measured values of bending rigidity and its anisotropy correspond to measurements of bending rigidity of carbon tows and simple model Equation 6.4. A rough estimation of bending rigidity of carbon NCF is given by the value 0.2–0.6 Nmm2/Ktex
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References
Boisse, P., A. Cherouat, J. C. Gelin and H. Sabhi (1999). Experimenal study and finite element simulation of a glass fibre fabric shaping process. Polymer Composites 16(1): 83–95. Cao, J., R. Akkerman, P. Boisse, J. Chen, H. S. Cheng, E. F. d. Graaf, J. L. Gorczyca, P. Harrison, G. Hivet, J. Launay, W. Lee, L. Liu, S. V. Lomov, A. Long, E. d. Luycker, F. Morestin, J. Padvoiskis, X. Q. Peng, J. Sherwood, T. Stoilova, X. M. Tao, I. Verpoest, J. Wiggers, A. Willems, T. X. Yu and B. Zhu (2008). Characterization of mechanical behavior of woven fabrics: experimental methods and benchmark results. Composites Part A 39: 1037–1053. Chen, B., A. H.-D. Cheng and T.-W. Chou (2001). A nonlinear compaction model for fibrous preforms. Composites part A 32: 701–707. Chen, Z. R., L. Ye and T. Kruckenberg (2006). A micromechanical compaction model for woven fabric preforms. Part I: Single layer. Composites Science and Technology 66(16): 3254–3262. Endruweit, A., S. Gehrig, and P. Ermanni (2003). Mechanisms of hydrodynamically induced in-plane deformation of reinforcement textiles in resin injection processes. Journal of Composite Materials 37(18): 1675–1692. Gutowski, T.G., J. Kingery and D. Boucher (1986). Experiments in composites consolidation: fiber deformation. Annual Technical Conference of the Society of Plastic Engineers. Brookfield: 1316–1320. Hammani, A. and B. R. Gebart (2000). Analysis of the vacuum infusion molding process. Polymer Composites 21(1): 28–40. Harrison, P., J. Wiggers, A. C. Long and C. D. Rudd (2003). Constitutive modelling based on meso and micro kinematics for woven and stitched fabrics. Proceedings ICCM-14. San Diego: CD edition. Hoersting, K. ed. (1998). Rationalising the production of long fibre reinforced composite materials using multiaxial multiply fabrics. Aachen, Shaker Verlag. Jiang, Y. and J. Hu (1999). Characterizing and modelling bending properties of multiaxial warp-knitted fabrics. Textile Research Journal 69(9): 691–697. Kawabata, S., M. Niwa and H. Kawai (1973). The finite-deformation theory of plain weave fabrics. Part I. The biaxial-deformation theory. Journal of the Textile Institute 64(1): 21–46. Kawabata, S., M. Niwa and H. Kawai (1973). The finite-deformation theory of plain weave fabrics. Part II. The uniaxial-deformation theory. Journal of the Textile Institute 64(2): 47–61. Launay, J., K. Buet-Gautier, G. Hivet and P. Boisse (1999). Analyse experimentale et modeles pour le comportement mechanique biaxial des renforts tisses de composites. Revue des composites et des materiaux avances 9(1): 27–55. Launay, J., G. Hivet, A. V. Duong and P. Boisse (2008). Experimental analysis of the influence of tensions on in plane shear behaviour of woven composite reinforcements. Composites Science and Technology 68(2): 506–515. Lebrun, G., M. N. Bureau and J. Denault (2003). Evaluation of bias extension and picture frame test methods for the measurement of intraply shear properties of PP/glass commingled fabrics. Composite Structures 61: 341–352. Lee, J. S., S. J. Hong, W. R. Yu and T.J. Kang (2007). The effect of blank-holder force on the stamp forming behavior of non-crimp fabric with a chain stitch. Composites Science and Technology 67(3–4): 357–366. Lomov, S. V., M. Barburski, T. Stoilova, I. Verpoest, R. Akkerman, R. Loendersloot and R. H. W. ten Thije (2005). Carbon composites based on multiaxial multiply stitched
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preforms. Part 3: Biaxial tension, picture frame and compression tests of the performs. Composites part A 36: 1188–1206. Lomov, S. V., P. Boisse, E. Deluycker, F. Morestin, K. Vanclooster, D. Vandepitte, I. Verpoest and A. Willems (2008). Full field strain measurements in textile deformability studies. Composites part A 39: 1232–1244. Lomov, S. V., T. Stoilova and I. Verpoest (2004). Shear of woven fabrics: Theoretical model, numerical experiments and full field strain measurements. Proceedings of the 7th Esaform Conference on Material Forming. Trondheim, Norway: 345–348. Lomov, S. V., T. Truong Chi, I. Verpoest, T. Peeters, V. Roose, P. Boiss and A. Gasser (2003b). Mathematical modelling of internal geometry and deformability of woven preforms. International Journal of Forming Processes 6(3–4): 413–442. Lomov, S. V. and I. Verpoest (2000). Compression of woven reinforcements: a mathematical model. Journal of Reinforced Plastics and Composites 19(16): 1329–1350. Lomov, S. V. and I. Verpoest (2006). Model of shear of woven fabric and parametric description of shear resistance of glass woven reinforcements. Composites Science and Technology 66: 919–933. Lomov, S. V., I. Verpoest, M. Barburski and J. Laperre (2003a). Carbon composites based on multiaxial multiply stitched preforms. Part 2: KES-F characterisation of the deformability of the preforms at low loads. Composites part A 34(4): 359–370. Lomov, S. V., I. Verpoest, T. Peeters, D. Roos and M. Zako (2002). Nesting in textile laminates: Geometrical modelling of the laminate. Composites Science and Technology 63(7): 993–1007. Lomov, S. V., A. Willems, I. Verpoest, Y. Zhu, M. Barburski and T. Stoilova (2006). Picture frame test of woven fabrics with a full-field strain registration. Textile Research Journal 76(3): 243–252. Long, A. (2000). Process modelling for textile composites. International Conference on Virtual Prototiping EUROPAM 2000. Nantes: 1–17. Long, A. C., B. J. Souter, F. Robitaill and C. D. Rudd (2002). Effects of fibre architecture on reinforcement fabric deformation. Plastics, Rubber and Composites 31(2): 87–97. Mohammed, U., C. Lekakou, L. Dong and M. G. Bader (2000). Shear deformation and micromechanics of woven fabrics. Composites Part A 31: 299–308. Nguyen, M., I. Herszberg and R. Paton (1999). The shear properties of woven carbon fabrics. Composite Structures 47: 767–779. Peng, X. Q., J. Cao, J. Chen, P. Xue, D. S. Lussier and L. Liu (2004). Experimental and numerical analysis on normalisation of picture frame tests for composite materials. Composites Science and Technology 64(1): 11–21. Robitaille, F. and R. Gauvin (1998a). Compaction of textile reinforcements for composites manufacturing. I: Review of experimental results. Polymer Composites 19(2): 198– 216. Robitaille, F. and R. Gauvin (1998b). Compaction of textile reinforcements for composites manufacturing. II: Compaction and relaxation of dry and H2O-saturated woven reinforcements. Polymer Composites 19(5): 543–557. Robitaille, F. and R. Gauvin (1999). Compaction of textile reinforcements for composites manufacturing. III. Reorganization of the fiber network. Polymer Composites 20(1): 48–61. Sharma, S. B., M. P. F. Sutcliff and S.H. Chang (2003). Characterisation of material properties for draping of dry woven composite material. Composites Part A 34: 1167– 1175.
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Willems, A., S. V. Lomov, I. Verpoest and D. Vandepitte (2008). Optical strain fields in shear and tensile testing of textile reinforcements. Composites Science and Technology 68: 807–819. Willems, A., S. V. Lomov, I. Verpoest and D. Vandepitte (2009). Drape-ability characterization of textile composite reinforcements using digital image correlation. Optics and Lasers in Engineering 47: 343–351. Yu, W. R., P. Harrison and A. Long (2005). Finite element forming simulation for noncrimp fabrics using a non-orthogonal constitutive equation. Composites Part A 36: 1079–1093. Yu, W. R., P. Harrison and A. C. Long (2004). Ideal forming of non-crimp fabric preforms through optimization of blank shape and blank holding force. Proceedings ESAFORM-2004. Trondheim: 309–312.
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Plate I Difference of the shear angle of the fabric B2 and frame shear angle (a), error bars show standard deviation; image of the deformed fabric B2, frame shear angle 14° (b) and distribution of the fabric shear angle (c) (Chapter 6).
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7 Modelling the deformability of biaxial non-crimp fabric composites P. HARRISON, University of Glasgow, UK, W-R. YU, Seoul National University, Korea and A. C. LONG , University of Nottingham, UK
Abstract: This chapter is focused on modelling the forming behaviour of biaxial non-crimp fabrics (NCFs). In Section 7.1, the motivation for modelling NCFs is given. Following a short description of the meso-structure of NCFs (Section 7.2) the effect of the stitch architecture on the shear and forming behaviour of NCFs is demonstrated. In Section 7.3, the two main approaches to modelling the forming behaviour of NCF are reviewed and in Sections 7.4 and 7.5, the capabilities, advantages and disadvantages of each method are considered. In Section 7.6, likely avenues for future research are outlined. Key words: non-crimp fabric forming, modelling.
7.1
Introduction
Most engineering fabrics are supplied as planar sheets of material and are not initially manufactured in the shape of the final component that they are intended to create. Instead, they are required to conform to the component’s surface geometry through fabric draping. This raises several questions that must be considered when a manufacturer sets out to manufacture a part. The initial questions relate to the forming process itself. • •
• • •
How to drape the component without creating forming-induced defects or, alternatively, where to introduce cuts and darts in the fabric prior to forming in order to prevent wrinkles occurring? If press-forming the part, what are the optimum forming conditions for the process, for example, what pressure should be applied around the perimeter of the fabric (using a so-called ‘blank-holder’) and is there an optimum blankholder pressure distribution that can reduce forming defects? If hand-forming the part, where is the best place to begin draping – on the top of the component, or does some other starting point provide better fabric drapability? Could pre-shearing the fabric prior to forming help reduce defects such as wrinkles? The problem can also be inverted: can the fabric’s structure be tailored by the material supplier to produce bespoke fabrics more suitable for forming over a given component geometry?
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A further question arises, more directly relevant to the subsequent resin infusion stage of the manufacture, but directly informed by results of the fabric forming, namely: •
How will the final draped fibre pattern affect infusion of the resin through the dry fabric and how can the infusion strategy be modified (for example, repositioning of resin inlet and outlet valves) to account for this draped fibre pattern? (See also Chapters 8–10.)
Finally, but of equal importance, are questions relating to the component’s final quality and structural performance. •
How will the final draped fibre pattern influence the component’s dimensional stability when removed from the mould (spring forward or spring back) and crucially, how will this fibre pattern affect the component’s final structural performance? (See also Chapters 11–14.)
Determining the answers to these questions is a difficult task and most manufacturers currently use a combination of technical skill, practical experience and trial and error to produce components of acceptable quality; a blend of art and science. However, numerical simulation and the use of optimisation algorithms can play an important role in producing better components, resulting in savings in time, cost and final component weight. Recent advances in computational power coupled with the complexity and rewards in determining ideal manufacturing solutions have motivated the development of computer-aided engineering (CAE) tools aimed at creating a virtual try-out space for the manufacture of textile composites. While some experimental characterisation work on the forming of multiaxial (triaxial) non-crimp fabrics (NCFs) has been published (Kong et al., 2004), to the best of the authors’ knowledge, all modelling work published so far has been limited to biaxial NCFs and consequently provides the focus of work reviewed in this chapter.
7.2
Behaviour of fabric architecture on the shear and draping behaviour of non-crimp fabrics (NCFs)
The unique fabric architecture of biaxial NCFs results in deformation mechanisms (see also Chapters 6, 8 and 16) particular to these materials (Long et al., 2002; Wiggers et al., 2003; Thije et al., 2003; 2005a; 2005b; 2007; Harrison et al., 2004a; Kong et al., 2004; Creech et al., 2003; Creech and Pickett, 2006). As with woven fabrics, micro-mechanisms include fibre–fibre interactions within the tows during both tow compaction (in-plane and through-thickness) and intra-tow in-plane shear. Certain meso-scale mechanisms are unique to NCFs: stitch strain and inter-stitch friction, stitch-tow interactions, and tow-slip through the stitching. In contrast, crossover slip involving relative lateral motion of the two layers of tows is common to both woven fabrics and NCFs; though this particular mechanism is much less
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obvious in woven fabrics as the interweaving of tows tends to restrict lateral motion in comparison to the relatively unconstrained tows in NCFs. The challenge to the modeller is in accounting for these mechanisms in NCFs during forming. As will be discussed, the approach adopted in modelling the material determines to a large extent which of these mechanisms are incorporated in the model. Figure 7.1 shows an example of the front and back faces of a +/−45° NCF knitted with a tricot stitch pattern. Figure 7.1a shows the NCF in an undeformed state with the two sets of fibres perpendicular (the fibre directions are indicated by
7.1 Shearing the fabric in different directions produces different amounts of strain in the fabric stitching, resulting in significantly different fabric shear compliance in the two directions. The superimposed arrows indicate the fibre directions in: (a) an unsheared fabric; (b) a fabric sheared parallel to the stitch direction; and (c) a fabric sheared perpendicular to the stitch direction.
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superimposed arrows). Figures 7.1b and c show the fabric when extended in the two different bias directions (at 45° to the original fibre directions), i.e. parallel and perpendicular to the stitch direction. The figure demonstrates how extending the fabric leads to trellis shear (the angle between the two sets of tows either increases or decreases) resulting in either stretching or compression of the fabric stitching. Note that this mode of deformation does not require the fibre tows to stretch, instead the two sets of tows rotate relative to each other (indicated by the change in the included angle between the arrows shown in Fig. 7.1). Extending the fabric parallel to the stitch, Fig. 7.1b, stretches the stitching, whereas extending the fabric perpendicular to the stitch, Fig. 7.1c, compresses the stitching. As one might imagine, this results in very different shear compliance depending on the direction of fabric shear. Typical shear force versus shear angle curves produced using picture frame tests, similar to those described in Chapter 6, are presented in Fig. 7.2. The tests were performed on a ±45° tricot warp knit NCF (Souter, 2001). Figure 7.2 clearly demonstrates the large difference in shear compliance of the NCF when shearing in opposite directions. The effect of this asymmetric shear response has an obvious influence on the forming behaviour of NCFs, as shown in Fig. 7.3. Here a NCF is draped over a symmetrical hemispherical geometry with symmetrical boundary conditions applied around the fabric blank-holder. This is the most obvious difference between the forming of NCFs and woven
7.2 Shear compliance curves for E-glass +/−45° tricot warp knitted fabric, highlighting the asymmetric shear properties due to the knitted thread. Here parallel indicates shearing parallel to the stitching direction (Souter, 2001).
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7.3 Formed shape of non-crimp fabric (Cotech Ebx318: +/−45° tows with chain stitch) after hemispherical forming showing asymmetric deformed shape due to the asymmetric shear behaviour (Souter, 2001).
fabrics and so any attempt to model the forming behaviour of NCFs must capture not only the strongly anisotropic mechanical response of the two directions of high modulus fibres, as with woven engineering fabrics, but also the asymmetric shear behaviour of the NCF resulting from its stitching. Strong differences in the degree of intra-ply slip seen in woven fabrics and NCFs are also evident in forming experiments; intra-ply slip is much more prevalent in NCFs. Thus, predictions of intra-ply slip should ideally also be possible when modelling NCFs.
7.3
Modelling strategies for NCF forming
Ideally, modelling predictions should be accurate (able to identify problem areas during draping and predict fibre angles), computationally inexpensive and input information should be simple and easy to acquire, preferably with a minimum amount of experimental characterisation. From a user perspective, models should also be easy to use and the software inexpensive to buy. The challenge in meeting these requirements has led to competing modelling strategies and the designer’s final choice of approach depends on the weighting assigned to the different goals. Kinematic mapping methods (e.g. Mack and Taylor, 1956; van der Ween, 1991; Long and Rudd, 1994; Hancock and Potter; 2006a; 2006b) are computationally much less expensive than the finite element (FE) method and first order approximations of the forming behaviour can readily be obtained with minimal user training. A recent advance enables a user-interactive approach allowing quick investigation of different forming possibilities (Hancock and Potter, 2006a; 2006b). As such, the technique has become well established within composites
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manufacturing industries and a number of user-friendly codes are available commercially. However, most kinematic codes are designed to model the drape of woven fabrics. In order to capture the asymmetric material response of NCFs and also to include process boundary conditions, modifications to kinematic simulations have been made (Long, 2001; Long et al., 2002; 2005). This energybased kinematic method, reviewed in Section 7.4, provides an intermediate level of accuracy in modelling NCF forming, somewhere between the FE approach and unmodified kinematic mapping algorithms. However, when using the kinematic method one should keep in mind that under certain circumstances the technique can lead to significant errors (e.g. Vanclooster et al., 2009). FE simulations consider the mechanics of the forming process and can provide more accuracy. Not only are fibre angle predictions usually better, but wrinkling predictions and boundary conditions can also be modelled with greater accuracy than with kinematic models. FE simulations can also offer the possibility of predicting NCF-specific forming defects such as deviation from ideal trellis shear deformation, stitch breakage or tow pull-out (Creech et al., 2003; Creech and Pickett 2006; Thije et al., 2007). Even with these benefits, the FE method has yet to find widespread application in industry despite the availability of commercial codes dedicated to textile-forming mechanics. Reasons for the slow uptake of the FE method include the following. • • •
Much higher levels of user expertise and investment in staff training are required compared to that for kinematic codes. The constitutive models for engineering fabrics and NCFs necessary for the FE method are still undergoing development and validation. Correct material characterisation and consequent parameter determination for these models requires considerable time and expertise.
An example of how FE forming simulations can be used in the design of NCF components is given in Chapter 16.
7.4
Energy-based kinematic mapping
Kinematic modelling involves the assumption that the biaxial fabric deforms as a pin-jointed net (PJN). This means that the two sets of yarns are free to rotate at the crossovers between yarns and also that the yarns are inextensible. This approach provides a fast, first-order approximation to the draping behaviour of the fabric across a given geometry but, in its original form, the method does not include the asymmetric shear behaviour of the fabric or the effect of boundary conditions (see Section 7.2) and is thus limited in its ability to predict defects such as wrinkling or to provide much information on the effect of the boundary conditions for the forming process for NCFs. However, a modified version of the PJN technique has been proposed (Souter, 2001; Long, 2001; Long et al., 2002; 2005) based on an energy minimisation argument. The method behind the modified PJN technique
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involves optimisation of the simulations’ ‘generator paths’, the paths of two fibres passing over the component, for which the intersection angle between the paths is specified and from which the kinematic constraint of fibre inextensibility allows the rest of the draping pattern to be calculated. This modified PJN energy minimisation technique incorporates the material’s shear behaviour, albeit in a simple manner, and thus provides a numerical simulation option lying somewhere between the FE and basic PJN methods, both in terms of computation time and accuracy.
7.4.1 Modelling asymmetric shear behaviour In this modified approach (Souter 2001; Long et al., 2002; Long et al., 2005) the strain energy required to produce each mapping is calculated iteratively, with the mapping resulting in the lowest energy assumed to represent the actual behaviour of the fabric. The total strain energy is the sum of two components: the shearing energy involved in forming the material and the frictional energy involved in pulling the material from inside the blank-holder. The shear strain energy (Us) can be calculated simply from the area under the torque-shear angle curve: [7.1] where T(θ) is the torque required to reach a shear angle θ and can be obtained directly from a picture frame (PF) test (see Chapter 6) or alternatively predicted using analytical or numerical sub-models (see section 7.4.2). The total energy is calculated within the fabric drape simulation by summing the contribution at each node (tow crossover). A simple way to determine the drape pattern corresponding to the minimum energy is to use an iterative scheme and involves finding the two intersecting paths that result in the lowest total energy. To do this, a Hooke and Jeeves minimisation method is used, where the generator path is defined one step at a time from a user-defined starting point. Each successive set of nodes is optimised by iterating the generator path angle until the minimum energy for this iteration is determined. The procedure is described in detail elsewhere (Souter, 2001).
7.4.2 Prediction of trellis shear force versus shear angle behaviour for NCFs using analytical models As discussed in Section 7.2, various deformation mechanisms act during the forming of NCFs. Some of the mechanisms are relevant to ideal trellis shear; the deformation assumed in the kinematic mapping approach to modelling NCF forming. Other mechanisms, i.e. intra-ply slip, allow alternative deformation kinematics to occur. In an attempt to predict rather than measure the shear force
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versus shear angle input curves required in the energy-based kinematic mapping approach, energy contributions for each of the deformation mechanisms operating during ideal shear conditions were calculated, using a series of analytical or semianalytical sub-models (Harrison et al., 2003). Specifically, contributions from stitch strain, inter-stitch friction, fabric compaction and crossover friction were modelled. The assumption of ideal trellis shearing, which is implicit in the kinematic mapping approach, means that intra-ply slip mechanisms are not considered and so the model is unable to predict defects arising from intra-ply slip. Unit cell stitch model Using a geometric unit-cell stitch model, various energy storage/dissipation mechanisms can be analysed, including: stitch tension and inter-stitch friction. Consider the unit tricot stitch illustrated in Fig. 7.4. Shear deformation requires that sections of the stitch not parallel to the tow direction must change dimensions. The variation of c and d with shear angle, θ, can be determined from geometric constraints. Thus, [7.2]
[7.3]
7.4 The central diagram shows one example of a unit cell for a ±45° tricot warp knit non-crimp fabric. The diagrams on either side show the orientation of the stitch in relation to the front (left) and back (right) surfaces of the non-crimp fabric. Referring to the central diagram, the upper layer of tows run vertically (solid grey lines) and the bottom layer of tows run horizontally (dashed grey lines). The stitch runs over the tows (d, black solid line), pierces through the fabric (with a thickness, T ) and then runs under the tows (c, black dashed line).
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To determine the variation of the through-thickness stitch segments, T (see Fig. 7.4) the relationship between the stitch tension and tow compaction is required. As a first approximation, T is assumed constant with respect to shear angle (Souter, 2001). This is a reasonable assumption for dry fabrics with low initial fibre volume fraction, as the thickness variation only becomes relevant at high shear angles, where compaction forces dominate. Thije et al., (2005) confirmed this approximation for up to 30° of shear, beyond which thickness increases were observed (see also Chapter 8). Presuming the stitch passes freely through the stitch crossovers (illustrated in Fig. 7.5), the tension in the stitch can be considered constant through the entire length. Summing the overall length of the c, d and T sections gives the overall stitch length, L, in terms of shear angle. From this, the strain in the stitch εs, where the subscript s indicates that variables are related to the stitch, can be determined as [7.4] where Lo is the unstressed stitch length. The stitch is manufactured under a given strain, and so Lo does not necessarily correspond to L when θ = 0, the stitch length at zero shear. The stitching used in the material shows a fairly linear stress–strain relationship so that, prior to failure stitch stress, σs, is related to stitch strain as σs = Es εs. In terms of stitch tension, Ss = As·σs where As is the cross-sectional area of the stitch thread. The energy due to stitch extension, Us, is determined by integrating the stitch tension with respect to stitch length to find [7.5] Equation 7.5 applies for tension only, as the stitch shows virtually no compressive stiffness. This energy can be normalised with respect to the surface area of the unit cell, 2c0h0, and added to the energy contributions from other shear mechanisms. For a shear test in which the whole fabric is in constant, pure shear, this energy
7.5 An enlarged view of a stitch crossover. At the point at which the stitch passes through the fabric, it is constrained by the loop from a previous stitch (adapted from Wiggers, 2007).
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can be differentiated with respect to shear angle to produce an overall shear torque per unit length, τ, from which the shear force per unit length due to stitch extension can be calculated by dividing by cosΘ. Experimental observations confirm that the stitching does move through the fabric during shear, as assumed in the above analysis. A simple model for approximating the frictional resistance to stitch movement was proposed. Referring to Fig. 7.5, the stitching is taken to be stationary at the apex of the loop, as this is a point of symmetry with respect to both stitch tension and geometry. Considering the loop section of the stitch, c in Eq. 7.2, and the diagonal section of the stitch, d in Eq. 7.3, if the rate of strain imposed in these is not equal then the corresponding unequal tension would cause thread to pass from one to the other. Approximating the lateral force at the point of contact to the tension in the stitch, the frictional resistance, Ff, is given as Ff = µsSs, where µs is the dynamic friction of stitch on stitch movement. This force can be integrated with respect to distance and multiplied by the number of contact points in the unit cell (four) to find the energy dissipation due to stitch–stitch friction, Uf. This can subsequently be combined with the other energy dissipation/ storage mechanisms to find the total shear force of the fabric. Compaction model As a NCF is sheared and the degree of compaction within the fabric changes, energy stored or dissipated during this change can be estimated using compaction models. For convenience, the Cai and Gutowski (1992) model for compaction of lubricated fabrics, as adapted by McBride (1997) for dry aligned E-glass tows, has been used. Thus, given the following variation of volume fraction with shear angle (assuming constant thickness), [7.6] this equation is considered valid until Vf approaches the maximum volume fraction of 85% (McBride, 1997) at about θ = 60° (note, this is about twice the angle measured by Thije et al., 2003). Assuming zero axial strain, compaction stress lateral to the fibre direction, σc, can be derived as [7.7] where eb is the applied lateral strain, and the constants are evaluated as suggested by McBride (1997) for dry E-glass. The applied lateral strain can be expressed in terms of fibre volume fraction, which in turn can be related to the shear angle. This stress can be integrated to produce an energy term, Uc, the energy storage/ dissipation due to compaction. As indicated earlier, this can be added to the other energy contributions to find the total energy storage/dissipation. Conveniently, σb can also be used to provide an estimate of the pressure parameter in the crossover model, Pj, as discussed in the crossover model section.
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Crossover model In a woven textile composite, a crossover may be defined as the in-plane contact area existing between two individual tows. If the in-plane intra-tow shear rate of the individual tows is less than the average in-plane shear rate across the fabric then relative motion between the faces of the tows occurs. The relative velocity between the faces can be estimated using Eq 7.8 [7.8] . where is the relative velocity field between the crossovers, γt is the in-plane shear strain rate in both sets of tows and in the following calculation is considered constant in time, ω is the relative angular shear rate of the two sets of tows, θ is the material shear angle and X, Y are the position co-ordinates, with the origin at the centre of the crossover. If the normal pressure and coefficient of friction between the tows is known then a measure of the energy dissipation during shear can be made. Comparison of contributions of different mechanisms The separate normalised force contributions from each mechanism are shown in Fig. 7.6 and suggest that for a constant thickness assumption, the stitch tension provides the dominant contribution to the total shear force at low θ, with stitch friction providing the next largest contribution. At higher θ the compaction contribution becomes the most important mechanism. The crossover contribution appears to be negligible until relatively high values of θ. The sudden increase of
7.6 Four separate contributions to the total normalised shear force of the stitch fabric (from Wiggers, 2007).
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7.7 Forming set-up for Tay nose cone using a spring-loaded blankholder, also indicating line of maximum shear along which shear angle measurements were taken (from Long et al., 2005).
this contribution can be explained by the sharply increasing normal pressure, Pj, predicted by Eq. 7.6 and 7.7, as the fabric is compressed towards its maximum possible fibre volume fraction. Figure 7.7 shows that stitch contributions and fabric compaction are essential for accurate modelling of NCFs. Contributions from friction occurring between crossovers due to tow rotation are much less important and can probably be neglected.
7.4.3 Modelling the effect of the blank-holder During the energy minimisation algorithm, nodes are mapped to the surface one step or annulus at a time, so that at each step the area covered has grown by one row of nodes in the warp and weft directions. To incorporate the blank-holder friction energy contribution at each step, firstly the undeformed net-shape of the fabric is calculated. For every node around the perimeter of this undeformed net-shape, the distance to the initial starting (ply/tool contact) point is calculated. The projected distance between the corresponding draped node and the starting point is also calculated. The difference between these values represents the amount of material pulled through the blank-holder during the mapping. Frictional energy is calculated as the product of blank-holder force, friction coefficient and linear distance pulled through the blank-holder, multiplied by 2 as there are two contact interfaces. The total frictional energy dissipated during the mapping for the latest step is added to the total intra-ply shear energy and then minimised for each net-draping increment. In order to compare the modified code predictions with experiments, the forming of a jet engine nose cone was analysed (Long et al., 2005), using the tooling shown in Fig. 7.7. The pressure supporting the fabric was varied using eight spring-loaded pressure-pads around the blank-holder. Clamping force was varied by adjusting the spring compression for each pressure-pad, allowing the pressure to be varied around the perimeter. A uniform clamping pressure was used for all experiments. Simulation results are shown in Fig 7.8 and clearly show the
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7.8 Predicted fibre patterns for nose cone draped with tricot-stitched non-crimp fabric, with BHF of 0N (left), 126N (centre) and 252N (right) (from Long et al., 2005).
effect of the NCF’s asymmetric shear behaviour and also how the asymmetry of the draped fibre pattern decreases with increasing blank-holder pressure, an effect validated by their experiments and by others (Lee et al., 2007).
7.4.4 Modelling statistical variation of the manufacture process One important factor considered in other manufacturing environments is the prediction and optimisation of product variability and discard rates. Fabric reinforcements are variable in geometry; for example, tow spacing and orientations show a statistical distribution. This can lead to variable preform quality, ultimately increasing unit cost. Thus, understanding and predicting the effects of variability on the final part should allow variability to be controlled (see also Chapter 9). Variation in inter-tow angles for a nominally ±45° NCF, taken directly from the roll, i.e. before draping, has been measured (Endruweit et al., 2004; Yu et al., 2005a). Tow angles were found to adhere closely to a normal distribution, with a standard deviation of 5.6°. Long et al. (2005) presented a simple technique, using the Monte Carlo method, to incorporate the NCF fibre angle variability into the energy-based kinematic model. Predictions showed how this initial fabric variability could produce significant variation in the code’s fibre angle draping predictions. Clearly this variability can subsequently affect further processing behaviour, such as infusion (see Chapters 8 to 10) and ultimately will influence the final mechanical properties of the formed component (see Chapters 11, 14 and 16).
7.5
Finite element modelling of forming for NCFs
FE analysis of the forming of biaxial engineering fabrics is relatively young (e.g. Boisse et al., 1997) compared to the kinematic approach (e.g. Mack and Taylor, 1956). Having said this, intense effort over the past decade or so has resulted in an
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extensive body of work in this area. However, despite the large volume of work on woven fabrics, so far relatively little attention has been paid specifically to modelling the forming of NCFs using the FE approach. Notable exceptions include the work of Yu et al. (2005a; 2005b), Creech et al. (2003) and Creech and Pickett (2006) and Thije et al. (2003; 2005a; 2005b; 2007). Both Yu et al. (2005a; 2005b) and Creech and Pickett (2006) employed an explicit rather than an implicit FE numerical technique (Abaqus Explicit™ and PAM-CRASH™) when modelling the forming of the NCF sheet over tooling, due to its suitability in analysing problems with complex and changing contact conditions (see also Chapter 16). When modelling woven fabrics, both continuous and discrete modelling approaches, or a combination of these two, can be found in the literature. The same is true for modelling of NCFs; both Yu el al. (2005b) and Thije et al. (2005a; 2005b; 2007) adopted continuum approaches with twodimensional models implemented in structural membrane and/or shell elements, while Creech et al. (2003) and Creech and Pickett (2006) used a mixed, semidiscrete approach, incorporating solid elements to model individual tows and bar elements to represent the stitching.
7.5.1 Modelling asymmetric shear behaviour The constitutive model of Yu et al. (2005b) originally developed for woven fabrics, consists of two parts: contributions from fibre directional properties and shear properties. To model the stress and strain relationship dependent on the fibre directional properties, a non-orthogonal equation was developed in an explicit mathematical form using a homogenisation method taking into account the fabric architecture and yarn stiffness (Yu et al., 2002). The shear component of the equation was developed using a covariant analysis of the traction vector acting along the side of a biaxial fabric undergoing PF-type deformation. This resulted in an equation relating the in-plane shear stress in the NCF sheet to the shear force measured by PF tests on the same material. Thus, by fitting a polynomial function to the measured PF shear test result, a convenient method of determining the shear parameters of the model directly from test results was devised. The only change in the original model required in accommodating the asymmetric response of the NCF, rather than the symmetric response of a woven fabric, was to include different polynomial functions according to the direction of shearing of the NCF (with respect to the orientation of the stitch pattern). The approach also allows simple incorporation of the shear force versus shear angle predictions discussed in Section 7.4.2, rather than using PF test data to produce shear input data for the model, resulting in a fully predictive approach (Harrison et al., 2004a). Thije et al. (2003; 2005a; 2005b) originally used a viscous constitutive model, based on the ideal fibre-reinforced fluid model proposed by Spencer (2000) to model NCFs. In later work they implemented a hyperelastic constitutive equation and applied this to model NCFs (Thije et al., 2007). Both these models are
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symmetric in their shear response; thus, in order to model the asymmetric behaviour, the contribution to the total stress in the material due to the stitching was calculated using a vector representation for the stitch. Strains in the stitch were calculated via multiplication of the stitch vector by the deformation gradient tensor. Tensile stress–strain data for the stitching allowed conversion of strain to stress. This simple approach provided the stress contribution from stretching of the stitch and consequently an asymmetric shear response in the shear force versus shear angle curve during the simulation. However, the method neglects any contribution from inter-stitch friction, which, according to Fig. 7.6, is probably significant. Other model parameters accounting for trellis shear resistance due to compaction and rotation of the tows were determined via experimental testing. Finally, the approach adopted by Creech and Picket (2006) is based on the actual meso-scale architecture of the NCF, resulting in a geometrically more complicated but more realistic model than those adopted by Yu et al. (2005b) and Thije et al. (2003; 2005a; 2005b; 2007) (see also Chapter 16). A consequence is FE models with large degrees of freedom, e.g. 120 000 solid and 70 000 bar elements, and therefore much larger computation times. The two sets of tows within the fabric were modelled by two layers of solid elements divided into discrete rows and the stitch was modelled using bar elements, see Figure 7.9 (from Creech and Pickett, 2006). Thus, the model represents a special case in which the stitch positioning results in discrete tows within the fabric (in practice the more general situation is that the stitching tends to pierce tows resulting in so called ‘fish-eye’ openings in the fabric rather than discrete and continuous tows, see Chapter 6 for more details on the NCF’s internal geometry). They used a bi-phase material model for the solid tow elements (PAM-CRASH, 2000), fitting the transverse compression properties using PF test data, though the constant stiffness parameter in the bi-phase model resulted in problems with the fitting. The stitch properties were determined through PF tests using an analytical expression for the strain versus fabric shear angle, see Eqs 7.2–7.4 in Section 7.6. The approach assumed that most of the shear force produced by the NCF at low shear angles was due to the stitch contribution, an assumption confirmed in Fig. 7.6. Connector elements were used to model friction between tow and stitch (solid elements and bar elements), though here again inter-stitch friction was ignored.
7.9 A ‘representative cell’ of the meso-mechanical model for non-crimp fabric (from Creech and Pickett, 2006).
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7.5.2 Modelling of intra-ply slip The approach of Yu et al. (2005a; 2005b) while being fully predictive and relatively simple, prohibits prediction of any of the intra-ply slip mechanisms that can occur in NCFs. In contrast, the work of Thije et al. (2003; 2005a; 2005b; 2007) involves a method of modelling tow slip along the axial direction of the tow (see Fig. 7.10). To do this, they added additional layers and degrees of freedom to a membrane element, effectively creating a multi-layer element (Thije, 2005b). A similar methodology has also been used by the same group to model multi-layer forming of woven fabrics (Thije et al. 2009). The method provides a computationally efficient approach to calculating the contribution to the total stress due to tow slip along the tow directions (as opposed to crossover slip). However, predictions of the magnitude of the cumulative tow slip in their forming simulations have yet to be published. The model proposed by Creech and Pickett (2006) offers an intuitive but computationally more expensive way of determining intra-ply slip. In this case, both tow slip along the tow longitudinal directions and lateral crossover slip can be predicted. Both methods adopted by Thije et al. (2005a; 2005b) and Creech and Pickett (2006) require tow pull-out characterisation tests to determine the value of the tow/stitch friction coefficient (Kong et al., 2004).
7.10 Slip of the tows through the stitches in their axial direction (from Thije et al., 2005).
7.5.3 Modelling of out-of-plane bending stiffness The out-of-plane bending stiffness of engineering fabrics is partly responsible for the wrinkling behaviour during forming. Two-dimensional constitutive models are suitable for implementation in either membrane or shell elements. Membrane elements only allow calculation of in-plane stresses and assume zero out-of-plane bending stiffness, an assumption which can possibly overestimate the tendency of
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the fabric to wrinkle during forming. Thin shell elements treat the material as a continuum of small but finite thickness and automatically determine the associated out-of-plane bending stiffness from the elements in-plane properties. For engineering fabrics, which in practice do not behave as a continuum, the usual shell element formulation can lead to an unrealistically high out-of-plane bending stiffness and therefore lead to under-predictions of the wrinkling behaviour of the sheet. Yu el al. (2005c) presented a method of decoupling the in-plane and out-ofplane properties for shell elements, permitting more accurate modelling of the fabric’s wrinkling behaviour. In contrast, the method adopted by Creech et al. (2006), which involved the use of solid elements to represent the tows, meant the axial stiffness of the fabric had to be significantly decreased from its actual value in order to match the bending properties of the fabric with experiments. However, the stiffness still remained high enough to prevent significant stretching along the fibre directions during forming simulations. Thije et al. (2003; 2005a; 2005b; 2007; 2009) used a membrane element formulation for their simulations, neglecting any effect of out-of-plane bending stiffness.
7.5.4 Modelling the effect of the blank-holder The effect of increasing the blank-holder pressure in forming experiments was discussed in Section 7.4.3; increasing pressure tends to reduce the asymmetry of the draped fibre pattern for NCFs (Long et al., 2005; Lee et al., 2007). A suitable choice of friction coefficient between the NCF and tooling allows the effects of blank-holder pressure to be studied conveniently in FE simulations. Various doubly curved male tool geometries have been used to explore this effect. In Yu et al. (2005b), the effect of the blank-holder force on the forming behaviour over a hemisphere was investigated. Figure 7.11 shows how the asymmetry of the fabric drape pattern changes as the force on the blank-holder increases from 0 N to 5000 N. As with the kinematic energy-based simulations described in Section 7.4, the increase in the blank-holder force resulted in greater symmetry of the draped fibre pattern. Thije et al. (2005) similarly showed how introducing friction at the boundary reduced asymmetry when forming over a topped cone geometry.
7.5.5 Modelling statistical variation of the manufacture process In Section 7.4.4 an attempt to model the natural statistical variation in fibre angle of NCFs ‘off the roll’, using the energy-based kinematic method was described. A tentative first step to introduce the same variability into FE simulations was presented in Yu et al. (2005a). Though, as acknowledged by the authors, the method of randomly assigning fibre shear angles to elements meant that the fibre path was not preserved between adjacent elements, resulting in spurious stress predictions. In his PhD thesis, Wiggers (2007) describes a more consistent way of
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7.11 Effect of BHF on the formed shapes (from Yu et al., 2005).
generating a full-field variable fibre angle distribution for introduction into FE models, in future this variability could be incorporated into FE simulations.
7.6
Future trends
Optimisation algorithms have already been employed to explore the manufacturing design space associated with forming woven fabrics, such as blank-holder pressure and pressure distribution (Long et al., 2006). This approach involved the use of a simple and efficient forming code to narrow the design space using a genetic algorithm, followed by the use of a more accurate but computationally
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slower model in the final stages of optimisation. It is easy to see how a similar strategy could be adopted in optimising the forming of NCFs; with energy-based kinematic (e.g. Long et al. 2005) and continuum models (e.g. Yu et al. 2005b; Thije et al. 2007) performing the initial search while more detailed but computationally expensive models (e.g. Creech and Pickett, 2006) are employed in the final stages; providing detailed predictions of potential defects such as those described in Chapter 19. This approach will become ever more attractive as computational power continues to increase and textile-specific solid modelling software becomes more widely available for NCFs (e.g. TexGen; WiseTex). Further efforts to incorporate variability into simulations (see Sections 7.4.4 and 7.5.4), producing probabilistic rather than definitive predictions (Long et al., 2005; Yu et al., 2005a) and the consequent impact of this variability on final composite properties (Potter et al., 2008) is also a likely future development. Also, replacing time-consuming characterisation tests, such as those described in Chapter 6, using a multi-scale modelling strategy is a key issue. Once again, increases in computational power mean that numerical models at the micro-scale will become more feasible (Durville, 2008) eventually replacing less accurate analytical models (Cai and Gutowski, 1992; McBride 1997).
7.7
Further information and advice
Due to space limitations, only the constitutive models that have been directly applied to modelling NCFs have been reviewed. Several other models developed for woven fabrics have been proposed, which could potentially be adapted in modelling NCFs (e.g. Aimene et al., 2008; 2010; Xue et al., 2003; Lee et al., 2008; Peng et al., 2010). Also, another consideration when modelling the forming of biaxial fabrics that has been discussed in the literature, but not in this chapter, is the numerical problem of element locking that can occur when the fibre directions of the fabric are not aligned with the mesh (Yu et al., 2006; Thije and Akkerman 2008; 2009). Such locking can produce spurious results in FE simulations if the user is unaware of the problem.
7.8
References
Aimene, Y, Hagege, B, Sidoroff, F, Vidal-Sallé, E, Boisse, P and Dridi, S, 2008, Hyperelastic Approach for Composite Reinforcement Forming Simulations. International Journal of Material Forming, 1: 811–814. Aimene, Y, Vidal-Sallé, Hagege, B, Sidoroff, F and Boisse, P, 2010, A hyperelastic approach for composite reinforcement large deformation analysis. J. Comp. Mat., 44, 1, 5–22. Boisse, P, Borr, M, Buet, K, Cherouat, A, 1997, Finite element simulation of textile composite forming including the biaxial fabric behaviour. Compos Part B-Eng; 28B: 453–64. Cai Z and Gutowski, T, 1992, The 3D Deformation Behaviour of a Lubricated Fiber Bundle, Journal of Composite Materials, 26, 8, 1207–1237.
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Creech G, Pickett AK, Greve L, 2003, Finite element modelling of non crimp fabrics for draping simulation. Sixth International ESAFORM Conference on Material Forming. Salerno, Italy, 863–66. Creech G and Pickett AK, 2006, Meso-modelling of Non-Crimp Fabric composites for coupled drape and failure analysis, J Mater Sci, 41, 6725–6736. Durville, D, 2008, A finite element approach of the behaviour of woven materials at the microscopic scale. Eleventh Euromech-Mecamat conference Mechanics of microstructured solids: cellular materials, fiber reinforced solids and soft tissues, Torino, Italy. Endruweit, A Long, AC Robitaille, F Rudd, CD, 2004, Dependence of permeability variations on the textile structure, Proceedings of the eleventh European Conference on Composite Materials, Rhodes, Greece. Hancock, SG and KD Potter, 2006a, The use of kinematic drape modelling to inform the hand lay-up of complex composite components using woven reinforcements, Composites Part A, 37, 413–422. Hancock, SG and Potter, KD, 2006b, Implementation and applications of virtual fabric placement in forming fabric reinforcement for production of complex shaped components. Eighth International Conference on Textile Composites, Nottingham, UK. Harrison, P, Wiggers, J, Long, AC and Rudd, CD, 2003, A constitutive model based on meso and micro kinematics for woven and stitched dry fabrics. Fourteenth International Conference on Composite Materials, 14–18 July, San Diego, California, USA. Harrison, P, Yu, WR, Wiggers, J and Long, AC, 2004a, Finite Element Simulation of Fabric Forming, Incorporating Predicitons of a Meso-Mechanical Energy Model. Seventh International ESAFORM Conference on Materials Forming, 28–30 April, Trondheim, Norway. Kong, H, Mouritz, AP and Paton R, 2004, Tensile extension properties and deformation mechanisms of multiaxial non-crimp fabrics. Comp Struc, 66, 1–4, 249–259. Lee, JS, Hong, SJ, Yu, WR and Kang, TJ, 2007, The effect of blank-holder force on the stamp forming behaviour of non-crimp fabric with chain stitch. Comp. Sci. Tech., 67, 357–366. Lee, W, Cao, J, Badel, P and Boisse, P, 2008, Non-orthogonal constitutive model for woven composites incorporating tensile effect on shear behaviour. Int J Mater Form Suppl, 1, 891–894. Lin, H, Wang, J, Long, AC, Clifford, MJ and Harrison, P, 2007, Predictive modelling for optimization of textile composite forming. Composites Science and Technology, 67, 15–16, 3242–3252. Long, AC and Rudd CD, 1994, A simulation of reinforcement deformation during the production of preform for liquid moulding processes. International Mechanical Journal of Engineering and Manufacturing, 208, 269–278. Long, AC, An iterative draping simulation based on fabric mechanics, 2001. Proceedings of the fourth ESAFORM Conference on Materials Forming, Liège, Belgium. Long, AC, Souter, BJ, Robitaille, F and Rudd, CD, 2002, Effects of fibre architecture on reinforcement fabric deformation. Plastics Rubber & Composites, 31, 87–97. Long, AC, Wiggers, J and Harrison, P, 2005, Modelling the effects of blank-holder pressure and material variability on forming of textile preforms. Ninth International ESAFORM Conference on Material Forming, 2, 939–942, April, 27–29 April, Cluj-Napoca, Romania. Long, AC, Skordos, A, Harrison, P, Clifford, M and Sutcliffe, M, 2006, Optimisation of Sheet Forming for Textile Composites Using Variable Peripheral Pressure. Society for the Advancement of Material and Process Engineering (SAMPE), 27–29 March, Paris, France.
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Mack, C, Taylor, HM, 1956, The fitting of woven cloth to surfaces. J Textile Inst, 47(8), 477. McBride, TM, 1997, The Large Deformation Behaviour of Woven fabric Microstructural Evolution in Formed Textile Composites. PhD Thesis, Boston University College of Engineering. PAM-CRASH Theory Manual, 2000, ESI Group. Peng, XQ, Guo, ZY, Rehmen, ZU and Harrison, P, 2010, A Simple Anisotropic Fibre Reinforced Hyperelastic Constitutive Model for Woven Composite Fabrics. Thirteenth International ESAFORM Conference on Materials Forming, 7–9 April, Brescia, Italy. Potter, KD, Khan, B, Wisnom, MR, Bell, T and Stevens, J, 2008, Variability, fibre waviness and misalignment in the determination of the properties of composite materials and structures. Composites: Part A, 39, 9, 1343–1354. Souter, BJ, 2001, Effects of Fibre Architecture on Formability of Textile Preforms, PhD Thesis, University of Nottingham. Spencer, AJM, 2000, Theory of fabric-reinforced viscous fluids. Composites: Part A, 31, 1311–1321. ten Thije, RHW, Loendersloot, R and Akkerman, R, 2003, Material characterisation for finite element simulations of draping with non-crimp fabrics. Sixth ESAFORM conference on Materials Forming, Salerno, Italy, 859–862. ten Thije, RHW, Loendersloot, R and Akkerman, R, 2005, Drape simulation of non-crimp fabrics. Eighth ESAFORM conference on Materials Forming, Cluc Napoca Romania, 991–994. ten Thije, RHW and Akkerman, R, 2005, Finite element simulation of draping with noncrimp fabrics. Fifteenth International Conference on Composite Materials, Durban, South Africa (CD-ROM). ten Thije, RHW, Akkerman, R and Huétink, J, 2007, Large deformation simulation of anisotropic material using an updated Lagrangian finite element method, Computer Methods in Applied Mechanics and Engineering, 196, 33 34, 3141–3150. ten Thije, RHW and Akkerman, R, 2009, A multi-layer triangular membrane finite element for the forming simulation of laminated composites. Composites Part A, 40, 6–7, July, 739–753. ten Thije, RHW and Akkerman, R, 2008, Solutions to intra-ply shear locking in finite element analyses of fibre reinforced materials. Composites Part A, 39, 7, 1167–1176. TexGen 2008 http://texgen.sourceforge.net/index.php/Main_Page (accessed 23 February, 2010). Vanclooster, K, Lomov, SV, Verpoest, I, 2009, Experimental validation of forming simulations of fabric reinforced polymers using an unsymmetrical mould configuration. Composites: Part A, 40, 530–539. Van Der Ween, F, 1991, Algorithms For Draping Fabrics on Double-Curved Surfaces. International Journal for Numerical Methods in Engineering, 31, 1415–1426. Wiggers, J, Long, AC, Harrison, P and Rudd, CD, 2003, The Effects of Stitch Architecture on the Shear Compliance of Non-Crimp Fabrics. Sixth International ESAFORM Conference on Materials Forming Symposium on Composite Forming Processes, 28–30 April, Salerno, Italy. Wiggers, J., Analysis of Textile Deformation during Preforming for Liquid Composite Moulding. PhD thesis, University of Nottingham, 2007. WiseTex http://www.mtm.kuleuven.be/Research/C2/poly/software.html (accessed 23 February, 2010).
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Xue, P, Peng, XQ and Cao, J, 2003, A non-orthogonal constitutive model for characterizing woven composite. Composites Part A, 34, 2,183–93. Yu, WR, Pourboghrat F, Chung, K, Zampaloni, M. and Kang, TJ, 2002 Non-orthogonal Constitutive Equation for Woven Fabric Reinforced Thermoplastic Composites, Composites Part A, 33, 8, 1095–1105. Yu, WR, Harrison, P and Long, AC, 2005a, Finite Element Forming Simulation of NCF Considering Natural Fibre Variability. Eighth International ESAFORM Conference on Materials Forming, 27–29 April, Cluj-Napoca, Romania. Yu W.R., Harrison P. and Long A.C. 2005b, Finite Element Forming Simulation for Noncrimp Fabrics using a Non-Orthogonal Constitutive Equation, Composites Part A, 36, 1079–1093. Yu, WR, Zampaloni M, Pourboghrat, F, Chung K and Kang TJ, 2005c Analysis of flexible bending behavior of woven preform using non-orthogonal constitutive equation, Composites Part A, 36, 6, 839–850. Yu, X, Cartwright, B, McGuckin, D, Ye, L and Mai, YW, 2006, Intraply shear locking in finite element analysis of woven fabric forming processes. Composites Part A, 37, 790.
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8 Permeability of non-crimp fabric preforms R. LOENDERSLOOT, University of Twente, The Netherlands Abstract: Experimental permeability data of non-crimp fabrics (NCFs) is discussed in this chapter. The chapter starts with a general introduction on permeability, followed by a discussion on experimental permeability data. The influence of geometrical features of the textile architecture, in particular the stitching, is discussed in the third section, whereas the relation between fabric deformation and permeability is addressed in the fourth section. Two types of deformation can be distinguished: compression and in-plane shear. Both are addressed in this section. The chapter ends with concluding remarks, including comments regarding the benchmark project recently initiated and some future developments. Key words: permeability, experiments, textile geometry, compression, shear deformation.
8.1
Introduction
The permeability of a porous medium has been defined by Darcy (1856) as ‘the easiness with which a fluid, subject to a macroscopic pressure gradient, flows inside a porous medium’. Strictly speaking, the permeability only depends on the geometric characteristics of a given porous medium. It is a property of significant importance in the field of composite material processing technologies of the family of liquid composite moulding (LCM) processes, such as resin transfer moulding (RTM), vacuum-assisted resin transfer moulding (VARTM), liquid resin infusion (LRI), resin film infusion (RFI) and resin infusion under flexible tooling (RIFT). Knowledge of the permeability of a fibre reinforcement does not only allow estimation of the processing time, but also evaluation of the success rate or robustness of the process. Hence, a better quality control is achieved, which is crucial in manufacturing structural, load-bearing parts in, for example, aircraft applications. Such parts generally have a high fibre content and often also a complex geometry. Simulations are desirable to assess the robustness and quality of the injection or infusion process designed for this type of application, whilst avoiding costly experimental programmes. Therefore, detailed knowledge on the permeability of textile reinforcements is of utmost relevance. The permeability of textile reinforcements has been investigated by a large number of researchers. Research activities range from theoretical and numerical studies to experimental studies, using different methods and different measuring techniques. Despite a considerable history of research, a standardised measurement has not yet been established. A key factor is the large variation found in the results, which is also addressed in Chapter 9. Clearly, measuring the permeability of a 166 © Woodhead Publishing Limited, 2011
Permeability of non-crimp fabric preforms
167
textile reinforcement is not at all trivial. The discussion in this chapter is – in line with the topic of the book – limited to measurements of non-crimp fabric (NCFs). However, the reader should be aware of the fact that the topics addressed also partly apply to measuring the permeability of textile reinforcements in general. The results presented in the literature (see Section 8.2 for more details) show large deviations. Differences in measured permeability can be as large as an order of magnitude. Moreover, a significant amount of scatter is generally observed. The source of these differences can be attributed to a number of reasons, which are becoming more and more accepted. • • •
The permeability experiment is sensitive to precise conditions. The method of measuring can affect the results. The internal geometry of textile reinforcements has a certain degree of variability, directly affecting the fluid flow in the material.
It is beyond the scope of this book to discuss these topics in detail. The focus will remain on the experimental results obtained for NCF, rather than an elaborate discussion on the origin of deviations caused by the measuring technology applied. However, it is accepted that this type of deviation exists and hence it is considered as important to mention the methods applied, even without the formulation of a judgement. An exception is the last point, concerning the internal geometry of the fabric. The internal geometry of NCF is discussed in detail in Part II of this book. The effects on the permeability of the internal geometry, including fabric deformation (see also Part I), is addressed here. Research over the past few years has established a theoretical foundation for the concept that the variability in the internal geometry is one of the main factors in the scatter observed in the permeability (Bechtold and Ye, 2003; Chen and Papathanasiou, 2008; Endruweit et al., 2006a, 2006b; Frishfelds et al., 2003; Hoes, 2002; Hoes et al., 2004; Loendersloot, 2006; Loendersloot et al., 2006; Lundström et al., 2000b, 2004, 2010; Nordlund, 2006; Nordlund et al., 2006). Here, the focus is on the identification based on observations from experiments, whereas the link to modelling strategies is discussed in Chapter 9. Relevant sources of permeability data are found in the results of the fifth Framework EU research programme FAiLure, performance and processing prediction for enhanced design with non-crimp fabric COMposites – GRD12001-40184 (FALCOM), the TECABS Brite Euram project and measurements performed by the author in an EU-funded Marie Curie Fellowship programme (HPMT-CT-2000-0030) at the Katholieke Universiteit (KU) Leuven. These results are supplemented with results obtained in the permeability benchmark project, initiated by S.V. Lomov (KU Leuven) and B. Laine (ONERA) at the seventh FPCM conference, organised at the École des Mines de Douai, France 2006. Other results found in the literature are added to the list of results, providing an overview as complete as possible of experimental permeability data.
© Woodhead Publishing Limited, 2011
168
Non-crimp fabric composites
8.2
Experimental permeability results
Various methods are available to measure the permeability of a textile reinforcement. A concise discussion on these methods is presented to better understand the results obtained and reported in the literature. Secondly, an overview is presented of the results found in the literature.
8.2.1 Measuring technologies The internal geometry of an NCF has to be described at multiple scales, see Figure 8.1, in order to fully capture its deformability (as discussed in Part I) and also to model its permeability (as will be discussed in Chapter 10). Three levels are distinguished: the scale of the preform (macro: 10−1–100 m), the scale of the bundles and stitches (meso: 10−3–10−2 m) and the scale of the fibre filaments (micro: 10−5 m). However, it is extremely difficult, if not impossible, to quantify the effects of multiple length scales in permeability experiments. The only practical solution appears to be to measure the permeability at a macro scale (preform scale) under various conditions and attempt to explain the global observations with model predictions based on multi-scale models. The theory applied to calculate a permeability value from experimental data is based on Darcy’s law: [8.1] with v the fluid velocity vector, K the permeability tensor, µ the dynamic viscosity of the fluid and ∇P the pressure gradient vector. This could be considered as a homogenised relation. The permeability tensor K contains the orthogonal components
8.1 Schematic representation of a non-crimp fabric. The geometry of a non-crimp fabric can be assessed at three different length scales: the preform scale (macro: 10−1–100m), the scale of the bundles and stitches (meso: 10−3–10−2m) and the fibre filament scale (micro: 10−5m). This meso level representation does not correspond to non-crimp fabrics of later date, which possess more homogeneously spread plies of fibres, rather than individual fibre bundles in each ply (meso scale image courtesy of R.H.W. ten Thije).
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Permeability of non-crimp fabric preforms
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of the macroscopic permeability. The meso- and microscopic effects are not directly captured by this value, but may appear by variations in the macroscopic permeability depending on the measuring conditions. The permeability measured can therefore appear to be dependent on more than the geometry only (Kim and Daniel, 2007). Various measuring technologies have been developed. Initially, only the in-plane permeability of fabrics (K1, K2) was investigated, since only plate-like structures were manufactured using LCM production technologies. Recent developments in structural, load-bearing aircraft components have raised the need for a complete characterisation of the permeability tensor. The difficulties involved in measuring a three-dimensional (3D) permeability in a single measurement are in general avoided by measuring the in-plane and out-of-plane or transverse permeability K3 separately, although a few references are available (Ahn et al., 1995; Saouab et al., 2001; Stöven et al., 2003) on measuring the 3D permeability tensor. Stöven et al. (2003) performed 3D measurements on NCFs, which are presented in this chapter. A brief discussion on measuring conditions is considered appropriate, prior to a more detailed discussion on the experimental results of the permeability measurements. First of all, a distinction is made between pressure-driven and flow-driven measurements. Injection of the fluid at a constant pressure can lead to high fluid flows in the first moments of the measurement, potentially resulting in problems such as fibre-wash and other instabilities. A constant flow rate requires a more complex control and different flow regimes can occur (hydrostatic or capillary pressure driven flows) due to the large difference in pressure gradient during the process. A steady state is obtained as the textile is fully wetted (Bréard et al., 2003). A more stable flow and higher reproducibility is obtained compared to transient permeability measurements. However, the saturated permeability cannot be measured by all injection strategies and, moreover, is most likely an inadequate estimate for the unsaturated permeability. Two variants of in-plane permeability measurements exist: line-injection and central injection, both conceptually shown in Fig. 8.2a and b. The theory to extract permeabilities from the measured quantities such as the flow-front position, pressure gradient and/or volumetric flow, is beyond the scope of this book. The reader is referred to other literature for theory and comparison of both technologies (Ferland et al., 1996; Han et al., 2000; Heardman et al., 2004; Lekakou et al., 1996; Lundström et al., 1999, 2002; Wang et al., 1994; Weitzenböck et al., 1999a, 1999b). The main characteristics of the measuring methods are listed in Table 8.1. The parallel injection strategy (Lundström et al., 1999) is also included in Table 8.1. A limited number of measuring devices for transverse permeability is developed (Drapier et al., 2002; Scholz et al., 2007; Van de Ven et al., 2006; see Figure 8.2c). The characteristics are listed in Table 8.1). In most cases, the saturated permeability is measured, although Drapier et al. (2005) reports on unsaturated transverse permeability measurements.
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170
Non-crimp fabric composites
8.2 Typical line, radial and transverse permeability measuring equipment. (a) Line injection set-up. Dashed lines indicate the upper mould half. The upper mould can either be rigid (RTM) or flexible (RFI, VARI, RIFT). (b) Radial injection set-up. Dashed lines indicate the upper mould half. The upper mould can either be rigid (RTM) or flexible (RFI, VARI, RIFT). (c) Cross-section of a transverse permeability measuring device. The preform is compressed between a honeycomb (or similar) construction. Generally, tube-shaped devices are employed.
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Permeability of non-crimp fabric preforms
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8.2.2 Measured permeabilities The earliest experimental permeability data on NCF date from the beginning of the 1990s (Gebart, 1992; Parnas et al., 1995; Steenkamer et al., 1995). Over the years, large differences are observed, which are partly attributed to differences in material and partly to evolutions in the measuring technology. The latter is also a result of an increasing understanding of the process parameters governing the flow through porous media, leading to a higher quality of measurements. However, there has also been a development in the fabric material itself, affecting the permeability. Early results generally refer to fabrics with a more distinct separation between individual bundles in each ply, which are stitched together to obtain their structural integrity. These fabrics are often referred to as ‘engineered fabrics’. NCFs of a later date tend to possess more evenly, and consequently more densely spread fibre plies, in which the distinction between individual fibre bundles has nearly vanished. The New Concept 2 (NC2) NCF (Drapier et al., 2002) manufactured by Hexcel is the latest example of the manufacturer’s attempts to increase the homogeneity of the individual fibre plies of the fabric (see also Chapter 2.4).
© Woodhead Publishing Limited, 2011
© Woodhead Publishing Limited, 2011
Prone to race tracking Single measurement required for full in-plane permeability tensor
Yes
Yes
Prone to race tracking
Multiple measurements required for full in-plane permeability tensor
Constant pressure
Constant flow rate
Robustness
Limited number of data points required ∼300 mm
Limited number of data points required
∼300 mm
Typical flow length
Visual flow front tracking possible
Visual flow front tracking possible
Data acquisition
More complex mould design required
Mould requirements low
Experimental complexity
Low
Low
Mathematical complexity
Yes
Yes
Yes
Yes
Saturated
Yes
Yes
Parallel injection
Unsaturated
Linear injection
∼200 mm
Higher number of data points required
Visual flow front tracking possible
More complex mould design due to clamping requirements
High
Potentially high mould deflections Single measurement required for full in-plane permeability tensor Allows measurements on sheared fabrics
Sensitivity for preform inaccuracies in the centre
Seldom
Yes
No
Yes
Radial injection
More complex mould design to allow fabric compression without introducing flow obstruction
Low
Potential absence of stable flow regime due to low flow length
Yes
Yes
Yes
Very limited
Transverse injection
∼200 mm (in-plane) ∼10 mm (transverse)
∼5–10 mm
Higher number of data Limited number of data points required points required
Limited visual flow Difficult flow front tracking front tracking possible
High
Single measurements required for full 3D permeability tensor
Yes
Yes
No
Yes
Three-dimensional
Table 8.1 Overview of general properties, advantages and disadvantages of permeability measuring technologies
Permeability of non-crimp fabric preforms
173
Another difference between the experimental results reported is the test fluid used. Micro-level flow phenomenon can be reflected in a different macroscopic permeability and explain differences in measured permeabilities. According to Luo et al. (2001), the effect is not significant compared to the experimental scatter. The combination of fibre sizing and test fluid is reported to have a more pronounced affect on the wetting permeability according to Sharma et al. (2009). A graphical overview of the permeabilities measured is found in Fig. 8.3. A distinction is made between the in-plane permeability of carbon and glass fibre fabrics (Fig. 8.3a and 8.3b, respectively) and the transverse permeability (all
8.3 Measured permeabilities. The labels refer to the fabrics listed in Tables 8.2–8.6. UT: University of Twente; NLR: National Aerospace Laboratories; CLS: Clausthal; CTS: Center of Structures Technologies; UoN: University of Nottingham; SiComp: Swedish Institute of Composites. (a) In-plane permeability of carbon fibre non-crimp fabrics. Note that fabrics B3 and B4 were measured by a number of institutes and that T1 and B3 comprises a series of different variants of the same fabrics. (Continued)
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174
Non-crimp fabric composites
(b) In-plane permeability of glass fibre non-crimp fabrics. (c) Transverse permeability of carbon and glass (B7 and T2 only) fibre non-crimp fabrics.
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Permeability of non-crimp fabric preforms
175
carbon fibre, except the biaxial fabric B7 and the triaxial fabric T2). The markers in the graphs indicate the type of measuring technology applied. Filled markers refer to saturated permeabilities, whereas the open markers refer to unsaturated permeabilities. The error bars are either based on the variability provided by the authors of the articles from which the data are extracted, or calculated from the data set available. No information on the variability is available for the data points without error bars. Moreover, the variability is only calculated if three or more permeabilities were available. The fabrics can be identified by the code (U = uniaxial, B = biaxial, T = triaxial, Q = quadriaxial, M = multiaxial, the subscript is the fabric number) and can be traced back in the Tables 8.2 to 8.6, which also include references to the articles from which the data are extracted. The variability is calculated assuming a lognormal distribution of the permeabilities measured. This assumption is based on the observations on the dimensions of the stitched induced distortions in the internal geometry (Loendersloot, 2006), which also exhibit a lognormal distribution. Another motivation is that the lower limit of the variability is unlikely low if a normal distribution is assumed. The upper and lower bounds s+ and s− of the variability are calculated as:
[8.2]
with:
[8.3]
and t0.95(N−1) the Student-t-distribution with N−1 degrees of freedom and a 95% – significance level, N the number of permeabilities measured Ki, and K the mean permeability. The subscript ln indicates the value is calculated in the logarithmic space. Note that the value of a Student-t-distribution with 2 degrees of freedom (three measurements) equals approximately 4.3. The scatter can therefore be quite large, given the low number of measurements that is generally performed. A number of observations can be made from the graphs. The most obvious one is the huge differences between seemingly similar fabrics. The lowest permeabilities for the carbon fibre NCFs are approximately 2–3·10−11 m2, whereas the highest values are approximately 1–3·10−9 m2. The most striking point of this observation
© Woodhead Publishing Limited, 2011
© Woodhead Publishing Limited, 2011
U3
Ahlstrom R12-256
Ahlstrom R12-256
Ahlstrom R12-256
Ahlstrom R12-256
Ahlstrom R12-256
Ahlstrom R12-256
TechTextiles E-LPb
TechTextiles E-LPb
TechTextiles E-LPb
TechTextiles E-LPb
(1)
(2)
(3)
(4)
(5)
(6)
(1)
(2)
(3)
(4)
Saertex 12K T700 600
U1
U2
Name
ID
—
—
—
—
0.266
0.266
0.266
0.266
0.266
0.266
0.64
ρA [kg·m−2]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[90]
θ [°]
1.64E-10
1.24E-10
3.20E-10
2.89E-10
—
5.00E-11
—
1.10E-10
2.24E-10
8.25E-10
—
K1,unsat [m2]
—
—
—
—
—
—
—
—
—
—
4.80E-11
K1,sat [m2]
3.93E-11
3.29E-11
8.67E-11
6.15E-11
8.00E-12
—
2.00E-11
—
3.50E-11
1.10E-10
—
K2,unsat [m2]
—
—
—
—
—
—
—
—
—
—
2.10E-11
49.9
49.9
44.3
44.3
55
59
48
52
45
35
60
K2,sat [m2] Vf [%]
1
1
1
1
17
15
17
15
13
10
5
Radial
Radial
Radial
Radial
Linear
Linear
Linear
Linear
Linear
Linear
Linear
N [-] Method
Table 8.2 Basic characteristics of uniaxial fabrics and characteristics and results of in-plane permeability experiments
Weitzenböck et al., 1999a
Weitzenböck et al., 1999a
Weitzenböck et al., 1999a
Weitzenböck et al., 1999a
Gebart, 1992
Gebart, 1992
Gebart, 1992
Gebart, 1992
Gebart, 1992
Gebart, 1992
Labordus, 2004
Reference
© Woodhead Publishing Limited, 2011
B3
B2
B1
ID
Saertex biaxial
Saertex biaxial
Devold biaxial
Devold biaxial
Devold biaxial
Devold biaxial
Devold biaxial
Devold biaxial
(2)
(3)
B(1)
B(2)
B(3)
B(4)
B(5)
B(6)
Saertex biaxial
(3)
Saertex biaxial
Saertex biaxial
(2)
(1)
Saertex biaxial
(1)
Name
0.534
0.534
0.534
0.534
0.534
0.534
0.329
0.329
0.329
0.322
0.322
0.322
[45/−45]
[45/−45]
[45/−45]
[45/−45]
[45/−45]
[45/−45]
[0/90]
[0/90]
[0/90]
[45/−45]
[45/−45]
[45/−45]
ρA [kg·m−2] θ [°]
2.47E-11
3.48E-11
7.25E-11
5.18E-10
5.33E-10
9.01E-10
2.66E-09
5.10E-09
3.50E-09
2.18E-09
4.30E-09
3.90E-09
2.60E-11
2.02E-11
8.40E-11
9.24E-10
6.56E-10
2.74E-09
—
—
—
—
—
—
1.62E-11
2.93E-11
7.13E-11
—
—
—
6.00E-10
2.59E-09
3.10E-09
8.71E-10
2.53E-09
2.99E-09
K1,unsat [m2] K1,sat [m2] K2,unsat [m2]
1.65E-11
1.68E-11
8.81E-11
—
—
—
—
—
—
—
—
—
K2,sat [m2]
54.9
54.9
56.69
57.45
54.85
50.28
52.28
42.68
36.97
52.17
41.78
36.18
Vf [%]
0
0
0
0
0
0
45
30
0
45
30
0
γ [°]
7
7
7
4
2
1
1
1
1
1
1
1
N [-]
Parallel
Parallel
Linear
Linear
Linear
Linear
Radial
Radial
Radial
Radial
Radial
Radial
Method
Table 8.3 Basic characteristics of biaxial carbon fibre fabrics and characteristics and results of in-plane permeability experiments
(Continued)
Loendersloot, 2006
Loendersloot, 2006
Loendersloot, 2006
Loendersloot, 2006
Loendersloot, 2006
Loendersloot, 2006
Loendersloot, 2006
Loendersloot, 2006
Loendersloot, 2006
Loendersloot, 2006
Loendersloot, 2006
Loendersloot, 2006
Reference
© Woodhead Publishing Limited, 2011
B6
B4
ID
Hexcel NC2
Hexcel NC2
(3)
Saertex 6K T700 600
Hexcel NC2
G
(2)
Devold biaxial
H
(1)
Devold biaxial
S
Devold biaxial
Devold biaxial
M
Devold biaxial
Devold biaxial
L
G(2)
Devold biaxial
(1)
Devold biaxial
T
Devold biaxial
F2
F1
Name
Table 8.3 Continued.
0.64
0.534
0.534
0.534
0.534
0.534
0.534
0.534
0.534
0.534
0.534
0.534
0.534
[0/90]
[45/−45]
[45/−45]
[45/−45]
[45/−45]
[45/−45]
[45/−45]
[45/−45]
[45/−45]
[45/−45]
[45/−45]
[45/−45]
[45/−45]
ρA [kg·m−2] θ [°]
1.80E-11
8.93E-11
—
1.54E-11
9.86E-11
2.60E-11
9.73E-11
5.89E-11
1.01E-10
3.84E-11
6.63E-11
1.64E-10
3.72E-10
—
—
8.00E-11
—
1.15E-10
2.39E-11
9.09E-11
6.45E-11
1.06E-10
4.62E-11
7.19E-11
4.28E-11
3.82E-10
—
4.22E-11
—
6.35E-12
—
2.02E-11
—
6.19E-11
—
—
—
—
—
K1,unsat [m2] K1,sat [m2] K2,unsat [m2]
—
—
3.29E-11
—
—
1.92E-11
—
7.30E-11
—
—
—
—
—
K2,sat [m2]
60
48
50
50.8
56.69
54.8
56.69
56.69
56.69
56.69
56.69
60.34
50.28
Vf [%]
0
0
0
0
0
0
0
5
0
0
0
0
0
γ [°]
5
4
6
11
7
7
7
7
7
7
7
8
6
Linear
Radial
Radial
Linear
Linear
Parallel
Linear
Linear
Linear
Linear
Linear
Linear
Linear
N [-] Method
Labordus, 2004
Thuis, 2003
Thuis, 2003
Thuis, 2003
Thuis, 2003
Thuis, 2003
Thuis, 2003
Thuis, 2003
Thuis, 2003
Thuis, 2003
Thuis, 2003
Thuis, 2003
Thuis, 2003
Reference
© Woodhead Publishing Limited, 2011
B13
B12
B11
NCS 82675
NCS 82675
NCS 81053
NCS 81053
NCS 81053
NCS 81053
NCS 81053
NCS 81053
NCS 81053
NCS 81053
NCS 81053
Ahlstrom
Ahlstrom
Ahlstrom
Ahlstrom
Ahlstrom
Ahlstrom
(2)
(3)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(1)
(2)
(3)
(1)
(2)
(3)
0.9
0.9
0.9
0.9
0.9
0.9
0.618
0.618
0.618
0.618
0.618
0.618
0.618
0.618
0.618
0.64
0.64
0.64
[0/90]
[0/90]
[0/90]
[0/90]
[0/90]
[0/90]
[0/90]
[0/90]
[0/90]
[0/90]
[0/90]
[0/90]
[0/90]
[0/90]
[0/90]
[0/90]
[0/90]
[0/90]
—
—
—
—
—
—
2.02E-10
2.22E-10
1.14E-10
1.18E-10
7.90E-11
5.43E-11
3.95E-10
6.91E-10
1.37E-10
1.09E-11
2.86E-11
4.93E-11
[45/−45] 2.19E-11
0.95
NCS 82675
FGE 106HD
B9
(1)
[45/−45] 1.51E-11
0.424
Cotech EBX 424
B8
B10
[45/−45] 2.10E-11
Saertex 0.616 V91025-00620
B7
2.09E-11
7.20E-11
1.65E-10
2.10E-11
7.66E-11
1.49E-10
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
3.36E-11
2.66E-11
3.90E-11
3.70E-11
4.34E-11
3.85E-11
1.97E-11
2.96E-11
6.71E-11
9.87E-12
2.17E-11
3.85E-11
1.84E-11
1.13E-11
2.10E-11
48.35
46.44
44.88
42.65
41.4
40
60
50
40
62
52
41
56
49
55
1.03E-11 60.3
2.43E-11 52.7
6.85E-11 46.9
1.95E-11 60.3
4.54E-11 52.7
1.41E-10 46.9
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
K1,unsat [m2] K1,sat [m2] K2,unsat [m2] K2,sat [m2] Vf [%]
Name
ID
ρA [kg·m−2] θ [°]
0
0
0
0
0
0
32
28
24
16
8
0
0
0
0
0
0
0
0
0
0
3
3
3
3
3
3
5
5
5
5
5
5
4
4
4
8
8
8
3
6
γ [°] N [-]
Linear
Linear
Linear
Linear
Linear
Linear
Radial
Radial
Radial
Radial
Radial
Radial
Radial
Radial
Radial
Radial
Radial
Radial
Radial
Radial
3D
Method
Lundström, 2000 (Continued)
Lundström, 2000
Lundström, 2000
Lundström, 2000
Lundström, 2000
Lundström, 2000
Hammani et al., 1996
Hammani et al., 1996
Hammani et al., 1996
Hammani et al., 1996
Hammani et al., 1996
Hammani et al., 1996
Hammani et al., 1996
Hammani et al., 1996
Hammani et al., 1996
Gauvin et al., 1996
Gauvin et al., 1996
Gauvin et al., 1996
Endruweit et al., 2006a
Endruweit and Ermanni, 2004
Stöven et al., 2003
Reference
Table 8.4 Basic characteristics of biaxial glass fibre fabrics and characteristics and results of in-plane permeability experiments
© Woodhead Publishing Limited, 2011
B20
Hexcel CD180 0.686
Hexcel CD180 0.686
Hexcel CD180 0.686
Hexcel DB170 0.595
Hexcel DB170 0.595
Hexcel DB170 0.595
Hexcel DB170 0.595
(3)
(1)
(2)
(3)
(4)
—
—
(2)
ELT850
B18
B19
EBXhd396
B17
—
(1)
EBX936
Cofab-A1118B —
(2)
0.806
0.806
0.806
Cofab-A1118B —
Devold
(4)
Devold
Devold
(3)
0.806
0.806
(1)
Devold
(2)
6.95E-11
5.04E-11
4.32E-11
7.55E-11
9.74E-11
—
—
5.50E-09
4.15E-09
3.08E-09
—
[45/−45] 1.68E-09
[45/−45] 1.56E-09
[45/−45] 1.35E-09
[45/−45] 1.25E-09
[0/90]
[0/90]
[0/90]
[0/90]
[45/−45] 5.52E-12
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
5.19E-11
9.97E-11
1.52E-09
1.22E-09
1.17E-09
9.00E-10
2.26E-09
1.54E-09
1.04E-09
1.48E-12
3.00E-12
5.42E-12
3.09E-11
1.82E-11
2.69E-11
5.23E-11
6.88E-11
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
37.6
43.9
51.2
58.6
42.2
50.6
57.3
55
55
55
49
49
57.2
52.5
52.5
3.46E-11 57.2
6.63E-11 52.5
K1,unsat [m2] K1,sat [m2] K2,unsat [m2] K2,sat [m2] Vf [%]
[45/−45] 6.54E-12
[0/90]
[0/90]
[0/90]
[0/90]
[0/90]
[0/90]
[0/90]
ρA [kg·m−2] θ [°]
(5)
Devold
(1)
Name
B16
B15
B14
ID
Table 8.4 Continued
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
—
—
—
—
—
—
—
6
6
6
—
—
—
—
—
—
—
Radial
Radial
Radial
Radial
Radial
Radial
Radial
Radial
Radial
Radial
Linear
Radial
Radial
Radial
Parallel
Parallel
Parallel
γ [°] N [-] Method
Steenkamer et al., 1995
Steenkamer et al., 1995
Steenkamer et al., 1995
Steenkamer et al., 1995
Steenkamer et al., 1995
Steenkamer et al., 1995
Steenkamer et al., 1995
Lekakou et al., 2006
Lekakou et al., 2006
Lekakou et al., 2006
Wang et al., 1994
Wang et al., 1994
Lundström et al., 2000
Lundström et al., 2000
Lundström et al., 2000
Lundström et al., 2000
Lundström et al., 2000
Reference
© Woodhead Publishing Limited, 2011
Q1
T1
ID
[45/90/−45]
[45/90/−45]
Devold Triaxial 0.801
Devold Triaxial 0.801
Devold Triaxial 0.801
Devold Triaxial 0.801
Devold Triaxial 0.801
F2
T
L
M
H
G(1) Devold Triaxial 0.801
G
B
Devold Quadriaxial
1.068
Devold Triaxial 0.801
[45/90/−45]
Devold Triaxial 0.801
F1
(2)
[45/90/−45]
B(3) Devold Triaxial 0.801
[45/0/−45/90]
[45/90/−45]
[45/90/−45]
[45/90/−45]
[45/90/−45]
[45/90/−45]
[45/90/−45]
Devold Triaxial 0.801
B
(2)
[45/90/−45]
ρA [kg·m−2] θ [°]
B(1) Devold Triaxial 0.801
Name
1.04E-10
1.60E-11
3.88E-11
9.62E-11
2.32E-11
1.88E-11
5.57E-11
2.12E-11
1.69E-10
1.74E-11
2.70E-11
6.07E-11
1.58E-10
1.72E-11
4.65E-11
1.14E-10
2.77E-11
2.50E-11
6.28E-11
3.81E-11
2.04E-10
1.66E-11
—
7.75E-11
K1,unsat [m2] K1,sat [m2]
1.43E-10
8.69E-12
7.83E-11
1.16E-10
2.79E-11
2.18E-11
3.19E-11
1.90E-11
2.92E-10
1.00E-11
1.83E-11
2.48E-11
K2,unsat [m2]
1.52E-10
9.36E-12
8.28E-11
1.25E-10
3.09E-11
2.46E-11
3.51E-11
2.46E-11
4.51E-10
1.18E-11
—
2.79E-11
56.57
54.7
56.57
56.57
56.57
56.57
56.57
60.74
50.28
54.6
56.25
56.57
3
5
5
5
5
5
5
5
4
5
5
5
Linear
Parallel
Linear
Linear
Linear
Linear
Linear
Linear
Linear
Parallel
Radial
Linear
K2,sat [m2] Vf [%] N [-] Method
(Continued)
Loendersloot, 2006
Thuis, 2003
Thuis, 2003
Thuis, 2003
Thuis, 2003
Thuis, 2003
Thuis, 2003
Loendersloot, 2006
Loendersloot, 2006
Loendersloot, 2006
Thuis, 2003
Reference
Table 8.5 Basic characteristics of triaxial (T), quadriaxial (Q) and multiaxial fabrics and characteristics and results of in-plane permeability experiments
© Woodhead Publishing Limited, 2011
M14−1
Q5
Q4
Q3
ID
DBLT1150E11-1 Liba Co
DBLT1150E11-1 Liba Co
DBLT1150E11-1 Liba Co
DBLT1150E11-1 Liba Co
DBLT1150E11-1 Liba Co
Ahlstrom
Ahlstrom
Ahlstrom
Technolglas
Technolglas
Technolglas
(2)
(3)
(4)
(5)
(6)
(1)
(2)
(3)
(1)
(2)
(3)
Saertex 32047
DBLT1150E11-1 Liba Co
(1)
Name
Table 8.5 Continued
3.654
0.9
0.9
0.9
0.9
0.9
0.9
1.13
1.13
1.13
1.13
1.13
1.13
[45/−45/0/90/0/ −45/45]S
[0/45/−45/90]
[0/45/−45/90]
[0/45/−45/90]
[0/45/−45/90]
[0/45/−45/90]
[0/45/−45/90]
[0/45/−45/90]
[0/45/−45/90]
[0/45/90/−45]
[45/0/−45/90]
[45/0/−45/90]
[45/0/−45/90]
ρA [kg·m−2] θ [°]
2.20E-11
—
—
1.56E-10
—
—
—
5.55E-10
9.10E-10
1.26E-09
1.40E-09
1.50E-09
2.22E-09
—
4.24E-11
8.02E-11
1.62E-10
1.26E-11
3.82E-11
9.96E-11
—
—
—
—
—
—
K1,unsat [m2] K1,sat [m2]
2.20E-11
—
—
7.90E-11
—
—
—
3.49E-10
3.23E-10
3.75E-10
4.01E-10
2.15E-10
1.15E-10
K2,unsat [m2]
—
1.66E-11
3.53E-11
7.91E-11
7.36E-12
1.34E-11
3.74E-11
—
—
—
—
—
—
55
56.1
50.9
46.7
60.9
54.2
48.8
49.4
49.4
49.4
49.4
49.4
49.4
1
4
4
4
3
3
3
4
4
4
4
4
2
3D
Parallel
Parallel
Parallel
Linear
Linear
Linear
Radial
Radial
Radial
Radial
Radial
Radial
K2,sat [m2] Vf [%] N [-] Method
Stöven et al., 2003
Lundström, 2000
Lundström et al., 1999
Lundström, 2000
Lundström, 2000
Lundström, 2000
Lundström, 2000
Chiu and Cheng, 2002
Chiu and Cheng, 2002
Chiu and Cheng, 2002
Chiu and Cheng, 2002
Chiu and Cheng, 2002
Chiu and Cheng, 2002
Reference
© Woodhead Publishing Limited, 2011
M14
Q2
B7 T2
B5
B4
ID
(2)
(1)
(2)
(1)
(8)
(7)
(6)
(5)
(4)
(3)
(2)
(1)
(7)
(6)
(5)
(4)
Saertex 32047
Hexcel NC2 Hexcel NC2 Hexcel NC2 Hexcel NC2 Hexcel NC2 Hexcel NC2 Hexcel NC2 – automotive Hexcel NC2 – automotive Hexcel NC2 – automotive Hexcel NC2 – automotive Hexcel NC2 – automotive Hexcel NC2 – automotive Hexcel NC2 – automotive Hexcel NC2 – automotive Saertex V91025–00620 Hexcel NC2 – wind energy Hexcel NC2 – wind energy Hexcel NC2 – aeronautic Hexcel NC2 – aeronautic
(3)
Hexcel NC2
(1)
(2)
Name
3.654
0.534 0.534 0.534 0.534 0.534 0.534 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.616 0.975 0.975 0.6 0.6
0.534
ρA [kg·m−2]
[45/−45/0/90/0/ −45/45]S
[0/0] [0/90] [0/90] [0/90] [0/90] [45/−45] [0/90] [0/90] [0/90] [0/90] [0/90] [0/90] [0/90] [0/90] [45/−45] [−45/45/0] [−45/45/0] [−45/0/45/90] [−45/0/45/90]
[0/0]
θ [°]
1.60E-12
— — — — — 2.41E-13 — — 6.64E-12 8.39E-12 3.78E-12 9.81E-12 2.09E-12 3.82E-12 6.50E-13 — — — —
—
K3,unsat [m2]
—
2.40E-14 1.10E-13 6.37E-13 1.51E-12 2.47E-13 — 4.46E-13 8.62E-13 — — — — — — — 9.96E-13 2.40E-13 1.06E-12 1.87E-13
2.10E-14
K3,sat [m2]
55
65 65 65 65 65 50.8 41 41 37 37 41 41 43 43 55 52 52 64 64
65
Vf [%]
1
1 1 1 1
1 1 1 1 1 15 1 1 4 4 4 4 4 4
3
N [-]
3D
Transverse Transverse Transverse Transverse Transverse Transverse Transverse Transverse Transverse Transverse Transverse Transverse Transverse Transverse 3D Transverse Transverse Transverse Transverse
Transverse
Method
Stöven et al., 2003
Drapier et al., 2002 Drapier et al., 2002 Drapier et al., 2002 Drapier et al., 2002 Drapier et al., 2002 Drapier et al., 2002 Elbouazzaoui et al., 2005 Elbouazzaoui et al., 2005 Elbouazzaoui et al., 2005 Elbouazzaoui et al., 2005 Elbouazzaoui et al., 2005 Elbouazzaoui et al., 2005 Elbouazzaoui et al., 2005 Elbouazzaoui et al., 2005 Stöven et al., 2003 Drapier et al., 2005 Drapier et al., 2005 Drapier et al., 2005 Drapier et al., 2005
Drapier et al., 2002
Reference
Table 8.6 Basic characteristics of biaxial (B), triaxial (T), quadriaxial (Q) and multiaxial fabrics and characteristics and results of transverse permeability experiments
184
Non-crimp fabric composites
is the permeability of materials with same fibres and stitching, but a biaxial or triaxial structure exhibits large differences. The number of layers does not seem to be the reason for the difference, as it is for woven fabrics which exhibit a significant dependency on the number of layers due to nesting (Hoes et al., 2004; Lomov et al., 2003). It can also be observed that a significant anisotropy is measured in the in-plane permeability. In general, the saturated permeability is higher than the unsaturated permeability. However, the number of fabrics for which both saturated and unsaturated permeabilities were measured is limited. Moreover, a few authors have reported the opposite (Drapier et al., 2005; Pillai, 2004). The difference between saturated and unsaturated permeability depends on the contribution of the capillary flow wetting the fibre bundle and affecting the flow at the flow front. The influence of the capillary forces is expected to be higher for lower injection pressures or lower flow rates (Verrey et al., 2006). The ratio between inter- and intra-bundle space is a geometrical parameter affecting the amount of capillary flow (Bréard et al., 2003). This ratio is determined by the fibre count and the homogeneity of the fibre bed (compare engineered fabrics with, for example, NC2 fabrics) which changes as a function of the compression of the fabric (see Section 8.4.1). The ratio generally also changes due to the saturation itself, as the fibre bundles swell after wetting. The ratio between the unsaturated and saturated permeability is written as: [8.4] The ratio χ is shown in Fig. 8.4. Limited information is available, particularly as only a number of fabrics have been measured at different fibre contents and different pressures. Nearly all results presented are obtained in the framework of the FALCOM project (fabrics B3, T1 and Q1, see Table 8.6 for the properties of the fabrics). Measurements were performed by the NLR, SiComp and the University of Twente (Loendersloot, 2006, Thuis, 2003). The exception is fabric Q5, which is a glass fibre fabric (Lundström et al., 1999). Despite the geometrical differences, see Table 8.7, there is no significant difference in the ratio χ for these fabrics. On the average, a ratio of approximately 0.8–1.0 is observed, with some anomalies. The fibre content of fabrics B3-B(1) and B3-F1 is equal. Hence the ratio χ is expected to be equal as well, which is clearly not the case. The difference is most likely found in the number of layers: one versus six. The ratio χ of fabric B3-F2 is extremely large compared to the other ratios. It is at the upper limit reported in literature (Drapier et al., 2005). The injection pressure during the wetting part was very low. Combined with the high fibre content, it is likely that capillary flow was dominant, resulting in a relatively high permeability. Once the preform was fully saturated, the effect of capillarity dropped and the pressure had to be increased to maintain the flow rate constant. According to Pillai (2004), the ratio χ cannot exceed the value 1. This holds if the same conditions apply, which is not the case for this particular
© Woodhead Publishing Limited, 2011
Permeability of non-crimp fabric preforms
185
8.4 Ratio of the unsaturated over the saturated permeability for the biaxial fabric B3, the triaxial fabric T1 and the quadriaxial fabrics Q1 and Q5. (a) Fabric B3. The letters refer to the type of fabric specified in Table 8.7. The numbers in the bars refer to the principal direction to which the data applies. (b) Fabrics T1, Q1 and Q5. The letters refer to the type of fabric specified in Table 8.7. The numbers in the bars refer to the principal direction to which the data applies.
© Woodhead Publishing Limited, 2011
186
Non-crimp fabric composites
Table 8.7 Properties of the base configuration of the Devold non-crimp fabrics defined in the FALCOM project
Areal density Fibre Fibre count Orientation Stitch Stitch linear density Knit pattern Gauge Stitch length Gap width
B3
T1
Q1
0.534
0.801
1.068
±45
45/0/−45/90
[tex]
Tenax HTS 5631 12K 45/90/−45 PES 7.6
[inch−1] [mm] [mm]
chain 5 2.5 0–2
[kg m−2] [−] [°]
Source: Thuis, 2003
measurement, but is the case for the measurements on fabric B3-B(3) for which a ratio below 1 is found. A high ratio for variant F2 is not found for the triaxial fabric. The injection pressure was substantially higher than the pressure during the measurement of the biaxial variant F2 (approximately 5 bar versus 1.5 bar). Analysing the results obtained for the triaxial and quadriaxial fabrics (Fig. 8.4b), it can be concluded that there is no significant difference for the different variants and between biaxial, triaxial and quadriaxial fabrics and between carbon fibre (B3, T1 and Q1) and glass fibre (Q5) fabrics. Other results in the literature report a wide range of values. Drapier et al., (2005) measured the unsaturated and saturated transverse permeability for the Hexcel NC2 fabric and measured a value of 8–10 for the ration χ, substantially higher than other results reported in literature (Ma and Shishoo, 1999: χ ≈ 0.4; and Binétruy and Pabiot, 1999: χ ≈ 1.5–2). Drapier et al. (2005) used relatively low injection pressures and high fibre contents. Their study also indicated a significant influence of the stitching density. This means that limited inter-bundle space is present apart from the stitch penetration areas. Therefore, a significant amount of capillary flow can be expected and therefore a high ratio of χ, comparable to the measurement on fabric B3-F2. A final observation from Figure 8.3 is that the transverse permeability is approximately two orders of magnitude lower than the in-plane permeability (see also Table 8.5). The research of Drapier and Elbouazzaoui (Drapier et al., 2002, 2005; Elbouazzaoui, et al., 2005) revealed a strong correlation between the stitch density and the permeability of transverse permeability of NC2 fabrics (as also concluded in Chapter 9). This is also a relevant result for the research to the processing of stitched preform packages (Han et al., 2003; Talvensaari et al., 2005; Rieber and Mitschang 2010), consisting of woven fabrics that are stitched together to increase the structural integrity of a complete (non-flat) preform. This
© Woodhead Publishing Limited, 2011
Permeability of non-crimp fabric preforms
187
process is also known as structural stitching. The stitching affects the mechanical properties of the finished product (Weimer and Mitschang 2001; Truong et al., 2005), but also the processing conditions, in particular since these products are often manufactured by resin infusion processes, hence they are governed by transverse resin flow.
8.3
Geometric effects
Typical geometrical features in the architecture of an NCF affect the flow of a fluid through the textile. On one hand, these geometrical features partly explain the differences observed in the permeabilities measured. On the other hand, they serve as input for permeability models, such as are discussed in Chapter 10. Two geometrical effects will be discussed. 1. Multi-layered NCFs versus multi-ply NCFs. 2. The effect of the stitching.
8.3.1 Multi-ply versus multiple layers NCFs are generally available as biaxial, triaxial and quadriaxial fabrics, though sometimes even more plies are stitched together to form a single layer of material (see, for example, Stöven et al., 2003). It is possible to build a preform using either multiple layers of biaxial NCFs or multiple layers of quadriaxial NCFs with the same number of plies and the same ply orientations. Consider, for example, the lay-ups: • •
[ [45,−45], [0,90], [90,0], [−45,45] ] [ [45,0,−45,90], [90, −45,0,45] ]
Both lay-ups have the same number of plies (8) and the same set of ply orientations (2 × −45, 2 × 0, 2 × 45, 2 × 90). The permeability of both preforms is therefore expected to be equal, according to the theories described in Advani et al. (1994), Lundström (2000) and Parnas (2000). The approach assumes plies with a unidirectional fibre bundle orientation. Inherently, it is assumed that the fluid flow through the fabric is not, or insignificantly, influenced by the geometrical characteristics induced by the stitches. This topic will be further addressed in the following section. One aspect related to the stitching is relevant to be mentioned here: A pattern of stitch threads covers the surface of a NCF. A small layer, typically of the order of magnitude of the diameter of the stitch yarn, is found between two individual layers. This layer forms a potential flow path, especially since a slight increase of the local fibre content of the plies will occur due to a thickness reduction of each layer, as schematically shown in Fig. 8.5. The measurements carried out in the framework of the FALCOM project (Thuis, 2003) are used to investigate this topic, as the base configuration fabrics (B3-B, T1-B and Q1-B; see Table 8.7) were all built with the same type of
© Woodhead Publishing Limited, 2011
188
Non-crimp fabric composites
8.5 Schematic cross-section of a biaxial and quadriaxial fabric, indicating the interlayer, bundle and layer thicknesses. A given thickness of the complete preform with an equal number of plies will give different values for the thicknesses for biaxial and quadriaxial fabrics. (a) Cross-section of a biaxial fabric. (b) Cross-section of a quadriaxial fabric.
fibres, employing the same type of stitching (chain knit pattern) and stitching material (polyester [PES]). The graphs in Figure 8.6 show the permeability measured of the biaxial (a), triaxial and quadriaxial (b) fabrics. The measuring condition differed as different equipment was used at each institute. The fibre content was set as close to 55% as possible with the equipment of the institutes. The measurements B3-B(1)–(3) (University of Twente) and B3-F1/2 (NLR) were performed at different fibre contents. Moreover, the number of layers was varied in the measurements at the University of Twente (1, 2, 4 for the measurements B3-B(1), B3-B(2) and B3-B(3)) whereas seven layers for the biaxial and five layers for the triaxial fabrics were used for the other measurements (except measurements B3-F1/2 and T1-F1, where the number of layers was six, eight and four, respectively, to achieve the desired fibre content). The equivalent permeability at a fibre content of 55% is calculated using the Kozeny–Carman equation (see Section 8.4.1). The relation to calculate the permeability Vf,source at an arbitrary fibre content Vf,target is based on the Kozeny– Carman equation (Williams et al., 1974, see also Section 8.4.1) reads: [8.5]
© Woodhead Publishing Limited, 2011
Permeability of non-crimp fabric preforms
189
8.6 Comparison of permeabilities at a 55% fibre content equivalent permeability for the fabrics B3-B, T1-B and Q1-B. The variants F1 and F2, measured by the NLR, refer to the same fabric at a lower and higher fibre content compared to variant B that was measured at the NLR. (a) Biaxial fabric B3-B. (b) Triaxial and quadriaxial fabric T1-B and Q1-B.
© Woodhead Publishing Limited, 2011
190
Non-crimp fabric composites
The light grey bars refer to the unsaturated, whereas the dark grey bars refer to the saturated permeability. The measured permeabilities of the biaxial fabric by the UT (B3-B(1)–(3)) are substantially higher than those measured by the NLR (B3-F1, B3-B(4), B3-F2), whereas those measured by SiComp (B3-B(5)–(6)) are substantially lower than the NLR results. The same trend is observed for the triaxial fabric: the permeability measured by SiComp (T1-B(3)) is lower than the permeability measured by the NLR (T1-B(1)). The measurements (T1-B(2)) performed with a third rig (radial injection at the KU Leuven) is in between the results of the NLR and SiComp. The lay-ups of the bi-, tri- and quadriaxial fabrics were not adapted to obtain an equal number of plies with the same orientation. The first and second principal permeabilities of the triaxial fabric (oriented in the 90° and 0° direction) are expected to be higher and lower, respectively than the principal permeability of the biaxial and quadriaxial fabrics, which are expected to be (nearly) isotropic. Due to the large variation in the experimental results, there is no clear indication of a higher permeability in the first principal direction. Furthermore, there is no significant difference between the permeabilities of the biaxial and quadriaxial fabrics, indicating that the number of plies versus the number of layers is of insignificant influence on the permeability measured. The effect of the number of layers can also be assessed, using the data measured on the biaxial fabrics. The measurements at the University of Twente were performed with one, two and four layers (the fabrics B3-B(1), B3-B(2) and B3-B(3) respectively). The bars in Fig. 8.6 show a consistent equivalent unsaturated permeability at a fibre content of 55% (light grey bars). The equivalent saturated permeability (dark grey bars) exhibit more variation and mutually differ significantly more than the unsaturated permeabilities. The variation appears to decrease with an increasing number of layers (for a constant fibre content, see remarks in Chapter 9, section 9.3.2). Large variations are not uncommon in permeability measurements, but these measurements on the single-, double- and four-layer fabrics were performed with the same equipment, material from the same roll, by the same operator and in a short period. Consequently, it is reasonable to exclude external effects as a major cause of the variation and attribute the variation mainly to the conditions inside the mould cavity. The permeability is more profoundly influenced by boundary effects at the interfaces of the fabric and mould for a low number of layers. Increasing the number of layers will decrease the contribution of boundary effects. The boundary conditions at the interface of the fabric and mould also depend on the stitching at the top and bottom faces of the fabric. Other than the interface between two layers of fabric, only one side of the interface is deformable (fabric), whereas the other is rigid and generally smooth (mould). The microscopic image of the cross-section of a biaxial fabric in Fig. 8.7 shows that it is not unlikely that small flow channels are formed. Note that the tri- and quadriaxial fabrics inherently suffer less from this type of boundary effect, as the number of plies automatically results in a larger number of ply–ply interfaces compared to the two ply–mould interfaces.
© Woodhead Publishing Limited, 2011
Permeability of non-crimp fabric preforms
191
8.7 Microscopy image of the cross-section of a biaxial non-crimp fabric. The stitch yarn passing over the top and yarns forming the loop at the bottom of the fabric create a small layer which can form flow channels enhancing the permeability.
Some conclusions can be drawn on the effect of the number of layers versus the number of plies, and the total number of layers in the preform. Unfortunately, the conclusion does not have a very firm character, as both the number of measurements is limited and the variation of the results is large. Bearing this in mind, it is stated that: • •
The number of plies per layer is of insignificant influence on the permeability if the total number of plies remains equal. The total number of plies in the mould cavity has a significant influence on the amount of variation if the total number of plies is low.
The first conclusion implies that it should be possible to calculate the permeability of NCFs based on the permeability of single plies (but note that this ply permeability has to include all relevant geometrical features). The second conclusion indicates a structural difference with the permeability of stacks of woven fabrics: increasing the number of woven fabric layers leads to an increase in the variation on the permeability due to nesting (Hoes et al., 2004; Lomov et al., 2003), whereas the variation decreases with an increasing number of NCF layers.
8.3.2 Influence of stitching Several authors have reported on the effect of stitching on the internal geometry of NCFs and Chapter 4 of this book is entirely dedicated to this subject. It is known that stitching affects the structural properties of the composite (both strength and fatigue properties), which is mainly attributed to the formation of resin-rich areas (Truong et al., 2005). Limited experimental data are reported on the role the stitches and the stitching-induced geometrical characteristics on the flow pattern of the impregnating resin (Lekakou et al., 2006; Loendersloot, 2006).
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Firstly, it is important to analyse the flow path of the fluid. The flow front is observed in the transient permeability measurements, either visually (amongst others: Heardman et al., 2004; Loendersloot, 2006; Lundström et al., 2000) or digitally (amongst others: Hoes et al., 2002; Liu et al., 2007; Luthy and Ermanni, 2002; Luthy and Ermanni, 2003; Stöven et al., 2003; Visvanathan and Balasubramaniam, 2007; Yenilmez and Sozer, 2009). The resolution of these data (either digital images of the flow front, or sensor read outs) is insufficient to analyse the flow path in detail. Measurements were performed at the University of Twente using two transparent plates. The set-up is depicted in Fig. 8.8. The impregnating fluid is polyol, to which a penetrant fluid (Ardrox® Biopen P6F5) is added. The penetrant is fluorescent and hence allows the flow front to be traced more easily if ultraviolet or black light is used. The fabric B3–B (see Table 8.7) is employed. The progressing flow front is shown in Fig. 8.9. Macroscopically (Figure 8.9a), the fluid flows in machine direction. A pattern of lines corresponding to the direction of the fibres in the top ply is visible. This suggests a preferential flow along the fibre bundles. The overall flow in the machine direction is a combination from the flows through both plies, resulting in a straight (in the image: vertical) flow front. The images of Figure 8.9b show three close-ups of the fabric being wetted. The fluid is clearly concentrated around the stitches, according to the light grey colour, caused by the fluorescent penetrant. The images show that the fluid is also flowing along the stitches, apart from the preferential flow along the fibres. Based on this observation, an anisotropy is expected, even for
8.8 Experimental set-up to track the flow front in detail (courtesy of S.P. Haanappel). The set-up was also used to measure the thickness change of the cavity during impregnation of the fluid.
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8.9 Progressing flow front of a mixture of polyol–Ardrox® Biopen impregnating a biaxial non-crimp fabric (B3–B). (a) Complete impregnation cycle in six steps. (b) Three details of the flow front. (Photos courtesy of S.P. Haanappel).
symmetrically built NCFs. Moreover, the principal direction of the permeability of the fabric can be tilted with respect to the machine direction, depending on the stitch pattern; a chain-knit pattern will lead to a higher permeability in the machine direction and hence no tilt of the principal directions of the permeability but, for example, a tricot chain will lead to a small tilt (see also Chapter 9). The loops of the stitches on the bottom face of the fabric are, inherently to the production process (see Part I), oriented in the machine direction and hence only enhancing the permeability in that direction. However, the loops show a fair amount of tilt, as shown in Chapter 4 Fig. 4.6, depending on the stitch tension. The higher the stitch tension, the more the loops will be aligned in the machine direction. The anisotropy of symmetrically built fabrics (even number of plies per layer, Fig. 8.10a and b) is expected to become strengthened whereas the anisotropy of asymmetrically built fabrics (uneven number of plies per layer, Fig. 8.10c) is weakened by the stitching, since the first principal direction is oriented in the cross-direction due to the presence of the 90° ply. The anisotropy α is defined according to: [8.6]
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8.10 Comparison between the anisotropy of fabrics with an even and uneven number of plies. (a) Carbon fibre based biaxial and quadriaxial fabrics. (b) Glass fibre based biaxial, quadriaxial and multiaxial fabrics. (Continued)
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8.10 (c) Carbon and glass fibre based uniaxial and triaxial fabrics.
It should be noted that the anisotropy of fabrics measured with a linear injection strategy is based on the measurements of separate preforms. This generally leads to a reduced accuracy of the results. The loss of accuracy is attempted to be limited in the multi-cavity set-up (Lundström et al., 1999), which does use different preforms but a single preparation and injection phase. The measurements on the biaxial fabrics B3-B(4) (classic linear injection) versus B3-B(5) and B3-B(6) (multicavity linear injection) show no difference in results, but a comparison of the results on T1-B(1) and T1-G(1) (classic linear injection) and T1-B(3) and T1-G(2) (multi-cavity linear injection) with T1-B(2) (radial injection) shows a consistent deviation of the anisotropy measured employing the classic linear injection strategy. On average, an anisotropy of 0.7–0.8 is observed for the carbon fibre fabrics with an even number of plies. The fabrics B4(1)–(3) are an exception exhibiting a lower anisotropy than average, where as B6 and M14 are isotropic. The high anisotropy of the fabric B4 can be caused by the chain-knit stitch pattern, but there are no additional data available to explain why the anisotropy is significantly higher than the other chain knit fabrics (B3 and B6). The isotropy of fabric M14 indicates that the stitching on the top and bottom faces of a layer increases the anisotropy and, consequently, the more plies per layer, the more isotropic the material will be. The anisotropy of glass fibre shows a large amount of variation, even for a single type of fabric. There is insufficient data available to explain the variation.
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Some experimental results, such as those on fabric Q3, are very unlikely (α < 0.1). On average, the anisotropy seems to be lower for glass fibre fabrics, but there is no physical explanation for this observation. The fibre waviness discussed in Chapter 9 is a potential explanation, but the information available is insufficient to confirm this hypothesis. The expected strong anisotropy of the uniaxial fabrics is confirmed by Fig. 8.10c. The carbon fabric (U1) shows a weaker anisotropy compared to the glass fabrics (U2 and U3). The data set is too limited to state firm conclusions on this observation, in particular since the other results only concern a single triaxial carbon fibre fabric (T1). The results show more variation than the results on the bi- and quadriaxial fabrics, but it is difficult to attribute the variations to the specific characteristics (see Table 8.8) of the fabrics, in particular since only the permeability in machine direction was measured for the biaxial variations of these fabrics. On average, an anisotropy of 0.5–0.6 is observed. This corresponds to the a weighted mean of the anisotropies of a uniaxial fabric and a biaxial fabric: [8.7] The experimental results show that the presence of stitching does affect the anisotropy of the fabric. However, it is not possible to quantify the effect of the stitching properties on the anisotropy based on the results available. Table 8.8 Definition of the identifiers of the variants of the Devold non-crimp fabrics defined in the FALCOM project Sub-Id
Variable
B T L M H G F1
Base configuration Thermoplastic stitch thread 4.0 mm stitch length Mixed tricot-chain stitch pattern High stitch tension 2–5 mm gap width
F2
Higher fibre content (∼60%) Maximum free shear angle
S
Lower fibre content (∼50%)
Source: Thuis, 2003
8.4
Deformation and permeability
Deformation has a large influence on permeability. The two leading types of deformation are compression of the textile reinforcement and shear deformation. The effects of both are investigated experimentally by a number of researchers (Chen et al., 2001; Endruweit and Ermanni, 2004; Govignon et al., 2010;
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Heardman et al., 2001; Lai and Young, 1997; Loendersloot, 2006; Louis and Huber, 2003; Schuster et al., 2008; Smith et al., 1997; Stadtfeld et al., 2002).
8.4.1 Compression Two driving phenomena can be distinguished for fabric compression. Firstly, the fibre content of the fabric in relaxed state is lower than the fibre content desired and hence the fabric is compressed until the desired fibre content is obtained. Moreover, the level of compression can change during a resin infusion process (Govignon et al., 2010). Secondly, a trellis type of shear deformation, as occurs in double curvatures, results in fabric compression due to a reduction in the surface area. The effect of shear itself will be discussed more elaborately in section 8.4.2. Macroscopically, the relation of the fibre content Vf and the permeability K can be described with an empirical function, such as initially defined by Kozeny– Carman (Williams et al., 1974) and later adapted by various authors (Gebart, 1992; Berdichevsky and Cai, 1993; Cai and Berdichevsky, 1993) by introducing a distinction between flow longitudinal and perpendicular to the fibres or bundles. Senoguz et al. (2001) presented a convenient overview of the models available. Here, the relations for longitudinal and transverse flow as proposed by Gebart (1992) are used: [8.8a]
[8.8b] The variables rf and Vf,max refer to the fibre filament radius and maximum fibre content respectively. A hexagonal packing of the fibres is assumed here. Eq. 8.8 is effectively the original Kozeny–Carman equation with a specific value for the empirical Kozeny constant (Lundström, 2000). There is only a limited physical relation between the internal geometry of the fabric and the parameters in the functions (for example the factor 8/53) but the equations are slightly more applicable for NCFs, as they are derived for aligned fibre beds and not for fabrics with commingled yarns. However, the effect of stitching is not accounted for, although it has a clear influence on permeability. The same applies for the effect of fibre bundle waviness, which is discussed in Chapter 9. Compression of a fibrous preform yields a change in the ratio between the inter- and intra-bundle space. Basically, two phenomena occur: • •
Bundles are getting closer to each other (reduction of the inter-bundle space). Bundles are compacted (reduction of the intra-bundle space).
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It is therefore not only expected that the permeability decreases with an increasing level of compression of the fabric, but also that the ratio between the wetting and saturated permeability changes. However, there is no difference in the ratio χ for varying fibre contents, as discussed previously in Section 8.2.2 (see Fig. 8.4). The curves fitted through the permeability data of each set are shown in Fig. 8.11. The fitted fibre radii are listed in Table 8.9. In most cases, the model has the tendency to overestimate the permeability at higher fibre contents. The conclusion that can be drawn based on the available data, both on the measurements and the fabrics (fibre count, gap width, stitch density, etc.), is that Gebart’s equation provides a reasonable fit for the relation between the permeability and the fibre content. However, a more accurate model must incorporate information on the textile’s architecture and compression behaviour, in particular for the higher fibre contents.
8.4.2 Shear deformation NCFs tend to be very shear compliant. It was observed by several researchers (Endruweit et al., 2006b; Loendersloot, 2006) that NCFs can shear up to 5–7° Table 8.9 Fitted values for bundle radius rf based on a least squared approximation of Gebart’s equation (Gebart, 1992) on the experimental data of various fabrics. The fit for each class of materials is printed in italics. No distinction is made between saturated and unsaturated.
B3-B(1)–(3)
0.676E-04 0.656E-04 0.169
0.220
B3-F1B(4)F2
1.116 E-04 1.735E-04 0.013
0.118
T1-F1B(1) F2
0.451E-04 0.503E-04 0.135
0.069
Carbon B3T1
0.594E-04
0.347
U2
0.484E-04
0.048
0.393E-04
0.093
U3
0.468E-04
0.020
0.502E-04
0.028
Glass U
0.479E-04
0.034
0.430E-04
0.154
B10
0.170E-04
0.307
0.330E-04
0.388
B11
0.435E-04
0.405
0.267E-04
0.368
B12
0.373E-04
0.060
0.749E-04
0.386E-04
rf,unsat (90) [m]
1.185E-04 1.461E-04 0.426
0.081 0.009
rf,sat (90) [m]
εunsat εsat (90) [-] (90) [-]
rf,unsat (0) [m]
B13
rf,sat (0) [m]
εunsat (0) εsat (0) [-] [-]
ID
0.098 0.527E-04
0.074
B14
0.355E-04 0.403E-04 0.002
B19
1.985E-04
0.551
2.725E-04
0.253
B20
1.922E-04
3.963
1.892E-04
2.251
Glass B
0.284E-04
0.388
0.483E-04
0.624E-04 0.704E-04 0.008
0.322E-04
0.111
0.425E-04
Q5
0.373E-04
0.034
0.552E-04
0.355E-04
0.098
0.008
0.477
Q4 Glass Q
0.479
0.508E-04
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8.11 Comparison of relation between the permeability and the fibre content according to Gebart’s equation and experimental results for various fabrics. (a) Carbon fibre bi- and triaxial fabrics. (b) Glass fibre biaxial fabrics. (c) Glass fibre uniaxial fabrics. (d) Glass fibre quadriaxial fabrics.
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during handling (see also fabric B3-S, Table 8.8, Thuis, 2003 and Chapter 9). Typical shear diagrams of NCFs can be found in Chapter 6. The main reason for this low shear compliance is the absence of locking, as occurs in woven fabrics due to fibre commingling (see also Chapter 6). Moreover, it was established in previous section that the stitching affects the permeability of the fabric by the formation of additional flow paths. Shear deformation also changes the stitching and, therefore, an additional, stitching-dependent effect is observed in the relation between permeability and shear. Shear can be modelled as a rotation of the principal directions of the fabric. An unsheared fabric with an isotropic permeability will have an anisotropic permeability once it is sheared. The principle axes are oriented in the bisectrices of the ply orientation angles. This simplified approach allows for an estimation of the orientation of the principal permeabilities and the anisotropy, as proposed by Advani et al. (1994):
[8.9]
With Kx and Ky the longitudinal and transverse permeability of a unidirectional ply of fibres, θ the ply orientation and γ the shear angle. The transverse permeability is generally small compared to the longitudinal permeability (Gebart and Lidström, 1996; Smith et al., 1997): Ky<
[8.10]
Experimental results show deviations to this (simplified) theoretical approach, which can be attributed to the presence of the stitching. Firstly the additional flow paths, formed by the stitch threads on the top and bottom faces, affect both the orientation and the anisotropy of the permeability (as discussed in Section 8.3). On top of that, the stitching is also affected by applying a shear deformation to the fabric. Once sheared, the stitches are either tensioned or compressed, depending on the direction of shear and on the stitch pattern, as depicted in Fig. 8.12. This results in a non-symmetric permeability versus shear relation and an additional rotation ϕ of the principal directions. It can be concluded from this basic approach that, globally, the permeability is expected to obey Eq. 8.9 with ‘second order’ deviations due to the stitchinginduced geometrical characteristics of the fabrics. This implies that an increase in the first principal permeability is expected, as the fibres in the individual plies become more aligned, and a decrease of the second principal permeability,
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8.12 Effect of shear deformation on two different stitch patterns. (a) Tricot stitch in unsheared state. (b) Tricot stitch in sheared state. (c) Tricot-chain stitch in unsheared state. (d) Tricot-chain stitch in sheared state.
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effectively resulting in an increase of the anisotropy. Most authors presenting on the permeability of sheared fabrics show an initial increase of the first principal permeability followed by a decrease for larger shear angles. This decrease is due to the increasing fibre content. The increase of the fibre content Vf as a function of the shear angle γ reads: [8.11] with n the number of layers, ρA the areal density, ρ the density of the fibre material and hc the cavity height. The increase of the permeability due to the realignment of the fibres competes with the decrease due to the increasing fibre content. The question could be raised of whether the permeability of sheared fabrics has to be measured at the same fibre content, or with the same cavity height. The first is preferred from a modelling point of view, whereas the second method corresponds better to the practical situation, where the mould cavity thickness is defined. In the latter case, shear always results in a (locally) higher fibre content. Measurements on sheared fabrics were performed by the author on two types of biaxial NCF (B1 and B2, Table 8.3). The measurements were performed in the framework of a Marie Curie Fellowship at the KU Leuven. A radial measuring technology was applied and the measurements were performed on single-layer material, sheared at 30° and 45°. A second set of shear permeability data is provided by Hammani et al. (1996) (Fabric B11, Table 8.4, maximum shear angle 32°). The results are shown in Fig. 8.13. Both sets of data confirm the expectations discussed above. The general trend is that Eq. 8.9 is satisfied, although the decrease of the second principal direction is much lower than predicted. The first principal permeability increases up to a maximum, whereas the second principal permeability only decreases. The maximum is reached at a shear angle of approximately 30°, which is higher than the maximum reported in literature for woven fabrics (Heardman et al., 2001; Lai and Young, 1997) and higher than predicted based on Eq. 8.10 (shear angle: 10–15°). The plies in a biaxial NCF can be rotated further without suffering from locking, as occurs in woven fabrics. As a result, the decrease in permeability of woven fabrics is initiated at lower shear angles. Another explanation is found in the effect of shear on the stitching. The stitches induce a geometrical distortion in the fabric, which is changed with the changing shear angle. It was shown by Loendersloot (2006) that the dimensions of these distortions of the fabric B1, B2 and B3 (see also Chapter 4.5) reach a minimum value at approximately 30° shear. This was related to the stitch yarn diameter, or more precisely, the minimum space the stitching requires. The result is a minimum size of the flow channel, causing a higher permeability. The location of the maximum of the first principal permeability appears to be consistent, as it is equal for the three fabrics for which permeability of sheared preforms is available, despite the significant difference between the fabrics. The first two fabrics are carbon fibre based, whereas the last is glass fibre based.
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8.13 Permeability versus shear for the fabrics B1, B2 and B11. The solid and dashed lines correspond to the theoretical permeability shear relation for the first and second principal direction, respectively (with the unsheared permeability as the fixed reference value).
Although the stitch pattern of the latter is unknown, those of the two carbon fabrics are different, as are the ply orientations and the fibre count of the fibre bundles. Based on the standard level at the time of production of the glass fibre fabric, it is expected that it is a relatively open fabric, with clear separations and flow channels between the individual bundles. The newer carbon fibre based fabrics possess a much more homogeneous fibre bed, resulting in a high number of fibre crossings and only a few flow channels of larger length, as are expected for the glass fibre fabric. This would suggest that the model proposed by Advani et al. (1994) fits better on the glass fibre fabric. However, there is no clear evidence for this. The conclusion is that the influence of the stitching in both cases results in a significant difference compared to the theory based on unidirectional fibre beds only. The anisotropy of the fabrics is shown in Fig. 8.14. The solid line corresponds to Eq. 8.10. The trend is reasonably well predicted. In all cases, an initial anisotropy is observed, corresponding to the previous observation that a certain amount of anisotropy is expected due to the presence of the stitching (Section 8.3). The glass fibre fabric B11 exhibits a higher amount of anisotropy (αmeasured < αtheory) than predicted by Eq. 8.10, whereas for the carbon fabrics B1 and B2 a lower amount of anisotropy (αmeasured > αtheory) is observed for the sheared fabrics, but not for the
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8.14 Anisotropy of the permeability of the sheared fabrics compared to the predicted anisotropy shear relation (solid line). The dashed lines are shifted with respect to the solid line to fit the measured data in a least-square sense.
unsheared fabrics. The direction of shearing is part of the explanation. Consider the stitch patterns shown in Fig. 8.12. Initially, the first principal permeability will be oriented in the direction of the stitching, but will be switched as the fabric is sheared according to the direction indicated in the figure. As a result, the stitching will enhance the second rather than the first principal permeability. This results in a lower amount of anisotropy. The anisotropy of the fabrics is defined according to Eq. 8.6 and hence the switch of first and second permeability direction is implicitly accounted for. The six- and five-pointed stars in Fig. 8.14 correspond to the inverse of the anisotropies of fabrics B1 and B2, respectively. This implies an anisotropy without accounting for the switch of the principal directions of the permeability. The dashed lines are least-squared-based fits of Eq. 8.10 plus a constant shift Δα: [8.12] The fit is observed to agree well with the experimental results. The shift Δα for the fabrics B1, B2 and B11 is found to be equal to 0.2647, 0.1233 and −0.2022 respectively. The conclusion can be drawn that the initial anisotropy of the fabric, induced by the stitching, is maintained during shear, but it depends on the direction of shear and the shear pattern.
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According to Eq. 8.10, the principal direction of the permeability is aligned with the smallest bisectrix of the sheared orientation of the two plies (see also Chapter 10). However, it was already established that the stitching affects the orientation of the permeability. Hence, a difference is expected, depending on both the direction of shear and the stitch pattern (ϕ in Figure 8.10d). The orientation angle β of the principal directions for the two carbon fabrics is shown in Fig. 8.15. The error bars indicate the variability of the orientation of each measurement, based on a series of flow-front positions. A significant orientation angle is already observed for the unsheared fabric B1, which is even higher than expected based on the initial misalignment of the plies of 5–7° degrees (Endruweit et al., 2006; Loendersloot, 2006). Fabric B2 shows a lower orientation for the unsheared configuration. However, the orientation for the sheared configurations is comparable to that of fabric B1 and both show large difference between measurements. The dashed line corresponds to the relations derived by Lai and Young (1997) for the relation between the orientation and β and the shear angle γ : [8.13] with α the anisotropy and m a fit parameter to account for the deviation ϕ. The value for m was found by applying a least-squared approximation, yielding
8.15 Orientation angle β as a function of the shear angle γ for the fabrics B1 and B2 compared to the model proposed by Lai and Young, 1997.
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m = 0.501 and m = 0.489 for the fabrics B1 and B2 respectively. Lai and Young (1997) reported a value of 0.5865 and 0.723 for two different types of woven fabric. There is no physical interpretation for m, but it is clear that there is a significant difference between the actual orientation of the principal directions and those based on theory. This is at least partly to be attributed to the presence of stitching, as in most cases the fibres in the plies are equal, whereas woven fabrics often exhibit a certain amount of unbalance, causing the orientation to differ from theory.
8.5
Conclusions
The effects of a number of geometrical characteristics of NFCs on textile permeability were presented in this chapter. The presence of the stitching was recognised as an important factor in permeability. It was observed that experimental data show a significant number of inconsistencies. It is impossible to attribute the variations in the experimental data to either the measuring technology used or the geometrical characteristics. Partly because the total data set, despite its extent, is too limited. Measurements on the same fabric under different conditions (injection pressure, fibre content, different stitching, etc.) are seldom. Partly, the information provided with each measurement is too limited. Information on the experimental parameters is often missing, as is information on the fabric and stitching (fibre count, stitch pattern, stitch thread, etc.). These, however, are key issues for a well-founded assessment of the measured permeabilities and the scatter measured which, as reported by Lundström et al. (2000), can be in the order of 15% for in-plane measurements, even if the same equipment is used and a strict protocol is followed. The recent studies of Roy et al. (2007) Pillai (2009) and Tan and Pillai (2009) confirm these observations, but add a flow rate dependency to the accuracy of the experiment. A couple of years ago, an initiative was launched to start a benchmark project for measuring and calculating the permeability of textile reinforcements, including NCF. The aim of the benchmark project was, in the first place, to characterise the permeability of different types of fabric as a function of textile architecture, compression and shear deformation. Secondly, a standardised measuring technology was aimed for. This does not imply that only one type of measuring technology will be selected based on the results obtained by the participants. Rather, the conditions and protocols for the different technologies available will be defined, such that the currently observed variation in permeability can be explained and interpreted to a value to be used in numerical models. The last task in the project is the development of numerical models that are able to predict the permeability of a fabric based on the internal geometry of the textile. A lithographybased reference structure was developed (Morren et al., 2009) to validate the experiments as well as the numerical models. The discussion in this chapter has revealed a number of geometrical characteristics that are specific for NCF. It could therefore be argued that the reference geometry will not provide useful results for the models of NCF. A
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detailed analysis of the flow through the fabric as, for example, done by the experiments at the University of Twente (see Fig. 8.8), provide a more significant contribution to the understanding and interpretation of permeability measurements of NCF. The measurements as carried out by Drapier et al. (2002) and Elbouazzaoui et al. (2005) can be used to identify the effect of the stitching as they varied the stitch density over a conveniently wide range. A similar approach was followed in the FALCOM project (Thuis, 2003), where a number of variants of the same NCF were analysed. The measurements, performed by the NLR, SiComp and the University of Twente (Thuis, 2003; Loendersloot, 2006), were, however, not as conclusive as was hoped. A larger range of variability in the geometrical features may have been more effective. The success of the benchmark project does not only depend on the experimental and numerical efforts by the participants, but also on two other factors: • •
Completeness of the information on the geometrical characteristics of the fabrics studied. The recognition of the differences between woven fabrics and NCFs.
Addressing these differences in specific experiments will lead to a more fundamental understanding of the effect of textile geometrical characteristics on permeability. This will be an important input for permeability prediction models. This chapter did not elaborate on the measuring technologies themselves, or on the mathematics behind them. The reason for not addressing these topics is that they are not specific for NCF and there already exist a wide range of articles and books on this topic. The reader is in particular referred to the book edited by Advani et al. (1994) and the book by Parnas (2000), in which most of the topics on permeability measurements are discussed. Recent developments in permeability measuring technologies relate to a more automated process, in an attempt to both decrease the time required for a measurement and to increase the quality in terms or accuracy, repeatability and reproducibility. This implies that new types of sensors are being developed. The new generation of sensors is capable of detecting the position of the flow front. Either a large number of sensors is used (Hoes et al., 2002; Hoes, 2003; Liu et al., 2007) or sensors with a certain length or nonintrusive techniques (Danisman et al., 2007; Dominauskas et al., 2003; Dunkers et al., 2001; Gupta and Sundaram, 2009; Kueh et al., 2002; Luthy and Ermanni, 2002; Visvanathan and Balasubramaniam, 2007) are employed. The main goal is to increase the amount and quality of measured permeabilities to improve the qualification and quantification of the variability of the permeability.
8.6
Acknowledgements
The author acknowledges the partners of the EU-funded FALCOM project (GRD1-2001-40184) for allowing the publication of the data acquired in this project, the financial support of the European Commission of the TECABS Brite-Euram
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project and the Marie Curie Fellowship Programme (HPMT-CT-2000-0030); the author participated in these projects during his PhD research. Furthermore, the valuable input of S.P. Haanappel on his experiments with the penetrant fluid is acknowledged. Finally, the author thanks R.H.W. ten Thije for providing Fig. 8.1.
8.7
References
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Dunkers J.P., J.L. Lenhart, S.R. Kueh, J.H. van Zanten, S.G. Advani and R.S. Parnas (2001). Fiber optic flow and cure sensing for liquid composite molding Optics and Lasers in Engineering 35:91–104. Elbouazzaoui O., S. Drapier and P. Henrat (2005). An experimental assessment of the saturated transverse permeability of non-crimped new concept (NC2) multiaxial fabrics Journal of Composite Materials 39(13):1169–1193. Endruweit A. and P. Ermanni (2004). The in-plane permeability of sheared textiles. Experimental observations and a predictive conversion model Composites Part A 35:439–451. Endruweit A., P. McGregor, A.C. Long and M.S. Johnson (2006a). Influence of the fabric architecture on the variations in experimentally determined in-plane permeability values Composites Science and Technology 66:1778–1792. Endruweit A., A.C. Long, F. Robitaille and C.D. Rudd (2006b). Influence of stochastic fibre angle variations on the permeability of bi-directional textile fabrics Composites Part A 37:122–132. Ferland P., D. Guittard and F. Trochu (1996). Concurrent methods for permeability measurement in resin transfer molding Polymer Composites 17(1):149–158. Frishfelds V., T.S. Lundström and A. Jakovics (2003). Permeability of clustered fiber networks: modelling of the unit cell Mechanics of Composite Materials 39(3): 265–272. Gauvin R., F. Trochu, Y. Lemenn and L. Diallo (1996). Permeability measurements and flow simulation through fiber reinforcement Polymer Composites 17(1):34–42. Gebart B.R. (1992). Permeability of unidirectional reinforcements for RTM Journal of Composite Materials 26(8):1100–1133. Gebart B.R. and P. Lidström (1996). Measurement of in-plane permeability of anisotropic fiber reinforcements Polymer Composites 17(1):43–51. Govignon Q., S. Bickerton and P.A. Kelly (2010). Simulation of the reinforcement compaction and resin flow during the complete resin infusion process Composites Part A 41:45–57. Gupta N. and R. Sundaram (2009). Fiber optic sensor for monitoring flow in vacuum enhanced resin infusion technology (VERITy) process Composites Part A 40:1065–1070. Gutowski T.G., Z. Cai, S. Bauer, D. Boucher, J. Kingery and S. Wineman (1987). Consolidation Experiments for Laminate Composites Journal of Composite Materials 21:650–669. Hammani A., F. Trochu, R. Gauvin and S. Wirth (1996). Directional permeability measurement of deformed reinforcement Journal of Reinforced Plastics and Composites 15:552–562. Han K.K., C.W. Lee and B.P. Rice (2000). Measurements of the permeability of fiber preforms and applications Composites Science and Technology 60:2435–2441. Han N.L., S.S. Suh, J.-M. Yang and H.T. Hahn (2003). Resin fil infusion of stitched stiffened composite panels Composites Part A 34:227–236. Heardman E., C. Lekakou and M.G. Bader (2001). In-plane permeability of sheared fabrics Composites Part A 32:933–940. Heardman E., C. Lekakou and M.G. Bader (2004). Flow monitoring and permeability measurements under constant and transient flow conditions Composites Science and Technology 64:1239–1249. Hoes K. (2003). Development of a new sensor-based set-up for experimental permeability identification of fibrous media PhD-Thesis.
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Hoes K., D. Dinescu, H. Sol, M. Vanheule, R.S. Parnas, Y. Luo and I. Verpoest (2002). New set-up for measurement of permeability properties of fibrous reinforcements for RTM Composites Part A 33:959–969. Hoes K., D. Dinescu, H. Sol, R.S. Parnas and S. Lomov (2004). Study of nesting induced scatter of permeability values in layered reinforcement fabrics Composites Part A 35:1407–1418. Kim S.K. and I.M. Daniel (2007). Observation of permeability dependence on flow rate and implications for liquid composite molding Journal of Composite Materials 41(7):837–849. Kueh S.R.M., R.S. Parnas and S.G. Advani (2002). A methodology for using long-period gratings and mold-filling simulations to minimize the intrusiveness of flow sensors in liquid composite molding Composites Science and Technology 62:311–327. Labordus M. (2004). Permeability measurements: In plane and through the thickness Proceedings of FPCM-6 Newark, Delaware USA 477–481. Lai C.-L. and W.-B. Young (1997). Model resin permeation of fiber reinforcements after shear deformation Polymer Composites 18(5):642–648. Lam R.C. and J.L. Kardos (1989). The permeability and Compressibility of Aligned and Cross-Plied Carbon Fibre Beds During Processing of Composites Proceedings of ANTEC 1408–1412. Lekakou C., M.A.K. Johari, D. Norman and M.G. Bader (1996). Measurement techniques and effects on in-plane permeability of woven cloths in resin transfer moulding Composites Part A 27:401–408. Lekakou C., S. Edwards, G. Bell and S.C. Amico (2006). Computer modelling for prediction of the in-plane permeability of non-crimp stitch bonded fabrics Composites Part A 37:1–6. Liu Q., R.S. Parnas and H.S. Giffard (2007). New set-up for in-plane permeability measurement Composites Part A 38:954–962. Loendersloot R. (2006). The structure-permeability relation of textile reinforcements PhDThesis ISBN: 90–365–2337–0. Loendersloot R., S.V. Lomov, R. Akkerman and I. Verpoest (2006). Carbon composites based on multiaxial multiply stitched preforms. Part V: geometry of sheared biaxial fabrics Composites Part A 37:103–113. Lomov S.V., I. Verpoest, T. Peeters, D. Roose and M. Zako (2003). Nesting in textile laminates: geometrical modelling of the laminate Composites Science and Technology 63:993–1007. Louis M. and U. Huber (2003). Investigation of shearing effects on the permeability of woven fabrics and implementation into LCM simulation Composites Science and Technology 63:2081–2088. Lundström T.S., B.R. Gebart and E. Sandlund (1999). In-plane permeability measurement on fiber reinforcements by the multi-cavity parallel flow technique Polymer Composites 20(1):146–154. Lundström T.S. (2000). The permeability of non-crimped stitched fabrics Composites Part A 31:1345–1353. Lundström T.S., R. Stenberg, R. Bergström, H. Partanen and P.-A. Birkeland (2000). In-plane permeability measurements: a nordic round-robin study Composites Part A 31:29–43. Lundström T.S., S. Toll and J.M. Håkanson (2002). Measurement of the permeability tensor of compressed fibre beds Transport in Porous Materials 47:363–380.
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Lundström T.S., V. Frishfelds and A. Jakovics (2004). A statistical approach to permeability of clustered fibre reinforcements Journal of Composite Materials 38(13):1137–1149. Lundström T.S., V. Frisfelds and A. Jackovics (2010). Bubble formation and motion in non-crimp fabrics with perturbed bundle geometry Composites Part A 41:83–92. Luo Y., I. Verpoest, K. Hoes, M. Vanheule, H. Sol and A. Cardon (2001). Permeability measurement of textile reinforcements with several test fluids Composites Part A 32:1497–1504. Luthy T. and P. Ermanni (2002). Linear direct current sensing system for flow monitoring in Liquid Composite Moulding Composites Part A 33:385–397. Luthy T. and P. Ermanni (2003). Flow monitoring in Liquid Composite Molding based on linear direct current sensing technique Polymer Composites 24(2):249–262. Ma Y. and R. Shishoo (1999). Permeability characterization of different architectural fabrics Journal of Composite Materials 33(8):729–750. Morren G., M. Bottiglieri, S. Bossuyt, H. Sol, D. Lecompte, B. Verleye and S.V. Lomov (2009). A reference specimen for permeability measurements of fibrous reinforcements for RTM Composites Part A 40:244–250. Nordlund M. (2006). Permeability modelling and particle decomposition mechanisms related to advanced composite manufacturing PhD-Thesis ISSN: 1402–1544. Nordlund M., T.S. Lundström, V. Frishfelds and A. Jakovics (2006). Permeability network model for non-crimp fabrics Composites Part A 37:826–835. Parnas R.S. (2000). Liquid composite moulding, Hanser. Parnas R.S., J.G. Howard, T.L. Luce and S.G. Advani (1995). Permeability characterization. Part 1: A proposed standard reference fabric for permeability Polymer Composites 16(6):429–445. Pillai K.M. (2004). Modeling the unsaturated flow in liquid composite molding processes: a review and some thoughts Journal of Composite Materials 38(23):2097–2118. Rieber G. and P. Mitschang (2010). 2D permeability changes due to stitching seams Composites Part A 41:2–7. Roy T., H.Tan and K.M. Pillai (2007). A method to estimate the accuracy of 1-D flow based permeability measuring devices Journal of Composite Materials 41(17): 2037–2055. Saouab A., J. Bréard, P. Lory, B. Gardarein and G. Bouquet (2001). Injection simulation of thick composite parts manufactured by the RTM process Composites Science and Technology 61:445–451. Scholz S., J.W. Gillepsie jr. and D. Heider (2007). Measurement of transverse permeability using gaseous and liquid flow Composites Part A 38:2034–2040. Schuster M., A. Ogale, L. Peetz, J. Schuster and P. Mitschang (2008). Analysis of sewed preforms by visual on-line monitoring of stitch-hole variations under compaction Composites Science and Technology 68:312–320. Senoguz M.T., F.D. Dungan, A.M. Sastry and J.T. Klamo (2001). Simulations and experiments on low-pressure permeation of fabrics: Part II – the variable gap model and permeability prediction Journal of Composite Materials 35(14):1285–1322. Sharma S., D.A. Siginer, R.K. Dukipatti and K.A. Soschinske (2009). Effect of fiber sizing – test fluid interaction on the unsaturated and saturated flow in the VARTM process Journal of Composite Materials 43(15):1589–1601. Smith P., C.D. Rudd, A.C. Long (1997). The effect of shear deformation on the processing and mechanical properties of aligned reinforcements Composites Science and Technology 57:327–344.
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Stadtfeld H.C., M. Erninger, S. Bickerton and S.G. Advani (2002). An experimental method to continuously measure permeability of fiber preforms as function of fiber volume fraction Journal of Reinforced Plastics and Composites 21(10):879–899. Steenkamer D.A., S.H. McKnight, D.J. Wilkins and V.M. Karbhari (1995). Experimental characterization of permeability and fibre wetting for liquid moulding Journal of Materials Science 30:3207–3215. Stöven T., F. Weyrauch, P. Mitschang and M. Neitzel (2003). Continuous monitoring of three-dimensional resin flow through a fibre preform Composites Part A 34:475–480. Talvensaari H., E. Landstätter and W. Billinger (2005). Permeability of stitched preform packages Composite Structures 71:371–377. Tan H. and K.M. Pillai (2009). A method to estimate the accuracy of radial flow-based permeability measuring devices Journal of Composite Materials 43(21):2307–2332. Truong T.C., M. Vettori, S. Lomov and I. Verpoest (2005). Carbon composites based on multiaxial multiply stitched preforms. Part 4: mechanical properties of composites and damage observation Composites Part A 36:1207–1221. Thuis H.G.S.J. (2003). Measurements of permeability of different non-crimp fabrics FALCOM Deliverable D2.1.2/NLR-CR-2003–275 38p. Ven E.C. van de, R. Loendersloot and R. Akkerman (2006). Experimental investigation of the compressibility and permeability of fabric reinforcements Proceedings of FPCM-8 241–248. Verrey J., V. Michaud and J.-A.E. Månson (2006). Dynamic capillary effects in liquid composite moulding with non-crimp fabrics Composites Part A 37:92–102. Visvanathan K. and K. Balasubramaniam (2007). Ultrasonic torsional guided wave sensor for flow front monitoring inside molds Review of Scientific Instruments 78:8p. Wang T.J., C.H. Wu and L.J. Lee (1994). In-plane permeability measurement and analysis in liquid composite molding Polymer Composites 15(4):278–287. Weimer C. and P. Mitschang (2001). Aspects of the stitch formation process on the quality of the sewn multi-textile-preform Composites Part A 32:1477–1484. Weitzenböck J.R., R.A. Shenoi and P.A. Wilson (1999a). Radial flow permeability measurement. Part A: theory Composites Part A 30:781–796. Weitzenböck J.R., R.A. Shenoi and P.A. Wilson (1999b). Radial flow permeability measurement. Part B: application Composites Part A 30:797–813. Williams J.G., C.E.M. Morris and B.C. Ennis (1974). Liquid flow through aligned fibre beds Polymer Engineering and Science 14(6):413–419. Yenilmez B. and E.M. Sozer (2009). A grid of dielectric sensors to monitor mold filling and resin cure in resin transfer molding Composites Part A 40:476–489.
8.8
Appendix: nomenclature
Roman hc i K _ K K1 K2 K3
cavity height index permeability tensor averaged permeability first principal permeability second principal permeability third principal permeability
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[m] [-] [m2] [m2] [m2] [m2] [m2]
Permeability of non-crimp fabric preforms Kx Ky Klong Kperp – Kln Kunsat Ksat m n N P rf s+ s− sln t0.95 v Vf Vf,max
permeability in longitudinal direction in ply permeability in transverse direction in ply longitudinal permeability transverse permeability average permeability based on a lognormal data distribution unsaturated/wetting/transient permeability saturated/steady state permeability fit parameter number of layers number of elements/degrees of freedom pressure fibre (bundle) radius upper value variability of a lognormal distribution lower value variability of a lognormal data distribution estimate of standard deviation of a lognormal data distribution Student-t-distribution with a 95% significance level fluid velocity vector fibre content theoretical maximum fibre content
215 [m2] [m2] [m2] [m2] [m2] [m2] [m2] [-] [-] [-] [bar] [m]
[-] [m·s−1] [-] [-]
Greek
α β γ θ μ ρ ρA χ
anisotropy orientation angle of the first principal permeability shear angle ply orientation angle dynamic viscosity volumetric density areal density ratio of unsaturated over saturated permeability
Mathematical
Δ ∇
Difference gradient operator
Abbreviations U B T Q Mn
uniaxial fabric biaxial fabric triaxial fabric quadriaxial fabric multiaxial fabric with n plies
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[-] [°] [°] [°] [Pa·s] [kg·m−3] [kg·m−2] [-]
9 Understanding variability in the permeability of non-crimp fabric composite reinforcements A. ENDRUWEIT and A.C. LONG , University of Nottingham, UK
Abstract: This chapter discusses the variability in experimentally determined in-plane and through-thickness permeability values of non-crimp fabrics. Experimental uncertainties in permeability measurement are quantified for a specific measurement technique. Variability in local fibre orientation and fibre spacing in a fabric is described, and its influence on the local in-plane permeability is modelled for a representative material. Stochastic distributions of the local permeability are generated and implemented in flow simulations, which are evaluated statistically to estimate the global in-plane permeability and its variance and to predict probable outcomes of resin injections. The variability in through-thickness permeability is caused mainly by multi-layer effects such as misalignment, resulting in discontinuity of through-thickness pores. Key words: non-crimp fabrics, permeability, variability, resin flow, probabilistic methods.
9.1
Introduction
In liquid composites moulding (LCM) processes, composite components are produced by impregnation of a dry reinforcing textile structure with liquid matrix resin. As formulated in Darcy’s law, the resin flow during impregnation depends on the permeability of the textile material. Different models exist for reinforcement permeability, all of which describe a dependence on the fibre volume fraction and geometry parameters. However, such models generally involve one or more empirical parameters, so that in practice permeability must be determined experimentally for each material and over a range of fibre volume fractions. For description of fabric impregnation at the component scale (macro-scale), fibre volume fraction and permeability are typically assumed to be uniform. However, non-uniformity in the fibre volume fraction of actual fabrics, caused by local variation of fibre angles and fibre spacing across several unit cells, results in variability in the global permeability (Endruweit et al., 2006c). In multi-layer preforms, nesting, which was analysed in detail by Hoes et al. (2002), may induce additional permeability variations. However, for non-crimp fabrics (NCFs) with alternating layers of aligned fibre bundles, the effect of nesting is not expected to be significant. Variability in fabric permeability results in variability in mouldfilling patterns and injection times in processing of actual components. Therefore, product quality and production cycle time may be affected. 216 © Woodhead Publishing Limited, 2011
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Since textile reinforcements are often processed in thin shell-like structures, in-plane resin flow and in-plane permeability have been discussed extensively in the literature. The in-plane permeability of actual fabrics can be determined from quantitative evaluation of injection experiments, which implies homogenisation of local variations in material properties. The resulting global permeability values show, in general, high variations (e.g. Lundström et al., 2000a; Luo et al., 2001). For woven, unidirectional and stitch-bonded fabrics, Parnas et al. (1997) estimated the typical uncertainty (standard deviation/average value of a series of experiments) in measured permeability as ±20%. This variability is caused by variability in the fabric structure, but also by experimental errors (Pan et al., 2000). With increasing interest in the production of geometrically more complex thick structural components applying LCM technology, through-thickness resin flow becomes more relevant. However, information on the through-thickness permeability of actual bi-directional fabrics and its variability is sparse. In this chapter, the variability of experimentally determined in-plane and through-thickness permeability values of NCFs is quantified, and experimental uncertainties in permeability measurement are discussed. The material nonuniformity is related to the variability in local fibre orientation and the fibre spacing, and its influence on the local permeability is described. For the in-plane permeability, stochastic distributions of the local permeability are generated and implemented in flow simulations, which are evaluated statistically to estimate global permeability variations and to predict probable outcomes of resin injections. Whilst results are presented primarily for a single NCF, the concepts described are applicable to a wide range of textile reinforcements.
9.2
Material characterisation
All textile fabrics show, in general, some degree of non-uniformity, which affects the local permeability and contributes to the uncertainty in measured global permeability values. Local variations in fibre spacing and fibre angle, both of which are interdependent, are inherent to any fabric architecture. They may also be induced by the effects of gravity and handling during storage and transport, as well as by cutting, stacking and draping (i.e. localised shear deformation, see Chapter 8, Section 8.4.2) of fabric layers during preform preparation. In addition, the textile structure may be affected by quality issues such as missing yarns and irregularities in the stitching pattern (the latter specifically in the case of NCFs). While considerable efforts have been made to develop formulations for, in particular, the effect of drape on the fabric’s properties (e.g. Smith et al., 1997), variations due to external influences and quality issues are case-specific and cannot be discussed in a generalised way. Here, the material-inherent non-uniformity is discussed for the example of a ±45° NCF, in which two layers of unidirectional E-glass fibre yarns are stitchbonded using a high-drape tricot stitch construction (as in Endruweit et al.,
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9.1 Unit cell of a ±45° non-crimp fabric: definitions of the in-plane axis of the fibre tow cross-section, Rp, the spacing between the axes of adjacent fibre tows, a0, the inter-yarn angle, α, and the angle between fibre tow axis and fabric weft direction, χ.
2006c). The fabric is characterised geometrically by the superficial density S0 (nominal value 0.950 kg/m2), the average ratio of in-plane dimension of fibre tows Rp and fibre-tow spacing a0 (identical in both fibre directions) and the standard deviation σα of angles α between both fibre directions (Fig. 9.1). The angle χ between the fibre direction and the weft (transverse to roll) direction of the fabric, which is expected to have identical absolute values on both faces on the fabric and to coincide with half the angle α, was determined experimentally at various positions on both faces of the fabric by means of photographic imaging and digital image analysis. Statistical evaluation of the data indicates that χ is normally distributed with a mean value of 42.7° and a standard deviation of 5.6° (Fig. 9.2). From the value for χ, a standard deviation of 7.9° in the angle α between both fibre orientations can be determined from [9.1] which applies for symmetry reasons. The local superficial density of the fabric was determined experimentally by weighing series of specimens with given surface area. The specimens were stamped out from positions across the width of the fabric roll. For three different sizes of specimens, the masses were determined and evaluated statistically as indicated in Fig. 9.3. The histograms indicate that the width of the distribution of
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9.2 Distribution of angle χ between fibre direction and fabric weft direction; histogram and corresponding normal distribution; correlation coefficient R2 = 0.985 (adapted from Endruweit et al., 2006c).
9.3 Distributions of local superficial densities S0; evaluation is based on three different surface areas As of the specimens (Endruweit and Long, 2006b).
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Non-crimp fabric composites Table 9.1 Fabric superficial density S0, average ratio Rp/a0 and standard deviation of fibre angles σα. S0/g/m2
Rp/a0
σα
965 ±4 (±0.4%)
0.39
7.9°
Source: Endruweit et al., 2006c.
the superficial density increases with decreasing specimen dimensions, because of the increasing local resolution of the sampling procedure. Average values of Rp and a0 were determined visually from fabric specimens by photographic imaging and digital image analysis. Values of the parameters for geometrical fabric characterisation are summarised in Table 9.1. The relatively high value of σα and the significant deviation of the average value of Rp/a0 from the ideal value of 0.5 are caused by the stitches through the fabric and the resulting gaps, which cause local disturbances (waviness) in the otherwise aligned fibre bundles. The low relative variation in the superficial density indicates that the typical dimensions of material non-uniformities are smaller than the specimen dimensions. A study of different fabrics (Endruweit et al., 2006c) suggested that, for [9.2] Rp/a0 and σα are correlated via [9.3] Here, ωmax is the maximum frequency of the fibre tow waviness. Based on the values in Table 9.1, the constant of proportionality ωmax a0 is determined as 0.627. At a fibre spacing a0 of approximately 2.1 mm, the value of ωmax is 0.30/mm. To discuss the relation between stitching pattern and waviness, the configuration of the gaps as seen in Fig. 9.4 is represented schematically in Fig. 9.5. Simplifying the geometrical description proposed by Lomov et al. (2002), the tricot stitching pattern is characterised by the distance D between stitches and the stitch length L. Assuming that the fibres are oriented mainly at 45° to the stitch (warp) direction, the length of the gaps l and the width of the gaps w are approximated by [9.4] and [9.5]
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9.4 Effect of the stitching thread on the fibre configuration on both faces, (a) and (b), of the non-crimp fabric (adapted from Endruweit et al., 2006c).
9.5 Schematic configuration of the gaps in non-crimp fabrics; dashed lines indicate idealised fibre paths (Endruweit et al., 2006c).
where d is the diameter of the stitching thread. The opening angle of the gaps is [9.6] where [9.7]
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The angle γ /2, which describes local deviations of the fibre orientations from 45°, is expected to be related to the standard deviation of the angle χ and thus ultimately to determine ωmax. The ratio d/D is approximately 0.12, which according to Eq. 9.6 gives an angle γ /2 ≈ 3.5°. The measured variation in fibre angles is σχ = 5.6°. The values of γ /2 and σχ differ, because the actual fibre structure is not as regular as the idealised configuration. While Eqs. 9.4 to 9.7 refer to the specific case of frequently used ±45° NCFs, the waviness of fibre tows in any NCF is determined by the diameter of the stitching thread and the stitch density along the fibre tow direction. The influence of the stitching pattern on the fibre tow alignment is small, if the stitch direction coincides with the fibre orientation (e.g. in 0°/90° fabrics) and the stitches are positioned in inter-tow spaces. Relations of the type in Eq. 9.3 can be applied to fabrics of any architecture, but if a fabric is not bi-directional, σα needs to be defined differently, e.g. as the standard deviation of the distribution describing the angle between the fibre direction and a reference direction (as σχ). If the properties of fibre tows are not identical along different fibre directions, Rp, a0 and σα need to be determined separately for each direction.
9.3
Permeability measurement
9.3.1 Methods and errors In addition to the local non-uniformity of the textile structure, experimental errors contribute to the variability in measured permeability values. Experimental errors are uncertainties in each individual experiment for permeability measurement, induced by the limited accuracy of the experimental set-up and the data evaluation procedure. A general overview of concepts and techniques for permeability measurement is given in Chapter 8, Section 8.2. While, in the following, experimental errors are analysed for selected frequently used permeability measurement techniques, similar considerations apply to other methods. The in-plane permeability values K1 and K2 are frequently determined in unsaturated radial flow experiments at constant injection pressure, based on measurement of the extent of the flow front ellipse as a function of time (e.g. Endruweit et al., 2006c). For this type of experiment, the permeability of an anisotropic material in an equivalent isotropic system of elliptical co-ordinates is [9.8] as discussed, e.g. by Chan and Hwang (1991). Here, R1 is the semi-major axis of the flow front ellipse, R0 the radius of the circular injection gate, Δp the gauge
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pressure at the injection gate, t the time for the flow front to reach R1, Φ the porosity of the textile lay-up, and η the viscosity of the injected fluid. The equivalent injection gate dimension R01 in direction of R1 in elliptical co-ordinates is [9.9] where R2 denotes the semi-minor axis of the flow front ellipse. With R1(t) and R2(t) determined experimentally, the principal permeability values K1 and K2 are calculated from [9.10] Substituting [9.11] in Eq. 9.8, the experimental error of ke is [9.12] The uncertainties in the injection pressure Δp, the flow front arrival time t and the liquid viscosity η are given directly by the respective measurement errors. The uncertainty in the fabric porosity Φ is given by the uncertainty in cavity height h. According to Eq. 9.9, the uncertainty in R01 is [9.13] For the ratio of the axes of the flow front ellipse, R2/R1, the uncertainty can be estimated. The uncertainty in F can be determined statistically following the method suggested by Heardman et al. (2004). The through-thickness permeability can be determined in saturated unidirectional flow experiments at constant volume flow rate Q (e.g. Goulley et al., 1993). Measurement of the pressure drop Δp across the specimen allows [9.14] to be calculated, where h is the thickness of the specimen, A the cross-sectional area of the cylindrical flow channel and η the viscosity of the test fluid. The experimental error is calculated according to
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[9.15] The uncertainties in η, h and Δ p are given directly by the respective measurement errors. The uncertainty in the injection flow rate Q depends on the accuracy of the pump used. For the effective cross-sectional area of the flow channel, the uncertainty is determined by the uncertainty in diameter. For series of Nexp experiments, the contribution of the error in each individual experiment to the observed permeability variations is reduced by a factor Nexp−1/2. Variations in the permeability values, which are higher than the reduced error for the respective series of experiments, indicate variations in the fabric properties.
9.3.2 Results For the fabric described in Section 9.2, the in-plane permeability was measured in unsaturated radial flow experiments at constant injection pressure. Circular fabric specimens with a radius of 200 mm were placed in an injection tool, which is made from aluminium with an additional stiffening steel structure to minimise deflection. The fibre volume fraction was set by adjusting the cavity height. A test fluid, engine oil with given viscosity, was injected through a central circular injection gate with a radius of 5 mm. The flow front propagation along three co-planar axes was determined by evaluating the readings from an array of pressure transducers (Endruweit et al., 2006c). Implementation of a method derived by Weitzenböck et al. (1999a, 1999b) from Eqs. 9.8 to 9.10 allows the principal permeability values and the orientation of the principal permeability axes to be determined from the flow front position as a function of time. Additional injection experiments with a transparent upper half of the tool were conducted to verify visually that the flow fronts are approximately elliptical during impregnation, which is a premise for the validity of the evaluation procedure. Deviations of the flow front shape from a perfect ellipse (Fig. 9.6) are caused by local fabric nonuniformity. Considering all sources of uncertainty, the upper estimate for the experimental errors of ke according to Eq. 9.8 and of K1 and K2 according to Eq. 9.10 is approximately 14%. The results of experiments for three fabric layers, all at identical orientation, at a cavity height of 2 mm (Endruweit et al., 2006c) are listed in Table 9.2. For comparison, additional published data (average values and coefficients of variation) for different NCFs and fabrics of different architectures, which complement the average in-plane permeability values in Tables 8.2 to 8.5, are listed in Table 9.3. The observed coefficients of variation of 22.5% and 26.1% for K1 and K2 are in the same order of magnitude as typical values for different fabrics quoted in the literature. On the other hand, the expected error for the principal
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9.6 Example for experimentally determined flow front shape at a given injection time (extracted from photograph); grey area indicates impregnated fabric.
Table 9.2 Number of experiments Nexp, fibre volume fraction Vf, angle θ between fabric weft direction and principal flow direction, principal in-plane permeability values K1 and K2, and ratio of anisotropy K1/K2. Nexp
Vf
θ
K1/10−10 m2
K2/10−10 m2
K1/K2
20
0.56 ± 0.00 (± 0.8%)
112° ± 43°
0.219 ± 0.049 (± 22.5%)
0.184 ± 0.048 (± 26.1%)
1.19
Note: mean values, standard deviations and coefficients of variation are given where applicable. Source: Endruweit et al., 2006c
permeability values at Nexp = 20 is approximately 3%. The mismatch between the observed coefficients of variation and the expected error for the series indicates a strong influence of variations in the fabric properties on the results. The distributions of values for K1 and K2 and the corresponding normal distributions, which were determined from the average values and standard deviations in Table 9.2, are compared in Figs. 9.7 and 9.8. While there is a strong correlation between the original values of K1 and the normal distribution, the correlation for K2 is weaker. However, the trend identified by Hoes et al. (2002) for the permeability values to be normally distributed seems in general to be followed.
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Test method
Radial flow, unsaturated, const. injection pressure
Unidirectional flow, saturated, const. injection pressure
Unidirectional flow, saturated, const. flow rate
Source
Lundström et al. (2000a)
Lundström (2000b)
Pan et al. (2000)
Plain weave glass fibre fabric
0°/90° non-crimp glass fibre fabric
Quadric-axial non-crimp glass fibre fabric
0°/90° non-crimp glass fibre fabric
0°/90° non-crimp glass fibre fabric
Tri-axial non-crimp glass fibre fabric
Plain weave glass fibre fabric
Fabric type
0.382 0.126 2.96
0.54 0.61 0.45
0.45
0.720 0.209 0.996
0.53 0.60 0.49
0.432 0.766
0.57 0.53
1.65
0.378 0.755
0.55 0.53
0.47
0.888
K1/10−10 m2
0.50
Vf
Average
1.30
0.134 0.074
0.243 0.103 0.374
0.685
0.269 0.454
0.264 0.523
0.541
K2/10−10 m2
16% 18% 6%
27% 48% 15%
24%
4% 22%
29% 20%
22%
Var coeff
13%
11% 12%
11% 16% 8%
8%
6% 8%
24% 18%
16%
Table 9.3 Published average values and coefficients of variation of the principal in-plane permeabilities K1 and K2 of different fabrics at different fibre volume fractions Vf
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Radial flow, unsaturated, const. injection pressure
Radial flow, unsaturated, const. injection pressure
Endruweit et al. (2009)
Radial flow, unsaturated, const. injection pressure
Hoes et al. (2004)
Endruweit et al. (2006c)
Radial flow, unsaturated, const. injection pressure
Luo et al. (2001)
Satin weave carbon fibre fabric
Satin weave carbon fibre fabric Plain weave glass fibre fabric Unidirectional carbon fibre fabric
Twill weave glass fibre fabric Continuous glass filament random mat
Plain weave glass fibre fabric
Plain weave glass fibre fabric
6.334
1.395 0.386 1.665 0.557 0.472 0.194
0.58 0.68 0.43 0.52 0.61 0.70
1.240
0.53 0.49
0.328
11.861
2.56
0.56
0.28
0.53
1.79
2.06 0.75
0.49 0.54 0.42
4.73
0.43
0.457 0.208 0.129
0.165 0.067 1.274
1.140
0.650
0.246
10.423
1.23
1.44
1.97 0.69
4.59
1% 10% 8%
22% 36% 11%
8%
29%
18%
29%
19%
22%
6% 17%
18%
6% 9% 2%
20% 55% 8%
14%
26%
12%
28%
14%
20%
6% 33%
20%
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9.7 Distribution of principal in-plane permeability value K1; histogram and corresponding normal distribution; correlation coefficient R2 = 0.774 (adapted from Endruweit et al., 2006c).
9.8 Distribution of principal in-plane permeability value K2; histogram and corresponding normal distribution; correlation coefficient R2 = 0.430 (adapted from Endruweit et al., 2006c).
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9.9 Distribution of angle θ between fabric weft direction and principal flow direction; histogram and corresponding normal distribution; correlation coefficient R2 = 0.640.
The values of θ, which describe the angle between the main flow direction and the fabric weft direction, lie mainly in the range between 80° and 160° (Fig. 9.9). Visual inspection of the fabric (Fig. 9.4) suggests that the tricot stitching pattern creates more pore space between the fibres on face A than on face B. The difference in porosity, which was also observed and quantified by Lomov et al. (2002) for stitch-bonded carbon fibre NCFs, creates a preferential flow direction. Since the stitching thread on face A is doubled, its influence on the local porosity and permeability is higher than that of the thread on face B, thus resulting in enhanced flow along the thread on face A (in warp direction). Superposition of the effects of flow enhancement along the gaps between the fibres and along the fixation thread suggests that the value of the angle θ is between 90° and 135°. The experimental results show an average angle of 112° (Table 9.2), which indicates that the preferential flow direction is determined mainly by the fibre configuration on face A. A more general overview of the influence of the stitching pattern on the typical impregnation behaviour is given in Chapter 8, Section 8.3. Here, results are discussed in detail for one fibre volume fraction. Results presented elsewhere (Table 9.3) do not imply a dependence of the coefficient of variation on the fibre volume fraction for bi-directional fabrics with similar
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permeability values along both principal fabric directions. However, for unidirectional material with strongly anisotropic permeability, there is a trend for the coefficients of variation of K1 and K2 to increase with increasing number of fabric layers at given cavity height, i.e. increasing fibre volume fraction (Endruweit et al., 2009). This reflects the limited accuracy of the alignment of layers in the stack and a relatively high sensitivity of flow in the unidirectional layers to misalignment. An additional observation based on the values in Table 9.3 is that while there is a dependence of the permeability variations on the fabric architecture, no clear influence of the test protocol can be identified. Detailed analysis of the coefficients of variation of the global permeability for fabrics with different fibre angle variability at similar fibre volume fractions (Endruweit et al., 2006c) suggests that, starting from zero for a hypothetical perfectly uniform fabric structure, the global permeability variations increase rapidly with increasing σα. They reach a maximum at a relatively low σα and then decrease slightly with increasing σα. This decrease suggests that the fabric appears the more uniform at the macro-scale, the higher σα and the maximum frequency of the fibre tow waviness ωmax, i.e. the more periods of waviness there are across the injection tool. Thus, an increase in σα, indicating a continuous increase in local non-uniformity, does not necessarily translate into an increase in variability on a global scale. The through-thickness permeability was determined in saturated unidirectional flow experiments at constant volume flow rate according to Eq. 9.14 (Goulley et al., 1993). The upper estimate for the experimental error of K3 as defined in Eq. 9.15 is approximately 8%. The results of the flow experiments, which were carried out for six fabric layers at a specimen thickness of 4 mm to give the same target fibre volume fraction as for the in-plane experiments, are given in Table 9.4. At an expected error of approximately 2% for the series of Nexp = 21 experiments, the actual coefficient of variation of 17.5% indicates variability in the specimen properties. The distribution of values for K3 and the corresponding normal distribution are plotted in Fig. 9.10. The difference in the actual values of Vf in Tables 9.2 and 9.4 suggests a difference in S0 of 3%, which may be caused by variations between different material batches and the history of the specimens (transport, storage, handling). Table 9.4 Number of experiments Nexp, fibre volume fraction Vf, and principal through-thickness permeability value K3 (mean values, standard deviations and coefficients of variation are given where applicable) Nexp
Vf
K3/10−12 m2
21
0.59 ± 0.01 (±1.5%)
1.961 ± 0.344 (±17.5%)
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9.10 Distribution of principal through-thickness permeability value K3; histogram and corresponding normal distribution; correlation coefficient R2 = 0.735.
Studies of the through-thickness permeability of any type of fabric are generally sparse. Experimental results were presented by Goulley et al. (1993), Han et al. (2000) and Lundström et al. (2002). Scholz et al. (2007) found comparable results for the through-thickness permeability of various fabrics measured using gas flow and saturated fluid flow. Wu et al. (1994) addressed the problem of permeability changes induced by preform compression, and Endruweit et al. (2002) derived an empirical model for description of the influence of hydrodynamically induced compression on the through-thickness permeability. Drapier et al. (2002) found that the through-thickness permeability of a specific kind of stitch-bonded NCF increases linearly with increasing stitch density. Elbouazzaoui et al. (2005) observed a strong influence of K3 of various NCFs on the orientation of the layers relative to the flow direction, but could not explain their finding. It can be speculated that it may be a result of asymmetrical compression or deformation effects induced by the fluid pressure. Published values of K3 for various non-crimp fabrics and fibre volume fractions are compiled in Table 9.5, which complements Table 8.6. The variability of measured through-thickness permeabilities was quantified by Lundström et al. (2002) for a press fabric used for de-watering of paper. They found coefficients of variation of 12.4% at a fibre volume fraction of 0.63 and a mean permeability of 1.6 × 10−12 m2,
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Table 9.5 Published values of the through-thickness permeability K3 for different types of non-crimp fabric and different fibre volume fractions Vf (coefficients of variation are given where applicable)
σK3/K3
Source
Fabric type
Vf
K3
Wu et al. (1994)
Bi-axial non-crimp glass fibre fabric
0.36
6.1 × 10−11 m2
0.40 0.44 0.49 0.54
4.5 × 10−11 m2 3.4 × 10−11 m2 2.2 × 10−11 m2 1.8 × 10−12 m2
0.36
2 × 10−12 m2
0.43 0.53 0.61 0.68 0.79 0.65
1 × 10−12 m2 8 × 10−13 m2 6 × 10−13 m2 3 × 10−13 m2 7 × 10−14 m2 2.1 × 10−14 m2
0.65 0.65 0.65 0.65 0.65 0.41
2.4 × 10−14 m2 1.1 × 10−13 m2 6.4 × 10−13 m2 1.5 × 10−12 m2 2.5 × 10−13 m2 8.6 × 10−13 m2
9%
0.41 0.52
4.5 × 10−13 m2 2.4 × 10−13 m2
3% 8%
0.52 0.64
10 × 10−13 m2 1.9 × 10−13 m2
15% 13%
0.64 11 × 10−13 m2 No information 1.5 × 10−13 m2 given 6.0 × 10−13 m2
14%
Parnas et al. (1997) Endruweit et al. (2002)
Drapier et al. (2002)
Elbouazzaoui et al. (2005)
Scholz et al. (2007)
±45° non-crimp glass fibre fabric ±45° non-crimp glass fibre fabric
Bi-axial non-crimp carbon fibre fabric, [0]2 unstitched [0/90] unstitched [0/90] 1000 stitches/m2 [0/90] 4000 stitches/m2 [0/90] 16000 stitches/m2 [±45] 4000 stitches/m2 Bi-axial non-crimp carbon fibre fabric, face A Face B Tri-axial non-crimp glass fibre fabric, face A Face B Quadric-axial non-crimp carbon fibre fabric, face A Face B ±45° non-crimp carbon fibre fabric
and 18.6% at a fibre volume fraction of 73% and a mean permeability of 0.55 × 10−12 m2. For the through-thickness permeability of a plain weave glass fibre fabric, Scholz et al. (2007) determined coefficients of variation between 5% and 8%. As the only source to quantify the variability in K3 of various non-crimp fabrics, Elbouazzaoui et al. (2005) quote coefficients of variation between 3% and 15%. At identical target fibre volume fraction, the average values of K1 and K2 differ by a factor of approximately ten from the value of K3. The coefficient of variation is significantly smaller for K3 than for K1 and K2, suggesting that the variabilities
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in the in-plane and through-thickness permeability are caused by different mechanisms. Possible reasons for measured variations in the permeability values exceeding the experimental uncertainty are: • • •
shift of layers relative to each other, affecting the continuity of throughthickness pores; non-uniformity of the fabric superficial density; and increased porosity and permeability along the specimen circumference because of uncontrollable loss of fibre bundle segments.
Results presented by Drapier et al. (2002) imply that the fabric through-thickness permeability is dominated by gaps created around stitches, as illustrated schematically in Fig. 9.5. The influence of flow through fibre bundles is not significant, since the permeability of fibre bundles perpendicular to their axes is small. This suggests high sensitivity to continuity of the gaps through the specimen thickness, but no sensitivity to the actual fibre arrangement. The probability for formation of continuous through-thickness pores depends on the number of layers in the specimen, which may explain the trend for the coefficient of variation in Table 9.4 to be higher than those quoted by Elbouazzaoui et al. (2005) for a single fabric layer. Loss of fibre segments is a defect induced by specimen preparation and can be remedied by sealing of the flow channel along the specimen circumference.
9.4
Modelling and simulation
The range of probable outcomes of resin injections and the global permeability and its standard deviation, or an envelope for the flow front position at a given injection time, can be predicted from evaluation of stochastic flow simulations. The variability in global permeability can be related to the variability in local geometrical properties of non-uniform fabrics by generation of randomised porosity and permeability fields from continuous local fibre spacing distributions (Endruweit and Long, 2006b), which reflect the actual material variability discussed in Section 9.2. The average distance between the fibre tows is assumed to be relatively small compared to the dimensions of the disturbances along the fibre axes, which are estimated to be in the order of magnitude of the dimensions of at least several unit cells, and the fibre tows are treated as being piecewise parallel. The random fields of distances between the axes of parallel fibre tows, a varying along the x-direction and b varying along the y-direction (Fig. 9.11), are described by the expansions (Ghanem and Dham, 1998). [9.16] and
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9.11 Distances a and b between the axes of wavy fibre tows (Endruweit and Long, 2006b).
[9.17] where [9.18] and [9.19] The fabric architecture is characterised by a0, b0, the average values of a, b, and the in-plane dimension of the fibre tows Rp. The values of the frequencies ωai and ωbi and the phases ϕai and ϕbi, which describe the in-plane fibre tow waviness, are determined randomly on given intervals. While the phases have values between 0 and π, upper limits for the frequencies are determined by ωmax. Via ωmax, the generated porosity distributions are related to visually observed fibre angle variations in actual fabrics. Substitution of a and b in [9.20] where Vfmax is the fibre volume fraction in the fibre bundles, gives the local fibre volume fraction of the fabric, which in Fig. 9.12 is plotted as a function of the co-ordinates for a set of example parameters. From the fibre volume fraction, the local permeability of the bi-directional fabric is calculated as the thickness-weighted
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9.12 Typical random values of a, b and Vf as functions of the coordinates x, y; example for Rp/a0 = Rp/b0 = 0.4, ωmax = 50/m and Vfmax = 0.6; dimensions of the textile 500 mm × 500 mm (adapted from Endruweit and Long, 2006b).
average of the permeabilities of two unidirectional layers. According to Kozeny– Carman (Carman, 1937), the longitudinal and transversal principal permeability values of a single layer of unidirectional fibre material are estimated by [9.21] where Rf is the fibre radius and ci is a constant for material direction i. For simulation of radial resin injection into a non-uniform NCF placed in a flat mould, the equations describing flow of a viscous liquid through a porous medium, considering conservation of the fluid mass, were solved based on a non-conforming finite element method (Trochu et al., 1993), which is implemented in the PAMRTM software (ESI Group). Local values of fibre volume fraction and permeability were assigned to each finite element in the discretised mould geometry based on random values for the fibre spacing, which were generated by solving Eqs. 9.16
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and 9.17 for the co-ordinates of the element centre of mass. The dimensions of the finite elements impose a limit to the resolution of permeability variations. This may affect cases with high ωmax. To minimise the influence of the discretisation on the simulation results, the element dimensions should ideally be related to the unit cell dimensions a0 and b0. It is also to be remembered that Eq. 9.20 refers to a single fabric layer. If it is applied to a multi-layer preform, this implies that the behaviour of each layer is identical. If the individual layers are assumed to behave differently, fibre volume fraction and permeability can be calculated by thicknessweighted averaging. In this case, local variations of the multi-layer permeability, and thus the variability of the global permeability, are expected to decrease with increasing numbers of layers. Examples of simulated flow front shapes as a function of time for radial flow are shown in Fig. 9.13 for different parameters σα and Rp/a0. Comparison with Fig. 9.6 suggests that the approach discussed above allows qualitatively realistic simulation of the experimentally observed flow behaviour. Running randomised simulations and determining the time for the flow front to reach a given radial distance allows the effective global permeability to be calculated according to Eqs. 9.8 to 9.10. From statistical evaluation of series of simulations, coefficients of variation of the global permeability of 15.8% at Vf = 0.37 and 11.3% at Vf = 0.56 were derived for an average ratio Rp/a0 = 0.39 and σα = 7.9° (Endruweit
9.13 Examples for simulated flow front shapes in radial injection as a function of time for different parameters σα and Rp/a0; 5684 finite elements.
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et al., 2006c). Quantitative comparison of the latter value with the experimentally determined coefficient of variation at identical global fibre volume fraction (Table 9.2) indicates that the prediction is in the right order of magnitude, but due to oversimplification of the problem, underestimates measured permeability variations. The coefficient of variation of the global permeability as a function of ωmax (Fig. 9.14) shows the same trend as derived from experimental observations and discussed in Section 9.3.2. Elsewhere (as summarised in Endruweit and Long, 2006b), de Parseval et al. (1995) simulated one-dimensional flow with stochastic and regular local permeability variations. They observed that the global permeability is the spatial harmonic mean of the local permeability values. Padmanabhan and Pitchumani (1999) performed stochastic analyses of non-isothermal injection processes based on simulation of one-dimensional flow. The results of their study allowed optimum material and process parameters to be found in terms of minimum process output variability. For a rectangular mould with linear injection gate, Sozer (2001) simulated two-dimensional flow applying local permeability variations to observe the effect of preform non-uniformity on mould filling. Random variations of the local permeability of up to ±35% were reported to have no significant effect on the flow pattern, while variations in a specific pattern caused a more significant effect on the mould filling results. Using a similar approach for studying global permeability variations, Desplentere et al. (2004) assigned local permeability values for injection simulation not only randomly, but also imposing a correlation
9.14 Examples for the coefficients of variation of the global permeability as a function of ωmax.
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between the properties of adjacent material zones along the principal flow direction. It was found that for random assignment of local permeability values to discrete material zones, the variation of global permeability values was influenced by the size of the zones. For correlated local permeability values varying only along the principal flow direction, the results for the global permeability were in agreement with the observations of de Parseval et al. (1995). Lundström et al. (2004) determined non-uniform local permeability values from the dimensions of flow channels with variable widths between the fibre tows. For a completely random distribution of the local permeabilities, they found that the global permeability decreased with the maximum variation at unit cell level, while for a correlated distribution, the permeability could either increase or decrease. Endruweit et al. (2006a) generated discontinuous random permeability fields based on random local fibre angles, which were picked from the fibre angle distribution in an actual fabric. Qualitatively, this allowed realistic simulation of the experimentally observed flow behaviour. Quantitatively, the resulting variations in global permeability were found to be significantly smaller than experimentally observed variations. In general, the variability of the global permeability derived from stochastic simulations based on discontinuous random fields depends strongly on the discretisation, which does not necessarily coincide with the discretisation for calculation of local fluid pressure and flow velocity (i.e. finite elements). If the discretisation of the discontinuous local permeability is fine, the effect on the global permeability is small. Thus, stochastic simulations based on continuous random fields tend to give more realistic results. For the through-thickness permeability, Yu et al. (2003) presented a fractal model, which predicted experimental data for a stitched bi-directional glass fibre fabric with good accuracy. Ngo and Tamma (2004) predicted the through-thickness permeability of a three-dimensional orthogonal woven fabric based on a detailed geometrical description of the textile unit cell, and found qualitative agreement with experimental observations. Song et al. (2009) developed a unit cell based model and performed stochastic analyses for the example of a plain weave fabric. These showed that at a given fibre volume fraction, but different numbers of layers, the average value is constant but the standard deviation decreases with increasing number of layers. This reflects how shifting of layers relative to each other affects the continuity of through-thickness pores and thus results in variability. The same effect is expected to determine the variability in K3 of NCFs. Qualitative analytical estimations, assuming that zones of different permeability are effectively in series for in-plane flow and in parallel for through-thickness flow, suggest that local permeability variations have a less significant influence on the global permeability for through-thickness flow than for in-plane flow.
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Future trends
In this overview, stochastic description of the textile structure is focused on noncrimp fabrics. Similar considerations apply to fabrics of different architecture, as long as the required geometry parameters can be identified. While stochastic resin flow simulation was limited to the example of a flat plate, an approach for stochastic description of the local permeability as a function of discrete random fibre angles was also implemented in injection simulation for actual components with more complex geometries (Endruweit et al., 2006a). However, more realistic injection simulation for actual components would require a quantitatively more accurate approach for description of random effects to be combined with a model for fabric drape, i.e. local changes in fibre angle occurring when flat fabrics are conformed to doubly-curved surfaces. This problem is nontrivial and has not been addressed yet. Based on continuous random fields for description of variable fibre spacing, Crookston et al. (2008) generated distributions of the local micromechanical properties for stochastic analysis of the mechanical behaviour of laminates and identified the most probable failure scenarios from statistical evaluation of series of simulations. This illustrates that the approach implemented for calculation of permeability fields is also applicable to stochastic modelling of any other fabric property depending on the fibre volume fraction.
9.6
References
Carman PC (1937), ‘Fluid Flow through Granular Beds’, T I Chem Eng-Lond, 15, 150–156. Chan A W, Hwang S T (1991), ‘Anisotropic In-Plane Permeability of Fabric Media’, Polym Eng Sci, 31, 1233–1239. Crookston J J, Endruweit A and Long A C (2008), ‘A Model for Stochastic Characterisation of the Mechanical Properties of Textile Composites’, Proceedings of the 9th International Conference on Textile Composites, Newark, Delaware. de Parseval Y, Valery Roy R and Advani S G (1995), ‘Effect of local variations of preform permeability on the average permeability during resin transfer molding of composites’, Proceedings of the 53rd Annual Technical Conference of the Society of Plastics Engineers, Boston, 3040–3044. Desplentere F, Lomov S and Verpoest I (2004), ‘Influence of the scatter of preform permeability on the mould filling: Numerical simulations’, Proceedings of the 25th SAMPE Europe Conference, Paris, 331–336. Drapier S, Pagot A, Vautrin A and Henrat P (2002), ‘Influence of the stitching density on the transverse permeability of non-crimped new concept (NC2) multiaxial reinforcements: measurements and prediction’, Compos Sci Technol, 62, 1979–1991. Elbouazzaoui O, Drapier S and Henrat P (2005). ‘An Experimental Assessment of the Saturated Transverse Permeability of Non-crimped New Concept (NC2) Multiaxial Fabrics’, J Compos Mater, 39, 1169–1193. Endruweit A, Luthy T and Ermanni P (2002), ‘Investigation of the influence of textile compression on the out-of-plane permeability of a bidirectional glass fiber fabric’, Polym Composite, 23, 538–554.
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Endruweit A, Long A, Robitaille F and Rudd C D (2006a), ‘Influence of stochastic fibre angle variations on the permeability of bi-directional textile fabrics’, Compos Part A-Appl S, 37, 122–132. Endruweit A and Long A C (2006b), ‘Influence of stochastic variations in the fibre spacing on the permeability of bi-directional textile fabrics’, Compos Part A-Appl S, 37, 679–694. Endruweit A, McGregor P, Long A C and Johnson M S (2006c), ‘Influence of the fabric architecture on the variations in experimentally determined in-plane permeability values’, Compos Sci Technol, 66, 1778–1792. Endruweit A, Matthys K, Peiro J and Long A C (2009), ‘Effect of differential compression on in-plane permeability tensor of heterogeneous multilayer carbon fibre preforms’, Plast Rubber Compos, 38, 1–9. Ghanem R and Dham S (1998), ‘Stochastic Finite Element Analysis for Multiphase Flow in Heterogeneous Porous Media’, Transport Porous Med, 32, 239–262. Goulley G, Pitard P and Pabiot J (1993), ‘Longitudinal and transversal permeability measurement of glass fiber reinforcement for the modelling of flow in RTM’, Proceedings of the 6th European Conference on Composite Materials, Bordeaux, 83–88. Han K K, Lee C W and Rice B P (2000), ‘Measurements of the permeability of fiber preforms and applications’, Compos Sci Technol, 60, 2435–2441. Heardman E, Lekakou C and Bader M G (2004), ‘Flow monitoring and permeability measurement under constant and transient flow conditions’, Compos Sci Technol, 64, 1239–1249. Hoes K, Dinescu D, Vanheule M, Sol H, Parnas R, Belov E and Lomov S (2002), ‘Statistical distribution of permeability values of different porous materials’, Proceedings of the 10th European Conference on Composite Materials, Brugge. Hoes K, Sol H, Dinescu D, Lomov S and Parnas R (2004), ‘Study of nesting-induced scatter of permeability values in layered reinforcement fabrics’, Compos Part A-Appl S, 35, 1407–1418. Lomov S V, Belov E B, Bischoff T, Ghosh S B, Truong Chi S B and Verpoest I (2002), ‘Carbon composites based on multiaxial multiply stitched preforms. Part 1. Geometry of the preform’, Compos Part A-Appl S, 33, 1171–1183. Lundström T S, Stenberg R, Bergström R, Partanen H and Birkeland P A (2000a), ‘In-plane permeability measurements: a nordic round-robin study’, Compos Part A-Appl S, 31, 29–43. Lundström T S (2000b), ‘The permeability of non-crimp stitched fabrics’, Compos Part A-Appl S, 31, 1345–1353. Lundström T S, Toll S and Hakanson J M (2002), ‘Measurement of the permeability tensor of compressed fibre beds’, Transport Porous Med, 47, 363–380. Lundström T S, Frishfelds V and Jakovics A (2004), ‘A statistical approach to permeability of clustered fibre reinforcements’, J Compos Mater, 38, 1137–1149. Luo Y, Verpoest I, Hoes K, Vanheule M, Sol H and Cardon A (2001), ‘Permeability measurement of textile reinforcements with several test fluids’, Compos Part A-Appl S, 32, 1497–1504. Ngo N D and Tamma K K (2004), ‘Complex three-dimensional microstructural permeability prediction of porous fibrous media with and without compaction’, Int J Numer Meth Eng, 60, 1741–1757. Padmanabhan S K and Pitchumani R (1999), ‘Stochastic modelling of nonisothermal flow during resin transfer molding’, Int J Heat Mass Tran, 42, 3057–3070. Pan R, Liang Z, Zhang C and Wang B (2000), ‘Statistical characterization of fiber permeability for composite manufacturing’, Polym Composite, 21, 996–1006.
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Parnas R S, Flynn K M and Dal-Favero M E (1997), ‘A Permeability Database for Composites Manufacturing’, Polym Composite, 18, 623–633. Scholz S, Gillespie J W Jr and Heider D (2007), ‘Measurement of transverse permeability using gaseous and liquid flow’, Compos Part A-Appl S, 38, 2034–2040. Smith P, Rudd C D and Long A C (1997). ‘The effect of shear deformation on the processing and mechanical properties of aligned reinforcements’, Compos Sci Technol, 57, 327– 344. Song Y S, Heider D and Youn J R (2009), ‘Statistical Characteristics of Out-of-Plane Permeability for Plain-Woven Structure’, Polym Composite, 30, 1465–1472 Sozer E M (2001), ‘Effect of preform non-uniformity on mold filling in RTM process’, International SAMPE Technical Conference Series, 33, 176–189. Trochu F, Gauvin R and Gao D M (1993), ‘Numerical Analysis of the Resin Transfer Molding Process by the Finite Element Method’, Adv Polym Tech, 12, 329–342. Weitzenböck J R, Shenoi R A and Wilson P A (1999a), ‘Radial flow permeability measurement. Part A: Theory’, Compos Part A-Appl S, 30, 781–796. Weitzenböck J R, Shenoi R A and Wilson P A (1999b), ‘Radial flow permeability measurement. Part B: Application’, Compos Part A-Appl S, 30, 797–813. Wu C H, Wang T J and Lee L J (1994), ‘Trans-plane fluid permeability measurement and its applications in Liquid Composite Molding’, Polym Composite, 15, 289–298. Yu B M, Li J H and Zhang D M (2003), ‘A fractal trans-plane permeability model for textile fabrics’, Int Commun Heat Mass, 30, 127–138.
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10 Modelling of the permeability of non-crimp fabrics for composites B. VERLEYE, S.V. LOMOV and D. ROOSE, Katholieke Universiteit Leuven, Belgium
Abstract: Non-crimp fabrics (NCFs) are mainly used as textile reinforcement for composite materials. The simulation of the production processes of these composite materials requires an accurate value for the permeability of the reinforcement used. Like other textiles, NCFs are porous media and have a permeability value in accordance with Darcy’s law. At the K. U. Leuven, a dedicated solver has been developed for the computation of the permeability of textiles. The complex geometry of textiles and the fine fluid channels makes the computation of the permeability a challenge. NCFs are different to woven textiles. Here, the main source of scatter between experimental results is not nesting, but rather the size of the openings caused by the stitching. In this chapter, the numerical approach is explained in detail and the computed values are compared with experimentally obtained permeability data. A parametric study is performed to reveal the important characteristics that influence the permeability. Also, the influence of shearing on permeability is investigated. Key words: textile composite, non-crimp fabric, multiscale modelling, porosity, permeability, resin transfer moulding (RTM).
10.1
Introduction
Non-crimp fabrics (NCFs) are mainly used as reinforcement material for composite parts. A widely used fabrication technique for composite materials is liquid composite moulding (LCM), which includes subclasses like resin transfer moulding (RTM) and vacuum-assisted RTM (VARTM). LCM techniques have in common that a textile reinforcement is draped into a mould and a liquid resin is subsequently driven through the textile reinforcement. The mould geometry and the placement of the inlets and vents influence the final part quality and the process time. To optimise the production process, simulation software packages like PAM-RTM (PAM-RTM, 2010), RTM-Worx (Polyworkx, 2010), LIMS (Advani and Bruschke, 1994) or SimLCM (Kelly and Bickerton, 2009) can be used. These finite element or finite volume packages require a full characterisation of the textile. To predict, for example, the fill time and possible voids in the final part, an accurate estimate of the permeability is indispensible. The permeability is the parameter that relates the velocity of a fluid that flows through the textile and the force that induces the flow. Otherwise stated, the permeability tensor K is a geometric characteristic related to the structural features of the textile at several length scales. For a porous medium, the permeability tensor is defined by Darcy’s law: 242 © Woodhead Publishing Limited, 2011
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with u(x, y, z) the fluid velocity, Re the Reynolds number, Fr the Froude number, p(x, y, z) the pressure, f an external body force, and 〈 〉 denotes volume averaging. The equation is written in dimensionless form, with L the scaling parameter. It relates to the length scale of the problem, e.g. the unit cell dimension. The permeability can be determined experimentally, as described in Chapter 8 of this book. There are, however, several issues with experimental permeability characterisation. The whole process is time- and resource-consuming and values obtained with different experiments or set-ups suffer from large scatter (Hoes et al., 2002; Laine et al., 2010). Numerical computation of the permeability helps to deal with these issues. To compute the permeability of a NCF, a detailed computer model of the textile is required. For the computations presented in this chapter, the textile models were created with the textile modelling package WiseTex, developed at the K. U. Leuven (Verpoest and Lomov, 2005). It delivers a mesoscopic model of the textile that is used to compute different meso-scale parameters which are used as input for macro-scale simulations. For example, a meso-scale fluid flow simulation on the textile model allows one to determine the permeability, as will be shown in this chapter. An example of a unit cell of a model of a bi-axial NCF is shown in Plate II (see between pages 396 and 397). This model will be used further in this chapter. The geometrical data of the shown NCF can be found in Table 10.1. Fig. 10.1 shows the meaning of the dimensions listed in Table 10.1. These fabrics are also used in Chapters 6, 8 and 11 of this book. Textile reinforcements are deformed when they are draped into the mould, which means that the permeability value varies throughout the mould. Thus, not just one permeability value is required, but a value for every element or volume of the computational mesh that will depend on the local rate of shear, compression, nesting, etc. This variability is the main source of dry spot formation and differences in fill time when different runs of the same process are compared. A permeability prediction method should thus be fast, so that it can compute all these permeability values in an acceptable time. More importantly, however, the method must also capture the influence of the deformations on the permeability. Analytical formulas for the computation of the permeability of porous media such as textiles have been presented by several authors (Table 10.2). A drawback of analytical formulas, like the ones from Gebart (1993), Berdichevsky and Cai (1993) and Phelan and Wise (1996), is that they are only valid for simplified textile models. Still, these formulae are applied for validation of simulation software and for the computation of the intra-yarn permeability (section 10.2.3). The permeability can also be determined by numerical simulation of the fluid flow through a textile model and the subsequent use of Darcy’s law (Eq. 10.1). In order to have a fast permeability predicting method, Long et al. reduced the
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Table 10.1 Geometrical data of the undeformed quadri-axial (Q-0–45–90–45) and bi-axial (B1) fabric. Textile tag
Part
Property
Value
Q 0–45–90–45
Ply
Overall Vf Knitting pattern Spacing Areal density Ply Vf Fibre orientation d1/d2 Vf Face factor Back factor Reduction after shear Width/length ply 1 Width/length ply 2 Width/length ply 3 Width/length ply 4 Kxx Kyy Overall Vf Knitting pattern Spacing Areal density Ply Vf Fibre orientation d1/d2 Vf Face factor Back factor Reduction after shear Width/length ply 1 Width/length ply 2 Kxx Kyy
41.2% Tricot+chain 2.74/5.07 mm 667.9 g/(m2) 45% 0°/45°/90° −45° 0.07/0.14 mm 46.3% 7.47 5.48 1 0.66/NA mm 0.18/2.6 mm 0.18/2.6 mm 0.48/7.3 mm 8.83 E–04 mm2 1.28 E–03 mm2 38.5% Tricot closed 1.71/4.94 mm 309.7 g/(m2) 47% 45°/−45° 0.07/0.14 mm 45.4% 3.13 5.52 0.5 0.28/4.10 mm 0.46/6.90 mm 5.04 E–4 mm2 4.77 E–4mm2
Stitching yarn Openings
B1 45–45
Ply
Stitching yarn Openings
three-dimentional (3D) fluid problem to a simplified two-dimentional (2D) model (Wong, 2006). This grid average approach is well suited for parametric studies; however, it is not clear for which type of textile structures the method gives sufficiently accurate predictions of the permeability (Verleye et al., 2007b). Accurate predictions can be obtained by solving the 3D Navier–Stokes or Stokes equations or by solving an equivalent lattice Boltzmann model. Simulation tools based on a lattice Boltzmann model use a regular grid and avoid the difficult mesh generation. However, in order to be useful for parametric studies, the calculation of the permeability must be accurate and fast, which is not possible with the available lattice Boltzmann software (Belov et al., 2004). Direct solution
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10.1 Graphic representation of the geometrical values used in Table 10.1.
of the Navier–Stokes or Stokes equations can be done by a finite element (FE), finite volume (FV) or finite difference (FD) approach. FE and FV simulation tools which work on a non-structured mesh have the advantage that the geometry can be meshed accurately, but the disadvantage that they are not suited for automatic permeability computations, since these solvers require the mesh generation of the fluid region between the yarns of the textile. Authors (Laine et al., 2006; Takano et al., 2002; Robitaille et al., 2003) do not mention problems in that regard; however, we are not aware of published results for realistic volume fractions for which the textile model has sharper edges, posing problems to generating an appropriate mesh.
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Table 10.2 Several methods for the prediction of the permeability of textiles Method
Reference
Theoretical formulas Gebart 1992, Berdichevski and Cai 1993, Phelan and Wise 1996 FE modelling Laine, et al., 2006, Takano, et al., 2002, Robitaille, et al., 2003 Lattice Boltzmann Belov, et al., 2004 modelling Grid2D Wong, et al., 2006 Pore network model Nordlund Loendersloot Random walk methods
Delerue et al., 2003 Nordlund, 2006 Loendersloot, 2006 Van Siclen, 2002
Comment Inaccurate for realistic textiles Cumbersome meshing No acceleration techniques available No validation for different kinds of textile No satisfactory validation Simplified models Simplified models No satisfactory validation
In this chapter we discuss the FlowTex solver, developed at KU Leuven. FlowTex is dedicated to solving the flow through textile geometries, and subsequently computing the permeability via of Darcy’s law. The solver is based on a 3D finite difference discretisation of the Stokes equations. In the next section, the flow models and the numerical approach to solve them are explained. In section 10.4, the results of simulations are compared with experimentally obtained permeability values for un-deformed NCFs. Section 10.5 presents a parametric study to determine the most important geometrical characteristics of a NCF that influence the permeability. In Section 10.6 we further investigate the influence of one deformation, shear, and compare again with experimental values.
10.2
Numerical simulation
10.2.1 Fluid flow models Generally, the isothermal, irrotational flow of a Newtonian fluid is described by the Navier–Stokes partial differential equations: [10.2] These general equations are non-linear and not coupled for the pressure, which makes them hard to solve numerically. A typical technique to solve Eqs. 10.2 is time-stepping towards the steady state solution we are interested in, hence the presence of the time derivative in Eqs. 10.2. For low Reynolds numbers, the diffusion term in 10.2 is much larger than the convection term, so that the latter can be neglected. A rudimentary dimension analysis indicates that the Reynolds
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number we are dealing with is orders of magnitudes smaller than 1. For a typical RTM process, Aström (1997) mentions the following data: • • • •
u∞ = 0.001 m/s L = 0.005 m ρ = 103 kg/m3 μ = 0.1 Pa.s
and thus
For this low Reynolds number, Eqs. 10.2 can be simplified to the steady state Stokes equations [10.3]
which can be solved faster. If intra-yarn flow is neglected, these equations suffice to compute the flow field in the fluid region between the yarns. However, for dense textile structures like NCFs, taking into account the intra-yarn flow yields more accurate results (as will be show later on). To account for intra-yarn flow, one could model the textile on fibre level, and compute the flow not only between the yarns, but also between the fibres. However, a yarn consists of many thousands of fibres, of which a deterministic computer model cannot be made. Moreover, discretising such a complex structure would result in a prohibitively large computational grid. Therefore, we use a multi-scale approach. Instead of solving the Stokes equations, we now solve the Brinkman equations (Brinkman, 2001): [10.4]
on the whole domain. In the fluid region, Kyarn is infinity and Eqs. 10.4 reduce again to the Stokes equations. In the intra-yarn domain, Kyarn has a finite value, which is related to the volume fraction and the internal structure of the fibres inside the yarns. For flow simulations in the irregular geometry of a textile, we solve the Stokes Eqs. 10.3 or the Brinkman Eqs. 10.4 numerically on a regular grid with a finite difference discretisation. To this end, the geometry of the yarns is approximated to the first order. As an example, the first order approximation of the bi-axial NCF is shown in Plate II. Also shown in the figure are some streamlines of a computed solution. In the next subsections, we discuss some aspects of the solution technique. The complete numerical procedure is summarised in Fig. 10.2.
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10.2 A flow chart of the procedure to compute the permeability of a non-crimp fabric.
10.2.2 Boundary conditions A boundary condition must be imposed between the yarn and the fluid region. If we neglect the intra-yarn flow, the yarns are treated as impermeable. Each grid point of the voxel representation is then either located in the fluid domain (‘fluid points’) or in the solid yarn domain (‘solid points’). At the boundaries between the fluid and the solid, no-slip boundary conditions are imposed. We use a second-order discretisation of the Eqs. 10.2 except at the boundaries, where we use a first-order discretisation. Since the geometry is approximated to the first order, we cannot expect second-order accuracy near the boundaries. Including a second-order description of the geometry would not only lead to geometry modelling problems, but a second-order approximation of the boundary would also impose additional numerical stability problems. Although using a first-order approximation of the yarns means that fine meshes might be required to obtain an accurate result, it is shown in Verleye (2008) that permeability values are obtained within an acceptable computational cost. Boundary conditions must also be imposed on the boundary of the unit cell. In the X- and Y-direction (in-plane directions) it is obvious that periodic boundary conditions should be used because of the periodic structure of the textile. In the Z-direction (through the thickness direction), however, both periodic and wall conditions can be justified: several layers of textile are put on top of each other in the mould, so periodic boundary conditions are acceptable. However, the mould is closed under pressure, and the thickness of the textile specimen may be too small to
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neglect the influence of the closed mould. Moreover, if several layers are put inside a mould, nesting of the layers is inevitable. If two layers nest, they form a layer through which no fluid can flow in the Z-direction. Verleye et al. (2007a) show that for woven textiles which often nest, wall conditions in the Z-direction are the best option. However, NCFs do not nest as much as woven textiles (Lomov et al., 2002) and periodic boundary conditions are better suited here. This agrees with the conclusion of Chapter 8, where it is stated that nesting has much less influence on the permeability of NCFs than it has on the permeability of woven textiles. In many macro LCM simulations, 2D flow is assumed and the through thickness flow is neglected. However, when an extra layer with a low permeability is put on top of the preform to facilitate flow, or for very thick preforms, the flow in the third direction becomes significant. The simulations to compute the permeability of the NCFs that we discuss and validate in this chapter are 3D simulations, and can also be used to compute the permeability in the Z-direction.
10.2.3 Solution of the Brinkman equations If the intra-yarn flow is accounted for, no boundary conditions have to be imposed between the fluid and the yarn region, as the same Brinkman Eqs. 10.4 are solved on the whole domain. Laptev (2003) showed that this approach is the same as solving the Darcy equation in the porous region of the yarns, and the Stokes equation in the fluid region. The local parameter Kyarn is calculated analytically, based on the local volume fraction, and the dimension and direction of the fibres. Different formulae for the computation of the local permeability have been investigated: Verleye et al. (2009) show that the formulae by Gebart (1992)
[10.5]
agree the best with numeral results. Here, Kalong is the permeability along the direction of the fibres, and Ktrans the permeability in the transverse direction. The symbol r denotes the radius of the fibres, and Vf is the (local) volume fraction of the fibres in the yarn. The other three parameters, C1, Vm and c, relate to the packing of the fibres. Only Vm has a physical meaning, and is the maximum possible volume fraction for the chosen packing. For a quadratic packing of the fibres, [10.6] and c = 57. Note the resemblance between the formula for Kalong and the wellknown formula of Kozny–Carman (Carman, 1937). Once Kalong and Ktrans are
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computed, they are rotated into the XY system of the unit cell in which the flow equations are solved, which results in Kyarn.
10.2.4 Implementation A finite difference Navier–Stokes solver, NaSt3DGP, was developed at the Institute for Numerical Simulation at the University of Bonn (Griebel et al., 1998). The flow solver employs a Chorin projection method on a staggered grid for the solution of the Navier–Stokes Eqs. 10.2. In the staggered grid approach, the pressure is discretised at the centre of the cells, while the velocities are discretised on the side surfaces. This discretisation leads to a strong coupling between pressure and velocities, and therefore avoids the occurrence of unphysical oscillations in the pressure. From a numerical point of view, boundary conditions between the fluid and the solid region can be implemented in two ways: • •
boundary values are set explicitly in the solid cells which are bordered by fluid cells; and the boundary conditions are included in the equation to be solved in the boundary points in the fluid region.
NaSt3DGP sets the boundary values explicitly. On a staggered grid, this leads to the requirement that a solid point may not be bordered at two opposite sides by fluid points. When the solid region forms very fine structures, as is the case for random fibre assemblies, e.g. non-wovens, this constraint leads to a very fine mesh (finer than required to capture the geometry itself and to obtain a sufficiently accurate solution). More implementation details of the Navier–Stokes solver are discussed in Verleye (2008). In the adaptation of NaSt3DGP towards a finite difference Stokes solver, the discretisation has been realised on a collocated grid, i.e. all the unknowns are discretised in the centre of the cell, and the boundary conditions are included into the discrete system matrix. Discretisation of the Stokes Eqs. 10.3 yields a saddlepoint problem which can be written as [10.7] with A the diffusion matrix, B the mass conservation matrix, C equals 0 or contains stabilisation coefficients and f represents the external force on the system. Equation 10.7 is a linear system, and the PETSc library (Balay, 2010), which provides several iterative and direct methods to solve linear systems, is used to solve Eq. 10.7. Solving Eq. 10.7 with C = 0 results in slow convergence to solution for p with spurious oscillations. Therefore, stability coefficients are added to the matrix C. Stabilisation terms of the form λh2∇p are added to the conservation equation,
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with λ a free parameter and h the discretisation step in the respective direction (Elman et al., 2005, 2006). The choice of λ is not without consequences: a large λ introduces an error in the continuity equation and results in a non-divergence free flow field. On the other hand, a small λ results in slow convergence rate of the iterative solvers and if λ is chosen too small, the stabilisation effect disappears and unwanted pressure oscillations are present in the solution. Our numerical simulations and experience leads to the appropriate choice of λ = O(10−2).
10.2.5 Principal direction The permeability tensor K is a 3D tensor. However, in many practical applications, the out-of-plane direction Z is neglected because 3D macroscopic flow simulations are computationally too expensive, and the thickness of a couple of textile layers is usually much smaller than the other two dimensions of the mould. Fully written, the 2D Darcy’s law [10.8] gives more insight into the number of unknowns that have to be computed. The permeability tensor is symmetric, i.e. Kxy = Kyx (Mikelić, 2000; Whitaker, 1969), which yields three unknowns to be determined. Thus, to compute the complete tensor, two numerical simulations have to be performed, as one simulation only results in two equations. A simulation provides the permeability values in the XY direction of the unit cell of the textile. As the tensor is symmetric, there is another system X′Y′, in which the tensor K′ is diagonal. This is called the principal direction of the textile. In this system, Kxx will reach its maximal value and Kyy its minimal value (or the other way around). Figure 10.3 shows the result of a rotation of K with an angle α, for α = 0° . . . 45°, for the bi-axial textile of Plate II. We conclude that, for this model, the principal flow does not occur along the XY-axis of the unit cell, but in the direction 45° rotated from XY. For the remainder of this chapter, K denotes the permeability in the XY direction, K′ is the principal permeability tensor.
10.3
Experimental validation
Figure 10.1 shows the WiseTex model of both a bi-axial and a quadri-axial NCF. The details of the textiles’ geometries can be found in Table 10.1. The results of the computations and experiments at three different institutes (KU Leuven, École Polytechnique Fédérale de Lausanne and École des Mines [Douai]) are shown in Fig. 10.5. From Fig. 10.5, we conclude that the experimentally determined permeability values differ considerably, as no standard method to experimentally determine
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10.3 The permeability tensor components as function of the rotation of the tensor.
10.4 Comparison of the computed permeability with experimentally obtained values for the bi-axial and the quadri-axial non-crimp fabrics.
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10.5 Models of the sheared bi-axial non-crimp fabric (Plate II) for (a) γ = 15° and (b) γ = 45°.
permeability yet exists (Chapter 8). The computed results are a reasonably good approximation of the experimental results. Note that for the dense structure of NCFs it is necessary to include the intra-yarn flow into the computations to obtain good results. For the quadri-axial NCF the computed permeability without Brinkman flow is 5.3 E–04 mm2, which is a large underestimation of the experimentally determined permeability.
10.4
Parametric study
Several authors have investigated the influence of structural parameters on the permeability of NCFs, e.g. Nordlund (2006), Nordlund and Lundström (2005) and Loendersloot (2006). These works give good insight into the structural properties of NCFs and the influence of the structure parameters on the permeability. For the computation of the permeability, Loendersloot approximates the geometry of the NCF with a resistance network. Nordlund uses a CFD package for the fluid simulations but on simplified models of the NCFs. Loendersloot does not mention experimental values for absolute permeability, but only the anisotropy. Nordlund does, but unfortunately no detailed description of the textile is given, so the values cannot be compared with the results using our method. In this section, we investigate the influence of different geometrical parameters on permeability. The basic geometry for this study is the quadri-axial NCF shown in Plate II, and Table 10.3 presents the data of different NCFs, based on Q–0–45–90–45 (Table 10.1), but in each case one parameter differs slightly from the original one. For Q-tricot and Q-chain, the stitching pattern was changed from tricot-chain to tricot and chain respectively. For this specific case, the stitching pattern has no influence on permeability. For the Q-opening–7–5 and Q-opening–8–6, the openings in the plies caused by the stitching, are modelled smaller and larger respectively. Although the changes in the opening sizes do not influence the
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volume fraction, they have a significant influence on the permeability. For Q-yarn02, only the stitching yarn is changed to a thinner yarn. This thin yarn resides, however, in openings of the same size, which makes flow paths through those openings larger. As expected, this yields a larger permeability. Table 10.3 Geometrical data and computed permeability values of the perturbed quadri-axial model, used in the parametric study Textile tag
Part
Property
Value
Q tricot
Ply
Overall Vf Knitting pattern Spacing Areal density Ply Vf Fibre orientation
41.2% Tricot 2.74/5.07 mm 668.5 g/(m2) 45% 0°/45°/90° −45°
Stitching yarn
d1/d2 Vf
0.07/0.14 mm 46.1%
Openings
Face factor Back factor Reduction after shear Width/length ply 1 Width/length ply 2 Width/length ply 3 Width/length ply 4 Kxx Kyy
7.47 5.48 1 0.66/NA mm 0.18/2.6 mm 0.18/2.6 mm 0.48/7.3 mm 8.83 E–04 mm2 1.28 E–03 mm2
Ply
Overall Vf Knitting pattern Spacing Areal density Ply Vf Fibre orientation
41.2% Tricot+chain 2.74/5.07 mm 667.9 g/(m2) 45% 0°/45°/90° −45°
Stitching yarn
d1/d2 Vf
0.07/0.14 mm 46.3%
Openings
Face factor Back factor Reduction after shear Width/length ply 1 Width/length ply 2 Width/length ply 3 Width/length ply 4 Kxx Kyy Overall Vf Knitting pattern Spacing Areal density Ply Vf Fibre orientation
7.00 5.00 1 0.62/NA mm 0.18/2.6 mm 0.18/2.6 mm 0.44/6.6 mm 8.10 E–04 mm2 1.24 E–03 mm2 41.2% Tricot+chain 2.74/5.07 mm 667.9 g/(m2) 45% 0°/45°/90° −45°
Q opening 7–5
Q opening 8–6
Ply
(Continued)
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Modelling of the permeability of non-crimp fabrics for composites Table 10.3 Continued Textile tag
Q yarn02
Q chain
Part
Property
Value
Stitching yarn
d1/d2 Vf
0.07/0.14 mm 46.3%
Openings
Face factor Back factor Reduction after shear Width/length ply 1 Width/length ply 2 Width/length ply 3 Width/length ply 4 Kxx Kyy
8.00 6.00 1 0.71/NA mm 0.18/2.6 mm 0.18/2.6 mm 0.53/7.9 mm 9.60 E–04 mm2 1.33 E–03 mm2
Ply
Overall Vf Knitting pattern Spacing Areal density Ply Vf Fibre orientation
43.4% Tricot+chain 2.74/5.07 mm 667.9 g/(m2) 45% 0°/45°/90° −45°
Stitching yarn
d1/d2 Vf
0.05/0.07 mm 100%
Openings
Face factor Back factor Reduction after shear Width/length ply 1 Width/length ply 2 Width/length ply 3 Width/length ply 4 Kxx Kyy
7.47 5.48 1 0.66/NA mm 0.18/2.6 mm 0.18/2.6 mm 0.48/7.3 mm 1.75 E–03 mm2 2.39 E–03 mm2
Ply
Overall Vf Knitting pattern Spacing Areal density Ply Vf Fibre orientation
43.6% Chain 2.74/5.07 mm 666.8 g/(m2) 45% 0°/45°/90° −45°
Stitching yarn
d1/d2 Vf
0.07/0.13 mm 46.6%
Openings
Face factor Back factor Reduction after shearing Width/length ply 1 Width/length ply 2 Width/length ply 3 Width/length ply 4 Kxx Kyy
7.47 5.48 1 0.66/NA mm 0.18/2.6 mm 0.18/2.6 mm 0.48/7.3 mm 8.88 E–04 mm2 1.28 E–03 mm2
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The latter two cases show that an accurate modelling of the opening sizes is indispensible for an accurate permeability prediction. This is a difficult task, however, as openings will vary throughout the preform, and will change size because of deformations during the draping. Referring back to Fig. 10.4, we can conclude that the opening sizes of the NCF models were probably underestimated in comparison with the eventual NCF inside the mould. The computed permeability values are, however, still reasonable, not least if one considers the large scatter in the experimental results we are comparing.
10.5
Influence of shear
To fit inside the mould, the multiple layers of the textile reinforcement are deformed in several ways. The layers are compressed and stretched, they nest into each other and are sheared. All of these deformations have an important influence on the permeability magnitude, the anisotropy and the principal direction. In this section, the influence of shear on permeability is investigated. WiseTex allows for the creation of unit cell geometries of sheared textiles (Chapter 8). Figure 10.6 shows the models of the sheared bi-axial NCF with shear angle γ = 15° and γ = 45°. The computed permeability values in X- and Y-directions, the angle of the principal direction and the permeability values in the principal system of the three textile models are presented in Table 10.4. Loendersloot performed experimental permeability measurements on the aforementioned bi-axial NCF. In Table 10.4, the results of these experiments for the undeformed fabric and the 45° sheared fabric are summarised. Figure 10.6 is a repetition of a figure of Chapter 8: it shows the experimentally determined principal direction as a function of the shear angle. The experimental values show large scatter, which makes it difficult to compare the experimental data with the numerical values. The textile models are an average of all the possible real unit cells, so we expect that the computed permeability values are also an average of the measured data. From Table 10.4 and Fig. 10.6, we can conclude that the numerical values lie within the range of the scatter. Table 10.4 The computed and experimental permeability, permeability ratio and principal direction for the undeformed bi-directional non-crimp fabric, and the bi-directional non-crimp fabric sheared with 45° 0°
K1’ K2’ Alpha Gamma
45°
Num.
exp
Num.
exp
7.44 5.96 0.8 3
30 38 0.78 12
4.55 4.06 0.89 25
20–30 3–9 0.38–0.43 18–30
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10.6 The experimentally determined principal direction as function of the shear angle. The three solid dots are computed values.
10.6
Conclusion
The accurate and fast computation of the permeability of NCFs is possible, and allows one to avoid the difficulties of experimental determination of the permeability. The solution of the Stokes equations or the Stokes–Brinkman equations on a mesoscale model of the textile’s geometry yield accurate permeability estimations. A software package to solve these equations, FlowTex, has been developed at the KU Leuven. A parametric study shows that the most influential geometric parameter of the NCF model is the size of the opening caused by the stitching needle. Not only a single permeability value of the undeformed textile is important, however, but also the influence of deformations on permeability is indispensible input for macro-scale simulations. A comparison of the computed permeability of sheared models with experimental data demonstrates that the combination of a detailed model with the FlowTex software is a valuable method to compute the influence of shear on permeability.
10.7
Acknowledgements
The authors thank Prof. Griebel, M. Klitz and R. Croce of the University of Bonn for the interesting discussions and the collaboration on the adaptation of the NaSt3D-code (Griebel et al., 1998).
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This research is part of the project: Predictive tools for permeability, mechanical and electro-magnetic properties of fibrous assemblies: modelling, simulations and experimental funded by the IWT (Flemish government). This paper presents research results of the Belgian Network on Dynamical Systems, Control, and Optimization, funded by the Interuniversity Attraction Poles Programme, initiated by the Belgian State, Science Policy Office. The scientific responsibility rests with its authors.
10.8
References
Advani S, Bruschke M, Parnas R S (1994), ‘Resin transfer molding flow phenomena in polymeric composites‘, in Flow and rheology in polymer composites manufacturing, Amsterdam, Elsevier. Aström B T (1997), Manufacturing af Polymer Composites, Chapman and Hall. Balay S, Buschelman K, Gropp WD, Kaushik D, Knepley MC, McInnes LC, et al. (2010) Available from: http://www.mcs.anl.gov/petsc (accessed April 2010). Belov E B, Lomov S V, Verpoest I, Peeters T, Roose D, Parnas R S, Hoes K, and Sol H (2004), ‘Modelling of permeability of textile reinforcements: lattice Boltzmann method’, Composites Science and Technology, 64, 1069–1080. Berdichevsky A and Cai Z (1993), ‘Preform permeability predictions by self-consistent method and finite element simulation’, Polymer Composites, 24(2), 132–143. Brinkman H (1949), ‘On the permeability of media consisting of closely packed porous particles’, Applied Scientific Research, 1(1), 81–86. Carman P (1937), ‘Fluid flow through granular beds’, Transactions of the Institution of Chemical engineers, 15, 150–166. Delerue J F, Lomov S V, Parnas R S, Verpoest I and Wevers M (2003), ‘Pore network modelling of permeability for textile reinforcements’, Polymer Composites, 24(3), 344–357. Elman H C, Silvester D J and Wathen A J (2005), Finite elements and fast iterative solvers, Oxford, Oxford University Press. Elman H, Howle V, Shadid J, Silverster D, and Tuminaro R (2006), ‘Least squares preconditioners for stabilized discretizations of the Navier–Stokes equations’, SIAM Journal on Scientific Computing, 27, 1651–1668. Gebart B (1992), ‘Permeability of unidirectional reinforcements for RTM’, Journal of Composite Materials, 26(8), 1100. Griebel M, Dornseifer T, and Neunhoeffer T (1998), Numerical Simulation in Fluid Dynamics, a Practical Introduction, Philadelphia, SIAM. Hoes K, Dinescu D, Sol H, Vanheule M, Parnas R, Luo Y, Verpoest I (2002), ‘New set-up for measurement of permeability properties of fibrous reinforcements for RTM’, Composites part A: applied science and manufacturing, 33(7), 959–969. Laptev V (2003), ‘Numerical solution of coupled flow in plain and porous media’, PhD thesis, Universität Kaiserslautern. Laine B et al. (2010), ‘Experimental determination of the permeability of textiles: a benchmark exercise’, in progress. Laine B, Hivet G, Boisse P, Boust F, Lomov S V and Badel P (2006), ‘Permeability of the woven fabrics’, In C. Binetruy, ed., Proceedings of the 8th international conference on flow processes in composite materials, 39–46.
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Loendersloot, R (2006), ‘The structure–permeability relation of textile reinforcements’, PhD thesis, Universiteit Twente. Lomov S V, Verpoest I, Peeters T, Roose D and Zako M (2002), ‘Nesting in textile laminates: geometrical modelling of the laminate’, Composites Science and Technology, 63(7), 993–1007. Mikelić A (2000), ‘Homogenization theory and applications to filtration through porous media’, in Filtration in porous media and industrial application, Berlin/Heidelberg, Springer, 127–214. Nordlund, M and Lundström, T S (2005), ‘Numerical study of the local permeability of noncrimp fabrics’, Journal of Composite Materials, 39 (10), 929–947 Nordlund, M (2006), ‘Permeability modelling and particle deposition mechanisms related to advanced composites manufacturing’, PhD thesis, Luleå University of Technology. PAM-RTM (2010), http://www.esi-group.com/products/composites-plastics/pam-rtm (accessed April 2010). Phelan F R and Wise G (1996), ‘Analysis of transverse flow in aligned fibrous porous media’, Composites Part A: Applied Science and Manufacturing, 27(A), 25–34. Polyworx (2010), http://www.polyworx.com (accessed April 2010). Robitaille F, Long A, Jones I and Rudd C (2003), ‘Automatically generated geometric descriptions of textile and composite unit cells’, Composites Part A: Applied Science and Manufacturing, 34, 303–312. Takano N, Zako M, Okazaki T and Terada K (2002), ‘Microstructure-based evaluation of the influence of woven architecture on permeability by asymptotic homogenisation theory’, Composites Science and Technology, 62, 1347–1356. Van Siclen C (2002), ‘Walker diffusion method for calculation of transport properties of finite composite systems’, Physical Review E, 65 (2), 1–6. Verleye B, Croce R, Griebel M, Klitz M, Lomov S V, Morren G, Sol H, Verpoest I, Roose D (2007a), ‘Permeability of Textile Reinforcements: Simulation; Influence of Shear, Nesting and Boundary Conditions; Validation’, Composites Science and Technology, 68(13), 2804–2810. Verleye B, Lomov S V, Long A, Wong C C and Roose D (2007b), ‘Permeability of textile reinforcements: Efficient prediction and validation’, in Proceedings of the 6th international conference on composite materials, 220–221. Verleye B (2008), ‘Computation of the permeability of multi-scale porous media with application to technical textiles’, PhD thesis, KU Leuven. Verleye B, Morren G, Lomov S V, Sol H, Verpoest I and Roose D (2009), ‘User-friendly permeability predicting software for technical textiles, Research Journal of Textile and Apparel, 13(2), 19–27. Verpoest I and Lomov S V (2005), ‘Virtual textile composites software WiseTex: integration with micro-mechanical, permeability and structural analysis’, Composites Science and Technology, 65(15), 2563–2574. Whitaker S (1969), ‘Fluid motion in porous media’, Industrial & engineering chemistry, 61(12), 32–46. Wong C C, Long A C, Sherburn M, Robitaille F, Harrison P and Rudd C D (2006), ‘Comparisons of novel and efficient approaches for permeability prediction based on the fabric architecture’, Composites Part A: Applied Science and Manufacturing, 37(6), 847–857.
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Plate II The WiseTex model of a biaxial and quadriaxial non-crimp fabric. The geometrical parameters are found in Table 1. For both models, the first order discretisation is shown, with some streamlines that demonstrate the solution of a flow simulation (Chapter 10).
Plate III (a) Finite element (FE) models of non-crimp fabric composites; (b) A typical FE mesh of a non-crimp fabric composite with the distortions induced by the stitching (Chapter 15).
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11 Mechanical properties of non-crimp fabric (NCF) based composites: stiffness and strength S. V. LOMOV, T. TRUONG CHI and I. VERPOEST Katholieke Universiteit Leuven, Belgium
Abstract: This chapter explores the behaviour of multiaxial multi-ply warp-knitted carbon/epoxy composites in tension, short beam shear test and in-plane shear test. The mechanical properties are reported and the damage initiation and development is investigated using acoustic emission and X-ray observations. The latter makes clear a sequence of damage progression in non-crimp fabric (NCF) composites under static loading. The behaviour of composites produced from sheared reinforcements is studied next, providing data for assessment of change of NCF composite properties over a three-dimensional (3D) shaped preform with local shear of the reinforcement. Key words: Mechanical properties, damage, acoustic emission, sheared reinforcement.
11.1
Introduction
This chapter presents results of experimental studies of carbon/epoxy composites, reinforced with non-crimp fabrics (NCF) (the abbreviation ‘NCF’ will be used in the chapter interchangably with ‘MMF’ for multiaxial multi-ply fabrics), which were a subject of experimental studies reported in Chapters 4 (internal geometry), 6 (deformability) and 8 (permeability), forming a consistent reference database. The main interest of these studies, apart from measuring the mechanical properties, is two-fold: first, to understand the influence of the disturbances of the fibrous plies inflicted by the stitching on the properties of the composite, and second, to reveal the nature of damage progression. The experimental investigations reported here were originally published in Truong Chi et al. (2005; 2008); the works of Mikhaluk et al. (2008), Edgren et al. (2004; 2005; 2006) and Mattsson et al. (2008) are also used in the discussion. The text of the chapter is largely based on Truong (2005). The reader is referred to these works for details of the experimental procedure and the comprehensive sets of data. The chapter covers tensile and shear behaviour of the NCF composites. Compression, impact and compression after impact of these composites is studied in Drapier et al. (1999), Saito et al. (2006) and Beier et al. (2007; 2008). The following chapters of this part (Chapters 12–17) describe in more detail the damage progression in NCF composites, their fatigue behaviour and the 263 © Woodhead Publishing Limited, 2011
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mechanical properties of structurally stitched NCF composites. The behaviour of NCF composites, studied experimentally in this chapter, is explored with modelling methods in Chapters 18–21.
11.2
Materials and composite production
The multiaxial multi-ply carbon reinforcement fabrics (MMF) were provided by Saertex Wagener GmbH & Co. KG. The (UD) fabric parameters, as specified by the manufacturer, are shown in Table 11.1. A unidirectional (UD) fabric ‘U’ is stabilised by a set of UD E-glass fibres. MMF B1, B2 and Q are the same as described with the same IDs in Chapter 4 and Chapter 6, and more details on the internal geometry of these MMFs can be found in these chapters (for example, the images of the fabric surface are shown in Fig. 6.1). To make it possible to produce the symmetric laminates, the quadriaxial and +45°/−45° fabrics were provided in two complementary forms where one is the mirror image of the other. It is, however, not necessary for 0°/90° material because by turning 0°/90° fabric face side down, the 90°/0° fabric can be obtained. In all cases, the fabrics are stitched by polyester (PES) yarn with a weight of 7.6 tex and an areal density of 6 g/m2, which makes up 1% to 4% of the total weight depending on the type of fabric. MMF are all produced based on UD plies with areal density of 150 g/m2. As discussed in Chapter 6, piercing a fibrous ply by a needle and forming of the stitching (warp-knitted) loop results in a certain disturbance of the uniform placement of the fibres. More precisely, the stitching causes deviation of the fibres in a ply from their uniform direction. These deviations produce fibre-free zones
Table 11.1 Specifications of multiaxial multi-ply carbon fabrics Description
Quadriaxial carbon fabric (Q)*
Biaxial carbon fabric +45°/−45° (B1) *
Biaxial carbon fabric 0°/90° (B2)
Unidirectional carbon fabric (U)
Orientation of plies, degrees
1) 0; + 45;90;−45 2) 0;−45;90; + 45
1) −45; + 45 2) +45; −45
0/90
0
Materials
12K Toray T700 50C, polyester stitching, 7.6 tex
12K Toray T700 60E, polyester stitching, 7.6 tex
24K, T600 polyester stitching, 7.6 tex
Toray 24K T700 31E, polyester stitching, 7.6 tex stabilised glass 13g/m2
Mass, g/m2 Stitching pattern
644 Tricot-warp
300 Tricot
307 Tricot-warp
165 Tricot-warp
* Quadriaxial and biaxial +45°/−45° fabrics were provided in two forms (1) and (2), respectively. One is the mirror of the other for symmetrical lay-up.
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near stitching locations. The fibre-free zones can be confined to an area surrounding the stitching (called ‘openings’ or ‘cracks’), or continuous ‘channels’ in the ply. When laying up the fabrics, the stitching yarns at the fabric surface create ‘gaps’ between fabrics. These ‘openings’ and ‘channels’ in the fibrous plies and ‘gaps’ between them cause resin-rich regions in the composites, affecting their mechanical performance. They can also change the permeability of the preforms, affecting their processability in RTM as discussed in Chapters 9–10. Shell Epoxy Resin Epikote 828 LV with hardener Epikure DX 6514 were used as a matrix. The mixing ratio between resin and hardener was 100/17. The RTM equipment at the Composite Laboratory of the MTM Department, Katholieke Universiteit (KU) Leuven, was used to make composite plates with a thickness of approximately 3.5 mm. Before placement of the fabrics, the mould cavity was warmed to 40°C. Fabrics were placed in the mould cavity in such a way as to get symmetry of stacking sequence about the plate mid-plane, with attention to the stitching and stabilised yarns. If the stitching or stabilising yarns are not in symmetry, warpage will occur in the composite plates, even though the stitching and stabilising yarns are a small fracion of the total fabric weight (maximum is 11% in UD fabrics). The stacking sequence of quadriaxial, biaxial +45/−45 and 0/90 laminates were (+45/90/−45/0/0/−45/90/+45)s, (+45/−45/+45/−45,+45/−45, +45/−45)s and (0/90,0/90,0/90,0/90)s, respectively. After degassing, the resin was injected into the mould cavity at a pressure of 2 bar for two minutes. After that, the pressure was increased up to 4–5 bar until the cavity was filled. During injection, vacuum of −0.5 bar was applied in the cavity. After injection, the mould was heated to 70°C for one hour to cure the resin. The composite plate was then demoulded and post-cured in an air oven at 160°C for one hour. The plates were cut using a diamond saw into specimens with dimensions specified by test standards. Because the mould cavity has a constant thickness, the actual fibre volume fraction of composite plates made from different fabrics varied from 37% to 46%. This range of fibre volume fraction is more characteristic for automotive applications.
11.3
Test procedures
The directions of tests performed on the composites were as follows: machine direction (MD) is the flow direction of fabric in the machine during production, while bias (BD) and cross direction (CD) are 45° and 90° relative to machine direction, respectively.
11.3.1 Tensile test ISO 527–4, ‘Test conditions for isotropic and an-isotropic fibre reinforced plastic composites’ was followed to prepare the specimens and perform the tensile tests. An Instron 4505 tensile testing machine with hydraulic clamps and a load
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cell of 100 kN was used with the crosshead speed set at 1 mm/min for the tests in fibre direction and 3 mm/min for the tests in off-fibre direction. To register the displacement in both length and width directions during the test, extensometers with gauge lengths of 50 mm and 12.5 mm respectively were attached to the specimen. The specimen dimensions were 250 mm by 12.5 mm. For each investigation, five tests were performed and their results were averaged.
11.3.2 Short beam shear test To determine the interlaminar shear strength of the composites in MD, short beam shear tests were performed following ISO 14130, ‘Fibre reinforced plastic composites – Determination of apparent interlaminar shear strength by short beam method’. An Instron 4467 testing machine was used, with a crosshead speed of 1 mm/min and a load cell of 30 kN. The diameters of the loading and supporting members were 10 mm and 5 mm respectively. The span used was 16 mm for specimens with dimensions of 30 mm by 15 mm and 3.4 mm thick.
11.3.3 In-plane shear test ASTM D 5379/D 5379M – 93 ‘Standard test method for shear properties of composite materials by the V-notched beam method’ was used to prepare the specimens and perform the test to measure in-plane shear properties of the materials including shear modulus (G) and shear strength (τ u). The Instron 1196 was equipped with a V-notched beam test fixture. Strain gauges with an active gauge length of 3 mm were used to measure the strain. The crosshead speed was set at 1 mm/min and a load cell of 20 kN was used. According to the standard, the quadriaxial, 0°/90° and UD laminates were tested in machine direction while the +45°/−45° laminate was tested in BD. The specimen dimensions were 76 mm by 19 mm and 3.4 mm thick. Three millimetre-thick end tabs were used to strengthen and stabilise the specimens. They also help to prevent compression failure.
11.4
Mechanical properties of non-crimp fabric (NCF) composites
11.4.1 Tensile properties The tensile properties of NCF laminates in different directions are shown and compared in Table 11.2 and Fig. 11.1. The tensile stress-strain diagrams of the quadriaxial (Q) laminates in different directions (Figure 11.1a) show that the material behaves almost linearly up to failure. The tensile properties of the Q laminates are determined primarily by the fibres in the loading directions, independent of the lay-up. Table 11.2 presents the
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Table 11.2 Tensile properties of multiaxial multi-ply fabrics reinforced epoxy composites in different directions Material
Q 0°/±45°/90°
B1 +45°/−45°
B2 0°/90°
U (not stabilised) U (stabilised)
Test direction
Modulus (GPa)
Strength (MPa)
Ult.strain (%)
Poisson ratio
Vf (%)
MD
32.8 ± 0.6
530 ± 26
1.76 ± 0.10
0.30 ± 0.02
42.1 ± 0.8
BD
32.5 ± 0.9
496 ± 26
1.81 ± 0.05
0.33 ± 0.02
40.3 ± 2.5
CD
34.1 ± 1.3
500 ± 23
1.61 ± 0.09
0.37 ± 0.05
MD
34.9
566.5
45
BD
36.0
553.8
45
CD
34.5
505.6
MD
9.9 ± 0.4
177.4 ± 3.9
8.7 ± 0.3
0.83 ± 0.04
39.4 ± 1.8
BD
44.8 ± 4.2
689 ± 47
1.6 ± 0.1
0.05 ± 0.01
39.4 ± 1.8
CD
9.5 ± 0.4
159.7 ± 1.7
9.4 ± 0.9
0.82 ± 0.04
44.5 ± 1.2
45
36.9 ± 1.1
BD
50.8
786.9
45
MD
45.5 ± 1.1
659 ± 36
1.55 ± 0.05
0.06 ± 0.01
39.5 ± 1.3
BD
9.1 ± 0.3
148.0 ± 6.2
11.97 ± 0.84 0.78 ± 0.02
40.8 ± 0.9
CD
43.6 ± 1.9
654 ± 32
1.59 ± 0.04
MD
51.5
750.8
CD
47.8
721.3
MD
95.1 ± 4.1
1317.3 ± 55.3
1.49 ± 0.06
0.37 ± 0.03
CD
5.3 ± 0.1
28.3 ± 5.1
0.55 ± 0.09
0.03 ± 0.01
0.05 ± 0.01
45
MD
99.6
1380.3
MD
94.3 ± 8.2
1233 ± 85
1.49 ± 0.09
0.32 ± 0.04
CD
7.8 ± 0.3
59.6 ± 1.4
0.84 ± 0.06
0.03 ± 0.00
MD
99.0
40.8 ± 0.9 45 42.9 ± 0.6 42.9 ± 0.6 45
1296.4
42.8 ± 0.8 45.9 ± 0.8 45
Note: ± standard deviation is shown in all the tables in the chapter Greyed cells: Experimental data normalised to the fibre volume fraction of 45% (for tests in fibre direction)
experimental data normalised at a fibre volume fraction of 45% using an approximate formula Enorm (45%) = E(Vf)·(45%)/Vf. The data show that the maximum variation in stiffness between different directions is about 4%, and the strains to failure in all test directions are close to each other. However, the strength and ultimate strain in MD and BD are slightly higher than those in CD of 10 %. According to Hoersting (1998), this phenomenon can be explained by fibre damage due to the stitching operation during fabric manufacturing. All the needles penetrate simultaneously in one line in CD. Therefore, the needles affect the entire length of a particular fibre bundle in a 90° ply. Due to the inertia of the fibre bundle, it cannot be thrust aside from all stitching sites simultaneously, leading to fibre damage. For the fibres in 45° and 0° plies, the needles only pierce into one place of many fibre bundles, so the fibre bundles are sufficiently flexible to avoid the needles and consequently fibre damage is less. The failure patterns of the Q specimens in three test directions illustrated in Fig 11.2A are almost the same. They
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11.1 Tensile stress–strain curves of multiaxial multi-ply fabric laminates in different directions: (a) quadriaxial, (b) biaxial +45°/−45°, (c) 0°/90° and (d) unidirectional laminate.
are characterised with transverse matrix break in 90° plies, shear failure combined with fibre break in +45° and −45° plies, fibre break in 0° plies and delamination. Table 11.2 and Fig. 11.1 present the tensile properties of biaxial laminates including B1 (+45°/−45°) and B2 (0°/90°) in different directions. The tensile properties of the composites based on two different biaxial fabrics in fibre direction and off-fibre direction respectively are very close to each other. In terms of mechanical performance, they are actually the same materials, as one is the other after a rotation of 45°. In other words, the effect of stitching patterns on the mechanical performance of biaxial composites is not significant, which is in agreement with the study by Asp et al. (2004). Unlike the quadriaxial laminates, the biaxial laminates are highly anisotropic materials, e.g. the modulus and strength in fibre directions (BD for +45°/−45°, MD and CD for 0°/90° laminates) exceed those in the other directions by a factor of five. Furthermore, the stress– strain curves of the tests in fibre orientation are linear, while in the other matrixdominated orientations a non-linear relation is observed. The tensile strength of B1 in BD and B2 in MD is slightly higher than that of B2 in CD. This can be explained by the different levels of fibre damage during the stitching process as discussed above. The failure pattern of the specimens tested in off-fibre direction (Fig. 11.2B,C) are similar and associated with matrix shearing, fibre debonding, fibre pull-out, inter-ply tearing and fibre breaks. In contrast, the same figures show
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11.2 Typical failure patterns of MMF composite specimens subjected to tensile loading in three different directions. Sample reinforcement: (A) quadriaxial (Q); (B) B1 (+45°/−45°); (C) B2 (0°/90°); (D) unidirectional.
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the failure pattern of specimens tested in the fibre direction with a rather ‘clean’ break, perpendicular to the loading direction. Cracks along the fibres in the top plies are also seen but no splitting between fibre bundles was observed. The results of tensile tests as well as stress–strain curves of UD laminates with stabilising glass yarns in CD and UD laminates with stabilising yarns removed are shown in Table 11.2 and Fig. 11.1. The results of the tests performed on the UD laminates with stabilising glass yarns show higher transverse properties (40% for stiffness and 100% for strength) compared to those of UD without stabilising glass yarns. Although the stabilising yarns take only a low fraction in the fabric (9% in weight), their contribution in CD is significant since the modulus of glass (70 GPa) is substantially higher than that of the matrix (3 GPa). The properties in MD are, however, similar for the two cases. The stress–strain curves of the tests in both MD and CD are linear. The averaged strain to failure of Q, B1 and B2 laminates tested in fibre directions (Table 11.2) is 1.7% and roughly 12% higher than that of UD laminates tested in fibre direction (1.5%), indicating a higher contribution of 0° plies into tensile properties of MMF laminates. This improvement may be associated with the lateral constraint provided by off-axis plies, which prevent the effects of splitting along the fibre in the 0° plies, preventing the specimens from falling apart. The failure process in 0° plies, which essentially controls the properties of the MMF laminates, is modified and results in higher strain to failure and strength. In addition, the stitching, which binds the plies in the layers together, may play a certain role in preventing the fibres in 0° plies from splitting. The effects of off-axis plies on restricting fibre splitting in the 0° plies can be seen clearly in the test on the UD laminates in machine direction (Fig. 11.2D). With only a small amount of stabilising glass yarns (9% in weight as mentioned) in CD, the fracture of the UD laminates is completely modified from severe splitting along fibres to a clean fracture surface perpendicular to fibre direction without any fibre splitting. This explains the fact that no splitting was found on the MMF specimens tested in fibre direction even with the 0° plies on the surface. The Poisson's ratio, which depends on fibre orientation, is also presented in Table 11.2. It can be seen that the fibres at ±45° relative to the loading direction facilitate the contraction in the width of the specimens, resulting in high Poisson's ratio (biaxial laminates tested in off-fibre directions). In contrast, the fibres perpendicular to the loading direction prevent the specimens from contracting in the width direction, leading to a very low Poisson’s ratio (UD laminates tested in CD and biaxial laminates tested in fibre direction). The quadriaxial laminates have fibres in both ±45° and 90° so they have an intermediate Poisson's ratio value. In the tensile test of MMF laminates in the fibre direction, it was observed that the stiffness of the materials increased, despite micro-damage occurring in the materials, approximately 7% compared to the initial value, over 1% of the applied strain. It is due to the strain-hardening behaviour of carbon fibres (Curtis et al., 1968; Shioya et al., 1996). Besides, the increase in stiffness may be attributed to
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the better fibre reorientation toward the loading direction due to micro-cracking in the matrix of the materials.
11.4.2 In-plane shear properties Table 11.3 shows the in-plane shear properties of matrix-dominated Q, B1, B2 and U laminates. It was found that the Q laminates have much higher shear strength and modulus compared to those of B1, B2 and U laminates (by a factor of four). The significantly higher in-plane shear properties of quadriaxial laminates can be explained by the presence of fibres in +45° and −45°, which took the tensile and compression loads in these directions. Figure 11.3c shows typical
11.3 Scheme of the shear Iosipesku test (a), typical stress-strain diagram (b) and typical failure patterns of quadriaxial (c), +45°/−45° (d), 0°/90° (e), unidirectional-CD (f) and unidirectional-MD (g) V-notch specimens for in-plane shear tests.
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Table 11.3 In-plane shear properties of multiaxial multi-ply fabric reinforced epoxy composites Material
Test direction
Shear modulus (GPa)
Shear strength (MPa)
Vf (%)
Q 0°/±45°/90° B1 +45°/−45° B2 0°/90°
Machine Bias Machine Machine Cross
11.3 ± 0.8 3.3 ± 0.3 2.3 ± 0.2 2.4 ± 0.4 3.6 ± 0.31
222.0 ± 13.9 61.5 ± 4.8 53.8 ± 1.9 71.3 ± 0.3 86.8 ± 6.9
42.1 ± 0.8 39.4 ± 1.8 39.5 ± 1.3 42.8 ± 0.8 45.9 ± 0.82
U
failure of Q specimens under in-plane shear loading with fibre breakage in +45°/−45° plies and delaminations. In theory, the shear properties of B1, B2 and U laminates in the mentioned test directions should be identical. However, experiment showed that their shear moduli separated themselves into two ranges, somehow related to the direction of fibres on the top plies/stacking sequence. On the one hand, the B1-BD* Fig. 11.3d and U-CD (Fig. 11.3f) specimens with fibres in the top plies perpendicular to the loading direction have a stiffness of 3.5 GPa. These specimens failed with two cracks at the notches parallel to the fibre direction due to a stress concentration and many cracks in the gauge section also parallel to the fibre direction. On the other hand, B2-MD (Fig 11.3e ) and U-MD (Fig. 11.3g) specimens with fibres in the top plies parallel to the loading direction have a stiffness of 2.5 GPa (around 30% lower than the other case). These specimens also failed with cracks parallel to the fibre directions. Compared to the properties of U-CD specimens, the test results of U-MD specimens are not only lower in modulus but also in strength. The U-MD specimens failed prematurely because fracture was initiated by a combination of shear and transverse tensile stresses at the notch roots (Broughton, 2000). A crack propagated along the notch-root axis, which is the path of least resistance. The specimens are completely separated into two parts as shown in Fig. 11.3g. It is quite difficult to determine the ‘real’ shear strength of B1, B2 and U-CD specimens due to the presence of fibres perpendicular to the loading direction. They bridge the material on both sides of the notches and continue to support the specimen even after initiation of damage. Therefore, no significant drop of stress can be seen during testing. As the test continues, the stress increases because fibres may reorient following shear failure and subsequently the fibre direction approaches ±45° relative to the loading direction, allowing them to carry a major of portion of the load. At a certain point, the test has to stop because the specimen hits the bottom of the fixture (Fig. 11.3a). Figure 11.3b presents a non-linear stress–strain curve of the biaxial laminates and the change of stiffness compared to its initial value. Due to damage development in the material, the shear stiffness decreases fast and * Short form to express B1 specimen tested in bias direction (BD). The same applied for other cases.
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steadily to 10% of the initial stiffness, after which the stiffness is almost constant up to the end of the test. Because of the absence of a significant drop in stress, the shear strength of the material is determined by the stress equivalent to the remaining stiffness of 10%, at which point the material is assumed to have completely failed.
11.4.3 Interlaminar shear strength (ILSS) The interlaminar shear strength (ILSS) of MMF reinforced epoxy composites is presented in Table 11.4. It is evident that the ILSS of the U laminates is up to twice that of the others. This phenomenon can be explained when observing the damage development in the material using an inspection camera during testing. In the test of Q, B1 and B2 laminates, it was observed that premature damage was initiated by off-axis fibres with cracks through the ply thickness in a region near the point of load application. Subsequently, they propagated in between plies as shown in Fig. 11.4a, b and c, resulting in low ultimate stress value. On the other hand, in the test of U laminates, cracks were initiated and propagated in between plies as depicted in Fig. 11.4d. By definition, the ILSS is obtained when the beam fails in the interlaminar shear mode by cracking along a horizontal plane between the lamina. So only the ultimate stress of the U laminate is the real ILSS of the material, while the results obtained from the tests on the Q, B1 and B2 laminates should be considered as intralaminar shear strength or transverse tensile strength at 45° relative to the loading direction.
11.4 Short beam shear test specimens after testing: (a) quadriaxial specimen, (b) +45°/−45° specimen, (c) 0°/90° specimen and (d) unidirectional specimen.
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Table 11.4 The interlaminar shear strength of multiaxial multi-ply fabrics reinforced epoxy composites Material
Test direction
Interlaminar shear strength (MPa)
Ultimate deflection (mm)
Vf (%)
Q B1 +45°/−45°
Machine Machine
36.2 ± 1.1 38.4 ± 1.2
0.5 ± 0.04 1.0 ± 0.10
43.8 ± 0.8 39.4 ± 1.8
Bias Machine Machine
46.0 ± 2.4 41.8 ± 2.1 73.7 ± 1.8
0.5 ± 0.04 0.4 ± 0.04 0.7 ± 0.03
36.9 ± 1.1 40.8 ± 0.9 42.8 ± 0.8
B2 0°/90° U
11.5
Mechanical properties of composites based on sheared MMCF
As discussed in Chapter 6, shearing during forming changes the fibre orientation, areal density and thickness of the fabric and hence the fibre volume fraction of the composites. The properties of composites reinforced with sheared MMFs were studied using biaxial fabric B1 and B2. The fabric was sheared as shown in Fig. 11.5, and than impregnated using the same RTM process as explained before. The resulting range of fibre volume fraction in the sheared samples is 23–39%.
11.5 Sheared specimens in shear frame, definition of shear angle and ply angle.
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Figure 11.6 and Table 11.5 present stress–strain curves and tensile properties in longitudinal and transverse directions (as defined in Fig. 11.5) of the composites based on sheared biaxial fabrics. The identical stress–strain curve for longitudinal and transverse direction of B1 laminates (named ‘undeformed material’) was included in Fig. 11.6a as a reference. Figure 11.7 shows the fracture of loaded specimens reinforced by non-sheared fabrics and fabrics sheared with various angles. Referring to the tensile diagrams of sheared materials (Fig. 11.6a), the stress– strain curve of the tensile test in the longitudinal direction has a nearly linear relation until failure; the higher the shear angle the more linear the stress–strain curve is. Experimental results in Table 11.5 and Fig. 11.6b also show that the tensile properties in the longitudinal direction increase as the shear angle increases, and at a higher rate, when the shear angle is above 30°. These phenomena can be explained by the decrease of ply angle and increase of fibre volume fraction, resulting from the increase in shear angle. A different behaviour of the sheared material in the transverse direction is observed in Fig. 11.6a. While the stiffness of non-sheared material decreases gradually due to tensile loading and a linear behaviour of sheared material in longitudinal direction, the stress–strain curve of the sheared materials in a transverse direction has three different regions. Initially, the
11.6 Tensile properties of epoxy composites reinforced by sheared biaxial fabrics at different shear angles in longitudinal and transverse direction: (a) typical stress–strain curves, (b) tensile properties of sheared B1 in longitudinal direction, (c) tensile properties of composites reinforced by B1 and B2 sheared at 45° and (d) tensile properties of sheared B1 in transverse direction.
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B1
22.5
20
50
30
30
45
45
0
46.4 ± 2.7 45.8 ± 1.3 31.2 ± 1.8 30 ± 0.1 21.4 ± 1.1 22.5 ± 0.1 19.6 ± 0.5 20 ± 0.1 35.2
32.0
26.1
22.6
39.4 ± 1.4
35.6 ± 0.9
24.2 ± 0.7
22.6 ± 0.9
6.6 ± 0.3 6.4 ± 0.4 18 ± 1.6 4.8 ± 0.3 34.2 ± 6.7 5.3 ± 0.1 44.4 ± 4.8 5.5 ± 0.1
experiment
Material Shear Theoretical Measured Vf, Vf, Modulus angle (°) ply angle (°) ply angle, theoretical measured longitudinal/ face/back (°) (%) (%) transverse GPa,
121.7 ± 5.1 108.3 ± 4.9 18.3 298.7 ± 20.9 4.5 47 ± 0.4 45.2 405.1 ± 48.3 5.2 39.7 ± 1.6 57.8 495.6 ± 37.4 5.5 40.4 ± 1.8 6.5
CLT 4.5 ± 0.5 3.8 ± 0.3 2.1 ± 0.2 2 ± 0.7 1.4 ± 0.1 1.4 ± 0.5 1.3 ± 0.2 0.8 ± 0.1
0.69 ± 0.02 0.74 ± 0.05 1.21 ± 0.08 0.35 ± 0.05 1.22 ± 0.03 0.13 ± 0.02 1.18 ± 0.11 0.18 ± 0.01
1.30 0.32 1.40 0.18 1.45 0.16
0.75
experiment CLT
Strength, Ult.strain, Poisson ratio longitudinal/ longitudinal/ longitudinal/ transverse MPa transverse (%) transverse
Table 11.5 Ply angles, fibre volume fractions and tensile properties of composites reinforced by sheared biaxial fabrics
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11.7 Typical failure patterns of composite specimens reinforced by non-sheared and sheared B1 composite due to tensile loading in longitudinal and transverse directions.
stress–strain curve increases almost linearly, followed by a plateau and, finally, a sudden decrease in stress. It is expected that by increasing the shear angle, the stiffness and strength of the sheared materials in the transverse direction decrease due to the increase of ply angle. However, it is shown that with an increase in sheared angle, the strength decreases and stiffness slightly increases (Fig. 11.6d). The decrease in stiffness due to fibre orientation was compensated by the stiffness enhancement contributed from the increase in fibre volume fraction. With the shear angle above 30°, the transverse properties of the composites do not change significantly with the change of shear angle. In this range, the laminates with ply angle relative to loading direction greater than 60° are matrix-dominated materials, which are not very sensitive to fibre orientation and fibre volume fraction. The failure patterns of the sheared materials loaded in the longitudinal direction are quite different from those of the others (sheared materials loaded in transverse
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direction and non-sheared materials), even with the small shear angle of 30° (Fig. 11.7). The fracture behaviour of the sheared B1 and B2 specimens under tension in longitudinal direction are almost the same, independent of shear angle and characterised with a ‘clean’ break perpendicular to the loading direction. Specimens mostly failed due to fibre breakage. In the transverse direction, the fracture behaviour of sheared materials (Fig. 11.7) is quite similar to that of nonsheared material, except the damage in the sheared materials is concentrated at the fracture region. A matrix crack parallel to the direction of the fibre in the outer plies through the entire thickness and width of the tested specimen, inter-ply tearing and fibre pull-out and fibre breakage are always observed at the fracture region of the loaded specimens. It seems that the fracture pattern of the sheared material relates to stitching patterns. In B1 specimens, the tricot stitching with a smaller stitching step (B = 1.71 mm) creates higher resistance to prevent pull-out of the fibre bundles. Consequently, B1 specimens (Fig. 11.7b, c, d) failed with more fibre breakage. The stress–strain curves of the composites reinforced by sheared 45° of B1 and B2 (Fig. 11.6c) are essentially identical, proving that there is no significant difference in the tensile properties of the composites reinforced by sheared B1 and sheared B2 fabrics. This means that the influence of stitching patterns on the shearing of biaxial fabrics and tensile properties of the sheared materials is minor, although the B2 fabrics can be sheared much easier than the B1 fabrics. A classical laminate theory (CLT) calculation with similar approach used for non-sheared material was performed to predict the modulus of the composites reinforced by sheared biaxial fabrics. The computation was based on the properties of carbon fibre and epoxy matrix and assumed that the laminates were made from perfect UD plies. The laminate properties were computed using the measured fibre volume fraction and ply angle. Chamis formulae were used for this calculation, with the following properties of fibres and the matrix. • •
Fibres: Young moduli E1 = 230 GPa, E2 = 14 GPa, Poisson ratios ν12 = ν13 = 0.23, ν23 = 0.23 (axis 1 corresponds to the fibre longitudinal direction). Matrix: Young modulus 2.7 GPa, Poisson ratio 0.4.
Figure 11.6 and Table 11.5 clearly show that above the shear angle of 30°, the difference in stiffness between experimental and CLT predictions in the longitudinal direction becomes significant and increases as the shear angle increases. Although damage in the sheared material subjected to tensile loading in the longitudinal direction initiates by shear failure (matrix cracks along the fibre direction), the behaviour of the material is very close to that of fibre-dominated laminates, i.e. linear stress–strain curve and specimens failed by fibre fracture. Consequently, any small error in fibre volume fraction and fibre orientation, which it is not possible to avoid in practice, results in a significantly synergetic effect on the mechanical properties. For example, CLT calculations show that the change of 1° ply angle (from 22.5° to 21.5°), which is the common local variation in fibre
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orientation of sheared fabrics (see Chapters 5 and 6), increases the modulus by 7% (from 45 to 48 GPa). Similarly, an error of 3.6% in measuring Vf (35.6% instead of 32%) results in 10% reduction in stiffness (45 GPa instead of 41 GPa). The observed differences may be specific for the particular test program: in the similar investigation reported in Smith et al. (1997) and Crookston et al. (2002), the CLT predictions worked fairly well for the sheared composites. The difference between CLT prediction and measurement, which increases with the increase of shear angle, can be partly attributed to an increase in density of the distortions caused by stitching in the sheared materials. By increasing the shear angle, the area of the fabric decreases leading to an increase in density of distortions created by stitching. The density of the distortions in the sheared materials in relation with the non-sheared materials of the same number of plies should follow the ‘Cos law’: density of defects in sheared material =
density of defects in non-sheared material [11.1] cos γ
where γ is the shear angle. Nevertheless, it is not the case for the transverse direction. The curves in Fig. 11.6d show that the CLT calculation predicts quite well the transverse modulus. As explained previously, in transverse direction the material with shear angle above 30° is matrix dominated, so the changes in fibre orientation and fibre volume fraction do not cause a significant effect on tensile modulus and strength.
11.6
Damage development in B2 (0°/90°) laminates
In the tensile tests for the B2 laminates in the fibre direction (i.e. MD and CD), it was observed that damage in the materials was initiated with transverse matrix cracks in 90° plies, followed by cracks along the fibres at 0°. These matrix cracks were distributed along the entire length of the specimen; however, they did not reduce the stiffness of this fibre-dominated material. Finally, the specimens failed due to breakage of the fibres in the 0° plies. As discussed previously, the presence of the 90° plies prevents the effects of fibre splitting in the 0° plies during the final failure of the specimen, although cracks parallel to the 0° fibres have already occurred. In addition to the main fracture, which leads to specimen rupture, other fractures were usually found close to the grips of the testing machine due to the release of high levels of energy stored in the specimens during loading. During the tensile tests in the off-fibre direction (i.e. BD), damage in the materials started with matrix cracks along the fibre direction (±45° relative to the loading direction). These cracks were also distributed along the entire length of the specimens. As the behaviour of these ±45° specimens is matrix dominated, the cracks result in a gradual decrease in stiffness. When the applied strain increased, the cracks developed to form longer cracks and the specimen started to separate when a crack went across its width.
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The damage development in B2 laminates under tensile loading, briefly described above, will be further characterised in this chapter by using various non-destructive testing (NDT) techniques, namely acoustic emission and X-ray radiography.
11.6.1 Acoustic emission Two acoustic transducers were placed on the specimens along the loading direction to record the acoustic emission during tensile tests, in which the specimens were loaded to final failure. Figure 11.8a,b presents the information obtained from these tests on the B2 laminates along the machine direction (MD) and bias direction (BD) respectively. The event counts, event energy, cumulative AE energy, and stress are plotted versus strain. Plots for the tests in the CD are essentially similar to the ones in the MD. This allows the assumption of an analogous damage development, in terms of AE events, in these two directions. Three main regions can be identified on the charts for the tests in both fibre and off-fibre directions. Considering the chart of the tests in MD and CD (Fig. 11.8a), it is possible to identify three regions determined by two transitions. The first transition strain εa is at 0.3% and second transition εb is in between 1.3–1.4%. In the first region, after a very short initial range of strains without any events, some AE signals are recorded. They are characterised with low energy content and low rate, which indicates a slow damage process. The AE events recorded in this stage show that micro damage occurs already at a low strain level, in the beginning of the test. The damage in this first region, indicated by AE signals, is mainly matrix cracks and local delaminations (as revealed by X-ray examination discussed below). They affect only the matrix, which has a low contribution to the overall stiffness of the material in these directions. The minor stiffness reduction caused by matrix damage might be compensated by the stiffness increase due to the strain stiffening behaviour of carbon fibres. In the second region, starting from the first transition strain εa = 0.3%, the number of events increases suddenly and the energy content of the events reaches higher levels. The damage development in this region is characterised by a constant rate of the AE events and it covers a wide range of strains until high deformation (almost to the end of the test). At higher strain, it is possible to identify a second transition strain indicated as εb in Fig. 11.8a. This transition is not as well defined as the first one, and appears between 1.3–1.4%. The counts versus strain curves of different tests reveal that the change of AE behaviour between region two and region three is progressive and characterised by a slow turn in the event plot. In the third region, the AE counts versus strain chart shows a higher rate of events. The increase in AE counts is unstable until the final failure of the specimen. This behaviour is explained by fibre-related damage that starts and grows at a high rate until the specimen ruptures.
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11.8 Typical AE counts, event energy, cumulative energy and stress– strain curve of the tensile tests in (a) the machine and cross direction and (b) in bias direction of the B2 laminates.
In terms of cumulative energy, similar AE behaviour can be observed from the plots in Fig. 11.8, i.e. three regions on the cumulative energy versus strain chart determined by two transition strains. In the first region, the energy content of the early events is very low. At higher strains, which are closer to the first transition εa, AE reveals events with a slight increase in energy content. Therefore, the cumulative energy plot shows a positive concavity, indicating an increase in the
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plot slope as the applied strain increases. This trend is maintained up to the centre of the second region, from which the cumulative energy plot changes its behaviour progressively, showing a knee on the curve, and turning into a negative concavity. In the second half of this region (0.8% to εb), the cumulative energy charts appear to stabilise themselves, showing a plateau that corresponds to the region of the events with low energy content. From a strain of about 1.2%, close to the transition strain εb, once again the cumulative energy versus strain chart increases with a rate higher than that at εa and shows a positive concavity. The energy of events also increases again to much higher levels when the applied strain increases. In this final region, the AE behaviour of the material is unstable until the final failure of the specimen. Graphs for the tests in BD (Fig. 11.8b) show a similar AE behaviour as described for MD and CD, i.e. three regions separated by two transitions can be defined in the AE and stress–strain curves. However, the total number of events recorded from the test in BD is much higher than that from the test in MD and CD (by a factor of three). This may be partially due to the higher strain to failure of the tests in BD (about ten times the strain to failure of the test in the MD and CD). Also, bias testing surely results in fundamentally different failure behaviour, perhaps with much more matrix cracking early on. Figure 11.8b shows that at the very beginning of loading, a few AE events occur and slowly increase in the first region. Unlike the tests in fibre direction, the stiffness of the specimen tested in BD decreases rapidly, and from the transition strain εa it progressively reaches a constant lower value. In this off-fibre direction, the material is matrix dominated and so the decrease in stiffness, first of all, is attributed to the non-linear behaviour of the matrix. Secondly, the matrix cracks and/or delamination indeed damage the matrix and strongly reduce the stiffness of the material. In the second region, which covers a wide range of applied strain from εa = 2% to εb = (10 to 12%), the number of events increases suddenly and at a nearly constant rate to the centre of the curve (at about 9%). The energy content of the events reaches higher levels. Crossing from the first region to the second, the stiffness of the material continues decreasing to a minimum value at strain of about 3%, then starts to increase slowly with applied strain. The slight increase in stiffness at higher strains (>4%) can be explained by a certain level of reorientation of fibres toward the loading direction. After that the fibres are either pulled out from the matrix or broken, leading to a complete separation of the specimen. The main damage mechanisms acting in this region, which are proven in the coming sections, are mainly matrix cracking and in-plane rotation of fibres, resulting in local delaminations. In the third region, the AE behaviour during damage in BD differs from that in MD and CD. The different behaviour is correlated with the damage mechanism in the specimen leading to the final failure. In the third region of the tests in fibre direction, matrix cracks along the fibres parallel to the loading direction and
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Table 11.6 The selected strain levels based on AE results for damage investigation using X-ray radiography (ε1 < εa < ε2 < εb < ε3) Test direction
ε1 (%)
ε2 (%)
ε3 (%)
MD and CD
0.2
0.8
1.3
BD
1.0
6.0
9.8
probably fibre breakage, which are the main failure modes, are initiated and actively develop, leading to an increase of the event rate with increase of applied strain. For the tests in BD, the fibre pull-out and some fibre breakage, developed from the existing damage, result in a constant rate of the events until the final failure of the specimens. The BD specimens fail with a slow separation into two parts, showing a progressive reduction of stress with the increase of applied strain. Considering the cumulative energy plots of the tests in BD, it is possible to identify a similar behaviour as previously described for MD and CD tests. The cumulative energy plot presents a positive concavity while crossing the transition strains εa and εb. However, while the cumulative energy curve presents a welldefined saturation trend in the centre of the second region for the tests along the fibre direction, it stabilises with a constant positive slope for the tests in BD. The AE observations allow identification of the strain levels ε1, ε2 and ε3*, characterising the damage development stages. Table 11.6 presents these strain levels used for the NDT inspections with X-ray radiography.
11.7
X-ray radiography
In Fig. 11.9, the results of progressive damage analysis obtained from X-ray radiography of B2 laminates loaded in the MD, CD and BD at different strain levels are presented. For the tests in the machine direction (Fig. 11.9a), consistent with the AE results, it is possible to identify from the X-ray image at strain ε1 = 0.2% some matrix micro-cracks oriented mainly in two directions. (Micro-cracks are difficult to detect by ultrasonic techniques, but they show up well with X-rays). The longitudinal cracks, which are parallel to the loading direction, are actually ‘thermal’ cracks (cracks due to differential shrinkage of fibre and resin during cure and subsequent cooling) as X-ray examination of the samples before test shows. They are certainly not cracks due to tensile loading because it is too early for the splitting mechanism, which leads to cracks along fibres in the loading direction, to occur. Once again, they appear to follow a particular pattern. Some transverse cracks starting from one edge of the specimen are shown in the detail box of * They are strains in the three regions, determined by AE event count and cumulative energy (see Figure 11.8).
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11.9 X-ray images of B2 specimens subjected to tensile loading at different strain levels. Test direction: (a) MD; (b) CD; (c) BD.
Fig. 11.9a. They are probably some small initiations of matrix cracks due to tensile loading. Increasing the strain level to ε2 = 0.8%, initial matrix micro-cracks multiply themselves and grow, forming full-width transverse matrix cracks. Most of them start from the edges, run across the width of the specimen for a certain length and then vanish, while the others span the whole width of the specimen. The
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transverse cracks are dominant, in spite of some micro-longitudinal defects that can be identified in the specimen. At higher strains ε3 = 1.3% while the transverse matrix cracks, which run across the width of the specimen, are saturated; longitudinal cracks increase and grow. The longitudinal cracks are probably due to the transverse tension resulting from straightening of the fibre bundles in the loading direction to accommodate the in-plane waviness created from the stitching. For the tests in CD (Fig. 11.9b), a similar damage process was observed. At strain ε1 some transverse micro-matrix cracks are detected, starting both from the edges and from inside of the specimen. They increase rapidly in number and dimensions at strain level ε2, and some longitudinal cracks may be detected. Moreover, some small delamination can be identified by the black spots along the edges and within the specimen. However, a close look at these X-ray images reveals that the cracks in the direction of the fibres on the outer plies are more apparent. In the specimens tested in the MD, the 0° plies are on the surface, leading to clearer longitudinal cracks in MD images. On the other hand, the transverse cracks are well identified in CD images because the 90° plies are on the surface of these CD specimens. This may be due to a stress concentration resulting from the edge effect and (to a minor extent) lower ability to absorb the penetrant (used to enhance the X-ray contrast) of the inner plies. For the tests in BD (Fig. 11.9c), at low strain ε1 = 1% the matrix cracks are formed along the fibre direction, oriented at −45°, relative to the loading direction. Similarly, in the case in MD and CD, cracks found at this strain level are mainly thermal cracks and follow a well-defined pattern. The images at different strain levels show that the unclear and short thermal cracks can be distinguished quite well from the tensile-induced cracks, which are sharp, straight and strictly follow the fibre directions. At higher strain ε2 = 6%, these matrix cracks develop, increasing in number, and form longer cracks following the fibre directions both at +45° and −45° relative to the loading direction. Most of them run from one edge of the specimen to the other. Small delaminations develop from the edges of the specimen, following existing matrix cracks. Also, some delaminations are generated from inside the specimen, at crossings of +45° and −45° matrix cracks. As the applied strain increases towards the end of the test, at a certain strain a crack runs across the width and thickness, and the specimens start to separate with fibre pull-out, leading to final failure. We see that damage in the material is not randomly distributed. In fact, it initiates and develops following preferred patterns. They are related to the structure of the reinforcement fabrics and correlate to the material architecture.
11.8
Damage initiation in non-sheared and sheared materials
The damage initiation strain was determined using AE registration as explained above and confirmed by the X-ray observations. First, comparing the damage
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Table 11.7 The summary of initial damage investigation of the composites reinforced by sheared B1 fabrics with different shear angles under to tensile loading in longitudinal and transverse directions (in comparison with the unidirectional and non-sheared material)
initiation strains for stitched MMF composites (0.2%, Table 11.6) and UD in transverse direction (0.6%, Table 11.7), one notes that the presence of the stitching dramatically lowers the damage initiation threshold. Stress concentration, caused by the stitching, leads to early transverse/shear damage in the fibrous plies of MMF composites. The mechanisms of this phenomenon are further investigated using finite element analysis in Chapter 19. For an overview on the effect of the deformation/shearing of the reinforcement fabric on damage initiation in the composites, the initial damage strains of the laminates reinforced by sheared B1 and those of UD are summarised in Table 11.7. This shows that the deformation of fabric (by in-plane shear) changes the damage initiation behaviour of the composites via the changes in fibre orientation. It is evident that, by increasing the shear angle, the sheared materials subjected to tensile loads in longitudinal and transverse direction tend to show the behaviour of the UD. In fact, the initial damage strains of the sheared material in transverse tension decrease, approaching the value of UD samples loaded in the transverse direction, when the shear angles of the reinforcement fabric increase. In the longitudinal direction, the initial damage strains of the sheared materials are not significantly affected due to the changes of the shear angle. However, the materials change their behaviour from shear-failure dominated (e.g. initial cracks are formed due to shear) to fibre-failure dominated (e.g. more linear stress–strain curves and fibre breaks are responsible for final failure).
11.9
Conclusions
The mechanical properties of the non-sheared and sheared MMF reinforced epoxy composites were experimentally characterised and theoretically predicted by CLT. For the non-sheared materials, the quadriaxial laminates show a quasi-
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isotropic behaviour, while the biaxial (+45/−45° and 0°/90°) and UD laminates clearly present an anisotropic behaviour, as expected. High in-plane shear properties of quadriaxial laminates compared with the others confirm that the in-plane shear properties are strongly dependent on the amount of +45° and −45° reinforcement. UD laminates have the highest interlaminar shear strength compared with those of quadriaxial and biaxial laminates. The anisotropic laminates reinforced by sheared biaxial fabrics show fibre-dominated behaviour in the longitudinal direction and matrix-dominated behaviour in the transverse direction. The tensile properties of MMF laminates are controlled essentially by the fibres/plies in the loading direction. However, the off-axis plies and probably the stitching tend to restrict any effect of splitting along the fibre in the 0° plies, hence improving the translation of fibre properties into the MMF laminates. Shearing changes the fibre orientation and fibre volume fraction, leading to changes in the properties of the composites. By increasing the shear angle, the tensile properties in the longitudinal direction increase while in the transverse direction the strength reduces and stiffness is hardly affected. A shear angle of γth = 30° for biaxial fabrics is not only the threshold during shearing of the fabrics (see Chapter 6) but also for the mechanical behaviour of the composites. For the non-sheared MMF laminates, damage initiation was found to be related to test direction, and independent on the lay-up, i.e. for the tests in the fibre direction, damage starts at 0.3% and for the tests in the off-fibre direction at 1.3%. For the sheared MMF laminates, shearing changes the fibre orientation and hence the behaviour of the composites, leading to a shear angle dependence of damage initiation.
11.10 References Asp, L. E., F. Edgren and A. Sjögren (2004). Effects of stitch pattern on the mechanical properties of non-crimp fabric composites. Proceedings ECCM–11: CD Edition. Beier, U., F. Fischer, J. K. W. Sandler, V. Altstadt, C. Weimer, H. Spanner and W. Buchs (2008). Evaluation of preforms stitched with a low melting-temperature thermoplastic yarn in carbon fibre-reinforced composites. Composites Part A – Applied Science and Manufacturing 39(5): 705–711. Beier, U., F. Fischer, J. K. W. Sandler, V. Altstadt, C. Weimer and B. Wolfgang (2007). Mechanical performance of carbon fibre-reinforced composites based on stitched preforms. Composites Part A 38: 1655–1663. Broughton, W. R. J. M. Hodgkinson, ed. (2000). Shear, Woodhead. Crookston, J. J., A. C. Long and I. A. Jones (2002). Modelling effects of reinforcement deformation during manufacture on elastic properties of textile composites. Plastics, Rubber and Composites 31(2): 58–65. Curtis, G. J., J. M. Milne and W. N. Reynolds (1968). Non-Hookean Behaviour of Strong Carbon Fibres. Nature 220(5171): 1024–1025. Drapier, S. and M. Wisnom (1999). Finite-element investigation of the compressive strength of non-crimp-fabric-based composites. Composites Science and Technology 59: 1287–1297. Edgren, F. and L. E. Asp (2005). Approximate analytical constitutive model for non-crimp fabric composites. Composites Part A 36: 173–181.
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Edgren, F., L. E. Asp and R. Ioffe (2006). Failure of NCF composites subjected to combined compression and shear loading. Composites Science and Technology 66: 2865–2877. Edgren, F., D. Mattsson, L. E. Asp and J. Varna (2004). Formation of damage and its effects on non-crimp fabric reinforced composites loaded in tension. Composites Science and Technology 64: 675–692. Hoersting, K. ed. (1998). Rationalising the production of long fibre reinforced composite materials using multiaxial multiply fabrics. Aachen, Shaker Verlag. Mattsson, D., R. Joffe and J. Varna (2008). Damage in NCF composites under tension: Effect of layer stacking sequence. Engineering Fracture Mechanics 75(9): 2666–2682. Mikhaluk, D. S., T. C. Truong, A. I. Borovkov, S. V. Lomov and I. Verpoest (2008). Experimental observations and finite element modelling of damage and fracture in carbon/epoxy non-crimp fabric composites. Engineering Fracture Mechanics 75(9): 2751–2766. Saito, H. and I. Kimpara (2006). Evaluation of impact damage mechanism of multi-axial stitched CFRP laminate. Composites Part A – Applied Science and Manufacturing 37(12): 2226–2235. Shioya, M., E. Hayakawa and A. Takaku (1996). Non-hookean stress-strain response and changes in crystallite orientation of carbon fibres. Journal of Materials Science 31(17): 4521–4532. Smith, P., C. D. Rudd and A. C. Long (1997). The effect of shear deformation on the processing and mechanical propertis of aligned reinforcement. Composites Science and Technology 57: 327–344. Truong Chi, T., D. S. Ivanov, D. V. Klimshin, S. V. Lomov and I. Verpoest (2008). Carbon composites based on multiaxial multiply stitched preforms. Part 7: Mechanical properties and damage observations in composite with sheared reinforcement. Composites Part A 39: 1380–1393. Truong Chi, T., M. Vettori, S. V. Lomov and I. Verpoest (2005). Carbon composites based on multiaxial multiply stitched preforms. Part 4: Mechanical properties of composites and damage observation. Composites Part A 36: 1207–1221. Truong, T. C. (2005). The mechanical performance and damage of multi-axial milti-ply carbon fabric reinforced composites. Department MTM. Leuven, Katholieke Universiteit, Leuven: 202.
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12 Damage progression in non-crimp fabric composites L. E. ASP, J. VARNA and E.MARKLUND, Swerea SICOMP and Luleå University of Technology, Sweden
Abstract: In this chapter, prevailing damage mechanisms in in-plane loaded non-crimp fabric (NCF) composites, as well as out-of-plane impact-loaded and subsequent in-plane compression-loaded NCF composite structures, are presented and discussed in detail. Particular emphasis is on the identification of differences and similarities in failure mechanisms for NCF composites to those in traditional tape-based composites. Key words: intralaminar cracks, interlaminar cracks, delamination, impact damage, damage growth, fractography.
12.1
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In this chapter, damage processes occurring in pristine and impacted carbon fibre non-crimp fabric (NCF) reinforced composite materials are described. As for conventional polymer composites, a number of damage modes occur in NCF reinforced composites. Damage processes take place at the different scales of heterogeneity in the composite. Intralaminar cracks (also called matrix cracks) form at the micro- and mesoscale of the NCF composite. That is, matrix cracks form due to high tensile or shear stress within and between fibre tows in a single lamella. A particular feature for textile composites such as NCF composites, is that the intralaminar crack plane is not exclusively transverse to the laminate plane, but also may be parallel to the plane of the laminate. Note that such ‘longitudinal’ intralaminar cracks are not to be confused with interlaminar cracks, i.e. delaminations, as they occur within individual fibre tows. Fibre failure also initiates at these scales. Tensile longitudinal failure of the NCF composite is due to failure of a number of individual fibres within a tow (i.e. at the microscale), similarly to what is observed for tape-based composites. Compressive failure on the other hand, is promoted by kinking failure of fibres in one localised cross-section of the entire fibre tow, and is influenced by the waviness of the tow, i.e. by features on the mesoscale. Finally, interlaminar cracks (delaminations) form and propagate between layers in NCF composites. The general mode I and mode II delamination growth processes are similar to those observed in tape-based composites, but are interfered with by the reinforcement architecture in NCF composites. Firstly, delamination growth within NCF blankets, i.e. between stitched layers (lamellas), affected by the presence of the 289 © Woodhead Publishing Limited, 2011
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stitching yarn and delamination growth between NCF blankets, rather than within the blankets, is promoted. Secondly, lamellas in NCF composites nest into each other. This also influences delamination growth. In general, nesting of lamellas and blankets results in significantly higher interlaminar fracture toughness (in both mode I and II) than is usually recorded for tape-based composites. Damage formation and residual strength of impacted NCF composites are affected by the reinforcement architecture and lay-up in a similar manner as for un-notched. Consequently, impact resistance and tolerance of NCF composites differ to those of tape-based composites. In general, NCF composites are less sensitive than tape-based composites to impact. In this chapter, prevailing damage mechanisms in in-plane loaded NCF composites, as well as out-of-plane impact loaded and subsequent in-plane compression loaded NCF composite structures, are presented and discussed in detail. Particular emphasis is on the identification of differences and similarities in failure mechanisms for NCF composites to those in traditional tape-based composites.
12.2
Damage progression in non-crimp fabric (NCF) composites due to in-plane loading
12.2.1 Tensile loading The sequence of failure events occurring in NCF composite laminates due to tensile loading is similar to that in tape-based laminated composites. Firstly, intralaminar matrix cracks occur in off-axis plies/bundles. Following this, interlaminar cracking may evolve prior to final failure of the composite by rupture of fibres parallel to the load. Although the sequence of events is similar and the mechanisms controlling intralaminar matrix cracking are the same, the damage modes are different. In this section, mechanisms controlling matrix cracking in NCF cross-ply laminates are described. To understand prevailing failure mechanisms in, and to allow modelling of, the NCF composite, architectural features must be characterised. In particular, characterisation of features on the mesoscale (i.e. fibre bundle shape and geometry, fibre tow crimp, nesting, etc.) is required. Although the name ‘non-crimp’ implies that fibres in each lamina are straight, characterisation of the NCF composite laminate fibre architecture reveals significant fibre undulation in individual lamina. This is illustrated in Fig. 12.1, where the lower 0° lamina features significant crimp. It should be pointed out that features like fibre tow crimp, nesting and to some extent fibre bundle geometry are affected by the lay-up and subsequent composite material processing. Consequently, it is important that influence of processing on these mesoscale features is appreciated for every NCF composite material. Matrix cracking in 90° layers of cross-ply NCF carbon fibre composites was analysed in detail by Edgren et al. (2004a). The identified
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12.1 Micrograph of a non-crimp fabric cross-ply laminate cross-section (Edgren et al., 2004a).
12.2 Schematic of intralaminar matrix tensile cracks in a) NCF and b) tape based composites.
damage modes are presented here to describe intralaminar matrix failure in NCF composites and how this differs from matrix cracking in tape-based laminated composites. A schematic of the identified damage modes is presented in Fig. 12.2. As illustrated in Fig. 12.2, there are four different types of matrix cracks that may occur in NCF composites in response to in-plane tensile loading. In contrast, in traditional tape-based composites there is only one type of matrix crack, bridging the 0°-layers through the entire 90° layer (Hashin, 1985; Varna and Berglund, 1991). The four types of matrix cracks occurring in NCF cross-ply composites in tension are described below.
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Whole cracks A crack extending from one 0° layer to another, i.e. which runs through two adjacent 90° bundles and the matrix separating these, is called a whole crack (see Fig. 12.2). An example of a whole crack is presented in Fig. 12.3. The whole crack is similar to the intralaminar crack prevailing in tape-based composites in the sense that it runs through the entire 90° layer. The amount of whole cracks found in a NCF cross-ply laminate is, however, relatively small. To illustrate this, recorded densities of whole, half and double cracks are presented in Fig. 12.4. Note that the crack density of whole cracks does not exceed 0.25 cracks per millimetre (cr/mm) at crack saturation. This is to be compared to the density of transverse cracks found in tape-based carbon fibre cross-ply laminates. Wang (1984) reported crack densities in the 90° layers of [02/90]S, [02/902]S and [02/903]S AS/3501–06 laminates up to 2.0 cr/mm. As is well known, the maximum crack density is inversely proportional to the ply thickness, and comparison makes sense only for layers with similar thickness. Furthermore, whole cracks are found to initiate at relatively high strain (>0.5%) (at high stress, some of the half cracks, see next section, propagate in the neighbouring bundle, and also dynamic effects facilitate whole crack formation).
12.3 Example of a whole crack running through two 90° fibre bundles (Edgren et al., 2004a).
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12.4 Densities (cracks/mm) of a) whole cracks, b) half cracks and c) double cracks (Edgren et al., 2004a).
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Half cracks The first type of crack to occur in the 90° bundle layer of an NCF composite is the half crack. Half cracks initiate at a tensile strain of about 0.4% (see Fig. 12.4b). At crack saturation, the half crack density is high (∼1.8 cr/mm) and thus comparable to the crack densities reported for tape based composites, as discussed above. Half cracks are oriented mainly transversely to the laminate mid-plane, only penetrating a single bundle. An example of a half crack is depicted in Fig. 12.5. The name is related to the feature that these cracks do not cross the whole middle layer, which for the studied cross-ply laminates consists of two fibre bundle layers oriented perpendicular to the loading direction. Instead, half cracks are always contained within a single 90° fibre bundle, without connection to cracks present in neighbouring fibre bundles. The domination of half cracks in 90° fibre bundle layers of NCF composite crossply laminates is important as it results in moderate stiffness degradation of the composite. The effect is schematically illustrated in Fig. 12.6. As is shown in the figure, the presence of half cracks results in a small crack opening compared to that from transverse cracks in tape-based composites (or whole cracks in NCF composites, for that matter). By this, a much smaller crack-opening displacement (COD), and therefore less stress reduction in the vicinity of the crack, results in the NCF composite compared to the tape-based composite. Consequently, for the NCF composite the reduction in stiffness due to intralaminar cracking is significantly smaller.
12.5 Example of a half crack running through one 90° fibre bundle (Edgren et al., 2004a).
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12.6 Schematic COD in (a) non-crimp fabric and (b) tape-based composites resulting from tensile loading.
Longitudinal Longitudinal cracks are never observed in traditional tape-based composites when loaded in in-plane tension. The longitudinal cracks extend parallel to the loading direction, similar to a delamination. However, the longitudinal crack extends predominantely within a 90° fibre bundle, see Fig. 12.2. In the study by Edgren et al. (2004a), longitudinal cracks were observed within fibre bundles and at bundle matrix interfaces (see examples in Fig. 12.7). Longitudinal cracks were most often located within bundles and only seldom observed to propagate in the matrix. Edgren et al. (2004a) demonstrated initiation of longitudinal cracks to be caused by the straightening of the 0° fibre tows in the neighbouring ply. Measured fibre tow waviness was predicted to cause initiation of longitudinal cracks at strains between 0.39–0.66% (Edgren et al., 2004a), depending on the fibre architecture alone. Consequently, following initiation of half cracks, longitudinal cracks caused by stress concentrations inherent to straightening of the 0° fibre tows will occur in regions with highly undulated neighbouring 0° fibre tows. Double cracks The fourth type of intralaminar matrix cracks occurring due to in-plane tensile loading are double cracks, see Fig. 12.2. This crack type is a combination of a half
12.7 Example of longitudinal cracks running through one 90° fibre bundle and along a fibre bundle/matrix interface (Edgren et al., 2004a).
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12.8 Example of a double crack running through on 90° fibre bundle (Edgren et al., 2004a).
crack and a longitudinal crack. Double cracks have a transverse branch like a half crack and a longitudinal branch as a longitudinal crack. The longitudinal part, with varying length, may be located in the central part of a bundle or at its boundary. These cracks usually form within single bundles and are not propagating in the matrix between two bundles. An example of a double crack is presented in Fig. 12.8.
12.2.2 In-plane compressive failure Although the use of NCF reinforcements in composite materials for primary structures is increasing simultaneously as the analysis capability and understanding of the materials also increases, a few issues for improvement for the continued success of the material have been identified. Most of these concern aeronautical applications. One of the most important issues raised concerns the low strength in compression. For aeronautic structural applications, NCFs have so far only been considered for structures predominately loaded in tension, e.g. the rear pressure bulkhead and lower wing skins. Asp et al. (2004) studied the effect of NCF textile architecture on compressive strength of the composite. The experimental results revealed that, in general, the compressive strength was only half of that in tension. Drapier and Wisnom (1999) predicted compressive strength of
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NCF composites to be inherent to kinking of the 0° fibre tows, resulting in an overall shear instability. Hence, reduced fibre tow waviness will increase the compressive strength of NCF composite materials. In order to establish experimental evidence of kinking in compression loaded composites Edgren et al. (2006) performed tests on NCF composite laminates. Tested specimens were analysed post-mortem and further evidence of kinking was established by polishing a number of interrupted test coupons through the thickness. The mechanisms controlling compressive failure identified in the study by Edgren et al. (2006) are reported in this section. As described in the introduction to this chapter it is possible to identify the mesoscale level as the level of the fibre tow. An earlier investigation (Edgren and Asp, 2005) of the material described here showed that the typical size of the imperfection (fibre tow wavelength, etc.) is in the order of millimetres. This is much larger than the typical size of the imperfection assumed for kink band formation in traditional tape-based composites, where the kink bandwidth is typically in the order of 10–20 fibre diameters (Fleck, 1997). According to the numerical results by Drapier and Wisnom (1999) entire fibre tows are expected to kink in NCF composites, i.e. resulting in kink bandwidths in the order of 2–3 mm. It was pointed out in the previous section that the mechanical properties of NCF composites depend on lay-up, fabric architecture, composite processing, etc. Consequently, in-plane compressive strength of an NCF lamina cannot be measured on unidirectional specimens, as is standard procedure for tape-based composites. Any attempt to do so will produce incorrect strength data as the fibre tow waviness in the laminate one wants to analyse will be different to that in the tested unidimensional laminate. Therefore, a procedure to determine the compressive strength of an NCF ply was developed by Edgren et al. (2006). In that study, tests were performed on quasi-isotropic (QI) [0/90/45/−45]S3 carbon fibre/vinylester laminates. The 20 mm-wide specimens were loaded in compression at different offaxis angles, thereby changing the compressive/shear stress ratio. Through analysis using classical laminate theory (CLT), the stress state in the most highly loaded ply at failure, i.e. the ply assumed to fail first, was calculated. Specimens were tested to failure at five different off-axis angles (angle between specimen longitudinal loading direction and 0°-fibre direction): 0°, 5°, 10°, 15° and 20°. A few tests of these specimens were interrupted prior to final failure and studied in a microscope in an attempt to verify the presence of kink bands. The loading was interrupted as acoustic activity was recorded in the specimen. Details of the specimen manufacture, preparation and testing are available in Edgren et al. (2006). Figure 12.9 depicts failed compression specimens. The failure is clearly visible as a line across the gauge section of the specimen. Figure 12.9a shows a 0° specimen on which the failure line is continuous and rotated approximately 12° from the direction perpendicular to the fibres (i.e. the loading direction). This behaviour was also found for other specimens exemplified by the 20° specimen in
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12.9 Quasi-isotropic specimens loaded to compressive failure; (a) 0°, (b) 5°, c) 15° and d) 20° off-axis angle (Edgren et al. 2006).
Fig. 12.9d. The failure of the outer layer, i.e. the 15° layer, of the 15° off-axis loaded QI specimen presented in Fig. 12.9c has grown in a few steps, where within each step the failure line is continuous and oriented perpendicular to the loading direction. In many cases, continuous failure lines extending perpendicular to the loading direction were also observed (Edgren et al., 2006). The failures observed on the surfaces of the specimens presented in Figure 12.9 are not necessarily the primary failures of the laminates. Internal plies parallel to the observed outer plies may have failed prior to these outer plies. To investigate this, studies of specimens interrupted prior to final failure were conducted (Edgren et al., 2006). Damage in the form of kink bands was indeed observed to have formed in 0° and 5° off-axis specimens at loads approximately 90% of the average failure load. In Fig. 12.10 kink bands and splits are clearly visible in the two outer tows of a central 5° off-axis ply after polishing. The splits do not pass the kink bands continuously, indicating that the kink bands developed prior to the splits. The kink bands shown in Fig 12.10 developed in tows located close to the specimen edges. However, kink bands were also found in internal tows in plies for other specimens. Thus, due to local imperfections (i.e. crimp) individual kink bands form in the interior of a ply prior to final failure. All kink bands identified in QI specimens by Edgren et al., (2006) had kinked out-of-plane, implying outof-plane crimp critical for the compressive strength of the material. A close-up of an individual kink band is presented in Fig. 12.11. As shown in the picture, two individual fibre tows (separated by a stitch yarn) have kinked in concert. The fact that individual fibre tows (in this case consisting of approximately 12 000 fibres) kink without causing catastrophic failure of the 20 mm-wide specimen is surprising. The width of the individual fibre tow is typically 2.5 mm; hence, breakage of a tow results in a very large flaw. Consequently, NCF composites offer a higher degree of notch insensitivity than do tape-based composites, which fail from kinking of 10–20 fibres, as described above. This notch insensitivity has proved important for the high impact damage tolerance reported for NCF composite structures (Edgren et al., 2004b) as described in Section 12.3.2, below.
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12.10 Kink bands found (circled) in a 5° ply of a 5° off-axis loaded QI specimen interrupted at 89% of average failure load (Edgren et al., 2006).
12.11 Detailed view of a kink band of a non-crimp fabric fibre tow.
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12.3
Damage progression in impacted NCF composites
In the first part of this section, characteristics of damage formed due to out-ofplane impact on carbon fibre NCF composite laminates are presented. In the second part, damage propagation to failure for these materials in subsequent in-plane compression-loaded residual strength tests is discussed. Throughout the section particular focus is given to the identification of differences in damage progression between NCF and tape-based composites. The section relies on previous investigations on impact-damaged sandwich panels for naval ships and monolithic aircraft-type laminates at Swerea SICOMP (Edgren et al., 2004b; Edgren et al., 2008; Edgren, 2005). Comprehensive descriptions of impact damage to tape-based composites have been given by Abrate (1991; 1994).
12.3.1 Impact damage formation In general, impact damage in composite laminates may consist of matrix cracks, delaminations and fractured fibres. Here, impact damage inflicted on sandwich panel face sheets is discussed. These results have been published by Edgren et al. (2004b) for QI carbon fibre/vinylester face sheet laminates. The general observations were later confirmed for monolithic carbon fibre/epoxy laminates (Edgren, 2005). The amount of damage in a laminate face sheet and the distribution of damage modes depend on the impact mass, impact velocity, geometry of the impacting objects and boundary conditions of the panel at impact (Abrate, 1991; 1994). Damage distribution in a sandwich panel carbon fibre/vinylester face sheet cross-section is schematically illustrated in Fig. 12.12. The impact damage caused by a 100 J impact (12.5 mm tup radius) is barely visible on the surface (i.e. so-called ‘barely visible impact damage’ [BVID]). No fractured fibres were detected for the BVID case. Furthermore, the amount of matrix cracks found in the NCF composite face sheet is less than what is usually found in tape-based laminates (Abrate, 1994). Figure 12.12 illustrates large delaminations resulting from the impact. These delaminations have primarily developed between layers with a difference in angle of 90°, i.e. at 0°/90° and +45°/−45° interfaces. This is consistent with what has been found for tape-based laminates (Abrate, 1994). It should be noted that this 90° difference in angle between two adjacent layers in the NCF composite is only found within the fabrics, i.e. between the stitched layers in the biaxial fabrics used. This implies that the stitching thread used in the NCF does not prevent delaminations developing within the fabric. An ultrasonic C-scan of a similar impact to that in the sectioned impactdamaged face sheet in Fig. 12.12 is presented in Fig. 12.13a. The projected area of the impact damage is fairly circular, as expected for a QI laminate. In Fig. 12.13a, individual delaminations extending in the ±45° direction can be
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12.12 Cross-section of a BVID in a [0/90/45/−45]S3 sandwich face sheet laminate resulting from a 100J impact (Edgren et al., 2004b).
12.13 Ultrasonic C-scan images of impacted [0/90/45/−45]S3 sandwich face sheet laminates: (a) BVID and (b) VID (Edgren et al., 2004b).
distinguished. These delaminations appear to have a rectangular shape rather than the traditional ‘peanut’ shape observed for delaminations found in impacted tapebased laminates. A general rectangular shape of delaminations caused by impact in NCF laminates was confirmed by ultrasonic microscopy. In Fig. 12.14, ultrasonic C-scans recorded using an ultrasonic microscope on a BVID in a [0°/90°/45°/−45°]s2 laminate are presented. In Fig. 12.14a, the delamination present between the third and fourth ply (counting from the impacted surface) is depicted. In Fig. 12.14b, the delamination present in between the fifth and sixth plies is shown. In both cases the rectangular geometry of the delaminations caused
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12.14 Ultrasonic C-scan images of individual delaminations in a [0/90/45/−45]S2 NCF laminate with BVID located between: (a) plies 3 and 4 and (b) plies 5 and 6 (Edgren, 2006).
by impact is observed. In Fig. 12.14b, delaminations in the lower ply interface (5/6) propagating from the upper delamination in Fig. 12.14a via matrix cracking can be seen (at A in Fig. 12.14b). Finally, an ultrasonic C-scan of a visible impact damage (VID) in the [0/90/45/−45]S3 NCF face sheet resulting from a 250 J impact is presented in Fig. 12.13b. The 250 J impact causes severe fibre damage at the point of impact, where a hole is punched. However, the projected area of the impact damage is almost constant.
12.3.2 Impact damage tolerance Residual compressive strength tests on impacted NCF composite sandwich and monolithic panels have been reported in (Edgren et al., 2004b; Edgren et al., 2008; Edgren, 2005). In these works, comprehensive fractographic investigations have been performed to identify mechanisms governing failure in compression after impact (CAI) loading. In a fractographic analysis of a CAI-tested panel it is difficult to separate damage due to increasing load up to collapse of the panel from ‘post collapse’ damage. Furthermore, it is difficult to find and identify the governing mechanism. In the case of the NCF CAI panels, the possible mechanisms controlling residual compressive strength are delamination growth (and subsequent compressive failure) and formation and growth of kink bands. In
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12.15 The dashed area is polished in the thickness direction for identification of kink bands.
an attempt to identify the critical mechanism in NCF panels, the CAI loading was interrupted and the damage developed during this load stage was studied by ultrasonic analysis using C-scan to identify delamination growth, as well as by polishing the area enclosing the impact damage area through the thickness to identify initiation of fibre tow kinking failures. The area of a sandwich face sheet studied after polishing through the thickness for identification of fibre tow kinking is indicated in Fig. 12.15. Delamination growth For all NCF composite material structures tested by Edgren et al. (2004b; 2008) and Edgren (2005) it was concluded that delaminations did not grow prior to collapse of the structure. In Fig. 12.16 ultrasonic C-scans of a monolithic CAI panel are presented. The C-scans represent the delaminated area after impact (a) and the damage after subsequent compression loading to 80–90% of the failure load (b). In Fig. 12.16b, the delamination area after significant acoustic activity in the panel during compression loading is presented – that is: damage growth has occurred in the laminate at this stage. Comparing the C-scans in Figs 12.16a and 12.16b, the projected area of the delaminations is approximately the same in the two pictures. This implies that the growth of delaminations does not control failure of CAI-loaded NCF composite panels. As described above, the largest delaminations are located within the fabrics (i.e. at 90° interface jumps). Thus, as these delaminations are formed due to mode II loading they may be bridged by
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12.16 Ultrasonic C-scans of monolithic CAL panel, (a) after impact and (b) after interrupted loading (Edgren, 2005).
undamaged stitch yarns. The presence of stitches may cause sufficient resistance for the delaminated member to buckle (Nilsson et al., 2001a). Thus, explaining the lack of delamination growth in the CAI-loaded NCF laminates as buckling of shallow delaminations is required for them to grow (Nilsson et al., 2001b). Kinking of fibre tows Fractographic findings for interrupted CAI tests on sandwich and monolithic panels employing optical microscopic studies of impact areas through the thickness, by grinding them down and polishing in steps, have been presented in Edgren et al. (2004b) and Edgren (2005). As discussed above, the method allows identification of fibre tow kinking occurring prior to catastrophic failure. For each ply location and length of prevailing kink bands were schematically recorded in damage maps. Each map was concluded by presentation of the collected kink bands in a projection through the laminate. A kink band damage map for the CAIloaded [0/90/45/−45]S3 NCF face sheet with a BVID (cf. Fig. 12.13a) is presented in Fig. 12.17. For this panel, severe kink band formation can be observed at a loading of 80–90% of the failure load. The length of the kink bands varied from a few millimeters to 22 mm. This extension of kink bands is much larger than what is usually found in tape-based laminates (Soutis et al., 2000). Kink bands were primarily kinking outwards and were mainly found in plies with the fibre direction parallel to the load. Kink bands were, however, also found in ±45° plies. Some of these kink bands propagated at an angle of approximately 45° to the loading direction, whereas some propagated normal to the load (see plies 11 and 19 in Fig. 12.17). The kink bands were found to initiate 5–15 mm away from the impact centre. Microscopy revealed that kink bands in 45° fibre tows have propagated step-wise. Within each growth increment, the kink band has grown in a direction almost perpendicular to the fibre direction (see Fig. 12.18).
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12.17 Kink bands found in the impacted skin of a [0/90/45/−45]S3 panel with BVID after interrupted loading.
12.18 Kink band formation in a 45° layer (Edgren et al. 2004b).
The results presented in Fig. 12.17 are from a sandwich panel. However, the identified mechanism corresponds to observations done on monolithic panels (Edgren, 2005). Consequently, CAI strength is controlled by formation and growth of kink bands for NCF composite face sheet sandwich as well as monolithic panels. Although delaminations do not propagate to cause catastrophic failure of the NCF composite panel they do play a role promoting kink band formation. In Fig. 12.19 kink bands that have grown almost perpendicular to the fibre tows in the upper 45° ply are visible after polishing (Edgren, 2005). The kink bands individually run through five fibre tows (approximately 15 mm long), initiating
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one to two fibre tows away from the centre of impact. At the upper right corner of the surface in Fig. 12.19 the second ply from the top (−45°) is visible. The kink band growing in ply 1 and ending in section A–A (marked in Fig. 12.19) can be seen in a micrograph taken along section A–A, presented in Fig. 12.20. A
12.19 Kink bands in the outer 45° ply of a monolithic CAI panel (Edgren, 2005).
12.20 Micrograph through section A–A in Fig. 12.19 (Edgren, 2005).
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delamination separates ply 1 from ply 2 in the central part of the picture. The kink band in ply 1 is formed at the right edge of the delamination. Note also that the delamination has terminated by growing down into the −45° ply as a matrix crack. Consequently, the presence of delaminations causes stress concentrations that promote kink band formation. Furthermore, kinking of 45° layers as well as the step-wise kinking within tows suggest high shear stress components in these stress concentrations. In CAI tests, stable growth of kink bands, from the centre and outwards, normal to the load direction, was observed on the laminate surface (Edgren et al., 2006). After substantial growth (exceeding 40 mm) the panel failed catastrophically. Bull and Edgren (2004) and Zenkert et al. (2005) reported strain measurements by full field digital speckle photography (DSP) on the impacted surface during a CAI test of a panel with BVID. In Fig. 12.21 longitudinal strain in the vicinity of the impact centre as measured by DSP is plotted. The dark region extending perpendicular to the loading direction in the centre of the image corresponds to compressive strains exceeding 1% (average strain to failure of an un-notched panel is approximately 0.9%). This region extends outwards during loading until final failure. The localised strain concentration to a band was inherent to stable growth of kink bands from the impact centre. Consequently, even a blunt BVID fails after formation of an extensive (∼45 mm) sharp notch and should be treated as such in attempts to model CAI strength (Edgren et al., 2006).
12.21 DSP image of longitudinal strain close to failure (εf =1%) (Edgren et al., 2008).
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12.4
Conclusions
In this chapter, mechanisms that control damage development and failure of NCF composites for some important load cases are presented. Firstly, failure of NCF laminates subjected to tensile and compressive in-plane load cases is described. In the case of tensile loading, formation of intralaminar matrix cracks has been demonstrated to differ significantly to that of tape-based composites – promoting formation of half cracks in 90° plies. By the dominance of half cracks, the resulting crack opening displacement is significantly less than that in tape-based composites, as is the reduction in in-plane stiffness. Secondly, in-plane compressive failure of un-notched specimens is demonstrated to be governed by kinking of entire fibre tows (i.e. 12 000 fibres). Significant kinking prior to specimen failure was observed, demonstrating great insensitivity to notches of the material. Following this, formation of impact damage for out-of-plane loading is discussed. The fibre tow architecture is shown to promote formation of rectangular delamination instead of the ‘peanut’ shaped delaminations commonly reported for tape-based laminates. Delaminations were found to form predominately within fabrics, leaving stitches to bridge them. Also, the amount of matrix cracking in NCF composites is, in general, less than that seen in tape-based laminates. Finally, compression after impact strength for NCF composite panels, for both sandwich as well as monolithic, is controlled by kink band formation and growth, even for blunt damage like barely visible impact damage. Presence of delaminations is important as kink band formation is promoted by stress concentrations at delamination edges. Delaminations growth, however, is hampered by the bridging stitches and their geometric shape preventing local buckling of the delaminated member.
12.5
References
Abrate S. (1991). Impact on laminated composite materials. Applied Mechanical Review 44:155–190. Abrate S. (1994). Impact on laminated composite materials: recent advances. Applied Mechanical Review 47:517–544. Asp L.E., F. Edgren and A. Sjögren (2004). Effects of stitch pattern on the mechanical properties of non-crimp fabric composites, Proceedings of 11th European Conference on Composite Materials, Rhodes, Greece. Bull P.H. and F. Edgren (2004). Compressive strength after impact of CFRP-foam core sandwich panels in marine applications. Composites Part B 35:535–541. Drapier S. and M.R. Wisnom (1999). Finite-element investigation of the compressive strength on non-crimp-fabric based composites. Composites Science and Technology 59:1287–1297. Edgren F., D. Mattsson, L.E. Asp and J. Varna (2004a). Formation of damage and its effects on non-crimp fabric reinforced composites loaded in tension. Composites Science and Technology 64:675–692.
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Edgren F., L.E. Asp and P.H. Bull (2004b). Compressive failure of impacted NCF composite sandwich panels – characterisation of the failure process. Journal of Composite Materials 38:495–514. Edgren F. (2005). Compressive failure of NCF composites. Proceedings of American Society for Composites 20th Technical Conference, Drexel University, Philadelphia, USA. Edgren F. and L.E. Asp (2005). Approximate analytical constitutive model for non-crimp fabric composites. Composites Part A 36:173–181. Edgren F. (2006), Physically based engineering models for NCF composites. PhD Dissertation. The Royal Institute of Technology (KTH), Sweden. Edgren F., L.E. Asp and R. Joffe (2006), Failure of NCF composites subjected to combined compression and shear loading. Composites Science and Technology, 66:2865–2877. Edgren F., C. Soutis and L.E. Asp (2008). Damage Tolerance analysis of NCF composite sandwich panels. Composites Science and Technology, 68:2635–2645. Fleck N. (1997). Compressive failure of composite materials. Advances in Applied Mechanics, New York, pp. 43–117. Hashin Z. (1985). Analysis of cracked laminates: a variational approach. Mechanics of Materials 4:121–136. Nilsson K.-F., L.E. Asp, J.E. Alpman and L. Nystedt (2001a). Delamination buckling and growth for delaminations at different depths in a slender composite panel. International Journal of Solids and Structures 38:3039–3071. Nilsson K.-F., L.E. Asp, and A. Sjögren (2001b). On transition of delamination growth behaviour for compression loaded composite laminates. International Journal of Solids and Structures 38:8407–8440. Soutis C., F.C. Smith and F.L. Matthews (2000). Predicting the compressive engineering performance of carbon fibre-reinforced plastics. Composites Part A 31:531–536. Varna J. and L.A. Berglund (1991). Multiple transverse cracking and stiffness reduction in cross-ply laminates. Journal of Composites Technology and Research 13:97–106. Wang A.S.D. (1984). Fracture mechanics of sublaminate cracks in composite materials. Journal of Composite Materials 6:45–62. Zenkert D., A. Shipsha, P.H. Bull and B. Hayman (2005). Damage tolerance assessment of composite sandwich panels with localised damage. Composites Science and Technology 65:2597–2611.
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13 Fatigue in non-crimp fabric composites K. VALLONS, Katholieke Universiteit Leuven, Belgium
Abstract: Knowledge of the fatigue behaviour of a material is essential for safe use in structural applications. This chapter discusses recent findings concerning the tensile fatigue properties of non-crimp fabric (NCF) composites (fatigue life, stiffness evolution and damage development). It is also briefly describes how fatigue influences the residual static performance of these materials. Key words: non-crimp fabric composites (NCF), fatigue, fatigue life, postfatigue residual properties.
13.1
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In most applications, materials are not simply subjected to static loading conditions; other loading modes are often equally, or sometimes more, important. For many applications, like cars and aeroplanes, it is very important to know how the material behaves under fatigue. This chapter focuses on the fatigue behaviour of non-crimp fabric (NCF) composites. The discussions are limited to tensile fatigue loading conditions. In most metals, tensile fatigue is characterised by the initiation of a single crack that then propagates until catastrophic failure, which occurs with little warning. Unlike metals, however, composite materials are inhomogeneous and anisotropic on the mesoscale. They accumulate damage in a general, rather than a localised, fashion, and, most often, failure does not occur by the propagation of a single macroscopic crack. The microstructural mechanisms of fatigue damage in a composite can include fibre breakage, matrix cracking, debonding, and delamination. These damage modes may occur independently or interact with each other, and the dominant mechanism can depend on material variables and testing conditions. This makes fatigue in composites a very complex issue (Harris, 2003). The present chapter deals with fatigue in one particular type of continuous fibre composite, the non-crimp fabric (NCF) composites. While fatigue in Unidirectional (UD) based laminates and woven fabric laminates has been investigated widely in the past, the knowledge about the specific fatigue properties of NCF composites is still relatively limited. The following paragraph discusses a number of recent findings concerning the fatigue life, damage development and stiffness evolution of composites based on NCFs. The influence of the composite orientation compared to the loading direction is also briefly considered. After that, the influence of fatigue loading on the residual static properties of the composite material is looked into. 310 © Woodhead Publishing Limited, 2011
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As mentioned in the introduction, the fatigue behaviour of composites is dependent on the reinforcement type. Even so, it has been shown that for different types of reinforcement, certain aspects of fatigue behaviour are comparable (Talreja, 2000; Schulte et al., 1987; Naik, 2003). The fatigue life curves for woven fabric composites, for example, are very similar to the ones for cross-ply UD-based laminates. This, however, does not mean that all aspects are the same. As will be illustrated in the following paragraphs, the damage development and the resulting stiffness evolution can be quite different. Since NCFs are essentially UD fibre layers that are stitched together, it can be expected that the fatigue behaviour of NCF composites will also largely resemble that of composites consisting of UD layers. However, as discussed in previous chapters, the stitching process introduces some geometrical artefacts in this type of fabric, which may influence the behaviour of the resulting composite. The presence of resin-rich zones on the stitching sites can, for example, result in stress concentrations, which could act as an initiator for damage during fatigue. The stitching process also introduces a slight in-plane waviness of the fibre bundles. This, again, could influence the fatigue behaviour of the final composite. Although the fatigue behaviour of NCF composites has received some attention in the recent past, available data still remain scarce. Most of the research concerns glass fibre based NCF composites, although some extensive studies on carbon fibre NCF composites have also been conducted. In general, these data indicate that the behaviour of NCF composites under fatigue loading is, as is often the case for woven fabric composites, largely similar to that of laminates made up of UD layers with similar fibre orientations (Gagel et al., 2006; Dyer and Isaac, 1998). In the following sections, the fatigue behaviour of NCF composites will be reviewed in more detail compared to that of composites with different types of reinforcements. In particular, the fatigue life, the development of fatigue damage and the evolution of stiffness during fatigue will be discussed.
13.2.1 Fatigue life Edgren et al. (2004) investigated the influence of the stitching parameters of the constituting NCFs on the fatigue life of several UD NCF composites and compared the results to the behaviour of a UD prepreg laminate. They found indications that a small stitch gauge in combination with a small stitch length can have a negative effect on fatigue life. They also remarked, however, that overall, the fatigue life of all tested NCF composites did not differ much from the fatigue life of the UD-based laminate. Throughout this chapter, the results of a recent study by the present author (Vallons et al., 2009a and 2009b) will be referenced regularly. For more clarity and completeness, an appendix in Section 13.6 gives a description of the NCF material
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used in the mentioned work. Figures 13.1 and 13.2 show the fatigue life curves obtained for the ±45° carbon fibre-epoxy NCF composite of that study in the matrix-dominated directions and the fibre directions (Vallons et al., 2009a and 2009b). The data show that samples in matrix-dominated directions fatigue-loaded
13.1 Fatigue life curves for the matrix-dominated directions (named MD and CD) of a ±45° carbon-epoxy non-crimp fabric composite with a fibre volume fraction of 58%. (R-ratio = 0.1, frequency 6 Hz). The arrows indicate samples that did not break (Vallons et al., 2009a).
13.2 Fatigue life curves for the fibre directions (named bias direction (BD)+ and BD−) of a ±45° carbon-epoxy non-crimp fabric composite with an average fibre volume fraction of 58%. (R-ratio = 0.1, frequency 6 Hz) The arrows indicate samples that did not break (Vallons et al., 2009a).
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up to one half of the tensile strength still have a fatigue life of more than 106 cycles. As shown in Fig. 13.2, in the fibre directions, the fatigue life at one half of the tensile strength is even higher (> 5 × 106 cycles). Figures 13.3 and 13.4 show the fatigue life curves for the bias direction and the warp direction of a twillweave carbon fibre-epoxy composite with the same fibre volume fraction as the
13.3 Fatigue life curve for the bias direction (BD) of a twill weave carbon fibre-epoxy composite with an average fibre volume fraction of 57%. (R-ratio = 0.1, frequency 6 Hz) (Vallons, 2009b).
13.4 Fatigue life curve for the fibre direction (FD) of a twill weave carbon fibre-epoxy composite (WFC) with an average fibre volume fraction of 57%. (R-ratio = 0.1, frequency 6 Hz). The arrow indicates a sample that did not break (Vallons, 2009b).
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NCF composite. In the bias direction, for each fatigue stress level, the fatigue life of the woven fabric composite is higher than that recorded for the ±45° NCF composite in the matrix-dominated directions. This is in accordance with the higher static strength of the woven fabric composite in this direction. In the fibre direction, the fatigue life curve of the woven fabric composite and that of the ±45° NCF composite nearly coincide. This again corresponds to the observed static tensile behaviour, which indicates that both the stiffness and strength of the two materials is approximately the same in the fibre directions. The results highlighted above indicate that, as is generally found for woven fabric composites, there is no significant difference between the fatigue life behaviour of NCF composites and that of composites based on UD layers. This, however, does not mean that the entire fatigue behaviour is identical. Due to the particular internal structure of NCF composites, it is not unlikely that there are differences in damage development and/or stiffness evolution.
13.2.2 Damage development The development of damage in a composite under fatigue will be dependent on the underlying mechanism, but also on the structure of the material itself. The damage process of continuous fibre composites in general under tensile–tensile fatigue can be roughly described as a three-stage process. Jamison et al. (1984) studied the development of damage during each of these three stages for graphiteepoxy cross-ply laminates based on UD prepregs, loaded in one of the fibre directions. They found that stage one consists of transverse crack formation with increasing density until a saturation state is reached. Stage two is characterised by axial splitting in the longitudinal plies and the occurrence of local delaminations, mostly at the intersection of the longitudinal and transverse cracks. In stage three, the delaminations grow and coalesce, and strip-like longitudinal regions are formed that finally fail by fibre breakage. The orientation of the fibres greatly influences the fatigue behaviour of the composite. The damage development pattern in an angle-ply laminate, for example, is different from that described above for cross-ply laminates (Talreja, 2000). When loaded in one of the two symmetry directions of a (±θn)s angle ply laminate, any ply in the laminate is subjected to in-plane normal and shear stresses. Isolating one ply out of the laminate, the behaviour is similar to that of a UD composite under inclined loading: failure will occur when a single crack grows in an unstable manner after it reaches a critical length by fatigue. In an angle-ply laminate, however, an additional aspect is present: the constraint of the ‘opposite sign’ ply. A crack in one single ply does not cause the laminate failure. Instead, the so-called ‘shear-lag’ process produces more ply cracks along fibres, which grow into the interlaminar surface, causing local delaminations and gradual stiffness decrease. Eventually, the delamination growth and coalescence results in ply separation and failure.
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Some in-depth studies on the damage initiation and development during tensile fatigue in composites based on UD layers were done in the past, for example, by Wevers (1987). Four different types of carbon fibre laminates were investigated: (+45°,−45°,+45°,−45°)s, (0°)s, (0°,+45°,−45°,90°)s, and (0°2/902°)s. The work of Wevers was mainly aimed at linking the energy in acoustic emission signals, as measured during the tests, to the different damage modes occurring during fatigue loading, by comparison with the observations from other non-destructive testing techniques like X-ray investigation and C-scan. The damage evolution observed for the different types of laminates was in good agreement with the discussion above: first, matrix cracks were formed in the 90° oriented layers (if present), followed by cracks in the ±45° layers and local delaminations between plies with different orientation. Later in the tests, delamination growth, fibre debonding and fibre failure were also noted before final fracture of the samples. The discussions above mainly concern laminates based on UD prepregs. However, the behaviour of woven fabric composites in tension–tension fatigue, parallel to one of the fibre directions, is largely similar to that of cross-ply UD layer-based composites (Talreja, 2000): first, matrix cracks appear in fibre bundles lying normal to the loading direction. On continued load cycling, some of these cracks are found to initiate local debonding of the cracked fibre bundle from the neighbouring bundle. This debonded surface is referred to as a local delamination. Also, Naik et al. (2001) concluded that the fatigue damage mechanism in woven fabric composites is similar to that in cross-ply laminates, except for the regular pattern of local debonding at the cross-over points between the yarns, and that this damage evolution was reflected in the stiffness loss curves as described above. Although rather limited, some data on the damage development during fatigue in NCF composite materials exist. For quadriaxial glass fibre NCF composites with an epoxy matrix, for example, Gagel et al. (2006) found that in contrast to conventional laminated composites, matrix cracking parallel to the fibres may be less critical in NCF composites with respect to its failure-causing role. Due to the stress concentrations at the tips of these intra-ply cracks, matrix cracking can cause fibre rupture in the adjacent layers and thus initiate final failure. In the case of NCF composites, however, with their fibre bundles slightly compacted by the stitching yarn and surrounded by the more ductile matrix material, Gagel et al. suggested that the stress concentrations at the crack tip may be released. Vallons et al. (2007) monitored the damage development in a biaxial carbon fibre NCF composite for tensile–tensile fatigue loads up to stresses corresponding to the initiation of damage in a static tensile test. Radiography revealed extensive matrix cracking in the off-axis oriented plies. No other form of damage could be detected up to very high numbers of fatigue cycles. A similar, but more elaborate study investigated the fatigue damage behaviour of another type of biaxial carbon fibre NCF composite, based on a chain-stitched ±45° NCF (Vallons, 2009a and 2009b, see also Section 13.5). In this case, tensile–
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tensile fatigue tests were also done up to stress levels corresponding to the onset of damage in a static tensile test (i.e. 25% of the ultimate tensile strength (UTS) for the given composite). The evolution of damage was monitored by penetrant-enhanced radiography. Under these relatively low-load fatigue conditions, the fatigue life was found to be quasi-infinite, although vast amounts of transverse matrix cracks were found to develop in the material. The radiography pictures (see, for example, Fig. 13.5) were used to determine the crack density at different cycle times for the fibre direction samples. As can be seen in Fig. 13.6
13.5 X-ray images showing transverse matrix cracks in a biaxial carbon-epoxy NCF composite, fatigue tested in the fibre direction up to 25% of the UTS, for (a) 5 × 105, (b) 106 and (c) 5 × 106 cycles. For each case, a front and a side view of part of a sample are shown (Vallons et al., 2009a).
13.6 Crack density as a function of the number of fatigue cycles in the two fibre directions of a ±45° carbon-epoxy non-crimp fabric composite, fatigue loaded up to 25% of the UTS (Vf = 58%, R = 0.1, frequency = 6 Hz) (Vallons et al., 2009a).
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and on the radiography images in Fig. 13.5, the crack density first increases steadily, but it then stabilises and reaches a saturation value. Interestingly, the number of transverse cracks in the material for a given number of fatigue cycles was found to be dependent on the lay-up, as can be seen on the figure. Even though damage does develop in this material for the applied fatigue conditions, failure of the material did not occur within practical cycling times (more than 5 × 106). Either, after the transverse crack density reaches a saturation value, no new damage is formed, implying that there is a stress threshold for the development of other types of damage (e.g. longitudinal cracks, delaminations), or these other types of damage will be formed eventually, but only at extremely high cycle times. In the second part of that same study (Vallons, 2009b), the damage development in the NCF composite during fatigue at higher maximum stresses was investigated, and compared to that in an equivalent woven fabric composite. A series of fibre direction NCF and woven fabric composite samples were loaded in tensile–tensile fatigue up to a maximum stress level of about 700 MPa (i.e. approximately 70% of the UTS). Under these conditions, the average fatigue life was about 106 cycles. The tests were stopped at different cycle numbers (103, 104, 105 and 25 × 104 cycles). At these moments, the samples were removed and the damage evolution in these samples was investigated by means of radiography and C-scan. The radiography pictures are shown in Fig. 13.7. After 103 cycles, the damage in the two materials is very similar: transverse cracks have developed in both, and no other damage is clearly present. After 104 cycles, short longitudinal cracks can be seen to have developed in the NCF composite, which appear to follow a diagonal pattern, like the stitching sites in this material. In the woven fabric composite, longitudinal cracks are also observed, as well as some delaminations. These can be distinguished on the pictures in Fig. 13.7 as the dark, ‘stain’-like regions. Delaminations are only observed in the NCF composite after 105 cycles, when the longitudinal cracks have grown in both materials, and the delaminations in the woven fabric composite have developed further. After 2.5 × 105 cycles, the delaminations in the NCF composite have also increased in size and number, but the extent of delamination in these samples is still smaller than that in the woven fabric composite samples. The results of the C-scans, shown in Fig. 13.8, more clearly show the evolution of the delamination area in the considered materials. From these pictures, it can also be noted that the delaminations in the woven fabric composite seem to be spread more or less evenly in the sample, while those in the NCF composite are distributed much more irregularly. The damage evolution in a NCF composite is thus largely similar to that in a composite based on UD layers. The type of damage in each of the three stages of the fatigue process is the same. However, as was noted in the study by Vallons (2009b), it is possible that the presence of the stitching influences the location and possibly also the initiation of this damage.
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13.7 X-ray images of a ±45° carbon-epoxy non-crimp fabric composite (left) and a carbon-epoxy twill weave composite (right) after tensile fatigue in the fibre direction (max. stress about 70% of the UTS) for (a) 103, (b) 104, (c) 105 and (d) 2.5 × 105 cycles (Vallons, 2009b).
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13.8 C-scan images of a ±45° carbon-epoxy NCF composite (left) and a carbon-epoxy twill weave composite (right) after tensile fatigue in the fibre direction (max. stress about 70% of the UTS) for (a) 104, (b) 105 and (c) 2.5 × 105 cycles (Vallons, 2009b).
13.2.3 Stiffness evolution Typically, composite materials under fatigue are characterised by a constant degradation in stiffness, due to the accumulation of damage, with increasing number of fatigue cycles. In the previous section it was mentioned that the damage development during fatigue in a composite based on UD layers can be described as a three-stage process. These three stages are also reflected in the stiffness degradation of samples during fatigue tests, as schematically illustrated in Fig. 13.9, where the modulus in the direction of the fatigue loading is represented schematically as a function of the number of cycles applied. In the first stage, the occurrence of transverse cracks causes a small but rather sharp decrease in stiffness of the composite. This decrease is dependent on the fibre volume fraction of the composite, but is generally limited to a few percent. Sometimes, the decrease in stiffness is compensated for by slightly improved fibre alignment. In stage two, the stiffness decreases further, but at a much slower and approximately linear rate. In the last stage, the stiffness drops abruptly when the final material failure occurs. The orientation of the fibres in a multilayer UD-based composite has an influence on the type and extent of damage that will develop in the material. Through the damage, this will therefore also have an effect on the stiffness decrease during fatigue. Philippidis and Vassilopoulos (2000), for example, showed that the stiffness variation during fatigue in UD-based angle-ply laminates is more pronounced for laminates with greater off-axis angles. As mentioned in the introduction of this paragraph, the fatigue life curves for woven fabric composites are very similar to the ones for cross-ply UD-based
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13.9 Schematic illustration of the effect of the three stages of the fatigue process on the normalised composite stiffness.
laminates. The stiffness evolution during fatigue, however, differs as a result of the different damage development in these two materials. Figure 13.10 shows a comparison between the normalised stiffness reduction of a woven fabric composite and that of a cross-ply laminate during fatigue (Schulte et al., 1987). The two curves coincide up to about 50% of the fatigue life. At this point, local delaminations at the interlaces in the woven fabric composite initiate and start to grow to form global delaminations, which reduce the stiffness of the woven fabric composite to a larger extent than the damage in the NCF composite.
13.10 Comparison of the stiffness decrease during fatigue in a cross-ply UD based laminate and an eight-harness satin weave composite (Schulte et al., 1987).
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For NCF composites, the global stiffness evolution during fatigue is, as is the damage development, again largely similar to that for UD-based laminates as, for example, was found by Dyer and Isaac (1998). They studied the stiffness decrease for 0°/90°, ±45° and quasi-isotropic glass fibre NCF composites under tensile– tensile fatigue, and noted a behaviour similar to that in Fig. 13.9. In accordance with the above-mentioned conclusion of Philippidis and Vassilopoulos (2000) for UD-based composites, the stiffness decrease for the 0°/90° NCF laminate was very small (about 20% at final fracture). The quasi-isotropic laminate retained about 50% of its initial stiffness value at failure. For the ±45° specimens, the stiffness degradation is the highest (60–70% at final fracture). The results of Dyer and Isaac are illustrated in Fig. 13.11. Ruggles-Wrenn et al. (2003) studied the cyclic tension behaviour in the 0° and the 45° direction of a stitch-bonded carbon fibre/urea-urethane matrix composite with a cross-ply lay-up and a quasi-isotropic lay-up. They also observed the greatest decrease in properties upon cycling in the 45° direction and the smallest decrease upon cycling in the 0° fibre direction. The quasi-isotropic lay-up showed intermediate results. In the first of the studies by Vallons et al., mentioned in the previous section (Vallons et al., 2007), where a biaxial carbon fibre NCF composite was fatigue loaded up to low stress levels (i.e. the stress at which damage initiates in a static
13.11 Normalised stiffness evolution during fatigue for different types of stitch-bonded GFRP laminates: (a) 0°/90°. (b) quasi-isotropic and (c) ±45°. The fibre weight fraction ranges from 55% to 70%. Maximum fatigue stress = 60% of the UTS, test frequency = 1 Hz, R-ratio = 0.1 (Dyer and Isaac, 1998).
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13.12 Average stiffness evolution for a ±45° carbon-epoxy non-crimp fabric composite (Vf = 58%), fatigue loaded in fibre direction up to 25% of the UTS. (R-ratio = 0.1, frequency = 6 Hz) (Vallons et al., 2009a).
test), the occurrence of the transverse fatigue cracks led to a small decrease in stiffness of about 5% in the fibre direction. In the second, more elaborate study, however (Vallons et al., 2009a, see also Section 13.5), no significant decrease in stiffness during the fatigue tests could be detected (see Fig. 13.12), although in both cases, a vast amount of transverse matrix cracks was present in the tested samples. The absence of a measurable decrease in stiffness due to the transverse cracks in the second study was explained by taking into account the higher fibre volume fraction in the composite material (57% compared to 41% in the first study). Due to this higher fibre volume fraction, the influence of the decrease in stiffness of the transverse fibre layers, caused by the cracks, is too small to be distinguished from the normal scatter on the material stiffness. If the stiffness loss due to the transverse cracks would be overestimated by disregarding the stiffness of the transverse fibre plies completely, it can be calculated that the stiffness of the whole composite would only be decreased by 3.5%. As mentioned earlier, Vallons (2009b) also investigated the damage behaviour during fatigue at higher maximum stresses (about 70% of the UTS). The stiffness evolution for these conditions was also monitored and compared to that of an equivalent woven fabric composite. In Fig. 13.13, the obtained static stiffness evolution of the two materials in fibre direction is plotted. The graph indicates that the stiffness decrease in the beginning of the test (up to about 104 cycles) is the same for the two materials. However, as noted above, the damage development in the NCF composite differs from that in the woven fabric composite for higher fatigue cycle numbers. In correspondence with the observation that delaminations develop earlier and to a greater extent in the woven fabric composite, the stiffness of the latter decreases more rapidly than that of the NCF composite. The discussion above leads to the conclusion that the stiffness evolution during fatigue in an NCF composite resembles closely that in a UD-based laminate. This corresponds to the similar damage development in these two types of composites.
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13.13 Evolution of the static stiffness of a ±45° carbon-epoxy non-crimp fabric composite and a carbon-epoxy twill weave composite during fatigue in fibre direction (max. fatigue stress about 70% of the UTS, R-ratio = 0.1, frequency = 6 Hz) (Vallons, 2009b).
Both retain a higher residual stiffness after a certain number of fatigue cycles than an equivalent woven fabric composite, which loses stiffness due to the early development of local delaminations.
13.2.4 Influence of fibre orientation An important characteristic of continuous fibre reinforced composites is that they are highly anisotropic in their mechanical properties. In fibre directions, they are very strong and stiff, but in off-axis directions, the properties are much lower. In large-scale composite structures with complex shapes, the fibre orientation spatially varies. This implies that composite elements are locally subjected to a certain degree of off-axis loading. It is therefore important to know the behaviour of these materials when they are subjected to such loading cases. Even a small misalignment of a few degrees between the fibres and the loading direction can have a detrimental effect on the properties. Such a misalignment could, for example, arise from an inaccurate placement of the reinforcements during the production of a composite part, or from errors in the fabric production. Although little work is available on the off-axis properties of cross-ply or textile composites, the properties of UD composites under off-axis loading conditions are relatively well known. Using the classical laminate theory (CLT), the elastic constants for a single off-axis UD ply can be easily predicted. Figure 13.14
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13.14 Variation of the elastic constants of a continuous E-glass fibre lamina with the fibre orientation angle (Mallick, 2008).
illustrates the theoretical variation of the constants for a UD glass-fibre laminate when the orientation is changed from 0° (on-axis) to 90° (transversal). The CLT can also be used to predict the stiffness of a multidirectional UD-based laminate in any direction. Kawai et al. have published an interesting series of articles on the dependence of the static and fatigue properties of different types of composite materials on the off-axis angle (Kawai et al., 2001, 2006 and 2008). In a first article (Kawai et al., 2001), the authors investigated the off-axis tensile–tensile fatigue behaviour of a UD carbon fibre-reinforced composite. The tensile strength and fatigue life for samples with an orientation θ of 0°, 5°, 10°, 15°, 20°, 30°, 45° and 90° was determined. The observed tensile strengths agreed very well with the predictions based on the Tsai–Hill criterion. From the tensile–tensile fatigue tests, they concluded that the off-axis fatigue life curves of the UD material are approximately described by straight lines irrespective of the fibre orientation. They are shown in Fig. 13.15. Kawai et al. also noted that, after normalising the fatigue life curves using the corresponding off-axis static strength, the different curves all fell within a narrow scatter band. In a subsequent paper (Kawai and Honda, 2008), the results of a study using a similar methodology to investigate the properties of a carbon-epoxy cross-ply (0°/90°) laminate for different off-axis orientations are reported. If the fatigue
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13.15 Room temperature fatigue life curves for a unidirectional carbon-epoxy composite with different off-axis orientations. (R = 0.1, frequency = 10Hz) (Kawai et al., 2001).
results are normalised by using the static strength, it was again found that the fatigue life curves for the different orientations coincide, see Fig. 13.16. As for the UD composite, Kawai et al. concluded that the fibre orientation dependence of the fatigue data can be effectively removed by this normalisation procedure. Moreover, they also made the remarkable observation that the normalised fatigue life curve for a cross-ply lay-up agreed very well with the one they obtained in the earlier study (Kawai et al., 2001) for the different orientations of a UD composite. Finally, Kawai also studied the behaviour of a carbon-epoxy plain weave composite under the same circumstances (Kawai and Taniguchi, 2006). Again, linear fatigue life curves in the on-axis directions were observed, on the condition that the fatigue test frequency was sufficiently low. For this plain weave composite, Kawai et al. reached a similar conclusion as for the UD laminate and the cross-ply composite discussed above: after normalisation of the fatigue life curves for the different orientations results with respect to the static strength, they are again found to overlap within a narrow scatter band. Data on the orientation dependence of NCF composites is particularly scarce. In the recent study by Vallons (2009b), a series of fatigue tests was done on a biaxial (±45°) NCF composite. The samples had a 5° off-axis orientation compared to one of the fibre directions. The tests were done up to a maximum stress level of about 25% of the UTS. This is the stress level at which damage initiates in a static tensile test in the fibre direction. Under these conditions, a
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13.16 Fatigue life curves for different off-axis angles of a cross-ply composite, before (a) and after (b) normalisation with respect to the static strength (Kawai and Honda, 2008).
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13.17 Results of tensile fatigue tests on 5° off-axis carbon-epoxy non-crimp fabric composite samples, compared to those for the on-axis samples. (Sample width = 25 mm, frequency = 6 Hz, R-ratio = 0.1) (Vallons, 2009b).
quasi-infinite fatigue life was found (no samples broke up to 107 cycles) for the on-axis fibre direction samples. Figure 13.17 shows the results of the 5° off-axis fatigue tests. The fatigue life curve for the on-axis fibre direction samples is also shown. From the graph, it could be concluded that the relatively small misorientation of 5° apparently not only has a detrimental effect on the static strength, but also on fatigue strength, since the average fatigue life was reduced to approximately 5 × 106 cycles. These results are similar to those observed by Kawai for a cross-ply UD-based composite (Kawai and Honda, 2008). However, it was noted that the test sample dimensions play a crucial role in this behaviour. The results mentioned above were obtained from test samples with standard dimensions (gauge length 150 mm, width 25 mm). Tests on samples with a smaller aspect ratio (i.e. wider samples) revealed that as the aspect ratio of the test samples decreases, the influence on the static strength and on the fatigue life of the material was decreased. The authors also noted that, remarkably, it seems that for samples with a smaller aspect ratio (i.e. wider samples), the fatigue life curve becomes less steep, and hence the influence of the misorientation would be less important for higher fatigue cycle times. However, since the number of data points for these types of samples was very limited, this conclusion remains somewhat unsure. The results in this study were for tensile–tensile loading only (R = 0.1). It can be expected that the influence of a small misorientation of the loadcarrying fibres will be more severe for loading cases that involve a compressive component (R < 0).
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13.18 Fatigue life curves for different orientations of a ±45° carbonepoxy non-crimp fabric composite. For the 5° off-axis tests, the results for three different sample widths are shown, for all other orientations, the sample width was 25 mm (R-ratio = 0.1, frequency = 6 Hz) (Vallons, 2009b).
The study by Vallons et al. (2009b) also looked into the behaviour of the ±45° NCF composite material for larger off-axis orientations. The fatigue life curves obtained for the different orientations are shown in Fig. 13.18. This graph also shows the results for the on-axis samples (0° direction), as well as the results from the 5° off-axis samples described above. It was concluded that the fatigue strength shows a similar behaviour as the static strength for varying orientation of the laminate. A sharp decrease in static strength was observed when the offaxis orientation varies from 0° to 15°. This is reflected in a large downward shift of the fatigue life curve. For larger off-axis angles, the decrease is much smaller. The curves for the 15°, 30° and 45° orientations are very close together, again reflecting the static tensile strengths, which were also very close together for these samples. As was done by Kawai et al. (2001, 2006 and 2008) for UD, cross-ply and woven fabric laminates, the fatigue life curves of the NCF composite were normalised with respect to the static strength. Figure 13.19 shows the obtained normalised fatigue life curves for the different fibre orientations. The graph indicates that, as was observed by Kawai et al. for the other types of laminates, this simple normalisation procedure effectively removes the fibre orientation dependence of the fatigue life in the NCF composite.
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13.19 Normalised fatigue stress versus number of cycles to failure for different orientations of a ±45° carbon-epoxy non-crimp fabric composite with an average fibre volume fraction of 58% (Vallons, 2009b).
13.3
Post-fatigue residual properties
As discussed in the previous paragraphs, fatigue introduces damage in composite materials. In general, this damage has an effect on the stiffness of the material as described above. Apart from the stiffness, the fatigue damage can also influence other static properties, like the tensile and compressive strength. In the study by Vallons et al. (2007), mentioned several times earlier in this chapter, biaxial carbon-epoxy NCF composite samples were tested in low load level tensile–tensile fatigue. After fatigue, the samples were subjected to static tensile tests to investigate the influence of the transverse fatigue matrix cracks on the residual static properties. In the fibre directions, no influence on the strength or failure strain was found, only a small decrease in stiffness, as mentioned before (see Section 13.2.3) and a slight increase in damage initiation strain, measured by means of acoustic emission. In the bias direction, however, a clear decrease in damage initiation strain and failure strain was observed. In the other study by Vallons et al. (2009a), as was mentioned in the previous paragraph, the transverse matrix cracks caused by fatigue at 25% of the UTS did not lead to a measurable decrease in stiffness of the biaxial carbon-epoxy NCF composite. Subsequent post-fatigue static tensile tests also did not reveal any change in the material strength.
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Higher-load fatigue tests (up to 70% of the UTS) did lead to stiffness loss and extensive damage in the composite (Vallons, 2009b). In the fibre direction of the biaxial NCF composite, a decrease in sample stiffness of approximately 9% after fatigue was found. However, the tensile strength after fatigue did not differ significantly from that prior to fatigue. This is not surprising, since the major form of damage present in these samples, i.e. delamination, seldom affects the tensile strength of a material. Therefore, it was also investigated what the influence of the fatigue damage was on the compressive strength. Both NCF composite and woven fabric composite samples were tested in fatigue up to 70% of the UTS and subsequently subjected to a static compression test. The results of these tests are shown in Fig. 13.20, where they are compared to the compressive strength of samples without prior damage. From the figure, it is clear that after fatigue, a pronounced decrease of the compressive strength was found for both materials. For the NCF composite, the post-fatigue compressive strength was 31% lower than the initial strength. The compressive strength of the woven fabric composite was reduced by 64%. The decrease in compressive strength observed by Vallons (2009b) is about twice as large for the woven fabric composite samples as for the NCF composite samples, although the scatter on the result for the latter was very large. This was attributed to the higher number of delaminations in the woven fabric composite after fatigue. As mentioned above, the presence of delaminations mostly does not play a significant role in tensile loading, but when a sample with delaminations is loaded in compression, the delaminations induce instability in the sample, which can lead to earlier failure. Although some delaminations were also found to be
13.20 Post-fatigue (PF) and intact compressive strength of a ±45° carbon-epoxy NCF composite (NCFC BD+) and equivalent woven fabric composite (WFC FD) (Vallons, 2009b).
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present in the NCF composite, they are much more irregularly distributed and fewer in number (see Section 13.2.2). This can also account for the large scatter on the obtained strength for this material: in compression tests, only a very small gauge length is used to avoid buckling effects. Due to the more scattered nature of the delaminations in the NCF composite, which could already be observed on the post-fatigue C-scan images in Section 13.2.2, the chance of having extensive delaminated areas inside this gauge length is smaller than for the woven fabric composite, where the delaminations are spread more evenly over the sample. The results of the NCF composite samples therefore will include those for samples with almost no delaminations present in the gauge length, as well as those for samples with many delaminations.
13.4
Conclusions and open questions
The studies cited in this chapter have suggested that, in general, the tensile fatigue behaviour of NCF composites appears to be quite similar to that of UD-based composites. For NCF composites, both the fatigue life and the type of damage that develops during fatigue seem to be equal to, or at least closer to, that in a UD-based laminate than to that in a woven fabric composite. However, there are indications that the specific internal structure of NCF composites can play a role in the fatigue process, for example, in the initiation sites of damage. It is therefore very important to conduct further studies, focusing on these particular aspects of the behaviour. As mentioned, data on the fatigue properties of NCF composites are still relatively scarce, and the major part of the studies focuses exclusively on the tensile fatigue behaviour. However, since it is known that the stitching process introduces a slight in-plane waviness in the fibrous plies, it is essential that also other types of loading, e.g. compression and bending, are considered. Extensive studies, concentrating specifically on the differences in fatigue behaviour of NCF composites as compared to composites with other types of reinforcements, and on the influence of the production parameters of the consisting NCFs on the final performance of the composite, will help to gain a deeper understanding of the material, and will certainly lead to a more confident use of NCF composites for various structural applications.
13.5
References
Dyer K. P. and Isaac D. H. (1998), ‘Fatigue behaviour of continuous glass fibre reinforced composites’. Composites Part B, 29, 725–733. Edgren F., Asp L. E., and Sjögren A. (2004), ‘Effects of stitch pattern on the mechanical properties of non-crimp fabric composites’, in ECCM 11, Rhodos, Greece. Gagel A., Lange D., and Schulte K. (2006), ‘On the relation between crack densities, stiffness degradation, and surface temperature distribution of tensile fatigue loaded glass-fibre non-crimp-fabric reinforced epoxy’, Composites Part A, 37, 222–228. Harris B. (2003), ‘A historical review of the fatigue behaviour of fibre-reinforced plastics’, in Harris B., Fatigue in composites, Cambridge, Woodhead, 3–35.
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Jamison R. D., Schulte K., Reifsnider K. L., and Stinchcomb W. W. (1984), ‘Effects of Defects in Composite Materials’, in ASTM STP 836, Philadelphia, American Society for Testing and Materials. Kawai M., Yajima S., Hachinohe A., and Takano Y. (2001), ‘Off-axis fatigue behavior of unidirectional carbon fiber-reinforced composites at room and high temperatures’, Journal of Composite Materials, 35, 545–576. Kawai M. and Taniguchi T. (2006), ‘Off-axis fatigue behavior of plain weave carbon/epoxy fabric laminates at room and high temperatures and its mechanical modeling’, Composites Part A, 37, 243–256. Kawai M. and Honda N. (2008), ‘Off-axis fatigue behavior of a carbon/epoxy cross-ply laminate and predictions considering inelasticity and in situ strength of embedded plies’, International Journal of Fatigue, 30, 1743–1755. Mallick P. K. (2008), ‘Fiber-reinforced composites: Materials, Manufacturing and Design. Third edition’, Boca Raton, CRC Press – Taylor & Francis Group. Naik R. A., Patel S. R., and Case S. W. (2001), ‘Fatigue Damage Mechanism Characterization and Modeling of a Woven Graphite/Epoxy Composite’, Journal of Thermoplastic Composite Materials, 14, 404–420. Naik N. K. (2003), ‘Woven-fibre thermoset composites’, in Harris B., Fatigue in composites, Cambridge, Woodhead, 295–313. Philippidis T. P. and Vassilopoulos A. P. (2000), ‘Fatigue design allowables for GRP laminates based on stiffness degradation measurements’, Composites Science and Technology, 60, 2819–2828. Ruggles-Wrenn M. B., Corum J. M., and Battiste R. L.(2003), ‘Short-term static and cyclic behavior of two automotive carbon-fiber composites’, Composites Part A, 34, 731–741. Schulte K., Reese E., and Chou T.-W. (1987), ‘Fatigue Behaviour and Damage Development in Woven Fabric and Hybrid Fabric Composites’, in Proceedings of Sixth International Conference on Composite Materials and Second European Conference on Composite Materials, London and New York, Elsevier Applied Science, 489–499. Talreja R. (2000), ‘Fatigue of polymer matrix composites’, in Kelly, A. and Zweben, C., Comprehensive composite materials, Elsevier Science Ltd, 529–552. Vallons K., Zong M., Lomov S. V., and Verpoest I. (2007), ‘Carbon composites based on multi-axial multi-ply stitched preforms – Part 6. Fatigue behaviour at low loads: Stiffness degradation and damage development’, Composites Part A, 38, 1633–1645. Vallons K., Lomov, S.V. and Verpoest, I. (2009a), ‘Fatigue and post-fatigue behaviour of carbon/epoxy non-crimp fabric composites’, Composites Part A, 40, 251–259. Vallons K. (2009b), ‘The behaviour of carbon fibre – epoxy NCF composites under various mechanical loading conditions’, Doctoral dissertation, Faculty of Engineering Sciences, Katholieke Universiteit Leuven, Belgium. Wevers M. (1987), ‘Identification of fatigue failure modes in carbon fibre reinforced composites’, Doctoral dissertation, Faculty of Engineering Sciences, Katholieke Universiteit Leuven, Belgium.
13.6
Appendix
In this section, a brief description will be given of the carbon/epoxy NCF composite used in the study by Vallons et al. (2009a and 2009b) that has been referenced many times in this chapter. A picture of the fabric used for this study is
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13.21 A picture of the biaxial carbon fibre NCF used in the study by Vallons et al. (2009a and 2009b). Table 13.1 Internal geometry characteristics of non-crimp fabric used by Vallons et al. (2009a; 2009b) Fabric parameter Areal density Fibre type Yarn Opening length (front), mm Opening length (back), mm Opening width (front), mm Opening width (back), mm Stitch gauge, mm Length of stitches, mm
540 g/m2 STS carbon fibre 24 K 9.6 ± 1.6 mm 11.9 ± 1.3 mm 0.26 ± 0.01 mm 0.23 ± 0.03 mm 5.3 ± 0.1 mm 3.3 ± 0.4 mm
shown in Fig. 13.21. It is a biaxial carbon fibre NCF in which the fibre directions are oriented ±45° relative to the machine direction. The fabric characteristics and the results of the internal geometry characterisation (dimensions of the openings, stitching parameters etc.) are listed in Table 13.1. The fabric was provided in prelaminated form, i.e. an epoxy resin film was attached to the back of the fabric. Composite plates were produced using a modified two-step resin film infusion process. In the first step, each prelaminated fabric layer was impregnated separately to produce a prepreg. In the second step, several prepreg layers were stacked to form plates. The average composite thickness was 2.10 ± 0.05 mm, with an average fibre volume fraction of 57 ± 1%. The lay-up sequence used for the plates was [−45, +45]2s. To ensure fully symmetrical plates, both a (+45, −45) fabric and a (−45, +45) fabric were used. In this way, the stitching direction was parallel in the different fabric layers in the plate.
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14 Mechanical properties of structurally stitched non-crimp fabric composites N. HIMMEL, Institut für Verbundwerkstoffe GmbH, Germany and H. HEß, BASF Engineering Plastics Europe, Germany*
Abstract: The mechanical performance of polymer matrix composites perpendicular to the laminate plane can be improved by the insertion of local through-thickness reinforcements into dry fibre preforms by structural stitching. On the other hand, the in-plane stiffness and strength properties of the laminate may be reduced by this process though the induction of in-plane fibre undulations and the formation of voids in the vicinity of stitches after resin infusion. In this chapter the effect of structural stitching on in-plane and out-of-plane properties of multidirectional non-crimp fabric (NCF) carbon fibre/epoxy laminates is illustrated. Ambivalent effects of the various stitching parameters on the mechanical properties were observed. A finite element based unit cell model was developed to estimate in-plane elasticity and strength coefficients of structurally stitched NCF laminates. Comparison with experimental results shows that stiffness and strength properties of structurally stitched NCF laminates can be predicted with satisfying accuracy. Key words: polymer matrix composite, epoxy resin, carbon fibre, non-crimp fabric, structural stitching, laminate properties, elasticity, strength, unit cell model.
14.1
Introduction
In comparison to metallic materials, carbon fibre-reinforced plastic laminates (CFRP) are quite attractive for lightweight applications, particularly in the aviation industry, because of their superior stiffness and strength to density ratio. The stitching technology in conjunction with resin infusion techniques provides manifold possibilities to economically manufacture small- to medium-sized CFRP structures, such as the Airbus A380 pressure bulkhead, a flap support beam and a flap load introduction rib (Stüve et al., 2006; Ogale and Mitschang, 2004; Weimer, 2003; Weimer et al., 2006; Havar et al., 2008). The possibility to insert local through-thickness reinforcements into non-crimp fabrics (NCF) by structural stitching is of particular interest to the composite engineer in laminates subjected to three-dimensional (3D) stresses (e.g. impact and damage tolerance issues). Furthermore, stitching enables attachment of metallic inserts to dry fibre preforms for load introduction (Molnár, 2007). In this chapter the term ‘structurally stitched laminates’ refers to polymer matrix composites reinforced by NCF, which are stitched through the total thickness of the lay-up prior to resin infusion; in contrast, * Formerly at Institut für Verbundwerkstoffe GmbH, Germany, where the work described in this chapter was carried out.
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laminates containing NCF with fibre rovings fixed by binding yarns but lacking structural stitching are referred to as ‘unstitched laminates’ (Fig. 14.1). Dexter and Funk (1996) and Iwahori et al. (2004) reported that the compression after impact (CAI) strength of laminates can be increased by a factor of 1.5 compared to unstitched laminates, based on studies of the effect of structural stitching on impact-loaded composites. Liu (1990) and Byun et al. (2005) observed a reduction of the impact damage area by up to 40%. However, the energy level relative to the thickness of the impacted laminate significantly influenced the effect of structural stitching on the CAI strength. While CAI improvements due to structural stitching were reported for impact energy to laminate thickness ratios between 3 and 5 J/mm, differences could not be observed below 2 J/mm (Aymerich et al., 2007; Mouritz and Jain, 1999). In Mouritz and Jain (1999), Drainsfield et al. (1998) and Wood et al. (2007) it was reported that structural stitching enhanced the effective mode I energy release rate GIR of composites by more than a factor of four compared to unstitched laminates. It was found that enhanced CAI and mode I energy release rate GIR data of the composite laminate are usually correlated to increased yarn diameters and stitch densities. With regard to the fibre types used for structural stitching, carbon and aramid yarns reduced crack propagation much more than glass, polyester, polyamide or sisal yarns (Dexter and Funk, 1996; Mouritz and Jain, 1999; Velmurugan and Solaimurugan, 2007; Mouritz et al., 1999; Sharma and Sankar, 1995; Ogo, 1987; Rong et al., 2002; Dransfield, 1994). The insertion of fibre yarns in the thickness direction of NCFs and preforms by structural stitching causes dislocations and undulations of the in-plane fibres in the vicinity of the stitching yarn as well as the formation of stitching voids which, after impregnation, consist of the impregnated yarns as well as a resin pocket. Loendersloot et al. (2006), Lomov et al. (2002), Truong et al. (2005), Vettori et al. (2004) and Truong et al. (2004) reported that non-structural stitching initiated early damage. With regard to the in-plane properties of structurally stitched composites, multiple and contradictory information are found in the open literature. Structurally
14.1 (Left) non-structural and (right) structural stitching, (a) schematic of modified lock stitch, (b) and (c) µ-CT photographs of structurally stitched laminate (lay-up [A1-(B/2)S-A2]-HTS, parameter configuration K 1).
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stitched laminates are reported to show about 10 to 20% reduced tension, compression and bending stiffness and strength coefficients compared to the unstitched reference, whereas in some cases no alteration or even moderate increase of these properties was observed (Stüve, 2006; Byun et al., 2005; Tong et al., 2002; Mouritz and Cox, 2000; Ogale, 2007; Mouritz et al., 1997; Beier et al., 2007). Despite improved impact resistance and damage tolerance, the stitching of NCF laminates can only be applied on an industrial scale if the mechanical characteristics, especially the in-plane properties, can be estimated fast, with a minimum of experimental effort. Analytical and finite element models exist for the prediction of mechanical properties of textile reinforced composites (Roth, 2005; Tan et al., 1997). In some models a unit cell (UC) approach is defined, which considers the reinforcing textile structures on a meso-scale but not on the scale of the individual fibre (Tan et al., 1997; Cox and Flanagan, 1997; Tang and Whitcomb, 2003). Models to estimate mechanical characteristics of NCF laminates are presented by Gonzáles et al. (2008), Ernst et al. (2007), Oakeshott et al. (2007) and Carvelli et al. (2004). Obviously the furthest developed tool to simulate textile-reinforced fibre-reinforced plastic (FRP) laminates is a software package of the Catholic University of Leuven, Belgium. It consists of the modules WiseTex for displaying the textile fibre architecture, LamTex for modelling the laminate structure, FETex and MeshTex for converting the WiseTex geometry in a finite element environment, TexComp for prediction of mechanical properties, FlowTex and Celper for estimation of permeability and VRTex for converting the WiseTex geometry in a virtual reality. These modules can be applied to simulate 2D and 3D weaves, 2D biaxial and triaxial braids as well as NCFs (Lomov et al., 2007; Lomov et al., 2005; Verpoest and Lomov, 2005). An even more sophisticated approach is the goal of the research project ITOOL (Integrated Tool for Simulation of Textile Composites). Based on existing and commercially available components in conjunction with additional calculation tools, an integrated solution for structural and process simulation of textile-reinforced FRP structures under static and dynamic loading shall be realised (Schouten, 2007; van den Broucke et al., 2007a; van den Broucke et al., 2007b). Scott et al. (2007), Karkkainen et al. (2007), Gui et al. (2005) and Gunnion et al. (2002) describe first approaches which allow the prediction of mechanical properties of structurally stitched composites.
14.2
Materials and stitching configurations
14.2.1 Non-crimp fabrics and resin High-tenacity (HT) HTA and HTS carbon fibre types and similar NCF configurations as well as equivalent stitching configurations were used in the presented investigations to assure comparability of the results. Type A1, B, B/2, and A2 carbon fibre non-crimp fabrics (Table 14.1) manufactured by Saertex GmbH & Co. KG were applied to produce [A1-B-A2], [A1-(B/2)S-A2] and [A1-(B/2)S-A2]2 laminates with 9-, 10- and 20-layer [+45/0/−45/0/900.5]S, [+45/0/−45/0/900.5]S and [+45/0/−45/(0/900.5)S/−45/0/+45]2 lay-ups (Fig. 14.2). © Woodhead Publishing Limited, 2011
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3
3
3
2
3
2
3
1
B HTA/S32CB680–00840– 01270–264000
A2 HTA/S32CY350–00828– 01270–264000
B/2 HTA/
A1 HTS/S32CY35K–00822– 01270–26400
B/2 HTS/V97590– 00430-T2540–000000
A2 HTS/S32CY35K–00823– 01270–26400
UD HTS/V98566–00290– 01270–000000
Number of layers
A1 HTA/S32CY350–00829– 01270–264000
Non-crimp fabric type/ supplier nomenclature Pattern
HTS
HTS
HTS
HTS
HTA
HTA
HTA
HTA
12
12/12/12
12/12
12/12/12
12/12
12/12/12
12/6/12
12/12/12 267/284/267 284/276/284 267/284/267 284/138 267/283/267 283/138 267/283/267 289
+45/0/−45 0/90/0 −45/0/+45 0/90 +45/0/−45 0/90 −45/0/+45 90
Warp
Warp
Tricotwarp
Warp
Tricotwarp
Warp
Tricotwarp
Warp
2.6
2.6
2.6
2.6
2.6
2.6
2.6
2.6
5.1
5.1
5.1
5.1
5.1
5.1
5.1
5.1
76
76
48
76
48
76
76
76
Linear density in dtex
Pitch Spacing length in mm in mm
Fibre Areal orientation weight ° in g/m2
Fibre type
Filament count × 1.000
Polyester binding yarn
Reinforcement
Table 14.1 Specifications of investigated carbon fibre non-crimp fabrics
6
6
4
6
4
6
12
6
Areal weight in g/m2
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339
14.2 Non-crimp fabric lay-ups for tension, shear, compression strength after impact, mode I energy release rate and compression tests.
All lay-ups are designed primarily for normal loading parallel to their x direction or for in-plane shear loading. Under normal loading, these laminates show a distinct orthotropic material behaviour, whereas under in-plane shear the corresponding mechanical properties should be independent from x and y. To manufacture laminate plates for specimen preparation, flat lay-ups from unstitched and structurally stitched NCFs were impregnated with resin transfer moulded (RTM) 6 aerospace grade epoxy resin (Hexcel Composites) using a vacuum-assisted resin infusion process and cured according to the supplier’s recommendation (Heß et al., 2007).
14.2.2 Structural stitching yarns, stitch type and stitching configurations E-glass stitching yarns with 150 twists/m and a linear density of 2 × 34 tex (68 tex) and 2 × 68 tex (136 tex) were used as upper yarns. The 68 tex E-glass yarn were also used as lower stitching yarn. To realise minimal fibre displacements within the NCFs a modified lock stitch was applied which places the interlace plane of the upper and lower yarns on the rear surface of the lay-up (Fig. 14.1). As shown in Fig. 14.3, pitch lengths p (i.e. distance between two stitches) and spacings s (distance between two parallel seams) of 3.3 mm and 5.0 mm in x and y, resulted in four patterns with an areal stitch density of 4.00, 6.06 and 9.18 cm−2. The investigated test configurations are listed in Table 14.2. The reinforcement
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14.3 Investigated stitching patterns and configurations as well as resulting stitch and reinforcement densities.
Table 14.2 Parameter configurations for uniaxial in-plane tension, compression and shear as well as out-of-plane compression strength after impact and mode I energy release rate testing of unstitched and structurally stitched non-crimp fabric laminates Configuration Loading Stitching Linear direction* direction yarn ld sd density in tex
Spacing s in mm
Pitch length p in mm
Reinforcement density RD in tex/cm2
Unstitched K1 K2 K3 K4 K5 K6 K7 K8 K9 K 10 K 11 K 12 K 13 K 14 K 15 K 16
– 5.0
– 5.0 3.3 5.0 3.3 5.0 3.3 5.0 3.3 5.0 3.3 5.0 3.3 5.0 3.3 5.0 3.3
– 544 824 824 1249 1088 1648 1648 2498 544 824 824 1249 1088 1648 1648 2498
–
– 68
3.3 x 5.0 136 3.3 x 68 y 136
5.0 5.0 3.3 3.3 5.0 5.0 3.3 3.3
* Shear loading in xy and yx planes under three-rail shear, or crack propagation direction under mode I loading
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density RD was used to characterise the inserted amount of structural stitching. RD is defined as the yarn density yd in tex per unit area of the stitched NCF in cm2 multiplied by a factor of 2 in the case of the modified lock stitch, as the upper yarn is present twice within one stitch (Fig. 14.1).
14.3
Characterisation of structurally stitched NCF laminates
14.3.1 Defect typology and characterisation Structural stitching voids were analysed by means of micrographs and computer tomography. The majority of these voids are diamond-shaped with the longer axis oriented parallel to the fibre direction of the individual layer, while voids with a similar geometrical shape but a much lower extension are generated by the NCF binding (Fig. 14.4). The optical characterisation clearly revealed that the crosssectional area and the width of the structural stitching voids increase with increasing yarn thickness which, on the other hand, did not significantly influence the void length. Furthermore, the void dimensions decrease from the outer surfaces to the centre of the laminate. In Fig. 14.5 the mean area and thickness data points together, as well as their corresponding scatter bands of structurally stitched [A1-B-A2]-HTA and [A1-(B/2)S-A2]2-HTA laminates are plotted versus the thickness coordinate z of the laminate. If the inner void geometry is not available from experimental data, these parameters can be modelled appropriately by parabolic functions, as also shown in this diagram.
14.4 (a) µ-CT picture (magnification ×6) and (b) micrograph (×20) through layer 3 (−45°) of a structurally stitched laminate parallel to laminate plane.
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14.5 Distribution of averaged void cross-section and width of structurally stitched laminates.
Laminate thickness and fibre content Investigations show that the laminate thickness as well as the fibre volume fraction is influenced by structural stitching. Roth and Himmel (2003) observed an increase of the laminate thickness and, consequently, a decrease of the fibre volume fraction with increasing reinforcement density (Fig. 14.6). In structurally stitched NCF laminates produced by vacuum injection, the amount of through-thickness
14.6 Normalised fibre volume content and thickness of structurally stitched CFRP laminates.
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reinforcement can influence the laminate thickness and the fibre volume content. While this effect was evident in [A1-B-A2] and [A1-(B/2)S-A2] laminates, only minor differences were evaluated in the [A1-(B/2)S-A2]2 composites with doubled thickness. This behaviour may be explained by differences in the compaction of the dry NCFs caused by the structural stitching and by varying evacuation conditions during resin infiltration.
14.3.2 Effect of structural stitching on mechanical properties of carbon fibre NCF epoxy laminates In the following figures, in-plane and out-of-plane data of structurally stitched carbon fibre NCF/epoxy laminates are presented as relative numbers normalised by the corresponding property of the unstitched reference laminate to demonstrate the effect of structural stitching. For more detailed information on the underlying test procedures, standards, specimen dimensions, data reduction procedures, etc., the reader is referred to Heß (2009) as well as Heß and Himmel (2010a). In-plane tension stiffness and strength Figure 14.7 illustrates the effect of structural stitching on the in-plane tensile modulus and strength of [A1-B-A2]-HTA laminates as a function of the reinforcement density RD. Both modulus and strength tend to decrease with
14.7 Normalised in-plane tensile modulus and strength of structurally stitched [A1-B-A2]-HTA laminates parallel to x depending on reinforcement density; unstitched laminate modulus and strength reference data 71 472 ± 3015 MPa (100 ± 4%) and 853 ± 24 MPa (100 ± 3%).
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increasing RD. The reduction rate mainly depends on the yarn diameter (cf. RD ranges between 544 and 1249 tex cm−2 as well as between 1088 and 2498 tex cm−2, corresponding to 68 and 136 tex yarns, respectively). Compared to the unstitched laminate, structural stitching reduces the in-plane tensile modulus by about 10% (normalised arithmetic mean ± coefficient of variation of K 1–K 16 90 ± 7%) together with a maximum reduction amounting to 24% (parameter configuration K 14; Roth, 2005; Heß et al., 2007). The application of a thicker stitching yarn generally causes a larger modulus reduction. On average, structural stitching reduced the in-plane tensile strength of the laminates to 86 ± 10% compared to the unstitched laminate. A maximum reduction of 36% was observed for K 14 while no effect was found for K 4. Again, the 136 tex stitching yarn caused a larger strength reduction than the 68 tex yarn. In-plane compression stiffness and strength The average in-plane compression modulus data of one half of the structurally stitched [A1-(B/2)S-A2]2-HTA laminates (K 2, K 3, K 4, K 7, K 11, K 12 and K 14) lie within the scatter band of the corresponding unstitched laminate (Fig. 14.8). Together with the remaining data which exceed the upper margins of the scatter band, a clear tendency, especially with respect to the effect of the stitching yarn density, could not be observed as to whether the modulus is
14.8 Normalised in-plane compressive modulus and strength of structurally stitched [A1-(B/2)S-A2]2-HTA laminates parallel to x depending on reinforcement density; unstitched laminate modulus and strength reference data 64 599 ± 2541 MPa (100 ± 4%) and 785 ± 42 MPa (100 ± 5%).
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increased or more or less constant by structural stitching (Heß et al., 2007). This is also reflected by an overall arithmetic mean of 104 ± 9% relative to the modulus of the unstitched laminate. Structural stitching with a 136 tex yarn resulted in a maximum increase or decrease of the compression modulus by 22 (K 5) and 6% (K 13). On average, the in-plane compression strength is reduced by about 19% due to structural stitching (81 ± 11%), while the maximum reduction of the compression strength observed was about 31% (K 16; Roth, 2005). A 136 tex stitching yarn tends to cause a higher strength reduction compared to a 68 tex yarn. In-plane shear stiffness and strength The effect of structural stitching on the in-plane shear modulus and strength of [A1-(B/2)S-A2]-HTS laminates is illustrated in Fig. 14.9. The increase of the through-thickness reinforcement tends to decrease both properties with a more pronounced effect on the shear strength. Higher modulus and strength reductions were observed by applying a 136 tex yarn. Structural stitching resulted in an overall reduction of the in-plane shear modulus to 90 ± 7% of the unstitched laminate with the maximum reduction of 15% determined for K 5. On average, the in-plane shear strength of [A1-(B/2)SA2]-HTS laminates due to structural stitching was reduced to 83 ± 6% in
14.9 Normalised in-plane shear modulus and strength of structurally stitched [A1-(B/2)S-A2]-HTS laminates parallel to x depending on reinforcement density; unstitched laminate modulus and strength reference data 13 492 ± 514 MPa (100 ± 4%) and 222 ± 24 MPa (100 ± 11%).
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comparison to the unstitched reference with maximum reductions between 10% (K 15) and 22% (K 8). Similar to uniaxial normal loading, the 136 tex yarn caused higher reductions than a 68 tex yarn. Compression strength after impact Figure 14.10 shows the normalised compression strength after impact (CAI) data of structurally stitched laminates relative to the unstitched reference as a function of the reinforcement density. The CAI strength tends to increase with increasing RD. As the mean CAI strength is almost identical for 68 and 136 tex yarns at a stitch density of 9.18 cm−2, this effect is mainly based on the increase of the stitch density, while it is not due to a change of the yarn density. On average, structural stitching resulted in a 10 ± 9% increase of the CAI strength. The maximum enhancement was 21% (K 4), while no effect or even a slight 3% reduction was found for the configurations K 13 and K 14.
14.10 Normalised compressive strength after impact (30 J) of structurally stitched [A1-(B/2)S-A2]-HTS laminates parallel to x depending on reinforcement density; unstitched laminate compression strength after impact reference data 192 ± 20 MPa (100 ± 10%).
Mode I energy release rate By carrying out tabbed double-cantilever beam (DCB) tests the mode I energy release rate of structurally stitched [A1-(B/2)S-A2]-HTS laminates, denoted as GIR, was determined and compared to the corresponding property GIc of the unstitched reference. Figure 14.11 shows the dependence of the normalised energy release
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14.11 Normalised mode I energy release rate of structurally stitched [A1-(B/2)S-A2]-HTS laminates for crack propagation parallel to x depending on reinforcement density; unstitched laminate mode I energy release reference data 0.95 ± 0.13 kJ/m2 (100 ± 14%).
rate on the reinforcement density. In comparison to the unstitched laminate, structural stitching considerably increased the GIR of the investigated laminates by a factor of 1.9. The highest GIR increase was realised, applying the 136 tex stitching yarn and the maximum stitch density (factor 3.0, K 16). For similar stitch densities Mouritz and Jain (1999) and Wood et al. (2007) reported GIR improvements between factors of 2.5 and 8.2 (136 tex glass yarn as well as stitch density 0.8 and 7.0 cm−2, respectively). However, even for identical composites and stitching configurations, a quantitative comparison of GIR data from the literature is rather difficult, due to the variability with respect to the specimen and test configuration as well as the evaluation method used to determine the energy release rate. The delamination started from the artificial pre-crack to propagate in the xy plane (delamination plane) within the matrix or the fibre/matrix interface after the specimen was subjected to low transverse tension loading, parallel to the thickness direction of the laminate. In the vicinity of a row of structural stitches located perpendicular to the crack propagation direction, stress transfer occurs from the DCB sub-laminates into the stitching yarns. In this situation the load, the crack opening displacement and the crack length rise until the yarn strength is reached. Yarn failure is correlated with an abrupt decline of the load followed by a regain of the load, crack propagation, stress transfer to and breakage of the subsequent yarn row.
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14.4
Simulation of mechanical behaviour of structurally stitched laminates
14.4.1 Unit cell model Based on a representative unit cell approach, a finite element model was developed to simulate the mechanical behaviour of structurally stitched NCF composite laminates and to predict in-plane elasticity and strength properties of this type of composite (Fig. 14.12; Heß et al., 2007; Heß and Himmel, 2007). Furthermore, the model allows one to predict the initiation of inter-fibre failure, total failure, the relocation of stresses caused by progressive IFF and the in-plane stress–strain behaviour of unstitched and structurally stitched laminates. In Fig. 14.13 and Fig. 14.14, the elasticity and strength prediction is outlined, while for more detailed information, including the mathematical formalisms, the reader is referred to Heß and Himmel (2010b). The parametric model is capable of generating complex unit cells considering the number, thickness and fibre orientation of the laminate layers, the cross-section and width of voids generated by the structural stitching, the stitch spacing, pitch length and stitching direction as well as the loading direction. Furthermore, local changes of the fibre volume fraction, as well as regions with undisturbed and disturbed fibre orientations within the laminate layers, are taken into account. The physically non-linear continuum mechanics-based failure analysis includes stress and strain analysis, fracture analysis and degradation analysis of structurally stitched laminates under in-plane tension, compression and shear loading. To estimate the stress exposure for fibre and inter-fibre failure, the
14.12 Unit cell model of a structurally stitched [A1-B-A2] laminate (configurations K 1 and 17; cf. Heß, Roth and Himmel, 2007).
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14.13 Simulation flowchart for the determination of elasticity constants of unstitched and structurally stitched non-crimp fabric laminates (in-plane loading).
14.14 Flowchart including strain and stress analysis, fracture analysis and degradation analysis for layer based prediction of strength properties of unstitched and structurally stitched non-crimp fabric laminates (Heß and Himmel, 2007).
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maximum stress criterion and Puck's action plane criterion for 3D stress states are used. Post-failure behaviour is modelled by partial stiffness degradation according to a Chiu model, which was modified to accommodate 3D stress states.
14.4.2 Prediction of elasticity coefficients As illustrated in Fig. 14.15, the reduction of the Young's modulus of tension-loaded [A1-B-A2]-HTA laminates due to structural stitching can be simulated. For seven out of 17 configurations (one unstitched and 16 stitched laminates) the predicted values (grey columns in Fig. 14.15) are within the scatter bands of the corresponding experimental data (white columns). The mean discrepancy of the calculated and experimental data, i. e. the arithmetic mean of absolute differences, was close to 5%. In general the simulation seems to overestimate the experiment (except of configurations K 6, K 7, K 8, K 12 and K 15). The maximum over- and underestimations of the modulus were 17% (K 14) and 11% (K 12 and K 6). The UC analyses of unstitched and stitched [A1-(B/2)S-A2]2-HTA laminates proved that the in-plane compressive modulus can be estimated with sufficient accuracy also (Fig. 14.16). The theoretically determined values of nine configurations are within the scatter bands of the corresponding experimental result with a mean overall deviation of 7%. In contrast to the prediction of the in-plane tension modulus, the unit cell analyses underestimate the compressive modulus for most of the configurations (except for unstitched laminate as well as
14.15 Comparison of experimentally and theoretically determined in-plane tensile modulus of unstitched and structurally stitched [A1-B-A2]-HTA laminates.
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14.16 Comparison of experimentally and theoretically determined in-plane compression modulus of unstitched and structurally stitched [A1-(B/2)S-A2]2-HTA laminates.
configurations K 3, K 13 and K 14). The maximum over- and underestimations were 4% (K 13) and 22% (K 5). Compared to the experimental data, the UC model allows prediction of the in-plane shear modulus of structurally unstitched and stitched [A1-(B/2)S-A2]HTS laminates to be done with reasonable accuracy (Fig. 14.17). The predicted shear moduli of both unstitched and nine structurally stitched configurations lie
14.17 Comparison of experimentally and theoretically determined in-plane shear modulus of unstitched and structurally stitched [A1(B/2)S-A2]-HTS laminates.
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within the scatter band of the corresponding test samples, with an average discrepancy of about 8% from the experimental results. Except for configuration K 1, the UC model generally overestimates the experimental results, with the maximum discrepancies of the predictions amounting to +16 (K 6) and −2% (K 1) relative to the experiment.
14.4.3 Prediction of in-plane strength components The comparison of numerical and experimental results shows that the reduction of the in-plane tensile strength of [A1-B-A2]-HTA laminates due to structural stitching can be simulated (Fig. 14.18). About half of the estimated strength values (the unstitched and eight stitched laminates) lie in the scatter band of the tensile experiments. In comparison to the mean values from the experiments, the theoretically determined strength data were lower (seven configurations), higher (six configurations) or in similar magnitude (three configurations and the unstitched laminate). The overall discrepancy of calculated and experimental data was about 8%.The maximum underestimation was in the order of about 18% (K 9), the highest overestimation was about 27% (K 14). The numerically determined compression strength of eight configurations (the unstitched and seven structurally stitched laminates) is within the experimental scatter bands of the [A1-(B/2)S-A2]2-HTA laminates with an averaged discrepancy of about 9% (Fig. 14.19). The UC model underestimates or overestimates the compression strength for seven and nine configurations, respectively. The maximum overestimation was about 12% (K 6), the maximum underestimation
14.18 Comparison of experimentally and theoretically determined in-plane tensile strength of unstitched and structurally stitched [A1-B-A2]-HTA laminates.
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14.19 Comparison of experimentally and theoretically determined in-plane compressive strength of unstitched and structurally stitched [A1-(B/2)S-A2]2-HTA laminates.
17% (K 1). In general, the compression strength predictions are too low for the 68 tex stitching yarn (except for K 11 and K 12) and too high for the 136 tex yarn (except for K 8). With regard to the in-plane shear strength, an overall difference of 6% between simulation and experimental results was found (Fig. 14.20). The UC model overestimates or underestimates the shear strength up to about 11% (K 2) and 14%
14.20 Comparison of experimentally and theoretically determined in-plane shear strength of unstitched and structurally stitched [A1-(B/2)S-A2]-HTS laminates.
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(K 15 and K 16), respectively. Ten of 17 calculated strength values (the unstitched and nine stitched laminates) lie within the scatter bands of the experiment.
14.5
Conclusions and future trends
The insertion of local through-thickness reinforcements into dry NCF preforms by structural stitching provides the possibility to improve the mechanical performance perpendicular to the plane of the composite laminate, namely their impact resistance and damage tolerance. On the other hand, the 3D reinforcement generates undulations and dislocations of the in-plane fibres associated with the formation of voids in the vicinity of the stitches after resin infusion with potentially adverse effects on the in-plane properties of the laminate, such as stiffness and strength. Experimental studies were carried out to investigate the effects of various stitching configurations on in-plane tension, compression and shear modulus and strength, as well as on the compression strength after impact and the GIR rate of structurally stitched carbon fibre NCF/epoxy laminates with 9-, 10- and 20-layer [+45/0/−45/0/900.5]S, [+45/0/−45/0/900.5]S and [+45/0/−45/(0/900.5)S/−45/0/+45]2 lay-ups. One major observation of the experiments was that structural stitching influences the geometric and mechanical properties of structurally stitched NCF laminates ambivalently. While the in-plane modulus and strength, as well as the GIR rate are mainly controlled by the diameter of the stitching thread, the stitch density influences the CAI strength (Table 14.3). Increasing the thread diameter and the stitch density leads to a decrease of the in-plane properties combined with an improvement of the CAI strength and the GIR rate. Nevertheless, a proper Table 14.3 Qualitative effect of structural stitching on in-plane and out-of-plane properties of non-crimp fabric laminates Property
Tensile modulus Tensile strength Compression modulus Compression strength Shear modulus Shear strength CAI strength Mode I energy release rate
Stitching direction
Increase of
x
y
Yarn diameter
Spacing
Pitch length
Stitch density
0 0 0 − 0 − 0
0 0 0 + 0 + 0
−− −− 0 −− − − 0
0 0 + 0 0 0 −
0 0 0 0 0 0 0
0 0 0 0 0 0 +
0
0
++
−
−
+
− negative −− strongly negative 0 negligible + positive ++ strongly positive
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selection of the stitching configurations allows achieving a useful compromise between both effects (Heß and Himmel, 2010b; Heß, 2009). A finite element based unit cell model was developed to predict in-plane stiffness and strength properties of unstitched and structurally stitched NCF composites. The UC model enables prediction of the initiation of inter-fibre failure, the relocation of stresses caused by progressive IFF and the in-plane stress–strain behaviour of this type of composite. The comparison of the predictions with the experimental results shows that the strength of structurally stitched NCF laminates under in-plane tension, compression or shear loading can be predicted with a reasonable accuracy. From the perspective of the studies carried out, future work on structurally stitched NCF composites should include the following issues: • • •
Out-of-plane stiffness and strength characterisation of structurally stitched NCF laminates. The effect of varying stitching yarn materials (C, Aramid), especially with respect to out-of-plane characteristics. extension of UC model to predict out-of-plane properties, such as elasticity, strength and CAI.
14.6
References
Aymerich A, Pani C and Priolo P (2007), ‘Effect of Stitching on the Low-Velocity Impact Response of [03/903]S Graphite/Epoxy Laminates’, Composites Part A, 38, 1174–1182. Beier U, Fischer F, Sandler J K W, Altstädt V, Weimer C and Buchs W (2007), ‘Mechanical Performance of Carbon Fibre-Reinforced Composites Based on Stitched Preforms’, Composites Part A, 38, 1655–1663. Byun J-H, Song S-W, Lee C-H, Um M-K and Hwang B-S (2005), ‘Impact properties of Laminated Composites Stitched with Z-Fibers’, in Proceedings of the 15th International Conference on Composite Materials ICCM–15, Durban, South Africa, June 27 – July 1, 2005 – CD-ROM. Carvelli V, Truong Chi T, Larosa M, Lomov S V, Poggi C, Ranz D and Verpoest I (2004), ‘Experimental and Numerical Determination of the Mechanical Properties of MultiAxial Multi-Ply Composites’, in Proceedings of the 11th European Conference on Composite Materials ECCM–11, Rhodes, Greece, May 31–June 3, 2004. Cox B N and Flanagan G (1997), Handbook of Analytical Methods for Textile Composites. Langley Research Center, Hampton, VA, NASA-CR–4750. Available from: http://ntrs. nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19970017583_19 97024417.pdf (accessed 7 April 2008). Dexter H B and Funk J G (1996), Impact Resistance and Interlaminar Fracture Toughness of Through-the-Thickness Reinforced Graphite/Epoxy, American Institute of Aeronautics and Astronautics, New York, USA, paper 86-CP1996, 700–709. Dransfield K A, Jain L K and Mai Y W (1998), ‘On the Effect of Stitching in CFRPs: I. Mode I Delamination Toughness’. Composites Science and Technology, 58, 815–827. Dransfield K, Bailie C and Mai Y-W (1994), ‘Improving the Delamination Resistance of CFRP by Stitching. A Review’, Composites Science and Technology, 50, 305–317.
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Ernst G, Vogler M, Hühne C and Rolfes R (2007), ‘Multiscale Simulation for Stiffnesses and Strengths of Textile Composites’, in Proceedings of the NAFEMS Seminar: Simulating Composite Materials and Structures, Bad Kissingen, Germany, November 6–7, 2007. González A, Graciani E and París (2008), ‘Prediction of In-Plane Stiffness Properties of Non-Crimp Fabric Laminates by Means of 3D Finite Element Analysis’, Composites Science and Technology, 68, 121–131. Gui L-J, Fan Z-J and Li Z-N (2005), ‘Study on Stiffness of Stitched Laminates’, Journal of Reinforced Plastics and Composites, 24, 1817–1836. Gunnion A J, Scott M L, Thomson R S and Hachenberg D (2002), ‘A Linear 3-D Finite Element Unit Cell Model for Fibre Waviness in Composite Materials’, in Proceedings of the 25th International Congress of the Aeronautical Sciences ICAS 2002, Toronto, Canada, September 18–23, 2002 – CD-ROM. Havar T, Middendorf P, Spenninger G, Göttinger M, Weimer C and Schmidt H (2008), ‘New Composite Load Introduction Rib for High Lift Devices’, in Proceedings SAMPE Europe Technical Conference, Augsburg, September 2008. Heß H and Himmel N (2007), ‘Finite Element Unit Cell Based Strength Prediction of Stitched CFRP Laminates’, in Proceedings of the 1st CEAS European Air and Space Conference, Berlin, Germany, September 10–13, 2007 – CD-ROM. Heß H, Roth Y C and Himmel N (2007), ‘Elastic Constants Estimation of Stitched NCF CFRP Laminates Based on a Finite Element Unit-Cell Model’, Composites Science and Technology, 67, 1081–1095. Heß H (2009), Experimentelle Charakterisierung und kontinuumsmechanische Simulation des Versagensverhaltens strukturell vernähter Faser-Kunststoff-Verbunde, Kaiserslautern, Institut für Verbundwerkstoffe GmbH, 2009 (IVW-Schriftenreihe Bd. 88). Kaiserslautern, Technische Universität, Dissertation. – ISBN 978–3–934930–84–1. Heß H and Himmel N (2010a), ‘Structurally Stitched NCF CFRP Laminates. Part 1: Experimental characterization of in-plane and out-of-plane properties’, Submitted to Composites Science and Technology for publication. Heß H and Himmel N (2010b), ‘Structurally Stitched NCF CFRP Laminates. Part 2: Finite Element Unit Cell Based Prediction of In-Plane Strength’, Submitted to Composites Science and Technology for publication. Iwahori Y, Horikawa S, Yamamoto M, Ishikawa T and Fukuda H (2004), ‘CFRP Strength Improvement by Carbon Fiber Stitching’, in Proceedings of the 49th International SAMPE Symposium, Long Beach, CA, USA, May 16–20, 2004 – CD-ROM. Karkkainen R L, Tzeng J T and Moy P (2007), ‘Finite Element Micromechanical Strength Modeling of Stitched 3D-Orthogonal Composites’, in Proceedings of the 52th International SAMPE Symposium, Baltimore, MD, USA, June 3–7, 2007 – CD-ROM. Liu D (1990), ‘Delamination Resistance in Stitched and Unstitched Composite Plates Subjected to Impact Loading’, Journal of Reinforced Plastics and Composites, 9, 59–69. Loendersloot R, Lomov SV, Akkerman R and Verpoest I (2006), ‘Carbon Composites Based on Multiaxial Multiply Stitched Preforms. Part 5: Geometry of Sheared Biaxial Fabrics’, Composites Part A, 37, 103–113. Lomov S V, Belov E B, Bischoff T, Ghosh S B, Truong Chi T and Verpoest I (2002), ‘Carbon Composites Based on Multiaxial Multiply Stitched Preforms. Part 1: Geometry of the Preform’, Composites Part A, 33, 1171–1183.
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Lomov S V, Dufort L, De Luca P and Verpoest I (2007), ‘Meso-Macro Integration of Modeling of Stiffness of Textile Composites’, in Proceedings of the 28th International SAMPE Europe Conference 2007, Paris, France, April 2–4, 2007 – CD-ROM. Lomov S V, Verpoest I, Bernal E, Boust F, Carvelli V, Delerue J-F, De Luca P, Dufort L, Hirosawa S, Huysmans G, Kondratiev S, Laine B, Mikolanda T, Nakai H, Poggi C, Roose D, Tumer F, Van den Broucke B, Verleye B and Zako M (2005), ‘Virtual Textile Composites Software WiseTex: Integration with Micro-Mechanical, Permeability and Structural Analysis’, in Proceedings of the 15th International Conference on Composite Materials ICCM–15, Durban, South Africa, June 27–July 1, 2005 – CD-ROM. Molnár P (2007), Stitching Technique Supported Preform Technology for Manufacturing Fiber Reinforced Polymer Composites, Kaiserslautern, Institut für Verbundwerkstoffe GmbH, 2007 (IVW-Schriftenreihe Bd. 74). Kaiserslautern, Technical University, Dissertation. – ISBN 978–3–934930–70–4. Mouritz A P, Baini C and Herszberg I (1999), ‘Mode I Interlaminar Fracture Toughness Properties of Advanced Textile Fibreglass Composites’, Composites Part A, 30, 859–870. Mouritz A P and Cox B N (2000), ‘A Mechanistic Approach to the Properties of Stitched Laminates’, Composites Part A, 31, 1–27. Mouritz A P and Jain L K (1999), ‘Further Validation of the Jain and Mai Models for Interlaminar Fracture of Stitched Composites’, Composites Science and Technology, 59, 1653–1662. Mouritz A P, Leong K H and Herszberg I (1997), ‘A Review of the Effect of Stitching on the In-Plane Mechanical Properties of Fibre-Reinforced Polymer Composites’, Composites Part A, 28A, 979–991. Oakeshott J L, Iannucci L and Robinson P (2007), ‘Development of a Representative Unit Cell Model for Bi-Axial NCF Composites’. Journal of Composite Materials, 41, 801–835. Ogale A (2007), Investigation of Sewn Preform Characteristic and Quality Aspects for the Manufacturing of Fiber Reinforced Polymer Composites, Kaiserslautern, Institut für Verbundwerkstoffe GmbH (IVW-Schriftenreihe Bd. 70). Kaiserslautern, Technical University, Dissertation. – ISBN 978–3–934930–66–7. Ogale A and Mitschang P (2004), ‘Tailoring of Textile Preforms for Fibre-Reinforced Polymer Composites’, Journal of Industrial Textiles, 34, 77–98. Ogo Y (1987), The Effect of Stitching on In-Plane and Interlaminar Properties of CarbonEpoxy Fabric Laminates. Delaware, University, Master, Thesis. Rong M Z, Zhang M Q, Liu Y, Zhang Z W, Yang G C and Zeng H M (2002), ‘Effect of Stitching on In-Plane and Interlaminar Properties of Sisal/Epoxy Laminates’, Journal of Composite Materials, 36, 1505–1524. Roth Y C (2005), Beitrag zur rechnerischen Abschätzung des Scheiben-Elastizitätsverhaltens in Dickenrichtung vernähter Faser-Kunststoff-Verbund-Laminate, Kaiserslautern, Institut für Verbundwerkstoffe GmbH (IVW-Schriftenreihe Bd. 55). Dissertation Technische Universität Kaiserslautern. – ISBN 3–934930–51–4. Roth Y C and Himmel N (2003), ‘Stitched Non-Crimp Fabric Laminates. From Manufacturing to In-plane Properties’, in Proceedings of the 14th International Conference on Composite Materials ICCM–11, San Diego, CA, USA, June 14–18, 2003 – CD-ROM. Schouten M (2007), ‘Integrated Tool for Simulation of Textile Composites: ITOOL. Proceedings of the 28th International SAMPE Europe Conference 2007, Paris, France, April 2–4, 2007 – CD-ROM.
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Scott M L, Thomson R S, Gunnion A J and Orfici A C (2007), ‘Simulation of Defects and Damage. Towards a Virtual Testing Laboratory or Composite Aerospace Structures’, in Proceedings CFK-Valley Stade Convention 2007, Stade, Germany, June 13–14, 2007 – CD-ROM. Sharma S K and Sankar B V (1995), Effects of Through-the-Thickness Stitching on Impact and Interlaminar Fracture Properties of Textile Graphite/Epoxy Laminates. Langley Research Center, Hampton, VA, NASA-CR–195042. Available from: http://ntrs.nasa. gov/archive/nasa/casi.ntrs.nasa. gov/19950019783_19951197 83.pdf (accessed 20 April 2008). Stüve J, Henkel F and Gries T (2006), ‘Complex Near-Net-Shape Reinforcement Structures. Textile Preforms for CFRP’, in Proceedings of the 27th International SAMPE Europe Conference 2006, Paris, France, March 27–29, 2006 – CD-ROM. Tan P, Tong L and Steven G P (1997), ‘Modeling for Predicting the Mechanical Properties of Textile Composites. A Review’, Composites Part A, 28A, 903–922. Tang X and Whitcomb J D (2003), ‘General Techniques for Exploiting Periodicity and Symmetries in Micromechanics Analysis of Textile Composites’, Journal of Composite Materials, 37, 1167–1189. Tong L, Mouritz A P and Bannister M K (2002), 3D Fibre Reinforced Polymer Composites. Amsterdam. Truong Chi T, Vettori M, Lomov S V and Verpoest I (2005), ‘Carbon Composites based on Multi-Axial Multi-Ply Stitched Preforms. Part 4: Mechanical Properties of Composites and Damage Observation’, Composites Part A, 36, 1207–1221. Truong Chi T, Vettori M, Ranz D, Lomov S V and Verpoest I (2004), ‘New Results on Mechanical Properties and Initial Damage of Multi-Axial Multi-Ply Carbon Fabrics Reinforced Epoxy’, in Proceedings of the 11th European Conference on Composite Materials ECCM–11, Mai 31–June 3 2004, Rhodes, Greece. Van den Broucke B, Drechsler K, Hanisch V, Hartung D, Ivanov D S, Koissin V E, Lomov S V, Middendorf P, Miravete A, Schouten M, Stüve J, Tolosana N, Verpoest I and Witzel V (2007a), ‘Multilevel Modeling of Mechanical Properties of Textile Composites: ITOOL Project’, in Proceedings of the 28th International SAMPE Europe Conference 2007, Paris, France, April 2–4, 2007 – CD-ROM. Van den Broucke B, De Verdiere M, Hertung D, Middendorf P, Pickett A, Angulo D R, Schouten M and Teßmer J (2007b), ‘Failure and Impact Modeling of Textile Composites: ITOOL Project’, in Proceedings of the 28th International SAMPE Europe Conference 2007, Paris, France, April 2–4, 2007 – CD-ROM. Velmurugan R and Solaimurugan S (2007), ‘Improvements in Mode I Interlaminar Fracture Toughness and In-Plane Mechanical Properties of Stitched Glass/ Polyester Composites’, Composites Science and Technology, 67, 61–69. Verpoest I and Lomov S V (2005), ‘Virtual Textile Composites Software WiseTex: Integration with Micro-Mechanical, Permeability and Structural Analysis’. Composites Science and Technology, 65, 2563–2574. Vettori M, Truong Chi T, Lomov S V and Verpoest I (2004), ‘Progressive Damage Characterization of Stitched, Bi-Axial, Multi-Ply Carbon Fabrics Composites’, in Proceedings of the 11th European Conference on Composite Materials ECCM–11, May 31–June 3 2004, Rhodes, Greece. Weimer C. Preform-Engineering (2003), Applied Technologies to Incorporate Part and Process Functions into Dry Textile Reinforcements, Composites Science and Technology, 63, 2089–2098.
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Weimer C, Miene A, van Laduyt E, Krajenski V, Köhnke B, Stadler F, Preussler M, Göttinger M, Bischoff T and Löhr F (2006), ‘Prozessbegleitende Schadensanalyse (PROSA). Ein wesentlicher Baustein für die kosteneffiziente Fertigung und Analyse von CFK-Strukturen’, in Proceedings Deutscher Luft- und Raumfahrtkongress 2006, Braunschweig, November 6–9, 2006. Wood M D K, Sun X, Tong L, Katzos A, Rispler A R and Mai Y W (2007), ‘The Effect of Stitch Distribution on Mode I Delamination Toughness of Stitched Laminated Composites. Experimental Results and FEA Simulation’, Composites Science and Technology, 67, 1058–1072.
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15 Predicting the effect of stitching on the mechanical properties and damage of non-crimp fabric composites: finite element analysis D.S. IVANOV, S.V. LOMOV and I. VERPOEST, Katholieke Universiteit Leuven, Belgium
Abstract: The stitching of unidirectional (UD) plies distorts and crimps the fibres and, inevitably, compromises the properties of the final part. Mesoanalysis, overviewed in this chapter, aims at prediction of the effect of stitching on mechanical performance, i.e stiffness, damage initiation threshold, stiffness degradation, non-elastic deformations, and strength. Various representative volumes and boundary conditions for modelling are discussed. The results are compared with the experiments described in Chapter 11. Key words: representative volume element, unit cell, boundary conditions, damage, failure mechanisms.
15.1
Introduction
The mechanics of non-crimp fabric (NCF) composite deformation are governed by its internal architecture: lay-ups, pattern of stitching loop, density of the distortions and their geometry. There is consistent experimental evidence that stitching affects the stiffness and all the aspects of failure behaviour: damage initiation, crack accumulation, strength, etc. (see Chapter 11). Hence, it is important to relate the internal structural geometry to the macro-mechanical response. This is the aim of the meso-scale analysis, i.e. the mechanical boundary value problem at the level of fibre bundles and distortions. In this problem, a representative volume element (RVE) is subjected to conditions that approximate loads that are transferred to the RVE boundaries by means of the surrounding media. Once the problem is solved, the average stresses over the volume characterise the effective stiffness response; local stresses and strains characterise the risk of a failure event. There are three primary issues that govern the efficiency of the two-scale analysis: 1. What is the minimum and sufficient size of the RVE? 2. How to imitate the load on the unit cell boundaries by boundary conditions (BC)? 3. How do the RVE and BC evolve along with the physical changes of the structure? 360 © Woodhead Publishing Limited, 2011
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There exist various models of internal composite geometry (see Fig. 15.1). The model peculiarities are governed by the target of analysis. Often the structure is approximated by a two-dimensional (2D) cross-section of the NCF through the laminate thickness. Drapier and Wisnom1,2 have used such a model for the
15.1 Various meso models of RVE for the biaxial 0/90 and multiaxial NCF composites: (a,b) Two configuration with different positions of 90° fibre bundles, adapted from Reference 3; (c,d) Models of NCF composite with two different waviness of 0°-yarns, adapted from Reference 1; (e,f) Geometrical models with various shapes of the UD fibre bundle and the fine mesh of the 90° ply, adapted from Reference 4; (g) Model of the ply with the rhombic distortion cause by the stitching, adapted from Reference 5; (h) 3D model for estimation of stiffness based on orientation averaging technique used in Reference 6. (Continued)
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(i) 3D model of multi-ply composite with rhombic distortions from Reference 7; (j) 3D model of the sheared laminate unit cell from References 8 and 9; (k) 3D model of NCF composite with channel-like distortions from Reference 10; (l,m) Superimposed mesh of 3D elements representing the plies and beam elements representing the stitching used in Reference 11 for two stitching configurations.
predictions of compressive strength and interlaminar shear behaviour with respect to the ply waviness. A similar 2D model has been proposed by Edgren et al.3 to study an effect of various crack dimensions on the stiffness of damaged composite. Zhao et al.4 used a 2D section of NCF for the modelling of progressive damage accumulation with the element discount method and studied the shapes of the fibre bundle cross-sections. Ernst et al.5 have introduced the RVE as a rhombic distortion in the unidirectional (UD) ply. At first, the ply properties are homogenised
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and the basic strengths of this ply are defined. Afterwards, these data feed the laminate meso model, where all the plies are considered homogenous. Hence, the model of the ply is 2D, but unlike in the previous models, the plane is aligned with the textile plane. Tessitore and Riccio6 have used the orientation averaging method to calculate effective stiffness of the NCF composite based on the spatial three-dimensional (3D) model. Hess et al.7 have proposed a 3D finite element (FE) model of structurally stitched composite as a set of rhombic distortions in the medium of fibre-reinforced ply. Lomov et al.8 have introduced a 3D model of the sheared and non-sheared composites for failure predictions. The model was based on measured distortion dimensions and accounted for the different geometries of adjacent plies. Michaluk et al.9 have used this model to study the energy release rate as the function of an intra-ply crack length. Gonzalez et al.10 have constructed a 3D model of NCF composite with straight channel-like resin-rich zones and local crimp of the fibre bundles. This model was used for the prediction of the effective stiffness and the plastic deformation accumulation. Tserpes and Labeas11 have proposed the superimposed mesh of 3D elements representing the UD plies and one-dimensional beam elements representing the stitching. The model was used to study failure process by means of the element discount method. Kurashiki et al.12 have implemented mesh superposition method to match the elaborated 3D geometrical model of the stitching yarn along with the robustly meshed model of the UD plies. They studied damage initiation, both in UD laminates and stitching yarns, and propagation by means of the element discount method. All the above-mentioned models use the assumption of continuous periodical prolongation of the RVE over the entire composite medium. In this chapter, the discussion of the RVE is followed by demonstration of various model applications, such as predictions of stiffness, failure initiation, non-linearity induced by plasticity and post-critical behaviour.
15.2
Representative volume element (RVE) of noncrimp fabric (NCF) composites
15.2.1 Definition of representative volume To perform the meso-scale analysis, an RVE of the composite medium has to be selected first. This volume has to be representative as an entity containing the sufficient information about the geometry of the entire composite (gRVE). The gRVE can be imagined as brick in a building. The complete structure may be composed of volumes identical to the gRVE. The operations allowable over this building block include parallel translation, rotations, and mirroring. The gRVE, which maps the structure by the parallel translation only, will be further called the unit cell. It must also be a mechanically representative volume (mRVE), i.e. a volume where the deformations and stress can be reproduced with accuracy against
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a reference full-scale solution. The choice of mRVE depends on how precisely we can imitate an interaction of the chosen volume with the dropped surrounding media. The interaction is simulated by means of BC. The most common assumption states that the considered volume is a unit cell embedded in the periodical/ symmetrical self-similar structure. This assumption leads to the known periodic BC restraining displacement on the opposite sides of the unit cell.13 The volume must also be a physically representative volume (pRVE). The selected volume has to remain representative through the physical transformation, such as plastic deformation or damage, occurring during the deformations. Obviously, if the unit cell is chosen to be an RVE, then it is supposed to remain periodical through the process of crack accumulation. As it will be shown below, it is not the case for the NCF composites. An example of NCF geometry Consider a typical example of the NCF-laminate geometry: biaxial multi-ply carbon reinforcement fabrics* (Fig. 15.1a). The textiles are produced based on the UD plies with an areal density of approximately 150 g/m2. The UD preforms are stitched by fine polyester yarns (7.6 tex) in a tricot pattern with an areal density of 6 g/m2, which contributes 2% of the total weight only. The stitching has no other function but to bind the plies together. If the pattern of the stitching yarns, i.e. locations where they pierce the plies, is aligned with the fibres, then long channellike openings are formed. If it is not co-directed with the ply orientations, the long triangular distortions/openings are induced.14 In general, the volume fraction and the geometry of the distortions in two stitched plies can be different. The reason for this is the non-symmetrical geometry of stitching loop on the front and back side of the laminate. To make the composite material balanced, the layers are often placed perpendicular to each other. Therefore, the stitching in the neighbouring layers runs in different directions. The relative position of the layers in laminate is not controlled. When impregnated, the distortions form the resin-rich zones (RRZs). Their volume fraction can exceed 10% and that makes a considerable difference in the composite deformation compared to the pure UD plies. Thus, the meso-RVE of this composite is composed on three sub-levels: ply, layer, laminate. To simplify the considerations, some geometrical features can be omitted in the first approximation. •
•
The fine polyester stitching yarns can be excluded for simplicity: their stiffness contribution is close to the one of the matrix. The effect of the stitching is accounted for by introducing matrix RRZs of proper dimensions at the stitching sites. Hence, the geometry of the stitching yarns will be not discussed further. The out-of-plane crimp of the plies is neglected; plies are assumed to be straight.
* The textile is provided by Saertex Wagener GmbH.
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15.2 In-plane geometry of the NCF and geometrical model of unit cells (produced in WiseTex, Ref.15).
The position of the RRZ within the layer is determined by the fibre orientation and the stitching pattern. The position of the layers within laminate is random: the layer orientation is controlled, but the relative shift of the RRZs belonging to neighbouring plies is not. Unit cells of ply, laminate, composite and damaged composite There are various options to choose a unit cell of the single ply. The orientation of the unit cell faces corresponds to vectors of periodicity along which the structure can be mapped/translated. One of the possibilities is to link the periodicity vectors to the stitching yarn pattern (Fig. 15.3), which results in a non-orthogonal geometry of the unit cell.
15.3 Non-matching skewed UCs of 2 plies and rectangular unit cell of the layer.
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If the stitching yarns are ignored, then the unit cell can be minimised, the boundaries are formed by connecting the closest stitching sites, which results in an orthogonal shape (Fig. 15.3). The unit cells shown above agree with the periodicity of the plies and the layer as whole. However, the unit cell of the layer is not necessarily the RVE of the laminate. Two factors violate periodicity in the thickness direction: 1. The layers in the balanced laminate have the opposite directions of stitching and therefore the unit cell shapes of adjacent layer do not match (Fig. 15.4); 2. The relative ply position is stochastic. Hence, even though the unit cell of the laminate is gRVE, strictly speaking it is impossible to choose the mRVE of the laminate operating with periodicity assumptions and periodical/symmetrical BC. Besides the discussed peculiarities of RVE in NCF composites, there are obstacles to keeping the volume representative during the process of the damage accumulation. Consider propagation of a single crack under in-plane loading, e.g., a uniaxial tensile test. Experiments show16 that the cracks in NCF composites often run along the fibres through the entire width of sample, crossing many unit cells in their paths. The propagation of the crack is almost instant in comparison with the timescales of quasi-static loading. Hence, we have to be able to model occurrence of an infinitely long crack crossing all the unit cells of the medium. The matrix intra-ply crack occurrence breaks the periodicity of the RVE of the layer. Figure 15.5 shows the consequent modelling of the crack propagation: in
15.4 Non-matching unit cells of two adjacent layers.
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15.5 Illustration of the non-periodical nature of the damaged composite.
the first stage the crack is unique: it runs throughout the unit cell ending at left and right boundaries. Periodicity leads to occurrence of the two new continuations of the crack, which also cross the cell leading to two new ‘endings’. The process continues until the cell is sliced to dust. In reality, the long tunnelling crack crosses different locations of the neighbouring unit cells. Hence, every unit cell starts exhibiting its own crack path relatively to the RRZs and the stitching repeat. That makes the cell not repetitive any more. It is important to note that the skewed non-orthogonal unit cells of the single ply would not expose this kind of problem if the unit cell boundaries were aligned with the fibre direction. In that case, the crack start and end points form a vector, which is parallel to the vector of periodical translation of the unit cell. Hence, the artificial multiplication of the crack density may not happen. However, this is only the case when stitching pattern agrees with the fibre orientation. It is possible to align the boundaries along the fibres only if the stitching steps in x and y directions gx, gy are linked to the fibre orientation α: [15.1] where N is an integer. Such a case is shown in Fig. 15.6 for N = 3. This factor helps to construct a skewed unit cell of the ply. However, even then the unit cell contours of one ply do not match those of the adjacent ply since the fibre directions (and RRZs) do not coincide. Thus, it can be concluded that an RVE does not exist in mechanical and physical senses along with the assumptions of periodicity in the thickness direction. Table 15.1 summarises these observations.
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15.6 Rectangular unit cell of the layer and non-matching skewed UCs of two plies where unit cell boundaries aligned with the fibre direction.
Table 15.1 Representative capability of the two considered unit cells with the classical periodic boundary conditions BC
gRVE
gRVE
gRVE
mRVE
pRVE
Ply
Layer
Laminate
Layer
Layer
PBC†
Yes
No
No
No
Yes
PBC
Yes
Yes
No
Yes
No
Level: Skewed unit cell of one ply* Rectangular unit cell of one layer
* With cell boundaries aligned with the fibres. † PBC– periodic BC.
Various options to handle non-periodicity The purpose of the modelling determines the choice of the RVE. There can be different ways to handle this problem, for instance: •
Neglecting the absence of the out-of plane periodicity. For elastic modelling and prediction of the damage initiation, a sufficiently good approximation is the unit cell of the layer with periodic BC both in-plane and out-of-plane: by that the structure is assumed to be periodical. It is equivalent to a modelling of one particular realisation of the unbalanced composite, in which all the stitching paths are aligned in one direction. It is often assumed that
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•
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the out-of-plane effects are of secondary importance in the in-plane strength and stiffness analysis. This approach exhibits a fundamental problem once the crack is explicitly/geometrically introduced. However, the stiffness, the failure initiation, and property degradation can be predicted with a good precision. Selecting a large RVE. In this case, an approach used for the randomised structures, such as UD composites at micro levels or biological tissues, can be used. An RVE can be chosen as a cluster of the unit cells. It is not possible to apply correct BC at the cluster boundaries since the unit cells of different layers do not match their shape. However, if the RVE is large enough, arbitrary BC can be applied on its boundaries. The only requirement for these conditions is to provide macro/applied strain over the volume of RVE. The obtained solution in the vicinity of the boundaries should be dropped out, but at a sufficient distance from the boundaries the solution can be assumed to be independent of the BC. This is a computationally costly option and the size of the region influenced by the boundaries should be studied in each particular case. Alternatively to the periodical assumptions of the unit cells’ interaction, we can try to imitate a more complex non-periodical interaction through adjusting BC. The purpose is to make a unit cell of only one layer the mRVE and have more freedom choosing the ply unit cell. This concept will be discussed further.
In the current study, two concepts of modelling are employed. For modelling stiffness, damage initiation, and extracting average post-critical behaviour of the ply, the rectangular unit cell with classical periodic BC is used. For modelling cracked laminate, the non-orthogonal unit cell of the ply is selected along with the new BC imitating interaction with the surrounding media.
15.3
Elastic analysis
15.3.1 FE model The FE model is based on the geometrical assumption mentioned before: stitching is manifested by the presence of RRZs. The distortions imposed by stitching cause local variation of orientation of the fibres. The orientation of the coordinate system is introduced as a linear function of the distance from the distortion boundaries. The ‘disturbed’ area width is of the same size as the local distortion width (Plate III, see colour section between pages 396 and 397). The local elastic properties of the fibrous bundles are calculated based on analytical formulas of Chamis,17 where the fibre volume fraction and the elastic properties of the fibres and matrix are the input parameters. The overall fibre volume fraction is equal in both the plies. However, since the RRZs have different dimensions, the local fibre volume fractions in the volumes of fibrous plies differ.
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Peculiarities of the model The meso model has several peculiarities, which can potentially cause severe numerical problems, such as sharp crack-like tips of the resin channels. This is an effect introduced by the homogenisation of fibrous ply properties, i.e. by the meso scale. In reality these sharp endings do not exist. Instead, there is a smooth flow of continuous fibres around RRZ. This is why there is no any definite boundary between the matrix of RRZ and the matrix of fibrous ply at the location where the two enveloping fibrous bundles meet. However, once we separate the two materials into pure matrix and UD, we inevitably end up with the sharp corner geometry. Another issue is the locations where three materials contact each other: two materials of fibrous plies and a matrix of RRZ. It is known18 that stress singularity at such a point may occur. In every particular loading case, these locations should be carefully checked. If the maximum stress or failure index reaches a maximum there, the next step is the mesh refining and a study of the mesh sensitivity issues. One of the robust engineering solutions to avoid the stress concentration can be to use only one element per ply thickness. By that, we ensure an automatic bilinear or quadratic approximation of the stress through the thickness, which is equivalent to the averaging of the stress field over the ply thickness. Hence, the three-point singularity is simply suppressed or locked. This approximation is close to reality: on the micro level a very local concentration effect would be smothered away and dispersed at the distance of several fibres from it.
15.7 Potential locations of an artificial stress concentration: (a) sharp ending of the resin-rich zones, (b) contact of three materials at one material point/node.
Damage initiation and stiffness response The stiffness constants and matrix intra-ply crack initiation are predicted reasonably well for both the sheared and non-sheared configurations (Table 15.2). The crack onset has been analysed using the Puck criterion19 (Fig. 15.8). The basic
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Table 15.2 Stiffness and damage features of the biaxial composites: experiment/FEA Shear angle (Ply angle) (°)
Fibre volume fraction (%)
Young modulus, GPa
Poisson's ratio
Strain at Strain at matrix failure (%) crack onset (%)
Stress at failure MPa
0 (±45) FEA 0 (±45) FEA 30 (±30) FEA 50 (±20) FEA 30 (±60) FEA 50 (±70) FEA
39.4
9.9 ± 0.4 9.9 6.6 ± 0.3 6.3 18.0 ± 1.6 20.7 44.4 ± 4.8 52.4 4.75 ± 0.25 4.7 5.53 ± 0.13 5.4
0.83 ± 0.04 0.83 0.69 ± 0.02 0.80 1.21 ± 0.08 1.44 1.18 ± 0.11 1.44 0.35 ± 0.05 0.304 0.18 ± 0.01 0.14
1.30 1.35 n/a 2.9 1.30 n/a 1.0 n/a 1.0 1.0 0.8 0.6
177.4 ± 3.9 n/a 121.7 ± 5.1 n/a 298.7 ± 20.9 329.3 495.6 ± 37.4 399.54 47.02 ± 0.43 n/a 40.42 ± 1.76 n/a
22.6 24.2 39.4 24.2 39.4
8.7 ± 0.3 n/a 4.5 ± 0.5 n/a 2.1 ± 0.2 2.02 1.3 ± 0.2 1.0 1.96 ± 0.70 n/a 0.80 ± 0.04 n/a
strengths of UD fibre bundle are extracted from the tests on composites with the same matrix and the fibres as used for production of the NCF ones, and fibre volume fraction of 42.9%.16 The strength along the fibre has been estimated by scaling the results of the UD composite tests to the fibre volume fraction of the composite. The results of the modelling are compared with the experimental measurements described in Chapter 11. Figure 15.8 shows that the stress concentration and, hence the failure index, in the ply matches the traces of the matrix rich zone in the neighbouring ply. The adjacent ply imposes additional out-of-plane forces on account of Poisson’s mismatch, as discussed above. The local width of the RRZ roughly correlates with
15.8 Stress exposure factor (SEF) in two plies of ±45° composite at applied deformation 1%.
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the magnitude of the stress and, consequently, with the risk of failure. The only stress concentration site that does not agree with the adjacent RRZ is in between the RRZ tips of the bottom ply. It happens because only a very narrow zone resists against the fibre rotation of the upper ply towards the load. For the rest of the ply, this rotation is compensated by the opposite fibre rotation of the upper ply itself. Consequently, the stress concentration and the failure risk are mainly defined by the width of the RRZs over the UD fibre bundle of the neighbouring ply. Hence, intra-bundle cracking in the balanced and unbalanced composites will be likely to initiate at the same applied load. Accounting for the real lay-up may benefit in more precise description of local stress distribution and stress variation from one unit cell to another. For the ±20°, ±30° composites the strain at the crack onset is estimated beyond the final failure. As opposed to predictions, experiments show matrix cracking prior to fibre rupture. However, unlike in the other laminates, these rare cracks appear at the edges only. The multi-scale concept does not describe the edge effects, since it employs periodic BC, i.e. infinite periodicity assumption, in plane of textile. According to common observations, in some cases the stress concentration in heterogeneous materials can be higher than in the centre zone or even singular. Hence, the FE analysis, aimed at description of the material but not macro-level samples, does not contradict to the experiments. The modelling predicts a premature fibre failure for ±30° and ±20° NCF composites – Table 15.2. This discrepancy is apparently attributed to the input values of the tensile strength of UD fibre bundle and non-accounted stiffening of the carbon fibre during loading.
15.4
Damage accumulation in NCF composites
15.4.1 Experimental observations The NCF composites exhibit high contrast of the properties in the fibre and non-fibre direction. The tests in non-fibre directions are particularly interesting since they tell more about the architecture, and hence can be more useful for the model validation. Chapter 11 presents the results for the sheared and nonsheared biaxial NCF composites, where the carbon fibres are oriented at the angles ±θ ° to the loading direction. A brief selection of these results will be also given in this paragraph to emphasise some aspects of the composite deformation. The off-fibre tests can be grouped in three categories based on mechanical behaviour of the specimens: (1) θ = ±30°, ±20°, (2) θ = ±60°, ±70°, (3) θ = ±45°. The composites deform non-linearly in all three cases. However, the major source of non-linearity is attributed to completely different mechanisms
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of deformation: plasticity and matrix micro failure in the first case, meso cracking in the second, and the combination of all the damage modes in the third. The ±45° specimens exhibit the highest non-linearity with a large deformation at failure, exceeding the tensile strain to failure of both the components: carbon fibres and epoxy matrix (Fig. 15.9). Tests on UD laminate ±45° are known for the high ratio of the local ply shear stress to the normal stress. When the lay-up changes, normal stresses in transverse (θ → ±90°) or longitudinal (θ → ±0°) directions become dominant. In tests on NCF composites, it is observed that the non-linearity and the strain at failure decrease when the shear angle (and hence the lay-up angle ±θ) increases – the material exhibits a brittle response. It is known that epoxy-based UD composites deform almost linearly up to failure if loaded in fibre or cross-fibre directions. Hence, the source of non-linearity is the shear response of the UD plies. These observations also agree with the known behaviour of the epoxy, which exhibits a moderate strain to failure in pure tensile tests of 4%, extreme brittleness in triaxial stress state of 0.6% (occurring in the UD composite in transverse tension), and extreme toughness in pure shear of up to 20% and higher.20,21 The tensile curves of these composites are smooth up to the final failure. The mechanism of the failure depends on the lay-up. In the non-sheared configurations extensive transverse cracking is accompanied by delaminations. It further leads to
15.9 Tensile tests of NCF composites in longitudinal direction (Vf – fibre volume fraction, ± 20°, ±30°, ±45° – the ply angles).
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fibre pull-out and separation of the specimen. The failure of the sheared composites is on account of the fibre rupture. In the second group of specimens, the composites deform linearly up to the strain level where extensive cracking starts – Fig.15.10a,b. From the point 1 (Fig.15.10c,d) the composites drastically change their behaviour. ±60° specimens exhibit a plateau, where the stress remains constant when the deformation is increasing (Fig.15.10a,c) (stage 1–2). At this stage, the tensile curves become less stable (more ‘jumpy’) and the scatter of the experiments increases. This plateau nearly disappears for the ±70° specimens (Fig.15.10b,d) (stage 1–2). Stage 1–2 is followed by a sudden drop of the instant modulus (stage 2–3). Hereafter, the composite exhibits a low residual resistance (stage 3–4). This plateau resembles the diagram of an ideal plasticity; however, the origin of this process is completely different. It relates to the matrix intra-ply cracking. The presence of the plateau in ±60° specimens and the absence of the plateau in ±70° specimens indicates that in one case the material is capable of supporting deformation of the adjacent cracked ply and in the other case the cracked plies are too weak, for there is a higher angle between the fibres and the loading direction.
15.10 Tensile diagrams of sheared non-crimp fabric composites (a) ±60°, (b) ±70° (x-axis corresponds to the loading direction in 0°, the curves for 4 representative samples are shown) and corresponding sketches of these diagrams: 0–1 linear stage of the deformation, 1–2 unstable post-critical stage, 2–3 sudden drop of the instant modulus, 3–4 low residual resistance of the broken material.
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It can be assumed, that at the point 2 (Fig.15.10c,d) crack density reaches a saturation level and the delamination starts, which makes the mutual support of the cracked ply impossible and, hence, the resistance capacity of the material drops down. The residual stiffness of the broken composites can be addressed to the polyester stitching and sparse and curved stabilising glass yarns. The tensile diagrams for the ±45° lay-up for high and low fibre volume fraction are very different. The increase of fibre volume fraction pronouncedly change the composite ability to resist the load: it slightly increases the strength but doubles the strain at failure.
15.4.2 Boundary conditions for a damaged composite The idea discussed further is based on the concept proposed for textile laminate with crimped yarns,22 i.e. woven or braided. It has been found that the stress distribution in a textile with periodically stacked laminate depends on the number of plies in the laminate and on the ply position: it is different at the surface or inside the composite medium even for the case of in-plane loading. This means that the unit cell of one ply, being gRVE, is not an mRVE if the classical periodic or symmetric BC are used. It has been proposed to construct BC on a unit cell of a single ply that can accurately reproduce interaction with the other unit cells and hence, the stress distribution at different locations in the laminate. This was performed by recording displacement from the boundary value problem with periodically constrained boundaries, scaling the solution to satisfy the global equilibrium conditions, and then applying the obtained function as the BC separately for the inner and outer plies. Further, we show the applicability of a similar methodology to the case of the NCF laminate. In order to verify the discussed approach for the case of NCF composites, consider the following example. The lower and upper plies of the layer unit cell are separated. The solution with the symmetric BC on the laminate unit cell is interpreted as a reference solution. The purpose of the exercise is to construct the BC on unit cells of plies, which would reproduce stress-strain state in the laminate unit cell. If the test problem proves the new BC to be valid then analogical concept can be used to construct BC for a laminate. The constructed BC must represent the mechanics of the composite deformation. Under stress perpendicular to the fibre direction, the matrix tends to extend or contract along the fibres. The Poisson’s ratio of the epoxy (0.4) is much higher than the Poisson’s ratio of the UD ply and close to the one of the absolutely incompressible isotropic material (0.5). Therefore, when applying e.g. in-plane compression, the matrix is pushed in the out-of-plane/thickness direction. Correspondingly, under the transverse tension the matrix tends to contract more strongly than the UD ply. Hence, for the NCF composites the deformed shape is a bubble (compression) or a valley (tension) over the RRZ. This mechanism is especially pronounced for the composites with triangular channels because the low Poisson’s of UD ply in fibre direction restrict the deformation of the epoxy in the plane of the textile (Plate IV).
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The out-of-plane motion due to the mismatch of Poisson’s ratios has two important consequences. 1. Constraints of the adjacent ply restrict this out-of-plane motion, creating the state of hydrostatic tension or compression in the RRZ. 2. Concentration of the transverse stress in the adjacent fibrous ply.
Test problem The targeted BC are supposed to match a shape of the ply exhibited in the out-ofplane displacement of the RRZs. It is proposed to record the deformed shapes of the plies separately and then combine them to get the searched profile. Consider the mode of uniaxial deformation 〈εxx〉 in a symmetrically stacked laminate (Fig. 15.11). The reference solution is obtained on the entire two-ply unit cell with the symmetry BC on the outer surfaces and translation periodic BC on the side boundaries. The ply solution is searched in several steps. On the first stage, the upper and bottom plies are considered separately and two independent boundary value problems are solved. The solution is constructed by applying symmetric BC on the outer surfaces and unconstrained free traction on the inner contacting surface. Hence, the ply is allowed to deform freely in the thickness direction. The displacements on the inner interface boundary of the upper ply uU,t=0 and bottom ply uL,t=0 differ and depend on the ply architecture. The free boundary provides minimum energy of deformation, as it is constrained the least in comparison with any other BC, providing the same macro deformation and in-plane periodicity. It is assumed that the deformed shape of the ply in the laminate is as close as possible to this minimal energy state realised in this displacement field. However, there is another adjacent ply, which has its own nonmatching deformed shape. Hence, the actual deformed shape of the interface u I
15.11 Scheme of the ply deformation considered apart: symmetric BC.
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15.12 Density of the local stress across the fibres and distribution of this stress for reference solution on the laminate unit cell and for the solution with composed BC on ply unit cell. The applied strain is: 〈εyy〉 = 0.1%, 〈εij = 0 (ij ≠ yy).
the functions is composed from the solutions uU,t=0 and ply uL,t=0 : uI = uI (uU,t=0, uL,t=0). The displacement field in between the plies is estimated as an arithmetic average of the eigen shapes of the individual plies (Fig. 15.11). [15.2] Eventually, the resultant function is applied as BC for both the upper and lower plies. The obtained stress distribution is compared to the reference solution in Fig. 15.12. The resultant stress distribution is very close to the reference one. A reasonable coincidence is found not only for the maximum and minimum values, but also for the stress density and stress distribution within the unit cell. Hence, the concept of averaging BC can be used for modelling of the nonperiodic balanced architectures. The displacement profiles obtained on one laminate unit cell with free out-of-plane displacement can be rotated, randomly shifted and applied as BC for the considered unit cell as shown in Fig. 15.13. Modelling cracks on the meso scale In this sub-section, the potential for modelling of the cracks in the NCF composites is shown. The purpose is to study the effect of intra-ply cracks and inter-ply delaminations on the stiffness degradation of the laminate. The analysis is based
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15.13 Constructing BC for the balanced laminate: the deformed shape of the neighbouring ply imposes BC for the considered unit cell, sx and sy are the random shifts.
on the non-orthogonal unit cell of ply with boundaries aligned along the fibres. As it has been discussed before, in general it is not possible to choose a unit cell of the damaged material, since the repetitive architecture induced by regular stitching is violated by the crack pattern. Therefore, the exact relative position of the RRZ should be neglected for this case. In fact, the real structure is substituted with an equivalent one, which has the same RRZ dimensions, spacing, and volume fraction, but different pattern of RRZ (Fig. 15.14). As it can be suggested from the previous analysis, the RRZ width has the primary effect on the stress concentration; the RRZ volume fraction has the primary effect on the stiffness of the composite. For the sake of convenience, the crack is modelled along the unit cell boundaries by means of releasing the BC. This trick is equivalent to introduction of a periodic
15.14 The considered unit cell and the contours of the unit cells in the adjacent ply of the sheared NCF (±30°).
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intra-ply crack pattern. The periodicity of the cracks corresponds to the periodicity of the RRZ. Likewise, the release of the outer surfaces is equivalent to the introduction of inter-layer delaminations. The unit cells of the adjacent plies are assumed to be the same, and hence, the RRZ dimensions calculated on top and bottom side of RRZ are simply averaged. To make such an analysis possible, the BC imitating other plies have to be constructed. The shape of the other unit cell in the other plies does not match the one of the considered unit cell (Figure 15.14). The intersection of the boundaries of these two plies subdivides the unit cells into fragments. Within each of them there is mirror symmetry relative to the vertical axis connecting the upper and bottom corners of the fragment. The unit cell of the adjacent ply can be mapped by 180° rotation of the considered unit cell around this axis. This symmetry gives a known relation between the displacements at the symmetrically correspondent points: [15.3] where ũ is the periodical constituent of the displacement vector, x is the horizontal axis, y is the vertical axis of rotation, z is the out-of-plane axis and 1 and 2 are the correspondent points. There can be different options for implementations of these ply-interaction conditions. (1) By means of constraint equations at the correspondent points. This option demands creation of a specific symmetric pattern of nodes on the unit cell surfaces for each of the fragments. On the other hand, the nodes on the opposite edges have to be also arranged in periodical order for setting periodic BC. These two mesh requirements can run into conflict. Hence, these constraints are hard for implementation and the second option for ply interaction modelling can be considered. (2) By means of constructing the displacement field on the outer surfaces, as suggested in the previous paragraph. In the latter case, the modelling is performed in several steps. It is needed so solve a sequence of boundary value problems: (a) to calculate displacement profile for the unit cell with the free unconstrained outer surfaces, (b) to record the obtained displacements and to extract the linear part of them, (c) to rotate the obtained displacement field around the symmetry axis for each of the fragments, (d) to average the rotated and the original displacements, i.e. to get the resultant displacement profiles at the interface of the interacting plies, and (e) to add linear constitutive to the obtained displacement fields and apply it as BC on the outer surfaces. The calculations are performed for the three configurations: (1) intact material, (2) material with periodical pattern of intra-ply cracks, (3) material with interlayer delaminations at one of the two outer faces. The results are summarised in Table 15.3. As expected, the drop of the secant moduli after the damage occurrence is more pronounced for the ±20° configuration. The failure index does not drop too much after occurrence of damage, which means that the next failure event can be expected soon after the previous one. This
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Table 15.3 The drop of secant moduli and failure index after occurrence of intra-ply cracks and inter-layer delaminations Shear angle (Ply angle)(°)
30 (±30) 50 (±20)
Crack
Delamination
Crack
Esecant/Eintact (%)
Esecant/Eintact (%)
Failure index/ failure index (intact) (%)
71 61
47 33
91 88
15.15 Distribution of transverse stress in the intact and cracked composite.
prediction agrees with the saw-like tensile diagram, where we can observe a cascade of events, separated by small strain increments. An instant modulus of the teeth on this saw decreases with growth of the strain. In the NCF composites, the origin of the strain concentration is the mismatch of Poisson’s ratios of RRZ and the adjacent UD ply. Unlike in UD laminated composites, the crack does not fully releases the stress concentration in its vicinity (Fig. 15.15). The stress concentration zones form long traces at an angle to the unit cell/crack boundary. The cracks lead to unloading of a very small fraction of these zones in vicinity of the boundaries. The model with the explicitly introduced cracks does not predict the abrupt failure of the ±20° samples and long cracking stage at constant stress level of ±30° samples. To simulate that, a gradual evolution of the crack density has to be included in the model. Nevertheless, the presented modelling gives a clear idea about the evolution of internal stress distribution and property degradation, which can be expected during the damage accumulation process. Post-critical behaviour of elementary ply: inverse numerical experimental problem Meso modelling requires assigning the material behaviour to the elementary UD fibre bundle. This data can be extracted from the tests on UD composites. However, these tests can characterise the material only up to the moment of the
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cracking onset, when the sample integrity fails. On the other hand, laminated composite can survive long after cracking initiation due to the support of the neighbouring plies. The stiffness at the post-critical stage is governed by the internal architecture and, generally, may no longer be considered as the material behaviour. Hence, an inverse experimental-numerical procedure can be useful to reconstruct the local post-critical behaviour of the plies. Conventionally, the UD ±45° laminates serve to extract the shear diagrams of UD ply as far as the local stress state in this test is shear dominated. In order to use NCF composite for this purpose, several factors need to be accounted for: (1) there are the resin-rich zones in the plies of the NCF composites – up to 12% of volume fraction for the composites considered here, (2) geometry of these zones is different for the upper and bottom plies; (3) as a result, fibre volume fractions of the upper and bottom ply are different. Additionally, there is a need to account for the important mechanical factors: (1) reorientation of the fibres (so called ‘scissoring’), which is widely recognised to be important23,24 and (2) evolution of the Poisson coefficient. Therefore, the analytical formulae cannot be used in these tests, especially at the post-critical stage of deformation. Instead, the shear degradation of the UD plies is adjusted by means of an FE modelling so as to fit the experimental diagram, accounting for geometry of the composite, the fibre reorientation, evolution of the elastic constants, transverse and shear degradation of plies, and failure initiation. For applying the inverse procedure, it is necessary to construct a degradation scheme, which expresses an effect of damage on all the stiffness components. This scheme establishes the link between the degradation of Young’s and shear moduli. For this application, the scheme of Murakami25,26 has been chosen. The choice of this scheme does not significantly influence the final result of the modelling since the transverse moduli of the UD ply hardly affect the overall stiffness in this test. The inverse procedure is founded on the assumption that the degradation of the shear modulus is the main source of the non-linearity. It can be summarised as the sequence of steps: 1. Calculate the boundary value problem imitating the tensile test and find the response of the medium. 2. Compare the stress response provided by the model σ FE y and corresponding value σ Exp at the same applied strain 〈 ε 〉. Find the ratio of these values y y [15.4] 3. Scale down the current shear modulus Gi12 by the global experimental+1 numerical stress ratio R: Gi12 = RGi12. 4. Recalculate the boundary value problem at the same applied strain: analyse if the new value of σ xFE is sufficiently close to the searched value.
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5. If the ‘proper’ value of Gi12 is found, define whether the stage of the meso cracking has started based on local stress distribution. If yes, calculate the coupled degradation factors for the other elastic moduli. 6. Reorient the fibres according to the local shear angle. Following Zinoviev27 it is done as following: φ i = φ i−1 − Δγ i/2, where φ i is the fibre orientation on the i-th step, and Δγ i is the increment of the shear angle. The FE model accounts for a local fibre deviation from the general orientation caused by the stitching. The procedure is organised such that elements having the same fibre orientation maintain the common orientation after the coordinate system is updated, i.e. rotation of the fibre direction is assigned to the entire group of elements based on average shear angle increment in it. 7. Calculate average stress and strain intensity in the matrix-rich zones. Scale down the matrix Young’s modulus to satisfy the stress–strain intensity diagram. In the inverse procedure, the degradation of the damage parameters does not play the crucial role, since major contribution to the global stiffness of the composite comes from the local shear stress and tensile stress along the fibres. 8. Calculate the evolved Poisson’s ratio with regards to the new Young’s modulus and the constant bulk modulus. 9. Recalculate the global stiffness of the composite and proceed to the next load increment – Step 1. The resultant diagrams are presented in Figure 15.16. The UD plies exhibit a perfectly plastic behaviour, which is in agreement with the behaviour of the epoxy matrix in shear.
15.16 Shear diagrams ‘extracted’ from two tensile tests (with different total fibre volume fraction) of biaxial ±45° NCF composites via inverse FE procedure; Vf denotes fibre volume fractions (dots – numerical values, solid lines – polynomial approximation). Vf = 0.273, 0.244 relates to the upper and bottom plies in experiment with total Vf = 0.22, Vf = 0.475, 0.425 relates to another experiment with total Vf = 0.39.
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The extracted non-linear shear diagram is applied as the input data for the modelling of the composite plastic response. For simplicity, the unit cell is treated as a three-component material: matrix and two fibrous plies. The stiffness evolves simultaneously for all the elements of each of the components. The change of the state is governed by the stress averaged over the correspondent volume. The obtained diagrams are normalised with respect to the initial shear modulus of the UD fibre bundle. Comparison of secant moduli reduction is given in Fig. 15.17. Non-linearity of the ±20°, ±30° composite is entirely associated with non-linearity of the shear diagram. The transverse degradation is not ‘switched on’ owing to the earlier fibre failure. Obviously, the shear-induced non-linearity taken as material property describes the experimental data quite well.
15.17 Normalised secant moduli Esec in the tensile tests of NCF composites. Figure represents only the non-linearity associated with plasticity but not the final failure. The prediction of strength can be found in Table 15.2
15.5
Conclusions
The meso-scale modelling shows capacity to predict important features of the composite deformation and failure: stiffness, damage initiation, non-linearity induced by plastic deformations and cracking, stiffness degradation, strength and strain at failure, failure mode, etc. All this creates a solid basis for understanding the material behaviour and modelling at a higher (macro) level of parts with complex shapes. Despite seemingly simple geometry, the NCF composite exhibits a fundamental problem and paradoxes of meso-scale analysis. It has been shown that damage breaks the periodicity of the architecture. That has to be reflected in the BC. In this study a simple and yet efficient concept of constructing BC has been proposed.
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15.6
References
1. Drapier S., Wisnom M.R. Finite-element investigation of the compressive strength of non-crimp-fabric based composites, Compos Sci Technol 1999; 59: 1287–97. 2. Drapier S., Wisnom M.R. A finite-element investigation of the interlaminar shear behaviour of non-crimp-fabric-based composites, Compos Sci Technol 1999; 59: 2351–62. 3. Edgren F., Mattsson D., Asp L.E., Varna J. Formation of damage and its effects on noncrimp fabric reinforced composites loaded in tension, Compos Sci Technol 2004; 64: 675–692. 4. Zhao L.G., Warrier N.A., Long A.C. Finite element modelling of damage propagation in non-crimp fabric reinforced composites, Compos Sci Technol 2006; 66: 36–50. 5. Ernst G., Vogler M., Hühne Ch., Rolfes R. Multiscale progressive failure analysis of textile composites, Compos Sci Technol 2010; 70: 61–72. 6. Tessitore N., Riccio A. A novel FEM model for biaxial non-crimp fabric composite materials under tension, Computers and Structures 2006; 84: 1200–1207. 7. Hess H., Roth Y.C., Himmel N. Elastic constants estimation of stitched NCF CFRP laminates based on a finite element unit-cell model, Compos Sci Technol 2007; 67: 1081–1095. 8. Truong T.C., Ivanov D.S., Klimshin D.V., Lomov S.V., Verpoest I. Carbon composites based on multi-axial multi-ply stitched preforms. Part 7: Mechanical properties and damage observations in composites with sheared reinforcement, Composites: Part A 2008; 39: 1380–1393. 9. Mikhaluk D.S., Truong T.C., Borovkov A.I., Lomov S.V., Verpoest I. Experimental observations and finite element modelling of damage initiation and evolution in carbon/ epoxy non-crimp fabric composites, Engineering Fracture Mechanics, 2008; 75(9): 2751–2766. 10. Gonzalez A., Graciani E., Paris F. Prediction of in-plane stiffness properties of noncrimp fabric laminates by means of 3D finite element analysis, Compos Sci Technol 2008; 68: 121–131. 11. Tserpes K.I., Labeas G.N. Mesomechanical analysis of non-crimp fabric composite structural parts, Composite Structures 2009; 87: 358–369. 12. Kurashiki T., Hamada K., Honda S., Zako M., Lomov S.V., Verpoest I., Mechanical Behaviors of Non-Crimp Fabric Composites Based on Multi-scale Analysis, Proceedings of International Conference on Composite Materials ICCM–17 27–31 July 2009, Edinburgh, UK 13. Lomov S.V., Ivanov D.S., Verpoest I., Zako M., Kurashiki T., Nakai H., Hirosawa S. Meso-FE modelling of textile composites: Road map, data flow and algorithms, Compos Sci Technol, 2007; 67(9): 1870–1891. 14. Loendersloot R., Lomov S.V., Akkerman R., Verpoest I. Carbon composites based on multiaxial multiply stitched preforms. Part 5: Geometry of sheared biaxial fabrics. Composites: Part A, 2006; 37: 103–113. 15. Verpoest I., Lomov S.V. Virtual textile composites software WiseTex: integration with micro-mechanical, permeability and structural analysis, Compos Sci Technol 2005; 65(15–16): 2563–2574. 16. Truong Chi T., Vettori M., Lomov S.V., Verpoest, I. Carbon composites based on multiaxial multiply stitched preforms. Part 4: Mechanical properties of composites and damage observation, Composites: Part A, 2005; 36: 1207–1221.
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17. Chamis C.C. Mechanics of composite materials: Past, present and future. J Compos Technol and Research, 1989; 11(1): 3–14. 18. Sihn S., Iarve E.V., Roy A.K. Three-dimensional analysis of textile composites: Part I: Numerical analysis, Int J of Solids and Structures, 2004; 41: 1377–1393. 19. Puck A., Kopp J., Knops M. Guidelines for determination of the parameters in Puck’s action plane strength criterion, Compos Sci and Technol, 2002; 62: 371–378. 20. Fiedler B., Hojo M., Ochiai S., Schulte K., Ando M. Failure behavior of an epoxy matrix under different kinds of static loading, Compos Sci Technol, 2001; 61(11): 1615–1624. 21. Asp L., Berglund L., Gudmundson A. Effects of a Composite-like Stress State on the Fracture of Epoxies, Compos Sci Technol, 53(1): 27–37, 1995. 22. Ivanov D., Lomov S.V., Verpoest I. Stress distribution in outer and inner plies of textile laminates and novel boundary conditions for unit cell analysis, Composite A, 2010; 41(4): 571–580. 23. Greve L., Pickett A.K. Modelling damage and failure in carbon/epoxy non-crimp fabric composites including effects of fabric pre-shear, Composites: Part A, 2006; 37: 1983–2001. 24. Sapozhnikov S.B., Prediction of deformation and biaxial strength of fibre reinforced laminates for wwfe by using micromechanics, Proceedings of 13th European. conf. on Composite Materials, Stockholm, Sweden, June 2–5, 2008, CD-edition. 25. Murakami, S. Mechanical modeling of material damage. J Applied Mech 1988; 55:28. 26. Zako M., Uetsuji Y., Kurashiki T., Finite element analysis of damaged woven fabric composite materials, Compos Sci Technol, 2003; 63 (3–4): 507–516. 27. Zinoviev P.A., Grigoriev S.V., Lebedeva O.V., Tairova L.P. The strength of multilayered composites under a plane-stress state, Compos Sci and Technol 1998; 58: 1209–1223.
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Plate II The WiseTex model of a biaxial and quadriaxial non-crimp fabric. The geometrical parameters are found in Table 1. For both models, the first order discretisation is shown, with some streamlines that demonstrate the solution of a flow simulation (Chapter 10).
Plate III (a) Finite element (FE) models of non-crimp fabric composites; (b) A typical FE mesh of a non-crimp fabric composite with the distortions induced by the stitching (Chapter 15).
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Plate IV Out-of plane displacement of non-crimp fabric composite with periodicity in the thickness direction. Matrix of the upper ply sinks due to the mismatch of the Poisson ratios with UD fibrous ply, and so does the matrix of the upper layer, which sucks up the upper unidirectional ply underneath and forces it to extend. (Chapter 15).
Plate V Shear angle distribution in the pitch horn using (a) conventional draping starting from the apex and (b) a bias curve, (courtesy of Eurocopter) (Chapter 16).
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16 Modelling drape, stress and impact behaviour of non-crimp fabric composites A. K. PICKETT, University of Stuttgart, Germany
Abstract: Each layer of non-crimp fabric (NCF) in a blanket has fibres that are essentially straight with a distinct orientation and uniform thickness. Consequently, for analysis purposes, each layer may be treated as an individual ply in classical laminate theory (Jones and Pickett, 2005). Similarly, it is reasonable to apply the same assumptions to a finite element (FE) analysis and most work to date has treated each layer as a quasi-unidirectional ply. However, some provisos need to be considered. First, bi-axial NCFs are commonly used for complex doubly curved geometries and can be required to undergo considerable drape deformation. This draping will deform fabric architecture changing properties such as infusion permeability and mechanical stiffness. Characterisation of mechanical properties for deformed NCF is a topic of current research; see for example Crooktson, Long and Jones (2002) for elastic properties, Greve and Pickett (2006) for failure, and Chapter 11 for mesoscopic analysis of deformed NCF. FE analysis of NCF covers a wide range of applications including draping, resin infusion, residual stress, static stress and impact analysis, amongst others. A brief review of relevant FE methods is first given, followed by their application to drape, infusion and stress/impact analysis, with some examples. Key words: simulation, non-crimp fabrics, draping, infusion, analysis, impact.
16.1
Finite element (FE) methods for drape, stress and impact analysis
The two main classes of finite element (FE) method are ‘implicit’ and ‘explicit’ analysis (Cook, Malkus and Plesha, 1989). Generally, implicit methods are widely used for problems such as stress analysis, which may be linear or nonlinear with geometric and/or material nonlinearity; whereas explicit methods are preferred for dynamic, highly nonlinear contact dominated problems. Both methods use conventional FEs to discretise the structure, but differ in the solution algorithm used. The implicit method assembles individual element stiffness matrices [ke] to obtain the structure stiffness matrix [K] which, after inversion, yields structure nodal displacements {u} for a given applied nodal loading {P}, [16.1] From nodal displacements {u} element strains are computed; the element stresses follow from elements strains and the material constitutive law. Problems involving 386 © Woodhead Publishing Limited, 2011
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contact, buckling and material nonlinearity yield a nonlinear stiffness matrix [K] which requires a CPU intensive iterative ‘Newton–Raphson’ type solution. The alternative explicit algorithm uses a different solution strategy and poses the problem as a dynamic one, using the linearised equations of motion, [16.2] where {u}n, {u˙}n and {ü}n are vectors of nodal displacement, velocity and acceleration; n is the cycle number at time position Tn (after nΔT timesteps). The mass, damping and stiffness matrices are [M], [C] and [K], respectively, and {Pext}n is a vector of applied external nodal forces. Material damping is usually neglected and the term [K]{u}n is replaced by the equivalent internal nodal force vector {Pint}n, giving Newton's second law of motion, [16.3] Assuming a lumped mass distribution gives a diagonal matrix [M] and the solution for nodal accelerations {ü}n is trivial. The nodal velocities {u˙}n + 1/2 and nodal displacements {u}n : 1 are obtained by integration using the central finite difference operators,
[16.4]
Explicit integration is ‘conditionally stable’ requiring a timestep given by ΔTcritical (≤ Lmin/c), where c is the material wave speed (=√(E/ρ)), Lmin is the smallest element size, E is material Young’s modulus and ρ is material density. Generally, the implicit method is superior for static and mildly nonlinear composite stress analysis; whereas the explicit method is best for highly nonlinear impact and crash-type problems. Draping simulation is most commonly undertaken with an explicit algorithm due to contact analysis requirements. However, previous clear distinctions on which algorithm is best for which application are becoming increasingly blurred as grater computer power and code improvements open new fields of application for each algorithm type.
16.2
Laminate analysis and FE stiffness for non-crimp fabric (NCF)
For a single composite ply in a NCF the mechanical stiffness is governed by Hooke’s Law for an orthotropic material, Fig. 16.1. From this basic description, classical laminate theory (CLT) performs a transformation of each ply stiffness matrix [Q] to an off-axis stiffness matrix [Q ¯] in the common global frame (x,y,z) system and is then summated to give the full
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16.1 Hooke's law for an orthotropic ply and fibre axis system.
laminate stiffness matrix. In abbreviated notation, the full laminate stiffness matrix comprises of the extensional matrix [A], the extension-bending coupling matrix [B] and the bending matrix [D] which relate laminate forces {N} and moments {M} per unit length to mid-plane strains {εo} and curvature/twists {κ},
[16.5]
and
[16.6]
where,
[16.7]
In the above expressions, zk and zk–1 are upper and lower surface position of the kth layer in the laminate of n plies. For linear stress analysis, conventional coupon testing gives the necessary mechanical data in the fibre and transverse directions.
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For failure analysis the computed stresses (or strains) for a given loading are evaluated against test failure values in a selected failure criteria. And for impactand crash-type analysis the mechanical properties are usually damaged (reduced) after initial failure, according to a strain-based damage function to account for material softening effects in the post-failure phase. Typically FE analysis of NCF uses multi-layer shell elements, Fig. 16.2, in which each layer of the shell represents one ply. The element stiffness matrix [ke] is given by,
16.2 A multi-layer element and the element stiffness matrix.
– where [B] is an element specific strain-displacement matrix depending on nodal – coordinates and [D] is the material stiffness matrix which is formulated in an identical fashion to the [A,B,D] stiffness matrix in laminate analysis. Again, the [D–] matrix is constant for linear stress analysis, or non-constant if failure- or damage type analysis is required and thus necessitating an iterative non-linear solution. In extreme cases, such as impact, the explicit method is usually preferable.
16.3
FE methods for infusion analysis
Today, several commercial codes, for example PAM-RTM™ (ESI Group 2009) and LIMS (Advani, Bruschke and Parna 1994), are available for resin infusion modelling of dry textiles. These FE-based codes model tooling, the fabric as a permeable medium and boundary conditions such as resin inlets and air outlet vents. A high level of sophistication can be added with pressure dependent permeability and thermo-viscous resin viscosity that can include effects of cure kinetics requiring a full thermal history modelling of the process. Typical objectives for infusion simulation are minimisation of infusion times and identification and elimination of dry areas; defects such as high porosity and fibre washing can be indirectly predicted from resin pressure and flow velocity information. FE analysis of resin flow is based on Darcy's Law for flow through a porous medium. This assumes the fluid to be a Newtonian incompressible liquid which is valid for LRI flow processes, [16.8]
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where is the flow velocity, ∇P the pressure gradient averaged over the length of the medium ΔL. The fabric permeability is denoted K and resin viscosity µ, both of which are determined from experimental testing; see also Chapter 10 on meso-permeability modelling. The assumption for a Newtonian incompressible fluid requires the continuity condition ∇ = 0. Coupling this with Eq. 16.8 gives the governing Laplace equation for fluid pressure field within the region permeated by the fluid (Mathur et al., 2001), [16.9] Equation 16.9 is solved numerically as an FE problem in conjunction with boundary conditions governing inlet pressure (P = inlet pressure), Dirichlet boundary conditions at the flow front (P = 0) and Neumann boundary conditions requiring zero flow velocity normal to the mould walls (∇ .n = 0), where n is the wall normal vector.
16.4
Draping and FE simulation
Fabrics undergo preferential deformation mechanisms that are controlled by their architecture. Figure 16.3 shows schematically the predominant deformation modes for a typical bi-axial type fabric; usually inter-fibre shear, or the ‘trellis’ mode, offers least resistance to loading and consequently most woven-type fabrics adapt their shape by shearing mechanisms. The type of weave (plain, twill, etc.), or the type of stitch used in a bi-axial NCF will determine fabric shear resistance, which may also have a symmetric, or non-symmetric shear response. If the NCF contains three or more principal fibre directions, such as tri-axial NCF, then shearing is usually restrained. Inter-tow sliding is a secondary mode of deformation
16.3 Examples of principal deformations modes in a bi-axial fabric (Rudd et al., 1997).
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16.4 Solution scheme of a kinematic drape algorithm.
occurring at higher shear angles and is more prevalent in NCF materials, for which the lack of tow interlocking results in less constraint at cross-over positions. Other minor deformation modes are also possible, including yarn buckling in compression or yarn straightening in tension. Today, the most popular method for drape analysis is based on the original kinematic methods developed in the 1950s (Mack and Taylor, 1956) which essentially use mapping algorithms to fit a flat fabric to the desired geometry. This method is computationally fast, robust and requires only minimal input for geometry and certain ‘starting point’ information. Originally the method was intended for balanced woven fabrics, but it can be reasonably applied to bi-axial NCFs, provided inter-tow slippage mechanisms can be neglected. Briefly, the algorithm requires two initial fibre directions (L1,L2) of the ‘net’, the edge length of the net segments (a, b) and a single starting point (P) to be specified (Fig. 16.4). Working outward from this starting point the draped fibre paths are found by solving the intersection of each pin-joint node, Eq. 16.10a, and enforcing the intersect to lie on the geometry surface, Eq. 16.10b, [16.10a]
[16.10b] As the above equations suggest, the method can be idealised as the intersection of two spheres of radius a and b, centred at points (i−1, j) and (i, j−1) with the geometry surface at xij, yij zij. The main limitations are that it is a purely geometric fitting process that does not consider fabric mechanical behaviour or process effects such as friction. Some work has tried to overcome these limitations; for example, Long, Souter and Robitaille (2001) have considered a non-symmetric shear model for certain NCFs to account for effects that stitching style and its interaction with tows can have on shear behaviour, and PAM-QUIKFORM (ESI Group, 2009) allows controlled transverse extension in the mapping process to account for loose stitching styles. A further limitation of the method is the requirement to specify a single starting point and prescribe two principle yarn directions; both of which control the solution and may not be correct.
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The following industrial part illustrates kinematic draping of a NCF part using the commercial code PAM-QUIKFORM™ (Weiland et al., 2009). Plate V (see colour section between pages 396 and 397) shows the draping of one ±45° layer from a single point source located at the apex of the geometry. Plate V(b) illustrates a typical enhancement to the method in which the analysis (and process) requires the fabric shearing to emanate outward from a specified line. In both cases, the fabric undergoes a maximum shear strain of 30°, but very different shear distributions and locations of maximum shear occur. FE modelling of draping allows a fabric constitutive law and representation of process parameters such as tooling and blankholder friction to be used. Generally, the fabric is treated with a phenomenological law that attempts to represent in-plane stretch, bending and shear behaviour obtained from simple coupon testing. For bi-axial NCF, a conventional woven-type fabric law can be used, although such an approach will not model potential inter-tow slippage mechanisms between adjacent plies in the blanket. Alternatively, Fig. 16.5 shows a more advanced representation to approximate these mechanisms; in this case each ply is treated as an independent layer of FE (shells), with connection link elements to represent the stitching and slip mechanisms between plies (Creech, Pickett, and Greve, 2003). Parameters for in-plane moduli E1 and E2 can be estimated, or determined from coupon testing, Fig. 16.6(a). For intra-ply shear stiffness G12, either the bias extension test or ‘picture frame’ test is used (Long, 2005); the latter can also provide important information on shear locking angle. Figure 16.6(b) shows an example picture frame test and simulation data for a chain-stitched NCF (430 gm−2 carbon fabric from Saertex). In the constitutive model shear locking is imposed by rapidly increasing G12 once the experimentally observed locking angle is reached. Dry friction is determined from simple testing of fabrics as shown schematically in Fig. 16.6(c). If membrane-type FEs are used fabric bending stiffness is neglected, whereas for shell-type elements, which can predict buckling, a bending stiffness must be specified. This is usually determined from a simple fabric overhang test based on the ASTM procedure (D1388–96(99)), Fig. 16.6(d), which is used to calibrate the numerical model.
16.5 Two stacked plies and constitutive laws for non-crimp fabric.
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16.6 Example testing methods for fabric drape properties: (a) in-plane tension, (b) shear, (c) friction, and (d) bending properties.
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Plate VI compares typical kinematic and FE simulation results for draping of a bi-axial NCF over a half-hemisphere mould. The effect of blankholders, which maintain tension in the fabric as it is formed, can only be represented in the FE simulation. Numerous bi-axial NCF types have been investigated (Vinot, 2005) and the trends in Plate VI are typical. Generally, test and numerical results are in close agreement with kinematic results tending to overestimate shear strains. The FE analysis tends to predict lower shear strains due to other deformations being represented, such as transverse in-plane stretching (in the stitch direction). Furthermore, the inclusion of process effects from friction and blankholders will also influence results. A typical industrial simulation to drape an automotive floor pan with bi-axial NCF is shown in Plate VII. Meshes for the punch, die and blankholders are usually generated from CAE data and define contact surfaces for the tooling. The bi-axial fabric is represented with the approach depicted in Fig. 16.5, with shell elements having a length of 5 mm so that potential fabric buckling may be detected. Also shown in Plate VII is a contour plot of shear strain distribution and the experimental draped preform.
16.5
Infusion simulation
The following example considers infusion of the previous draped rotor blade pitch horn (Weiland et al., 2009). Plate VIII shows the so-called zone definition model in which each zone is assigned a thickness and permeability data. In each zone the fabric thickness is based on design considerations and is modified due to shearing; the permeability data should correspond to fabric in the sheared state. In this study, a pragmatic approach was used to assign estimated average values for each zone; however, current research is aimed at linking drape and infusion codes so that accurate information is transferred on an element-by-element basis. The preliminary analysis, Plate IX, uses two-dimensional (2D) shell elements that ignore through-thickness effects to estimate resin flow front evolution. The resin is RTM6 and is assumed to have a constant viscosity equal to 0.1 Pa sec. The NCF permeability is assumed to be isotropic and equal to 2*10−11 m2 with a porosity of 0.5. Two infusion strategies are compared and shown in Plate IX using blue lines to denote injection runners and green lines for outlet vents; in both, the injection overpressure is 1 bar. Analysis shows the injection times for the two cases are similar; 895 secs and 805 secs for the circumferential and axial injection respectively; however, the latter axial case presents a higher risk as flow fronts do not remain straight and there is a likelihood of air entrapment as the two flow fronts meet.
16.6
Stiffness and failure
As previously discussed, FE stress analysis of NCF composites can use a multilayered shell FE with a unidirectional (UD) composites model for each layer of the
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16.7 a) Test setup for loading of the NCF curved beam, b) Finite Element representation c) Fibre orientations from kinematic drape analysis
NCF. The following example (de Luca P et al., 2006) from the CEC project Falcom (CEC 2006) considers a complex J-section curved beam loaded under four point bending, Fig. 16.7. The section has a quasi-isotropic layup with additional interspersed 0° (axial) plies. Each ply in the NCF uses High Tensile Strength (HTS) fibres with RTM6 resin having a fibre volume fraction of 60% and the mechanical data in Table 16.1. The FE model of the test set-up uses multi-layered shell elements and the specified mechanical properties. The ends are fixed, with free rotation about the lateral axis and an imposed vertical downward displacement at the two locations shown. Two analyses have been considered; namely, Case 1 using fibre directions according to the original ‘straight’ beam configuration and Case 2 using fibre direction taking into account reorientations during draping of the curved geometry. Figure 16.7(c) shows typical fibre reorientations for a single ply obtained from a PAM-QUIKFORM™ kinematic analysis. Implicit FE stress analysis of the two cases highlight important differences between analysis results, Plate X. Case 1, as expected, gives a uniform maximum stress distribution along the lower face, Plate X(b); whereas Case 2 shows a varying stress distribution with a critical stress concentration to the left of the centreline, Plate X(c). This location and the FE prediction of maximum failure load using a Tsai-Hill failure criterion are in close agreement with test measurements, Plate X(a). Table 16.1 Mechanical and failure data for a single ply (NCF HTS-RTM6) Stiffness data Property Value
E11 (MPa) E22 = E33 (MPa) G12 (MPa) 130000 9500 4300
Property
F1T (MPa) F2T = F3T (MPa) F1C (MPa)
Value
1600
G13 (MPa) G23 (MPa) v12=v13=v23 3000 2500 0.3
Failure data
60
900
F2C = F3C (MPa) 200
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F6 (MPa) 110
F4=F5 (MPa) 60
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16.7
Impact and failure
Failure modelling of NCF is straightforward by treating each ply in the laminate as a quasi-UD composite for which a wide number of failure criteria have been proposed; see for example the critical assessment in a world-wide exercise (Hinton, Kaddour, and Soden, 2004). In impact delamination, there is a further potential failure mode to be considered. The through-thickness stitching does increase fracture toughness for each blanket, but delamination is still possible, particularly in the resin-rich layers between blankets. Modern FE codes have a wide range of ply failure criteria and now begin to implement delamination criteria using cohesive zone elements (Allix, Ladèveze and Corigliano, 1995). Only a brief introduction is given here for the popular Ladevèze and Le Dantec ply damage model (Ladevèze and Le Dantec, 1992) and the cohesive zone delamination model, both of which now appear in several commercial FE codes. The Ladevèze and Le Dantec model has been successfully applied for damage and failure prediction of NCF materials and has also been adapted in research work for failure of sheared fabrics (Greve and Pickett, 2006). This model considers the laminate to be constructed from elementary UD plies, Fig. 16.8, with each ply having a constant thickness and fibres running in one principal direction. A state of plane stress is assumed and subscripts 1, 2 and 3 denote fibre, transverse and through-thickness directions respectively. A classical continuum damage mechanics is used to degrade elastic properties; but, in this case fibre, transverse and shear damage are decoupled. Thus, for an orthotropic ply, with damage, the stress–strain relationship is given by, [16.11] where the stiffness matrix [C] has the following form and coefficients,
[16.12]
with .
[16.13]
The corresponding stress and strain vectors are, [16.14]
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and [16.15] 0 In the above equations, E011 and E22 are elastic moduli in the fibre and transverse 0 directions, Gij is shear modulus, and v0ij is Poisson's ratio. The matrix dominated 0 0 elastic moduli, E022, G12 , and G23 , are modified by the damage functions (1–dij) from damage initiation up to ultimate failure. Two scalar damage functions d22 and d12 are introduced, having the range 0 (no damage) to 1.0 (fully damaged) to describe matrix damage development in the ply transverse and shear directions, respectively. In addition to elastic damage the model has a superimposed matrix plasticity contribution, which is also dependent on damage evolution. A particular advantage of this model is the well-defined experimental test program for parameter identification. In recent years the ‘cohesive zone’ interface has become a popular technique to model inter-ply delamination in laminate composites. The approach uses a failure criterion to identify crack initiation and an energy criterion to control subsequent crack growth. Essentially, the ‘tearing’ interface ties adjacent elements together along a predefined failure surface using interface constraints. These constraints characterise the mechanical stiffness, strength and fracture energy absorption of the interface material. Figure 16.9(a) shows the attachment of two surfaces; arbitrarily called the ‘slave’ and ‘master’ surfaces. At initialisation, each slave node on a slave surface is attached to a fictitious ‘shadow’ node created on the adjacent master surface (element). During deformation the relative movement of the slave and shadow nodes provide normal and shear deformations to be used in the mechanical law for elastic-damaging traction and shear resisting forces. The main features of the interface mechanical law are shown in Fig. 16.9(b) for normal (mode I) loading. A simple linear elastic law is assumed up to failure stress σImax. Thereafter, linear damaging is activated such that, at final separation δImax, the fracture energy of the tied interface has been absorbed. That is, the area under the curve corresponds to the critical energy release rate GIC generated in creating the fracture surface. Thus σImax, δIC and δImax are selected so that the elastic damage curve fulfils the required criteria.
16.8 Notation for the elementary ply.
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The following formulae describe mode I failure; identical arguments and equations are used for mode II by interchanging E0, σImax, δI and GIC with G0, σIImax, δII and GIIC. The through-thickness composite normal modulus is E0. At the maximum normal stress σImax damage is initiated and the stress displacement law then follows a linear damage equation of the type, [16.16] where dI is the damage parameter, varying between values of 0 (undamaged) and 1 (fully damaged), E0 is the modulus, L0 the normal distance between the original position of the slave node and the master element and δI the deformed normal separation distance of the slave node and master element. The area under the stress-displacement curve in the elastic range GIA is the fracture energy required to initiate damage of the interface and is given by, [16.17] The total areas under the load-displacement curve is the critical energy release rate required for failure of the interface (including both the elastic and damage zones) and is given by, [16.18] The values of GIC and GIIC and other model parameters can be obtained via the standard Double Cantilever Beam (DCB, 1999) and End Notched Flexure (ENF, 1993) tests. Also, in real materials, there is a coupling between normal and shear loading and the critical fracture toughness. This interaction can be determined using the Mixed Mode Bending (MMB) test (Reeder and Crews 1989) to provide the coupling parameter η used in the following mixed mode interaction model, [16.19] where GI and GII are instantaneous values and GIC and GIIC are experimental values measured by the DCB and ENF tests. Example solutions using this approach, including validation against DCB, ENF and MMB tests have been presented for composites delamination modelling of NCF (Greve and Pickett, 2006). Figure 16.9 illustrates typical experimental testing of a ±45° NCF DCB specimen to obtain fracture toughness GIC. This data is then used in an FE model of the DCB specimen with delamination interface to obtain a good agreement with test measurements for crack opening force versus crack opening displacement.
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16.9 The inter-ply delamination model. (a) an attached node (adjacent ‘slave’ node) constrained to an element ‘master’ surface and (b) diagram of the stress-crack opening curve for mode I loading.
Table 16.2 Properties for an ‘equivalent’ NCF/LY3505 ply Elastic properties 0 v 12 0.30
Et011 = Ec011 (GPa) 127.8
E 022 (GPa) 7.127
0 G 12 (GPa) 4.85
0 G 23 (GPa) 4.85
Fibre damage parameters Tension t ε 11l 0.0132
t ε11u 0.0132
Compression t d 11u γ 0.9 0.1
c ε 11l 0.0080
c ε 11u 0.0081
c d 11u 0.9
Shear/transverse damage law YC (√GPa) 0.0668
Y0 (√GPa) 0.0049
Y′C (√GPa) Y′0 (√GPa) 10E06 10E–6
b 2.7
Y′S (√GPa) 10.0
YR (√GPa) 0.0667
dmax 0.9
Plasticity law R(p)=βpa R0 (GPa) β (GPa) 0.017 0.934
a 0.586
The following material data and study involves impact loading of a quasiisotropic NCF composite laminate (Pickett, Fouinneteau and Middendorf, 2009). The material is a bi-axial NCF (6k HTA tows, 540g/m2 manufactured by Saertex) with LY3505 resin (manufactured by Huntsman). Table 16.2 summarises the mechanical and failure data for a single ply for the Ladevèze and Le Dantec model, and Table 16.3 gives the delamination data obtained from DCB testing. The impact simulation using an explicit FE code is shown in Plate XI. In this particular study the composite plate is pre-loaded prior to impact to investigate effects of pre-stressing on failure mechanisms. Test and simulation results show a good agreement for delamination, area of ply damage and impact force time history response.
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Table 16.3 Parameters for the delamination interface for materials NCF/LY3505 Parameters
Notation
NCF/LY3505
Distance for kinematics computation (mm) Normal modulus (GPa) Shear modulus (GPa) Normal propagation stress (GPa) Shear propagation stress for delamination (GPa) Mode I fracture Energy (J/mm2) Mode II fracture Energy (J/mm2)
hcont E0 G0 σ prop I σ IIprop GIC GIIC
0.5 7.8 2.5* 0.003 0.035 0.47E–03 2.0E–03
* Estimated
16.8
References
Advani, SG, MV Bruschke, and R Parna. Resin transfer molding. In Flow and rheology in polymeric composites manufacturing, by SG Advani, 465–526. Amsterdam: Elsevier Publishers, 1994. Allix, O, P Ladeveze, and A Corigliano. ‘Damage analysis of interlaminar fracture specimens.’ Composite Structures 31 (1995): 61–74. CEC. ‘Failure, performance and process prediction for enhanced design with Non Crimped Fabric composites.’ Falcom EC project G4RD-CT–00694, 2006. Cook, RD, MS Malkus, and ME Plesha. Concepts and applications of Finite Element analysis. 3rd Edition. Wiley, 1989. Creech, G, AK Pickett, and L Greve. ‘Finite Element modelling of Non Crimp fabrics for draping simulation.’ The 6th International ESAFORM Conference on Material Forming. Salerno, Italy, 2003. 863–866. Crooktson, JJ, AC Long, und IA Jones. ‘Modelling effects of reinforcement deformation during manufacturing on elastic properties of textile composites.’ Plastics, Rubber and Composites 32, Nr. 2 (2002): 58–65. D1388–96(99). ‘Standard test method for stiffness of fabrics.’ ASTM, West Conshohocken (USA). DCB. Fibre-reinforced plastic composites – Determination of Mode I interlaminar fracture toughness, GIC, for unidirectionally reinforced materials. USA: ISO international standard DIS15024, 1999. de Luca P et al. ‘Predicting mechanical performance of composite parts through manufacturing simulations.’ SAMPE Europe, 2006: 515–525. ENF. ‘ASTM draft standard D30.06: ‘Protocol for interlaminar fracture testing, EndNotched Flexure (ENF).’ 1993. ESI Group. 99 Rue des Solets, Silic 112, 94513 Rungis-Cedex, France, 2009. Greve, L, and AK Pickett. ‘Modelling damage and failure in carbon/epoxy Non Crimp fabric composites including effects of fabric pre-shear.’ Composites: Part A 37, no. 11 (2006): 1983–2001. Greve, L, and AK Pickett. ‘Delamination testing and modelling for composite crash simulation.’ Composites Science and Technology 66 (2006): 816–826. Hinton, MJ, AS Kaddour, and PD Soden. ‘Recommendations for designers and researchers resulting from the world-wide failure exercise.’ Composites Science and Technology 64, no. 3–4 (2004): 589–604.
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Jones, IA, and AK Pickett. ‘Mechanical properties of textile composites.’ In Design and manufacture of textile composites, by AC Long, 292–329. Cambridge, UK: Woodhead Publishing in Textiles, 2005. Ladevèze, P, and E Le Dantec. ‘Damage modelling of the elementary ply for laminated composites.’ Composites Science and Technology 43 (1992): 257–267. Long, AC. Design and manufacture of textile composites. Cambridge, UK: Woodhead Publishing in Textiles, 2005. Long, AC, BJ Souter, and F Robitaille. ‘Mechanical modelling of in-plane shear and draping for woven and Non-Crimp reinforcements.’ Journal of Thermoplastic Composite Materials 14 (2001): 316–326. Mack, C, and HM Taylor. ‘The fitting of woven cloth to surfaces.’ Journal of the Textile Institute 8 (1956): 477–488. Pickett, AK, MRC Fouinneteau, and P Middendorf. ‘Test and modelling of impact on preloaded composite panels.’ Applied Composite Materials 16, no. 4 (2009): 225–244. R Mathur et al. ‘Flow front measurements and model validation in the vacuum assisted resin transfer molding proces.’ Polymer Composites 22, Nr. 4 (2001): 477–490. Reeder, JR, and J Crews. ‘Mixed-mode bending method for delamination testing.’ AIAA Journal 28, no. 7 (1989): 1270–1276. Rudd, CD, AC Long, KN Kendall, and GCE Mangin. Liquid moulding technologies. Cambridge, England: Woodhead Publishing, 1997. Vinot, L. ‘Advanced fabrics textile draping.’ MSc Thesis Cranfield University, United Kingdom, 2005. Weiland et al. ‘Manufacture of a rotor blade pitch horn using novel binder yarn fabrics.’ 17th International Conference on Composite Materials. Edinburgh, United Kingdom, 2009.
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Plate IV Out-of plane displacement of non-crimp fabric composite with periodicity in the thickness direction. Matrix of the upper ply sinks due to the mismatch of the Poisson ratios with UD fibrous ply, and so does the matrix of the upper layer, which sucks up the upper unidirectional ply underneath and forces it to extend. (Chapter 15).
Plate V Shear angle distribution in the pitch horn using (a) conventional draping starting from the apex and (b) a bias curve, (courtesy of Eurocopter) (Chapter 16).
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Plate VI (a) Finite element model and (b) test setup for draping of a non-crimp fabric hemisphere: (c) contour plot of finite element fabric shear and (d) comparison of fabric shear angle around a 90° quadrant of the hemisphere base for test, finite element and kinematic draping (Chapter 16).
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Plate VII Example of non-crimp fabric finite element drape simulation of a non-crimp fabric floor pan (courtesy of ESI and Sotira) (Chapter 16).
Plate VIII View of the model zones for thickness and permeability variations (Courtesy of Eurocopter) (Chapter 16).
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Plate IX The two different infusion strategies and contours of filling times: left views for a circumferential infusion line with axial flow and right views for axial infusion lines and circumferential flow lines (Chapter 16).
Plate X Test and analysis results for 3 point loading and failure of a non-crimp fabric spar: lower left view for analysis failure contours not taking into account fibre reorientation during manufacture and lower right view for improved analysis failure contours which include the effects of fibre reorientation (Chapter 16). © Woodhead Publishing Limited, 2011
Plate XI Parameters for the delamination interface model for materials NCF/LY3505 (* estimated) (Chapter 16).
Plate XII C-scans of impacted non-crimp fabric and prepreg specimens (30J) (Chapter 18).
Plate XIII Typical blade layout IEC class II 40m blade detailing the laminate constructions based on non-crimp fabric reinforcement materials (Chapter 21).
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17 Modelling stiffness and strength of non-crimp fabric composites: semi-laminar analysis E. MARKLUND, J. VARNA and L. E. ASP, Swerea SICOMP and Luleå University of Technology, Sweden
Abstract: In this chapter, engineering models based on semi-laminar considerations, particularly considering features on the mesoscale, for computation of non-crimp fabric composite stiffness are addressed. Both analytical and finite element models are employed on different scales in the material. Thereafter, engineering models based on laminate considerations with simplistic descriptions of the mesoscale features for strength modelling are presented. Key words: microscale, mesoscale, laminate theory, failure criteria.
17.1
Introduction
Over the last decade, engineering-type models have been developed to allow efficient analysis of non-crimp fabric (NCF) composites’ constitutive properties and strength. As illustrated throughout this book, the architecture of NCF composites implies that these materials are heterogeneous, not only on the microscale, but also on the mesoscale. On the mesoscale, the laminas, due to the knitting procedure, are divided into distinct regions with fibre tows surrounded by resin. The stitch yarns are probably affecting strength more than stiffness. Although, owing to the composites’ imperfect bundle structure, the effect on stiffness can be rather significant in an indirect way. For the purpose of performance prediction, models considering the heterogeneous characteristics of NCF composites on the micro- and mesoscale, as well as on the macroscale, are required. Figure 17.1 shows a cross-section of a cross-ply laminate and illustrates the heterogeneous architecture of the material. The laminate is built up by paralleloriented fibre tows in a layer stitched together with neighbouring layer(s) of fibre tows oriented in other direction(s), typically with a polyester thread. Distinct fibre tows in an NCF lamina are readily seen in Fig. 17.1. Material heterogeneities on different scales are identified: (i) on the microscale, inherent heterogeneity due to the fibre-matrix microstructure within distinct fibre tows (tow cross-sections appear as bundles) is similar to that found in unidirectional (UD) composite lamina; (ii) on the mesoscale, i.e. at the lamina level, including effects of neighbouring layers. There are two features of heterogeneity dominating. Firstly, distinct fibre bundles separated by regions of resin are present, rather than the homogeneously distributed fibres in a conventional UD lamina. Secondly, the 402 © Woodhead Publishing Limited, 2011
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17.1 The hierarchical structure of a typical non-crimp fabric composite laminate.
ideally straight (non-crimped) fibre tows exhibit different degrees of waviness (see Fig. 17.1, which shows proof of rather high waviness of the 0° fibre tows, extending in the horizontal direction of the picture). Both these features must be treated on the mesoscale, either by unit cell descriptions, e.g. in finite element (FE), or by homogenisation. Apart from that, the nature of mesoscale heterogeneity for NCF composite laminates does not differ much from that of UD composite laminates. However, two distinct differences should be noted. Firstly, in NCF composites a number of individual lamina in the stack are stitched together, depending on the choice of fabric, e.g. biaxial or triaxial NCFs. Secondly, NCF composite laminae (layers) nest, resulting in partly integrated plies. This nesting is partly caused by the presence of the stitching thread. Considering these features, NCF composites can be addressed as being semi-laminar; and, finally (iii) on the macroscale, similar to tape-based composites, heterogeneity is caused by the difference in fibre orientation between the laminae. This is illustrated in Fig. 17.1. Consequently, correct homogenisation treatment of the micro- and mesoscale heterogeneities will allow use of classical laminate theory (CLT) for modelling structural performance at this level. An advantage for modelling is that critical heterogeneous features are identified on length scales that are sufficiently different, and therefore multiscale analysis is possible, instead of considering the whole complexity of the system included in one model. As will become apparent during the course of this chapter, relatively simple analytical tools or more advanced FE modelling procedures, or a combination of these, may be applied on the various length scales to obtain NCF
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laminate properties. Starting from the microscale, homogenised stiffness properties and important features that governs strength are elucidated. Results are then carried up the chain as input to the mesoscale models. The same methodology is applied to link mesoscale features with macroscale characteristics. The purpose with such multiscale analysis will be to extract information about critical parameters on each scale depending on knowledge of the material’s inner structure. Finally, the aim of the multiscale analysis will be to accurately predict the mechanical performance of complete structures made from NCF composites. However, from a designer’s perspective, performing the multiscale approach (which will be unique for each individual NCF composite detail) is unrealistic, since the steps required to perform a complete analysis are very time-consuming. Instead, the preference for a designer would be a ‘black box’ modelling tool, which contains sufficient accuracy under all conceivable circumstances. Obviously, in the development of this black box, multiscale analysis is an absolute necessity. From a designer’s point of view, the required inputs, illustrated by the flowchart in Fig. 17.2, may very well come directly from manufacturing process simulations. To date, no such tool is available, and therefore Fig. 17.2 is rather representing the vision of all efforts currently underway in terms of multiscale modelling. This chapter is not intended to give a full review of all required analysis. Instead, emphasis is put on specific analyses for better understanding of important aspects regarding micro- and meso-parameters and their influence on overall stiffness and strength. Alongside this, the chapter also comprises state-of-the-art engineering models for semi-laminar NCF composites in terms of constitutive modelling and failure criteria.
17.2 Required inputs and obtained outputs from the ‘black box’ modelling tool developed by multiscale analysis.
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The chapter starts with description of various stiffness models employed on different scales in the material. Both analytical and FE modelling is considered. Analytical models usually significantly differ from detailed FE representations of NCF composites, which employ representative volume elements (RVEs) by consideration of distinct features in repeating unit cells (RUCs) in simplistic models. Engineering models based on semi-laminar considerations, particularly considering features on the mesoscale, for computation of NCF composite stiffness are also addressed. Thereafter, engineering models based on laminate considerations with simplistic descriptions of the mesoscale features for strength modelling are presented.
17.2
Stiffness models
As demonstrated above, NCF composites are heterogeneous materials with a quasi-laminar structure, each lamina consisting of theoretically straight fibre tows with distinct orientation and resin cylinders with complex cross-sections aligned parallel to them. In this section, these constituents of a lamina (fibre tows and matrix regions) are called ‘mesoelements’. Each tow is characterised by the fibre volume fraction Vf in it. Thus, the average volume fraction of fibres in a layer Vaf is defined by [17.1] where Vb is the bundle (tow) volume content in the layer. Unfortunately, the fibre tows have certain out-of-plane waviness (see Section 17.2.2 for details), which together with previously described features makes accurate prediction of the NCF composite stiffness a very difficult task. To make the problem solvable, several simplifications (idealisations) of the mesostructure have to be made, and models have to be developed to convert the original geometrical features into effective properties of the idealised structure. A possible workflow to illustrate this concept is shown in Fig. 17.3. The properties’ calculation may be simplified by performing homogenisation separately on both micro- and meso-length scales: •
Microscale homogenisation is over the fibre and matrix microstructure within the bundle. It is best performed using the Composite Cylinder Assemblage (CCA) model, developed by Hashin and Rosen (1964) and Hashin (1983) and improved by Christensen and Lo (1979) who introduced a self-consistent modelling scheme to calculate the transverse shear modulus. These models, which are the most accurate for UD composite stiffness determination were further generalised by Marklund et al. (2008) to include hollow fibres with cylindrical orthotropic walls typical when natural fibres are used in composites. As a result the bundle or layer transverse isotropic elastic properties are obtained. Certainly, FE-based numerical methods may be used analysing RUCs as an alternative route. The most convenient strategy is then
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17.3 Possible approach when modelling stiffness properties for non-crimp fabric composites using multiscale analysis.
•
to assume that fibres are sequenced in square or hexagonal fibre packing arrangements. On the mesoscale, fibre tows are considered as homogeneous materials, and in order to calculate macroscale properties, homogenisation is performed over the mesostructure RVE which consists of mesoelements corresponding to bundles (of different orientation) and matrix regions. The size of the RVE depends on the periodicity or randomness of the bundle placement in different lamina. If a repeating element can be identified in the structure, the analysis becomes significantly simplified. An example of that is possible (existing or assumed) periodicity in the NCF composite thickness direction. The homogenisation can contain several sub-steps where certain mesoelements are replaced by geometrically simpler objects, but with effective properties as for the original mesoelements. Examples are: (i) the bundle structure in some layers is replaced by uniformly distributed UD composites; (ii) the imperfect complex bundle geometry is replaced by ideally straight bundles with simple cross-section. As a result of the analysis on this scale, macroscopic constitutive properties of the NCF composite are obtained.
In the following subsections, the methods applicable on each scale will be inspected and models for replacing imperfect mesoelements with simpler effective elements will be discussed in detail.
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17.2.1 Microscale modelling of elastic properties of fibre tows The output of the microscale modelling is a fibre tow considered as a homogeneous transversely isotropic material, see Fig. 17.3. Therefore, on the microscale, each tow may be described as a UD composite with certain fibre content and the homogenised bundle properties may be calculated using micromechanical expressions for long fibre composites and/or RUC representations of assumed fibre arrangements. The simplest models available in any textbook (Agarwal and Broutman, 1990) are based on the constant strain assumption, i.e. rule of mixtures (ROM) type of averages for longitudinal modulus and Poisson’s ratio, or constant stress assumption based harmonic averages (transverse and in-plane shear modulus). Instead of the latter, it is common to use the more accurate Halpin-Tsai expressions which were originally introduced as simple functions that fit numerical elastic properties data (Halpin and Kardos, 1976). These expressions are given by: [17.2] Here, X represents any of the moduli that are to be determined. Indices f and m are referring to fibre and matrix respectively. ξ is a parameter that depends on reinforcement geometry and the particular elastic property being considered (in a more general sense it may also be used as a parameter for fitting the expression, Eq. 17.2, to experimental data). For fibres with circular cross-section the usual choice is ξ = 1 for in-plane shear modulus and ξ = 2 for transverse modulus. A semi-analytical micromechanical model valid for orthotropic phase materials and for an arbitrary number of phases was developed by Marklund et al. (2008) to study the effect of various constituent stiffness properties on an aligned wood fibre composite. The model is a straightforward generalisation of Hashin’s CCA model and Christensen’s self-consistent approach. It was shown that all engineering constants for the composite cylinder may be calculated (with required accuracy) from knowledge of the constituent properties by setting up and solving a system of linear equations using appropriate continuity and interfacial conditions. Using the properties from Table 17.1, the same concentric cylinder assemblage model (here referred to as CCA self-consistent when modelling transverse properties) has been used in the calculation of homogenised bundle stiffness properties, together with the more convenient ROM and Halpin-Tsai expressions for comparing purposes. FE calculations are performed using square and hexagonal RUCs, see Fig. 17.4. Note that, due to the chosen RUCs (square and hexagonal) the homogenised material is NOT transversely isotropic. The transverse shear modulus G23 of these RUCs does not exactly obey the familiar expression G23 = E2/2(1 + ν23) for transversely isotropic materials.
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Table 17.1 Assumed fibre and matrix properties used in the micromechanical study Property
Carbon fibre, HTS
Epoxy matrix
E1 [GPa] E2 [GPa] G12 [GPa] ν12 ν23 α1 [µm/m°C] α2 [µm/m°C]
233 23 20 0.2 0.2 −0.5 10
3.0*
0.38 81**
* Secant modulus corresponding to 1% strain; ** Including effects of chemical shrinkage
17.4 Repeatable unit cells in the micromechanical analysis.
The result of the investigation is shown in Figs. 17.5–17.7. Figure 17.8 shows the shear moduli obtained using the CCA model. For all calculations, the matrix secant modulus corresponding to 1% strain has been used. From Fig. 17.5 it is clear that the two FE arrays give practically identical results, and is in excellent agreement with the two analytical models, CCA and ROM. Thus, the conclusion is that the simple ROM model is sufficient for computing the value of the longitudinal modulus from constituent properties. Regarding the transverse modulus, Fig. 17.6, it is seen that the two FE approaches lead to quite different results. The square RUC predicts higher values of transverse modulus than the hexagonal RUC, with an overestimation of up to 17% for Vf = 0.6. The analytical models give slightly different results. The CCA, self-consistent model is practically coinciding with the hexagonal RUC, whereas Halpin-Tsai lies in-between the values of hexagonal and square arrays. It is well established within the composite community that a hexagonally packed array is a more realistic configuration than a squared one, therefore, the CCA self-consistent approach may be seen as the most accurate analytical model. However, it is emphasised that the Halpin-Tsai expressions can be fitted to give a perfect correlation with the hexagonal RUC by a different (lower) ξ parameter.
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17.5 Longitudinal modulus as a function of fibre volume fraction.
17.6 Transverse modulus as a function of fibre volume fraction.
The comparison for major Poisson’s ratio is presented in Fig. 17.7. The two FE predictions are very close, with only minor discrepancies for higher fibre volume fractions. The CCA model is again in excellent agreement with the hexagonal array. The simple ROM model gives slightly overpredicted result for all fibre volume fractions. As a final step in the analysis, simulated values of shear moduli are shown in Fig. 17.8. For comparison, bounds, as described by Hashin (1983) for transverse
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17.7 Poisson's ratio as a function of fibre volume fraction.
17.8 Shear moduli as a function of fibre volume fraction.
shear modulus are also included. It is seen that the CCA self-consistent model is indeed within the bounds, as expected. For low fibre volume fractions, the result is very close to the lower bound, and then steadily moving away towards the upper bound as the fibre volume fraction is increased. It is noteworthy that for the in-plane shear modulus G12, the CCA model and Halpin-Tsai equation (with ξ = 1) give exactly the same result.
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17.2.2 Effective longitudinal modulus of curved tows Stiffness of NCF composites is dominated by the stiffness of the fibres. The fibres are oriented in the individual plies, as described in the introduction. Generally speaking, the stiffness of a NCF composite laminate is lower than that of a corresponding tape-based laminate. The lower stiffness is due to an inherent undulation of the fibre tows in the individual lamina, as illustrated in Fig. 17.1. Typically, reported stiffness for NCF composites is ten percent lower than that of comparable tape-based composites (Bibo et al., 1997). The fibre waviness causing this stiffness reduction is inherent to the mesostructure of the NCF, as tows are pressed between tows oriented in other directions. Depending on the geometry and position of these neighbouring fibre tows, regularity in the fibre tows’ waviness results. Knowledge of the fibre tows’ waviness parameters (wavelength and amplitude) allows for modelling of the effective elastic constants of the tows and to subsequently replace them with idealised straight tows possessing these effective properties. The idealised tows with effective properties of the wavy tows are used in NCF composite macro properties modelling using mesoelements. An engineering model to account for stiffness loss in NCF composites caused by material orientation irregularity (imperfection) on the mesoscale was developed by Edgren and Asp (2005). To date, this is the only model considering mesoscale waviness of a single constrained NCF lamina alone to model stiffness by application of CLT for the semi-laminar NCF composite. The approach taken to model NCF composites was inspired by model development by Cox and Dadkhah (1995) and Lee and Harris (1990) for woven composites. In all these works, curved beam models were described and corresponding theoretical stiffness knock-down factors due to out-of-plane waviness of the layers were defined. In the paper on NCF composites Edgren and Asp (2005) describe the wavy pattern and how the tow layer waviness is affected by the position of the layer relative to the mould surface, etc. Based on this knowledge, a mathematical model was developed to calculate the effect of tow layer waviness on the axial stiffness of the lamina. Figure 17.9 illustrates the approach defining the theoretical stiffness knock-down factor, η, for a wavy layer (i.e. the curved beam) related to that of a straight layer as, η = E1/E0. No closed-form expressions for the axial stiffness knock-down factor, η were produced. Models were derived, considering a half wavelength of a sinus-shaped fibre tow. Figure 17.10 illustrates the curved beam model with a fixed fibre tow end. Knock-down factors were derived for three different boundary conditions (free, fixed and spring-supported ends). Figure 17.11 illustrates the nature of the
17.9 Reduced axial modulus Ex due to tow waviness.
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17.10 The curved beam model with fixed fibre tow ends.
17.11 Sensitivity of the knock-down factor, η, on the: (a) wave amplitude and (b) maximum angle of misorientation (fixed beam end boundary condition).
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knock-down factors’ dependence on wave parameters, i.e. wavelength (λ) and amplitude (A). In Fig. 17.11, computed knock-down factors for a lamina using the model, considering a fixed beam end as a function of amplitude (Fig. 17.11a) or maximum angle of misorientation (Fig. 17.11b) are presented (A0 = 78.7 µm). In the figure, predictions for three different crimp wavelengths are plotted. It is seen that the resulting knock-down factor is dependent on the relationship between crimp wavelength and amplitude, and hence angle of maximum misorientation. The beauty of this method is that the consideration of crimp at the lamina level only, allows use of conventional CLT on the macroscale to model laminate behaviour. For this reason, the approach provides a method to model NCF composite materials in a similar manner to UD layer-based laminates employing knock-down factors in concert with the micromechanical models described in section 17.2.1. In order to validate the stiffness, knock-down models considering out-of-plane waviness developed by Edgren and Asp (2005) were compared to experimental data. Predictions considering measured fibre tow waviness were compared to test data from the same laminates. Knock-down factors were first derived for each ply in cross-ply and quasi-isotropic laminates, considering measured standard deviations of orientation for the individual plies by image analysis. These knockdown factors were then incorporated in the laminate analysis to compute the axial laminate stiffness, reducing the stiffness parallel to the nominal fibre direction of the individual plies. The original ply properties, considering ideally straight fibre tows in the lamina, were computed, homogenising the material on the microscale. Results from predictions employing the knock-down model considering fixed fibre tow ends and experiments are presented in Tables 17.2 and 17.3. Table 17.2 Axial modulus and major Poisson's ratio for a non-crimp fabric cross-ply laminate (standard deviation within brackets)
Ex [GPa] νxy
Experimental
Predicted
58.1 (1.2) 0.057 (0.017)
58.4 0.033
Source: Edgren and Asp (2005)
Table 17.3 Axial modulus and major Poisson's ratio for a non-crimp fabric quasi-isotropic laminate (standard deviation within brackets)
Ex [GPa] νxy
Experimental
Predicted
39.8 (0.91) 0.31 (0.01)
40.5 0.33
Source: Edgren and Asp (2005)
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As illustrated by the results presented in the tables, the model considering fixed fibre tow ends works very well to predict the laminate constitutive properties. If one assumes straight fibres in the analysis, i.e. η = 1, the predicted axial stiffness for the cross-ply and the quasi-isotropic laminates are 62.7 GPa and 44.1 GPa, respectively, overestimating the laminate stiffness by as much as 10%. The suggested model does not predict Poisson’s ratios satisfactorily as it does not take the effects of layer in-plane waviness into consideration.
17.2.3 Simplified geometrical models for the mesostructure Without doubt, the simplest way for treating the tow-type mesostructure of the NCF composite is by ignoring its significance. The bundle/resin region structure in a layer is replaced by a homogeneous layer with effective properties. The effective properties of a layer are calculated using the average fibre content of the layer Vfa in the CCA model. This assumption implies that the non-uniformity of the distribution of fibres in the layers (bundle structure) only has a secondary effect on elastic properties and we may replace the heterogeneous mesostructure by a homogeneous material as shown in Fig. 17.12a. If the described ‘smearing out’ is performed for all layers we obtain an ‘effective laminate’ which is treated by CLT. Due to iso-strain assumption in CLT, the calculated strains in all layers will be equal to the macroscopically applied strain. By this homogenisation approach, it is not possible to calculate the real strains in the mesoelements. Depending on the objective of the calculation, only some layers with the mesoheterogeneity may be replaced by material homogeneous on the mesoscale. For example, if the significance of mesoscale geometry of the 90° layer on elastic properties of a cross-ply NCF composite is studied, the meso-heterogeneous 0° layer is replaced by its ‘smeared out’ representative and vice versa if the effect of bundle structure in the 0° layer is assessed. If more detailed analysis of the bundle mesostructure is to be performed, the bundle geometry has to be simplified similarly to how it was done previously with curved tows, replacing them in the model with straight tows with effective
17.12 Representation of non-crimp fabric composite layer: (a) homogenisation in a layer; (b) simplification of the mesoscale geometry.
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properties of the curved ones. This time we are discussing the transverse crosssection of the tow (for clarification, note that ‘bundles’ are throughout the text referring to tow cross-sections). The real transverse cross-section of the bundle is not even well defined since fibre volume fraction in the bundle is decreasing when approaching the bundle/matrix pocket interface. Furthermore, it is definitely not elliptical as shown in Fig. 17.12, cf. Fig. 17.1. In order to simplify the analysis, the real mesogeometry (‘quasi-elliptical’ cross-section of the bundle) is replaced by a rectangular cross-section containing the same fibre content in the bundle Vf and bundle content in the layer Vb, see Fig. 17.12b. Certainly, this procedure affects the stress distribution close to the corners and interfaces, but it has less significance when average stress/strain within a bundle and composite stiffness are analysed. After this geometry simplification the stiffness of the NCF composite in Fig. 17.13a can be relatively easily analysed accounting for its meso architecture using the ‘3D FE’ model described in next section.
17.13 The schematics of [0,90]s non-crimp fabric composite mesoscale structure: (a) simplified RVE; (b) a ‘super-element’ No1; (c) 2D model consisting of 9 ‘super-elements’.
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In-plane stiffness of NCF composites The architecture of NCF composites described above shows similarities to woven fabric composites and therefore methods and theoretical models used for woven fabric composites are relevant also here. Ishikawa and Chou (1982; 1983) proposed two models for woven composites named the mosaic and fibre undulation models. These models used the idea of dividing the RVE into infinitesimal strips where CLT can be used to calculate the properties of the strip. The mosaic model disregarded the waviness of the yarn which is always present in woven fabrics, whereas the fibre undulation model included the waviness. Two-scale homogenisation of the RVE was performed, first creating a homogenised material in each bundle of the composite (microscale homogenisation). The constitutive equation of the RVE was then to be derived by dividing the RVE into elements, where each element in the composite has a stiffness matrix defined by its mesoelements (bundle and matrix regions). Similar methods with different complexity to obtain the stiffness matrix were used in Kurath and Karayaka (1994), Jiang et al. (2000) and Wu et al. (2002). The objective in this section is to compare models of different degree of accuracy to calculate NCF composite in-plane stiffness. The real NCF composite geometry is replaced by a straight fibre bundle structure with rectangular crosssection shown in Fig. 17.13a. The main trends are revealed, analysing responses to normal loading. Normal stiffness elements are discussed in details whereas only a limited amount of results for shear properties is presented. The models used to analyse the cross-ply composite in Fig. 17.13 are briefly described below. • •
3D FE is a three-dimensional (3D) FE model with bundle structure in both 0° and 90° layers (as shown in Fig 17.13) and considered as the reference model. It is the most accurate and will be used to evaluate the models. 3D FE Hom-0° is the next numerical model in the sequence of reduced complexity. It is a 3D FE model were the 0° layer bundle structure is replaced by a UD layer according to section 17.2.3. The bundle structure is kept in the 90° layer only.
The potential for local through-the-thickness averaging of stiffness can be realised, observing the composite in Fig. 17.13a from the top. In Fig. 17.13c we can recognise 9 ‘super-elements’ each of them consisting of four mesoelements stacked in a certain sequence in the thickness direction, see Fig. 17.13b. In this approach, which was introduced in Mattsson and Varna (2007), the RVE is considered as a two-dimensional (2D) structure of ‘super-elements’ as shown in Fig. 17.13c. Homogenisation through the thickness is performed in each ‘super-element’ to obtain its stiffness matrix, assuming that in-plane strains in all mesoelements in the ‘super-element’ are equal (iso-strain condition). This assumption means that CLT can be used to calculate the stiffness of a ‘super-element’. The NCF composite is replaced by a 2D structure divided into ‘super-elements’ and each ‘super-element’ is a homogeneous material. The in-plane stiffness of the 2D structure can be found:
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(i) numerically using the FE model in 2D formulation referred to as 2D FE model; (ii) using an approximate analytical solution referred to as partial iso-strain model. In the partial iso-strain model, the 2D structure is divided in ‘rows’ and ‘columns’ which we call ‘vectors’. The strain transverse to the ‘vector’ is assumed the same in all ‘super-elements’ belonging to this ‘vector’, but it is different than in other ‘vectors’. The magnitude of the strain depends on the resultant stiffness of the row obtained as a result of the solution. This means that straight lines in the 2D structure remain straight after deformation. Additionally, conditions are: (i) the total deformation in a certain direction is equal to the sum of transverse deformations of ‘vectors’; (ii) global equilibrium is satisfied in any direction and in any crosssection. Finally, we introduce the iso-strain model, which can be considered as an extreme case of the partial iso-strain model with additional constraint that in-plane strains in all super-elements are the same. Since all mesoelements in the superelement have the same strain, this method actually assumes the same strain in all mesoelements of the composite. This strain is equal to the applied strain, implying that the expression for NCF composite stiffness turns to rule of mixtures: [17.3] In Eq. (17.3) Vk is the volume fraction of the mesoelement in the NCF composite,
[Q–]k is the in-plane stiffness matrix of the mesoelement in global coordinates and
[Q]RVE is the in-plane stiffness matrix of the composite. In spite of oversimplified assumptions, this approximation is expected to lead to rather good results if the composite contains many layers randomly shifted in horizontal directions. Finally, the CLT model is based on laminate analogy: homogenisation is performed over both 0° and 90° layers. Each layer with a bundle structure is replaced by a UD layer with the average volume fraction of fibres, see Sections 17.2.1 and 17.2.2, and CLT is used for NCF composite stiffness. Comparative analysis of stiffness models In order to validate and compare the homogenisation methods described in the section above, parametric studies, analysing the stiffness matrix of NCF composite laminates were performed for both carbon fibre (CF) and glass fibre (GF). In this case only in-plane elements of the stiffness matrices are considered. Stiffness of the RVE of a cross-ply NCF composite with lay-up [0, 90]s, containing nine ‘super-elements’ as shown in Fig. 17.13, was calculated using the six homogenisation models described in the previous section. The thickness to length ratio of the RVE in Fig. 17.12 was constant and set to (L90+LM)/t90=10. SOLID185, which is an eight-node structural solid element with three degrees of freedom at each node, was used in all 3D FE models. The number of elements for the 3D FE calculation was 3200 for normal loading and 1600 for shear loading. Plane82 elements were used in the 2D plane stress case. The number of elements was 256.
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Since the RVE is symmetric, only the upper half of the RVE was modelled. The two considered types of boundary conditions were: •
•
Normal loading: the nodes at the two related surfaces (x = 0 and x = Lx or y = 0 and y = Ly), of the repeating element were coupled so that two corresponding nodes experienced the same tangential displacement. Nodes at the top surface were coupled to have equal displacement in z-direction. Strains εxRVE = 1% and εyRVE = 0 were applied. Shear loading: the same coupling conditions as already described for normal loading were applied. In addition, coupling of nodes at related surfaces in thickness direction was applied, so that two corresponding nodes experienced the same displacement in the out-of-plane direction (z-direction). In this case a tangential displacement of 0.25% of the side length of the RVE was applied to each side’s surface resulting in a total of 1% engineering shear strain.
The elastic properties of constituents and bundle properties for selected fibre content in the bundle Vf = 55% were calculated using the CCA model described in 17.2.1. The results and also the average layer properties for a given bundle content in the layer Vb are given in Table 17.4. Two values of Vb were used (50% and 80%) the former corresponding to very distinct resin regions between bundles, whereas the latter is with small resin pockets. First the effect of boundary conditions at the top surface on the stiffness was analysed using the 3D FE model. The coupled node boundary condition (the same z-displacement for all nodes), which simulates a periodic lay-up in the thickness direction was compared with free surface condition. The results for CF cross-ply composite (Vb = 0.5) presented in Table 17.5 show that the model becomes stiffer if the nodes are coupled on the top surface. The difference is, however, in most cases negligible. Nevertheless, in the following, for the sake of consistency, the coupling on the top surface will be used for all relevant FE models dealing with stiffness predictions.
Table 17.4 Material properties used in the numerical analysis Carbon fibre
EL [GPa] ET [GPa] GLT [GPa] GT3 [GPa] νLT νT3
Fibre
Fibre bundle Vf =0.55
230 30 20 12 0.2 0.25
128.1 10.36 3.66 3.67 0.269 0.407
Hom. layer V af =0.275 Vb =0.5 65.81 6.21 2.09 2.07 0.317 0.498
Glass fibre Hom. layer V af =0.44 Vb =0.8
Fibre
Fibre bundle Vf = 0.55
103.2 8.42 2.89 2.92 0.288 0.442
76 76 31.1 31.1 0.22 0.22
43.4 12.61 3.9 4.59 0.28 0.374
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Table 17.5 Effect of boundary conditions applied to the surface of the representative volume elements on stiffness elements calculated using a three-dimensional finite element model
Q11 [GPa] Q12 [GPa] εx 1,3,7,9 εx 2,8 εx 4,6 εx 5
3D finite element model Free top surfaces nodes
3D finite element model Coupled top surfaces nodes
36.405 2.008 0.877 1.123 0.796 1.204
36.555 2.106 0.902 1.098 0.848 1.153
From Tables 17.6 and 17.7, it is obvious that all homogenisation techniques predict the stiffness of the laminate with accuracy sufficient for practical needs. The iso-strain model gives the highest stiffness of all models. This is due to the very rigid constraint that all mesoelements have the same strain as the RVE strain. The partial iso-strain model, on the other hand, allows the different ‘superelements’ to have a unique strain in each super-element belonging to the same row or column and the model becomes less stiff compared to the iso-strain model. Nevertheless, the partial iso-strain model is still stiffer than the 2D FE model, partially due to the assumption that each super-element after deformation of the laminate retains its rectangular shape. Homogenisation over only the 0° layer using 3D FE Hom-0° model generally gives lower stiffness than the most accurate reference 3D FE-model with bundle structure. Homogenisation over only the 0° layer using 3D FE Hom-0° model gives higher stiffness than homogenisation over all layers (CLT). A general observation from these results is that the stiffness in the NCF composite is slightly overestimated if models based on ‘super-elements’
Table 17.6 Stiffness of a [0, 90]s carbon fibre non-crimp fabric composite, according to different homogenisation models Stiffness [GPa]
Vb=0.5 Q11 Q12 Q66 Vb=0.8 Q11 Q12 Q66
3D finite element
3D finite element Hom-0°
Classical laminate theory
Isostrain
Partial Iso-strain
2D finite element
36.555 2.106 2.115
36.553 2.046 2.095
36.355 1.989 2.090
36.847 2.154 2.469
36.775 2.126 –
36.646 2.099 –
56.299 2.505 2.911
56.297 2.473 2.895
56.190 2.441 2.890
56.522 2.546 3.183
56.491 2.534 –
56.461 2.528 –
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Table 17.7 Stiffness of a [0, 90]s carbon fibre non-crimp fabric composite according to different homogenisation models Stiffness [GPa] Vb=0.5 Q11 Q12 Q66 Vb = 0.8 Q11 Q12 Q66
3D finite element
Classical laminate theory
Iso-strain iso-strain
Partial
15.78 2.372 2.177
15.466 2.181 2.144
16.356 2.556 2.591
16.039 2.413 –
23.27 3.034 3.06
23.074 2.92 3.019
23.74 3.19 3.377
23.58 3.12 –
are used. The calculated stiffness increases when more constraint on deformation is applied. The sequence of models is: 2D FE, partial iso-strain; iso-strain. Models based on homogenisation replacing the bundle mesostructure by a homogeneous layer with the same average fibre content give the lower bound to stiffness. More homogenisation (CLT model) leads to lower stiffness. Comparing carbon and glass fibre composites, we see that carbon fibre composites show less ‘dispersion’ in results than glass fibre composites regarding the different homogenisation models. This is not surprising since the deformation of the NCF laminate in a given direction is mostly controlled by longitudinal properties of bundles in this direction, which means that higher-stiffness carbon fibre bundles are controlling the stiffness of the laminate to a higher degree than bundles with lower stiffness in the glass fibre composite case. It must be noted that the discussed differences between model predictions are very small in and, in most of the practical cases, they are negligible. Thus, any of the described models has sufficient accuracy for stiffness prediction.
17.3
Strength models for non-crimp fabric (NCF) composites
Whereas in-plane stiffness may be readily predicted with rather high accuracy using conventional engineering models as described previously, prediction of strength properties is unfortunately not as straightforward. However, if considering NCF structures as being semi-laminar, the possibility of applying conventional laminate theory models appears. Certainly, successful use of these models relies on correct idealisations of important micro- and mesofeatures that governs ‘ply strength’. In this section, a semi-laminar analysis regarding compressive strength, and a combined micro–meso approach regarding transverse matrix failure within fibre bundles, are presented. Failure criteria for prediction of bundle strength are also addressed. For information about tensile strength and interlaminar shear strength the reader is directed to papers by Mattsson et al. (2008) and Drapier and Wisnom (1999).
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17.3.1 Compressive strength in the nominal bundle direction Compressive strength of NCF composites has been reported as being as low as half of that in tension, see e.g. Asp et al. (2004). The compressive strength of composites is known to be strongly affected by the material internal structure, see Fleck (1997). The relatively low compressive strength of NCF composites compared to tape-based composites has been analysed in detail by Edgren (2006). The main reason for the low compressive strength is the heterogeneous mesoscale structure, especially fibre tow waviness, of NCF laminates. The dominating mechanism of compressive failure is plastic fibre microbuckling, as described by Fleck (1997). This mechanism is plastic shear instability, where initially misaligned fibres cause shear strains to localise in a small region. Fibres fail into small segments, which rotate under increased load. The fibre segments form a band, called kink band, with fibre segments rotated an angle (φ0+φ) from the main fibre direction. The kink band grows at an angle β to the fibre direction. Fleck and Budiansky (1990) derived an expression, Eq. 17.4, for the response of a kink band in a rigid, perfectly plastic material to remote loading by axial compressive stress and shear stress, as illustrated in Fig. 17.14. [17.4]
17.14 Schematic of fibre bundle waviness and kinking failure in NCF composites, from Edgren (2006).
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where σ ∞x is the remote longitudinal stress in the composite, τy is the composite shear yield strength, τ xy∞ is the remote shear stress in the composite, φ0 is the initial fibre misalignment, φ is the additional fibre rotation caused by the remote loading and , where β is the kink band angle (see Fig. 17.14) and σTy is the yield stress in pure transverse tension. Edgren et al. (2006) suggested a method that allows the criterion by Fleck and Budiansky, Eq. 17.4, to be used on the homogenised laminas in the L-T system, using e.g. CLT. Here the criterion is applied to the composite material within fibre tows. The criterion in Eq. 17.4 is applied in the L-T system, following the crimped fibre tow, see also the criterion suggested by Joffe et al. (2005). Assuming linear elastic response, Eq. 17.4 is rearranged to instead be applicable in the lamina coordinate system, L-T: [17.5] In Eq. 17.5 σL and τLT are the stresses acting on the NCF composite lamina. σc0 and τLT0 are the uniaxial compressive strength and shear strength of the NCF lamina material respectively. Hence, Eq. 17.5 allows the strength parameters needed to be determined from tests on the NCF composite, and not its constituents. Nevertheless, since the manufacturing parameters affect the material structure, and thus its properties, measurements on isolated individual plies may still be difficult. As discussed earlier, design parameters, i.e. ply strength and constitutive properties, depend on the NCF composite architecture. Consequently, ply strength must be measured for the material configuration in which it will be used (the same NCF process parameters and same composite lay-up). That is, e.g. the axial compressive ply strength data for a quasi-isotropic (QI) laminate must be achieved for the QI laminate, made from e.g. biaxial NCF blankets, and not from UD compression tests as advisable for laminated composites made from prepregs. In a first attempt to determine the strength parameters in Eq. 17.5, tests were performed on the QI laminate, loaded in compression parallel to the 0° tow plies. Through CLT the longitudinal compressive strength, σc0, of the ply material was calculated. Here it was assumed that failure of a compression loaded QI specimen is governed by the strength of the most highly loaded ply, in this case the 0° ply. Furthermore, compression tests were performed on specimens, which were cut at five different off-axis angles, θ, (angle between specimen longitudinal loading direction and 0° fibre direction); θ = 0°, 5°, 10°, 15° and 20°. In these specimens, the 0° layer becomes the θ layer and remains the highest loaded ply. Failed specimens for all off-axis angles are presented in Fig. 17.15. The pure shear strength, σLT0, was determined using an in-plane shear test in compression. This test was performed on cross-ply laminates, rotated 45° to the direction of loading. Results from all tests are plotted in Fig. 17.16.
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17.15 Overview of the off-axis QI-laminate test specimens failed in compression.
17.16 Stresses in 0° plies at specimen failure. Stresses calculated with CLT. Failure criterion according to Eq. (17.5) plotted with dashed line, from Edgren et al. (2006).
As shown in Fig. 17.16, the experimental results are in fair agreement with the criterion. The criterion expressed in Eq. 17.5 requires measurement of two strength parameters: the uniaxial compressive strength and the shear strength of the kinking lamina. However, the criterion is only valid if fibre kinking drives failure. Tested off-axis specimens, with 0° to 20° off-axis angles, all failed by fibre kinking. However, the specimens subjected to pure shear did not. Obviously, it is hard to think of a pure shear test that would result in fibre kinking. For this reason, no shear strength measured with such a test, e.g. Iosipescu or ±45° tensile or compression tests, will be physically meaningful for validation of the criterion. Consequently, the off-axis compression tests are employed to determine the strength parameters σc0 and τLT0. Figure 17.17 illustrates the derivation of these parameters following a best-fit procedure of the criterion in Eq. 17.5. A linear fit through the four experimental points deviates slightly from the dashed line, see Fig. 17.17. This thus implies that the longitudinal compressive strength, σL0, is
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17.17 Linear fit to experimental values compared with prediction from criterion, from Edgren et al. (2006).
underestimated by an ordinary compression test. This is supported by observations on tubular specimens by Jelf and Fleck (1994). Extrapolation of the linear fit through the off-axis points yields longitudinal compression strength of −1042 MPa. This is approximately 10% higher than the compressive strength retrieved from the 0° compression test. Likewise, extrapolation to the shear axis yields that the shear strength is slightly overestimated by the in-plane shear test. The extrapolated shear strength is approximately 6% lower than the measured shear strength. In conclusion, off-axis tests provide a way for measurement of the strength input parameters required to predict compressive strength of NCF composites using Eq. 17.5. Based on these results, it is recommended that off-axis tests be used for determination of strength parameters in the criterion.
17.3.2 Strength transverse to the fibre direction Combined micro-meso approach for prediction of transverse matrix crack initiation Damage initiation and evolution in NCF composites leading to final failure includes a multitude of mechanisms and phenomena on several length scales. Usually they are considered as isolated from each other or the interaction is described in an approximate way. Powerful numerical and analytical tools are used to understand the phenomena and to quantify their effect on performance. From an engineering point-of-view, however, a computational scheme for NCF composite structures where all mechanisms would be explicitly present and analysed is too complex and time consuming. Rapid methods for macroscopic
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performance prediction of NCF composites, with limited input regarding mesoscale details, are requested. Obviously it becomes more crucial when dealing with large structures. As discussed previously in the introduction, an elaborated methodology for the gathering of the relevant input data and for the multiscale analysis is currently not available. This chapter is aimed at formulating some guidelines and recommendations to create it. The following discussion is focussed on matrix failure (MF, sometimes also referred to as inter-fibre failure, IFF) where the damage is initiated and propagates in the matrix or at the fibre/matrix interface. Since it is expected that, at least in the near future, shell elements will still be the number-one choice for analysis of composite structures, we have to accept that a layer of NCF composite, which consists of oriented bundles and a small amount of stitches in the thickness direction, in the modelling will be replaced with an ‘effective’ (equivalent in terms of performance and its effect on the composite plate) UD composite layer with effective stiffness and failure properties. The efficiency of this approach for stiffness determination was demonstrated in Section 17.2. The problem with strength properties of the effective UD layer is much more complex and has to involve analysis on two length scales. Direct measurement on isolated lamina in the NCF composite is not feasible. It does not represent the performance of this layer in the composite in a correct way: due to the mesostructure (bundle structure etc.) the stress state in bundles strongly depends on the interaction with surrounding layers of bundle mesostructure. For example, a single layer with a bundle mesostructure loaded transverse to the bundle would have constant stress in any cross-section (iso-stress model). In NCF laminates this layer is surrounded by other layers with high stiffness in the considered direction, and it is more like an iso-strain than iso-stress case. Certainly, modelling cannot replace all tests, and experimental failure data for the used fibre/ matrix/interface system are still required. At one representative volume fraction of fibres they could be gathered using UD composites with non-bundle structure (rather uniform fibre distribution) or even by testing of single-layer NCF composites, assuming that the mechanisms are the same, they are known and described by easy-to-use models. If the previous applies, the properties of more complex NCF composites of the same material may be calculated, based on the above experimental data. For example, each bundle in an NCF composite has several thousand fibres and can be considered as a UD composite with fibre volume fraction higher than the average. Therefore, the bundle MF strength is expected to be different to the one obtained in the test with the UD composite having the same fibre/matrix/interface system. At this stage the knowledge obtained from micromechanism analysis on the fibre/matrix scale has to be used to suggest simple expressions to recalculate the tested UD composite strength to the bundle strength in the NCF composite. The procedure is rather straightforward if the failure initiation mechanism has not changed due to increased fibre content. This is expected to hold if the fibre content in UD
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composite test is not too different than in the bundle. This procedure is analysed in the following section. In the next step of the bundle strength determination, the effects leading to higher strength of a layer in composite than in an isolated layer have to be accounted for (so called in situ strength, well known as an increased first crack formation strain in thin layers of laminates in tension) (Bader et al., 1979; Flaggs and Kural, 1982). These effects are larger for thin layer composites and the main cause is suppression of surface defect growth in composites and limited defect size due to very thin layers (Berglund et al., 1991). After that, the mesoscale failure analysis takes place. According to the above discussion we have defined that the effective layer strength is equal to the in situ MF strength of the bundle. Failure criteria based on the average stresses acting on the fracture plane in the bundle may be used. It has to be realised that the average strain/ stress in the bundle is different than in the corresponding layer with uniformly distributed fibres. These differences and the way to describe them are discussed in the following section. Analytical expression for evaluation of the average strain in a bundle at given applied macrostrain are presented. The bundle geometry, its volume fraction in the layer and elastic properties of the bundle and surrounding layer (bundles) are the most significant parameters. The effect of stitches would be best described by their effect on bundle geometrical parameters and on the stress state applied to the bundle. 3D stress state (out-of-plane stresses) may be introduced also by non-uniform out-of-plane bundle alignment in adjacent layers and by complex geometry of the loaded structure. Obviously, MF due to high distortional or dilatational stresses may occur also in the matrix pockets between bundles or, due to stitching, transverse shear or tensile cracks at the bundle/matrix interface may appear. These damage modes and interbundle delamination are not analysed in this chapter. The failure criteria used for bundle failure analysis are discussed in the next section. A critical analysis of available criteria is presented and their strength, problems and weaknesses are revealed. On all scales, thermal stresses due to mismatch in thermal expansion coefficients have to be accounted for. Microscale strength modelling A detailed analysis is performed considering FE RUC representations of an NCF bundle microstructure. A triaxial stress state is built up from the combined contributions of mechanical loading, thermal shrinkage after curing at elevated temperature, as well as cure shrinkage due to a volume change during the chemical reaction in the manufacturing process. In this step, a suitable failure criterion and thermo-elastic properties of the neat matrix are needed. The strategy will be to utilise commonly used failure/yield criteria for isotropic polymers, in order to predict failure initiation in the matrix. The von Mises theory is widely accepted as most suitable in predicting the failure of isotropic ductile materials under multiaxial stress. However, it should be noted that this formulation does not allow
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for different strengths in compression and tension and is therefore unsuitable for materials with this feature. For materials that display different yield stresses in tension and compression, such as glassy polymers, this difference is attributed to the effect of hydrostatic stress on shear-driven yielding. Therefore, the classical yield criteria, e.g. von Mises and Tresca, have been modified to account for this effect, e.g. by Bowden and Jukes (1972). They suggested the following modified von Mises criterion: [17.6] Whereas the modified Tresca criterion is given by [17.7] P is the hydrostatic stress according to P = (σ1 + σ2 + σ3)/3. k0 is the shear yield stress in absence of any overall hydrostatic pressure and µ is a parameter needed to be determined from experiments. For the Tresca criterion, the principal stresses must be ordered σ1 > σ2 > σ3. Another, slightly different, pressure dependent form of von Mises criterion was presented by Raghava et al. (1973) and it reads: [17.8] There are several strategies of how to obtain the unknown parameters (k0, µ, A and B) in these expressions. The most convenient would be that of performing uniaxial tension and compression tests, resulting in the parameters shown in Table 17.8. In Table 17.8 σyt and σyc are the yield strengths in uniaxial tension and compression respectively. Although these models are intended to be used on homogeneous isotropic materials, several studies, usually in conjunction with
Table 17.8 The parameters in Eqs. (17.6–17.8) as determined by uniaxial tension and compression tests Criterion
k0
A
B
Modified von Mises
−
−
Modified Tresca
−
−
Raghava
−
µ
−
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micromechanical approaches, utilising these criteria to predict onset of matrix failure in composites have been conducted. For instance, Asp et al. (1996) used von Mises criterion and the dilatational energy density criterion to predict failure initiation in the matrix within a GF/EP composite. The criterion first to reach its critical value in any point of the matrix was assumed to initiate failure. Asp et al. assumed different periodical fibre packing arrangements and conducted FE investigations to locate the critical zones in the matrix. A similar approach to the one by Asp et al. (1996) is the so-called strain invariant failure theory (SIFT) proposed by Gosse and Christensen (2001). For more detail of this approach the reader is also directed to the papers by Tay et al. (2005; 2006). For the purpose of analysis of local stresses and strains within bundles loaded in transverse tension and compression, a micromechanical study was conducted using the commercial FE code ANSYS®. Two fibre packing arrangements were analysed: square and hexagonal. For each case a parameterised RUC was constructed (shown in Fig. 17.18) so that volume fraction and number of elements could be easily altered. Due to the uniformity and symmetry of the fibre packing arrangements, all quantities averaged over RUC are also averages over the whole RVE: bundle cross-section in the NCF composite. The matrix is assumed to be perfectly bonded to the fibres throughout the analysis. Both matrix and fibres are assumed to be linearly elastic with properties according to Table 17.1. Thermal residual stresses were introduced by cooling from 180°C to room temperature (RT). The matrix modulus was adjusted during this step to fit the average 1% strain secant modulus in the temperature interval as determined by means of DMTA, resulting in an ‘average modulus’ of 2.5 GPa to compensate for the softening of the matrix at high temperatures. The 1% strain secant modulus (as determined at RT, see Table 17.1) was then used in a subsequent calculation step when mechanical loading was applied. The strain introduced due to the chemical reaction during curing is treated in an effective way: the thermal expansion coefficient is chosen slightly higher than what is normally measured on a standard epoxy polymer (EP). Obviously, this approach is a rough approximation, and a more accurate analysis may be performed by using a nonlinear material model, including viscoelastic effects and cure kinetics. The used element type was SOLID45, which is a 3D structural solid element defined by eight nodes having three degrees of freedom at each node. One element was used in fibre direction, and generalised plane strain condition was constructed by coupling of nodes on the surfaces perpendicular to that direction. Mechanical strain was introduced by applying, over the right edge of the RUCs in Fig 17.18, a constant displacement. Over the top surface, constraint was applied to ensure a straight line after deformation (coupling of nodes in three directions on the top surface). Thus, transverse matrix failure initiation was calculated, considering both thermally induced stresses and the imposed mechanical load for a fictive CF/EP composite with fibre and matrix properties, according to Table 17.1. The modified Tresca criterion, using matrix strength properties σyt = 82 MPa and σyc = 128 MPa,
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17.18 Hexagonal and square fibre arrangement used in the micromechanical analysis. Due to symmetry only a quarter of the RUCs are modelled.
was applied to square and hexagonal packed fibre arrangements giving the results for bundle scale strain at failure initiation shown in Fig. 17.19. The assumption was that failure initiation occurs when the stress state becomes critical for a single element. It has been checked, however, that the localised stress state in elements surrounding the failed element have approximately the same stress level, so that the results are not the product of any mesh artefacts. The stress in the bundle at failure initiation, displayed in Fig. 17.20, was calculated from failure strain using fitting expressions for elastic properties of the square and hexagonal RUCs shown in Figs. 17.5–17.7. The results in Figs. 17.19–17.20 reveal some interesting information regarding transverse failure in the assumed fibre arrays. Transverse failure strain in tension is significantly higher for the hexagonal than the square RUC, especially for high fibre volume fractions. Transverse failure stress in tension is also higher for the hexagonal RUC. Furthermore, it is rather constant up to Vf = 0.7. In compression both types of RUC seem to be significantly underestimating the ultimate strength (as normally measured on UD plies). Obviously, this is due to the fact that the criterion may only predict onset of yielding on a very localised scale. For macroscopic ply rupture, additional stress, reflecting crack growth processes and further matrix yielding would be required. This additional stress will be much less significant under tension compared to compression, since the typical neat epoxy matrix is failing in a brittle manner under tension (with typical macroscopic failure strains of 5%). In compression, on the other hand, extensive yielding and very high local strains are expected (macroscopic strains for a typical neat epoxy matrix may reach over 50%).
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17.19 Transverse failure strain initiation for the two fibre arrangements loaded in tension and compression.
17.20 Transverse failure stress initiation for the two fibre arrangements loaded in tension and compression.
Certainly, the absolute values for failure presented here, which depend on the chosen input parameters in the Tresca criterion, may be rather different compared to experimental observations. Some epoxy systems are better described by modified von Mises type of criteria, and some systems by the modified Tresca criterion. For example, it appears reasonable to use a yield criterion, such as modified Tresca, which is based on a directional parameter (maximum shear stress) when the plastic deformation is localised in shear bands. Conversely, a
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yield criterion, such as modified von Mises or Raghava, which is based on a nondirectional parameter (octahedral shear stress) seems more plausible to use when plastic deformation is diffused throughout the whole material. Furthermore, in this analysis no regard has been paid to the fibre/matrix interface properties, or if the matrix contains manufacturing defects such as voids, etc. Interface failure is usually also observed on the fracture surface and the angle of the fracture surface is about 53°. These features are not related to the initiation discussed here. Finally, the transverse compressive strength may not be accurately captured by this linear elastic ‘initiation’ approach. Average strain in the bundle of the NCF composite If micromechanical strength modelling is used to predict failure within the bundle structure, a suitable approach to link stress/strain between micro-, meso- and macroscale is necessary. FE studies have shown that the transverse strain in a fibre tow may be significantly lower than the strain in the adjacent longitudinal tow or the macroscopic applied strain in the same direction. Hence, the approaches using any kind of iso-strain assumptions are inadequate. A more accurate model to predict the average transverse strain in the bundle was developed by Mattsson and Varna (2007), analysing by FE the importance of media surrounding the 90° bundle in cross-ply composites. The simplified mesoscale structure with rectangular cross-section bundles shown in Fig. 17.21 was used and plane strain analysis performed. The same volume fraction Vf of fibres in the bundle and the bundle volume content in the layer as for the initial non-idealised mesostructure Vb was retained. Certainly, this procedure affects the stress distribution introducing artificial stress concentrations close to the bundle corners and interfaces, but it has minor significance when the average in-plane strain in a bundle is analysed. The boundary conditions and the deformed shape of the bundle/resin interface are schematically shown in Fig. 17.22. 0°-layer thickness in these calculations was equal to the 90° layer thickness. Some results at 1% applied strain to the composite are presented in Table 17.9. Calculations were performed for two boundary condition cases on the top surface: ‘free nodes’ where the surface was free, and ‘coupled nodes’ where the displacements in z-direction of the surface nodes were coupled. The average strains in the bundles are insignificantly higher when nodes are coupled. This study showed that an increase of the 90° bundle to matrix stiffness ratio leads to a decrease of the average strain in the 90° bundle. An increase in the 0° bundle stiffness leads to an increase of the average strain in the 90° bundle. Higher 90° bundle volume fraction in the layer leads to larger average strain in the bundle (it approaches the applied strain value). The influence of these parameters was analysed and fitted by simple expressions. The ratio of transverse strain in the bundle, εba x90, to strain applied to the RVE, εxRVE, was expressed through a power
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17.21 Simplification of mesogeometry.
17.22 Model used for parametric study of interface distortion between 90° bundle and matrix.
Table 17.9 Average transverse strain in bundle at 1% applied strain: [0 90]s Mat.
L90
LM
E0 [GPa]
E90 [GPa]
εbax90 (free nodes)
εbax90 (coupled nodes)
Carbon fibre
8 5 8 5
2 5 2 5
128.1 128.1 43.4 43.4
10.36 10.36 12.61 12.61
0.92 0.866 0.882 0.797
0.927 0.874 0.894 0.813
Glass fibre
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Table 17.10 Average transverse strain in the bundle dependent on its geometry: [0 90]s
Material
E90 (L90+LM)/t90=8 L90/t90 LM/t90 E0 (GPa) (GPa)
Carbon fibre 5 Glass fibre 5
5 5
128.1 43.4
FEM 10.36 0.839 12.61 0.769
Model 0.833 0.746
εbax90 (free nodes) (L90+LM)/t90=10 (L90+LM)/t90=15
FEM 0.866 0.797
FEM 0.902 0.835
Model 0.911 0.865
Effect of bundle width/thickness ratio
law dependence, and a linear superposition of these separate contributions was suggested for a general case, according to: [17.9] Here, V90/(1 − V90) = L90/LM is the parameter characterised by bundle volume fraction in a layer, see Fig 17.21. E0/E90 is the stiffness ratio between the constraint layer (it has been homogenised) and the transverse modulus of the bundle, whereas EM/E90 is the matrix and bundle transverse modulus ratio. Via the parametric FE study the parameters, B1 = 0.153, B2 = 0.115, B3 = 0.175, k1 = −0.433, k2 = −0.342 and k3 = 0.628 were found as the best fit to the available data. The effect of the bundle shape at fixed Vf and Vb is presented in Table 17.10, showing how, with increase of bundle width/thickness ratio, the average bundle strain approaches the applied strain value. This process is faster in the CF composite because the stress transfer depends on the adjacent layer elastic modulus, which is higher for the CF composite. A model accounting for this effect was presented in Mattsson and Varna (2007). Failure criteria for bundle mesostructures in combined 3D loading The failure theories described in the previous section are restricted to elastically isotropic materials. However, composite plies and laminates have directionally dependent strength, and they have several distinct failure modes. These anisotropic materials display more complex interaction of multiaxial stresses and strains, making the development of reliable failure theories much more difficult. There are theories that have been used with some success, but they are (to the authors’ knowledge) only verified for 2D cases. The most popular models are the so called ‘global criteria’. These usually assume that the failure envelope in a stress or strain space is a single function. Most of these models are belonging to the group of criteria known as ‘interactive failure criteria’. Initial efforts to formulate an interactive failure criterion are credited to Hill (1950). Extension of the von Mises
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criterion to materials with anisotropic properties was presented by Hill (1950) and later applied to composite laminates by Azzi and Tsai (1965). The general form of a majority of these interactive criteria is shown in tensor notation below [17.10] where i = 1,2 . . . 6. Fi and Fij are strength tensors of second and fourth order respectively. Azzi and Tsai (1965) considered an extension of the von Mises failure criterion. The failure bound in terms of the stresses was described by letting Fi = 0 and β = 1. In Tsai and Wu (1971), on the other hand, the failure criterion is represented as a more general quadratic function in terms of stresses according to [17.11] for α = β = 1. For a general anisotropic 3D case, the Tsai-Wu criterion contains 27 independent strength components (6 linear and 21 quadratic terms). For the special case of material symmetry, namely transverse isotropy, which is relevant when analysing the strength within the NCF composite bundle structure, the number of independent strength components reduces to seven (two linear and five quadratic terms). The strength tensor coefficients in Eq. 17.11 may be determined via the engineering strengths from relatively simple test methods, except the so-called interaction coefficients F12 and F23, which require complicated biaxial testing. Most often such data are not available and the criterion relies on an estimation of the interaction coefficients. The single expression, Eq. 17.11, is very attractive to use, since it may be straightforwardly implemented into any commercial FE code. However, as argued by Hashin (1980), the criterion has its shortcomings since it does not distinguish between failure modes and aims to relate all failure modes to a smooth single curve. Hashin also highlighted an obvious problem with the model by showing that failure under biaxial tensile loading would depend on the values of the compressive failure stresses, which is physically unreasonable. Therefore, in attempts to develop more physically reasonable failure theories, which aim to correlate a failure mechanism (failure mode) with the failure envelope, some authors have introduced modal failure theories, see for example Hashin (1980) Feng (1991), Puck and Schürmann (1998, 2002) and Pinho et al. (2005). The premise of such theories is that anisotropic materials may fail by multiple independent mechanisms, therefore, their failure bounds in a stress or strain space are not required to be smooth, but simply piecewise smooth (Hashin 1980). Regarding transverse MF under combined 3D loading, the work by Puck and Schürmann (1998, 2002) and Pinho et al. (2005) is of considerable interest for analysing failure within bundles. In the so called ‘Puck criteria’ the MF criteria are based on Mohr’s fracture hypothesis stating that failure is exclusively created by the stresses acting on the fracture plane. Depending on whether the fracture plane’s normal stress component is tensile or compressive, a possible quadratic criterion for prediction of MF under a general 3D loading condition may be expressed by:
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[17.12]
[17.13] The criteria are solely formulated in terms of stresses acting on the fracture plane which may be calculated by usual stress transformation expressions relating local to global stresses. R is the strength value, with upper index A to clarify that it belongs to the fracture plane (or ‘action plane’). Lower index N is for normal direction to the fracture plane, T represents transverse direction and L longitudinal (fibre) direction (Puck and Schürmann used different notation). Upper index (+) stands for tensile stress and (−) for compressive stress. The parameter p represents gradients of the fracture body (failure envelope) at certain locations. Note that the expressions 17.12 and 17.13 do not exactly correspond to the original ‘Puck criteria’. An advantageous feature of these criteria is that they provide additional information about the failure, such as the fracture plane angle, which may be important for subsequent delamination initiation predictions. The influence of high σ1 (fibre) stresses may be incorporated in two ways: (i) by an additional term in the criteria, or (ii) by modifying the strength parameters R so that they depend on the state of σ1 stress (the rationale behind this is that high fibre stresses might promote localised fibre damage which in turn acts as initiation sites for MF). It is recognised that the criteria, Eqs. 17.12 and 17.13, could be used to predict MF initiation within bundles for NCF composites which, due to the inherent tow waviness, may exhibit rather significant out-of-plane stresses under in-plane loading (Edgren et al., 2004). Furthermore, the expressions are attractive to use, since they allow for a straightforward link between criteria for conventional prepreg laminates and semi-laminar composites like NCFs (considering failure within bundles). The major obstacle to successfully adopting these expressions to NCF composites will be the establishment of the strength parameters R. No tests that can verify the accuracy of the model have ever been designed nor performed for NCF composites. Therefore, relying on test data for glassy polymers under triaxial stress states, an alternative route could be to elucidate these parameters by the use of the micro- and mesomechanical analysis suggested in this chapter. Work on this subject is currently ongoing.
17.4
Conclusions
This chapter comprises methodologies for the gathering of relevant stiffness and strength parameters via multiscale analysis of the NCF composites’ hierarchical structure. It may be seen as a piece of the puzzle in the development of the
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(currently not available) ‘black box modelling tool’. The chapter is intended to formulate some guidelines and recommendations in its creation. Regarding stiffness; it was shown that the stiffness of an ideally straight, transversely isotropic fibre tow, may be calculated either by analytical models or by FE representations of assumed fibre arrangements. By employing knock-down factors due to tow wavelength and amplitude, these results may then be transferred to calculate effective properties of the curved tow. This was demonstrated for tows having out-of-plane waviness (obviously, the tows may also have some amount of in-plane fibre undulation). NCF composite stiffness was then further analysed using approximate methods with different level of complexity: (i) smearing out the bundle structure in a layer, replacing the NCF composite by a laminate using CLT; (ii) assuming iso-strain for all mesoelements; (iii) assuming that the composite consists of ‘super-elements’ and that the stiffness matrix of it can be obtained by the iso-strain assumption for its constituents, thus reducing the inherently 3D stress problem to a 2D problem. It was found that for stiffness calculations all homogenisation methods used in this study have sufficient accuracy considering a 3D FE model as the reference case. The differences between predictions of different models are so small that it is unrealistic to use test results to determine the most appropriate model. Regarding transverse matrix strength: (i) the microscale analysis demonstrated in Section 17.3.3 renders the bundle transverse failure strength as a function of its fibre content. If the experimental values at one volume fraction are known, the parameters in the criteria can be identified and the microscale modelling will give strength dependence on fibre content for this particular fibre/matrix/interface system. This means that; (ii) strength of a bundle in an NCF composite made of this type of composite is known (for all possible stitching procedures leading to all possible bundle contents and fibre contents in the bundle). The elastic properties of the bundle are also known using methods described in 17.2. The in-plane strains applied to the bundle (for a given strain applied to the NCF composite) are also known from the analysis in 17.3.2. Failure analysis may therefore be performed. If layers are thin the strength could be increased by introducing an appropriate ‘in situ’ factor. Finally, (iii) large out-of-plane stress components may be acting on the bundle due to imperfect geometry or structural effects. For this and other reasons more complex failure criteria may be used to predict failure. In this case the data from (ii) are still a necessary input.
17.5
References
Agarwal B.D. and L.J. Broutman (1990). Analysis and Performance of Fiber Composites, second edition. John Wiley & Sons. Asp L.E., L.A. Berglund and R. Talreja (1996). ‘Prediction of matrix-initiated transverse failure in polymer composites.’ Composites Science and Technology 56:1089–1097. Asp L.E., F. Edgren and A. Sjögren (2004). ‘Effects of stitch pattern on the mechanical properties of non-crimp fabric composites,’ Proceedings of 11th European Conference on Composite Materials, Rhodes, Greece.
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Azzi V.D. and S.W. Tsai (1965). ‘Anisotropic strength of composites.’ Experimental Mechanics 5:283–288. Bader M.G., J.E. Bailey, P.T. Curtis and A. Parvizi, (1979). ‘The mechanisms of initiation and development of damage in multi-axial fibre reinforced plastics laminates, Proc. 3rd Int Conf on Mech Behaviour of materials, ICM 3, Cambridge, England, 3:227–239. Berglund L.A., J. Varna and J. Yuan (1991). ‘Effect of intralaminar toughness on the transverse cracking strain in cross-ply laminates.’ Advanced Composite Materials, the Official Journal of the Japan Society for Composite Materials 1:225–234. Bibo G.A., P.J. Hogg and M. Kemp (1997). ‘Mechanical characterisation of bi-directional intraply hybrid laminates.’ Composites Science and Technology 57:1221–1241. Bowden P.B. and J.A. Jukes (1972). ‘The plastic flow of isotropic polymers.’ Journal of Materials Science 7:52–63. Christensen R.M. and K.H. Lo (1979). ‘Solutions for effective shear properties in three phase sphere and cylinder models.’ Journal of the Mechanics and Physics of Solids 27:315–330. Cox B.N. and M.S. Dadkhah (1995). ‘The macroscopic elasticity of 3D woven composites.’ Journal of Composite Materials 29:785–819. Drapier S. and M.R. Wisnom (1999). ‘A finite-element investigation of the interlaminar shear behaviour of non-crimp-fabric-based composites.’ Composites Science and Technology 59:2351–62. Edgren F., D. Mattsson, L.E. Asp and J. Varna (2004). ‘Formation of damage and its effects on non-crimp fabric reinforced composites loaded in tension.’ Composites Science and Technology 64:675–692. Edgren F. and L.E. Asp (2005). ‘Approximate analytical constitutive model for non-crimp fabric composites.’ Composites Part A 36:173–181. Edgren F. (2006), ‘Physically based engineering models for NCF composites’. PhD Dissertation. The Royal Institute of Technology (KTH), Sweden. Edgren F., L.E. Asp and R. Joffe (2006), ‘Failure of NCF composites subjected to combined compression and shear loading’. Composites Science and Technology, 66:2865–2877. Flaggs D.L. and M.H. Kural (1982). ‘Experimental determination of the in situ transverse lamina strength in graphite/epoxy laminates.’ Journal of Composite Materials 16: 103–116. Fleck N. A. and B. Budiansky (1990). ‘Compressive failure of notched carbon fibre composites due to microbuckling’. In: Dvorak G.J. (ed.), Inelastic Deformation of Composite Materials, Springer, New York, 235–274. Fleck N. A. (1997). ‘Compressive failure of fibre composites’. Advances in Applied Mechanics, Academic Press, 43–117. Gosse J.H. and S. Christensen (2001). ‘Strain invariant failure criteria for polymers in composite materials.’ AIAA-2001–1184. Halpin J.C. and J.L. Kardos (1976). ‘The Halpin-Tsai equations: a review.’ Polymer Engineering and Science 16:344–352. Hashin Z. and B.W. Rosen (1964). ‘The elastic moduli of fiber-reinforced materials.’ Journal of Applied Mechanics 31:223–232. Hashin Z. (1980). ‘Failure criteria for unidirectional fiber composites.’ Journal of Applied Mechanics 47:329–34. Hashin Z. (1983). ‘Analysis of Composite Materials – a survey.’ Journal of Applied Mechanics 50:481–505. Hill R. (1950). The Mathematical Theory of Plasticity. New York, Oxford University Press.
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Ishikawa T. and T.W. Chou (1982). ‘Elastic behaviour of woven hybrid composites.’ Journal of Composite Materials 16:2–19. Ishikawa, T. and T.W. Chou (1983). ‘One-dimensional micromechanical analysis of woven fabric composites.’ AIAA Journal 21:1714–1721. Jelf P.M. and N.A. Fleck (1994). The failure of composite tubes due to combined compression and torsion. Journal of Material Science. 29:3080–3084. Jiang Y., A. Tabiei and G.J. Simitses (2000). ‘A novel micromechanics-based approach to the derivation of constitutive equations for local/global analysis of a plain-weave fabric composite.’ Composites Science and Technology 60:1825–1833. Joffe R., D. Mattsson, J. Modniks and J. Varna (2005). ‘Compressive failure analysis of non-crimp fabric composites with large out-of-plane misalignment of fiber bundles.’ Composites Part A 36:1030–1046. Kurath P. and M. Karayaka (1994). ‘Deformation and failure behaviour of woven Composite Laminates.’ Journal of Engineering Materials and Technology 116: 222–232. Lee J.W. and C.H. Harris (1990). ‘A deformation-formulated micro-mechanics model of the effective Young's modulus and strength of laminated composites containing local ply curvature.’ In: Garbo S.P. (ed.), Composites Materials: Testing and Design. ASTM STP 1059. American Society for Testing and Materials. 9:521–563. Marklund E., J. Varna, R.C. Neagu and E.K. Gamstedt (2008). ‘Stiffness of aligned wood fiber composites: effect of microstructure and phase properties.’ Journal of Composite Materials 42:2377–2405. Mattsson D. and J. Varna (2007). ‘Average strain in fiber bundles and its effect on NCF composite stiffness.’ Journal of Engineering Materials and Technology 129:211–219. Mattsson D., R. Joffe and J. Varna (2008). ‘Damage in NCF composites under tension: Effect of layer stacking sequence.’ Engineering Fracture Mechanics 75:2666–2682. Pinho S.T., C.G. Dávila, P.P. Camanho, L. Iannucci and P. Robinson (2005). ‘Failure models and criteria for FRP under in-plane or three-dimensional stress states including shear non-linearity.’ NASA/TM-2005-213530. Puck A. and H. Schürmann (1998). ‘Failure analysis of FRP laminates by means of physically based phenomenological models.’ Composites Science and Technology 58:1045–1067. Puck A. and H. Schürmann (2002). ‘Failure analysis of FRP laminates by means of physically based phenomenological models.’ Composites Science and Technology 62:1633–1662. Raghava R., R.M. Caddell and G.S.Y. Yeh (1973). ‘The macroscopic yield behaviour of polymers.’ Journal of Materials Science 8:225–232. Tay T.E., G. Liu and V.B.C. Tan (2006). ‘Damage progression in open-hole tension laminates by the SIFT-EFM approach.’ Journal of Composite Materials 40:971–992. Tay T.E., S.H.N. Tan, V.B.C. Tan and J.H. Gosse (2005). ‘Damage progression by the element-failure method (EFM) and strain invariant failure theory (SIFT).’ Composites Science and Technology 65:935–944. Tsai S.W., and E.M. Wu (1971). ‘A general theory of strength for anisotropic materials.’ Journal of Composite Materials 5:58–80. Wu Z.J., D. Brown and J.M. Davies (2002). ‘An analytical modelling technique for predicting the stiffness of 3-D orthotropic laminated fabric composites.’ Composites structures 56:407–412.
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18 Aerospace applications of non-crimp fabric composites P. MIDDENDORF and C. METZNER, EADS Innovation Works, Germany
Abstract: This chapter reviews the specific requirements, successful applications and future trends of non-crimp fabric (NCF) composites in the aeronautic sector. Starting from a state-of-the-art overview of composite primary structures, key issues explaining the low usage of NCF today are reflected on, with a focus on the generally inferior damage tolerance performance of resin-infusion-based composites when compared with tough prepreg (pre-impregnated) systems. However, there are at least two major success stories for NCF composites in recent aircraft programmes: the Airbus A380 rear pressure bulkhead and the A400M cargo door. Looking ahead to the challenges of the next generation of composite aeronautic structures, it seems likely that this list will be extended in the near future. Key words: composite, non-crimp fabric, aeronautic, Airbus, damage tolerance.
18.1
Introduction
Due to their superior weight-specific stiffness and strength and their potential for integral design, the use of composites in aeronautic applications is increasing. Some historic milestones are summarised in Gay et al., 2007. • • • • •
Composites made of hemp fibre and phenolic resin used on the British Spitfire aircraft of World War II. Applications of glass fibre/honeycomb-core sandwich fairings since 1950. The development of Boron/epoxy composites for military aircraft structures since the 1960s, with early applications, e.g. for the skin of the horizontal stabiliser box on the American Grumman F–14 Tomcat fighter (Jones, 1998). Increasing use of carbon/epoxy since 1970, Introduction of Kevlar/epoxy in 1972.
In most cases the initial applications were for military aircraft with use in commercial aircraft following quickly. In this industry segment, a steep ramp-up of composite primary structures may be observed during the last decade, see Fig. 18.1. Whilst the share of composite structures in the Airbus A340 was around 17%, this increased to 25% for the A380 and to about 50% for the upcoming A350 XWB. 441 © Woodhead Publishing Limited, 2011
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18.1 Evolution of composite structures within Airbus fleet (Petiot, 2007).
18.2 Composite applications on the Airbus A380 (Airbus, 2006).
The materials and process types of the referenced applications are important in commercial aircraft structures as well as the proportion of composite materials used. Taking the example of an Airbus A380 as shown in Fig. 18.2, the following conclusions may be drawn:
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Besides GLARE,® nearly all applications are carbon fibre reinforced polymer (CFRP), most of them having thermoset matrices. Currently, the base material for the majority of composite parts is prepreg, with only a few exceptions in resin infusion technology. Amongst these few applications, most are non-crimp fabric (NCF) composites (see also section 18.3).
18.2
Aeronautic requirements
In aeronautic primary structures, impact is the most critical load case consideration for liquid moulded composite materials because the infusion resins are optimised for effective processing, e.g. low infusion viscosity and extended pot-time. Therefore, the toughening of the matrix is decreased when compared to the impact tolerance of, e.g., modified prepregs. Because the reinforcement fibres in laminates manufactured by vacuumassisted resin transfer moulding (VARTM), RTM or resin film infusion (RFI) processes are the same as those used for prepreg, the in-plane mechanical performance is almost equal. The performance shortcomings of liquid moulded composites can be shown in their out-of-plane properties, such as impact resistance. The respective dynamic loads generate enlarged areas of damage within infusion materials when these are compared to prepreg. This is caused by the brittle matrix behaviour as shown in Plate XII (see colour section between pages 396 and 397) in the example of the C-scans of post-impact specimens (150 × 100 mm2, thickness 4 mm, quasiisotropic stacked, impact load 30 J) manufactured with NCF/standard infusion resin (epoxy) and standard prepreg tape. Tests show the residual compression strength of the unmodified infusion material to be about 35% lower than the prepreg performance, caused as illustrated by an area of damage which is 3.5-times larger. Several approaches are being developed for countering the decreased damage tolerance. Highly undulated textiles, e.g., woven or conventionally braided, are inherently more damage-tolerant compared to NCFs or unidirectional (UD) materials. Use of highly undulated reinforcement fibres prevents the growth of cracks, whilst dynamic out-of-plane loading leads to much smaller areas of damage. Despite shortcomings in the in-plane compression strength of highly undulated textiles, the residual performance after higher impact loads (>30J) is usually better than the properties of NCF or of UD material, due to decreased areas of damage. The modification of liquid resin infusion materials with low- or no-fibre crimp, produces promising results by the insertion of inherently tough particles into the matrix system. The mainly thermoplastic-based particles, e.g., polyamide or polyethersulfone, can be inserted as a fleece, powder binder or thin yarn into the textile preform. These toughening agents modify the brittle interfaces of the
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18.3 Residual compression strength and delaminated areas against impact energy.
composite material after the resin infusion process in which cracks occur during impact. The reduced areas of damage lead to increased residual strength following impact, as presented in Fig. 18.3. Besides the damage tolerance performance, which is more resin-related, further specific requirements for aeronautic applications with respect to NCF composites are: formability for high curvatures and low area/weight relationship for skin lay-ups. The formability of dry textiles is one of the interesting benefits of liquid moulding technology. Prefabricated textiles such as NCF and woven or braided materials can be draped into complex two dimensional curved moulds without any fibre crimp or folds which could affect mechanical performance. During draping, the dry textile, for example biaxial NCF, is deformed in a shear mode so that the reinforcement fibre orientation and area/weight relationship may be partly changed. These parameters can be simulated or measured and have to be taken into account during the design stage. The formability of NCF is affected by the stacking sequence, ply area/weight relationship, fibre type and the tension and stitching pattern of the consolidation stitching yarn. An inserted binder may be used to fix the textile preform into the default geometry. This binder may be inserted between each processed ply or as a preliminary in the textile. Preliminary binder insertion improves the stability of the textile preform, but decreases formability due to blocking the shear performance of the fibre plies. The complex draping process is performed manually, but full automation will be feasible in the near future. This will significantly reduce lead time and costs, so improving consistency and quality assurance. Further benefits can be achieved with a low area/weight relationship per ply. State of the art in NCF technology is about 130 g/m2 per C-fibre ply which gives a minimum laminate thickness of less than 1.0 mm (quasi-isotropic symmetrically
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stacked laminate at 60% fibre volume content). Weight savings can therefore be achieved through adapting laminate orientation and thickness.
18.3
Application examples
18.3.1 Airbus A380 rear pressure bulkhead The first application of a composite rear pressure bulkhead (RPB) in a commercial aircraft was on the Airbus A340–500/600. Whilst the conventional A340 concept was based on prepreg fabric, the next generation has been developed with textile technology using carbon NCF, which has been applied on the A380, in which it was used for one of the biggest aeronautic NCF composite parts. The pressure bulkhead is a load-bearing primary structure which separates the pressurised fuselage from the non-pressurised rear section (see Fig. 18.2). Due to the nature of the internal pressure load, it is designed as a membrane structure with integrated stiffeners. In addition to the pure structural requirements such as stiffness and strength, the design must also meet strict fire, smoke and toxicity specifications. The A380 RPB is produced at the Airbus plant in Stade, near Hamburg. The preform is made from multiaxial carbon fibre NCF supplied by Saertex. For preform integration and handling, a gantry sewing machine is used to join the dry fabrics by blind stitching, finally forming an eight-metre-wide carpet. This preform is draped over a positive mould and then laminated using the resin film infusion (RFI) process (Fig. 18.4). After an initial curing of the 3 mm thick basic laminate
18.4 Draping of the non-crimp frabric carpet in the Airbus A380 Rear Pressure Bulkhead production.
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and the attachment of stringers, the part is finally cured in an autoclave. The finished bulkhead weighs about 240 kg and is 6.2 metres by 5.5 metres in size. Airbus, EADS Innovation Works, Saertex GmbH and KSL Keilmann GmbH cooperated closely on the research, development and production of the A380 pressure bulkhead (EADS, 2004).
18.3.2 Airbus A400M cargo door The rear cargo door of the pressurised fuselage of the new Airbus Military transport aircraft A400M, is within 7 × 4 metres of the dimensions of the A380 rear pressure bulkhead. It also consists largely of multiaxial carbon NCF with additional UD fabric for local reinforcements and skin lay-up. But in contrast to the RFI process of the RPB, the A400M cargo door is processed without an autoclave, using the EADS/Premium Aerotec patented vacuum-assisted process (VAP) infusion technology (Fig. 18.5). Completed layers are placed into the mould directly from the roll and reinforcement layers are cut by an NC cutter, then positioned using laser projection. The skin has 16 stringers on the inner surface which are infiltrated and cured in one shot, together with the skin lay-up. The fully integrated design saves around 3000 joint elements in the consequent assembly process. This reduces lead time and costs, together with a significant weight improvement (PAG, 2009). As well
18.5 Airbus A400M Cargo Door manufactured at Premium Aerotec, inside view.
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18.6 Airbus A400M Cargo Door, outside view.
as the stiffened skin, the frames and the central beam are made of NCF and UD layers for local reinforcement of the upper flange. These parts are manufactured in a female mould as the exterior dimensions are important in the assembly process (Fig. 18.6). The A400M cargo door is manufactured at Premium Aerotec site, Augsburg and received the JEC Innovation Award in 2009.
18.3.3 Further applications on sub-structure level Besides the large-scale structures described above, there are some additional aeronautic applications on the sub-structure level. For commercial aircraft, these are principally the Airbus A380 flap track CFRP parts such as diaphragms, side shells and straps which are manufactured with NCF/epoxy infusion resin in VAP technology by Premium Aerotec. For helicopter composite airframes and business jet primary structures, smaller components made of carbon NCF are already in production or in the preparation phase.
18.4
Future trends
In common with other branches of industry such as automotive or wind energy, the challenge in the application of composite materials in future aeronautic structures will consist mainly of cost reduction when compared with state-of-the-art
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prepreg technology. The volume of production will have to increase to meet the demands of the next generation commercial aircraft programmes. NCFs in combination with a highly automated production line (cutting, handling, draping, performance fixation) have the potential to offer many advantages. As mentioned in Section 18.2., an important prerequisite for the increased application of this technology is the improvement of the damage tolerance behaviour of NCF/epoxy infusion resin systems. The insertion of thermoplastic particles into the textile preform is promising in this respect, but several issues must be taken into consideration when incorporating these materials into future aircraft structures. • • •
Toughening particles inserted into the textile raw material, e.g., as a powder binder, may reduce the formability due to the decreased textile shear performance of the C-fibre filaments. During the infusion process, potential washout or preliminary dissolution in the resin may occur. This is not acceptable as homogeneous material properties need to be ensured. Some thermoplastic toughening agents tend to absorb water. In combination with a decreased glass transition temperature, this may cause shortcomings in the laminate performance under hot/wet conditions.
Most of these issues can be addressed by selection of materials and improvement of the insertion approach, so as to generate high-impact resistant laminates with small delaminated areas which have high in-plane compression properties. This results in high residual strength even under hot/wet conditions. Promising, stateof-the-art toughening agents offer the possibility of inserting high-temperature melting polyamide fleece between each C-fibre ply. Performance regarding the delaminated area and residual strength is presented in Plate XII and Fig. 18.3.
18.5
References
Airbus Material Dialogue, Bremen, 2006. EADS Corporate Media, International Air Show ILA, Berlin, 2004. Gay D, Hoa S V (2007), Composite materials: design and application, 2nd ed, Boca Raton, CRC Press. Jones R M (1998), Mechanics of Composite Materials, 2nd ed, New York & London, Brunner-Routledge. Petiot C (2007), Design of High-performance Composite Structures – State-of-the-Art, and Challenges, in Guedra-Degeorges D & Ladeveze P (eds), Course on Emerging Techniques for Damage Prediction and Failure Analysis of Laminated Composite Structures, Toulouse, Cepadues Editions. Premium Aerotec, Premium Aerotec wins JEC 2009 Innovation Award, Press release, 2009.
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Plate XI Parameters for the delamination interface model for materials NCF/LY3505 (* estimated) (Chapter 16).
Plate XII C-scans of impacted non-crimp fabric and prepreg specimens (30J) (Chapter 18).
Plate XIII Typical blade layout IEC class II 40m blade detailing the laminate constructions based on non-crimp fabric reinforcement materials (Chapter 21).
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19 Non-crimp fabric: preforming analysis for helicopter applications F. DUMONT and C. WEIMER, Eurocopter Deutschland GmbH, Germany
Abstract: This chapter deals with the preform manufacturing stage of non-crimp fabric (NCF) reinforced composite. An introduction is given to the concept of tailored reinforcement (TR), together with an overview of the forming techniques for NCF reinforcement with respect to quality. The main deformation modes of dry NCFs are presented. Finally, a description of the main defects occurring during preforming is given. Key words: non-crimp fabric, forming, preforms, deformation modes, defects.
19.1
Introduction
Characterised by high development efforts and medium production volumes, the aeronautical industry will ensure its competitiveness with an improved time and cost to market. Efficient lightweight design of composite parts will become a key factor to enhance the mechanical performance, to ensure weight saving and to achieve cost and fuel efficiency for aircraft and helicopters, it also makes an important contribution to facing rising environmental challenges. Carbon fibre reinforced polymer composites (CFRP) are state-of-the-art in high-performance helicopter structures such as airframes, empennage, or rotor blades. Eurocopter's TIGER and NH90 structures largely consist of CFRP materials (Weimer and Dumont, 2009). Currently, the majority of structural parts consist of prepreg materials made of hand lay-up and cured in autoclave. Cost drivers are hand-work, autoclave usage and quality control respective inspection. The future success of new helicopter programmes strongly depends on developing costefficient manufacturing methods as well as on optimising concurrent engineering processes for complex CFRP parts. A promising process type is liquid composites moulding (LCM) based on preform resin impregnation. Processes such as resin transfer moulding (RTM), or vacuum-assisted process (VAP) allow for automation, out-of-autoclave curing and online quality management (OQM). The quality of the part is firstly determined by the preform preparation.
19.2
Preform techniques for non-crimp fabrics (NCFs)
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and thus reduces the possibility of process automation. In addition, autoclave curing, which is mandatory for high-performance prepreg parts, is long and expensive (Åström, 1997). With preforming and liquid resin infusion, faster cycle times and a higher degree of automation are achievable. Preforms are often manufactured from woven fabrics. The yarns of available woven fabrics are usually oriented in a 0° and 90° direction (Haberkern, 2006). The need for fibres with 45° orientation in most structural applications increases the material cut-off and impedes a continuous manufacturing process. Another drawback of woven fabrics is their reduced mechanical properties due to the nonlinearity of the tensile behaviour caused by the crimp of the fibres (Hamila and Boisse, 2007). A NCF is a stack of unidirectional (UD) plies combined by a stitching process. Those fabrics are available with varying fibre orientations, e.g. [0°/90°], [+/− 45°] or [+/− 60°]. This enables a continuous manufacturing of multilayered preforms. The UD character of the plies enhances the mechanical properties compared to woven fabrics. These advantages explain the use of NCF for preforms. On the other hand, the forming properties of NCF differ from woven fabrics due to the asymmetry of the layers and the influence of the stitch, and need to be specifically studied.
19.2.1 Technical principle The manufacturing of preforms applies the principle of tailored reinforcements (TR) which involves the use of bound NCFs.
19.2.2 Preform process chain Two-dimensional (2D) preforming starts with a continuous multi-layer stacking sequence lay-up which is considered as a basic module for specific designs. Thanks to an automated lay-up machine, manufacturing of design-optimised lay-up packages becomes possible with different kinds of semi-finished products. The device is presented in Fig. 19.1. If required, a stitching step is carried out to achieve 2.5D semi-finished goods (so-called Intermediate Preforms, IP) with variation in thickness. As mentioned earlier, an alternative is the heating activation of the thermoplastic binder product. The lay-up plane is linked to a cutter machine which cuts the IP contours off, creating separated semi-products. Those semiproducts are then shaped during a forming step described in detail later. After the forming stage, the tailored reinforcements become sub-preforms (SP). Finally, 3DSP assembly is carried out again by stitching or by a new binder activation. The process concludes with a compaction step and a net-shape cutting. Fig. 19.2 illustrates this process chain for preforming.
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19.1 Automated lay-up machine.
19.2 Non-crimp fabric preform process chain with quality gates (QG).
19.2.3 Tailored reinforcements Tailored reinforcements are semi-finished goods based on lay-up packages fixed together. The principles of lock stitch 2D automatic sewing machines have been introduced in Chapter 3. Additional descriptions have been given by Beier et al. (2007). The use of tailored reinforcement reduces the number of parts to be handled
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and makes possible the use of net-shape processing. On top of that, an integrated online quality assurance becomes possible (Dumont and Goettinger, 2009).
19.2.4 Types of forming methods A forming methodology is defined by the combination of a forming device and process parameters. It has a significant influence on the draping results (Long, 2007). The position, order and magnitude of the draping force application all contribute to the draping result (Tucker, 1997). The representations of these acting forces are made through the use of parameters such as draping force, tool friction, diaphragm properties, tooling displacement speed or forming vacuum level. The varying draping force and direction during manual draping disqualify the hand lay-up process as a suitable and reproducible preforming process. The automated forming processes described here are potential candidates to be embedded at an industrial level. Figures 19.3 to 19.5 show representations of the process principles. The first promising process is the single diaphragm forming, which combines the advantages of manufacturing reproducibility with a flexible formed shape capability. As depicted in Fig. 19.3, the tailored reinforcement is positioned between the tool's upper surface and a silicon membrane. A vacuum is set up between the base surface and the diaphragm, which deforms until a uniform pressure is applied on the upper surface of the tool. The reinforcement then conforms to this target shape. Heating can thus be applied in order to activate the binder solidification before demoulding the sub-preform. A second selected forming process is the drape forming (also known as stamping or match mould forming) where the tailored reinforcement is placed between two complementary hard tools, the male and female dies. A representation is given on Fig. 19.4. The forming of tailored reinforcements with drape forming has been revealed to be possible without additional restraint. The upper tool is closed and the preform is clamped before handling to the final preform. A third process has eventually awoken interest at an industrial level, despite its relative complexity: the stretch
19.3 Example of diaphragm forming for non-crimp fabric tailored reinforcements.
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19.4 Example of drape forming (or stamping) for non-crimp fabric tailored reinforcements.
19.5 Example of stretch forming for non-crimp fabric tailored reinforcements.
forming process (or deep-drawing). Largely used for metallic materials (Rohleder et al., 2002), the process is based on plug and ring forming (without female die) and characterised by additional boundary conditions introduced by blankholders (friction plate or springs). It is described in Fig. 19.5.
19.2.5 Final preform The sub-preforms (SP) are assembled to obtain the final preform. This near-net final preform will be put on the mould, compacted and then impregnated with resin.
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The binding of many layers together allows for a net-shape preforming (with variations in thickness, for example) and a better reproducibility. As depicted in Chapter 3, sewing is a common means of preform binding and assembly. Nowadays, new tackifying products have emerged that give reliable alternatives to ensure the stiffness for preform handling during manufacturing. Available as flakes or powder, they could be easily integrated in the preforming process. They contain a thermoplastic component fraction which is activated through heating. The heated activation time potentially slows down the manufacturing cycle time and may represent a drawback. Automation is again at this stage a major aspect. Basically, two different types of assembly can be distinguished, alike to the other preforming steps. Sewing robots have been developed especially for structural stitching in 3D. They can be flexibly equipped with different stitching heads (see Chapter 3). An alternative is an in situ activation of a binder material.
19.3
Main NCF deformation mechanism observed during preforming
For an extensive bibliographical study and complete definition of the deformability of the NCF material, one can refer to Chapter 6. This section will be focused on phenomenological descriptions used to define the global and local quality parameters of an NCF preform and to quantify their conformity thresholds. Table 19.1 illustrates the deformation described hereafter. Due to the low coefficient of thermal expansion of carbon fibres at the processing temperatures, the thermal deformation modes were disregarded as a possible mode of deformation in this approach. The main mode of mechanical deformation in NCF is the in-plane shear. Similar to the woven fabrics the planar shear is defined as a rotation of a yarn of one direction relative to the yarn of the other direction. Contrary to woven architectures, the rotation point is not the crossover anymore, but another reference point like the stitched point. High shear deformation angles can be achieved before the fabric starts locking, which is a sign of better drapability of the NCF-reinforcement. When extended to the macro level, a complete UD layer of the reinforcement shears (rotates) relatively to the other. The denomination is then intra-ply shear. Inter-fibre slip occurs when a fibre starts sliding through the fabric. Due to stitch looseness, the possibility exists for individual yarns to slide locally, relative to the parallel yarns (pull-out or fan effect), or to the ones from the other direction (nesting effect). Extension of this phenomenon is possible, creating subsequent an intra-ply slip. In this case, an entire zone of UD fibres moves relative to the other UD fibres, creating a planar shift. During the forming step, tension forces act in the fibre direction due to the friction and restrain contacts. This results in an elongation of the fibres. Until now fibre breakage was not as yet observed in industrial preforms.
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Table 19.1 Classification of deformation mechanisms during non-crimp fabric preforming Deformation mode
Level
Representation
In-plane shear
Meso
No
Intra-ply shear
Macro
Yes
Inter-fibre slip
Meso
Yes
Intra-ply slip
Macro
Yes
Fibre buckling
Meso/macro
Meso: yes Macro: no
Fibre extension
Meso
No
Fibre/ply compaction
Meso/macro
No
Fibre/ply bending
Meso/macro
No
Stitch stretching/ compaction
Meso
Yes
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19.6 Deformations of stitch yarns leading to loss of contact between stitch yarn and non-crimp fabric reinforcement itself.
During in-plane shear and intra-ply shear, the fibres are laterally compressed, leading to a mesoscopical reorganisation of the reinforcement. This effect stops when the planar shear locking angle is reached and wrinkles appear. Out-of-plane bending of fibres and reinforcement is of utmost importance during the forming stage of textile reinforcement as focused in Boisse et al. (2010). Two stitch deformation modes have been observed during preforming and deal with stretching and compaction. The deformations of fibres bundles implied by stitch yarn stretching have been depicted by Loendersloot (2005). Stitch compaction results from a lateral fibre compaction leading to loss of contact between stitch yarn and reinforcement itself, as depicted in Fig. 19.6.
19.4
Preforming defect analysis
During the intensive experimentation campaigns conducted on preforming for helicopter parts by Eurocopter, five NCF-specific defects have been identified (Dumont, Goettinger 2008). Contrary to the material production defects depicted through the quality testing method illustrated in the Chapter 5, the defects presented here are related to the forming stage and are observed during the preforming of the parts. Figure 19.7 shows local views of test preforms, illustrating the observed local flaws on each face. Due to the asymmetry of the layers and the influence of the stitch, the two sides of the bidirectional NCF reinforcement react differently and
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19.7 Terminology of defects observed on non-crimp fabric-preforms.
have to be presented separately. The following defect descriptions are complementary to Chapter 6, where mechanical deformability is extensively presented. The first potential concern deals with undulation of the fibres, accompanied with planar lateral compression of counter layer fibres and as such the space between those fibres decreases. This in-plane buckling (tagged as IB) is possibly comparable to the out-of-plane wrinkling often observed in draped woven fabrics. However, this extensive deformation occurs in the absence of outof-plane deformation, as the forming technique (described in Section 19.2.4.) produces a compression force on the reinforcement and impedes greatly the
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19.8 Limit fibre path (in white) of a preform on a helicopter frame.
wrinkling formation. This buckling is located on the outer side of a curved U-profile where the main radius decreases. Secondly, structure decomposition (SD) may be observed. It is due to a strong gradient in the path length of adjacent fibres, implying the local destruction of the NCF structure. This case is to be seen on a curved U-shape profile when one fibre remains complete (depicted as the limit fibre) and its adjacent fibre has been cut (conforming to the flattening contour). This implies a strong discrepancy of path length between the limit fibre and its neighbour. The limit fibre is showed in Fig. 19.8. The defect depicted as ‘compaction and stretch’ (C&S) is a combination of a lateral compaction of one fibre direction and stretch of the counter-fibre direction. The localisation of this defect is possible on the inner side of a curved U-profile where the main radius increases. In this extension it designates the opposite deformation of the fibre buckling described above (defect IB). Another potential flaw is a UD-ply slip relative to each other, and is denoted as intra-ply slip (IPS). Caused by the difference of fibre path lengths in each direction on a curved profile, the defect appears on the outer side of a curved profile where one fibre direction is orientated radial to the main curvature. It is noted that IPS arises often in combination with the SD defect. The last identified flaw is the presence of an opening or void (VO) on one face of the NCF reinforcement. Parallel fibres do not remain parallel locally, as in-plane forces act perpendicular to the fibre and cause an opening between adjacent yarns. These in-plane forces could be created during the reinforcement manufacturing by the sewing threads, forming a so-called fisheye (see Chapter 5) or afterwards during the preforming. During the impregnation of the preform, these defects lead to local resin accumulation and local weaknesses.
19.5
Conclusion and future trends
In this chapter, an overview has been given on the preform manufacturing stages of NCF-reinforced composite. The complete preforming chain has been introduced and commented upon. Moreover, the concept of tailored reinforcement has been presented, together with an overview of the forming techniques for NCF-tailored reinforcement with respects to quality. The technology has proven industrial readiness for many aerospace applications. Table 19.2 gives an overview of © Woodhead Publishing Limited, 2011
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such applications and the main benefits achieved by applying NCF processing technologies. The main deformation modes of dry NCFs have been detailed. Finally, a description of the main possible defects occurring during preforming has been given.
Table 19.2 Applications and main benefits achieved by applying the preform processing technologies based on non-crimp fabrics Applications
Description
Floor cover plate – Automated 2D lay-up of cross-ply stack – In-mould forming – Minimal number of individual sub-preforms
Structural longeron – High process stability – In-mould forming – Minimal number of individual sub-preforms
Curved frame – Weight saving – Non-developable near net-shape – Minimal number of individual sub-preforms
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Some very complex shapes can be formed from composite sheets, while other simpler shapes cannot be formed without a strong tendency to develop defects. This is the case for most industrial parts, for which an optimised forming methodology and procedure have to be found. This goal is being pursued at industrial level by using manufacturing process simulations coupled with a series of tests at industrial level (Dumont, Weimer 2008). Applying those models at an early stage of the design chain remains challenging and will need a consequent resource investment, together with an improved coordination between the research centres dedicated to the material characterisation, the companies releasing software tools and the final users like composites manufacturing companies.
19.6
References
Åström BT (1997), ‘Manufacturing of Polymer Composites’, Chapman and Hall, 103–106. Beier U, Fischer F, Sandler J K W, Altstadt V, Weimer C, Buchs W (2007), ‘Mechanical Performance of Carbon Fibre-Reinforced Composites Based on Stitched Preforms’, Composites Part A, 38, 1655–1663. Boisse P, Hamila N, Vidal-Salle E, Dumont F (2010), ‘Simulation of wrinkling during textile composite reinforcement forming. Influence of tensile, in plane shear and bending stiffnesses’, Composites Science and Technology (in press). Dumont F, Weimer C, Soulat S, Launay J, Chatel S, Maison-Le-Poec S (2008), The 11th International Conference on Material Forming ESAFORM, 23–25 April 2008, INSA, Lyon, France. Dumont F, Goettinger M, Weimer C (2008), ‘Analysis of NCF-preforms for helicopter composites parts’, The 9th International Conference on Textile Composites Texcomp, 13–15 October 2008, University of Delaware, Newark, USA. Dumont F, Goettinger M, Weimer C (2009), ‘Eurocopter Preform Analysis System’, ESAFORM Industrial Prize Award 2009, The 12th International Conference on Material Forming ESAFORM, 27–29 April 2009, University of Twente, Enschede, The Netherlands. Haberkern H (2006), ‘Tailor-made reinforcements’, Reinforced Plastics, 50, 4, 28–33. Hamila N, Boisse P (2007), ‘A Meso–Macro Three Node Finite Element for Draping of Textile Composite Preforms’, Applied Composite Materials, 14, 235–250. Long A C (2007), Composite forming technologies, Cambridge, Woodhead Publishing Limited. Loendersloot R, Lomov SV, Akkerman R, Verpoest I (2005), ‘Carbon composites based on multiaxial multiply stitched preforms. Part V: geometry of sheared biaxial fabrics’, Composites Part A: Applied Science and Manufacturing, Volume 37, Issue 1, January 2006, Pages 103–113. Rohleder M, Roll K, Brosius A, Kleiner M (2002) ‘Investigation of Springback in Sheet Metal Forming Using Two Different Testing Methods’, International Journal of Forming Processes, (3/4), 347–360. Tucker CL (1997), ‘Forming of Advanced Composites’, in T. G. Gutowski (ed.), Advanced Composites Manufacturing, John Wiley & Sons Inc., 297–372. Weimer Ch., Dumont F (2009), ‘Manufacturing Process Simulation Tools for Faster Industrialisation of Composite Parts’, Sampe Europe Technical Conference & Exhibition SETEC 2009, Filton, UK, September 17–18th 2009.
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20 Automotive applications of non-crimp fabric composites B. SKÖCK-HARTMANN and T. GRIES, Institut für Textiltecknik (ITA) of RWTH Aachen University, Germany
Abstract: After a brief introduction to the history of automobile construction, the trend towards lightweight construction not only with metals but also towards multi-material constructions is explained. At present, short fibre reinforced sheet moulding components (SMC) and bulk moulding components (BMC) components are the dominant composite materials in the automotive sector. Today the use of non-crimp fabrics (NCF) is limited to automobiles in the luxury segment. Following this some recent examples of NCF components are discussed. These components only find application in high-end cars. The reasons for NCF components not being used for the mass production of automobiles are explained. Future trends of the mass production of textiles for automobile applications are outlined. Innovations and market potentials are shown. Key words: tailored non-crimp fabric, tailored braid, automotive, single-step preforming, multi-step preforming.
20.1
Introduction
When the first cars were built in 1885, they consisted simply of a coach car and a combustion engine. Around 1900, the first moulded steel frames were used. As a reaction to the increasing demand for cars, in 1922, the first industrial press for sheet metals was used for the production of car body parts. Thus automobiles with a wooden frame and a body consisting of plywood and metal sheets could be produced. In the 1920s, Lancia made the most progress concerning car body work. First the Lancia Lamda was designed, incorporating a self-supporting body. On this basis, Kässbohrer developed a sports car with a single-part aluminum cast body. Already in the 1940s, Henry Ford was the first to use natural fibres, which had been soaked with plastics, in the construction of an automobile. These first fibres were soya and hemp. Unfortunately, Ford’s car stayed unique and all further efforts fell victim to World War II. Even then, the high potential for weight reduction of about 50% has been stated (Greulich, 2007). The development of modern high-performance fibre-reinforced composites began about 50 years ago, when glass fibre reinforced plastics (GFRP) were tested and used for structural components of military planes and gliders. In 1953, glass fibres arrived in the automotive industry. Amongst others, Chevrolet used them for their Corvette (Ehrenstein, 2006). One of the first European cars made from 461 © Woodhead Publishing Limited, 2011
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GFRP was a Lotus sports car from 1962 (Anon., 2009). Chevrolet started using frontends made of glass fibre mat thermoplastics (GMT) as a standard feature in the 1975 model Monza. The same year, Porsche introduced the first completely galvanised steel body. Carbon fibre monocoques had been introduced for Formula 1 cars in 1981 (Ehrenstein, 2006). Already at that time, manufacturers were striving for lightweight construction in automobiles. However, this was not achieved by using fibre reinforced composite materials, but through the use of tailored blanks and the construction of aluminum sheet metal bodies. Aluminum became more and more important in the automotive business, resulting in the aluminum space frame design, which was developed for the Audi A8 in 1994. Only towards the end of the 1990s, the potential of fibre-reinforced plastics for applications in the mass production of automobiles was investigated (Derks et al., 2007). As a result, automobile manufacturers started research on multi-material methods of construction in 2000. Thus the weight reduction can be increased and the applied material can be adapted exactly to specific demands. Multi-material methods of construction have also been the topic of an EU project called ‘Super Light Car’, which is shown in Fig. 20.1. The Super Light Car consists of aluminum (sheet metal as well as cast parts), magnesium, steel and fibre-reinforced plastics (Berger et al., 2009). Looking closely at recent methods of body construction, one can find numerous different materials. In automobile construction, a general trend towards the use of composite materials and multi-material designs is apparent. However, the employed composite materials are almost exclusively short fibre reinforced sheet moulding components (SMC) or bulk moulding components (BMC) parts (JEC, 2009). The use of continuous fibre reinforced plastics is limited to unidirectional (UD) prepregs, due to their good mechanical properties. Prepregs consist of fibres and resin. They can be set hard by applying pressure and raised temperatures, but this process requires a hot press or an autoclave. In today's automotive industry, applications of glass or carbon fibre prepregs only appear in luxury and sports cars
20.1 Super Light Car (Berger et al., 2009).
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(Feraboli et al., 2004; Schauerte et al., 2007). The established technologies for the production of such prepregs suffer from the amount of parts needed. Therefore, many steps of the production process are dominated by manual work. Since an automated production has not yet been developed, cycle times for prepreg manufacturing are very long and not suitable for mass production. Moreover, material costs are very high and the raw materials require special storage conditions. Therefore, prepregs are used for components only in small serial applications with 100 to 500 pieces per year, as in Formula 1 cars. A notable share of the body parts, the chassis, the monocoque and the wheel suspensions incorporate prepreg systems. The use of NCF in automotive engineering occurs in the field of preform technology. The process of preforming is understood as the production of near-net shape textile preforms. By soaking them with resin via resin infusion (RI) or resin transfer moulding (RTM), these preforms become finished products (Räcker, 1997). At present, NCFs are rarely used for automobile parts, due to the missing automated process chains. The textile fabrics and binders are draped manually. With the existing preforming technologies, preforms and components made of NCF can be manufactured in quantities up to 5000 pieces per year using the resin infusion process. This is why, as well as prepregs, NCF are only used in small series cars like luxury class or sports class vehicles. With the use of an automated preforming process and resin transfer moulding, it will be possible to produce up to 50 000 pieces per year with more simple geometries and a two-sided formwork in the process of consolidation. Nevertheless, for these technologies only very few examples are available on the market. At present, preforming also still requires many steps of manual work. Fabrics are draped manually in the forming tools and the application of the binder to fix the single fabric layers is also a manual operation. The exploitation of new applications of continuous fibre reinforced components for the construction of vehicles requires the automation of the whole process. Short terms of tool occupancy and integrated means of quality control, included in automated processes, are the only way through which an economic mass production can be achieved. Figure 20.2 shows possible processes of manufacturing continuous fibre reinforced components, depending on complexity and quantity of the parts. Small quantities of parts can be produced as prepregs in different levels of complexity. The whole production is done manually. Components based on NCF are produced manually or are automated, depending on the number of units. Since NCF show limited drapability, the production of complex geometries based on NCF is not yet possible. Additionally, increasing complexity and quantity of components requires the simultaneous performance of several steps of production. Thus, the flexibility of the production process is decreased (Grundmann, 2009). The many advantages of continuous fibre reinforced materials over other, comparable materials can be seen in the flexible, lightweight design and very
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20.2 Production of parts of different complexity and quantity (Grundmann, 2009).
good environmental tolerance. The latter results from the small amount of raw materials needed for production and manufacturing, as well as the low fuel consumption, if used for vehicle components. Further spreading of continuous fibre reinforced composite parts runs aground on the low degree of automation in the production of corresponding component materials (Köth, 2003). Another reason is the high price for reinforcing fibres, which results from the low demand. This is also true if prepregs are used as raw materials. Preforms with reinforcing textiles have the potential of reducing production costs significantly by 20–30%. This is due to less expensive raw materials, less complicated terms of storage and the possibility of automation (Geßler et al., 2002). At present, the most prominent hindrance to an economic production of fibre-reinforced composite parts must be seen in the fact that textile preforms are not yet manufactured in an automated process and thus are neither cost efficient nor of constant quality. Contemplating the cost distribution for the manufacturing of a continuous fibre reinforced component in a preforming process, 50–60% of the component costs are generated during the preforming process (Fig. 20.3). Thus, new automated production processes for the manufacturing of fibre-reinforced composites made of NCF have to be developed. Although possible solutions for a partially automated production have already been developed, these works do not suffice to enable an economic manufacturing of fibre-reinforced composite components in practice. In this context, the research carried out within the framework of INTEX (Geßler et al., 2002) and PROPreform-RTM (Weimer et al., 2002) are worth mentioning. Further research activities focused on finding properties of components and methods for
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20.3 Distribution of costs in the prefoming process adopted by Gojny et al. (2008).
calculations, as well as the production of display models. These have been carried out within the framework of SPP 1123 (Hufenbach, 2007). In the European research project TECABS, a carbon fibre floor panel made of NCF was realised. Therefore, new technologies and methods have been developed with which up to 50 000 parts per year can be produced, by realising 50 units per day. This was achieved by developing RTM processes and new resin technologies, which allow fast production cycles and are cost effective. Also, the preform technology has been optimised to shorten the production time and to realise an integrated construction of the component to reduce the number of parts. In addition, different CAE tools have been developed in this project. Thus, the textile geometry can be described by the orientation of the yarns inside the textile. Further on, the mechanical performance of the reinforced structure can be predicted by building the stiffness of the matrix. The permeability of the textile reinforcement fabrics can also be simulated. The researchers were also able to develop numerical tools for quick simulation and to generate a tool to predict the costs (Verrey et al., 2006; Carrera et al., 2007). An automobile body made of continuous fibre-reinforced composites has been developed in the Japanese research project NEDO. In this project, new preform and RTM technologies have been developed to realise short cycle times. Beyond that, joining technologies for metal and reinforced composites have been generated, as well as simulation technologies for energy absorption. Additionally, recycling technologies for fibre-reinforced plastics have been examined (Takahashi et al., 2007).
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Automation of the whole process chain for mass production, optimisation of the flow of information with special consideration of interfaces, and a transfer to practice are prerequisites for an economical implementation of this technology. Only if these are achieved, can the technology arrive at medium-sized businesses, e.g. automotive suppliers.
20.2
Applications of non-crimp fabrics (NCF) in the automotive industry
20.2.1 Car roof, roof carline and hybrid constructions at BMW Group The first application of NCF in batch production of automobiles can be found at BMW AG, Munich, Germany. They employed NCF with 150 g/m2 and 300 g/m2 mass per unit area and fibre orientations of 0°, +45 and −45° (Derks et al., 2007). BMW AG, Munich, Germany, incorporates the process of preforming for the manufacture of components. For the production of the preforms, the required layers are made from the above-mentioned NCF. Between two layers, a binding agent is applied to keep the fibres in place. Before the stack of layers is shaped in the preforming tool, the semi-finished textile products are heated with an infrared spotlight. After the shaping, the semi-finished product is called a preform. One example of an NCF component produced by BMW AG, Munich, Germany, is the roof carline for the BMW M6. It has been realised as a glued shell construction (Fig. 20.4) (Derks et al., 2007). Another example for the serial use of textile-reinforced composite materials at BMW AG, Munich, Germany, is the roof of the BMW M3 (Fig. 20.5), which has
20.4 Roof carline BMW M6 (Derks et al., 2007).
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20.5 Roof of the BMW M3 (Frei, 2008).
been developed as a composite of a woven fabric and a glass NCF. Utilisation of a fibre-reinforced plastic structure for the roof resulted in a weight reduction of 5 kg compared to a conventionally built roof. In order to achieve a class-A surface, the outer shell consists of a carbon-woven fabric that is coated with a special clear varnish (Frei, 2008). BMW components are impregnated in a RTM process (Derks et al., 2007). The complete process chain from preform production to the assembly of the roof is shown in Fig. 20.6.
20.6 Industrial-scale manufacturing of the CRP-roof for BMW M3 (Frei, 2008).
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20.7 Side frame of the BMW Hydrogen 7 (Derks et al., 2007).
NCF are also used for hybrid methods of construction at BMW Group, Munich, Germany. Within these, preforms consisting of NCF are glued to conventional body-part materials. Glue is spread across the complete surface of the preforms. Incorporating these hybrid constructions helps to improve the properties of the body and to meet crash regulations and stiffness requirements. A typical example is the side frame of BMW Hydrogen 7 (compare Fig. 20.7). Due to the very small quantity of required parts, at present, they are still laminated manually (Derks et al., 2007).
20.2.2 Boot lid of Lamborghini’s Gallardo Spyder Another example for the use of NCF-based components in the automotive industry is the boot lid of Lamborghini's Gallardo Spyder. The required properties of this component have been derived from a comparable part with an aluminum shell structure. Compared with the aluminum tailgate, which consists of nine single items and two additional plastic air outlets, the CRP component requires only two single parts. One inner and one outer shell need to be assembled, as can be seen in Fig. 20.8 (Derks et al., 2007). The realisation of this FRP boot lid includes UD and biaxial NCF with layers oriented in a 0°, ±45° and 90° direction. For the outer shell, carbon fibres are used, while the inner shell is produced with GFRP to reduce material costs. For the manufacturing of fibre-reinforced components from textile preforms, the RTM process is employed. Due to the homogeneous surfaces produced by the viscous resins used for RTM, the potential for achieving class-A surfaces with the RTM process is higher than with prepreg systems (Derks et al., 2007). The cycle time for the production of a tailgate is 30–45 minutes. The painting of the boot lid is realised offline, in order to spare the component from the high temperatures of online painting. With this component a weight reduction of 5 kg, as compared with the aluminum part, could be achieved. At the same time a class-A surface is realised (Deinzer et al., 2007). The readily produced and built-in part can be seen in Fig. 20.9.
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20.8 Integrated construction (Deinzer et al., 2007).
20.9 Lamborghini Gallardo Spyder with built-in FRP boot lid (Deinzer et al., 2007).
20.3
Research and development for the use of NCF in automotive applications
Currently, automated process chains with short cycle times for production of continuous filament plastics based on NCF are a major obstacle for the
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establishment of NCF in the automotive industry. Today, fibre-reinforced plastics based on NCF are manufactured in a manual preforming process. To expand the lightweight construction and use of continuous fibre reinforced plastics in the automotive industry, there are different research approaches for the development of automated process chains. Thereby, there is a distinction between single-step and multi-step preforming.
20.3.1 Single-step preforming The single-step preforming is characterised by the fact that a near net-shaped textile preform with variable thickness and variable layer structure is produced in a single production step. The braiding process is actually used as single-step preforming in industrial applications. An example, therefore, is the overbraiding process used for front and rear bumpers in the BMW M3 series manufactured by SGL Kümpers GmbH, Lathen, Germany. Other single-step preforming processes like multiaxial warp-knitting are currently developed with the aim to produce NCF with individual layer construction in order reduce waste and expenditure of work. The focus of a research group (FOR 860) at RWTH Aachen University, Germany, is to develop economic mass production of structural components made of continuous filament plastics based on NCF for automotive applications. There the single-step preforming of NCF is used, for which an integrated modular machine concept was developed that is able to produce continuously semi-finished fabrics on the basis of NCF. The results are tailored NCF. They have the properties of finished reinforcing structures and the novel developed production process is able to reduce handling processes and further production steps. In doing so, local reinforcement structures like, for example, 0° layers or additional NCF can be integrated into the manufacturing process. A picture of this newly developed feeder module is shown in Fig. 20.10. With this feeding module for multiaxial warp-knitting machines, reinforcing structures for high-volume applications can be realised (Greb et al., 2009; Kruse et al., 2009). In addition to producing adjusted NCF, the aim of research is to be able to adjust the drapability of NCF locally in the direction of the manufacturing process, without interrupting the production process. Thereby the drapability is especially affected by the warp-knitting stitch pattern and the tension of the knitting thread. The lower the thread tension, the easier the reinforcing fibres can move within the meshes. A certain amount of tension is needed to ensure a good bond between the individual layers and to avoid undulations (Hufenbach, 2007). Considering these circumstances, it is the aim to realise high drapability in special areas of the textile by varying bond type and tension thread locally. To change the binding continuously during the production process, a new electromechanically driven guide bar was developed. With these enhancements of the warp-knitting machine, it is possible to produce pre-assembled NCF which have a locally recruited
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20.10 Feeding module for multiaxial warp-knitting machines (Kruse et al., 2009).
drapability. Thus it is possible, for example, to produce the desired fabric with the appropriate characteristics and an adjusted drapability in certain areas for a particular component (Greb et al., 2009; Kruse et al., 2009). In addition to this, Cetex GmbH, Chemnitz, Germany has developed a variable delivery for filaments on multiaxial NCF. Hereby, it is possible to realise reinforcing fabrics for plane faces, shells and nodes elements. In this project, the multiaxial warp-knitting machine has been equipped with an additional module. This module can realise a displacement of the chaining thread and can change the concentration of the chaining thread by storing individual rovings or filaments. This is achieved by a folding gate with thread guides, see Fig. 20.11 (Heinrich and Vettermann, 2009). With this additional module, the following yarn displacements can be realised (examples in Fig. 20.12). This recently developed process technology to manufacture customised reinforcement structures was verified by a demonstrator component. The demonstrator was a locally reinforced tank wall from the automotive industry. With these two developments for the production of adjusted textile on the basis of the multiaxial warp-knitting technology, reinforcing structures can be manufactured cheaper and more automated. Therefore,
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20.11 Folding gate with thread guides (Heinrich and Vettermann, 2009).
20.12 Possible reinforcement yarn displacements (Heinrich and Vettermann, 2009).
reinforcement fabrics are produced with a fibre orientation that corresponds to the loading cases of the component. Thus, a near-net shape manufacturing of planar components, such as tailored NCF, can be realised in one process step and the processing time for the manufacturing of automobile parts on the basis of these semi finished products can be reduced.
20.3.2 Multi-step prefoming The production of a near-net shaped textile preform in a multi-step preforming process is a result from several production steps. Using the multi-step preforming
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it is possible to produce components with a high complexity. First, NCF or woven fabrics and other sub-preforms, like braided structures, are manufactured. By bringing together the semi-finished textile products in a preformed tool with the production steps cutting, handling and draping, a near-net shaped preform is created, which is fixed by joining or binder application. In various research projects (Geßler et al., 2002; Hufenbach et al., 1999) procedures for individual steps of the preform manufacturing process have been compiled. These procedures were developed and investigated separately. As a result, separate tailored solutions for the individual process steps are available. In order to be able to produce components automatically, a flexible manufacturing cell for the production of three-dimensional textile preforms was realised at the Institute für Textiltechnik, RWTH Aachen University, Germany. Figure 20.13 shows the manufacturing cell, which is known as the preform centre. In this manufacturing cell, a robot is equipped with a tool changing system that can implement automatically the individual steps which are necessary for the production of fibre-reinforced plastics on the basis of NCF. By using a tool changing system, it is possible to equip the robot with different tools (Fig. 20.14). For the illustration of a process chain for the production of three-dimensional textile preforms, the following tools are available: • • • • •
gripper, sewing heads, tufting head, binder application system and quality monitoring.
By changing the different tools, it is possible to produce textile preforms in a single manufacturing cell in an automated way. The testing of this manufacturing cell was examined using examples from the automotive industry. The results are presented briefly below.
20.13 Preform centre (Grundmann, 2009).
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20.14 Production steps in a preform centre.
Car roof segment Using a car roof segment, a semi-automated process for the manufacturing of this component was developed in the research project ‘AutoPreforms’. This component is realised using four layers of a multiaxial NCF with a lay-up of 0° / 90°/ +/−45°. The mass unit per area of the NCF used is 840 g/m2. In order to receive an aesthetic carbon appearance, a woven fabric is used as a top layer. In addition, metal inserts are integrated into the component to allow the mounting of attachment parts. Profiles with integrated foam core are used to stiffen the component design. These profiles are made as preforms, prior to the actual manufacturing of the roof segment. These pre-produced parts integrated into the preforming process of the roof segment are called sub-preforms. To realise the profiles, NCF were draped around a foam core and secured by seams. A schematic diagram of the realised component is shown in Figure 20.15.
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20.15 Preform of a roof segment (Grundmann, 2009).
During the production process of the roof segment, first the sub-prefoms are manufactured manually. The roof segment is then manufactured fully automated in a preform centre. First, the textile semi-finished products are cut at the cutter table and then draped in the mould using a gripper. Before the next textile layer is applied, binder is applied to ensure fixing of the layer system. These steps are repeated until the desired layer stack is obtained. In addition, the metal inserts are integrated into the textile preform. After the desired layer stack is realised, the sub-preforms are applied to the shell element and then fixed by sewing. Automobile underbody structure The production of an automobile underbody structure was also realised with a semi-automated process. Figure 20.16 shows the complete manufacturing technique of an automobile underbody structure on the basis of NCF. First, the needed NCF layers are cut and then draped into the mould. For the integration of attachment parts, metallic inserts are integrated into the textile preform during the preforming process. To realise this component, a large number of manual handling steps are required, since there is no automated draping process for these complex geometries. By using a braided side skirt, the production process is more economical, because the number of handling steps is reduced (Grundmann, 2009). In addition to this, complex draping tools have to be developed which significantly simplify the draping in the mould and reduce the cycle time for the component manufacturing. Grundmann has developed a software tool to analyse the process chain assessment, which deals with the economics of the textile preforming and can help to optimise the existing preforming processes (Grundmann, 2009).
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20.16 Preforming of an underbody structure (Grundmann, 2009).
20.4
Future trends
Due to rising oil prices and legislation introduced to reduce carbon dioxide emissions, the need for lightweight structures in automotive applications is constantly growing. The aim is to reduce the weight of vehicles, because driving resistance is linked directly to the car’s weight. Beside the use of new metals and aluminium, one approach to achieve that aim lies in the use of textile-reinforced composites, which provide high strength and high stiffness at a low weights. Today, composites are expensive high-performance materials, which find their applications in small series and niche markets (Fig. 20.17). To establish NCF in the field of new lightweight structures for applications in automotive engineering, there is still the need for extensive research. The target is to make composites based on NCF into a high-performance material for mass
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20.17 Trends in fibre-reinforced composite production.
20.18 Comparison of steel and textile production lines.
production with great potential for material and energy conservation. Therefore, new production technologies are needed which are able to cope with the challenges of large-scale serial production. Looking at the metal industry, special tailored materials like tailored blanks and tailored tubes have been developed (e.g. ThyssenKrupp). These components have the advantage of combining weight reduction with economic production methods. Tailored blanks are characterised by homogeneous thickness of the final part independent of the degree of deformation. Before forming a final part with a complex geometry, tailored blanks are flat metal sheets which provide local differences in thickness. In tubular forms, tailored tubes are available and have the same advantages as tailored blanks. These special tailored components are used in the automotive industry for body structure systems and are finally joined using robot-assisted handling and metal joining technologies like conductive welding (Fig. 20.18).
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To be competitive in this market with textile-reinforced structures made of NCF and other textile fabrics, new production technologies for near-net shape reinforcement structures (tailored NCF and tailored braid) which enable economic large-scale production have to be developed. Compared to the metal process, textile structures equivalent to the tailored blank and the tailored tubes already exist today or are currently being developed in research projects. Tailored noncrimp fabrics are comparable to tailored blanks (Fig. 20.18). These textile products can be manufactured in a single-step preforming process using multiaxial noncrimp fabric technology. Thus, local changes in the thickness of the NCF during the production process can be realised. By locally varying knitting patterns and stitch length in addition to the changes in thickness, the drapability of these fabrics can vary locally. To achieve a defined geometry for a special component, the tailored NCF will be cut to the required dimension. Textile production technologies equivalent to the metal tailored tube process are overbraiding, 3D weaving or 3D braiding (Fig. 20.18). These production processes are capable of realising changes in cross-section geometry, local changes in thickness and to produce shaped textile tubes and profiles. Combined with pultrusion technology, constant profile geometries can be realised. For the production of a textile-reinforced component with complex geometry, robot-assisted handling and joining technologies are available for the processing of textile reinforcements. To handle the textile fabrics and the textile preforms (tailored NCF and tailored braids) during the multi-step preforming process, cryogrippers (ice-grippers) and needle-grippers can be used. In addition, textile joining technologies exist for an automated robot-assisted production. This can be done using blind-stitch technology, tufting technology or similar one-sided sewing technologies. These automated textile handling and joining technologies are used for the assembly of textile sub-preforms like tailored braids or tailored NCFs. These production technologies, which are currently developed and optimised, represent the key to large-scale production of textile-reinforced composites for automotive applications based on NCF. To make these automated textile process chains even more economical, Grundmann (2009) developed a tool for planning effective production chains. The whole picture of an integrated development and implementation of the full textile process chain cannot exist without integrated virtual production planning. Thus, especially for multi-layered integrated reinforcements, virtual tools for the simulation of the geometrical shape, the draping behaviour and of course for the calculation of the mechanical properties for the dimensioning of the final part are required and currently under investigation at various research institutes.
20.5
Conclusion
At present, there are several applications of reinforced components made of NCF in single high-performance vehicles on the market. In order to establish
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textile-reinforced components made of NCF in the automotive industry, new production technologies have to be developed, which are able to meet the challenges emerging with large-scale production. One major step towards this aim is to develop automated preforming technologies which allow short, and therefore economical, cycle times. Furthermore, quality assurance systems, especially for certified products like automotive parts are needed and have to be developed and implemented in new production chains. Today, textile technologies already provide promising, but so far isolated solutions. Combining these solutions and adapting them to the individual needs of the automotive industry together with adjusted simulation tools will eventually lead to the breakthrough of these textile production technologies, especially for NCF in automotive applications.
20.6
References
N.N., Waldeckische Landeszeitung Frankenberger Zeitung, Osnabrück, Germany, http:// www.wlz-fz.de/Welt/Kultur/Uebersicht/Reise-durch-Automobilgeschihte (accessed 18 January 2010). Berger L, Lesemann M and Sahr C (2009), ‘SuperLIGHT-CAR: innovative Multi-MaterialBauweise’, Leightweight design, vol. 2, no. 6, pp. 43–49. Carrera M, Cuartero J, Miravete A, Jergeus J and Fredin K (2007), ‘Crash Behaviour of a Carbon Fibre Floor Panel’, International Journal of Vehicle Design, vol. 44, pp. 268–281. Deinzer G, Reim H, Hermes C, Schneidewind T, Masini A and Enz J (2007), ‘Class A mit CFK – Beispiel Heckklappe Gallardo Spyder’, in VDI (ed.), Kunststoffe im Automobilbau, Düsseldorf, VDI. Derks M, Birzle F and Pfitzer H (2007), ‘CFK-Technologie bei der BMW Group – Heute/ Zukunft’, in VDI (ed.): Kunststoffe im Automobilbau, Düsseldorf, VDI. Ehrenstein G (2006), Faserverbund-Kunststoffe: Werkstoffe: Verarbeitung, Eigenschaften, 2nd edn, Erlangen; München; Wien, Hanser. Feraboli P and Masini A (2004), Development of carbon/epoxy structural components for a high performance vehicle, Composites Part B, 35, 323–330. Frei P (2008), Serienfertigung von Faserverbundstrukturen am Beispiel des BMW M3 CFK-Daches, in AVK (ed.), Tagungshandbuch der 11. internationalen AVK-Tagung: 22–23 September 2008, Messe Essen, Essen, AVK– Industrievereinigung Verstärkte Kunststoffe e.V. Geßler A, Gliesche K, Keilmann R, Laourine E, Kröber J and Pickett A (2002), Textile Integrationstechniken zur Herstellung vorkonfektionierter Verstärkungsstrukturen für FVK “INTEX”: BMBF 03N3060, Ottobrunn, EADS. Gojny F, Heine M and Kümpers F.-J (2008), ‘Verarbeitungstechnologien für Kohlenstofffasern’, in Composites in Automotive & Aerospace, Materialica 2008, München, 16.02.2008, S. 6 Greb C, Schnabel A, Kruse F and Gries T (2009), Automated Production of Textile Preforms for Structural Fibre-Reinforced Plastic Components, in Küppers B (ed.), 2nd Aachen Dresden International Textile Conference, Aachen, DWI an der RWTH Aachen. Greulich S (2007), Biopolymere für den technischen Eunsatz im Automobilbau, in VDI (ed.), Kunststoffe im Automobilbau, Düsseldorf, VDI. Grundmann T (2009), Automatisiertes Preforming für schalenförmige komplexe Faserverbundbauteile, Aachen, Shaker.
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Heinrich H-J and Vettermann F (2009), ‘Gestaltungsmöglichkeiten für bionische Verstärkungsstrukturen durch variable Filamentablage auf Multiaxialgelegen’, paper presented to the scientific meeting 48. Chemiefasertagung Dornbirn, Dornbirn, 16–18 September 2009. Hufenbach W (ed.) (2007), Textile Verbundbauweisen und Fertigungstechnologien für Leichtbaustrukturen des Maschinen- und Fahrzeugbaus: textile Verstärkungen Halbzeuge und deren textiltechnische Fertigung, Dresden, SDV – Die Medien AG. Hufenbach W, Rödel H, Langkamp A and Herzberg C (1999), ‘Beanspruchungsgerechte 3D-Verstärkungen durch funktionsgerechte Nähtechnik’, paper presentet to the scientific meeting Materialica 1999, München, 27–30 September. JEC (ed.), Composite Materials in Automotive, Paris, JEC Group, 2007. Köth CP (2003), ‘Pulver, Kohle, Kosten: ein neuartiges Pulver senkt die Herstellungskosten von CFK- und GFK-Verbundwerkstoffen; die Serienanwendung rückt damit in greifbare Nähe’, Automobil Industrie, vol. 48, no. 3, pp. 94–95. Kruse F, Schnabel A, Behling T and Gries T. (2009), ‘Automated textile preforming of semi-finished fabrics for the mass production of fibre-reinforced plastic components’, paper presented to the scientific meeting ITMC 2009 : Intelligent Textiles and Mass Customisation, Casablanca, 12–14 November. Räckers B (1997), ‘Faserverbundwerkstoffe, Entwicklungstrends am Beispiel des Airbus’, in Friedrich K (ed.), Verbundwerkstoffe und Werkstoffverbunde, Frankfurt am Main, DGM Informationsgesellschaft, pp. 3–14. Schauerte O, Schreiber W, Finkbeiner A, Ene E and Starmann D (2007), ‘Der Einsatz von leistungsfähigen Kunststoffen im Bugatti Veyron’, in VDI (ed.): Kunststoffe im Automobilbau, Düsseldorf, VDI. Takahashi J, Uzawa K, Ohsawa I, Kitano A, Yamaguchi K and Usui K (2007) ‘NEDO Project “Automotive Light Weight Structural Elements of CFRP Composites”: Recycle and LCA’, Journal – Society of Automotive Engineers of Japan, vol. 61, 10, pp. 47–51. Verrey J, Wakemann M D, Michaud V and Manson J-A E (2006), ‘Manufacturing cost comparison of thermoplastic and thermoset RTM for an automotive floor pan’, Composites: Part A, vol. 37, pp. 9–22. Weimer C, Mitschang P and Neitzel M (2002), ‘Continous manufacturing of tailored reinforcements for liquid infusion processes based on stitching technologies’, in Bhattacharyya B (ed), 6. International Conference on Flow Processes in Composite Materials, Auckland, University of Auckland, Department of Mechanical Engineering, Paper No. FPCM6-DE–2.
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21 Non-crimp fabric composites in wind turbines G. ADOLPHS and C. SKINNER, OCV Technical Fabrics, Belgium
Abstract: Historical development and modern use of non-crimp fabric (NCF) in wind energy applications such as blade and nacelle are given. The influence of fabric processing such as skewing, resin infusion and pre-impregnation (prepreg) are also shown. Key words: wind energy, blade design, specific strength, resin infusion, nacelle design.
21.1
Introduction
21.1.1 The oil crisis as the initiator for wind energy The trigger for the development of the modern wind power industry is often described as the energy crisis of 1973. The ‘oil price shock’ of 1973 initiated a public debate about the dependence of Western economies on oil imports so, in addition to energy saving measures, politicians turned their attention to the search for alternative energy sources. This led to the development of many programmes, such as the those sponsored under the US Federal Wind Energy Programme (1973),1 the formation of the National Swedish Board for Energy Source Development (1975), a range of experimental turbines in Denmark and a range of government subsidised programmes in Germany led by the Bundesministerium fur Forschung und Technologie, which ultimately led to the construction of the ‘Growian’ (Gross Windkraft-Anlage) which gained much notoriety.2,3 In many cases, these extensive government-funded programmes resulted in little tangible development of the industry and, after the crisis, only one country demonstrated the consistently successful operation of wind turbines: Denmark. The basic technical concepts of the turbines employed had been developed in the beginning of the 20th century by Poul La Cour (Askov, Denmark), Albert Betz (Göttingen, Germany) or Palmer Cosslett Putnam (Vermont, USA) and had found relatively widespread adoption due to the superiority of the design due to the following characteristics. • •
Sleek, fast-running propeller designs which produce low thrust at high torque and can more easily withstand high wind speeds. Rotor speed and power output can be controlled by pitching the blades and this also provides effective protection against extreme wind speeds. 481 © Woodhead Publishing Limited, 2011
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Fibre-reinforced composite materials allow aerodynamically optimised shapes and enabling highest efficiency of the unit while being lightweight, fatigue and weather resistant.
In this area some small- and medium-sized manufacturing firms in Denmark, for example, VESTAS, seized an opportunity of constructing these three-blade rotors and grid connections and started to sell these wind turbine concepts to private owners or farmers. These were typically small units (60 kw) with rotors of 15–16 m. In 1986, these units contributed ∼1% of Denmark′s power requirements, but from this point began to grow exponentially based on clearly defined permits and the availability of appropriate testing stations.
21.1.2 The evolution material choice in wind rotor blade technology Rotor blade technology for these wind turbines has evolved in the 40 years since the ‘energy crisis’ of the 1970s and now can be associated more with lightweight aeronautical engineering than with conventional mechanical engineering.4,5 In contrast to all other components of the turbine which can be ‘borrowed’ for existing fields of engineering, the rotor blades must be developed to match the load spectrum of a given turbine. However, in contrast to aircraft engineering the cost structure of wind energy operation prohibits traditional aircraft manufacturing methods and production technology and was adopted from other fields. In the case of rotor blades the transfer primarily comes from the modern boat building and industrial engineering where fibreglass composites predominate.6 The rotor blades of older Danish wind turbines were almost always manufactured by former boat builders. In the past, the starting point for rotor blade design was the question of which material would be the most suitable. Design and manufacturing methods are in reality determined by which material is the most suitable. In other words, it is impossible to separate material and manufacturing process. Analysis of materials common in aerospace engineering highlights the following materials as ‘suitable in principle’ for rotor blade construction.7 • • • •
Aluminium. Titanium. Steel. Fibre composite material (glass, carbon, aramide).
The most important properties by which a first assessment can be made are • •
specific strength (strength/density); modulus of elasticity;
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21.1 Comparison of unit material cost per unit of strength for a beam in bending under a cyclic load analogous to a wind rotor blade.9
• •
specific modulus (modulus of elasticity/density); ∧ ∧ fatigue strength after 10 7 to 10 8 load cycles.8
Comparison of the material properties highlights that the excellent balance of properties exhibited by fiber glass/epoxy composites making them ideal choices for delivering cost effective strength in engineering configurations as found in wind rotor blades. Figure 21.1 shows different material options in terms of their specific strength and specific cost performances. Fibre glass/epoxy has both a low mass and cost per unit of strength which explains its adoption as the material of choice for rotor blades.
21.2
Development of non-crimp fabric (NCF) composites in wind energy
21.2.1 The impact of infusion technology on NCFs
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21.2 Blade length over time, main years of build of different blade lengths.
21.2.2 Traditional woven structures in wind rotor blades From the inception of the wind energy industry in Denmark, the materials chosen for the construction of the wind rotor blades for fibre-reinforced composites was based on reinforcing structures taken from the boat building industry. From the mid-1970s, the reinforcement materials typical used in the construction of composite craft were: •
woven roving using plain ligament and equal amount in warp and weft fibre in 300, 500, 600 and 800 gr/m2 total area weight;
21.3 Typical blade design, middle section, two shear webs, source: presentation M. Zvanik, Owens Corning and DIAB, CFA Show 2001, Tampa, Florida.
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combination of these typical woven materials produced in combination with chopped fibre mat of 300 and 450 gr/m2, creating combination products, mostly used were woven roving of 500 and 600 gr/m2 and mat of 300 gr/m2; and unidirectional woven roving of 600 gr/m2 and 800 gr/m2, later as well of 1200 gr/m2 having a percentage of warp reinforcement of usually 90%.
Instead of using +/−45° biaxial non-crimp fabric (NCF) woven fabrics were laid up at an angle of 45° converting warp in +45° and weft in −45° or vice versa. A typical blade design during this period was using the unidirectional (UD) fabrics to form spar caps, woven fabrics for the skin structure and shear web and complexes for the coupling area.
21.2.3 Introduction of skewed fabrics in the late 1980s An evolution in the construction of reinforcements for the wind rotor blades was the use of skewed fabrics in the late 1980s. In this process a woven weft UD is skewed to a 45° fabric during winding or unwinding and at the same time another woven fabric is skewed to −45°. During the assembly process the individual fabrics are combined by a warp-knitting operation similar to the combination structures described earlier. Figure 21.4 shows this process schematically. The process also allowed the addition of chopped fibre to modify the infusion
21.4 Schematic of a typical skewing process using a Malimo or Liba knitting machine.
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characteristics of the complexes. The materials from this type of process are still in use today in the construction of wind rotor blades. Another option was during the 1980s and 1990s to use sequential weft insertion warp-knitting machines which produce a weft UD fabric and skew this fabric to the desired +45° or −45° angle and assemble two skewed fabrics with or without chopped. As the knitting operation inserts the weft yarns one by one, they were already NCF by today's standards. However, the described skewing and assembly process causes fibre misalignment and distortion of the selected fibre orientation. Both effects have shown inferior mechanical properties.10 During the 1980s it was as already possible to produce +/−45° structures in a direct process by early weft-laying NCF machines, but they lacked a suitable adjustment to produce true parallel weft. The weft structure was crosslaid and the resulting mechanical laminate properties were inferior to the true parallel weft insertion materials. As these materials were expensive, they were used to little extent. Production methods used by the vast majority of blade producers were still hand lay-up.
21.2.4 Vacuum-assisted resin transfer and the growth of NCFs To make the blade longer and aerodynamically more effective, the materials needed to improve. For a longer blade an increase in material stiffness is desirable and more valued. Appropriate scaling factors which relate properties to rotor diameter have been published.11 Importantly, for the development of the wind rotor blade technology a new process technology was developing. The vacuum-assisted resin infusion process or vacuumassisted resin transfer moulding (VARTM) or vacuum infusion process (VIP) became increasingly popular. This methodology allowed an increment in material stiffness by incrementing the fibre volume fraction from 35% to 40% fibre volume fraction (FVF) typical of a hand lay-up to 50% to 55% FVF by the VARTM process. The effect on laminate tensile stiffness made out of UD NCF fabrics is an increase from approximately 25–30 GPa to over 37 GPa, which means an increase of around 25%. In woven structures, a higher area weight causes a dense structure of reinforcement material which needs to be interlaced, which causes increased crimp of the reinforcement fibre. In an NCF this effect is drastically reduced as reinforcement fibre is laid parallel and the formed ply of reinforcement is laid one over the other. The new vacuum processes not only delivered an increment in mechanical properties. Heavyweight NCF could still be impregnated and a high fibre volume fraction could be achieved. The combination of both the NCF reinforcements and the VARTM process allowed wind blade producers to benefit from the improved cost and reduced production time which offered this combination. Reduced costs and higher stiffness facilitated the development of longer and more efficient blades.
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Table 21.1 Possible and frequently used warp weight (in bold) in unidirectional materials Warp roving Gauge [tex] [yarn/inch]
[yarn/cm]
1200 1200 1200 1200 1200 1200 1200 1200 2400 2400 2400 2400 2400 2400 2400 2400
1.97 2.36 2.76 3.15 3.54 3.94 4.72 5.51 1.97 2.36 2.76 3.15 3.54 3.94 4.72 5.51
5 6 7 8 9 10 12 14 5 6 7 8 9 10 12 14
Area weight [gr/cm2] 236 283 331 378 425 472 567 661 472 567 661 756 850 945 1134 1323
Many of these early NCF materials used in the VARTM processes were UD materials. The main glass roving available were 1200 tex and 2400 tex, and rarely 1500 tex and 2200 tex. Taking usually available knitting machine elements the following area weights shown in Table 21.1 could be produced, with the highlighted combinations being the more frequent versions observed in the industry. Apart from the UD NCF, multiaxial fabric as +/−45° biaxials are needed in the laminate design of modern windmill blades. During the 1980s the first parallel weftproducing multiaxial warp-knitting machines were presented and allowed the production of true parallel weft at adjustable angles ranging from 90° to around 30°. As well as with UD fabrics, a range of biaxial fabrics established itself as a function of available glass roving and cost efficiency in production.12 Early version of these fabrics have been produced using 68 tex to 134 tex glass yarn and +/−45° fabrics of around 300 gr/m2 were produced. The laminate thickness in longer blades increased. Heavier area weight could be used. Consequently 200 tex direct roving was used to produce biaxial fabrics of 450 gr/m2 and today 300, 600 and 1200 tex direct roving is used to produce +/−45° biaxial fabrics of 800 gr/m2, 1000 gr/m2 and above.
21.2.5 Development of weft technologies in NCF reinforcement structures Over time the machine technology also allowed a more precise insertion of weft yarns. While in many older machine configurations the weft lay-up was not
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21.5 Description of typical weft insertion possibilities using NCF production machine.
synchronised with the exact production speed, cross weft or substantial parallel weft was inserted as shown in Figure 21.5. Modern-day machines for the production of NCF structures with numerical control allow for the construction of true parallel weft. As consequence of the irregular crossover of weft reinforcement local small defects are common in the types of fabrics resulting in lower mechanical properties. A more tailored used of multiaxial material can be found in the production of substructures of wind rotor blades as, for example, flanging rings. These are designed to allow the blade to be screwed to the cone and are coupled with the main blade laminate. This construction can be prepared by infusion together with the main shell or potentially produced as a separate part and are assembled in a final production stage by structural adhesives. The screws can be of a T-bolt type or carrot type, glued in screws. The T-bolt type needs in general a laminate design adequate to absorb the shear loads and pressure caused by the T-bolt and its design is similar to laminate designs for riveting with an approximate amount of 50% UD and 50% of a +/−45° biaxial oriented fiber.13 An example can be named a flanging ring build-up by winding 45°/90°/−45° in 200/400/200 gr/m2 triaxial fabric. A glued-in screw can in general terms build up by much higher UD-oriented designs. An example is a flanging ring build-up by +80°/0°/−80° 300/60/300 gr/m2 oriented NCF multiaxial fabric produced in a fabric winding operation. Generally, it is possible to describe the construction of a typical wind rotor blade using NCF reinforcement structures using a range of typical styles as in Figure 21.5.14 As it can be seen in Plate XIII (see between pages 396 and 397), a substantial part of the laminate is build-up by UD and triaxial NCF fabrics. In common designs, the UD NCF portion in a modern wind rotor blade is 50–60% of the NCF fabrics. Triaxials are reduced in favor of UD and biaxial +/−45° fabrics in bigger blades. Shear webs are build mainly using NCF constructions of +/−45° materials. In such designs a critical area in a blade is the large flat surface area towards the root. In this area the loads are more complex caused by combinations of air pressure, flap-wise deflection and edge-wise deflections. Local stress concentrations can occur and buckling can be caused in the compression zone under deflection. An image from possible buckling is described in Fig. 21.6.
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21.6 Buckling simulation of a blade (Locke J., Valencia U., ‘Design Studies for Twist Coupled Wind Turbine Blades’, SAND 2004-0522, Albuquerque/Wichita, USA).
21.2.6 The use of UD prepregs in wind rotor blade design An alternative design option developed by Danish wind rotor blade manufacturers is shown in Fig. 21.7. The figure highlights that in this construction the shear web construction commonly associated with the VARTM process to produce a full blade have been replaced by a central ‘wingbox’ structure. The top and bottom of these constructions are built up using UD reinforcements and both sides have the function of the shear web. The box structure holds approximately 85% of the mechanical load and is covered by a fairing that is glued on. The UD structure is composed of UD prepreg and biaxial dry fabrics. Other biaxial prepregs build up the sidewalls together with core material, forming said shear web. The fairing is designed using a combination of triaxial and biaxial prepreged NCF fabrics and core materials. Pre-impregnated reinforcement fibre and fabrics, a material type and related vacuum-bagging process used mainly for aerospace part manufacture, show, as the infusion process, a clear improvement in mechanical properties versus the hand lay-up process. As the materials used are pre-impregnated, their commercial use requires a refrigerated supply chain, a precise cut, lay-up and debulking process to remove trapped air in between the material layers. A common step in the process in aerospace applications is to use an autoclave to compact the material under higher
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21.7 Central spar design typical of those used commercially by VESTAS and Gamesa.
than atmospheric pressure. Because of the immense size of wind turbine blades and their components or subparts this cannot be done for economic reasons. However, tools must be heated up to around 80°C to cure the used epoxy resin system. The UD prepreg approach, however, holds some advantages with respect to NCF, as it can be made of 100% oriented fibre structures in an UD direction, no weft is necessary and the amount of resin can be precisely adjusted to the required tolerances and the resins can have higher viscosity than resin systems used for the infusion process. Triaxial and biaxial prepreg show no or little differences to material used in the infusion process and demonstrate very similar mechanical properties. The reason is that those prepregs are made entirely out of the same NCF. With respect to the use of carbon fibre for UD structures as spar cap (or girder) the UP prepreg process offer some advantages. • •
The impregnation process can be controlled and adjusted to produce a full impregnation of the carbon fibre prior to their use in the moulding application. The impregnation process can be adjusted to increment the amount of resin in the UD prepreg vs. VARTM thus reducing the fibre volume fraction. This reduces overall material cost and reduces the carbon prepreg laminate modulus. The reduction in modulus improves the compatibility with glass fibre prepreg in hybrid carbon–glass designs too.
The major loads that wind rotor blades are subjected to aerodynamic loads as thrust and lift on the blade. Thrust is causing a flap-wise deflection, aerodynamic lift causes a mixed flap and edgewise bending and the torque to spin the rotor and produce energy. Torsion loads twisting the blade along their axis are caused by thrust and lift. The blade mass is subject to both gravity and inertia loads. Gravity loads pull the blade down and act as an edgewise load. Inertia loads are caused by the rotation and by vibrations. Lower masses and reduced vibrations reduce substantially these loads (Plate XIV).15 All these loads cause multiple static and dynamic stresses which any material used on the construction of a wind rotor blade must be able to withstand over the designed lifetime which is commonly between 20 and 25 years. To determine the suitability of a reinforcement material for this operating environment a range of tests are therefore carried out to show the suitability of the used materials. These
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are described by standards edited by the main certification bodies.16 All NCF materials to be used in a wind rotor blade have to be tested according to these standards. The main parameters are • • •
tensile strength and modulus in reinforcement direction and transversal direction; shear strength and modulus; and fatigue strength in three different load ratios up to two million load cycles.
Another important parameter is the thickness of the fabric used. As wind rotor blades are built by lay-up of individual NCF or prepreg layers, at each start and end of a new layer, a drop in laminate thickness is generated. This causes a sudden difference in laminate properties and a shear tension at the cut edge of the new layer in the boundary between new layer and existing laminate. The material design must withstand the deformation at these boundaries over time. Another specific requirement is caused by frequent lightning strikes to wind energy converters. NCF materials that are used in wind turbine blades must, in addition, show a uniform dielectric behavior and must not offer undesired local conductivity.
21.3
NCF materials used in nacelle construction
In almost all horizontal wind energy converters, the key components of the machine are housed in a closed nacelle on top of the tower as a prolongation of the turbine axis. In reality, the design concept of the nacelle is defined by the arrangement of the drive turbine and the generator. Ease of assembly and total cost are also key defining factors in the nacelle construction. The most common design is of either a welded bedplate or a cast bedplate, on which the non-load bearing structure is attached. Various materials have been used for this non-load bearing structure such as aluminium or steel structures. Because of their light weight, facility to be designed in distinctive free-form designed shapes, very good corrosion and weather resistance, these shells have been made using glass fibre reinforced composite materials for the past decades. The nacelle design and production methods have followed closely the evolution of rotor blades. At one hand, most of the designers used in dimensioning and layout of blades worked in the design and laminate layout of nacelles, and on the other, the requirements with regard to lifetime, weight and cost are similar. So it is no wonder that when hand lay-up dominated the blade manufacture, nacelle covers, as shown in Plate XV, were initially produced in a hand lay-up processes, but when blade manufacture went to infusion processes, the nacelle production went too. Today there are two basic processes used. One is VARTM, as used in blade manufacture, but using the more convenient 0/90 biaxial NCFs instead of more costly biaxial +/−45° laminates, and, to build up the required
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thickness as well, a combination products of NCF with mat, sometime with enhanced resin flow properties. The other process applied is RTM light where a rigid mould and semi-flexible counter (male) mould is used. Advantages of this system are both outside and inside smoother finishes, but the resin amount needed is higher. A compressible reinforcement material is needed too which increases cost.
21.4
Future trends
Currently there are several issues related to the future use of NCF in the efficient construction of wind rotor blades. Production consistency One of the major concerns is the high irregularity of mechanical properties as a consequence of fibre misalignment, local imperfections as missing or displaced reinforcement fibre and wrinkles of the reinforcement structure formed in the laminate. Other issues can be attributed to material and processes variations. Foaming of the resin, incomplete wet-out, or an excessive exothermic reaction or ‘heat generation’ during the reaction of the used resins cause a further deterioration of the laminate properties. Even though the required security factors against failure are estimated on statistical requirements lower than in aerospace applications the level of inherent over design due to these factors has an increasing impact as blades become longer and heavier in the drive to lower of cost of electricity generation through wind power. Manufacture of larger and longer blades To be able to produce bigger and bigger blades and due to the challenge of transporting structures higher than 5 m in a cost-effective manner, new concepts have been evolved. One possibility is to build a blade in segments or sub-assemblies which are assembled or produced as preassembled dry structure, so called preforms. These parts are either infused as a whole or, if produced independently, assembled using structural adhesives. Examples of this type of approach are pioneered by companies such as Blade Dynamics (Plate XVI). Optimisation of the aerodynamic performance of wind rotor blades In the drive to constantly reduce the cost of wind energy, there is a tendency to the production of sleeker and aerodynamically more efficient blades. To realise these types of designs, the requirement for sophisticated fibre and NCF fabric properties increases, providing another challenge for the producers of NCF reinforcement structures.17
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References
1. Goodmann Gr., F. R; Vachon W.A.; United States Electricity Utility Activities in Wind Power, Fourth International Symposium on Wind Energy Systems, Stockholm, Sweden, Sept. 1–24, 1982; Hydro-Quebec: Project Eole, 4-Mw Vertical Axis Aerogenerator, Montreal, 1985. 2. Ministry of Energy (Danish Energy Agency): Wind Energy in Denmark, Research and technological Development, 1990. 3. Friis, P., Large Scale Wind Turbines, Operating Hours and Energy Production, Elsam Project A/S. Internal Report, 1993. 4. Thomas Ackermann, Lennart Söder, Wind energy technology and current status: a review Renewable and Sustainable Energy Reviews, Volume 4, Issue 4, December 2000, Pages 315–374. 5. C. Soutis, Fibre reinforced composites in aircraft construction Progress in Aerospace Sciences, Volume 41, Issue 2, February 2005, Pages 143–151. 6. Isao Kimpara, Use of advanced composite materials in marine vehicles, Marine Structures, Volume 4, Issue 2, 1991, Pages 117–127. 7. L.M. Wyatt : Materials for MW sized aerogenerators Part 2. Materials characteristics Materials & Design, Volume 4, Issue 5, October–November 1983, Pages 880–884. 8. Christoph W. Kensche: Fatigue of composites for wind turbines, International Journal of Fatigue, Volume 28, Issue 10, October 2006, Pages 1363–1374. 9. Data from internal analysis by Owens Corning, 2010. 10. Mandell, J.F., Samborsky, D.D., and Cairns, D.S., ‘Fatigue of Composite Materials and Substructures for Wind Turbine Blades’, Contractor Report SAND2002-0771, Sandia National Laboratories, Albuquerque, NM 2002. 11. Manwell J.F, McGowan J.G, Rogers A.L., Wind Energy Explained, University of Massachussetts, Amherst, USA. 12. P.J. Hogg, A. Ahmadnia, F.J. Guild: The mechanical properties of non-crimped fabricbased composites, Composites, Volume 24, Issue 5, July 1993, Pages 423–432. 13. Michaeli/Huybrechts/Wegener, Dimensionieren mit Faserverbundkunststoffen, Hanser, 1995. 14. Generic IEC Class II blade construction – Owens Corning internal information 2010. 15. Det Norske Veritas, Guidelines for Design of Wind Turbines, DNV/Risoe, Copenhagen, Denmark, 2nd Edition. 16. Germanischer Lloyd, Guidelines for the Certification of Wind Turbines, Edition 2010, Hamburg, Germany, 2010]. 17. Locke J., Valencia U., ‘Design Studies for Twist Coupled Wind Turbine Blades’, SAND 2004-0522, Albuquerque/Wichita, USA]
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Plate XI Parameters for the delamination interface model for materials NCF/LY3505 (* estimated) (Chapter 16).
Plate XII C-scans of impacted non-crimp fabric and prepreg specimens (30J) (Chapter 18).
Plate XIII Typical blade layout IEC class II 40m blade detailing the laminate constructions based on non-crimp fabric reinforcement materials (Chapter 21).
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Plate XIV Blade deflecting under loads, coloured areas indicate highest stresses (Chapter 21).
Plate XV Nacelle cover under load (wind, snow). (Source M. Zvanik, OC Presentation CFA 2001, Tampa, FL). (Chapter 21).
Plate XVI Production in segments: Shell, spar cap, and root joint/ flanging reinforcements (Chapter 21).
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22 Cost analysis in using non-crimp fabric composites in engineering applications P. SCHUBEL, University of Nottingham, UK
Abstract: This chapter describes the process for cost modelling non-crimp fabric (NCF) based composite structures. The chapter first looks at an overview of cost modelling techniques used in the composites industry and then focuses on the technical cost modelling (TCM) approach which is used in the case study. The case study presented investigates the cost centres for a 40 m wind turbine blade shell using NCF and a variety of manufacturing processes. Key words: technical cost modelling (TCM), non-crimp fabric, wind energy, wind turbine blades, cost analysis.
22.1
Introduction
This chapter describes the process for cost modelling a range of non-crimp fabric (NCF) based composite structures. The use of composite materials and type of processing method can almost always be seen as a trade-off between cost and performance. At one end of the scale are low-investment processes such as spray-up, which for example, compete favourably with wooden construction on a cost and performance basis. At the other end of the scale, there are aerospace processes involving considerable investment and full exploitation of composite advantages. High-performance materials and processing methods usually incur high costs and in some instances (e.g. satellite applications) this cost can be easily justified. Industries such as the automotive and wind energy industries are largely governed by the trade-off between cost and performance, which makes cost modelling an important aspect in advancing areas of design and manufacture. A simplistic view of this trade-off is shown in Fig. 22.1. This chapter focuses on the costs associated with the use of NCF in thermoset composites manufacture and uses a generic 40 m wind turbine blade as an example throughout the chapter. A wind turbine blade provides an excellent example to demonstrate technical cost modelling of NCF as they almost completely consist of unidirectional (UD) and multiaxial NCF. The 40 m blade being studied is a generic blade that consists of a two-part (upper and lower) aerofoil shell with a structural spar (main load-carrying member) (Fig. 22.2). This cost analysis will only be concerned with the manufacture of the two aerofoil shells.
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22.1 The decision process relating part manufacture to cost effectiveness.
22.2 General shape of the shells and spar (including root joint).
22.2
Costing methodologies: current approaches
Cost modelling for composite components can be approached in a variety of ways, depending on what specific information is required. A good review of the various approaches currently exists (Bernet et al., 2002; Wakeman et al., 2005;
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Willden, 1997). Popular techniques include comparative techniques (Bader, 2002), process-orientated cost models (Gutowski, 1999; Choi, 2009; Kassapoglou, 1997), parametric cost models (Schubel, 2010; Ye et al., 2009) and process flow simulations (Barlow et al., 2002). These methods can provide a good guide to component cost, depending on your application and skill level. However, if all these seem daunting, then there is always experience based estimating! Comparative techniques are historically based and are therefore not suited to novel materials and processes. Process-orientated cost models are more adaptive, enable identification and quantification of part cost drivers and are sensitive to improvements in manufacturing processes (Bernet et al., 2002). However, they require in-depth knowledge of the manufacturing process and part geometry. Parametric models are flexible in their approach and allow easy manipulation of process and economic factors for sensitivity studies (Bernet et al., 2002). One drawback of parametric models is that each step in the manufacturing process operates independently from another, which typically results in underestimation of manufacturing cost. However, this problem is easily overcome by incorporating process flow simulations, which simulate the dynamics of a manufacturing process with a representation of the interactions between the different manufacturing operations. Benefits derived from implementing a process flow simulation model include the ability to predict cycle time and the capacity of the process (Bernet et al., 2002). The author's preferred method for cost modelling NCF based components is termed technical cost modelling (TCM), which is explained in more detail in Section 22.3 and is used in the case study (Section 22.4). This combined parametric and process flow simulation method is widely used throughout industry and allows good manipulation of data with fast analysis and moderate set-up time of the model. As a result, the TCM technique requires reasonable understanding of the manufacturing processes as it is an event-driven model. The TCM used in this chapter was created in Microsoft (MS) Excel™ with an MS Visual Basic™ analysis programme. The TCM approach is loosely based on the ACCEM model (LeBlanc et al., 1976) and has been comprehensively explained by Wakeman (Long, 2005). The most important thing to understand about cost modelling is that the results will only ever be as accurate as the input data.
22.3
Technical cost modelling
22.3.1 Overview TCM is a top-down approach designed to follow the logical progression of a process flow with a set of parametric equations for each level of detail available to the estimator. At the lowest levels, the cost of alternative designs and manufacturing methods can be estimated in order to make trade-offs. The TCM
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database provides labour standards for each type of material, as well as material prices, scrap allowances and learning curve factors. The results are an estimate of total component production costs. As mentioned earlier, TCM is event driven, which requires all relevant process steps to be defined for a particular component and manufacturing process. Therefore, the model is set up in discrete sections to reflect key areas/stages of manufacture, i.e. as costs are aggregated at higher levels, those components contributing most heavily to total product cost are isolated. It is from this basis that tooling, capital equipment, floor space and materials can be assigned. This is then coupled to overall variables such as plant capacity, program life, labour etc. (as illustrated in Fig. 22.1). Throughout a TCM analysis, all process parameters and production variables are assigned to cost centres such as: • • • • • • • •
Interest and depreciation Maintenance Utilities Floor space and building Tooling Labour Materials Transportation
This allows identification of cash-flow throughout the manufacturing process. It is the contribution of these cost centres which provide the total manufacturing cost. With this knowledge of the most prominent cost drivers, design engineers and managers can make cost-effective design decisions.
22.3.2 Setting global simulation variables One of the first steps to setting up a TCM for NCF processing is to define the global simulation variables that define the manufacturing plant and process. These will vary depending on the manufacturer and industry sector. However, general factors listed in Table 22.1 remain the same. Other factors such as insurance, selling costs, administration, transport, R&D etc are also part of the manufacturing cost. However, this information is not always readily available.
22.3.3 Part definition Detailed knowledge of the part geometry/complexity is not necessary for TCM. However, the more information you have on specifics, the more accurate the model inputs will be. Crucial inputs include part surface area – used throughout materials calculations and part perimeter – used in building utilisation calculations. As an example, Fig. 22.3 shows the relationship between part surface area and cost for the manufacture of the shells for a large wind turbine blade produced from
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Non-crimp fabric composites Table 22.1 Global simulation variables affecting all processes Variable
Units
Typical values (40 m blade)
Parts per annum Plant capacity volume Part programme lifetime Direct labour rate Indirect labour factor Interest rate on capital Building cost Machine residual value Capital equip depreciation period Installation cost Auxiliary equipment Equipment occupancy factor Insurance Energy costs
# # years £ / hour % % £ / m2 / year % years % % % % £ / hour
1500 260 3 11.09 100 7.50 72.90 5 10 10 15 200 0 0
22.3 Effect of part area on component cost for the shells of a large wind turbine blade manufactured using VI and NCF.
wind energy grade NCF and epoxy using the vacuum infusion (VI) process. The part area and perimeter for the generic 40 m blade shell was calculated as 270 m2 and 192 m, respectively. Once the costs have stabilised with increased production volumes or parts per annum (PPA), a clear linear relationship between cost and part area is seen for this
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case. This is partly due to the fact that materials costs make up a significant proportion of the total costs and, as mentioned earlier, part surface area is a direct driver for material costs in TCM.
22.3.4 Effect of production volume Production volume affects the cost and efficiency of manufacture for all components, irrespective of whether they are made from composites, steel, plastics etc. Typically, fixed costs such as capital equipment (Section 22.3.6) need to be seen as a trade-off against production volume. In respect to automated machines, such as ATL, AFP, braiding, winding etc, deposition rates typically dictate the capacity limits. NCFs are typically processed in low to medium volume production, where manual labour techniques are typically employed, as high-cost capital equipment would not be amortised over uneconomical volumes (Fig. 22.4). However, industry (in particular the wind energy industry) is realising the need for higher deposition rates through automation and are investigating novel ways of depositing and consolidating 300 mm to 1200 mm wide rolls of NCF in dry and prepreg forms. Current development areas include variations on the ATL principal.
22.4 Production volumes for thermoset and thermoplastic manufacturing adapted from (Manson et al., 2000).
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With reference to Fig. 22.3, it can be seen that there is an initial high component cost at low volumes (approximately 50 to 100 parts) due to the inability to amortise high fixed costs such as tooling and capital equipment associated with blade manufacture using NCF. The initial dramatic drop is then followed by a series of steps which stabilise with increased production volumes. The steps are a function of maximum capacity which can be a result of labour capacity, equipment capacity or as in this case, tooling capacity. Although the use of NCF improves the drapability and deposition rate of the reinforcement material over that of wovens, a bottleneck still appears due to the total tool usage time; this includes curing and bonding. This particular TCM has been setup to automatically include additional resources to meet the intended capacity. Therefore, at each step, there is a large capital cost that needs to be amortised at that particular production volume. As the production volume increases, resource sharing takes over and the cost of additional resources to meet production are easily amortised; leading to a stabilisation in production cost. At this point, costs such as labour and materials are the dominate drivers.
22.3.5 Materials In most composite materials processing, material costs make up a significant proportion of the overall component cost. Therefore, accurate reporting on material costs is crucial to cost modelling. The NCF and associated costs seen in Table 22.2 are given as examples and are current volume prices for early 2010. On average, it can be assumed that wovens cost 20% more than their NCF equivalent. The TCM process typically relates material costs to component surface area, requiring material costs to be stipulated as a function of surface area (£/m2). However, a common practice is to stipulate material costs as a function of weight (i.e. £/kg), which is easily interchanged by knowing the density of the material (Table 22.3). It is important to understand that materials do not just mean
Table 22.2 Material cost comparison: non-crimp fabric and woven Weight (g/m2)
Construction
0/90 0/90 +/−45 +/−45 0/−45/90/+45 0 0/90 0/90
Non-crimp fabric Non-crimp fabric Non-crimp fabric Non-crimp fabric Non-crimp fabric Non-crimp fabric Woven Woven
400 600 400 600 800 300 400 600
Cost E-glass (£/kg)
Carbon (£/kg)
3.90 2.77 4.20 3.08 3.38 2.94 4.66 3.26
43.70 43.40 40.80 40.30 50.40 46.70 45.10 44.90
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Table 22.3 Material information Variable
Units
Typical values (40 m blade)
Material ID
#
£/kg
Non-crimp fabric biaxial E-glass 600 (g/m2) prepreg 45% resin 2.68
% g/cc
7 1.8
Material description Cost Units Wastage Density
Table 22.4 Material costs Description
Unit cost
Gelcoat Non-crimp fabric Prepreg E-glass Non-crimp fabric Prepreg carbon Non-crimp fabric E-glass dry fabric Non-crimp fabric Carbon dry fabric Epoxy resin E-glass tows (2400 tex) Carbon tows (48K) E-glass prepreg tows Carbon prepreg tows Bond resin Release agent Solvent
6.71 2.68 18.80 1.31 16.84 2.50 0.74 11.41 1.00 23.49 6.04 0.50 0.10
£/kg £/kg £/kg £/kg £/kg £/kg £/kg £/kg £/kg £/kg £/kg £/m £/m
Waste 5% 1–7% 1–7% 10% 5% 10% 7% 7% 1% 1% 10% 5% 5%
reinforcement and resin in TCM. Included in this family are all consumables ranging from gelcoat, solvents, release agent, vacuum consumables etc. Basic material costs used in the current TCM model are shown in Table 22.4 and are obtained from a variety of sources. Materials and prices are based on the majority of sales within the wind turbine blade manufacturing industry for that particular type of product and are assumed to be ‘volume’ prices where available. Simple rule-of-mixtures costs are used for liquid composite moulding (LCM) processes such as VI and light resin transfer moulding (LRTM), with volume fraction and wastages taken into account. Wastage is set for each material individually. Within the materials specification in TCM it is also important to express a value for wastage/scrap for each material. This is typically represented as a percentage and is completely dependent on the material type, manufacturing process, etc. For example, it may be reasonable to assume +10% resin wastage for
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a VI process when you consider the amount of resin left in the infusion pot, infusion pipe, resin traps, breather membrane and flashing. In the case of NCF, even 30% waste is not uncommon, even with computer-optimised nesting. Materials costs are heavily influenced by volume of purchase, currency exchange rates, oil prices and global demand. The latter was clearly demonstrated in the carbon fibre market where demand outstripped supply during 2003 to 2008 as a result of significant uptake in commercial aircraft manufacture; resulting in up to 66% price increases (see Table 22.5). Prices appear to have stabilised with the introduction of additional carbon fibre production plants. In the example of a 40 m wind turbine blade shell manufactured using VI with a range of prices for NCF E-glass reinforcement (Fig. 22.5); the impact on total component cost is instantly observed. At the time of writing, the volume price on wind energy grade NCF was approximately £2/kg; however, this chart demonstrates the impact on cost that could be seen if any of the earlier mentioned
Table 22.5 Non-crimp fabric carbon biaxial cost between 2003 and 2010 Year
Material
Cost (£/kg)
2003 2008 2010
Carbon 12k biaxial non-crimp fabric Carbon 12k biaxial non-crimp fabric Carbon 12k biaxial non-crimp fabric
12 20 16
22.5 Effect of reinforcement cost on component cost for the shells of a large wind turbine blade manufactured using VI and NCF.
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influences such as currency exchange or global demand dramatically changed. Figure 22.5 also illustrates the cost difference in producing a 40 m blade from NCF (£2/kg) to an equivalent woven (£2.4/kg). The use of NCF in wind turbine blade manufacture has a 4.2% cost saving to the total blade shell cost when compared to an equivalent woven.
22.3.6 Capital equipment In all processing there is some element of capital equipment that needs to be considered and factored into the overall cost of the component. Capital equipment includes items seen in Table 22.6, although prices can vary dramatically depending on the scale of production. Presented are some guide costs for equipment related to large scale wind turbine blade manufacture. The elements of cost that need to be considered are detailed in Table 22.7 and clearly show that the initial purchase cost of the equipment is only a proportion of the true cost to the process. Table 22.6 Typical equipment costs for processing of large wind turbine blades using non-crimp fabric thermoset composites Equipment
Cost (£)
Overhead crane Gelcoat applicator Vacuum unit Tool heaters Freezer Adhesives applicator
500k 40k 20k 100k 100k 60k
Table 22.7 Capital equipment variable definitions Variable
Description
Purchase cost Residual value Parts per machine Length Width Occupancy factor Power usage Depreciation Auxiliary equipment cost Installation cost Reliability Machine lifetime Machine maintenance Tooling maintenance
£ % # Machine length (m) Machine width (m) Extra room taken up by auxiliary equipment (%) kW % % Percentage of purchase cost (%) Percentage time working (%) Effective machine lifetime (years) Factor used to account for machine maintenance cost Factor used to account for tooling maintenance cost
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Non-crimp fabric composites Table 22.8 Tooling variable definitions Variable
Description
Cost Parts per tool Tooling type Tooling lifetime
£ # Reference Number of hits lifetime
22.3.7 Tooling Tooling costs vary considerably depending on the size of the component, manufacturing method employed and annual production volumes (Table 22.8). These parameters dictate whether low-cost tools (composite) or high-cost tools (aluminium, chrome plated steel) are utilised. Tooling costs can make up a considerable proportion of the total component cost (especially for low volume production) and an understanding of how the tooling cost amortises is essential to cost efficient manufacturing. Using the example of a 40 m wind turbine blade shell mould set, composite tooling costs are around £1.2 million, which when amortised over a 100% utilisation factor for three years, the tooling cost accounts for 6.9% of the total blade cost. In contrast, if the same tooling was made from aluminium at a cost of approximately £2.1 million, then the tooling cost accounts for 11.5% of the total blade cost. It is this 4.6% cost difference between the two tooling types which means that all large-scale wind turbine blade shell tooling is produced from lowcost composite materials.
22.3.8 Cost modelling variables TCM is an event-driven costing tool and requires the manufacturing process to be detailed in such a way that it allows individual costs to be assigned to processes so that true and complete costing can be captured. There are different levels of detail that can be employed when setting a model and assigning events. This level of detail is influenced by many things, mainly information availability. A comprehensive list of cost modelling variables is shown in Table 22.9, which provides a good guide to the level of information required to implement a TCM.
22.4
Case study: 40 m wind turbine blade shell
22.4.1 Introduction The TCM approach detailed in Section 22.3 was used to compare the cost of manufacture of a 40 m wind turbine blade shell set with multiple manufacturing techniques. The six processes compared are; hand lay-up prepreg, VI, LRTM,
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Table 22.9 Cost modelling variables Variable
Acronym
Variable
Acronym
Parts per annum Plant capacity part program life part area part thickness Machine lifetime Tooling lifetime Labour cost Indirect labour factor Fringe factor Hours per day (labour) Hours per day (equipment) Days per year Interest rate Building cost Machine residual value Installation cost Auxiliary equipment Equipment occupancy factor Insurance Selling / general admin expense R&D allowance
PPA PLC PPL PAA PAT MAL TOL LAB IND FRL PDL PDE DPY INT BIL RES IST AUX EOF INS ADM RND
Materials Electricity cost Miscellaneous consumable
ELC MIS
Event step variables Cycle time Labour level Raw material Machine width Machine length Capital equipment cost Machine reliability Machine maintenance factor Tooling maintenance factor Utilities levels electricity Utilities levels misc. Tooling type Tooling lifetime (hits) Tooling cost Parts per tool Production shift Step yield
CYC LLV RAW MAW MAL CEC REL MMF TMF UTI UTM TOO TOL TOC PPT SHI STY
Table 22.10 Reinforcement types associated with the six manufacturing processes Manufacturing process
Reinforcement type
Hand lay prepreg Vacuum infusion (VI) Light transfer moulding (LRTM) Automated tape laying (ATL) Automated fibre placement (AFP) Overlay braiding
Non-crimp fabric Non-crimp fabric Non-crimp fabric Unidirectional tape Unidirectional tows Unidirectional tows
automated tape laying (ATL), automated fibre placement (AFP) and overlay braiding (Table 22.10). Of these manufacturing processes, NCF is used in the hand lay-up prepreg, VI and LRTM. Each event, therefore, has an assigned cycle time, labour usage, tooling and capital equipment. For all analyses presented, dedication of capital equipment is employed. No detailed consideration was given to plant layout in this work. An example of the primary events for the hand lay-up prepreg process is shown in Table 22.11. Cycle times have been established for the hand lay-up prepreg
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Table 22.11 Process cost model events for hand lay-up prepreg shell Event
Description
Materials
1 2 3 4 5 6 7 8 9 10 11 12
Prepare shell tool Gel coat Lay prepreg (shell) Apply vac bag consumables (shell) Check Vacuum Prepreg cure Remove consumables Trim shell Assembly-bond to spar Demould Store
Release agent gel coat Prepreg E-glass RFI consumables
Shell/spar bond resin
process and VI whilst the remaining processes have been determined experimentally. Processes such as ATL, braiding and AFP are highly automated and employ minimal manual labour.
22.4.2 Results The overall results for the six manufacturing processes for the shell structure are shown in Fig. 22.6. The results have been calculated over 2500 PPA to demonstrate individual blade cost as production increases.
22.6 Cost per part (shell) vs. production volume for the six manufacturing processes.
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The cost of manufacture for the two halves of the shell is shown to fall rapidly up to a production level of around 400 units per annum for each of the six processes studied. After this, the cost stabilises up to 1000 units and generally plateaus thereafter. In each of the six cases studied, a step change can be observed roughly every 200 units as a result of multiple parallel tools being brought online to accommodate the annual capacity – this is a function of a set of predefined variables. The step changes are less pronounced as the PPA increase, due to the cost of additional tooling being distributed over an ever-increasing unit count. Over the six processes, the cost of shell manufacture generally ranges from £29 396 to £35 625 per part (based on 1500 PPA), with ATL and braiding making up these two extremities, respectively. The two benchmark systems (hand lay-up prepreg and VI) lay somewhat in the middle of these upper and lower extremities at £31 918 and £30 849 respectively. If the prepreg and liquid resin infusion (LRI) moulding techniques are isolated, then the two theoretical cost-effective manufacturing processes are ATL and LRTM respectively, with an average cost benefit of 8% over the benchmark systems. On a production run of 1500 per year, this equates to a potential cost saving of £3.8 million per annum. ATL and the hand lay-up prepreg (benchmark) both utilise a similar principal fabric system (prepreg) and therefore are a good comparison between automation and non-automation manufacture. Equipment depreciation costs (Fig. 22.7) from the purchase of the ATL facility are depreciated over ten years, as stated in Section 22.4.1, and rapidly off-set through the direct cost savings derived from reduced labour input and lower waste material levels. LRTM is best compared to the VI benchmark due to its similarity in using a form of LRI. Cost savings for LRTM are not fully recognised until after 300 PPA
22.7 Part cost of the shell split by process – based on 1500 PPA.
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where additional tooling costs are absorbed by the production volume. An overall cost saving for LRTM verses VI is seen due to reduced cycle times and consumables (Fig. 22.7). Overlay braiding shows a 15% increase in cost over the benchmarks and exhibits exaggerated step changes in cost every 200 PPA on average. This is due to the increased manufacture time, additional processes (core manufacture) and high investment. AFP shows good potential; however, current material prices restrict its full cost effectiveness. This situation will change with increased uptake of the technology.
22.4.3 Cost breakdown A cost breakdown at three production levels for the shell production is shown in Fig. 22.8. In all cases, raw material costs are fixed and labour costs remain unchanged with production levels. The variables tend to be tooling and maintenance costs which are proportionately high at low production levels (230 PPA = 1 part per working day). Interest and depreciation is also a contributing factor for high investment processes such as ATL, braiding and AFP. However, in some cases this is off-set with high production volumes.
22.8 Split by process for the six case study processes at three volume levels.
22.4.4 Conclusions The methodology and results for a TCM exercise based around a 40 m wind turbine blade produced using NFC have been presented. Assumptions were made to create a general structure that could be applied to all scenarios. A comparison
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of NCF-based manufacturing processes (hand lay-up prepreg, VI and LRTM) and automated fibre deposition processing (ATL, AFP and braiding) were compared and yielded results for a 40 m wind turbine blade shell production. Large blade shell production costs are predominantly influenced by labour costs and component area. If these two parameters are already fixed (i.e. an existing production site or set-up in a particularly high labour cost area), then results indicate that development should focus on reducing materials cost and reducing deposition time. It has been shown that NCF is a more cost-effective material over wovens for the case presented and the use of efficient NCF-based manufacturing processes such as LRTM warrants further investigation. Benefits to cost of manufacture through automation and tooling are clearly observed utilising this cost modelling exercise. However, significant downstream benefits can also be realised although not accounted for in this model. Benefits, such as improved quality control through automated processing and tighter dimensional tolerances have a direct impact on scrap rates.
22.5
Acknowledgements
The author would like to acknowledge funding from the Technology Strategy Board and other anonymous research projects for enabling the development of the TCM tools used in this case study. The author also wishes to thank anonymous consultants and manufacturers within the wind energy industry for providing valuable benchmark data in order to calibrate the TCM.
22.6
References
Bader, M. G. (2002) Selection of composite materials and manufacturing routes for costeffective performance. Composites: Part A, 33, 913–934. Barlow, D., Howe, C., Clayton, G. and Brouwer, S. (2002) Preliminary study on cost optimisation of aircraft composite structures applicable to liquid moulding technologies. Composite structures, 57. Bernet, N., Wakeman, M. D., Bourban, P. E. and Manson and J. A. E. (2002) An integrated cost and consolidation model for commingled yarn based composites. Composites: Part A, 33, 495–506. Choi, J. W. (2009) Architecture of a knowledge-based engineering system for weight and cost estimation for a composite airplane structures. Expert systems with applications, 36, 10828–10836. Gutowski, T. G. (ed.) (1999) Advanced composites manufacturing, New York, Wiley. Kassapoglou, C. (1997) Simultaneous cost and weight minimization of composite-stiffened panels under compression and shear. Composites: Part A, 28A, 419–435. Leblanc, D. J., Lorenzana, J., Kokawa, A., Bettner, T. and Timson, F. (1976) Advanced Composite Cost Estimating Manual. Volume I. NORTHROP CORP HAWTHORNE CA AIRCRAFT DIV, AFFDL-TR–76–87. Long, A. C. (ed.) (2005) Design and manufacture of textile composites, Cambridge England, Woodhead Publishing Limited.
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Manson, J. A. E., Wakeman, M. D. and Bernet, N. (2000) Composite processing and manufacturing – an overview. In Kelly, A. A. Z. C. (ed.). Oxford, Elsevier Science. Schubel, P. J. (2010) Technical Cost Modelling for a Generic 45m Wind Turbine Blade Produced by Vacuum Infusion (VI). Renewable Energy, 35, 183–189. Wakeman, M. D., Sunderland, P. W., Weibel, N., Vollmann, T. and Manson, J. A. E. (2005) Cost and implementation assessment illustrated through composites in the automotive industry – part I : methodology. Willden, K. (1997) Advanced technology composite fuselage manufacturing. National Aeronautics and Space Administration (NASA), report CR–4735. Ye, J., Zhang, B. and Haiming, Q. (2009) Cost estimates guide to manufacturing of composite waved beam. Materials and Design, 30, 452–458.
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Index
[A1-B-A2]-HTA laminates, 341, 343, 350, 352 in-plane tensile modulus, 350 in-plane tensile strength, 352 normalised in-plane tensile modulus and strength, 343 [A1-(B/2)s -A2]2 -HTA laminates, 341, 344–5, 350–4 in-plane compression modulus, 351 in-plane compressive strength, 353 normalised in-plane compressive modulus and strength, 344 [A1-(B/2)s -A2]2 -HTS laminates, 345–6 in-plane shear modulus, 351 in-plane shear strength, 353 [A1-(B/2)s -A2]-HTS laminates normalised compressive strength after impact, 346 normalised in-plane shear modulus and strength, 345 normalised mode I energy release rate, 347 Abaqus Explicit, 157 ACCEM model, 496 acoustic emission, 280–3 advanced synchron weave fabric set-up, 24 illustration, 24 working principle, 24 aerospace applications aeronautic requirements, 443–5 C-scans of impacted non-crimp fabric and prepreg specimens, Plate XII residual compression strength and delaminated areas against impact energy, 444 application examples, 445–7 Airbus A380 rear pressure bulkhead, 445–6 Airbus A400M cargo door, 446–7 further applications on substructure level, 446–7 inside view of Airbus A400M cargo door, 446 non-crimp fabric carpet draping in Airbus A380 RPB production, 445 outside view of Airbus A400M cargo door, 447 future trends, 447–8 non-crimp fabric composites, 441–8 composite applications on Airbus A380, 442
evolution of composite structures within Airbus fleet, 442 Airbus A340, 441, 445 Airbus A380, 441 flap track, 447 rear pressure bulkhead, 445–6 Airbus A350 XWB, 441 Airbus A400M, 446–7 Airbus Industry Material Specifications (AIMS), 104 angle ply laminate, 314, 319 anisotropy, 193, 195, 201 ARAMIS strain-mapping system, 123 Ardrox Biopen P6F5, 192 ASTM D 1388–96, 392 ASTM D 5379/D 5379M – 93, 266 Audi A8, 462 automated analysis defects in fibre placement in non-crimp fabrics for composites, 103–14 motivation, 103–4 non-crimp fabric detailed picture, 107, 108 future trends, 111–14 blisters on different prepreg materials, 113 woven fabric area coverage via transmitted light device, 113 yarn width of warp yarns in a woven fabric, 112 gap and knitting errors, 109 motivation, 103–4 quality analysis by digital image analysis final results of different non-crimp fabrics, 110 grey value distribution histogram, 108 system, 106 working principle, 106–9 automated fibre placement (AFP), 505, 508 automated tape laying (ATL), 505, 507 automation, 71–2 automotive applications boot lid of Lamborghini Gallardo Spyder, 468–9 built-in FRP boot lid, 469 integrated construction, 469 car roof, roof carline and hybrid constructions at BMW Group, 466–8 BMW Hydrogen 7 side frame, 468
511 © Woodhead Publishing Limited, 2011
512
Index
CRP-roof industrial-scale manufacturing for BMW M3, 467 roof carline BMW M6, 466 roof of BMW M3, 467 future trends, 476–8 steel and textile production lines, 477 trends in fibre reinforced composite production, 477 multi-step preforming, 472–6 automobile underbody structure, 475–6 car roof segment, 474–5 preform centre, 473 production steps in preform centre, 474 roof segment preform, 475 underbody structure preforming, 476 non-crimp fabric composites, 461–79 cost distribution in preforming process, 465 production of parts of different complexity and quantity, 464 research and development, 469–76 Super Light Car, 462 single-step preforming, 470–2 feeding module for multi-axial warp-knitting machines, 471 folding gate with thread guides, 472 possible reinforcement yarn displacements, 472 ‘AutoPreforms,’ 474 average volume fraction, 405 B2 laminates, 279–83 barely visible impact damage, 300, 301, 304 bending hysteresis, 136 bi-axial carbon reinforcement fabrics, 364 bias direction, 265, 280, 312, 313, 314, 330 bias extension test, 117, 130, 392 biaxial fabrics, 118 biaxial non-crimp fabric composites deformability modelling, 144–62 modelling strategies, 148–9 energy-based kinematic mapping, 149–56 manufacture process statistical variation modelling, 156 modelling asymmetric shear behaviour, 150 modelling the effect of blank-holder, 155–6 predicted fibre patterns for nose cone, 156 fabric architecture behaviour on the shear and draping behaviour, 145–8 +/−45° NCF knitted with tricot stitch pattern, 146 NCF formed shape, 148 shear compliance curves for E-glass +/−45° tricot warp knitted fabric, 147 finite element modelling, 156–61 forming finite element modelling BHF effect on the formed shapes, 161 intra-ply slip modelling, 159 manufacture process statistical variation modelling, 160–1 meso-mechanical model representative cell, 158 modelling asymmetric shear behaviour, 157–8 modelling the effect of the blankholder, 160 out-of-plane bending stiffness modelling, 159–60
tows slip through the stitches in their axial direction, 159 future trends, 161–2 trellis shear force prediction vs shear angle behaviour using analytical models, 150–5 compaction model, 153 crossover model, 154 different mechanisms contributions, 154–5 forming set-up for Tay nose cone, 155 separate contributions to total normalised shear force of fabric stitch, 154 stitch crossover view, 152 unit cell stitch model, 151–3 unit tricot stitch, 151 biaxial warp-knitted non-crimp fabrics, 6–14 coursewise and non-coursewise weft insertion, 6 fabric set-up, 6 feeding module, 7–10 bobbin creels and cheese creel, 9 creel, 9 hook, needle and pin-hook system, 8 machine equipment, 10 weft carriage system, 7–8 weft thread transport system, 8–9 machine operation, 13–14 stitch types, 12, 13 pillar, tricot and plain stitch types, 13 take-up module, 12–13 cutting devise and vacuum cleaners, 13 fabric takeoff, 13 fabric wind-up, 13 warp-knitting module, 10–12, 13 knitting elements and walking needle concept, 10 loop formation process, 10–11 walking needle, 11 weft-thread sinkers, 12 yarn let-off, 12 working principle, 6–13 warp-knitting machine with biaxial weft insertion, 7 black-box modelling tool, 436 blisters, 113 BMW Hydrogen 7, 468 BMW M3, 467, 470 BMW M6, 466 bobbin threads, 69 Boltzmann model, 244–5 bonded tape non-crimp fabrics, 30–1 fabric set-up, 30 multiaxial bonded tape NCF, 31 working principle, 30–1 bonded thread non-crimp fabrics, 31–2 biaxial and multiaxial bonded thread NCF, 31 biaxial bonded thread non-crimp fabric production process, 32 fabric set-up, 31 working principle, 32 boundary conditions, 248–9, 375–83 braiding technology, 69 Brinkman equations, 247, 249–50 bulk moulding components (BMC), 462 BVID see barely visible impact damage
© Woodhead Publishing Limited, 2011
Index CAI see compression after impact carbon-epoxy cross-ply laminate, 325–6 carbon-epoxy NCF composites, 330 carbon-epoxy plain weave composite, 326 carbon fibre composites, 420 carbon fibre-reinforced plastic laminates, 335 carbon fibre reinforced polymer composites (CFRP), 449 carbon fibres, 50, 57, 104 carbon sewing threads, 69 carriage, 54 CEC project Falcon, 395 Celper, 337 Chevrolet, 462 Chiu model, 350 Chorin projection method, 250 Christensen’s self-consistent approach, 407 clamping system, 128 classical laminate theory (CLT), 278–9, 297, 324–5, 387, 403, 411, 413, 420, 436 cohesive zone interface, 397 ‘compaction and stretch’ (C&S), 458 compaction model, 153 Composite Cylinder Assemblage, 405 composites fibre placement defects automated analysis in non-crimp fabrics, 103–14 future trends, 111–14 motivation, 103–4 non-crimp fabric quality analysis by digital image analysis, 106–11 non-crimp fabrics quality characteristics, 104–6 non-crimp fabric preforms structural stitching, 67–82 applications and future trends, 81–2 quality aspects for structural stitching, 74–81 stitching technology and sewing machines, 70–4 threads for structural stitching technology, 68–70 non-crimp fabrics production, 3–37 3-D woven and non-interlaced non-crimp fabric, 27–30 fixation by adhesion, 30–3 future trends, 35–7 non-crimp fabrics overview, 4 non-crimp woven fabrics, 23–7 production technologies comparison, 33–4 warp-knitted non-crimp fabric, 5–22 weft-knitted non-crimp fabric, 22–3 compression after impact, 302, 336, 346, 354 core spun yarns, 69 Cos Law, 279 cost analysis 40 m wind turbine blade shell case study, 504–9 cost breakdown, 508 cost per part vs production volume, 506 part cost of shell split by process, 507 process cost model events for hand lay-up prepreg shell, 506 reinforcement types associated with six manufacturing process, 505 split by process for the six case study processes at three volume levels, 508
513
non-crimp fabric composites in engineering applications, 494–509 costing methodologies, 495–6 decision process relating part manufacture to cost effectiveness, 495 general shape of shells and spar, 495 technical cost modelling, 496–504 capital equipment, 503–4 cost modelling variables, 504, 505 effect of production volume, 499–500 materials, 500–3 part definition, 497–9 technical cost modelling (TCM) setting global simulation variables, 497, 498 tooling, 504 crack density, 315–17 crack-opening displacement, 295 crochet technology, 69 cross direction, 265, 282 crossover model, 154 Culimeta, 69 3D FE Hom-0°, 416, 419 ‘3D FE’ model, 415, 416, 436 damage accumulation, 372–83 boundary conditions, 375–83 experimental observations, 372–5 damage development, 314–19 damage progression impacted NCF composites, 300–7 BVID and VID impacted sandwich face sheet laminates, 301 BVID in a sandwich face sheet laminate, 301 dashed area polished in the thickness direction, 303 delaminations in a NCF laminate with BVID, 302 impact damage formation, 300–2 impact damage tolerance, 302–7 longitudinal strain close to failure, 307 monolithic CAL panel, 304 in-plane loading, 290–9 crack-opening displacement schematic, 295 double crack, 296 half crack running through one 90° fibre bundle, 294 in-plane compressive failure, 296–9 intralaminar matrix tensile cracks, 291 longitudinal cracks, 295 NCF cross-ply laminate cross-section, 291 quasi-isotropic specimens loaded to compressive failure, 298 tensile loading, 290–6 whole crack, 292 whole cracks, half cracks and double cracks densities, 293 kink bands 5° ply of a 5° off-axis loaded QI specimen, 299 detailed view, 299 formation in a 45° layer, 305 impacted skin of panel with BVID, 305 monolithic CAI panel micrograph, 306 outer 45° ply of monolithic CAI panel, 306 non-crimp fabric composites, 289–308
© Woodhead Publishing Limited, 2011
514
Index
Darcy’s Law, 168, 216, 242–3, 246, 389 deformability bending, 136–9, 140 diagrams, 137 heavy carbon tows bending rigidity, 139 rigidity, 137 biaxial tension, 128–32, 140 biaxial tensile tester and sample clamping, 129 equipment and samples, 128 fabric compression diagram, 131 fabrics tension, 130 simplified models validity, 132 tension diagrams, 128–32 compression, 132–6, 140 first compressive cycle, 135 nesting coefficients, 136 nesting effect in the fabrics, 136 test results, 133–4, 135 trends in the compressive behaviour, 134–5 modelling in biaxial non-crimp fabric composites, 144–62 energy-based kinematic mapping, 149–56 fabric architecture behaviour on the shear and non-crimp fabrics draping behaviour, 145–8 finite element modelling, 156–61 future trends, 161–2 modelling strategies for non-crimp fabric forming, 148–9 non-crimp fabric composites manufacture, 117–40 non-crimp fabric, face and back samples, 120 non-crimp fabric parameters, 119 tests summary, 120 shear, 118, 120–8, 139–40 diagrams, 124–8 difference of shear angle of fabric B2 and frame shear angle, Plate I picture frame, 121 picture frame test, 121–3 SC, ST, and SS tests diagrams, 124 shear force tests diagram, 127 two fabrics shear diagrams comparison, 126 delaminations, 289–307, 317, 320, 323, 331–2, 347 DIN 65148, 62 Dirichlet boundary conditions, 390 double-cantilever beam (DCB) tests, 346–7, 398, 399 double cracks, 295–6 90° fibre bundle, 296 drape forming, 452 dry friction, 392 E-glass fibre, 325 EN 13427, 43 EN 13473, 42 EN 13427-1, 44 EN 13473-1, 43 abbreviations for material type, 44 code letter for binding system type, 45 End Notched Flexure test, 398 engineered fabrics, 171 EP 1 352 118 B1, 63–4 Epikote 828 LV, 265
Epikure DX 6514, 265 European standard EN 13473, 85 failure index, 370, 371–2, 379–80 FALCOM project, 184, 187, 209 fatigue appendix, 333–4 biaxial carbon fibre NCF, 334 NCF internal geometry characteristics, 334 carbon-epoxy NCF composite and carbonepoxy twill weave composite after tensile fatigue fibre direction for 103, 104, 105 and 2.5 × 105 cycles, 318 fibre direction for 104, 105 and 2.5 × 105 cycles, 319 damage development, 314–19 crack density, 316 transverse matrix cracks in a biaxial carbon-epoxy NCF composite, 316 fatigue life curves bias direction of a twill weave carbon fibre-epoxy composite, 313 different off-axis angles of cross-ply composites, 327 different orientations of a ±45° carbon epoxy NCF composite, 329 fibre direction of twill weave carbon fibre-epoxy composite, 313 fibre directions of carbon-epoxy non-crimp fabric composite, 312 matrix dominated directions, 312 room temperature fatigue life curves for unidirectional carbon-epoxy composite, 326 influence of fibre orientation, 324–30 normalised fatigue stress vs. number of cycles to failure, 330 tensile fatigue tests results, 328 variation of elastic constants, 325 non-crimp fabric composites, 310–34 fatigue life, 311–14 open questions, 332 post-fatigue residual properties, 330–2 post-fatigue and intact compressive strength, 331 stiffness evolution, 319–24 average stiffness evolution, 323 fatigue process on the normalised composite stiffness, 320 glass fibre-reinforced polymer laminates normalised stiffness evolution, 321 quasi-isotropic and ±45°, 322 static stiffness evolution, 324 stiffness decrease, 320 fatigue life, 311–14 FETex, 337 fibre distortion, 92 fibre placement defects automated analysis in non-crimp fabrics for composites, 103–14 future trends, 111–14 motivation, 103–4 non-crimp fabric quality analysis by digital image analysis, 106–11 non-crimp fabrics quality characteristics, 104–6
© Woodhead Publishing Limited, 2011
Index
515
fibre sizing, 70 fibre-tow spacing, 218 fibre tow waviness, 220, 230, 234 filled markers, 175 finite difference, 245 finite element analysis non-crimp fabric composites, 360–83 damage accumulation, 372–83 elastic analysis, 369–72 representative volume element, 363–9 finite element method, 148 finite element model, 369–72 damage initiation and stiffness response, 370–2 peculiarities, 370 finite element simulation, 149, 245 finite volume simulation, 245 fisheye openings, 107, 158, 458 FlowTex, 246, 337 fluid flow models, 246–8 fold-wound non-crimp fabrics, 32–3 fabric set-up, 32 fold-winding system, 33 working principle, 33 Formula 1, 462 free nodes, 431 frictional energy, 155 Froude number, 243
infusion technology, 483–4 injection flow rate, 224 injection pressure, 223 Instron 1196, 266 Instron 4467, 121, 132 Instron 4505, 265–6 Integrated Tool for Simulation of Textile Composites, 337 inter-tow sliding, 390 interactive failure criteria, 433 interlaminar cracks see delaminations intermediate preforms, 450, 453 INTEX, 464 intra-ply slip (IPS), 458 intralaminar cracks, 289–91 double cracks, 295–6 half-cracks, 294–5 longitudinal cracks, 295 schematic, 291 whole cracks, 291–4 ISO 527–4, 265–6 ISO 3374, 46, 47 ISO 4921, 47 ISO 14130, 266 ISO/DIS 1268-1, 45 iso-strain model, 419 ITOOL see Integrated Tool for Simulation of Textile Composites
Gebart’s equation, 198 GLARE, 443 glass fibre composites, 420 glass fibre mat thermoplastics (GMT), 462 glass fibre NCF composites, 311, 315 glass fibre reinforced plastics (GFRP), 461–2 ‘global criteria,’ 433 global delamination, 320 global permeability, 237 ‘Growian,’ 481 gRVE, 363, 366, 375
Jeeves minimisation method, 150
half-cracks, 294–5 crack-opening displacement, 295 densities, 293 one 90° fibre bundle, 294 Halpin-Tsai expressions, 407–10 hand lay-up prepreg, 504 process cost model events, 506 Hashin’s CCA model, 407–10 Hexcel, 171 Hexcel Fabrics, 59 Hexcel-patent, 59–61 Hooke method, 150 Hooke’s law, 387 impact damage formation, 300–2 tolerance, 302–7 delamination growth, 303–4 kinking of fibre tows, 304–7 in-plane buckling, 457 in-plane compressive failure, 296–9 in-plane dimension, 218 in-plane permeability, 217 in-plane permeability values, 222, 223, 224 in-plane shear test, 266 in-situ strength, 426
Karl Mayer Textilmaschinenfabrik GmbH, 51, 54, 57 Kawabata Evaluation System (KES-F), 127 kinematic mapping methods, 148 kink bands, 298–9, 304–7, 421 5° ply of a 5° off-axis loaded QI specimen, 299 detailed view, 299 formation in a 45° layer, 305 impacted skin of panel with BVID, 305 monolithic CAI panel micrograph, 306 outer 45° ply of monolithic CAI panel, 306 knitted web, 86 Kozeny–Carman equation, 188, 197 Lamborghini Gallardo Spyder, 468–9 laminate thickness, 342–3 LamTex, 337 Lancia Lamda, 461 Laplace equation, 390 lapping diagram, 88 LCM see liquid composite moulding Leicester notation, 88 Leno weave, 25–6 fabric set-up, 25 uniaxial and biaxial reinforcement, 25 working principle, 25–6 technique, 26 LIBA Maschinenfabrik GmbH, Naila, 47, 52 LIBA Max 3 CNC, 47 clamping sequence, 53 computer-controlled weft-insertion system, 48 taper-layer system, 52 transport-chain, 52 light resin transfer moulding (LRTM), 501, 504, 507–8 LIMS, 242, 389
© Woodhead Publishing Limited, 2011
516
Index
liquid composite moulding (LCM), 166, 216, 242, 449, 501, 507 liquid resin infusion (LRI), 166 flow process, 389–90 local delamination, 314, 315, 320, 324 local permeability, 237–8, 249 longitudinal cracks, 295 longitudinal intralaminar cracks, 289 loop formation process, 10–11 illustration, 11 LY3505 resin, 399 machine direction (MD), 265, 280 Marie Curie Fellowship, 204 master surface, 397 match mould forming, 452 matrix cracks see intralaminar cracks mechanically representative volume (mRVE), 363–4 MeshTex, 337 meso-analysis, 360–83 see also finite element analysis meso models, 361–2, 370 see also finite element model meso scale modelling, 383 see also finite element analysis mesoelements, 405, 417 micro-level flow phenomenon, 173 microscale homogenisation, 405 Mixed Mode Bending (MMB) test, 398 MMF see multiaxial multiply fabrics mode I energy release rate, 346–7 modified Tresca criterion, 427, 428 modified von Mises type of criteria, 430 Monte Carlo method, 156 Monza, 462 multi-ply carbon reinforcement fabrics, 364 multiaxial multiply fabrics, 85, 263 failure pattern, 269 mechanical properties, 274–9 reinforced epoxy composites in-plane shear properties, 272 interlaminar shear strength, 274 tensile properties, 267 specifications, 264 tensile stress–strain curves of laminates, 268 multiaxial warp-knitted non-crimp fabric, 14–20 coursewise and non-coursewise weft insertion, 14 fabric-set-up, 14–15 schematic set-up with non-coursewise weft insertion, 15 feeding module, 17–20 creel, 19 machine equipment, 20 pin-pin, needle-field and clamping system, 18 spreading device with electrodes, 20 stationary and mobile weft-insertion portal, 18 weft carriage system, 17–18 weft thread transport system, 18–19 take-up module, 20 warp-knitting module, 20 working principle, 15–17 coursewise multiaxial warp-knitting machine, 16
non-coursewise multiaxial warp-knitting machine, 17 NaSt3DGP, 250–1 Navier-Stokes equations, 244–6 see also NaSt3DGP NCF see non-crimp fabrics NEDO, 465 nesting behaviour, 97 Neumann boundary conditions, 390 Newtonian incompressible liquid, 389–90 Newton–Raphson type solution, 387 Newton’s second law of motion, 387 NH90, 449 non-crimp fabric composites see also structurally stitched NCFcomposites aerospace applications, 441–8 aeronautic requirements, 443–5 application examples, 445–7 future trends, 447–8 automotive applications, 461–79 future trends, 476–8 research and development, 469–76 average transverse strain in bundle at 1% applied strain, 432 dependent on its geometry, 433 boundary conditions for a damaged composite, 375–83 constructing BC for the balanced laminate, 378 drop of secant moduli and failure index, 380 elementary ply post-critical behaviour, 380–3 local stress density and distribution, 377 modelling cracks on the meso scale, 377–80 normalised secant moduli in tensile tests, 383 out-of plane displacement, Plate IV ply deformation, 376 shear diagrams from two tensile tests, 382 test problem, 376–7 transverse stress distribution, 380 unit cell and the contours of the unit cells, 378 compressive strength in nominal bundle direction, 421–4 fibre bundle waviness and kinking failure, 421 linear fit to experimental values compared with prediction from criterion, 424 off-axis QI-laminate test specimens failed in compression, 423 stresses in 0°-plies at specimen failure, 423 cost analysis of engineering applications, 494–509 case study, 504–9 costing methodologies, 495–6 technical cost modelling, 496–504 damage accumulation, 372–83 experimental observations, 372–5 tensile diagrams, 374 tensile tests in longitudinal direction, 373 damage development in B2 laminates, 279–83 acoustic emission, 280–3
© Woodhead Publishing Limited, 2011
Index AE counts, event energy, cumulative energy and stress–strain curve, 281 strain levels based on AE results, 283 damage initiation in non-sheared and sheared materials, 285–7 initial damage investigation, 286 damage progression, 289–308 impacted NCF composites, 300–7 in-plane loading, 290–9 drape, stress and impact behaviour modelling, 386–400 finite element method, 386–7 finite element methods for infusion analysis, 389–90 draping analysis and finite element simulation, 390–4 finite element drape simulation, Plate VII kinematic and finite element simulation results, Plate VI kinematic drape algorithm solution scheme, 391 principal deformations modes in bi-axial fabric, 390 shear angle distribution in pitch horn, Plate V testing methods for fabric drape properties, 393 two stacked plies and constitutive laws for NCF, 392 effect of stitching on the mechanical properties and damage, 360–83 internal composite geometry models, 361–2 elastic analysis, 369–72 artificial stress concentration, 370 finite element model, 369–72 stiffness and damage features, 371 stress exposure factor, 371 fatigue, 310–34 appendix, 333–4 damage development, 314–19 fatigue life, 311–14 influence of fibre orientation, 324–30 open questions, 332 post-fatigue residual properties, 330–2 stiffness evolution, 319–24 fibre arrangements loaded in tension and compression transverse failure strain initiation, 430 transverse failure stress initiation, 430 finite element model and FE mesh, Plate III impact and failure, 396–400 equivalent NCF/LY305 ply properties, 399 inter-ply delamination model, 398 parameters for delamination interface for materials NCF/LY3505, 400, Plate XI test and simulation results for DCB tests, 399 infusion simulation, 394 different infusion strategies and contours of filling times, Plate IX model zones for thickness and permeability variations, Plate VIII laminate analysis and finite element stiffness, 387–9 Hooke’s law for orthotropic ply and fibre axis system, 388
517
multi-layer element and element stiffness matrix, 389 laminate hierarchical structure, 403 layer representation, 414 materials and composite production, 264–5 multi-axial multi-ply carbon fabric specifications, 264 mechanical properties, 266–74 failure pattern, 269 in-plane shear properties, 271–3 interlaminar shear strength, 273–4 MMF in-plane shear properties, 272 MMF interlaminar shear strength, 274 MMF tensile properties, 267 shear Iosipesku test, 271 short beam shear test specimens after testing, 273 tensile properties, 266–71 tensile stress–strain curves, 268 mechanical properties based on sheared multiaxial multiply fabrics, 274–9 failure patterns, 277 ply angles, fibre volume fractions and tensile properties, 276 sheared specimens in shear frame, 274 tensile properties, 275 representative volume element, 363–9 NCF plane geometry and unit cell geometrical model, 365 non-matching skewed UC’s, 365 non-matching unit cells of two adjacent layers, 366 non-periodical nature of the damaged composite, 367 rectangular unit cell, 368 representative capability with the classical periodic boundary conditions, 368 representative volume definition, 363–9 required inputs and obtained outputs from ‘black box’ modelling tool, 404 simplified geometrical models for mesostructure, 414–20 boundary conditions applied to surface of representative volume elements, 419 comparative analysis of stiffness models, 417–20 in-plane stiffness, 416–17 material properties used in numerical analysis, 418 mesoscale structure, 415 stiffness of carbon fibre non-crimp fabric composite, 419, 420 stiffness and failure, 394–5 mechanical and failure data for single ply, 395 notation for elementary ply, 395 test and analysis results for failure, Plate X stiffness and strength, 263–87 materials and composite production, 264–5 test procedures, 265–6 stiffness and strength modelling, 402–36 stiffness models, 405–20 axial modulus and major Poisson’s ratio for NCF cross-ply laminate, 413 axial modulus and major Poisson’s ratio for NCF quasi-isotropic laminate, 413
© Woodhead Publishing Limited, 2011
518
Index
curved beam model with fixed fibre tow ends, 412 effective longitudinal modulus of curved tows, 411–14 fibre and matrix properties used in micromechanical study, 408 longitudinal modulus, 409 microscale modelling of elastic properties of fibre tows, 407–10 Poisson’s ratio, 410 possible workflow of multiscale analysis, 406 reduced axial modulus due to tow waviness, 411 repeatable unit cells, 408 sensitivity of knockdown factor, 412 shear moduli, 410 transverse modulus, 409 strength models, 420–35 strength transverse to fibre direction, 424–35 average strain in NCF composite bundle, 431–3 failure criteria for bundle mesostructures, 433–5 hexagonal and square fibre arrangement, 429 mesogeometry simplification, 432 micro-meso approach for transverse matrix crack initiation, 424–6 microscale strength modelling, 426–31 model used for parametric study of interface distortion, 432 parameters as determined by uniaxial tension and compression tests, 427 test procedures, 265–6 in-plane shear test, 266 short beam shear test, 266 tensile test, 265–6 textile preforms deformability, 117–40 bending, 136–9, 140 biaxial tension, 128–32, 140 compression, 132–6, 140 shear, 118, 120–8, 139–40 variability in permeability of composite reinforcements, 216–39 future trends, 239 material characterisation, 217–22 modelling and simulation, 233–8 permeability measurement, 222–33 wind turbines, 481–92 development in wind energy, 483–91 future trends, 492 materials used in nacelle construction, 491–2 X-ray radiography, 283–5 B2 specimens subjected to tensile loading, 284 non-crimp fabric preforms, 492 analysis for helicopter applications, 449–60 automated lay-up machine, 451 defect analysis, 456–8 limit fibre path of preform on a helicopter frame, 458 terminology of defects, 457 deformation mechanism during preforming, 454–6 classification of deformation mechanism, 455 stitch yarns deformations, 456
future trends, 458–60 applications and main benefits, 459 NCF tailored reinforcements diaphragm forming, 452 drape forming, 453 stretch forming, 453 non-crimp fabric process chain with quality gates, 451 permeability, 166–209 deformation and permeability, 196–208 experimental permeability results, 168–87 geometrical effects, 187–96 nomenclature, 214–15 techniques for non-crimp fabrics, 449–54 final preform, 453–4 process chain, 450–1 tailored reinforcements, 451–2 technical principle, 450 types of forming methods, 452–3 non-crimp fabrics see also specific non-crimp fabrics 3-D woven and non-interlaced non-crimp fabric, 27–30 2D, 3D and non-interlacing weaving, 29 fabric set-up, 28–9 orthogonal, multilayer, and angle-interlock fabric structures, 28 production technologies categorisation, 28 working principle, 29–30 areal weight estimation, 45–7 necessary characteristics and resolution of used balance according to ISO 3374, 47 suggested method for cutting out fabric specimens, 46 automated analysis of fibre placement defects for composites, 103–14 curvature in knitting rows, 111 detailed picture, 107, 108 exemplary defects, 105 future trends, 111–14 gap and knitting errors, 109 motivation, 103–4 quality analysis by digital image analysis, 106–11 quality characteristics, 104–6 bonding patterns, 47, 48 commonly used bonding patterns, 48 carbon biaxial cost between 2003 and 2010, 502 computer-controlled weft-insertion system, 47–50 patented in DE 19726831 C2, 49 transport chain and layer-carriage, 50 deformability modelling, 144–62 energy-based kinematic mapping, 149–56 finite element modelling, 156–61 future trends, 161–2 modelling strategies for non-crimp fabric forming, 148–9 draping behaviour and fabric architecture behaviour on the shear, 145–8 +/−45° NCF knitted with tricot stitch pattern, 146 NCF formed shape, 148 shear compliance curves for E-glass +/−45° tricot warp knitted fabric, 147
© Woodhead Publishing Limited, 2011
Index EN 13473-1 abbreviations for material type, 44 code letter for binding system type, 45 EP 2003232 A1 carriage, gripper and tape movements during a lay-up sequence, 57 offline spread tape placing sequence into the transport-chains, 58 online tow spreading system, 56 principle of combined creel and spreading-unit, 56 existing machines outstanding patents, 47–59 fixation by adhesion, 30–3 bonded tape, 30–1 bonded thread, 31–2 fold-wound, 32–3 ‘Hexcel-patent’ – EP 0972102 B1, 59–61 basic architecture of modern machines similar to Hexcel concept, 61 overview of the range of the patent, 60 important terms and definitions, 43–5 data-block 1, 44 data-block 2, 44–5 data-block 3, 45 designation system for multiaxial non-crimp fabrics [EN 13427-1], 44 internal geometry characteristics, 334 layer orientation definition, 45, 46 ISO/DIS 1268-1/EN 13473-1, 46 LIBA Max 3 CNC clamping sequence, 53 computer-controlled weft-insertion system, 48 taper-layer system, 52 transport-chain, 52 materials and stitching configurations, 337–9 modelling of permeability for composites, 242–58 experimental validation, 251–3 influence of shear, 256–7 numerical simulation, 246–51 parametric study, 253–6 new weft-thread transport systems, 50–4, 55 Karl Mayer type clamping system for spreading tapes, 51 principle for transport belts use between the warping needles [DE19852281 C2], 55 online tow spreading and feeding systems, 54–9 device to feed fibrous bands into a knitting machine [DE102005008705 B3], 59 overview, 4 preform process chain with quality gates, 451 preforming analysis for helicopter applications, 449–60 deformation mechanism during preforming, 454–6 future trends, 458–60 preform techniques, 449–54 preforming defect analysis, 456–8 preforms structural stitching for composites, 67–82 applications and future trends, 81–2 quality aspects for structural stitching, 74–81 stitching technology and sewing machines, 70–4
519
threads for structural stitching technology, 68–70 product patents, 61–4 adhesive immobilisation on the surface of semifinished textile products (DE 102008004112 A1), 64–5 integrated manufacturing process for stringer stiffened panels (DE 102005052573 A1), 61–3 integrated production process, 62 non crimp fabrics stitched together using a fusible thread (EP 1 352 118 B1), 63–4 test specimen preparation, 63 textiles adjustment at the rotor blade mould vertical surfaces, 64 production for composites, 3–37 future trends, 35–7 preforming technologies, 36 production methods classification and standardisation, 42–7 classification, 43 production technologies comparison, 33–4 classification, 34 realisable productivity and complexity, 34 production technologies standardisation, 42–65 quality analysis by digital image analysis final results of different non-crimp fabrics, 110 grey value distribution histogram, 108 system, 106 working principle, 106–9 understanding and modelling stitching effect on geometry, 84–101 change in the geometry after shearing, 98–100 fibres distortions in the plies, 92–8 fibrous plies general parameters, 85–6 non-crimp fabric geometrical model, 100 stitching geometry, 86–92 warp-knitted, 5–22 biaxial, 6–14 coursewise and non-coursewise characteristics, 5 multiaxial, 14–20 spacer, 21–2 weft-knitted, 22–3 biaxial and multiaxial weft-knitted non-crimp fabric, 22 fabric set-up, 22–3 multilayer weft-knitted non-crimp fabric structures, 23 working principle, 23 woven fabrics, 23–7 advanced synchron weave, 24 Leno weave, 25–6 Tape weave, 26–7 non-periodicity, 368–9 noobing, 28 normal loading, 418 off-fibre tests, 372–3 oil price shock, 481 open markers, 175 overhang test, 392 overlay braiding, 505, 508
© Woodhead Publishing Limited, 2011
520
Index
PAM-CRASH, 157, 158 PAM-QUIKFORM, 391–2, 395 PAM-RTM, 242, 389 partial iso-strain model, 417, 419 patent DE 1020055052573 A1, 61–3 patent DE 102005052573 A1, 61–3 patent DE 102008004112 A1, 64–5 patent DE 102005008705 B3, 59 patent DE 10214140 B4, 52 patent DE 19726831 C2, 47–50, 49 patent DE 19852281 C2, 55 patent EP 1 352 118 B1, 63–4 patent EP 2003232 A1 carriage, gripper and tape movements during a lay-up sequence, 57 offline spread tape placing sequence into the transport-chains, 58 online tow spreading system, 56 principle of combined creel and spreadingunit, 56 patent EP 0972102 B1, 59–61 patent EP 1512784 B1, 57 permeability characteristics and results biaxial, triaxial, quadriaxial and multiaxial fabrics and transverse permeability experiments, 183 biaxial carbon fibre fabrics, 177–8 biaxial glass fibre fabrics, 179–80 in-plane permeability experiments, 176–82 triaxial, quadriaxial, and multiaxial fabrics, 181–2 uniaxial fabrics, 176 and deformation, 196–208 compression, 197–8, 199–200 fitted values for bundle radius, 198 relation between permeability and fibre content, 199–200 experimental permeability results, 168–87 experimental validation, 251–3 bi-axial vs. quadri-axial non-crimp fabric, 252 sheared bi-axial non-crimp fabric models, 253 tensor components, 252 geometrical effects, 187–96 influence of shear, 256–7 permeability values and angle of principal direction, 256 principal direction as function of shear angle, 257 material characterisation, 217–22 angle χ distribution between fibre and fabric weft direction, 219 fabric superficial density, average ratio, and standard deviation of fibre angles, 220 gaps configuration, 221 local superficial densities distributions, 219 stitching thread on fibre configuration, 221 unit cell, 218 measurement, 171, 173–87, 222–33 base configuration properties of Devold NCF, 186 distribution of angle θ between fabric weft and principal flow direction, 229 distribution of principal in-plane permeability value K1, 228
distribution of principal in-plane permeability value K2, 228 distribution of principal through-thickness permeability value K3, 231 experiment results for three fabric layers, 225 fabric unsaturated ratio over saturated permeability, 185 flow experiment results for six fabric layers, 230 flow front shape at a given injection time, 225 glass and carbon NCF permeability, 174 illustration, 173 methods and errors, 222–4 principal in-plane average values and coefficients of variation, 226–7 results, 224–33 through-thickness permeability values, 232 measuring technologies, 168–71, 172 measuring methods main characteristics, 172 NCF internal geometry at multiple scales, 168 transverse permeability measuring device cross-section, 171 typical line, radial and transverse permeability measuring equipment, 170 modelling and simulation, 233–8 coefficients of variation of global permeability, 237 distances between axes of wavy fibre tows, 234 function of the co-ordinates for a set of example parameters, 235 simulated flow front shapes in radial injection, 236 modelling in non-crimp fabrics for composites, 242–58 geometrical properties, 245 prediction of textile permeability, 246 undeformed quadri-axial and bi-axial fabric geometrical data, 244 multi-ply vs multiple layers, 187–91 biaxial and quadriaxial fabric crosssection, 188 biaxial NCF microscopy image, 191 permeabilities at 55% fibre content equivalent permeabilty, 189 nomenclature, 214–15 non-crimp fabric preforms, 166–209 numerical simulation, 246–51 boundary conditions, 248–9 Brinkman equations solution, 249–50 computation flow chart, 248 fluid flow models, 246–8 implementation, 250–1 principal direction, 251 parametric study, 253–6 perturbed quadri-axial model, 254–5 WiseTex model of biaxial and quadriaxial non-crimp fabric, Plate II shear deformation, 198, 201–8 effect on Tricot stitch patterns, 202–3 fabrics permeability vs shear, 205 orientation angle, 207 permeability anisotropy of sheared fabric vs shear relation, 206
© Woodhead Publishing Limited, 2011
Index stitching influence, 191–6 carbon and glass fibre based uniaxial and triaxial fabrics, 195 experimental set-up to track the flow front in detail, 192 fabrics anisotropy vs with even and uneven number of plies, 194 identifiers of Devold NCF variants, 196 polyol-Ardrox biopen flow front, 193 variability in non-crimp fabric composite reinforcements, 216–39 future trends, 239 permeability tensor, 242–3, 251 PETSc library, 250 physically representative volume (pRVE), 364 picture frame test, 117, 121–3, 392 pin-jointed net (PJN), 149, 150 pitch lengths, 339 plastic fibre microbuckling, 421 plastic shear instability, 421 ply deformation, 376 Poisson coefficient, 381 Poisson’s ratio, 407 polyol, 192 porosity, 223 Porsche, 462 power law, 133 prepregs, 462 pressure drop, 223 principal direction, 251, 257 PRO-Prefrom-RTM, 464 Puck criteria, 370–1, 435 quality monitoring, 106 rear pressure bulkhead, 445–6 reinforcement density, 339–41, 343–4 relative bending rigidity, 139 repeating unit cells (RUC), 405 representative volume elements (RVE), 360, 405, 416, 417–18 definition, 363–9 handling non-periodicity, 368–9 NCF geometry example, 364–5 unit cells of ply, laminate, composite and damaged composite, 365–8 meso models biaxial 0/90 and multi-axial NCF composites, 361–2 resin, 337–9 resin film infusion (RFI), 166, 443 resin infusion, 463 resin infusion under flexible tooling (RIFT), 166 resin-rich zones (RRZ), 364–5, 378–9 resin transfer moulding (RTM), 67, 166, 242, 443, 463, 465, 468 Reynolds number, 243, 246–7 rotor blade technology, 482–3 RTM6, 394 RTM-Worx, 242 rule of mixtures (ROM), 407–9 SAERfix EP, 65 SAERfix UP, 65 SAERTEX Wagner GmbH & Co. KG, 64 scissoring, 381
521
semi-laminar analysis non-crimp fabric composites stiffness and strength modelling, 402–36 stiffness models, 405–20 strength models, 420–35 sewing robots, 72 shear lag, 314 shear loading, 418 shear locking, 392 shear strain energy, 150 sheet moulding components (SMC), 462 short beam shear test, 266 simple linear elastic law, 397 single-step preforming, 470–2 skewed fabrics, 485–6 slave surface, 397 SOLID45, 428 spacer warp-knitted non-crimp fabric, 21–2 fabric set-up, 21 illustration, 21 working principle, 21–2 double needle bar raschel machine, 22 spacings, 339 stamping, 452 standard deviation, 218 stiffness evolution, 319–24 stitch density, 346, 354 stitch type, 339–41 stitching, 336 change in the geometry after shearing, 98–100 biaxial non-crimp fabric, 99 configurations, 339–41 distortions, 92–6 carbon non-crimp fibre distortions, face and back, 93 classifications, 92–4 dimensions, 95–6 dimensions definition of an opening, 94 fibre distortions dimensions in different non-crimp fabrics, 96 openings and channels inside a composite plate, 94 width distribution of fibre distortions, 95 effect on mechanical properties and damage of NCF composites, 360–83 damage accumulation, 372–83 elastic analysis, 369–72 internal composite geometry models, 361–2 representative volume element, 363–9 fibres distortions in the plies, 92–8 fibre volume fraction in the plies and deviations of fibre directions, 97–8 gaps between the non-crimp fabric layers in a laminate, 97 fibrous plies general parameters, 85–6 geometry, 86–92 stitching loops actual spacing, 89 stitching sites positions, 89 knitting patterns, 86–9 knitting needles and guides interaction, 87 pattern formation, coding and knitting patterns, 88 stitching loop geometry, 90–2 stitching loops shapes, 91 stitching yarn dimensions, 91
© Woodhead Publishing Limited, 2011
522
Index
understanding and modelling the effect on non-crimp fabrics geometry, 84–101 geometrical model of NCF in WiseTex software, 101 non-crimp fabric geometrical model, 100 stitching–compression (SC), 123 stitching–shear (SS), 123 stitching–tension (ST), 123 Stokes equations, 244–7 strain invariant failure theory (SIFT), 428 stress concentration, 371–2 structural stitching, 187, 336 advantages and challenges, 68 applications and future trends, 81–2 effect on mechanical properties, 343 ellipse formation laminate with half axis, 77 layer set-up influence in the laminate, 77 machine parameters, 78 thread material, 78 factors influencing laminate and part quality, 68 non-crimp fabric preforms for composites, 67–82 quality aspects, 74–81 reduction in ellipse size by preform compaction, 79 seam type related applicability of stitch types and threads, 76 stitch density on compaction pressure, 80 stitching on biaxial NCF flow front, 81 surface characteristic due to fibre concentration and matrix shrinkage, 79 stitch formation lock stitch formation, 71 one-side stitch and micrograph, 73 stitching heads and stitch formation using blind stitch, 73 tufting head and stitch formation diagram, 74 stitching technology and sewing machines, 70–4, 75 2D-sewing plant for manufacturing of plane preforms, 75 flexible robot systems, 75 stitch type and related influence on preform characteristics, 72 threads, 68–70 carbon fibre sewing threads types, 70 classification for yarn types to be used for stitching, 69 structural stitching yarns, 339–41 structurally stitched laminates, 335 structurally stitched NCFcomposites [A1-B-A2]-HTA laminates in-plane tensile modulus, 350 in-plane tensile strength, 352 normalised in-plane tensile modulus and strength, 343 unit cell model, 348 [A1-(B/2)s -A2]2 -HTA laminates in-plane compression modulus, 351 in-plane compressive strength, 353 normalised in-plane compressive modulus and strength, 344 [A1-(B/2)s -A2]2 -HTS laminates in-plane shear modulus, 351 in-plane shear strength, 353
[A1-(B/2)s -A2]-HTS laminates normalised compressive strength after impact, 346 normalised in-plane shear modulus and strength, 345 normalised mode I energy release rate, 347 defect typology and characterisation, 341–7 averaged void cross-section and width, 342 compression strength after impact, 346 in-plane compression stiffness and strength, 344–5 in-plane shear stiffness and strength, 345–6 in-plane tension stiffness and strength, 343–4 laminate thickness and fibre content, 342–3 µ-CT picture and micrograph, 341 mode I energy release rate, 346–7 normalised fibre volume content and thickness, 342 structural stitching on mechanical properties, 343 future trends, 354–5 structural stitching on in-plane and out-of-plane properties, 354 materials and stitching configurations, 337–41 carbon fibre NCF specifications, 338 non-crimp fabrics and resin, 337–9 parameter configurations, 340 stitching patterns, resulting stitch and reinforcement densities, 340 structural stitching yarns and stitch type, 339–41 tension, shear, compression strength after impact, mode I energy release rate and compression tests lay-ups, 339 mechanical behaviour simulation, 348–54 flowchart for determination of elasticity constants, 349 flowchart for strain and stress analysis, fracture analysis and degradation analysis, 349 in-plane elasticity and strength properties, 350–2 in-plane strength components, 352–4 unit cell model, 348–50 mechanical properties, 335–55 future trends, 354–5 NCF laminates characterisation, 341–7 non-structural and structural stitching, 336 structure decomposition, 458 sub-preform, 453 super-elements, 416, 419, 436 Super Light Car, 462 superficial density, 218, 220 tailored reinforcement manufacturing, 450 tailored reinforcements, 451–2 Tape weave, 26–7 fabric set-up, 26 weave made of rovings, 26 working principle, 26–7 illustration, 27 TECABS, 465 technical cost modelling (TCM), 496–504 capital equipment, 503–4 costs for processing large wind turbine blades, 503
© Woodhead Publishing Limited, 2011
Index tooling variable definitions, 504 variable definitions, 503 cost modelling variables, 504, 505 effect of production volume, 499–500 thermoset and thermoplastic manufacturing, 499 global simulation variables affecting all processes, 498 materials, 500–3 cost comparison of non crimp fabric and woven, 500 effect of reinforcement cost on component cost, 502 material costs, 501 material information, 501 non-crimp fabric carbon biaxial cost between 2003 and 2010, 502 part area on, 500–3 part definition, 497–9 part surface area and cost for manufacture of shells of large wind turbine blade, 498 setting global simulation variables, 497, 498 tooling, 504 tensile fatigue, 310 tensile loading, 290–6 tensile test, 265–6 tensile–tensile fatigue tests, 315–16 TexComp, 337 textile reinforcements, 72, 103 textured threads, 69 thermoplastic sewing threads, 68 through-thickness permeability, 223, 230–1 TIGER, 449 tows, 93 transverse failure stress, 429 transverse matrix strength, 436 Tresca criterion, 427, 430 Tsai-Hill failure criterion, 395 Tsai-Wu criterion, 434 twisted multifilament yarns, 69 uniaxial deformation, 376 unidirectional-based composites, 319, 321, 328 unidirectional-based laminates, 310, 311, 321, 323–5 unidirectional prepregs, 489–91 unit cells, 337, 363, 383 model, 348–50 ply, laminate, composite and damaged composite, 365–8 rectangular unit cell of layer and non-matching skewed UC’s, 368 representative capability with the classical periodic boundary conditions, 368 stitch model, 151–3 unstitched laminates, 335 Vacuum-assisted Resin Infusion (VARI), 67 vacuum-assisted resin transfer moulding (VARTM), 166, 242, 443, 486–7, 489, 491 vacuum infusion, 486, 501, 504, 507–8 VESTAS, 482 Vetrotex, 69 viscous constitutive model, 157 visible impact damage (VID), 301, 302 von Mises failure criterion, 434 von Mises theory, 426–7
523
warp-knitting, 5, 86 waviness, 220 weft carriage system, 7–8 illustration, 8 weft technologies, 487–9 whole cracks, 291–4 densities, 293 two 90° fibre bundles, 292 wind turbines blade deflecting under loads, Plate XIV evolution material choice in wind rotor blade technology, 482–3 possible and frequently used warp weight in unidirectional materials, 487 skewing process using Malimo or Liba knitting machine, 485 weft insertion possibilities using NCF production machine, 488 future trends aerodynamic performance optimisation, 492 larger and longer blades manufacture, 492 production consistency, 492 production in segments, Plate XVI materials used in nacelle construction, 491–2 nacelle cover under load, Plate XV non-crimp fabric composites, 481–92 blade length over time, main times of build of different blade lengths, 484 typical blade design, middle section, two shear webs, 484 non-crimp fabric composites development, 483–91 buckling simulation of a blade, 489 central spar design, 490 impact of infusion technology, 483–4 skewed fabrics introduction in late 1980s, 485–6 traditional woven structures in wind rotor blades, 484–5 typical blade layout IEC class II, Plate XIII unidirectional prepregs in wind rotor blade design, 489–91 vacuum-assisted resin transfer and growth of non-crimp fabrics, 486–7 weft technologies development in non-crimp fabric reinforcement structures, 487–9 oil crisis as initiator for wind energy, 481–2 unit material cost per unit of strength for a beam, 483 WiseTex, 243, 256–7, 337 model of biaxial and quadriaxial non-crimp fabric, Plate II woven fabric composites, 311, 317, 331 woven non-crimp fabrics, 23–7 advanced synchron weave, 24 Leno weave, 25–6 Tape weave, 26–7 wrapping technology, 69 X-ray radiography, 283–5 yarn density, 341, 344–6 yarn failure, 347 zone definition model, 394, Plate VIII Zwick machine, 121
© Woodhead Publishing Limited, 2011
