Mechanical Testing of Advanced Fibre Composites

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MTAPR 11/21/2000 8:55 PM Page i

Mechanical testing of advanced fibre composites

MTAPR 11/21/2000 8:55 PM Page ii

MTAPR 11/21/2000 8:55 PM Page iii

Mechanical testing of advanced fibre composites Edited by J M Hodgkinson

Cambridge England

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Published by Woodhead Publishing Limited, Abington Hall, Abington Cambridge CB1 6AH, England www.woodhead-publishing.com Published in North and South America by CRC Press LLC, 2000 Corporate Blvd, NW Boca Raton FL 33431, USA First published 2000, Woodhead Publishing Ltd and CRC Press LLC © 2000, Woodhead Publishing Ltd, except chapters 6, 8, 11 and 15, Crown copyright. 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 publishers cannot assume responsibility for the validity of all materials. Neither the authors nor the publishers, 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 the publishers. The consent of Woodhead Publishing and CRC Press 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 or CRC Press 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. Library of Congress Cataloging in Publication Data A catalog record for this book is available from the Library of Congress. Woodhead Publishing ISBN 1 85573 312 9 CRC Press ISBN 0-8493-0845-3 CRC Press order number: WP0845 Cover design by the ColourStudio Typeset by Best-set Typesetter Ltd., Hong Kong Printed by TJ International, Cornwall, England

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Contents

Preface List of contributors

1

xi xiii

Introduction j m hodgkinson

1

References

3

2

General principles and perspectives s turner

4

2.1 2.2 2.3 2.4 2.5 2.6

Mechanical testing in perspective Formal framework for mechanical test methods Special features of the mechanical testing of composites Nature and quality of test data Mechanical tests for long-fibre composites Concluding comments References Bibliography

4 10 13 19 24 33 34 35

3

Specimen preparation f l m atthews

36

3.1 3.2 3.3 3.4 3.5 3.6

Introduction Laminate production Quality checking Specimen preparation Strain gauging Summary References

36 36 39 39 41 42 42 v

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vi

Contents

4

Tension e w godwin

43

4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8

Introduction Testing equipment Specimen details Test procedure Data reduction Material and sample preparation Practical example Future developments References

43 50 56 62 64 67 70 71 73

5

Compression f l m atthews

75

5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8

Introduction Types of test Standards Specimen preparation Specimen configurations Execution and problems Typical results Conclusions References

75 76 82 83 85 87 89 97 97

6

Shear w r broughton

100

6.1 6.2 6.3 6.4 6.5

Introduction Test methods Summary of test methods Comparison of data Recommendations and concluding remarks Acknowledgements References

100 101 118 118 118 122 122

7

Flexure j m hodgkinson

124

7.1 7.2 7.3 7.4 7.5 7.6

Introduction Three-point and four-point flexure tests Comparison of recommended test methods Failure modes Typical data Steel versus soft lined rollers

124 125 128 133 133 138

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Contents

vii

7.7 7.8

Through-thickness flexure Conclusions References

140 141 141

8

Through-thickness testing w r broughton

143

8.1 8.2 8.3 8.4 8.5 8.6

Introduction General issues Tensile test methods Compression test methods Shear test methods Concluding remarks Acknowledgements References

143 144 146 156 160 167 167 168

9

Interlaminar fracture toughness p robinson and j m hodgkinson

170

9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8

Introduction Terminology and typical values Overview of test methods and standards Mode I testing Mode II testing Mixed mode I/II Multidirectional laminates Conclusions References

170 170 173 178 194 200 204 206 207

10

Impact and damage tolerance p j hogg and g a bibo

211

10.1 10.2 10.3 10.4 10.5 10.6 10.7

Introduction Impact testing Damage tolerance – compression after impact (CAI) tests Boeing test methods and related variants Data interpretation Standardisation status Future trends References

211 211 228 229 235 241 243 244

11

Fatigue p t curtis

248

11.1 11.2

Introduction Basic test philosophy

248 249

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Contents

11.3 11.4 11.5 11.6 11.7 11.8

Machines and control modes Presentation of data Monitoring fatigue damage growth Potential problems Fatigue life prediction Post-fatigue residual strength References

254 256 256 261 264 266 266

12

Environmental testing of organic matrix composites g pritchard

269

12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9 12.10 12.11 12.12

Introduction Why environmental testing? Environmental threats to composites Standard tests Sample conditioning Experimental approaches Determination of sorption behaviour Lowering of Tg by absorbed liquids How do composites perform in adverse environments? Diffusion of liquids into composites Classification of absorption categories Edge corrections References

269 269 270 271 275 276 278 279 280 284 288 289 291

13

Scaling effects in laminated composites c soutis

293

13.1 13.2 13.3 13.4 13.5 13.6

Introduction Background Investigation of failure Practical application examples Specialised scaling techniques in composites Concluding remarks References

293 294 294 304 308 311 312

14

Statistical modelling and testing of data variability l c wolstenholme

314

14.1 14.2 14.3 14.4 14.5

Introduction Importance of looking at data plots Basic statistics Distribution of sample statistics Testing for differences between samples

314 314 316 317 317

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Contents

ix

14.6 14.7

Comparing several samples simultaneously General linear model (GLM) References

325 331 339

15

Development and use of standard test methods g d sims

340

15.1 15.2 15.3 15.4 15.5 15.6

Introduction Development of test methods Validation of test methods Sources of standards and test methods Harmonisation of composite test methods Recommended mechanical test methods References Bibliography – selected ISO standards Appendix – contact details for standards organisations

340 341 343 347 352 355 355 356 357

Index

359

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Preface

Mechanical property data are essential in the design process if structures are to perform as intended – reliably and cost-effectively for their full life. However, there are no data without testing at some stage. But what tests should be carried out to give the required data? How, precisely, should the tests be conducted, and who says so? What does the data actually mean? How reliable are the data produced? Are data obtained from small test specimens meaningful when large structures are being designed? What effect will the operating environment have? Fortunately most, if not all of these questions have been answered in the case of isotropic solids, giving a starting point for the development of mechanical test methods for more complex materials such as advanced fibre composites. This book attempts to set out the current position with regard to these potentially highly anisotropic materials, which are finding repidly increasing applications despite their complexity. The expression ‘advanced fibre composites’ probably means different things to different people. To many it might encompass only carbon and a small group of thermoplastic fibres including aramid and polyethylene, to the exclusion of glass fibres. However, in some industrial applications, glass fibres, whilst not necessarily being deemed as advanced in any particular sense, are the only fibres which can fulfil the specific design and environmental requirements. So perhaps the term ‘advanced’ in this context is really application driven. As far as this book is concerned much of the discourse surrounds high modulus, high strength fibre/plastic matrix composites, but not exclusively so, it is high performance which is the key. It has been left to the author(s) of each chapter to judge for themselves, from their own interests and experience, precisely what to include. It is in any case quite clear that, for most of the mechanical test methods described, relatively minor modifications allow perfectly good results to be obtained across the whole range of fibre/matrix combinations, from the most exotic to the most humble. This book has developed out of a short course of the same title which xi

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xii

Preface

has normally run on a yearly basis at Imperial College (London University) since 1989. The course has now seen over 250 delegates ‘graduate’; they have come from a wide variety of industry sectors and from all over the world. The course has been supported by experts in their field from Queen Mary and Westfield College (London University), the National Physical Laboratory, the Defence and Evaluation Research Agency and City University. I am indebted to these colleagues, and those from Imperial College, who have not only taught on the course but have also given up a great deal of valuable leisure time providing their copy for the book. A special thankyou goes to Professor Geof Pritchard, the only contributor to the book who hasn’t taught on the course, which has a section on Environmental Effects but, in comparison to the book chapter, is probably woefully inadequate. In recognition that not everybody has the same interests in life, this book is organised in chapters dealing with particular types of test (tension, compression, shear, etc.), allowing the reader to ‘dip in and out’ as he/she wishes. It is my hope that the reader finds the book both informative and interesting and that it encourages best practice as it is currently known, across the various industrial sectors making use of fibre-reinforced plastic matrix composites. It is as well to remember that a bad test is not worth doing and that even the best test can be done badly. It is all in the detail. JM Hodgkinson

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List of contributors

Dr G A Bibo British Aerospace Australia 41-45 Burnley Street Richmond Victoria, 3121 Australia Dr W R Broughton National Physical Laboratory Teddington Middlesex TW11 0LW Professor P T Curtis Structural Materials Centre Building A7, Room 2008 Farnborough Hampshire GU14 6TD E W Godwin Centre for Advanced Composite Materials Imperial College Prince Consort Road London SW7 2BY Dr J M Hodgkinson Centre for Advanced Composite Materials Imperial College Prince Consort Road xiii

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xiv

List of contributors

London SW7 2BY Professor P J Hogg Department of Materials Queen Mary & Westfield College University of London 327 Mile End Road London E1 4NS Professor F L Matthews Centre for Composite Materials Imperial College Prince Consort Road London SW7 2BY Professor G Pritchard York House Moseley Road Hallow Worcestershire WR2 6NH Dr Paul Robinson Department of Aeronautics Imperial College Prince Consort Road London SW7 2BY Dr G D Sims National Physical Laboratory Teddington Middlesex TW11 0LW Dr C Soutis Department of Aeronautics Imperial College Prince Consort Road

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List of contributors London SW7 2BY Dr S Turner Department of Materials Queen Mary & Westfield College University of London 327 Mile End Road London E1 4NS Professor L C Wolstenholme School of Mathematics City University Northampton Square London EC1V 0HB

xv

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MTA1 11/22/2000 8:49 AM Page 1

1 Introduction J M HODGKINSON

In the mind of the general public the term ‘composite materials’ is largely either misunderstood or not understood at all. There is a reasonable idea of what might be expected of some other materials and what they might be used for. Steel is used for fabricating the skeleton of many buildings (or inside the concrete) and for most automobile body shells; copper is used for electrical wiring; aluminium is used a lot in aeroplanes; plastics (of whatever colour) are used for almost everything. However, even with these isotropic homogeneous materials there is little real understanding of why they are used for particular applications. This is not an unreasonable situation. Most people have more to concern themselves about in their lives than why a specific screw could be made from steel, brass or a plastic. It does not matter whether people understand, or not. Quite rightly the expectation is that the goods that they purchase, or make use of in some way, are fit for purpose. This is where the mechanical and other types of materials testing comes in. In order to design a structure or component so that it is efficient and fit for purpose, the shape of each subcomponent needs to be decided upon, taking into account the material it is to be made from. This means that careful consideration must be given to the intimate relationship between how the component is supposed to perform in service and the properties of the material from which it is made. This can be a tricky balancing act even with isotropic homogeneous materials but substantially more difficult when attempting to make use of materials which are not isotropic and not homogeneous. How does one go about deciding what a material is capable of, mechanically speaking? Well, first one needs to know what the beast one is dealing with is made of, and in this book we are concerned with what are generally termed advanced fibres in a plastic matrix. The fibres involved in the discussion are carbon, aramid and glass, normally continuous rather than short fibres. The resins considered are epoxies and a variety of thermoplastics. For the most part, but not exclusively, we are concerned with laminates of 1

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Mechanical testing of advanced fibre composites

these fibres and resins. Given any knowledge of the way that homogeneous materials react to the application of loads of varying types, it does not take much thought to come to the conclusion that these fibre-reinforced plastics are an entirely different breed, and that considerable thought and experimentation might be needed to describe, adequately well, their mechanical properties. This is what this book is all about. We need to be able to establish how these materials react to all types of loading, be they tensile, compressive or shear, of short-term or long-term duration, or cyclic, in the presence of high or low temperatures, or other environments which might significantly modify their behaviour, in the same way that we can for homogeneous materials. Designers can then make use of the information to create structures which perform within the design requirements. These structures include large parts of military and civil aircraft, racing cars, automobiles, buses, coaches, lorries, railway and military vehicles, boats, ships and other marine vehicles, a wide variety of sports, home, office, recreational and other leisure goods and, increasingly, civil engineering structures. The tests which can be carried out to ascertain the behaviour of these materials depend on testing machines which have been designed and built, not necessarily with this particular range of materials in mind, but are generally adequate for the purpose. Quite frequently it is the subtesting equipment (i.e. testing jig), specimen design and other experimental arrangements which address the special reqirements of these materials. Subsequent chapters in this book describe the specimen design and how the tests might be carried out, as far as possible to best practice, under different loading regimes, with due regard given to the statistical analysis of the data produced and progress in the development of test methods from initial conception to full international acceptance. During the period of this book’s development there have been numerous initiatives by standards organisations worldwide to update existing methods and produce new standard test methods to satisfy (or at least to attempt to satisfy) the particular requirements of advanced fibre-reinforced plastic matrix composite materials. The ‘push’ for these better, or new, test methods to be developed, refined, written into standardised form and finally adopted, preferably at international level, has come from the ‘grass roots’, largely (but not exclusively) driven by the aerospace industry. Although it is clear that many other organisations were involved in these developments in the 1980s and 1990s (and might have been equally concerned about the dearth of appropriate standardisation for this class of materials), a key catalyst appears to have been the Composites Research Advisory Group (CRAG), which set about in the early 1980s to attempt to define what the best practice should be over a range of test methods. The

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Introduction

3

Group reported the results of its preliminary deliberations in 1985 and in a final report1 in 1988, but by this time numerous sections of industry, research organisations and university researchers (primarily but not exclusively in the UK) were making use of the recommendations. The CRAG recommendations were proposed to the British Standards Institution and subsequently had a considerable effect in the development of new international standards. From start to finish the process has taken the best part of 20 years to establish a fairly coherent and comprehensive body of standards at international level. One is tempted to suggest that this is an extraordinarily long time. It is also a time during which the influence of the aerospace industry on the future of composite materials has diminished somewhat. At least we are left with the legacy of the standards.

References 1. P T Curtis (ed.), CRAG Test Methods for the Measurement of the Engineering Properties of Fibre Reinforced Plastics, Royal Aircraft Establishment, Technical Report 88012, February 1988.

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2 General principles and perspectives S TURNER

2.1

Mechanical testing in perspective

2.1.1 Overall objectives of mechanical testing Humanity’s utilization of materials has always been supported by testing activities, which have developed over the centuries from crude tests of the fitness-for-purpose of service items to the modern science-based procedures that support all aspects of the science and technology of materials and their utilization. There is now a mutual dependency between advances in scientific knowledge and test method development, with first one and then the other providing an enabling facility for further progress in the development of versatile evaluation programmes capable of supporting various essential industrial operations. In the particular case of mechanical tests those operations include: • • • • • • •

quality control quality assurance comparisons between materials and selection design calculations predictions of performance under conditions other than those of the test indicators in materials development programmes starting points in the formulation of theories.

This list is a simplification, in that some of the functions overlap and several are linked by lateral connections which become effective at various stages in the conversion of materials into end-products. But, in isolation, these functions make different demands on the data, and therefore, the resources that are deployed need to be matched carefully to the demands of particular circumstances. For instance, quality control can usually be achieved by the use of simple test procedures provided that they reflect relevant mechanical characteristics of the product; the simplicity of the test procedure and precision of the data are usually deemed far more 4

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General principles and perspectives

5

important than scientific rigour and accuracy whereas, in contrast, the priorities would be reversed for a procedure used to generate data for a design calculation. Some test methods are multipurpose via a variety of operating procedures. Thus, a conventional tensile test operated under fixed conditions may serve a quality control function whereas, operated with controlled variation of influential factors such as temperature and straining rate, it may provide a first-order estimate of load-bearing capability. On the other hand, some test methods are uniquely dedicated to a single purpose and the data they yield could be misleading if used in a wider context. There is another complication in materials testing. The property value derived from a mechanical test varies with the state of internal order of the tested item, which for many classes of material is sensitive to the production route and other factors. Each sample or test specimen is then unique, and derived data must be regarded as relating just to it, rather than to the material in general. The corresponding properties of the latter, or of other samples, have to be inferred. There are, therefore, far-reaching ramifications for the scope of test programmes, evaluation strategies, the mode of utilization of the data, design procedures and so on. The variations in material state are commonly in the molecular or atomic orders which, after the processing stage, slowly change towards a state of greater order. In a fibre composite the molecular reordering process generally occurs in the matrix and at the fibre–matrix interfaces. However, the dominating source of variation is the spatial distribution of the fibres, which may change inadvertently during the manufacturing stage, or may be changed deliberately by the fabricator to induce a particular mechanical effect. Thus the trains of inference that, for a simple class of material, lead from test specimens, to sample, to material and finally to end-product, are more tenuous and less reliable and may even be inappropriate for longfibre composite systems.This occurs to the point where ‘test specimen’ tends to be replaced by ‘test coupon’, the concept of sample is largely discarded in favour of items such as subelements and substructures and ‘material’ is replaced by ‘structure’.1 These changes are functional rather than cosmetic, signifying a testing strategy linked more closely to engineering than to physics, though the testing of structures, substructures and so on supplements rather than replaces the testing of coupons. The suite of tests used for the evaluation of the mechanical properties or attributes of a material expand in range and complexity with the severity of the anticipated service but also as the class of material changes from isotropic to anisotropic and from homogeneous to heterogeneous. Thus, numerous methods are deployed to measure the mechanical properties of long-fibre composites. In most cases they are elaborated variants of the tests that have traditionally been used for other classes of material, for example,

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metals and plastics, and they are described in standard test methods, the scope of which is variously international, national, industrial sector and company. However, whilst the technical details of such standard test methods are always explicit, the underlying rationale is generally unstated there; and in the absence of such statements, the special stipulations on test configurations and procedures can seem to be demanding, costly and irksome. In comparison, other classes of material may seem to be simpler in general characteristics and more amenable to rational evaluation but those classes may well have seemed correspondingly difficult to evaluate during their novelty and development phases. For example, the testing of thermoplastics during the period 1940 to 1970 was fraught with misleading test data and imperfect rationale. It finally transpired that the initial confusing multiplicity of test methods could be reduced and rationalised through the agency of refinements to the theories of mechanics and through the testing of ‘critical basic shapes’ that function as a formal set of substructures. There is some evidence that the same rationalisation process is taking place in the field of long-fibre composites, but a reliable comparison is elusive because the market environment for thermoplastics was, and remains, very different from that in which long-fibre composites exist. There is, of course, an extensive literature on the manufacture, properties and service performance of composites, but only a small proportion of it relates either directly or peripherally to mechanical testing. A short bibliography at the end of this chapter cites a number of text books which are intended to complement the present work. The list includes one text (Brownlee) which sheds precomputer light on the subject of practical statistics.

2.1.2 Service-pertinent mechanical properties of long-fibre composites Long-fibre composites are generally required to function as load-bearing structures. It follows that elastic modulus, strength, ductility and fracture toughness are particularly important properties. The property values and general chartacteristics manifested by long-fibre composites and other, similar materials are the resultants, via various combination rules, of the properties of the separate constituents. However, the realities of practical situations may violate the rules, so that a datum derived from a particular test procedure may be a biased or invalid indicator of the property, or attribute, that the test ostensibly measures. The apparent interlaminar shear strength of a long-fibre composite derived via flexure of a short beam is one such vulnerable quantity, because the beams often fail by a combination of several fracture/rupture processes that frustrate any attempt to assign a proper value to the postulated property. There is, also,

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a more fundamental issue. The polymeric nature of most matrix materials introduces viscoelastic characteristics into the mechanical behaviour of composites such that, depending on local circumstances, the concepts of elastic modulus, strength and ductility may have to be expanded to embrace phenomena such as creep, stress relaxation, creep rupture and fatigue, and attributes such as impact resistance. Any modern textbook discussion of the mechanical properties of the matrix materials (i.e. plastics) is likely to include this extended range of topics. Corresponding treatments, including this one, of long-fibre composites tend to concentrate on the four primary properties and pay less attention to ‘time-dependent’ or ‘ratedependent’ aspects of those properties – except for fatigue, which has been studied comprehensively. The relative neglect of some features of the mechanical behaviour may have arisen mainly because viscoelastic characteristics are reflected in only some composite structures in some stress fields whereas, in contrast, anisotropy is a dominant feature of many structures, with modulus and strength often varying much more with stress axis than with elapsed time or straining rate. Additionally, the superposition of viscoelasticity on to anisotropy introduces formidable analytical difficulties and increases the testing burden two-fold or three-fold, so the long-standing tendency for long-fibre composites to be regarded as anisotropically elastic rather than anisotropically viscoelastic is explicable as a pragmatic compromise. However, that compromise offers no universally safe solution to loadbearing calculations, since a large composite structure might creep to an unacceptable degree because of unpredicted creep in a single element. At the present time the vast majority of applications for long-fibre composites have little reason to consider time-dependent effects; this situation may change when such materials are used more extensively in, for example, heavy civil engineering applications, where design lives of 50 years or more are required. Little is known about the time-dependent behaviour of longfibre composites, although it is generally recognised that any effects are likely to manifest themselves when the materials are subjected to shear or through-thickness loading. It is highly likely that new test methods will need to be developed to tackle measurement of the viscoelastic properties of this class of materials, because those presently available appear to be inadequate in a number of ways.2 Strength is often loosely related to the elastic modulus, both being similarly sensitive to the volume fraction of the fibres and their alignment relative to the stress field. Ductility, or toughness if the item is a substructure or a structural element, is a more complex matter. For a homogeneous material it is inversely related to modulus; a rough working rule is that steps taken to enhance the modulus, for example, by modification of the composition, tend to diminish the toughness and vice versa; and similar

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correlations arise for long-fibre composites, but the simple inverse relationship is distorted and partly obscured. This is primarily because the rationale breaks down when the dimensions of the stress field irregularity near the crack tip are similar in magnitude to the scale of the heterogeneity. This particular detail exemplifies a general point that the mechanical evaluation of composite samples does not lie exclusively within the formal framework defined by continuum mechanics; their heterogeneity and their anisotropy dictate a larger repertoire of tests than would suffice for a sample of a more conventional material. Thus, for example, for long-fibre composites, modulus and strength measurements in flexure and uniaxial compression are as important as, and sometimes more important than, tests in tension and can be regarded as complementary to them, whereas for homogeneous samples they often play only a supplementary role. The mechanical properties depend on several variables of the composition: • • • • • • •

properties of the fibre surface character of the fibre properties of the matrix material properties of any other phase volume fraction of the second phase (and of any other phase) spatial distribution and alignment of the second phase (including fabric weave) nature of the interfaces.

Mechanical properties also depend on the many details of the processing stage, particularly those affecting the degree of adhesion between fibre and matrix and the physical integrity and overall quality of the final structure. If the mechanical properties of the fibre and the matrix are known, mathematical models enable the corresponding properties of samples with particular fibre volume fractions and fibre spatial arrangements to be calculated, but the models are imperfect. The fibre alignments in test coupons and service items generally deviate from the ideal states assumed for the models, and the properties deviate correspondingly from the calculated predictions. The effectiveness of the coupling between the phases in a composite is also an influential factor. It is neither fully quantified nor properly understood. Good coupling seems to be desirable where a composite with high moduli is the objective and also, in many cases, where high strengths are required. The lines of reasoning are less clear where toughness is the objective. Poor coupling is advantageous in that local decoupling between fibre and matrix can arrest, or deflect, a growing crack and extensive decoupling is an effective mechanism for energy absorption. On the other hand, a decoupled fibre may act as a stress concentrator and promote failure.

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General principles and perspectives

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2.1.3 Mechanical testing strategy for long-fibre composites Despite the complications of heterogeneity, interfaces and anisotropy, the property data for long-fibre composite test coupons conform in many respects to the conventional definitions for homogeneous isotropic materials, apart, that is, from additional subsidiary definitions and nomenclature to accommodate the anisotropy and special property definitions, where there is no homogeneous isotropic counterpart, for example, the interlaminar shear strength. Even so, the almost infinite variety of possible spatial arrangements of the fibres and fibre volume fractions raises doubts about whether any particular combination of matrix and fibre should be regarded as a typical and characterising material state. The different fibre–matrix assemblies are each unique, so that, even more so than for processingsensitive homogeneous materials, a tabulation of property values derived from one structural assembly has a restricted field of relevance. On the other hand, since the mechanical testing of a long-fibre composite is a costly process, there usually has to be a pragmatic compromise between the desirability of test data for several different structures and the need for testing economy. Evaluation programmes are therefore often constrained by financial considerations, although the potentially harmful effects of such constrains may be offset by the adoption of a different testing strategy.1 The spatial distribution and alignment of the reinforcing phase are often so arranged as to satisfy a particular service requirement, and sometimes to attain an unusual combination of attributes in an end-product. Data derived either from test coupons cut judiciously from such structures, or from special subelements tested in their entirety,1 may reflect the loadbearing capability of the complete structure. Such data are unlikely to have any claim to generality but, in addition to their direct relevance to a particular structure, they should give an insight into the range of values of the ‘property’ that could be manifest in service and thereby provide quantitative options in design calculations. On the other hand, conventional data from specimens consisting of uniaxial arrays of fibres, and from lamellae with specific fibre alignments, have some general downstream utility via the mathematical models mentioned previously. Preferential alignment of fibres in one direction tends to confer property deficiencies such as low strength and modulus in a transverse direction. Similarly, stacks of lamellae with different fibre alignments are prone to out-of-plane distortions.Test programmes for such specimens, or samples, should include checks on the possible deteriorations and imperfections. Additionally, deficiencies in the production processes may give rise to inadvertent variations in fibre alignment, and so on, and the behaviour of the test coupon, or end-product, may therefore deviate from what might be expected and/or may vary from item to item.

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2.2

Formal framework for mechanical test methods

The foundation of satisfactory test methods for the measurement of mechanical properties is the theory of mechanics. That theory became well entrenched for homogeneous isotropic elastic materials during the nineteenth century and was progressively extended later to accommodate inhomogeneity, anisotropy and anelasticity, all of which are characteristic features of long-fibre composites. If the material under investigation is viscoelastic, it is convenient for a mechanical test to be regarded as consisting of the application of an excitation and the observance of the response of the test piece, with the relationship between the two defining a property. This seemingly cumbersome approach, or something similar, is an inescapable consequence of the nature of viscoelasticity; it requires that the simple elastic constitutive equations relating stress to strain be replaced by convolution integrals but, when the viscoelasticity is not dominant, some of those integrals can be replaced by simple weakly time-dependent coefficients. Irrespective of the types of excitation and response, in most mechanical tests, forces are applied and displacements ensue. In a few, the displacements are imposed, athough that necessarily requires the prior application of forces. Mechanical properties derived from such tests have to be defined in terms of the relationships between the stresses and the strains. Translation from force to stress, and from displacement to strain, is relatively straightforward if the tested item is homogeneous and isotropic, but more complex if it is heterogeneous and/or anisotropic. The basic assumption of linear elasticity theory is that the response to an excitation is a linear function of all the components of the excitation tensor, Equation [2.1]: sij = cijklekl

[2.1]

where sij and ekl are the stress and strain tensors, respectively, with cijkl being the stiffness coefficients. Each suffix has possible integral values 1, 2 or 3. Alternatively (Equation [2.2]), e = sijklskl

[2.2]

where sijkl represents the compliance coefficients. Because of symmetry in the stress and strain tensors, only 21 of the 81 stiffnesses and compliances are independent, and that number is reduced further if there are symmetries in the material (i.e. if the material is not fully anisotropic), see Table 2.1. The most general case, with 21 independent elastic coefficients, is so complex as to be virtually unmanageable in both the analytical and experimental aspects. However, this extreme situation rarely arises in practice

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Table 2.1. Classes of symmetry. Type of material symmetry

Number of independent elastic coefficients

None (triclinic) One plane of symmetry (monoclinic) Three planes of symmetry (orthotropic) Transversely isotropic (one plane of isotropy) Isotropic

21 13 9 5 2

because the fabrication processes impose some order, either from deliberate intent or inadvertently. If the material is isotropic the relationships between the stress and the strain are relatively simple and the coefficients reduce to the two moduli of isotropic elasticity theory. Elasticity theory relates to a continuum but composites are heterogeneous and therefore the equations are an imperfect representation. However, they suffice in many cases provided that the scale of the interphase discontinuities is small relative to the size of the test specimen. Stipulations on the size of test specimens in the standard test methods covering modulus and strength ensure that the heterogeneity does not distort the derived data, but there are difficulties at the micromechanical level, for instance in estimates of the stress field at the tip of a crack. The case usually considered analytically is orthotropy, which is conferred approximately by a uniaxial array of fibres in long-fibre composites, by uniaxial drawing of fibres and films and by other directional processing of thermoplastics. The stress–strain relationship for an orthotropic system is given by Equation [2.3]: s 11 c11 s 22 c 21 s 33 c31 = t 23 0 t 31 0 t 12 0

c12 c 22 c32 0 0 0

c13 c 23 c33 0 0 0

0 0 0 c44 0 0

0 0 0 0 c 55 0

0 0 0 0 0 c66

e 11 e 22 e 33 g 23 g 31 g 12

[2.3]

where the cij are the stiffness coefficients, the first suffix denotes the direction of the normal to the surface to which the stress or strain relates and the second suffix denotes the strain axis or the line of action of the stress; g is the shear strain, t is the shear stress, s is the tensile stress and e is the tensile strain. See Fig. 2.1 for clarification. The strain–stress relationship is similar and is expressed as Equation [2.4]:

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Mechanical testing of advanced fibre composites 3

2

s33 1

t31

t32

3

t23

t13

2

s22

t21 t12 1

s11

2.1 Principal directions and stress components for an orthotropic material.

e 11 s11 e 22 s 21 e 33 s31 = g 23 0 g 31 0 g 12 0

s12 s 22 s32 0 0 0

s13 s 23 s33 0 0 0

0 0 0 s44 0 0

0 0 0 0 s 55 0

0 0 0 0 0 s66

s 11 s 22 s 33 t 23 t 31 t 12

[2.4]

where the sij are the compliance coefficients. In Equations [2.3] and [2.4], e11, e22 and e33 are the principal strains and s11,s22 and s33 are the principal stresses. The compliance matrix can be rewritten in terms of the more familiar engineering/physical constants Eii, nij and Gij, Equation [2.5]: 1 E11 -n12 E11 -n13 E11 0 0 0

-n 21 E22 1 E22 -n 23 E22 0 0 0

-n31 E33 -n32 E33 1 E33 0 0 0

0 0 0 1 G32 0 0

0 0 0 0 0 0 0 0 1 G31 0 0 1 G12

[2.5]

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General principles and perspectives

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where G12 is the in-plane shear modulus (see plane number 3 in Fig. 2.1) and nij is Poisson’s ratio for transverse strain in the j direction when the specimen is stressed in the i direction. Because the matrix materials are viscoelastic, those stiffness and compliance coefficients that relate to deformations in the matrix vary with rate of straining, duration of loading and so on, and are therefore viscoelastic functions similar to those that describe the mechanical behaviour of plastics and on which there is an extensive literature. In contrast, there is a relative dearth of information on the time dependence of the stiffness and compliance coefficients relating to long-fibre composites and a general ignorance about the nature of the interactions between them. Despite its imperfections, the existing formal framework contains justifications for the various constraints and stipulations that have been imposed on test configurations and test procedures for long-fibre composites.

2.3

Special features of the mechanical testing of composites

2.3.1 Features arising from the theory of anisotropic elasticity The principal precautions that are necessary during the mechanical testing of long-fibre composites are in relation to: • • • • •

generation of a uniform stress field in the critical reference volume avoidance of overwhelming ‘end-effects’ attainment of adequate loading levels without damage or failure near the loading points appropriate specimen dimensions related to the scale of structural inhomogeneities tension–shear coupling.

The first four precautions apply similarly to the testing of homogeneous isotropic materials and give rise to various stipulations about specimen dimensions, test configurations and machine specifications, although heterogeneity and anisotropy entail more severe constraints and introduce additional considerations. Some of these complications reflect a greater stringency in Saint Venant’s Principle when the specimen is a composite. In its original form, for isotropic materials, it states that any differences in the stress states produced by different but statically equivalent load systems decrease with increasing distance from the loading points, the differences becoming insignificant at distances greater than the largest linear dimension of the area over which the loads are acting. In an anisotropic

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Mechanical testing of advanced fibre composites

specimen, the region of uniform stress is approached much more gradually. It has been shown that the decay length, l, is of the order: 1

Ê E11 ˆ 2 b Ë G12 ¯

[2.6]

where b is the maximum dimension of the cross-section. For rectangular strips subjected to traction at their ends, Equation [2.7]: 1

b Ê E11 ˆ 2 lª 2p Ë G12 ¯

[2.7]

where l is the distance over which a self-equilibrated stress applied at the ends decays to 1/e of its end-value. The ratio E11/G12 may have a value lying between 40 and 50 for a unidirectional composite with a carbon-fibre volume fraction of 0.6. The value would be about 3 for an isotropic specimen and if Equation [2.7] is valid for the anisotropic case, as it should be, the respective decay lengths are in the ratio of about 3.5 : 1. Other difficulties arise when the test configuration is such that the principal directions of the stress and strain tensors do not coincide with the symmetry axes of the specimen. This can easily be shown for a thin laminate (e.g. a single lamella) for which a state of plane stress can be assumed, such that: s33 = 0, t23 = 0, t31 = 0

[2.8]

e33 = s33s11 + s32s22

[2.9]

and

which is therefore not an independent coefficient, in which case, Equation [2.4] reduces to Equation [2.10]: e 11 s11 e 22 = s 21 g 12 0

s12 s 22 0

0 s 11 0 s 22 s66 t 12

[2.10]

An important feature of Equations [2.3], [2.4] and [2.10] is that the normal and shear components are uncoupled; in other words, normal stresses do not induce shear strains and shear stresses do not induce normal strains, but this situation prevails only when the coordinate system for the stress field coincides with the symmetry axes. For a lamella whose material axes are aligned at an angle q in the 1–2 plane to the stress axis, the relationship in Equation [2.10] becomes:

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General principles and perspectives ex s11 e y = s 21 g xy s61

s12 s 22 s 26

s16 s x s 26 s y s66 t xy

15

[2.11]

where s11 = m 4 s11 + m 2 n 2 (2 s12 + s66 ) + n 4 s22

[2.12]

in which m and n are cos q and sin q, respectively. The other terms have a similar form. The normal and shear modes are now coupled. That is, a tensile stress induces some shear and a shear stress induces some tensile strain. The expression for s11 may be rearranged into Equation [2.13]: 1 cos 4 q Ê 4 1 1 ˆ sin 4 q = + sin 2 q cos 2 q + Ë E45 E90 E0 ¯ E0 E0 E90

[2.13]

to give the in-plane variation of tensile modulus for this simple system of anisotropy. The consequences of Equation [2.11] and similar relationships are important: •

•

if the principal axes of the stress field do not coincide with the symmetry axes of the specimen, extraneous forces and deformations will arise; e.g. flexed coupons may additionally twist and tensioned coupons may exhibit in-plane shear. if a laminate consists of unidirectional lamellae lying at various angles to each other, deformation mismatches occur at the interfaces because of the different degrees of tension/shear coupling in the various lamellae. The severity of the effects will depend on the stacking sequence, the degree of asymmetry, the test modes, the clamping arrangements and so on, and may be sufficient to cause delamination, especially at the edges. In summary, the principal practical consequences of anisotropy are:

1 2 3

4

severe ‘end-effects’, which extend in the direction of higher stiffness (a function of both the specimen geometry and the anisotropy) premature failure in grips or at other loading points premature delamination at free edges, or other unintended failure modes.They tend to arise from the interactions between the macrostructure of the composite and even the simplest system of external forces. property imbalances between, say, a tensile modulus (or strength) dominated by the properties of the fibre and a shear modulus (or strength) governed largely by the properties of the matrix.

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These consequences entail special constraints on test configurations, specimen geometries and stacking sequences in laminates. They also sometimes induce behaviour in subelements, substructures and structures that is unique to anisotropic systems.

2.3.2 Features arising from practical realities The results from experimentation are sometimes erroneous because the requirements to ensure accurate data are onerous and not always achievable. Additionally, errors arise from imperfections originating in the fabrication stage. The possible defects include imperfect alignment and dispersion of the fibres, broken and kinked fibres, incompletely wetted fibres, voids and general mismatches between the constituents. The tensile modulus along the fibre direction of a composite containing a unidirectional, parallel array of fibres provides a simple example of the effect that fabrication defects can have on properties. The modulus can be estimated using the ‘Rule of Mixtures’ equation: Ec = jEf + (1 - j )Em

[2.14]

where Ec is the Young’s modulus of the composite, Ef the Young’s modulus of the fibre and Em the Young’s modulus of the matrix, with j being the volume fraction of the fibres. In practice the simple Equation [2.14] usually has to be modified to: Ec = hohljEf + (1 - j )Em

[2.15]

where ho is the efficiency factor for fibre orientation and hl the efficiency factor for fibre integrity (length and effective length). Usually Ef >> Em so that: Ec hohljEf

[2.16]

the upper bound of which is: Ec = jEf

[2.17]

and lower values of Ec reflect the fabrication deficiencies mentioned above. Research indicates that the properties of the fibres can be utilized with an efficiency of about 85% for modulus and about 70% for strength. With this as an upper bound, the simple tensile test procedure on this type of coupon provides a first-order assessment index of the quality of composite attainable from a particular fibre–matrix combination. The situation is much more complex for other stress fields and/or other fibre–matrix assemblies, where the matrix and the interface may be sources of weakness. The interlaminar shear strength, the shear modulus, the properties in the transverse direction and those under uniaxial compression are

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General principles and perspectives

17

all sensitive to the properties of the matrix and reflect the potential deficiencies of fibre composites. For such situations a third efficiency factor has to be incorporated into any analogue of Equation [2.15], to quantify the effectiveness of the fibre–matrix coupling. It follows, therefore, that the firstorder assessment by tensile testing is insufficient for many purposes and anything other than the most elementary evaluation programme should include tests in at least one additional and fundamentally different deformation mode. A popular test procedure which utilizes a different deformation mode purports to measure the interlaminar shear strength, by three-point flexure of a short beam. The span/depth ratio of the beam is so chosen that the beam should fail by interlaminar shearing rather than by tensile failure. In practice, failure is often mixed mode because the properties vary from point to point and therefore critical stresses may arise simultaneously at several positions; it is not unusual for evidence of tensile failure in the tension face of the beam, fibre buckling in the compression face of the beam and interlaminar shear at a mid-plane, all to be found in one specimen. Additionally, the configuration dimensions favourable for shear failure are such that the shear stress prevailing at the instant of failure cannot be calculated with high precision or accuracy. Even so, in principle the failure should be either at a fibre–matrix interface or in the matrix, and hence the measured value should not exceed about 60 MN m-2 for any of the plastics–matrix composites currently available. When higher values than this are reported, it is probable that some fibres were misaligned and had an orientation component out of the plane of the laminate, so that the measured breaking force was partly attributable to the stretching and possible fracture of some fibres. In such cases the tensile properties should correspondingly be lower than normal for the particular fibre volume fraction and fibre disposition. A similar role can be played by uniaxial compression tests, but they are fraught with practical difficulties associated with the transfer of force from the actuator to the test specimen. Irrespective of whether the ends of the specimen are clamped or free, a compromise has to be found between the ideal long slender specimen which tends to buckle under axial loading and the short wide specimen that is mechanically stable but yields data distorted by frictional or mechanical constraints at the thrust plates. Apart from the associated inaccuracies and imprecisions, the lateral strains are tensile in character and can cause phase separation in some composite structures when the coupling is weak; axially aligned fibres may become unsupported columns which then tend to buckle with damage developing progressively, whereas under tensile stress the fibres would contribute fully to the strength and modulus along that axis. Irrespective of the deformation mode and the anisotropy, elastic modulus is a bulk property and, provided the dimensions of the specimen are much

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Mechanical testing of advanced fibre composites

greater than the scale of the inhomogeneity, it is amenable to measurement and calculation. Strength and ductility, to some degree, are ‘local’ properties and therefore susceptible to structural discontinuities; consequently, the property values tend to be more variable and the test methods less soundly based than those for modulus. In particular, the methods used for the measurement of fracture toughness are not entirely satisfactory, mainly because the fractures seldom progress as a single crack and the critical region (i.e. the crack tip) is of the same order of magnitude as the scale of the heterogeneity.

2.3.3 Samples and specimens for mechanical tests The samples from which specimens are taken for test purposes are usually in one of three forms: pultrusions, filament-wound tubes and flat sheets, all of which may be tested in their entirety, or used as a source of smaller test pieces. The first two forms were chosen partly for fabrication convenience and partly for their correspondence to important industrial production processes. In pultrusions, the fibres are mainly aligned along the pultrusion axis; in filament-wound tubes the fibres may be aligned circumferentially or along spirals (often opposed, balanced spirals), and in other filament wound shapes the fibres can be placed to optimum effect. Also, these fabrication processes facilitate good consolidation of the structure and relatively voidfree end-products. Commercially produced flat sheets fall into four classes, with radically different fibre dispositions: • • • •

randomly oriented fibres (mainly random in the plane of the sheet rather than three-dimensionally random) layers of uniaxially oriented fibres variously aligned with respect to a reference axis layers of woven fabric variously aligned with respect to a reference axis sandwich structures.

The four classes of sheet, the pultrusions and the filament-wound structures offer various anisotropy options, ranging from isotropic in the plane to severely anisotropic and even some reinforcement in the third direction, which relate to a range of downstream composite structures. It is obviously imperative that any quoted properties data be qualified by a clear description of the volume fraction and spatial arrangement of the fibres in the structure, substructure, element, subelement or coupon that is tested. For the singular case of laminates consisting of unidirectional laminae arranged with their fibre-alignment axis varying from layer to layer, which are

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General principles and perspectives

19

Table 2.2. Laminate code. Guide to the notation Orientation of each lamella is expressed in degrees between the filament axis and the x-axis Positive angle is clockwise looking towards the layup tool surface Lamellae are listed in sequence, starting from layup tool surface Successive layers of different orientation are separated by/ Subscripts denote repeat lamella orientation The beginning and end of a code are marked by brackets, after which subcript T indicates that total laminate is shown and subscript S indicates that only one half of a symmetric laminate is shown

Examples of stacking sequence code

+45,-45,0,90 = +45/-45/0/90 +45,-45,0,0,90 = +45/-45/02/90 +45,-45,0,90 = (+45/-45/0/90)T 90,0,45,45,0,90 = (90/0/45)S ¯)S 90,0,45,0,90 = (90/0/45

popular for research purposes, there is an agreed notation which describes the stacking sequence, see Table 2.2. The properties of coupons cut from laminates vary with the stacking sequence, the alignment of the specimen axis in relation to the pattern of fibre orientation and, to a lesser degree, the in-plane position of the specimen. Some companies (e.g. in the automotive and aircraft industries) have in-house sheet cutting patterns designed so as to minimize the cost of specimen preparation and simultaneously to maximize the information derivable from each sheet. Local agreements on collaboration sometimes result in a group of companies adopting the same lamination and sheet cutting patterns. Similarly, the properties of pultrusions, filament-wound structures and coupons cut from both sources depend on the fibre disposition, but the testing emphasis is on structures (e.g. tubes, small pressure vessels, etc) for which there are special standard tests, rather than coupons, although filament-wound rings are tested in several standardised configurations such as diametral compression of an intact ring, flexure of a curved segment cut from the ring, torsion of a cut but otherwise complete ring and so on.

2.4

Nature and quality of test data

The factors that have to be considered in assessing the quality of mechanical properties data include the following:

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20 • • • • •

Mechanical testing of advanced fibre composites precision accuracy authenticity and typicality relevance to the test objectives physical significance.

Precision and accuracy are easily amenable to statistical analysis but are not unambiguously separable in a small set of data. The last three factors are not so readily quantifiable because of the possible uniqueness of each test coupon, or service item, although experimentation dedicated to particular issues can circumvent that difficulty in principle, if not always in practice. Similar values of a notional property are generated by replicate tests, but there is usually some scatter. The resultant distribution of values in a set is compounded of varabilities related to: • • •

precision of the measurements accuracy of the measurements variations in the structure of the test coupons in the set.

Overall, the interspecimen variability is an indicator of the quality of the data, but it cannot identify the separate causes unless the test programme has been specifically designed to do so. The mean value and a measure of the width of the distribution (e.g. the standard deviation) characterise the distribution of values in a set of independent measurements. They constitute only estimates of the mean value, and so on, of the distribution for all members of the population. Alternative characterising indicators are the median and the range. The median gives less weight to extreme values than the mean does and is thereby a superior measure in some circumstances; the range is less quantitatively justifiable than the standard deviation as a measure of the variability. The standard deviation is the square root of the variance, and that is given by Equation [2.18]:

(Â xi ) 1 È 2 s = ÍÂ xi n - 1 ÍÎ n 2

2

˘ ˙ ˙˚

[2.18]

where s is the standard deviation of a set of results, n the number of specimens in the set and xi the individual values. The symbol s denotes the standard deviation of the data from the tests on a set of specimens, and the standard deviation of the entire population is usually denoted by s. Apart from their direct role as a measure of the variability in a set of data, the variance and the standard deviation enable inferences to be drawn about:

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General principles and perspectives • • • • •

21

confidence limits for a set of data reliability of apparent differences between sets of data combined uncertainty of measurements when there are several sources of variability separate variabilities when several factors have affected a set of data goodness of fit when correlation between a dependent and an independent variable is derived.

Variance and standard deviation say nothing about the physical significance of a set of data, the difference between sets, correlations and so on, and in isolation they are likely to be misleading if the distribution of property values is multimodal, because what may then actually be variation would be presented as variability. They are also ineffectual if the criterion of acceptability is a boundary value rather than a mean value, because the number of requisite test results increases disproportionately as the probability level approaches the upper or lower limit of unity or zero. Some experimental and service situations are fraught with both extreme value and multimodality difficulties, as explained later in this section. Multimodality arises when the individual specimens in a set do not all respond similarly to the imposed excitation. This is commonly encountered in certain types of strength test, where the failure may be variously due to shear at an interface, tensile failure in fibres, compression buckling of fibres and so on. The overlapping distributions of strength values associated with the different processes can be identified and quantified by several techniques ranging from the construction of simple histograms to elaborate numerical manipulation, but ideally any such analysis should be supported by visual evidence of the different modes of behaviour. The standard deviation may be converted into confidence limits on the mean value via the expression: ±L = s e

t n

[2.19]

where L is the confidence limit for some specified probability level (usually 95%), se is the estimated true standard deviation (i.e. s above), n is the number of specimens and t is the Student’s t. t/ n decreases as n increases, as shown in Table 2.3 for 95% confidence limits. Thus, for example, if the mean value, x , has been derived from a set of ten specimens there is a 95% probability that the true mean value (i.e. from an infinite set of specimens) will lie within the range x = 0.715 se.

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Mechanical testing of advanced fibre composites Table 2.3. Variation of t / n with n.

n

t n

n

t n

n

t n

5 6 7

1.24 1.05 0.93

8 9 10

0.84 0.77 0.715

15 20 30

0.555 0.47 0.37

Similarly, judgements can be made as to whether an observed difference between the mean values from two sets of data are statistically significant via the calculation of t from the expression: t=

x1 - x2 se

n1 n2 n1 + n2

[2.20]

where 2

2

se =

(n1 - 1) s1 + (n2 - 1) s 2 n1 + n2 - 2

2

[2.21]

and the suffixes 1 and 2 denote the two sets. Reference to the standard tabulation of Student’s t then gives the level of significance of the observed difference. The identification of individual variances when several are affecting the overall variability in a set of data relies on a procedure referred to, unsurprisingly, as the analysis of variance.Where there are several influential variables, which may not be completely uncoupled, and where the effects of each one cannot be varied methodically and independently of the others (i.e. in the usual industrial situation), it is necessary in the interests of testing economy and statistical efficiency that the test programme be appropriately designed. Correlation coefficients are also limited in what they signify unless they are supported by physical evidence. Lifetime curves (e.g. fatigue and creep rupture data) are particularly challenging because the regression curve is often nearly horizontal. At any particular level of severity the number of cycles or the time to failure is highly variable, typically two decades on a logarithmic scale. A shallow slope tends to worsen the variability because a small variation in the applied severity converts into a large change in lifetime. The practical concerns are the severity level below which no failures occur, the investment in testing that will enable that limiting level to be determined with a high degree of confidence and the

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General principles and perspectives

23

risks entailed in extrapolating experimental data to times significantly longer than the duration of the tests. A nearly flat, featureless regression curve based on unimodal sets of lifetimes observed at different severity levels may suddenly change slope as a second failure mode suddenly intervenes. Statistical analysis of data embraces techniques ranging from simple estimates that entail nothing more that mental arithmetic to elaborate calculations requiring modern computing power. The latter are now much in vogue as a support for scientific experimentation, but they should be regarded with some circumspection because their superiority over the elementary methods rests mainly on their ability to extract more information from scattered data and not on an enhanced ability to provide a rationale. Thus, enhanced confidence limits on a set of data do not in themselves endow the result with a physical significance, justify an extrapolation beyond the range of the data, signify that an observed correlation is evidence of a causal relationship or imply that other inferences may be drawn from the data. That reservation is not intended to discredit statistical analysis nor is it an endorsement of the view of a very famous physicist who said, ‘If your experiment needs statistics, then you should have done a better experiment.’ With regard to the latter, it is undoubtedly true that an elaborate statistical analysis cannot improve the data derived from a poorly conducted or poorly designed experiment. However, in some instances impeccable experimentation nevertheless yields high variability and statistical analysis may then be the only route to the extraction of information from the data. The value of such analysis varies with the circumstances. Commercial benefits can accrue from minor differences in the properties of competing materials but, on the other hand, an observed difference may be statistically significant but physically unimportant and even a perfect correlation does not alone signify a causal relationship. Overriding all other considerations, however, is the fact that the penalties for malfunction in service may be severe. Therefore, validation test programmes for service items or prospective service are necessarily cautious and expensive. Apart from the precautions that have to be taken to ensure that tests are properly conducted, any data that indicate the enhancement of a property must be interpreted with caution because the advantage of a favourable trend in one property with respect to some independent variable may be completely offset by the disadvantage of a simultaneous unfavourable trend in another property. For example, precise uniaxial alignment of fibres maximises the attainable tensile modulus in that direction but the modulus in a transverse direction, the transverse strength, the torsional rigidity and the interlaminar shear strength are all adversely affected; the implications for testing strategy and evaluation costs are obvious.

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2.5

Mechanical tests for long-fibre composites

2.5.1 Primary properties An extensive infrastructure of test methods and procedures has had to be developed to support the composites business, but the great variety of composite structures, the complexities of the properties, the diversity of service applications and the immediacy of particular commercial pressures have resulted in the developments often being arbitrary and narrowly specific rather than interconnected elements of a coherent evaluation system. Thus, the particular role of any one test method as part of the testing infrastructure is often obscure, and the test may seem to be merely one of an agglomeration of methods rather than one of a coherent system. Even a cursory inspection of the established standard test methods reveals that there are conflicting recommendations for some test procedures, coexisting minor variants of some methods and some owing more to expediency than to science. There are also some major omissions from the repertoire of commonly used tests. Even so, a logical pattern of test procedures and inferential steps can be discerned under the conflicts and confusions of the fine detail, which provides a unifying framework against which any inconsistencies and deficiencies can be set in proper perspective. This chapter seeks to set that perspective. It is generally agreed that a minimum requirement for the assessment of the three primary properties of a long-fibre composite (modulus, strength and ductility) are those parameters listed in Table 2.4, or other, very similar parameters. Table 2.4 quite properly stipulates moduli in tension, flexure and uniaxial compression, which would provide a superfluity of tests for an isotropic homogeneous sample, but which are necessary for a long-fibre composite sample for the reasons touched upon earlier. On the other hand, the minimum requirement falls far short of comprehensively quantifying the stiffness and strength tensors, and it neglects the viscoelastic aspects of behaviour. In fact, despite the list giving the minimum requirement, no single investigating body is likely to carry out all of those tests as a general routine procedure because various sectors of the industry have different objectives for their evaluation programmes. With some oversimplification it can be said that manufacturers of fibres are mainly interested in the mechanical properties manifest in fibre-dominated situations (e.g. the properties in tension and flexure of samples containing uniaxial arrays of fibres). Manufacturers of resins tend to rely mainly on those tests that entail compression and shear modes of deformation, which are sensitive to the quality of the fibre–matrix coupling. The downstream industries need to supplement the data of Table 2.4 with data directly related to service situations.

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General principles and perspectives

25

Table 2.4. Primary mechanical properties essential for an evaluation of a long-fibre composite. Tensile modulus Compressive modulus (uniaxial) Flexural modulus Shear modulus (in plane) Lateral contraction ratiosa Tensile strength Compressive strength (uniaxial) Flexural strength Apparent interlaminar shear strength Fracture toughnessb (various modes) a In principle these quantities need not be measured provided the various corresponding moduli are known. b There is as yet no firm consensus about which deformation modes are the most informative in relation to service.

Several of the properties listed in Table 2.4 might be cited as essential constituents in an evaluation of a homogeneous single-constituent material, and the same test machines might be used for both that class of material and long-fibre composites. Thus, for tensile and uniaxial compression testing, irrespective of the class of material, the primary requirements are that the testing machine should be ‘axial’ (i.e. the force should act along the longitudinal axis of symmetry), the specimen should be long and slender, the strain should be measured on a gauge section sufficiently remote from the grips to ensure that they exert no influence on the result (i.e. with due allowance for Saint Venant’s Principle) and, for strength measurements, fracture should occur within that section. The additional stipulations for tests on composites are secondary in nature although important nevertheless; they include specified minimum dimensions for test bars, to ensure that they are larger than the scale of the inhomogeneities and the size of any likely defect, testpiece grips commensurate with the overall properties and additional measurements related to the anisotropy, and so on. In practice, tensile machines are seldom axial, which can severely distort a tensile property datum if the testpiece has a high modulus and/or is not ductile. Extensometers tend to slip. Alternatively, strain gauges can interfere with the local strain. Testpieces tend to slip from the grips, or break there rather than within the gauge length. In addition, specimen size may be dictated by extraneous factors such as the availability of adequate samples, the cost of fabrication of test coupons, the load capacity of test machines and so on. Furthermore, even though the breaking force and

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Mechanical testing of advanced fibre composites

ultimate extension of long-fibre composites may be measured accurately, the conversion of those quantities into failure stress and failure strain, respectively, are arbitrary and unreliable procedures because of the heterogeneity. All that may be claimed is that the notional failure stress and notional failure strain may be measured precisely. Flexure is a popular deformation mode for modulus measurements because it requires simpler apparatus and test specimens than tension. However, if the specimen is inhomogeneous, or if the properties vary otherwise through the thickness of the beam, the flexural response to transverse forces cannot properly be translated into a modulus because of the way in which the stiffness of the beam is dominated by the outer layers.This is generally termed ‘stacking sequence dependence’. In a tension test on a composite coupon with a laminated structure the properties of individual layers contribute in parallel and without bias (apart from tension–shear coupling) to the overall property. The force–deflection relationship defines a notional modulus which reflects the fibre alignments in the individual lamellae irrespective of the stacking sequence. In a flexure test, on the other hand, the contribution of each lamella depends on its disposition with respect to the neutral axis and hence the datum generated in the test is the stiffness of the particular beam rather than a modulus. The practical constraints on the dimensions of specimens in flexural tests correspond to those implicit in the Bernoulli–Euler elastic beam theory, with modifications necessitated by the high ratio of the Young’s modulus to the shear modulus. The relevant equation for a homogeneous, isotropic specimen subjected to three-point flexure is Equation [2.22]: d=

PL3 Ê Eh 2 ˆ 1 + 4bh3 E Ë GL2 ¯

[2.22]

where d is the deflection at the mid-point of the beam, P is the load at the mid-point, L is the span, b is the width, h is the thickness, with E and G being the flexural and shear moduli, respectively. Equation [2.22] is approximately valid for long-fibre composites if the substituted values of the moduli are appropriate for the particular anisotropy. Various modifications to the second term within the brackets (which are multiplying factors not very different from unity) have been proposed to allow for the heterogeneity; but even as it stands, the equation sets an approximate lower limit for the span/thickness ratio if shear is not to contribute significantly to the deflection of the beam. For example, the Young’s modulus of a unidirectional composite with a carbon-fibre volume fraction of 0.60 may be 120 GN m-2 and the shear modulus may be only 3 GN m-2, so that the span/thickness ratio should satisfy the condition:

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General principles and perspectives L2 > 100 40 h 2

27 [2.23]

if the shear correction is to be less than 1% of the measured value. This ratio is higher than the 16 : 1 normally regarded as sufficient for an isotropic material. A ratio of 60 : 1 is recommended by ASTM (American Society for Testing and Materials) for carbon-fibre reinforced resins. At the other extreme, the span/thickness ratio is variously specified as between 3 : 1 and 5 : 1 for the short-beam shear test, to favour interlaminar shear failure, but the high transverse forces that are required to flex a thick beam can cause excessive distortion or damage near loading points and thereby change the effective span. The damage can be limited and a tendency for fibres to buckle out of the compression face of the test piece can be reduced by the use of larger radii for the loading and support anvils. However, the greater the radii, the greater the uncertainty about the effective span, and ASTM D790-86, for instance, recommends that the radii should be no greater than four times the beam thickness. Apart from its uses as an alternative, or as a supplement, to tension, flexure is often the only practicable deformation mode for macrocomposite structures such as laminated honeycomb sandwich panels. Local crushing and indentation at loading points are a common difficulty with such specimens, and flat loading pads usefully replace cylindrical anvils. The specific details of tensile, flexural and other mechanical tests vary from company to company within a country, from country to country and with the nature of the sample. Most of the variations dictated by the nature of the sample are necessary for technical reasons, for instance, to accommodate specimens in which the axis of fibre orientation does not coincide with the stress axis, although others appear to have no more justification than casual prejudice. Similarly, the specifications for end-tabs, which have been used almost universally to reduce the probability of failure initiating at the grips during a tensile test, vary widely. End-tabs can also facilitate accurate alignment of the specimen in the test machine, provided that they are symmetrical and properly positioned on the specimen, but if they are deficient in these respects they can cause misalignment and introduce stress concentrations. In the absence of systematic evidence to the contrary, one must assume that the various specified test procedures might yield different values for modulus and strength on specimens of the same composition. Some light was shed on the issue in a paper by Sottos et al.,3 who compared the results obtained on one fibre–resin formulation in four different laminate layups by use of three standard test methods with permitted variants. In the case of tensile modulus and tensile strength there were 17 sets of data, with five specimens in each set. The coefficients of variation for the

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modulus measurements varied from 0.013 to 0.120 with a mean value of 0.068. For the strength they varied from 0.041 to 0.140 with a mean value of 0.075. Such coefficients of variation compare unfavourably with corresponding data for other classes of material (e.g. thermoplastics and thermosets) but they are similar to the coefficients reported elsewhere for other composite materials. For instance, values of 0.079, 0.080, 0.083 and 0.100 were tabulated by Johnson4 for tensile modulus measurements on a polyester resin with four different volume fractions of glass fibre and Owen et al.5 reported even higher levels of variability for sheet moulding compounds. It seems likely that relatively high coefficients of variation are an inherent characteristic of composite materials in general, probably caused by local variations in fibre volume fraction, fibre alignment and void content. Sottos et al.3 concluded that ‘with one or two exceptions, the different standards do, in fact, give data which are probably not significantly different’. They did, however, note that the recommended use of only five specimens for each data set was barely adequate for discrimination between the mean values when the coefficients of variation are at the level found in their test programme. Taking the mean values of the coefficients of variation as typical for this type of measurement and on the basis of a normalised distribution, one might expect 95% confidence limits in the region of 0.08 to 0.10 for sets of five specimens. The specifications for the other types of test listed in Table 2.4 are similarly varied, and the sparse published information on variability suggests similar coefficients of variation, though Sottos et al.3 reported lower mean coefficients of variation of 0.043 for ‘modulus’ and 0.056 for strength measured in flexure. In general, the possible disparities in measured property values arising from the different specimen dimensions have not been quantified, nor, until recently, has there been much advocacy of the merits of international standardisation. It seems that the active groups have a vested interest in perpetuating their use of whatever procedures had been adopted initially, probably because it enables them to make the best current use of their archive data, which are often extensive and which, in the absence of a science-justified database, are a pragmatic basis for materials selection and end-product design. If high variability is an inherent characteristic of fibre–composite materials and if, because of that, the various standard tests do not give obviously different results, except possibly via the generation of large sets of data, there is no reason for them all to be retained unless there are independent grounds for their retention. On the other hand, by a parallel argument it should not matter if they are retained because the disparities could be largely ignored. Substantial savings in evaluation costs could be achieved if this matter were to be resolved. However, little effort

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is expended on the acquisition of facts about the relative merits of the various standard procedures and the comparative variabilities, partly because of vested interests and partly because the statistically sound test programmes that would be necessary would be costly and rather tedious to conduct.

2.5.2 Engineering properties data The test programme implied by Table 2.4 has been expanded in scope by arbitrary procedures to satisfy various downstream requirements which vary from company to company. Table 2.5 lists the tests stipulated by a large commercial aeroplane manufacturer in the USA as being necessary in the ‘initial testing’ phase. The call for ‘open hole’ tests reflects reservations about the reliability of the theories of failure and about the relevance and relative paucity of the empirical evidence from conventional fracture toughness tests. The protagonists of such tests sometimes seem to be preoccupied with a search for authentic and/or definitive data which is perpetually frustrated by a preponderance of mixed-mode failures in their experiments. The same is true of short-beam shear testing. However, since most service failures are also mixed mode, it may be that the use of data generated through an empirical matching of laboratory configurations to service situations would be a better option than the use of arbitrary and unreliable data generated in a formally correct way. It could also be argued that a fracture which features all possible failure mechanisms indicates that the ultimate properties of fibre, matrix and interface were well balanced in the item and were being fully utilised in the composite structure. The inclusion of the sixth and seventh items in the list of Table 2.5 is a pragmatic response to the fact that in-service conditions can be arduous and may induce severe deteriorations in the structure and performance that are not revealed, or implied, by the data generated by traditional mechanTable 2.5. Primary engineering properties for preliminary selection of composite materials. Tensile strength at room temperature Uniaxial compression at room temperature Interlaminar shear at room temperature Open hole tension at room temperature Open hole compression at 93°C Hot /wet compression strength Edge-plate compression strength after impact at room temperature

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ical tests. It also compensates for the disparity which exists between the properties measured in a traditional evaluation programme and the attributes that are required of a serviceable end-product. Apart from the limitations mentioned above, the tests listed in Tables 2.4 and 2.5 generate only so-called ‘single-point’ data. These may be useful for quality control and materials selection purposes, but are of limited utility in design calculations for load-bearing service, for which creep, creep rupture, fatigue and other phenomena are relevant considerations. The previously mentioned partial failure of the composites testing community to recognise that viscoelastic behaviour is likely in some circumstances has been corrected, in that the automotive, aerospace and chemical plant industries demand creep, creep rupture and fatigue data, overlain by information on the degenerative effects of various environments. The list of topics of concern to end-users is formidable; the main headings of a list emanating from an automotive company in the USA are given in Table 2.6 as an example. Despite the inclusion of long-term data in the wants lists, the dearth of data in this area of durability persists. This leads directly to a common form of data misuse, namely short-term modulus and strength data being used in a design context of long-term load-bearing capability without an appropriate allowance being made for the ‘elapsed time’ effect. The errors are not serious when the fibres dominate the response, because the time dependence is then slight, but when the stress field is such that the matrix is influential, the neglect of time dependence may lead to inadequate load-bearing cross-sections and a short service lifetime.

Table 2.6. Primary data and design data as envisaged by the automotive industry.a Elastic and strength properties at various temperatures in the range -40°C to 150°C Effect of loading rate on tensile and compressive properties in the range 1.67 ¥ 10-3 s-1 to 1.67 ¥ 10 s-1 Long-term material propertiesb Environmental effects on long-term properties Energy absorption upon impact Manufacturing effectsc Characterisation of joints and fasteners a

This information is extracted from a document emanating from one company in the USA, but it is very similar to the data requirements stated by German, French and British automotive companies. b Creep, fatigue, residual strength after fatigue, effect of notches and holes on those properties. c Properties in ribs, bosses, at knit-lines, etc.

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Because impact is a common service hazard, impact testing features increasingly in evaluation programmes. Current test practices for composites loosely follow the standardised procedures recommended for unreinforced plastics, but the specimen dimensions and other details of the test configuration were chosen either arbitrarily or in attempts to simulate commonly encountered structural features. The test configurations are: • • •

bars in tension beams in flexure plates in flexure.

The impact is variously by swinging pendulum, falling dart, driven dart, spring-driven projectile and air-driven projectile, all of which deliver relatively low velocity impacts, and do not simulate aggressive service impacts. They do correspond, however, to the casual service hazard of a minor impact that may cause only slight direct damage but nevertheless leave the item prone to premature failure by a different mechanism during subsequent service. There have been a number of notable studies which have covered quasi-static through to ballistic impact.6 Many of the early impact studies, most notably by Adams7 of the University of Wyoming, USA, made use of the flexed beam methods, but the flexed plate configuration has now become the more popular. The former methods enable the measured quantity to be related to the overall anisotropy of the plate from which the beams have been cut, whereas the latter almost automatically identifies the easiest failure path and corresponds more closely than the flexed beam to the situation prevailing during a casual impact on a service item. However, the response to impact of a conventional laboratory test piece may, nevertheless, be very different from that of a service structure. Apart from a tenuous geometric similarity between the flexed plate test configuration and service impacts, a useful practical advantage is that the preparation of the test specimens is relatively undemanding, because results are generally not so sensitive to the quality of the edges as those from flexed beams. Various shapes and sizes of specimen, support and impactor have been employed and, similarly, so have various impactor velocities and incident energies. The use of a circular support constitutes a perpetuation of the general practice that has been established and standardised for unreinforced plastics. The use of a square aperture seems to have been encouraged by the manufacturers of test machines in the USA; it may be felt that a square aperture corresponds more closely than a circular one to the majority of panels in service. Another unresolved issue is international standardisation of the size of the aperture, the striker and so on, the details of which strongly affect the apparent impact resistance and the mode of failure.

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Each of the dimensional factors affects the stress field at and near the point of impact. The analysis for a flexed laminated plate is beset with uncertainties and the theoretical stress field will be distorted by the onset of even minor damage, so that comparisons between data emanating from different sources are likely to be unreliable until standardised test practices are established. Additionally, a distinction has to be drawn between the strain energy imparted to the entire structure (test specimen or service item), which can be measured, and the local strain energy density initiating and subsequently sustaining the failure processes, which cannot be measured. Impact tests at low incident energy provide insights into the mechanics of fracture. The data obtained set the impact resistance of composites in perspective relative to that of other classes of material; for example, in one of the standard flexed plate configurations an incident energy of 1–2 J suffices to damage a 16-ply laminate slightly and less than 10 J creates extensive damage, whereas in the same test configuration many unreinforced thermoplastics have impact resistances in the region 60–80 J. The slight damage incurred in a superficially innocuous impact may weaken a structure directly, by introducing stress concentrators and local weaknesses, or indirectly, through the creation of pathways for the subsequent ingress of water or solvents. The mechanical deterioration attributable to the damage may be assessed in various ways, for example strength in flexure of sandwich structures, or tensile and compressive strength, but the currently popular method is edge compression of a plate. In that test a rectangular plate is impacted transversely at low incident energy and then subjected to in-plane compression by force applied along one edge. The initial impact, which has not yet been standardised internationally, is such as to produce ‘barely visible damage’. However, that criterion is subjective, and the visible damage is known not to correlate well with the amount of damage as assessed by ultrasonic absorption, or with the residual strength of the damaged structure. Quite extensive internal delamination can occur with no apparent damage at the surface. Therefore, the several variants of the ‘damage tolerance test’ all stipulate relatively large plates to reduce the possibility of the internal damage extending to the edges, and this large size entails edge supports for the plate during the compression phase and a large load-capacity test machine. The collapse load cannot be translated into a specific physical property because practical factors limit the attainable precision in an edge-loading configuration. Also, prior damage can only be known accurately by dissection, and so on. Thus, the test is arbitrary and data emanating from various sources may not be directly comparable, so that the links between experimental data and service performance are tenuous and largely unquantified at present.

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The cost of comprehensive evaluations such as that implied by Table 2.6 is high and, in consequence, the downstream demand for data is rarely met in full, so that there is some uncertainty over which sector(s) of the industry should bear the main burden of the testing. There is a tendency for the data demands of a user industry to be excessive and, correspondingly, there is a tendency for information supplied by a materials producer to be the bare minimum and to be selectively biased to the advantage of the particular product. It is likely that the pragmatic compromise that always has to be achieved is determined more by the politics of the marketplace than by scientific rationalisation. Even so, the financial penalties for using inappropriate data can be severe. Overdesign is expensive and inefficient. Underdesign leads to malfunction, so that reliable design data are a prime requirement for most projects. Those properties tend to be dominated by the properties of the matrix and the fibre–matrix interface to varying degrees.

2.6

Concluding comments

A survey in 1987 of the then-current range of standardised, or semistandardised, mechanical tests8 concluded that the existing system of standardised test methods was deficient in three respects: •

• •

there were too many variants of some tests and a dearth of hard evidence about the effects of the variations on the reliability of the generated data some tests were not fit for their intended purpose some important phenomena and properties were neglected by the testing community.

Some tests for modulus and strength were deemed to be fit for their intended purpose; some (modulus and strength in uniaxial compression, modulus in shear, interlaminar shear strength, impact resistance, fatigue resistance) were deemed marginally or conditionally fit-for-purpose; others (damage tolerance, fracture toughness) were deemed not fit-for-purpose and some (creep, creep rupture) were seldom carried out. This unsatisfactory state of affairs was attributed in the report to the fragmented nature of the industry, poor interaction between academy and industry and a collective failure to establish an adequate infrastructure. Little has changed in the intervening years but even so, imperfect though the testing infrastructure might be, each test event contributes a datum to the hierarchy of information that supports each downstream operation. An apparent insufficiency of information/data is common to all classes of material, because evaluation programmes may be curtailed by constraints on costs, test procedures may be inappropriate for the intended

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purpose and circumstances may be such that direct testing cannot cover the requirement when, for instance, a specified load-bearing lifetime is much longer than the allocated product development time. Such testing insufficiencies are common in industry, particularly when the materials are novel, or the applications are innovative, but there is a set of procedures that partly compensate for them. In general, limited laboratory test data can be ‘adjusted’ or extended by one or more of the following procedures to match them to the data demands for particular end-products or components in specific service: • • • •

interpolation between data measured at standardised excitation levels and ambient conditions extrapolation of durability data to longer times than the duration of the tests, or to other frequencies acceleration of failure processes by exposure to aggressive environments allowance for likely changes of state in an end-product during its service lifetime.

Provided there is an established justifying rationale, even single-point data of the type listed in Table 2.4 can be used in a wider context than that implicit in the defined scope of the tests, especially if results can be interpreted in the light of previously established correlations with service performance. For long-fibre composites, although adjustment for the fibre volume fraction, for the spatial distribution of the fibres and for component size and shape is commonplace via the combination of simple tests and mathematical models, some of the ground rules for the adjustment procedures mentioned above have not yet been firmly established. Further consolidation of the prediction procedures is hampered by the high cost of the enabling tests and the validating stage, by the large number of possible combinations of matrix type, fibre type, fibre volume fraction and spatial arrangement, by a dearth of certain classes of critical data and by the ineffectual information pathways available. The ineffectual pathways were identified and remedial action was proposed in the survey referred to earlier.8 Testing is usually the first stage in the process of the prediction of service performance. However, inaccurate, incomplete or inappropriate test data will almost inevitably lead to questionable predictions and a consequential tendency for overdesign in prospective load-bearing structures.

References 1. R Martin, ‘Composite structures: a dual approach to design’, Materials World, 1995 3(7) 320–2.

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2. P J Hogg, ‘Designing for creep in composites’, Proceedings of the International Conference on Designing Cost-effective Composites, The Institution of Mechanical Engineers, London, UK, 15–16 September 1998, Professional Engineering Publishers, 1998, 93–106. 3. N R Sottos, J M Hodgkinson and F L Matthews, ‘A practical comparison of standard test methods using carbon fibre reinforced epoxy’, Proceedings of the Sixth International Conference on Composite Materials, Imperial College, London, UK, 20–24 July 1987, eds F L Matthews, N C R Buskell, J M Hodgkinson and J Morton, Elsevier Applied Science, London, 1987, Vol 1, 1.310–20. 4. A F Johnson, Engineering Design Properties of GRP, British Plastics Federation Publication No 215/1, 1978. 5. M J Owen, A M Tobias and H D Rees, ‘Design limits for polyester SMCs’, Plastics and Rubber Processing and Applications, 1984 4(4) 349–54. 6. W J Cantwell and J Morton, ‘Comparison of the low and high velocity impact response of CFRP’, Composites, 1989 20 545–51. 7. D F Adams and J L Perry, ‘Instrumented Charpy impact tests of several unidirectional composite materials’, Fibre Science and Technology, 1975 8 275–302. 8. P J Hogg and S Turner, The Mechanical Testing of Long-fibre Composites: Harmonisation and Standardization in the UK, Report for the Department of Trade and Industry, UK, January 1988 (Copies are available from Prof. P J Hogg, Materials Department, Queen Mary and Westfield College, London).

Bibliography 1. K A Brownlee, Industrial Experimentation, London, HMSO, 1957. 2. C A Dostal (ed), Engineered Materials Handbook, Vol 1: Composites, ASM International, Materials Park, Ohio, 1987. 3. J M Whitney, I M Daniel and R B Pipes, Experimental Mechanics of Fiber Reinforced Composite Materials, SESA Monograph No 4, Society for Experimental Stress Analysis, Brookfield Center, Connecticut, 1982. 4. L A Carlsson and R B Pipes, Experimental Characterization of Advanced Composite Materials, Prentice Hall, Englewood Cliffs, New Jersey, 1987.

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3 Specimen preparation F L M ATTHEWS

3.1

Introduction

There are a number of subsidiary, but vital, issues that are complementary to the main activity of mechanical testing. These issues, taken together, constitute the preparatory work required to produce test specimens of adequate quality. If insufficient attention is given to any of these activities, the results from a particular test could be invalidated. The following remarks relate to the use of specimens of high performance composites fabricated from continuous preimpregnated fibres, the subject of this text. The four stages considered are: laminate production; quality checking; specimen manufacture; application of strain gauges. The final three stages would, of course, apply to any material.

3.2

Laminate production

Thin sheets, known as laminates, usually 1 or 2 mm thick for coupon specimens, are manufactured from layers of fibres preimpregnated with partially cured (if epoxy-based) resin prepreg. The matrix is usually an epoxy, but BMI (bismaleimide) and thermoplastic prepregs are also used. It should be noted that the following discourse relates mainly to epoxy prepregs (owing mainly to their popularity). It should, however, be pointed out that the preparation of laminates with thermoplastic matrices is in many ways a similar but more straightforward process, because the plastic resin is not required to cure, but simply ‘melts’ at a suitably high temperature and resolidifies when cooled. A single prepreg layer is usually 0.125 or 0.25 mm thick and the fibres are either continuous and parallel (unidirectional), or in the form of a woven fabric. The prepreg is supplied as ‘tape’, normally 0.3 m wide (but suppliers having width preferences, woven materials being generally wider than unidirectional products), sandwiched between protective layers of paper or plastic and wound on a reel. If epoxy, the prepreg should be kept in a freezer 36

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until it is required; if thermoplastic, low temperature is not a requirement but it is advisable to store the material in a clean, light-free environment. Shelf-life (for epoxies) is normally around 18 months and will be clearly stated by the supplier; thermoplastics, on the other hand, generally degrade very slowly at ambient temperatures. If the prepreg has exceeded its lifetime it can probably still be used for a further six months, at least. However, its suitability should be checked by moulding a test panel, or by checking the cure state of the matrix resin using differential scanning calorimetry (DSC). Appropriate lengths are cut from the reel and placed on top of each other with the fibres in each layer oriented relative to one another in a predetermined sequence. Hand tools, such as a ‘Stanley’ knife drawn against a hard edge, are usually satisfactory for cutting. Fabric prepreg can be cut using shears or scissors. Where available, a rotary knife or water jet could be used. The protective layers are removed before each layer is placed on that previously laid down, and the layer carefully smoothed out to prevent air entrapment. It is essential that the layers are aligned with reference to a datum, since even a few degrees’ misalignment can cause a dramatic effect on mechanical properties. With properly prepared prepreg the edge of the protective backing sheets can be used as a reference. Care must be taken to ensure that twisted or knotted fibre bundles, or prepreg areas containing gaps between bundles, are not included in the laminate. Following completion of the layup, the stack of prepreg layers is prepared for curing in the case of epoxies, or consolidation for thermoplastics. The epoxy resin, which forms the matrix of the composite, is formulated for autoclave curing; the whole curing process lasts several hours and involves a combination of vacuum, raised temperature (to 120 or 175°C for epoxies, often higher for thermoplastics) and raised pressure. The prepreg layers are contained within a sealed ‘blanket’ as illustrated in Fig. 3.1. To prevent the laminate sticking to the base and caul (pressure) plates, the latter can be coated with release agent, or layers of release fabric or a polymeric film are inserted between the plates and the prepreg. A disadvantage of the second approach is that an impression of the fabric is left on the surface of the laminate, thus making it difficult to detect the fibre orientation in the surface layers with the naked eye. As an alternative to autoclave curing it is possible to use a heated press, in which case it is necessary to monitor separately the state of resin gelation, or a press-clave. The latter device, illustrated in Fig. 3.2, is placed in a heated press, in combination with a separate high pressure supply and a vacuum source.A heated press, with facilities for rapid cooling of its platens, would be used for processing advanced thermoplastic prepregs. Clearly the size of the laminate that can be produced will be determined by the size of press available.

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Mechanical testing of advanced fibre composites Vacuum bagging material

Air breather cloth

Laminated composite plate

Peel ply

Pressure plate

Vacuum connection Melinex Sealing tape

3.1 Arrangement for producing laminates by autoclaving.

Top plate Melinex Bleed cloth Peel ply Laminate Peel ply Perforated PTFE Peel ply Frame

Baseplate Vacuum connection

Pressure vessel

Baseplate

3.2 Layout of a press-clave.

Pressure connection Diaphragm Top plate Laminate, etc. Frame Vacuum connection

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3.3

39

Quality checking

The manufacturing process, if not properly controlled, can introduce defects into the laminate. Typical defects are voids (small cavities in the resin), delaminations (unbonded areas between layers) or, unusually, longitudinal cracks (lack of bonding between fibre and matrix). Voids can be caused if the prepreg is not allowed to warm to room temperature before laying-up, thus introducing moisture into the prepreg stack. Delaminations can be caused by entrapped air or the inclusion of pieces of backing sheet. Longitudinal splitting and delamination can occur in multidirectional laminates as a result of thermal stresses induced during cooldown from the curing temperature. All the above defects will degrade mechanical properties, particularly in compression, shear and flexure. It is, therefore, important that their presence is detected so that faulty laminates can be discarded. The standard method of detection is to use ultrasonic C-scan, which is good at detecting inclusions, porosity and delaminations, or, possibly, X-ray techniques, which can detect through-thickness cracks.

3.4

Specimen manufacture

Specimens, as defined by the relevant standard, or test to be carried out, are cut from the laminates using a diamond-tipped saw. The normal blade has 600 grit, but a cleaner cut, with less damage to the laminate, is obtained with 800 grit. In the latter case the blade can become clogged with debris and frequent cleaning may be required. Laminates produced by autoclaving will have a feathered edge which must be removed. It is clearly vital that edges produced after trimming, which effectively act as a datum for subsequent specimen cutting, are correctly aligned with the fibres in the layers. A commonly used method for establishing the 0° direction of a cured laminate prior to cutting is to split off a narrow strip of material along this direction (in multidirectional laminates this can be done if the 0° layer is made slightly wider), but it has been shown that this approach may not be sufficiently accurate, and a preferred method1 is to mark the outermost ply by scoring across in the 90° direction in a nonstressed region. High temperatures are generated during dry cutting, which can cause local degradation and damage at the machined edge. This can be largely prevented by the use of a coolant (water), but subsequent drying-out steps must be taken to remove any absorbed liquid from the specimen. Generally, specimen blanks are machined oversize, final dimensions being achieved by grinding. Drilling is readily achieved with tungsten carbide or diamond tipped bits,

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the laminate being supported by a (sacrificial) backing plate. It is advisable to use a drill bit tip angle of 55–60° for thin laminates and 90–100° for thick sections, rather than the usual 120°. Other operations are best achieved by grinding. Clearly, appropriate support is needed for thin laminates if through-thickness shaping is to be carried out. Kevlar fibre-reinforced materials need special attention. Owing to the nature of the fibre it is difficult to avoid a ‘furry’ edge. Specially adapted impregnated wheels can be obtained for cutting. Another alternative is to use a high pressure water jet. For many tests, for example tension and compression, it is often necessary to bond end-tabs to the specimen; this is done to diffuse the gripping loads and prevent failure at the specimen ends. According to the particular requirements, the tabs may be of aluminium alloy, GFRP (glass-fibre reinforced plastic) or CFRP (carbon-fibre reinforced plastic). When the tabs are of composite, the preferred method is to stick strips to the trimmed laminate before cutting into specimens. This approach is not only quicker, but it also ensures alignment of tabs and specimen. When the tabs are metal this approach cannot be adopted and the tabs must be bonded to individual specimens, using a jig to give accurate positioning. Surfaces where end-tabs are to be bonded should be abraded in order to remove surface contamination, whilst taking care not to damage the outermost fibres. This is done most easily, particularly if the laminate surface is rough, by grit blasting, the only objection to this method being that the surface may itself become contaminated, either by grease carried by the grit or embedment of the grit. Surfaces not needing to be abraded can be protected by masking with self-adhesive tape. The grade of grit used, typically 80–120 grade, does not appear to be critical if care is taken to avoid excessive abrasion and damage to the composite. The dust left behind on the material after grit blasting is most easily removed by flushing under running water. If the water lies on the surface in an unbroken film, a good standard of surface cleanliness is indicated. The amount of water absorbed by the laminate will be small, particularly if the material is dried immediately after washing. After drying, the surfaces are solvent wiped and bonded. Commercial ‘two-tube’ epoxy resin has been found to be suitable for bonding end-tabs to be used for tests at room temperature and should be applied sparingly to both bonding surfaces. The joint, when assembled, can be contained in a simple vacuum bag which will apply an adequate clamping force and remove entrapped air. The tab material can be located by using small pegs inserted in notches cut through the tab and test materials. An alternative to low temperature curing adhesive is to use bonding film which is cured under elevated temperature and pressure, although in some cases this can cause thermal stresses sufficient to split a 0° laminate. Whatever adhesive

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is used it should be tough, with a greater failure strain than that of the material under test. CRAG2 specifies that it should have a shear strength greater than 30 MPa. Special adhesives would be preferred for fatigue testing or high temperature work. An incidental advantage in using GFRP end-tabs is that the material is translucent and any gaps in the glue film can be seen by visual examination. Even if the joint is strong enough to withstand specimen failure loads, gaps in the glue line can result in uneven stresses in the underlying composite and cause premature failure.1 The crucial issue when bonding is to ensure that both the specimen and the tabs are properly prepared. Composites need to be degreased and abraded to remove all traces of release agent transferred during moulding. This procedure should be followed by wiping with a solvent. Similar procedures should be followed when making bonded joints. In addition to degreasing, aluminium alloy tabs need to be etched in chromic acid or phosphoric acid.

3.5

Strain gauging

All mechanical tests will involve the measurement of displacements or strains, as defined by the appropriate standard. When strain gauges are called for, it is important to follow the recommended procedures.The length of the gauge may be specified by the relevant standards, but should always be significantly shorter than the gauge length of the specimen. Composites can cause particular difficulties not encountered with metals.3 The issues that must be addressed are as follows: 1

2

3

4

5

High gauge resistances are desirable because high voltages (2–4 V) with low current can then be used; this improves hysteresis effects and zero load stability. If possible, use gauges with lead wires attached, or solder wires to the gauge before installation; this should avoid soldering damage to the composite. Ideally the pattern of the autoclave scrim cloth should be removed before gauge installation; this is particularly important if contact adhesives are used. Corrections may be necessary to gauge transverse sensitivity effects; errors of over 100% between actual and measured strains can be obtained. Gauges must be precisely aligned; errors of 15% can result from a 2° misalignment. There is no universally acceptable way of ensuring alignment. The scrim cloth pattern can be misleading. Sometimes C-scan after installation can be useful, or checking with failure surfaces after fracture.

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Mechanical testing of advanced fibre composites Dummy gauges are the preferred method for temperature compensation but, again, precise alignment is needed. It is necessary to mount the dummy gauges on an ‘identical’ piece of laminate, with the same orientation relative to the fibres as used for the active gauges.

3.6

Summary

In summary, it is essential that careful and consistent procedures are followed at every stage of specimen production. Failure to do so will throw doubt on the validity of any data generated.

References 1. P W Manders and I M Kowalski, ‘The effect of small angular fiber misalignments and tabbing techniques on the tensile strength of carbon fiber composites’, 32nd International SAMPE Symposium, Anaheim, CA, USA, eds R Carson, M Burg and K J Kjoller, Society for the Advancement of Material and Process Engineering, Covina, CA, USA, 1987. 2. P T Curtis (Ed), CRAG Test Methods for the Measurement of the Engineering Properties of Fibre Reinforced Plastics, Royal Aircraft Establishment, Farnborough, UK, Technical Report 88012, 1988. 3. M E Tuttle and H F Brinson, Resistance Foil Gauge Technology as Applied to Composite Materials, Report No. VPI-E-83-19, Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA, June 1983.

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4 Tension E W GODWIN

4.1

Introduction

Put simply, the purpose of a tensile test is to determine the ultimate tensile stress (UTS) and tensile modulus (E) of a material, and with additional instrumentation Poisson’s ratio may also be measured. However, a closely observed test of a material under controlled conditions should provide a great deal more information about the way it behaves under load. A composite may split or delaminate, for instance, and studying the material as it is subjected to increasing load may give an insight into the ways in which damage initiates and develops. Finally, the nature of failure is seen; it may be brittle, with no warning, or it may be preceded by obvious audible or visible signs. All such information is useful; knowledge of the UTS and the way in which failure occurs is vital if serious use is to be made of the material. Mechanical testing began being carried out on a scientific basis in the second half of the nineteenth century when metals were the commonest engineering material. The use of high performance composite materials, as distinct from ‘reinforced plastics’, as major load-carrying materials began almost a century later, and it follows that the test methods initially used to test composites were based very closely on ‘metallic’ techniques. Testing of metals is not a particularly difficult task, being aided by the strainhardening isotropic homogeneous nature of the material. At its simplest, a piece of stock material can be pulled in a testing machine and fail in its midlength: locally reducing the cross-section of the testpiece (‘waisting’) can ensure that failure occurs away from the grips. The inadequacy of established tensile testing techniques when used with composites became apparent in the 1960s, and emphasised how different the behaviour of composites could be from that of metals. The key differences are that composites, by definition, are inhomogeneous and may, as a result of their twophase nature, exhibit weakness under a particular loading mode, whilst having high strength under other modes. Thus a waisted specimen could fail 43

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because the low shear strength of the material results in the wider, or thicker, part of the specimen simply shearing away from the body of the specimen before reaching the tensile failure stress. The variety of specimens in use at that time is seen in the proceedings of the first ASTM (American Society for Testing and Materials) sponsored conference on testing and design of composite materials (ASTM STP 460).1 These are illustrated in Fig. 4.1. The names given to the designs are evocative (dog-bone, waisted, bow-tie) but the specimens themselves showed various failings which have been widely reported. Although in its time the elongated bow-tie was described2 as being the only design of GFRP (glassfibre reinforced plastic) specimen to fail consistently in the gauge length, that too has become obsolete. The ratio of UTS to ultimate shear strength was then roughly 4 : 1. By 1974 it had been calculated that, for a ratio of 16 : 1 (a value somewhat less than today) a radius of 1000 mm was needed to achieve an acceptable ratio of shear/tensile stresses in the specimen. The shouldered and waisted designs, which clearly owed their origins to metals testing, have ceased to be used and, of the geometries in use at that time, only the parallel-sided end-tabbed type remains in use today. The characteristics of the tab material may be radically different from that of the test material, being chosen to provide adequate gripping and protection of the underlying material. This, of course, exemplifies composites design, which is a matter of building up rather than machining down to size. Moreover, the properties of the material may be varied as required within the thickness of the material. It is important to understand that, where composite materials are concerned, there are two separate, and possibly distinct aims when carrying out a materials test. The first is to establish fundamental material properties for subsequent use with structural analysis and design techniques. These properties, sometimes referred to as ‘single ply data’, are obtained from well-aligned unidirectional fibres loaded in a variety of directions. If the fibres are aligned in the loading direction, this represents something of an ultimate test condition where the stresses developed will be higher than is possible with any other layup of the same fibres; conversely, if the fibres are at 90° to the loading direction, the testpiece is weak and requires careful handling. The second aim is to determine the properties, or investigate the behaviour, of an existing material. This is likely to involve testing material with fibres lying at a number of angles to the principal loading direction. In many cases this may require a clear understanding of laminate analysis techniques, and of the behaviour of non-axial fibres in a laminate, if sensible use is to be made of the results of the test. Again, there are two fundamental problems to be addressed in mechanical testing, irrespective of the material under test. The first of these is to minimise and, ideally, to eliminate undesirable interactions between

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Tension 76.2 R

45

57.2

(a) 19.1

12.7 114.3 between grips at start of test

215.9 End of test material

30° bevel ± 45° tab material

4.8 Ø

12.7

(b)

12.7 69.9

(c)

76.2 254.0 53.8

6.4 R

12.7

4.8 Ø

19.1

12.7 292.1 76.2 R

6.4 Ø

(d)

12.7 19.1

57.2 215.9

57.2

6.4 Ø (e)

12.7 19.1

57.2

228.6 45° bevel

(f)

12.7 50.8

254.0 31.8 R

6.4

(g)

19.1 57.2

50.8 203.2

4.1 Tensile test specimens being used in 1969.1 (a) ASTM D 638 plastics specimen; (b) straight-sided, tabbed (Dastin); (c) longneck, bow-tie (Dastin); (d) tabbed, shouldered, for 90° fibres (Hoggart); (e) tabbed, straight-sided, 0° fibres; (f) tabbed, straightsided (Elkin); (g) tabbed, dog-bone (Rothman and Molter). R = radius, ∆ = diameter.

the means of load application and the test material. This is particularly relevant in the case of composite materials where loads, frequently very large loads, have to be introduced into the body of a material through an inherently weak phase (the matrix) without overloading the outer layers of fibres. Depending on the construction of the material, these outer

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fibres may account for most of its strength and, because of their position, are susceptible to damage.The second is that of producing as nearly pure a state of stress, in this case tensile stress, as possible.Actually, it may be argued that such a stress state is never achieved in practice and that the nearest approximation occurs when a very long, very thin filament is tested. However, as there is a requirement to test bulk samples of material, then the object of specimen design must be to minimise the problems outlined above, whilst producing the best approximation to a pure stress within the testpiece. Testpiece specifications and testing procedures are detailed in a number of published standards, or guides, four of which are summarised in Table 4.1 and illustrated in Figs. 4.2 and 4.3. These are ASTM D3039,3 BS2782,4 CRAG5 and ISO 527.6 This is a very small selection from the standards which are available, but studying them serves to demonstrate how many details vary from one standard to another. They reflect a range of opinions about how a specimen should be designed and how a test should be carried out. It is assumed that tests will be carried out in accordance with one of these procedures wherever possible, but situations can arise where, for one reason or another, a standard design of specimen cannot be used. This ±45° composite tabs 15.0 (a)

56.0

1.0 7° (90° optional) 1.5 250.0 25.0

(b)

25.0

2.0

1.5

175.0 ±45° composite tabs

(c)

15.0 (0° matl.) 25.0 (90° matl.)

50.0 Edge of grips 250.0 Composite or light alloy tabs

(d)

50.0

100.0 to 150.0 1.0 (0° material) 2.0 (90° material)

1.0 (0° material) 2.0 (90° material)

0.5 to 2.0

10.0 (0° material) 20.0 (90° material) 0.5 to 2.0

200.0 to 250.0

4.2 Current tensile specimens for use with aligned (0° and 90°) fibrereinforced material: (a) ASTM D 30393 (0°); (b) ASTM D 30393 (90°); (c) ISO 5276 (0°); (d) CRAG5 methods 300 (0°) and 301 (90°).

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Unbonded abrasive cloth tabs 25.0 2.5

(a) 250.0

25.0 (Strength measurements) 12.5 (Modulus measurements) 45.0 (b)

1.0 to 10.0

3.0 (min)

200.0 (min) Composite or light alloy tabs 20.0 (min) 10 t (typ)

(c)

50.0 (min)

100.0 (min) or W(1+1/tan) 1.0 to 4.0

0.5 to 2.0

4.3 Current tensile specimens for use with non-0° fibre-reinforced material: (a) ASTM D 3039;3 (b) ISO 527;6 (c) CRAG5 method 302.

chapter aims to give some background to the reasons leading to one choice of detail or another, and it is intended that it should act as a guide to a testing technique that will enable valid tests to be carried out in such cases. If excessive reference appears to be made to the ASTM standard, this should not be seen as a sign of bias, rather that ASTM generally gives more information than most other standards for the rationale behind details of specimen design and testing procedure. Such additional information and guidance are often invaluable to the practitioner, and are a welcome feature of the ASTM standards series, which other standards organisations might emulate to their own credit. Whilst the majority of tensile tests are directed towards establishing tensile modulus, ultimate tensile stress and lateral contraction ratio (Poisson’s ratio) under tensile load, simple modifications to the specimen enable a number of other factors to be investigated. Notch sensitivity and bolt-bearing tests are two examples, and the Composites Research Advisory Group (CRAG)5 gives recommendations for testpiece dimensions. Tensile loading regimes are also used for two popular forms of shear test. One of these is the lap shear test which, in turn, can be modified to investigate the behaviour of adhesive and mechanically fastened joints.The other is the ±45° shear test.

1.0 to 10.0 ± 0.5 Machined if necessary 25 ± 0.5 for strength 12.5 ± 0.5 modulus only 200 (min) Gauge (free) length 110 min

1.0 (0° UD) ±4% 2.0 (90° UD) " 2.5 (Other)b "

15 (0° UD) ±1% 25 (90° UD and other)

250 ± 4% (0° UD and other) 175 (90° UD) Gauge length 10 to 50

56 (0° UD) 25 (90° UD)

1.5

0°/90° GFRP, commonly applied at +/-45° Emery cloth (Other)

Thickness (t)

Width (W )

Overall length (L)

Tab length (LT)

Tab thickness

Tab material recommended

Similar to that under test

Not less than 3 mm

45 (min)

Composites incorporating mat, cloth, woven rovings including prepregs.

Balanced symmetric composites reinforced with continuous or discontinuous high modulus fibre.

Applicability

BS 2782: part 3: method 320 E, EN 61

ASTM D3039

Standard

GRP for hot/moist conditions Light alloy ‘satisfactory’ for ambient conditions

0.5 to 2.0

50 (min)

100 to 150 + 2LT

10 to 20, uniform

1.0 ± 0.04 (Method 300) 2.0 ± 0.04 (Method 301)

Unidirectional fibrereinforced plastics 0° (Method 300) 90° (Method 301)

CRAG methods 300 & 301

Table 4.1. Comparison of selected details of standard tensile test methods.a

0.5 to 2.0

+/-45° GFRP

0.5 to 2.0

50

150 ± 1 + 2LTc Gauge length 50 Greater of (100 + 2LT) or [w(1 + 1/tan q) + 2LT]2 If q < 15° L = (w/tan q + 2LT) where q = fibre angle 50 (min)

15 ± 0.5 (0°) 25 ± 0.5 (90°)

1 ± 0.2 (0°) 2 ± 0.2 (90°)

Fibre reinforced polymers ‘Not normally suitable for multidirectional materials’.

ISO 527

9t min. 10t typical absolute min 20

1 to 4

Multidirectional tape or woven fibre-reinforced materials. Must be axially orthotropic.

CRAG method 302

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Failure within 1 to 10 min, or strain rate = 0.01 min-1, or displacement = 2 mm min-1

Self-aligning recommended

0.1–0.3% chord 25–50% ultimate strain if ultimate strain <0.6%

Testing speed

Grips

Basis for modulus calculation Not applicable to materials with unidirectional reinforcement: use ISO 527

Linear portion of curve or tangent or secant at ‘required level of strain’

0–0.25% chord recommended but not mandatory

To cause failure within 30 to 90 s

10 mm min-1 (routine tests) 2 mm min-1 for determination of elongation/modulus Self-tightening suggested

90°

90°

b

All dimensions in mm. UD = unidirectional fibres, ‘other’ = balanced symmetric or random-discontinuous reinforcement. c 100 ± 1 + 2LT for filament wound test plates.

a

Notes

7° or 90° (0° UD) 90° (90° UD)

Tab end

0–0.25% chord

0.05–0.25% chord

Hydraulic preferred

2.0 mm min-1 (0°) 1.0 mm min-1 (90°)

90° Tab edge 7 mm within grips

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4.2

Testing equipment

4.2.1 Testing machines There are two classes of testing machine: those which apply a deadweight load to the testpiece, generally by hydraulic means, though formerly using weights and levers, and those which induce a load by applying a controlled deflection to the testpiece using a jack. It is important to appreciate the difference between the ‘soft’ characteristics of load control and the ‘hard’ loading provided by displacement-controlled loading. When the specimen weakens, under displacement control there will be a fall in load, whereas under load control an uncontrolled failure will occur as the machine tries to maintain load on a weakening testpiece. This can be dangerous and tends to preclude study of the mechanics of failure. Servohydraulic machines allow either of these loading regimes to be applied, as well as offering the availability of fatigue, programmed, strain-controlled and high-rate loading, but their high cost and relatively limited working distance tend to militate against them as a choice for general testing work. This leaves the screw-jack type of machine in a pre-eminent position. Certainly the use of this type of machine is assumed in most standards, which specify loading rate in terms of displacement per unit time. The mechanical side of testing machines (grips, loading frames, etc.) has not changed greatly over the years. The same cannot be said of control and data-logging equipment, of which the latter would now be expected to be computer-based, and the former may also involve extensive use of microelectronics. Testing machines are robust and do not normally wear out quickly. Their replacement cost is high, so a large amount of older equipment is still in use. It is, therefore, appropriate to assume that the reader of this chapter may not necessarily be using ‘state-of-the-art’ testing machines. Whilst microprocessor control can offer a wider range of control options compared with older machines and computer data logging greatly facilitates data acquisition and subsequent data reduction, much testing is still carried out using machines with a limited range of testing speeds and data may still be recorded only on a paper chart.

4.2.2 Data acquisition Typical standards require that the load indicating system should have an accuracy of 1% or better, and should be ‘substantially free from inertia’,3 a clear reference to mechanical chart recorders. Current equipment, using computer-based data acquisition systems, does not suffer from inertia as such, but the rate at which data are collected is important. Unless data points are collected at a suitable rate, important information may be lost in

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the interval between points. It is not uncommon to find that the maximum load displayed (instantaneous measurement) and the maximum load recorded for a test can vary by much more than 1%. A sophisticated datagathering algorithm might be expected to adjust the rate of data collection in conjunction with varying rates of change in load or strain, and so on. Most testing machine software is intended to be used in routine testing and permits automatic calculation of information such as elastic modulus, and statistical analysis of the results. However, it is often found that such systems are not particularly suitable for research work or other non-routine testing. If a pen recorder is used, or if stress and strain data are to be taken manually from a printed graph, it is advisable to scale the load and strain axes so that the graph has a gradient of roughly 45°, as this will give the greatest precision of measurement on each axis.

4.2.3 Grips Composite materials are usually gripped using some form of ‘friction grip’, where the load is transferred to the specimen through gripping faces which are roughened with serrations or a cross-cut pattern. A fine-scale roughening is recommended for use with composites in order to spread the gripping force over the largest possible area and to minimise damage to the specimen. An alternative, if only coarse grips are available, is to interpose abrasive covered cloth between the grip face and the specimen. In the event of grips having to be specially manufactureds for use with composites, the recommended methods for producing a gripping surface are to use either spark erosion or an electrodeposited abrasive surface. Parallel clamping grips, positively closed by manual or hydraulic means, allow the operator to control the gripping force on the specimen. Ideally, this should be no more than is necessary to grip the material under test until maximum load is reached. It has been observed in composites compression testpieces that an excessive clamping force distorts the outer fibres of the test material at the edge of the end-tab, causing a reduction in failure load,7 and the same may be found to apply to tensile tests. On the other hand, insufficient force will permit the specimen to slip, which generally leads to the surface in contact with the grip being torn off. This material then fills the serrations of the grip, with the consequence that no increase in clamping force is sufficient to grip the specimen, which has then to be removed and the grip surfaces cleaned. The position of the specimen can be adjusted both laterally and transversely. By attaching micrometer heads to the body of the grips it is possible to adjust the position of the specimen, relative to the axis of the machine, with a high degree of accuracy. Wedge grips, sometimes referred to as self-tightening grips, have gripping faces which slide on inclined planes, so that the gripping force increases with

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axial load. Such grips are widely recommended, although there is a body of opinion (including ISO 527)6 which regards the lack of control over the through-thickness clamping force as undesirable. It has also been observed that worn wedge grips can allow the jaw faces to slide at different rates, resulting in very large and undesirable shear stresses and a consequent tendency to bend the specimen. This should not happen if the alignment pins, specified by some standards, are used. An advantage with wedge grips is that the small gripping force at the start of a test can allow the testpiece to move slightly and thus correct any initial misalignment.

4.2.4 Alignment The lack of any yielding mechanism in composites means that even small misalignments, and the resultant bending, may result in large local stresses, so that accuracy of alignment is important if reliable results are to be obtained. It has already been noted that misalignment can be caused by inadequate grips. Alignment of the grips relative to each other is determined by the machine on which they are mounted. Testing machine manufacturers adopt one of two approaches to this. One is to mount the grips as rigidly as possible in a stiff testing frame and thus ensure that alignment is ‘built in’ to the machine; the other method is to mount one of the grips on a universal joint and allow it to self-align. Which method is preferable is probably a matter of personal choice, as neither is without its faults. The first requires that the machine should be built, and as importantly, maintained, to a high standard of accuracy. Maintenance of accuracy may not be easy to guarantee after the machine has seen a large amount of service, particularly in view of the large loads to which it is likely to have been subjected. The second method may give a false reassurance of accuracy, as alignment may be hampered in practice by friction in the universal joint, whilst flexibility in the load path may encourage a tearing failure across the specimen. Alignment of the testing machine can be checked using the method recommended by ASTM3 and ISO6. A specimen 25 mm wide (Fig. 4.4) is instrumented with three strain gauges, two of which are positioned at the outer edges of one face, whilst the third is in the centre of the reverse face. If alignment is perfect, all three gauges will give the same reading. Bending of the specimen, as a result of misalignment, causes differences between the outputs of the gauges. To eliminate any effects resulting from misalignment of the gauges, the specimen should be loaded in four positions. Starting with the initial position (1) these are: (2) rotated back-to-front only; (3) rotated end-for-end only; and (4) rotated back-to-front and end-for-end. The permissible limit for bending is that the sum of 4/3 the strain difference across a face plus the strain difference between the face and the mean strain

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W

Strain gauge 1 Strain gauge 3 Strain gauge 2

W/2

SG 1 & SG 2

L

SG 3

L/2

W/8

4.4 Specimen recommended by ASTM D 30393 and ISO 5276 for checking test machine alignment.

should be less than 3%6 or 5%3 of the mean strain. ASTM3 recommends checking alignment during modulus tests by the use of back-to-back transducers. Bending of the specimen will also occur if the fibre layers are not equally spaced, for instance as a result of poor consolidation, when the effective stiffness of the material will vary through its thickness, resulting in bending under tensile load.8 A similar effect may occur if the form of reinforcement varies through the thickness of the material; in these cases strains should be measured on both faces of the material if the modulus is being determined.

4.2.5 Strain measurement The choice of strain measurement technique is normally between extensometers and strain gauges, both of these methods having their advantages and disadvantages. The major problem with contacting extensometers, as far as the specimen is concerned, is that, in order to minimise errors, point contact is required. This is generally achieved on a flat specimen by the use of curved knifeedges and the concern is that high contact stresses may damage the outer fibres of a composite and lead to premature failure. It follows that contact

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forces should be kept as low as possible consistent with avoiding slippage. It is necessary to support the weight of any but the lightest clip gauge, because allowing it to hang from the specimen is likely to cause bending and impose relatively large contact stresses. Extensometers built into the testing machine avoid this problem. To avoid damaging the extensometer it should be removed, or released from the specimen, prior to failure, as the sudden, almost explosive, release of the large amount of elastic energy stored by many composites specimens can easily wreck even the most robust extensometer, as could be imagined from Fig. 4.5. Two-axis extensometers are available which measure lateral contraction for Poisson’s ratio determination, but it should be noted that the lateral strains concerned may be very small. Poisson’s ratios of less than 0.01 are not uncommon in composites. Non-contacting extensometers are also available. These avoid any contact damage and are sufficiently remote from the specimen to allow them to be used up to failure, but may not have sufficient resolution for use with stiff testpieces. A new generation of non-contacting extensometers, based on video technology and digital signal

4.5 Explosive failure of aligned unidirectional (0°) carbon-fibre reinforced plastic (CFRP).

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processing, appear to offer solutions to many problems connected with extensometry. The alternative to the extensometer is the electrical resistance strain gauge. The magnitude of change in resistance is generally about twice the magnitude of the strain change causing it, but even so it will be clear that very small resistance changes are being considered and they are generally measured using a form of Wheatstone bridge circuit. Strain gauges are designed and calibrated for use on specific metals, which means that errors will result when they are used on composites. These are described in detail,9 and referred to in Chapter 3, but a summary of possible errors is given here. Although the major sensitivity of the gauge is along its length, there is also a small sensitivity to transverse strain, which is allowed for during manufacture, by calibration to suit the Poisson’s ratio of the metal on which the gauge would normally be used. Inaccuracy will occur when the gauge is used on other materials, especially composites, which can have very different values of Poisson’s ratio, dependent on layup and testing direction relative to the fibre directions. This error can be compensated for if the gauge is calibrated against an extensometer on a sample of the material on which it is intended to be used. The calibration will, of course, vary considerably with the orientation of the gauge relative to the composite. Humidity and temperature changes leading to differing strains between the composite and the gauge itself can be minimised by the use of ‘dummy’ gauges, mounted on material identical to that under test and in the same atmosphere, in one arm of the bridge circuit. Self-heating of the gauge arising from the voltage drop across it, when in use, can also cause problems. Although this is small, the area available for heat dissipation is also small, and the resultant power density can be surprisingly large.This heating gives rise to spurious ‘apparent strains’, which should eventually reach an equilibrium condition. The problem is less apparent on materials with good thermal conductivity, but ‘thermal drift’ remains a problem when strain gauges are used on composites. If a pulsed power supply is not used, the problem can be alleviated by using high resistance gauges (350 W and above), excited with as low a voltage as possible (typically 1 to 2 V), and by using gauges with an active length of at least 3 mm, and preferably 6 mm or more, to give as large an area as possible for heat dissipation. Large gauges are preferable anyway as they are easier to align, and average out local strain variations. The latter can be important on material with a woven or braided reinforcement where strains may vary over the weave pattern. It is recommended that at the very least one repeat of the weave pattern should be covered by the gauge.An analysis of the problems to be considered when strain gauges are used with such materials is available.10 Local strain variations have also been known to cause premature failure of strain gauges. Correct alignment of the gauge is important, and it has been shown9 that

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significant errors can be caused as a result of careless application of strain gauges to composites. Although it is unlikely to be relevant to most composites, strain gauges can significantly reinforce weak or low modulus materials. Strain gauges are available as single gauges, or in ‘rosettes’ aligned at 30°, 45° or 90° to each other, either closely spaced or stacked. It is left to the user to decide whether or not the benefit of accurate alignment outweighs the possible thermal problems resulting from using stacked gauges. To avoid damaging the composite when attaching leads to the strain gauge, it is advisable to solder flying leads to the gauge before bonding it onto the test material. To ensure a good bond between the composite and the gauge, the area may be lightly grit-blasted, or manually abraded, whilst taking care only to abrade the resin-rich outer layer, and not to damage the fibres. The latter method is likely to be ineffective if the surface of the material is excessively rough. In extreme cases it may be necessary to fill the surface with resin before attaching strain gauges. Despite all the problems outlined above, it should be stressed that strain gauges are still an effective way of measuring strains, often the only practical method on complex structures, and are an accepted method of strain measurement on coupon tests. They are preferred by CRAG,5 because they generally give more reliable results than extensometers. Although strain gauges remain attached to the specimen up to failure, it may be found that they themselves fail before the failure strain of the composite is reached. They present a simple means of detecting bending of the specimen by monitoring the outputs of gauges positioned on each face of the material.

4.3

Specimen details

4.3.1 General A typical specimen is shown in Fig. 4.6, with related nomenclature. The nomenclature is not necessarily universal. The term ‘gauge length’, for instance, is used by many sources for the region given here as ‘free length’. It is a pity that this term is not more widely used, since it would then allow ‘gauge length’ to define the distance between extensometer contact points. The terms ‘testpiece’, ‘test coupon’ and ‘specimen’ are often used interchangeably, although there is an implication that ‘testpiece’ and ‘specimen’ are generic terms, whilst ‘coupon’ refers specifically to a sample cut from existing material. Any testpiece, or specimen, should be representative of the body of material from which it is removed. It should include a region of uniform stress over which strain measurements can be made (the gauge length) and in which, it is hoped, failure will occur. As far as this chapter is concerned, this

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'Square-ended' end-tab End tab thickness

End tab length Shoulder

Gauge length Free length

Widthwise waisting

Tapered end-tab Thickness Tab bevel angle

Through-thickness waisting

Width

4.6 Tensile specimens and nomenclature.

failure should be in a recognisably ‘tensile’ manner. The material should be flat, at least if fundamental materials properties are to be determined, although, where ‘industrial type’ laminates are concerned, it may be necessary to test the material ‘as supplied’. Tensile specimens typically lie in the range 10–30 mm wide with a length of 200–250 mm, the narrowest specimens being used for unidirectional material. The specimen should be long enough to avoid end effects (i.e. effects caused by load discontinuities associated with the region of load introduction, in accordance with Saint Venant’s Principle). ASTM D30393 recognises this by adding twice the width to the gauge length (but there is an ambiguity here, and it appears that what is meant is free length). Specimens with a woven or braided reinforcement must be wide enough to contain a reasonable number of unit cells of the reinforcement. Where high strength materials, or thick samples, of ‘real’ laminates are being tested, the size of the specimen may be limited by the maximum load capacity of the testing machine. In order to avoid failure at the ends of the specimen, where loads are applied, end-tabs are generally used to protect and reinforce the material. We have already seen that waisting and other machining of the testpiece are discouraged. Through-thickness machining is only applicable, in any case, for material with unidirectional reinforcement, because such machining of a multidirectional material would alter its effective composition. Even unidirectional material is altered to some extent by the removal of the resin-rich outer surface, and machining is also likely to damage the outermost remaining fibres of the specimen. In practice, it appears that the former effect predominates. The earlier version of CRAG method 300 used a specimen waisted through the thickness. This was found to give higher values for strength and stiffness than other methods using unwaisted testpieces11 and, apparently to avoid this inconsistency, the specimen has been superseded by an unwaisted design.

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4.3.2 Dimensions It has already been mentioned that unidirectional material is generally tested in order to obtain fundamental laminate properties. It follows from this that the material is generally prepared specifically for this purpose and may be manufactured to any chosen thickness which, in general, is as near as possible to either 1 or 2 mm. Too thin a laminate may give unrealistic results because the resin-rich surface means that the material will be relatively thick per layer of reinforcement. If too thick a laminate is used (i.e. a laminate containing more plies), its strength may exceed that of the adhesive joints between the specimen and end-tabs. A thick specimen is also more likely to suffer from poor consolidation and hence from the problems with bending referred to in the literature.8 Multidirectional material is often thicker than unidirectional and may, in some cases, require machining to a finished thickness. BS 27824 specifically refers to this by setting a maximum specimen thickness of 10 mm, stipulating that anything greater than this should be machined down to 10 mm and that material should be removed from one face only. Through-thickness machining of testpieces is a contentious matter, as it may alter the effective composition of the material, if only by removing the resin-rich layer which normally exists on the surface of composites. There is also the possibility of residual stresses within the material being released, leading to undesirable distortion of the specimen after machining. Edge effects are unlikely to affect the behaviour of unidirectional material, and a relatively narrow testpiece may be used.The recommended width has commonly been 10 mm but there is now a tendency towards 15 mm, which is the dimension specified by the current versions of both ASTM D30393 and ISO 5276. For transverse properties (i.e. unidirectional laminates tested in the 90° direction), the width in both cases is 25 mm with a specified thickness of 2 mm. Such specimens are delicate and susceptible to breakage when being handled, which no doubt in part accounts for the larger recommended dimensions. When samples are machined from material with a multidirectional reinforcement, the specimen geometry may be determined by the layup itself, needing to be wide enough to contain a representative sample of the reinforcement. Multidirectional reinforcements can also give rise to throughthickness tensile stresses at free edges, so that the width of the specimen should be sufficient to ensure that the region affected is only a small proportion of the total width. It is difficult to find definitive advice when the material to be tested contains angled fibres, but the CRAG5 recommendation that some angled fibres originating under an end-tab should run to the free edge of the testpiece appears likely to give a conservative result because, in practice, such fibres are likely to be more constrained. Woven

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and braided materials are special cases of multidirectional laminates and the specimen should, at the very least, be wide enough to contain a reasonable number of weave repeats, although it is likely that a width of 30 mm would be more than adequate in this respect. More serious problems are likely to come as a result of fibre waviness and edge effects. Because woven and braided materials contain out-of-plane fibres, severe edge effects can be encountered leading to through-thickness stresses which are capable of causing delamination at the specimen edges. The testing of laminates with fibres at angles of other than 0° and 90° is beset with problems. It is necessary to take great care when the results are being interpreted, and a good understanding of laminate analysis techniques is required, especially if few or no 0° fibres are present. Materials with mat or continuous strand reinforcement, being relatively weak compared with unidirectional material, present few problems in testing.

4.3.3 End-tabs Although not universally specified, end-tabs are used on the vast majority of specimens. Their purpose is to provide a compliant gripping surface, to feed loads into the underlying test material, and to protect the outer fibres of the specimen. During the evolution of composites specimen design, various materials have been used, including stainless steel, aluminium alloy and composites in various forms. The requirements are that the material used should be soft enough to be indented and firmly gripped by the jaws of the test machine, whilst being strong enough to transfer load into the body of the specimen. This suggests a combination of shear strength through the thickness, with sufficient axial tensile strength. The tab should not be so stiff as to prevent natural deformation of the specimen. Stainless steel is no longer specified (as it used to be by the ASTM) and the choice now is between aluminium alloy and composite. The most common tab material is probably E-glass laminate, although CRAG5 suggests using light alloy except when testing in hot, moist conditions. The significant advantage of composite tabs over metallic versions is that they and the specimen can be co-machined to size, which is far easier than bonding individual tabs to premachined specimens, and generally results in a better finished testpiece. There is no satisfactory common cutting process which can be used on both soft metal tab material and composite. Specimens with composite endtabs can be prepared by bonding, with an appropriate adhesive, strips of end-tab material (once properly described, if rather grandly, in BS2782 as parallelepipedic strips of material) to the test material before cutting, see Fig. 4.7. Attaching tabs in this way, rather than individually after cutting, helps to maintain them in good alignment. End-tabs with 0°/90° fibres are

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4.7 Specimen preparation. End-tab material has been attached to a panel of the test material. The waste section (foreground) shows pegs used to align the tab material. The trimmed specimen (background) is instrumented with a biaxial strain gauge rosette.

easily produced using commercially available laminates with woven reinforcements, material widely used in the electronics industry. Some standards organisations specifically refer to this tabbing material as ‘printed circuit board substrate’. ASTM at one time specified that the inner plies of composite tabs should be aligned with the outer layers of the specimen in order to avoid unwanted shear stresses, but the most recent version of ASTM D 3039,3 in common with the current ISO 527,6 has revived the use of end-tabs with reinforcement at ±45°. Use of such a material is not mandatory; for instance, it is permissible to use material identical to that under test. ASTM D 30393 specifies the use of unbonded abrasive tabs when testing material with nonunidirectional reinforcement, see Fig. 4.8. The reason for specifying the relatively inconvenient ±45° material, which must be either layed up specifically for this purpose or cut (with considerable waste) from 0°/90° woven material, is that it imposes less constraint on the specimen in both the longitudinal and lateral directions. It has been suggested12 that there is a decreased tendency for unidirectional specimens to split when tested using ±45° tab material. An improvement in measured strength of 18% was also reported when specimens with taper-ended ±45° tabs were compared with others having square-ended 0°/90° tabs. The use of end-tabs which finish abruptly at their inner end (referred to as square-ended or 90° bevel-ended tabs) is often criticised for introducing

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4.8 ASTM D 30393 specimen of 9-ply, 90°/0° CFRP. The specimen has failed in the centre of the free length, an ideal failure.

a stress concentration into the testpiece, and to alleviate this various ‘softening’ techniques are used. The traditional method is to finish the ends of the tabs with a shallow bevel. ASTM3 currently recommends tabs with a bevel end of 7° to 10° where wedge grips are used, square-ended tabs being acceptable with non-wedge grips; ASTM add the rider that use of the specified tabs ‘does not guarantee success for every existing or future material system’. ASTM used to recommend the almost universal use of tabs bevelled at 5° but it has been found that strain mismatch at the tip of the tab can induce peeling stresses large enough to detach the tab, frequently taking with it the outermost fibres of the specimen,13 as shown in Fig. 4.9. This is a case where a preconception, based on metals experience (i.e. the gradual change of section to minimise stress concentrations), fails to apply when used with composites. The ‘square-ended’ tab, as well as being simpler to manufacture, gives better results. Even so, there have been attempts to ‘soften’ the transition between the tab and the body of the specimen. Formerly, BS 27824 recommended that some 5 mm of the tab should be allowed to protrude beyond the edge of the grips, the idea being that the unclamped portion of the tab would be more compliant than the portion held within the grips. This contrasted with other standards, CRAG5 for instance, which specify that the edge of the tab should be level with the edge of the grip. This is fine in principle but fails in practice because many testing machine manufacturers chamfer the last few millimeters of the grip jaws so that the degree of softening, if any, is entirely dependent on the design of the jaws. In view of this it is perhaps surprising that only recently has the practice been adopted of gripping the specimen with the tab-end a specified distance

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4.9 Early ASTM D 3039 specimen design (5° tab tip) in 8-ply 0° CFRP. The tapered end-tabs have detached owing to peeling stresses at the tip of the tab. The through-thickness stresses were sufficiently high to detach the outer layer of carbon fibres.

inside the jaws. In the case of ISO 5276 this distance is 7 mm, whilst ASTM3 requires that the grips extend 10–15 mm beyond the beginning of the tapered portion of the tab. This method provides no softening at all but is, at least, reproducible.

4.4

Test procedure

Before the test is commenced, details of the material should be recorded, including fabrication details (stacking sequence and cure cycle), resin, fibre volume fraction, fibre details (type, manufacturer, diameter, surface treatment, etc.). If the specimen has undergone environmental conditioning, this should be described, together with details of the testing environment. The testing machine should be described, giving details of calibration date, gripping equipment, data-acquisition method and associated details. Details of strain measuring equipment or, if strain gauges are used, gauge factor, size, resistance and so on should be given. The dimensions of the specimen can then be measured, normally taking an average of three readings each of width and thickness. The opportunity can also be taken to examine the quality of the specimen; those with obvious notches or other machining damage should be discarded. ASTM D 30393 specifies the use of a ball-ended micrometer for thickness measurement, with a flat-anvil instrument to be used for width measurements, and recommends that the accuracy of the micrometer should be within 1% of the dimension being measured, which typically equates to ±2.5 mm, where

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thickness is concerned. The principle that accuracy in testing should begin with the measurement of the testpiece is excellent but, in practice, this is perhaps an excessively high degree of precision, and immediately prompts the (unresolved) question as to what allowance should be made for the rough resin-rich surface found on many laminates. ISO 5276 requires the use of a micrometer reading to 0.02 mm, a common toolroom standard. Whether such measuring equipment is used in practice or not, clearly it is necessary to use a device which will give a similar standard of accuracy, whilst not exerting sufficient force to deform the specimen. Calipers and micrometers with an electronic digital display are becoming popular, if only because they are easy to read without taxing the eyesight, but perhaps their use should not be encouraged, because they do not have a fixed zero reference and, therefore, despite having adequate precision, do not give a guaranteed standard of accuracy. Having taken such care with measurement, it may be found that the standard requires measured stresses to be ‘normalised’ (i.e. scaled) to the value that would have been obtained if material of a specified nominal thickness had been tested. After measurement and inspection, the specimen can be mounted in the grips. If one of the grips is articulated, this should be tightened first to prevent the specimen being subjected to large bending and twisting loads during tightening. Care should also be taken to avoid axially stressing the specimen whilst the grips are being tightened. ISO 5276 requires that any initial prestress should cause a strain of no more than 0.05%. The centreline of the specimen should be aligned with the axis of the testing machine so as to eliminate bending and asymmetric loading. If an extensometer is being used, this should be attached to the centre of the specimen and the initial gauge length measured. A small preload may be applied to the specimen before the extensometer is attached. Adequate guards should be placed round the specimen, or test machine, if there is any possibility of an explosive failure. The test can then be commenced. It used to be customary to specify loading rate in terms of testing machine speed (grip separation rate). Low speeds were not recommended in the interest of avoiding creep effects (if not boredom on the part of the operator), whilst high speeds were believed to lead to inaccuracy owing to viscoelastic effects. A problem that arises when specifying testing rate in this way is that the relationship between machine speed and the rate at which the specimen is extended is unknown, owing to lost motion in the machine, slippage of wedge grips and so on. It has been estimated that this can result in an actual strain rate 10–50 times lower than that calculated from the machine speed.3 It has been the custom of the CRAG5 guides simply to require that failure should occur within a specified time (30–90 s), with the preferred time being at the lower end of the range. The latest version of ASTM now also specifies a time-to-failure, in this case

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1–10 min – a radical difference from CRAG. This is given as a preferred alternative, the other options being a displacement rate of 2 mm min-1 or a strain rate of 0.01 min-1. ISO 5276 specifies a displacement rate of 2 mm min-1 for the testing of laminates with unidirectional (0°) reinforcement and 1 mm min-1 when testing material with 90° reinforcement.

4.5

Data reduction

4.5.1 Stress–strain curve The stress–strain curve shown in Fig. 4.10 includes all the features likely to be found in a loading curve, including evidence of changes in stiffness, progressive failure and so on. Many composite materials, particularly if they contain a large proportion of 0° fibres, have substantially linear stress–strain characteristics, but it is not uncommon for the curve to show non-linearities at the start of the test. This is generally dismissed as being due to the specimen ‘settling down’ in the grips, machine backlash being taken up, slippage and so on. The value of the load–displacement curve should not be underestimated here for, whilst it gives little information about specimen behaviour, it can contain useful information about such anomalies as gripping problems. In the days when data were recorded on paper charts, it was common to project the lower (linear) end of the load–displacement curve back to the axis and establish a false origin which could then be used as a basis for elastic modulus calculation (generally using a secant modulus at 0.0025 strain), but the practice of discarding the lower portion of the curve in this way is not now encouraged.

D

C 0.25% tangent

Stress

B

0.05%–0.25% secant

% Strain

A 0.1

0.2

0.3

0.4

0.5

0.6

4.10 Tensile stress–strain curve showing typical detail.

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4.5.2 Elastic modulus Three options are available when calculating the elastic modulus from a non-linear loading curve. The first of these is to take the modulus as being a tangent to the initial part of the curve, the second is to construct a tangent at a specified strain level and the third is to construct a secant (‘chord’ in ASTM) between two points given as A and B in Fig. 4.10, and typically at strain values of 0.0005 and 0.0025,6 or 0.001 and 0.003.3 [It should, perhaps, be noted here that there appears to be no universal agreement on the term used to express the value of a strain. Absolute values (e.g. 0.0025 strain) are becoming more common but, in the interests of avoiding decimals, the use of either microstrain or percentage strain is useful, in which case the equivalent value is expressed as 2500 mstrain or 0.25% strain, respectively.] Modulus values are given in these cases as ‘initial tangent modulus’, ‘B% tangent modulus’ and ‘A%–B% secant (chord) modulus’, respectively. The use of computer-aided linear regression methods may be allowed instead of a two-point basis for calculating these values.6 If the material is brittle and fails at a strain of less than 0.006, ASTM D 30393 recommends using a strain range of 25–50% of the ultimate.

4.5.3 Poisson’s ratio Poisson’s ratio can be calculated, if longitudinal and transverse strain data are available, using the same upper and lower strain limits used for the modulus calculation. Transverse data are generally low in value and may be seriously affected by spurious signals (noise) in the instrumentation. In this case, taking the ratio of regression fits to the graphs of transverse and longitudinal strain, which are obtained using simple computer graph-plotting software, should give reliable results.

4.5.4 Failure Other information available at the conclusion of a test is the failure mode of the specimen and the location of failure. It is normal to regard failures within the end-tab, shown in Fig. 4.11, or within a specified distance of the tab, Fig. 4.12, as being influenced by the grips, and therefore invalid. ASTM3 requires that the method of load introduction into the material should be re-examined if a significant number of failures occur in this way. BS 27824 requires that specimens which have slipped in the grips, broken in or within 10 mm of the grips, or given ‘manifestly inconsistent results for evident reasons’ should be discarded and replaced, whilst CRAG5 requires that specimens should fail ‘in the central region’ to be valid for design purposes. It is generally taken that if all the specimens tested fail at, or close to, the

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4.11 Early ASTM D 3039 specimen (5° tab tip) of 8-ply, 0° CFRP, showing failure within the end-tabbed region, leading to splitting of the specimen.

4.12 CRAG5 method 302 specimen in woven CFRP, showing failure close to the end-tab.

grips, the stresses obtained should be treated as ‘lower-bound values’. The practice of disregarding such failures is a contentious one, carrying as it does the suggestion of censorship of undesirable results, and it would seem to be better to adopt the practice given in ISO 5276 which requires a statement in the test report about whether any test specimens have been rejected and replaced, together with the reasons for doing so.

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4.13 CRAG method 302, quasi-isotropic specimen. One face shows 45° failure (upper), the opposite face shows transverse failure (lower). The light appearance at the edge of the end-tab is evidence of partial debonding.

ASTM D 30393 recommends using a three-part code when describing failures, where the first part indicates failure type (splitting, edge delamination, explosive, etc.), the second part indicates the failed area (in the gauge length, under the tabs, etc.) and the final part gives the location (top, bottom, left, right, etc.). Since it is possible to observe a variety of failure modes in apparently identical specimens from the same material, or even within a single testpiece (see Fig. 4.13), and also quite common to observe failure at more than one place in the specimen, it is important that full details of failures are given when the results are reported. It should also be made clear whether ‘failure stress’ refers to the first observed drop in load (point C in Fig. 4.10) or to the stress preceding complete failure (point D). It is normal to present data for each specimen (maximum stress, modulus, etc.) and not uncommon to include stress–strain data for each test. A more complete list of information to be included in the report is given in ASTM D 3039.3

4.6

Material and sample preparation

Sample preparation is covered elsewhere in this book (Chapter 3) but, at the risk of repetition, it is worth stressing those aspects which are particularly relevant to tensile testing.

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If the material is being prepared specifically for the determination of aligned fibre properties, then great care should be taken to ensure correct alignment of the fibres. Misalignment of fibres relative to the specimen axis, shown schematically in Fig. 4.14, results in a reduction in the effective width of the testpiece, and it has been shown that a misalignment of 1° can reduce the measured strength of a unidirectional laminate by over 30%.12 Misalignment of the specimen within the testing machine, or grips, leads to the effect suggested schematically in Fig. 4.14, and has a less significant effect on strength, but also leads to high scatter. The results of these effects are shown in Fig. 4.15. Note that cutting a testpiece so that its fibres are misaligned relative to the test axis is not the same as loading a testpiece with a similar misalignment. The former case results in a reduction in the effective width of the testpiece whilst the latter may largely be alleviated by compliance in the testpiece, the testing machine and (as already noted) the testpiece selfaligning as it settles in the grips.

Effective width

4.14 Schematics showing the effects of a 1° misalignment of the specimen in the test machine (left) and a 1° error in machining (right), showing reduction in effective width.

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2000

Aligned

500

Tested 1° misaligned with hydraulic grips

1000

Tested 1° misaligned with wedge grips

1500

Cut 1° misaligned

Ultimate tensile strength (MPa)

2500

Testpiece alignment

4.15 Effects of misalignment on measured strength.

The major advantage of using composite tabs has already been mentioned, namely, the ability to co-machine the tabs and test material. Machining is most easily carried out using an abrasive-edged cutting wheel which can be used dry with suitable dust extraction facilities, or water lubrication. Dry cutting may be criticised because of the risk of overheating the material, whilst an objection to wet cutting is the possibility of moisture absorption. It is important that the cut edges are free from notches and other cutting damage, and they may need to be finished by manual abrasion or a grinding operation. Early versions of ASTM D3039 recommended cutting the testpiece 3 mm oversize, before grinding to the finished width, but the latest recommendation is that final dimensions are reached using ‘waterlubricated sawing, milling or grinding’. Figure 4.16 shows how the strength of a specimen is affected by the quality of surface finish. Manual abrasion here consisted of nothing more

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2000

Ground

Abraded

1000

As cut

Ultimate tensile strength (MPa)

70

0

4.16 Effect of surface finish on specimen strength.

than rubbing the specimen edges on coarse (80 grit) aluminium oxide paper until all cutting marks were removed, a relatively crude and quick process. 320 grit silicon carbide paper is recommended by CRAG.5 Manual abrasion has been shown elsewhere13 to give an improvement of some 20% in measured strength. It is sometimes stated that polishing the edges of a specimen in this way ‘increases the strength of the specimen’, although in fact what has been observed is a reduction in the decrease in strength caused by cutting. Edge polishing should be carried out carefully to avoid radiusing the edge of the specimen, or introducing local variations in width, both of which may lead to increased scatter in test results.

4.7

Practical example

A panel was layed up from eight plies of unidirectional Hexcel T300/914 carbon/epoxy prepreg, taking care to maintain the fibre alignment. When cured, the material was end-tabbed to the then current ASTM D303976 specification using woven GFRP (0°/90° alignment), machined with a 5° bevel on the outer edge. Five specimens were cut and tested using a displacement rate of 5 mm min-1. Strains were measured using an

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Table 4.2. Tensile test results for a unidirectional (0°) CFRP. Specimen number

Failure stress (MPa)

Elastic modulus (GPa)

Failure mode and location

1

1618

125.8

2

1760

138.4

3

1364

122.1

4 5

1541 1391

146.2 138.7

In tab region at one end and cracked across 10 mm from other tab End-tabs peeled off, no material failure Failed at centre of gauge length Failed close to end-tab Specimen split, likely end-tab failure

Mean

1535 ± 164

143.2 ± 10

extensometer with a gauge length of 150 mm. Individual results are listed in Table 4.2. Three things are significant here. The first is the large variability in the results as shown by the standard deviations, over 10% in the case of failure stress. The second is the variety of failure modes, four being apparent in five tests. The final point is that the highest ultimate stress was given by a testpiece in which the test material did not fail. This emphasises the need to test more than one sample. Should this result be considered in isolation, it would normally be regarded as a lower bound value as the test material did not fail. Set in the context of four other tests, it is clear that this particular sample happened to be taken from an unusually strong part of the panel. Of course, if all five testpieces had not failed properly, then it would be valid to regard the set of tests as giving only a lower bound result. Incidentally, if there is a certain vagueness in the descriptions of the failures, this is because it is often impossible to identify the exact point of failure, and the sudden release of load as the specimen fails can cause secondary failures elsewhere in the testpiece.

4.8

Future developments

The design of test specimens continues to evolve. Often this is because techniques that were formerly adequate fail to work satisfactorily with new, higher strength materials. We have seen end-tabs with square ends, 5° and 7° bevel ends, in a variety of materials from stainless steel to ±45° composite. Stainless steel tabs attached with cyanoacrylate adhesive were once used with specimens waisted in width and thickness, true descendants of the fully

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machined metal specimen. Waisting is currently out of fashion, although there has been a tentative revival of through-thickness waisting. The splitting-off of the outer plies inherent with these specimens is regarded as effectively resulting in a specimen with integral end-tabs. All these details, together with width, thickness, testing rate and so on, have been specified by published standards at one time or another. Specifications are often accompanied by a clause to the effect that ‘tests which are carried out on specimens of different dimensions, or on specimens which are prepared under different conditions, may produce results which are not comparable’.6 Two questions are prompted by this. First, if these details are so important, how can they be allowed to vary between standards? Second, if results are only valid if comparisons between materials are made within a single method, what exactly is being measured? Over 100 years ago David Kirkaldy, who pioneered the scientific approach to mechanical testing, believed that the objective of testing should be to produce ‘Facts not Opinions’, and he had the phrase carved above the entrance to his testing laboratory.14 Yet it seems that where composites are concerned, opinions about how a test should be conducted may frequently obscure the facts of materials behaviour. Now that the preferred form for the test material is, almost universally, a parallel-sided strip, the only significant changes that can be made to the testpiece are the details of the end-tabs. As these are intimately involved in the transition from the various forces at the end of the testpiece to the stress in the gauge length, it seems logical that work should continue towards understanding, and then minimising any adverse influences between the tabs and the testpiece. Preliminary experiments15 suggest that radiusing the inner edge of the tab may successfully reduce stresses at the tab tip.Another factor to be investigated is the effect of an unbonded area at the end of the tabs. A radical alternative to the traditional specimen for gaining single-ply strength data has been described.13 Rather than all unidirectional material, the test material consists of nine layers of fibres laid alternately at 90° and 0°, with 90° fibres on the outside. The 0° fibres are thus protected from damage, whilst it is claimed that the cross-plied material is more representative of real composite structures. The ASTM D 30393 ‘multidirectional’ specimen shape, with unbonded abrasive end-tabs, was used (Fig. 4.8). The equivalent unidirectional strength is calculated simply by multiplying the strength of the cross-plied laminate by the ratio of unidirectional and crossplied Young’s moduli, the strains to failure being common to both. It was demonstrated that this method gives a higher value for strength, with lower scatter compared with the traditional ASTM fully unidirectional specimen. Whether this technique becomes adopted as a standard method remains to be seen.

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Current specimen designs have attracted criticism because they do not satisfy the criterion that ‘a specimen can characterise a material only when minor changes in dimensions do not result in a change in failure mode or measured strength’.13 Some standards organisations are adopting a less dogmatic attitude towards specimen design, to the degree that ASTM3 now describes it as being ‘to a large extent an art rather than a science’. Yet the finished specimen will be used as part of a scientific investigation of material behaviour, with none of the freedom of opinion often implied by ‘art’. There remains a driving force to examine current test procedures, to analyse what is and is not essential, to simplify specimen manufacture and, most important, to evolve test procedures which produce results which are dependable in characterising the material under test, preferably without the need to adhere to a rigidly defined test method.

References 1. Proceedings of the First Conference on Composite Materials: Testing and Design, ASTM STP 460, New Orleans, LA, 11–13 February, 1969. 2. S Dastin, G Lubin, J Munyak and A Slobodzinski, ‘Mechanical properties and test techniques for reinforced plastic laminates’, Proceedings of the First Conference on Composite Materials: Testing and Design, ASTM STP 460, New Orleans, LA, 11–13 February, 1969, 12–26. 3. ASTM D3039M, ‘Standard test method for tensile properties of polymer matrix composite materials’, American Society for Testing and Materials, 100 Barr Harbor Drive, West Conshohocken, PA 19428, USA, Vol 15.03, 1997. 4. BS 2782: Part 3: Method 320A-F, British Standards Institution, UK, 1976. 5. P T Curtis (ed), CRAG Test Methods for the Measurement of the Engineering Properties of Fibre Reinforced Plastics, Royal Aircraft Establishment, Farnborough, UK, Technical Report 88012, 1988. 6. BS EN ISO 527 Part 5, Tensile Test for Unidirectional FRP Composites, 1997. 7. J Haeberle, ‘Strength and failure mechanisms of carbon fibre-reinforced plastics under axial compression’, PhD Thesis, Imperial College, London University, 1992. 8. C Zweben, W S Smith and M W Wardle, ‘Test methods for fiber tensile strength, composite flexural modulus, and properties of fabric-reinforced laminates’, Proceedings of the Fifth Conference on Composite Materials: Testing and Design, ASTM STP 674, New Orleans, LA, ed SW Tsai, 1979, 228–62. 9. M E Tuttle and H F Brinson, ‘Resistance-foil strain-gage technology as applied to composite materials’, Journal of Experimental Mechanics, 1984 24(1) 54–6. 10. S T Burr, P G Ifju and D H Morris, ‘A method for determining critical strain gage size in anisotropic materials with large repeating unit cells’, Experimental Techniques, 1995 September/October, 25–27. 11. N R Sottos, J M Hodgkinson and F L Matthews, ‘A practical comparison of standard test methods using carbon fibre reinforced epoxy’, Proceedings of the Sixth International Conference on Composite Materials and Second European Conference on Composite Materials, London, Elsevier Applied Science, 1987.

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12. P W Manders and I M Kowalski, ‘The effect of small angular fiber misalignments and tabbing techniques on the tensile strength of carbon fiber composites’, 32nd International SAMPE Symposium, Anaheim, CA, eds R Carson, M Burg, K J Kjoller and F J Riel, SAMPE Covina, CA 1987, 985–1007. 13. L J Hart-Smith, ‘Generation of higher composite material allowables using improved test coupons’, 36th International SAMPE Symposium, 1991. 14. Carved above the door of Kirkaldy’s Testing and Experimenting Works, 99 Southwark Street, London, 1873. 15. K Bultheel, ‘Factors influencing the behaviour of tensile tests’, Eupoco MSc Dissertation, The Centre for Composite Materials, Imperial College, London, UK, June 1999.

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5 Compression F L M ATTHEWS

5.1

Introduction

Most lightweight structures and substructures include compression members, which may be loaded in direct compression, or under a combination of flexural and compressive load. The usual design process for lightweight structures attempts to introduce loads as pure compression and pure tension. The flexural loading of framework or sandwich constructions, for example, is transformed into essentially pure compression and tension loading of struts or facings. Composite materials are especially adaptable for such designs owing to their high orthotropy. The axial stiffness of compression members can only be controlled by the cross-sectional area. It is, therefore, proportional to the weight. The bending stiffness of axially compressed struts or panels is of particular importance, since in-service buckling must normally be avoided. This stiffness can be altered by geometric means, for example, the use of tubes rather than rods, sandwiches rather than plain plates, corrugation or the deployment of Tstiffeners.The stresses in a member of a given geometry can only be reduced by increasing the effective cross-section under load. It follows that high specific stiffness and strength in both tension and compression are desirable features for the ideal lightweight construction material. Fibre-reinforced plastic matrix composites are particularly valued for their high tensile strength. However, the comparatively low compressive strength of some composites, for example those reinforced with aramid fibres, reduces their potential applications. Ideally, fibrous composites would fail in compression using the full potential of the reinforcement. However, high modulus, highly anisotropic carbon and organic fibres are relatively weak in compression compared with intermediate modulus carbon or glass fibres. The ratio of compressive to tensile strength is low for the highly anisotropic fibres, but the compressive strength of glass fibres is probably higher than their tensile strength. For all this, the experimental evidence shows that the compression failure of composites 75

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containing fibres of high compressive strength is dictated by fibre buckling rather than fibre compression failure. Early attempts to predict microbuckling failure of composites modelled the fibres as plates on an elastic foundation and significantly overpredicted the critical stress. More recent non-linear models have been developed which fit the experimental data, making use of reasonable boundary conditions and input data. There is, however, no universal model which predicts compressive failure from the properties of the constituents. The situation is complicated by the difficulties surrounding the experimental determination of compressive strength for a given composite system and the mechanism(s) responsible for triggering compressive failure.1–4 It is probably fairly easy to be cynical about the results from many ‘roundrobin’ exercises, but the spread of results obtained has a cause or causes, one of which is usually the difficulty in performing the particular test method at all.A relatively recent round-robin into the compression strength testing of composite laminates5 was conducted with the cooperation of seven European laboratories, each using their own testing procedures. The influence of composite production was eliminated by each laboratory manufacturing one batch of material to be shared with the other six participants. Figure 5.1 shows the results sorted into categories of materials tested. If one wished to use this chart as a data base, it quickly becomes apparent that literally any compressive strength within the measured range could be assigned to any of the material systems examined. The range of results encompasses a factor of 2 for almost all of the systems. An alternative way of presenting the data is shown in Fig. 5.2, where the results are sorted into categories of the participating laboratories. A definite trend is now apparent, with the test results revealing a high dependence on the laboratory carrying out the test. Some laboratories generated generally higher results than others throughout the range of materials tested, even though all of the laboratories were known to be experienced in compression testing of composites and used standard test methods. It is clear that the test results are dependent on individual local testing practice, which includes parameters such as test method, actual testing experience and specimen preparation techniques.

5.2

Types of test

There are three basic methods of introducing a compressive load into a specimen, as illustrated in Fig. 5.3: direct loading of the specimen end, loading the specimen by shear, and mixed direct and shear loading. Direct loading of the specimen end, as specified for instance in ASTM (American

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2000

Compressive strength (MPa)

1500

1000

IM400/5245

HTA7/982

HTA7/6376

T400/6376

T800/6376

T800/924

T800/5245

500

0

5.1 Test results from a European round robin on compression strength testing of carbon-fibre reinforced plastics (CFRP), sorted into categories of material. , lab 1; , lab 2; , lab 3; , lab 4; , lab 5; , lab 6; , lab 7.

Society for Testing and Materials) D695M-91,6 is not suitable for high strength composites. Because of the low transverse and interlaminar strengths of these materials the specimens fail by end crushing, often referred to as ‘brooming’, and/or longitudinal splitting. Shear loading of the specimen end, which is usually tabbed in the same manner as for a tension specimen, is the most common method. Shape, material and precision of the end-tabs are likely to infuence the failure mode and strength result. One of the first fixtures to be developed using this principle is known as the Celanese fixture, which has its origins at the Celanese Research Center.7 The specimen is held in conical wedge grips which are accommodated in tapered sleeves. An outer cylinder maintains alignment of the parts. When load is applied to the sleeves it is transmitted to the specimen by shear, through friction between the specimen and the grips. A schematic diagram of the arrangement is shown in Fig. 5.4(a), with Figs. 5.5(d) and 5.6(b) showing the assembled and disassembled jigs. This fixture needs careful

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Compressive strength (MPa)

1500

1000

500 lab 1

lab 2

lab 3

lab 4

lab 5

lab 6

lab 7

0

5.2 Test results from Fig. 5.1 sorted into categories of participating laboratories. , T800/5245; , T800/924; , T800/6376; , T400/6376; , HTA7/6376; , HTA7/982; , IM400/524.

Direct end loading

Transverse load

Shear loading

Mixed shear/direct loading

5.3 Load introduction methods for compression tests.

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5.4 Diagrammatic representation of (a) Celanese, (b) IITRI jigs.

(a)

(b)

(c)

(d)

5.5 Several compression test jigs, fully assembled and on the same scale: (a) IITRI, (b) ASTM D 695 (modified), (c) ICSTM, (d) CRAG (Celanese).

adjustment to the thickness of the specimen if non-uniform load distribution on the cones is not to lead to distortion of the sleeves and friction with the outer cylinder. If precise overall specimen thickness dimensions are not adhered to, the conical wedges form a line contact with the outer sleeves, resulting in jig/specimen instability and, consequently, lower bound strength values. A fundamental modification of the Celanese fixture was developed by the Illinois Institute of Technology Research Institute (IITRI).8 Here, flat-

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(b)

(c)

5.6 Several disassembled compression jigs with specimens mounted, not to same scale: (a) IITRI, (b) CRAG (Celanese), (c) ASTM D 695 (modified).

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sided tapered grips, which fit into matching pockets in massive steel blocks, are used rather than conical ones, so that specimens of different thicknesses can be easily accommodated. The steel blocks are aligned by pillar guides and linear bearings. A schematic diagram of the IITRI jig is shown in Fig. 5.4(b) and the assembled and disassembled jigs are shown in Fig. 5.5(a) and 5.6(a). The weight of this fixture, at approximately 250 N, does reduce the ease of use quite significantly. Wyoming University modified Celanese fixture9 uses trapezoidal wedge grips similar to the IITRI fixture. This approach leaves the jig far less susceptible to the problems caused by specimen thickness variability, to which the original design using conical shapes is subject. It should be noted that in all the above-mentioned fixtures the specimen end is loaded throughthickness in order to generate the shear load. A typical representative fixture for mixed shear and end loading is the configuration originally proposed by Purslow and Collings and later modified by Port10 at what was the Royal Aircraft Establishment (now known as the Defence Evaluation and Research Agency, DERA, Farnborough, UK). The specimen is bonded into slots in aluminium end-blocks, shown schematically in Fig. 5.7(b). The amount of shear loading depends on the properties of the adhesive as well as on the thickness of the bond layer. In the modified ASTM D 695 method,6,11 load is applied in a similar way as shown schematically in Fig. 5.7(a), with the assembled and disassembled jig and specimen being shown in Fig. 5.5(b) and 5.6(c). A certain amount of the load is introduced to the specimen by shear through the end-tabs, depending on the stiffness of the tabs and bond layer. An additional alignment device is recommended. Although the specimen requires careful preparation, parallelism of the specimen ends being particularly important, and the test jig is of remarkable simplicity, cheap to manufacture and easy to use. Owing to the transverse constraint of Poisson’s deformation, the specimen may experience some transverse loading which, in turn, leads to friction between the support faces and the specimen. A variation of the RAE method is the fixture developed at Birmingham University.12 Here, an RAE-type specimen with a waisted gauge section is clamped within steel cubes at its ends rather than being bonded, as shown in Fig. 5.7(c). Thus, the specimen end is loaded directly and a portion of the load is transmitted by shear, depending on the clamping force. Mounting of the specimen is very simple. A further refinement of the Birmingham jig has been developed at Imperial College in London, UK.13 In addition to some modifications to the blocks in which the specimen is located, the whole fixture is placed in a four-pillar die set, thus ensuring good alignment. The fixture is shown in Fig. 5.5(c) and Fig. 5.8. Again, mounting and demounting of the specimen is very simple.

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(a)

(b)

(c)

5.7 Diagrammatic representation of (a) ASTM D 695 (modified), (b) RAE, (c) Birmingham test arrangements.

Die set 2

Upper grip End-tab 0/990° GRP

Testpiece Side restraint (optional)

Dimensions (in mm)

Ground flat

Clamping block Strain gauges 1

2 10 Weakly bonded area (e.g. PTFE tape)

Lower grip (exploded view) 40

Clamping screws

width 10

Hardened and ground loading plate

1.7 Standard specimen

Improved specimen

5.8 Imperial College (ICSTM) jig.

5.3

Standards

Of the methods referred to above, some have been adopted by the various standards organisations. The Celanese jig, in slightly modified form, is specified by the German standard DIN 29971 and by CRAG (Composites Research Advisory Group).14 The method is adopted within the ASTM D 3410 standard15 which, in addition, also embraces a version of the IITRI test jig. Of the others only the ASTM D 695 method,6 originally established for

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5.9 British Aerospace compression jig, a variant of the Celanese test method.

unreinforced plastics, has been taken up, but with a modification to the specimen. There are, of course, many company standards. The Boeing Aircraft Corporation use the modified ASTM D 695 and British Aerospace use their own variant of the wedge action-type of fixture. Figure 5.9 shows this jig partially disassembled. This jig combines features of the Celanese and IITRI fixtures and can be regarded as a synthesis of the two jigs. The IITRI wedge grips are contained in Celanese-type circular tapered sleeves. The outer cylinder which aligns the sleeves is an open frame rather than a closed shell, allowing access to the specimen. Quick release retaining pins ease handling of the jig. On the international scene, much work has been done in the development of an ISO standard for compression. This will be known in the UK as BS EN ISO 14126, indicating that it is adopted not only as the international standard but also has European and British status. Crucial elements of this new standard will also be adopted within the ASTM D 3410.

5.4

Specimen preparation

Specimen preparation is covered in more detail in Chapter 3. However, a few points are worth re-emphasis here. In order to ensure repeatability, special attention must be paid to the preparation of the specimens and a

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consistent procedure should be adopted. This includes laminate production, together with a quality check using, for example, ultrasonic C-scan, machining of the specimens from the laminate in the correct orientation to the fibre direction, moisture conditioning, measurement of dimensions and application of strain gauges. When using tabbed specimens the preferred approach is to adhere the tab material to the laminated panel before cutting individual specimens. This should ensure correct alignment of the end-tabs and hence minimise the effects of eccentric loading. The need to prepare the laminate and tab material properly prior to bonding cannot be overemphasised; failure to do so could well result in premature failure. Where the tab material is a fibrereinforced plastic, the above approach is relatively straightforward and cutting of the specimens poses no problem. However, cutting the laminate with metal end-tabs preadhered is not really an option; it is necessary to cut specimens from the laminate and then attach the end-tabs individually. Even greater care must then be taken to ensure correct alignment between specimen and end-tabs. A typical assembly procedure when composite end-tab material is used is illustrated in Fig. 5.10 and a prepared plate is illustrated in Fig. 5.11. In the latter, surfaces ‘a’ and ‘b’ are made square and at right angles by cutting on a diamond saw bench. It is not always necessary to grind surface ‘a’ but

Silicone rubber shim Double-sided End-tab Adhesive layer Composite adhesive tape

Adjustable alignment block

Flat ground plate

5.10 Laminate/end-tab plate assembly.

Surface 'c'

Surface 'a' Surface 'b'

5.11 Plate ready for cutting into individual specimens.

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if the specimen is to be end loaded, these surfaces must be as flat and parallel as possible and machine grinding becomes, in effect, mandatory. The whole plate can be dealt with in a single operation. In order to remove machining defects, surface ‘b’ should also be ground. It might be possible to do this manually by rubbing individual specimens on different grades of emery paper secured on a flat surface. However, best results in terms of dimensional tolerances will be achieved by machine grinding. Surface ‘c’ should be dealt with in a similar way to surface ‘b’. Where they are to be used, strain gauges should be affixed to both faces of a specimen. This allows comparative strains to be measured throughout the test and gives an early indication of any specimen bending (macrobuckling).

5.5

Specimen configurations

There are three basic specimen types: short unsupported gauge length, long supported gauge length and sandwich constructions. The use of sandwich specimens is relatively rare, owing to the additional expense and difficulty of their manufacture. It follows that the former two specimen configurations are those in more general use. Methods which propose the use of short unsupported specimens are generally appropriate for the measurement of the properties of unidirectional materials. Although specimens with other laminate layups may also be tested with these methods, it should be noted that the gauge length, however short, is unsupported and buckling failure is highly likely. Details of the specimen shapes recommended in CRAG 400, ASTM D 3410 and ASTM D 695 are shown in Fig. 5.12, which shows the now superseded ASTM D 3410 Celanese specimen, which had end-tabs with bevelled edges, with an angle of 9°, as well as the currently recommended specimen. The specimen to be used in the IITRI jig is identical to that used for the Celanese test, and for both jigs the specimen may be used without end-tabs where appropriate. Also shown are both types of specimen included in ASTM D 695. The ICSTM method also uses short, unidirectional tabbed specimens, although it too can accommodate untabbed specimen shapes. Typical dimensions of tabbed specimens are shown in Fig. 5.8, including the original and modified versions. The modified specimen was found to give more consistent results. Cross-ply GRP (glass-reinforced plastic) was adopted as the preferred end-tab material. Very few recommended test methods now advise the waisting of specimens. However, this used to be considered to be an acceptable means of ensuring failure in a particular region of the specimen. In some circumstances waisting can be considered as an optimised form of tabbing, but it

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W (a) LT

LT

GL

9° h A

W (b) LT

LT

GL

h A

(d)

(c)

LT

GL

GL

LT

W

h

W

Ah

5.12 Specimen configurations for (a) ASTM D 3410, Celanese and IITRI; (b) CRAG 400, Celanese; (c) ASTM D 695; (d) modified ASTM D 695 methods. W = specimen width, LT = end-tab length, GL = gauge length, h = specimen thickness, A = end-tab thickness.

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must be carried out with extreme caution and care, both in the actual machining operation and in order to maintain a symmetric specimen, otherwise bending will be introduced causing premature failure. Port10 showed that interfacial splitting due to excessive shear stresses can be avoided when the specimen is waisted following the taper contour equation, which gives the minimum gauge length: glmin = ln

Ê H ˆ Ê Sc ˆ h Ë h ¯ Ë Sis ¯

[5.1]

where glmin is minimum gauge length, H is the nominal specimen thickness, h is the minimum specimen thickness, Sc is the compressive strength and Sis is the interlaminar shear strength. A further variant on waisted specimens, for which good results are claimed, has been proposed by workers16 at the Defence Research Agency (DRA) Farnborough, UK (now known as the Defence Evaluation and Research Agency, DERA). In their approach a co-cured laminate is produced by sandwiching unidirectional material between layers oriented at ±45°. The latter are subsequently machined away in the gauge section to give a specimen with integral end-tabs. To avoid constraint at the ends, multidirectional specimens are usually much longer than unidirectional and, hence, have to be supported by an antibuckling guide. The CRAG method 401 is typical.14 Specimen details are given in Fig. 5.13, together with the recommended jig design. Sandwich specimens are usually designed to be tested as sandwich beams rather than sandwich columns, and are loaded in four-point bending.17,18 The top cover composite sheet is the specimen to be tested. A metal honeycomb core and a bottom cover sheet with greater stiffness and strength ensure that the specimen fails on the upper, compressive, side. In this way very thin specimens can be tested. The high costs incurred in the manufacture of this type of specimen have led to the development of a reusable sandwich beam.19 Here, the core in the test section is made of Plexiglas and a CFRP sheet used as the tension face. On the compression side, rather than being bonded, the specimen is clamped between two aluminium end caps. A form of sandwich column specimen uses the matrix resin as the core material. Excellent results are claimed for this specimen when tested in the IITRI jig.20

5.6

Execution and problems

Carrying out a compression test, or any other test for that matter, should be simple without sacrificing repeatability and reproducibility of the test results. These two terms can be used to characterise a test method and can be distinguished in the following way:

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LT

Specimen GL

LT b

0.16b

h End-tab 0.5–2 mm light alloy (or GRP for hot /wet tests)

5.13 CRAG multidirectional specimen with testing jig. Dimensions: W = 9 h minimum, typically 10 h (absolute minimum = 20 mm); LT = 40 mm minimum; h = 2–4 mm, depending on laminate configuration; GL = not less than W (1 + 1/tanq) or 100 mm, whichever is greater. q is the angle that the off-axis fibres make with the long axis of the specimen.

Repeatability same method identical material same lab same equipment same operator different sessions

Reproducibility same method identical material different lab different equipment different operator different sessions

As the main parameters influencing compression test results the following are suggested:

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Test method

•

Laboratory/operator

•

Operator

1 2 3 4 5 6 7

89

method of load introduction geometry of the test piece mechanical properties of tabbing method of laminate and specimen production condition of testing hardware care taken in performing the test assessment of results.

The test method and ways of laminate and specimen production have been addressed above; the need for standardisation has been stressed. The condition of testing hardware, for example parallelism of loading surfaces and the calibration of the load cell, can obviously influence results and can be regarded as being part of the ‘operator influence’, which naturally is not easy to define and is often held responsible for a number of effects. In particular, the assessment and interpretation of failure modes and test results are important in this context and depend on the experience of the tester. For example, partial loading of the rig will produce misleading results unless the stress–strain curves are examined critically. The aim of a test method should be to keep the influence of the operator as small as possible. Table 5.1 attempts to summarise the effects in compression testing and is a fair check list for potential testers.21 Failure to address the issues listed can lead to a variety of problems, either in execution of a test or in interpretation of evidence and results; some of these have already been mentioned. Whichever method is adopted, it is vital that the operator gains experience before using any data that are generated. Clearly the simpler the test jig, the quicker an efficient and reliable procedure can be established. One crucial item that should always be checked is the failure mode. Basically, the ideal failure occurs within the gauge section. However, sometimes failure may initiate close to the gauge length end of the end-tab and propagate into the gauge length. Such failure would be considered as valid, but any specimen failing within the grip/tab region should be regarded as invalid and the test repeated.

5.7

Typical results

There are a fairly large number of published sources reporting research and experimentation into the various compression test methods and quoting results found. ASTM D 3410 quotes a number of key references which support its conclusions in adopting the specific methods which it recommends. These works are cited in the reference list.17,22–26 In addition, there have been several major projects carried out at Imperial College to examine

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Table 5.1. Factors influencing the results of compression tests.21 Test method

Testpiece preparation

Method of load introduction shear mixed end/shear end

Method of laminate production prepreg layup procedure curing cycle curing device (autoclave, pressclave, heated press)

Testpiece geometry width unsupported length thickness Tabbing material aluminium steel GRP CFRP

Method of specimen production bonding surface preparation tabbing adhesive properties symmetry of tabbing alignment when machining specimen surface finish

Equipment

Operator influence

Calibration load cell transducers, etc. strain gauges

Measurement of testpiece dimensions micrometer, vernier, etc. removal of resin pimples

Accuracy parallelism of testing machine surfaces alignment of compression rig

Care taken in carrying out the test checking alignment ‘zero load’ at test start Analysis of test data assessment of failure modes classification of valid/non-valid failures check of unlikely results method of modulus determination

compression test methods. Largely, the data obtained from these projects support the results from research carried out elsewhere, although there is clear evidence that improvements in test technique can deliver higher values of compression strength. The background, experimental details and results from the various Imperial College test programmes are given in the following sections.

5.7.1 Background Staff and research students in the Centre for Composite Materials at Imperial College have been involved in a number of test programmes with the theme of investigating test methods for composite materials since 1985. These programmes have compared different test methods recommended by various standards organisations and company standards, in addition to

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the development of new test methods. Several programmes have examined compression test methods.

5.7.2 Experimental details and results 5.7.2.1 Programme 1 The first programme27 included CRAG method 400, ASTM D 3410 (Celanese), and both the standard and modified versions of ASTM D 695. Unidirectional and multidirectional laminates of XAS carbon and E-glass fibres both in 913 epoxy were investigated, these materials being supplied as prepreg by Ciba Geigy (now Hexcel). Tables 5.2 and 5.3 show the specimen dimensions and conditions used for the various tests. In the main, 2 mm thick (16-ply) laminates were used because the CRAG method insists on this thickness, although some tests were carried out on 3 mm thick material. Two different and relatively inexperienced operators carried out the tests, one on the CFRP, the other on the GFRP (glass-fibre reinforced plastic). The same test machine was used, but there was a 12 month gap between the two sets of experiments. The results are given in Tables 5.4 and 5.5. All of the stress–strain curves for unidirectional and 0°/90° CFRP and GFRP specimens were linear to high strains. However, the stress–strain

Table 5.2. Dimensions and test conditions adopted for compression tests on unidirectional XAS/913 carbon/epoxy. The D 695 specimen was also used for multidirectional tests. ASTM D 695M

Material thickness Gauge length Overall length Width End-tab thickness End-tab material End-tab profile Strain measurement Test speed (mm min-1)

modified

standard

2 5 75 10 2 carbon/ epoxy 90° —

2 80 80 19/12 — antibuckling guide — extensometer

All dimensions in mm.

1.0

1.0

ASTM D 3410 (Celanese)

CRAG 400 (Celanese)

2 12.7 139.7 6.35 1 steel

2 10 110 10 1 aluminium

9° strain gauge

90° strain gauge

1.3

1.3

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Table 5.3. Dimensions and test conditions adopted for compression tests on E-glass/epoxy. The D 695 specimen was also used for multidirectional tests.

Material thickness Gauge length Overall length Width End-tab thickness End-tab material End-tab profile Strain measurement Test speed (mm min-1)

ASTM D 695M Standard

ASTM D 3410

CRAG

2 80 80 19/12 — antibuckling guide — extensometer 1.0

3 12.7 139.7 6.35 1.5 0° E-glass 9° strain gauge 1.26

2 10 110 10 0.8 aluminium — strain gauge 3.25

All dimensions in mm.

Table 5.4. Compressive modulus and strength data for different layups of CFRP using several test methods. Test type CRAG ASTM ASTM ASTM ASTM ASTM

D D D D D

3410 695 (mod) 695 695 695

Fibre orientation

Elastic modulus (GPa)

Strength (MPa)

Uni Uni Uni Uni 0/90 ±45

106 101 — 107 72 18

1003 1082 1198 744 675 199

(4.4) (11.5) (7.4) (3.1) (0.5)

(100) (99) (180) (73) (56) (6)

Standard deviation in brackets.

Table 5.5. Compressive modulus and strength data for different layups of GFRP using several test methods. Test type CRAG ASTM ASTM ASTM ASTM ASTM

D D D D D

3410 695 (mod) 695 695 695

Fibre orientation

Elastic modulus (GPa)

Strength (MPa)

Uni Uni Uni 0/90 (90/+45/0/-45)2S (+45/0/-45/0)2S

43.6 44.5 37.4 24.1 23.0 27.6

1230 642 592 616 539 633

Standard deviation in brackets.

(2.7) (4.5) (2.2) (1.1) (1.7) (2.5)

(188) (46) (45) (39) (21) (76)

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curves for the remaining layups were non-linear from the start of the test. The results for compressive elastic modulus are quite reasonable across the different test methods and layups, the unidirectional CFRP ranging from 101 GPa to 107 GPa and unidirectional GFRP from 37.4 GPa to 44.5 GPa. The problems associated with the use of the Celanese jig in order to obtain acceptable strength data have been mentioned previously. These are largely due to difficulties in ensuring perfect alignment. This is reflected in the results obtained here. Whilst the strength results for the CRAG and ASTM D 3410 unidirectional carbon specimens are quite similar, they are well below what should be expected for this type of material. In fact they are lower than that obtained with the modified version of the ASTM D 695 method. The strength results for the standard D 695 unidirectional specimens are considerably lower owing to premature failure by crushing of the unsupported ends of the specimen, these results being only marginally greater than those for the 0°/90° specimens. As expected, the ±45° orientations using the D 695 jig gave a very low result. The strength data for unidirectional GFRP are widely different for the CRAG and ASTM D 3410 and D 695 specimens, with the CRAG results being higher than those achieved for the CFRP material and both ASTM results being of the same order as the D 695 tests on 0°/90° and quasiisotropic layups of both carbon and glass. This large discrepancy between the CRAG and ASTM D 3410 results, which on the face of it are obtained using essentially the same equipment, must be put down to misalignment and stability problems, and operator inexperience. 5.7.2.2 Programme 2 A series of experiments conducted on unidirectional CFRP (XAS/914C) supplied by Ciba Geigy (now Hexcel) gave comparative data for several test methods,21 the results being shown in Fig. 5.14. It should be noted that all testpieces, apart from those used in the Birmingham method, were tabbed with square, non-tapered GRP tabs. There are clear trends, with indirect methods yielding low results compared with methods where the load is partly introduced by shear and partly through the end of the specimen. Slight changes in specimen clamping resulted in changes of up to 30% of the measured compressive strength. The results suggest that too much variation is possible. The ICSTM method gave the highest results with the improved testpiece, employing debond inserts, showing a substantial increase over the standard specimen. Overall, the results, other than for the ICSTM jig, broadly agree with information published by other workers.

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Ultimate compressive stress (MPa)

1600 1400 1200 1000 800 600

CRAG(3)

IITRI

ASTM(1)

ASTM(2)

BI

BAe(1)

BAe(2)

BAe(3)

ICSTM(1)

ICSTM(2)

0

CRAG(2)

200

CRAG(1)

400

1

2

3

4

5

6

7

8

9

10

11

12

5.14 Results of compression tests on XAS/914C using different methods and specimen configurations.21 CRAG(1), standard CRAG specimen and fixture, several operators; CRAG(2), one operator, remachined grip surfaces, careful adjustment of the grip collets to the individual testpiece; CRAG(3), as CRAG(2), additionally tab tip debonding by bending the testpiece; IITRI, standard IITRI specimen and fixture, several operators; ASTM(1), modified ASTM D 695, testpiece 2 mm thick, end cap on one end; ASTM(2), as ASTM(1), testpiece 1 mm thick; BI, Birmingham method specimen tested in ICSTM rig; BAe(1), BAe standard rig and specimen, one operator; BAe(2), specimen fully gripped, 5 mm non-grit-blasted section under the tab tip; BAe(3), specimen partially gripped, 5 mm non-grit-blasted section under the tab tip; ICSTM(1), standard ICSTM specimen and fixture, several operators; ICSTM(2), improved specimen.

5.7.2.3 Programme 3 Tables 5.6 and 5.7 give results obtained for unidirectional AS4/PEEK (polyether ether ketone) (APC-2) using the ICSTM method21. The results given in Table 5.6 are for specimens machined from a 4 mm thick plate, with Table 5.7 giving results for the improved specimen, shown in Fig. 5.8, which had 5 mm adhesive cellulose tape placed under the end-

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Table 5.6. Compression data on AS4/PEEK (APC-2), machined specimen (ICSTM method). Specimen

Thickness (mm)

Width (mm)

CSA (mm2)

UCS (MPa)

Modulus (GPa)

1 2 3 4 5

1.97 1.98 1.97 1.99 2.00

9.95 9.97 9.96 9.96 9.92

19.60 19.74 19.62 19.82 19.84

1101 1111 1153 1149 1152

120.3 118.2 117.7 127.7 125.7

Statistics

Mean

sn -1

Cv (%)

UCS Modulus

1133 121.9

25.1 4.5

2.2 3.7

UCS is the ultimate compressive stress, CSA is the cross-sectional area.

Table 5.7. Compression data on AS4/PEEK (APC-2), with debond insert (ICSTM method). Specimen

Thickness (mm)

Width (mm)

CSA (mm2)

UCS (MPa)

Modulus (GPa)

1 2 3 4 5

2.23 2.22 2.22 2.22 2.23

9.98 9.95 9.91 9.96 9.94

22.26 22.09 22.00 22.11 22.17

1353 1456 1358 1597 1493

127.1 128.5 126.0 125.4 125.4

Statistics

Mean

sn -1

Cv (%)

UCS Modulus

1511 126.5

119.7 1.3

7.9 1.1

UCS is the ultimate compressive stress, CSA is the cross-sectional area.

tab tips as a debond insert. The specimens were instrumented with 2 mm strain gauges and the test speed was 1.5 mm min-1. Unlike the results for XAS/914C, the strength of the machined AS4/PEEK specimen is considerably lower than that of the improved specimen, 1133 MPa as opposed to 1511 MPa, although the scatter is lower for the machined specimen results. The explanation is to be found in the high failure strain and high shear strength of the PEEK matrix. The debond insert had the same effect as in the thermoset system, separating stress concentrators. The fracture surfaces were similar to those of the thermoset

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Table 5.8. Compression data on ICI ‘Plytron’ with different levels of fibre volume fraction. ‘B’ in the column ‘Failure’ indicates bifurcation of the strain signals. Nominal Vf (%)

Specimen

Thickness (mm)

CSA (mm2)

UCS (MPa)

Modulus (GPa)

Failure

23

1 2 3 4 5

1.95 1.94 1.94 1.96 1.96

18.93 19.26 18.86 19.40 19.46

721 542 696 519 624

23.2 20.0 22.4 20.8 20.0

B — B — B

29

1 2 3 4 5

1.86 1.89 1.88 1.90 1.87

18.49 18.79 18.65 18.87 18.61

770 727 823 850 635

25.6 24.0 26.4 28.0 23.2

B — B B —

35

1 2 3 4 5

1.99 1.97 1.95 1.94 1.93

19.76 19.44 19.38 19.26 19.16

991 924 892 937 1006

30.4 31.2 32.0 32.8 32.8

B B B B B

Statistics

Vf

Mean

sn -1

Cv (%)

UCS

23 29 35

620 761 950

89.8 85.0 47.5

14.5 11.2 5.0

Modulus

23 29 35

21.3 25.4 31.8

1.45 1.91 1.04

6.8 7.5 3.3

UCS is the ultimate compressive stress, CSA is the cross-sectional area.

system but with less splitting and brushing. This similarity suggests fibre microbuckling failure for both materials. 5.7.2.4 Programme 4 Again using the ICSTM method, data were obtained for a unidirectional E-glass fibre reinforced nylon (ICI ‘Plytron’).21 The material was supplied in the form of pultruded panels with nominal fibre volume fractions of 23%, 29% and 35%. The standard specimen configuration was used incorporating the same GRP end-tabs as in the tests on CFRP. The test speed was 3 mm min-1. Results are given in Table 5.8.

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The magnitude of stresses responsible for tab tip debonding depends on the ratio of composite stiffness to tab stiffness, and for a given tab stiffness the stresses are strain independent. Debonding of the tab tips occurred in all cases, mostly in a symmetric fashion, between 1% and 2.5% strain. Since the failure strain of glass fibre composites is high, tab debonding does not cause immediate failure but acts as a stress relief. Strain gauges located front and back on the specimens were able to detect the onset of tab debonding as a bifurcation of the strain signals. As seen in Table 5.8 most of the specimens exhibited this behaviour, suggesting macroinstability of the testpiece. Normalisation of the bending stiffness of the specimen (modulus of elasticity multiplied by the square of the testpiece thickness – to which Euler buckling is proportional) and plotting versus the ultimate compressive stress resulted in a linear relationship for tests where bifurcation occurred, again suggesting macroscopic instability. It is clearly important to design the specimen specifically for the material to be tested. The composite examined here did not exhibit significant stiffness decrease, but the relatively high stresses achieved by reducing stress concentrations did introduce the problem of macrobuckling, as was observed with CFRP.

5.8

Conclusions

Of the methods discussed here, the ICSTM jig is one of the simplest to use. It also gives the highest mean strengths, together with low scatter. However, although a simple method is important and desirable, other techniques can give higher than usual strengths provided adequate care is taken, the operator is experienced and, also, some modifications are made to the specimens.21 It is clear that whichever method is used, great care must be taken with specimen preparation, operator training and in the execution of the test.

References 1. C Soutis and N A Fleck, ‘Static compression failure of carbon fibre T800/924C composite plate with a single hole’, Journal of Composite Materials, 1990 24(5) 536–58. 2. C Soutis, ‘Measurements of the static compressive strength of carbon fibre epoxy laminates’, Composites Science and Technology, 1991 42(4) 373–92. 3. B Budiansky and N A Fleck, ‘Compressive failure of fibre composites’, J Mech Phys Solids, 1993 41 183–211. 4. C Soutis and R Tenchev, ‘A property degradation model for fibre microbuckling failure in composite laminates’, Sci Eng Composite Materials, 1995 4(1) 27–34.

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5. W t’Hart, R Aoki, H Bookholt, P T Curtis, I Krober, N Marks and P Sigety, ‘Garteur compression behavior of advanced CFRP’, AGARD 73rd Meeting of Structures and Materials Panel – Workshop on Advanced Composites in Military Aircraft, San Diego, CA, October 1991. 6. ASTM D 695M-91, ‘Standard test method for compressive properties of rigid plastics’, Vol 8.01, Annual Book of ASTM Standards, 100 Barr Harbor Drive, West Conshohocken, PA 19428, USA, Vol 8.01, 1994. 7. G C Grimes, Experimental Study of Compression–Compression Fatigue of Graphite/Epoxy Composites, ASTM STP 734, ed. C C Chamis,American Society for Testing and Materials, 1981, 281–337. 8. R M Lamothe and J Nunes, ‘Evaluation of fixturing for compression testing of metal matrix and polymer/epoxy composites’, in Compression Testing of Homogeneous Materials and Composites, ASTM STP 808, eds R Chait and R Papirno, American Society for Testing and Materials, 1983, 241–53. 9. J S Berg and D F Adams, ‘An evaluation of composite material compression test methods’, J Composites Technology and Research, 1989 11 41–6. 10. K F Port, The Compressive Strength of CFRP, Royal Aircraft Establishment, Farnborough UK, Technical Report 82083, 1982. 11. D H Woolstencroft, A R Curtis and R I Haresceugh, ‘A comparison of test techniques used for the evaluation of the unidirectional compressive strength of carbon fibre reinforced plastic’, Composites, 1981 12 275–81. 12. A J Barker and V Balasundaram, ‘Compression testing of carbon fibrereinforced plastics exposed to humid environments’, Composites, 1987 18(3) 217–26. 13. J G Haeberle and F L Matthews, ‘Studies on compressive failure in unidirectional CFRP using an improved test method’, Proceedings of ECCM-4, Stuttgart, EACM and GARE, eds J Fulles, G Gruninger, K Schulte, A R Bunsell and A Massiah, Elsevier Applied Science, September, 1990, 517–23. 14. P T Curtis, CRAG Test Methods for the Measurement of the Engineering Properties of Fibre-reinforced Plastics, Royal Aircraft Establishment, Farnborough, UK, Technical Report 88012, 1988. 15. ASTM D 3410/D 3410M-95, ‘Standard test method for compressive properties of polymer matrix composite materials with unsupported gage section by shear loading’, Annual Book of ASTM Standards, 100 Barr Harbor Drive, West Conshohocken, PA 19428, USA, Volume 15.03, 1997, 116–31. 16. P T Curtis, J Gates and C G Molyneux, An Improved Engineering Test Method for the Measurement of the Compressive Strength of Unidirectional Carbon-fibre Composites, DRA Farnborough, UK, Technical Report 91031, 1991. 17. N R Adsit, ‘Compression testing of graphite/epoxy’, in Compression Testing of Homogeneous Materials and Composites, ASTM STP 808, eds R Chait and R Papirno, American Society for Testing and Materials, 1983, 175–86. 18. ASTM D 5467–93, ‘Standard test method for compressive properties of unidirectional polymer matrix composites using a sandwich beam’, Annual Book of ASTM Standards, 100 Barr Harbor Drive, West Conshohocken, PA 19428, USA, Vol 15.03, 1997. 19. M B Gruber, J L Overbeeke and T W Chou, ‘A reusable sandwich beam concept for composite compression test’, Journal of Composite Materials, 1982 16 162–71.

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20. A S Crasto and R Y Kim, ‘Compression strengths of advanced composites from a novel mini-sandwich beam’, SAMPE Quarterly, 1990 22(3) 29–39. 21. J G Haeberle, Strength and Failure Mechanisms of Unidirectional Carbon-fibre Reinforced Plastics under Axial Compression, PhD Thesis, Imperial College, University of London, UK, December 1991. 22. K E Hofer and P N Rao, ‘A new static compression fixture for advanced composite materials’, Journal of Testing and Evaluation, 1977 5(4) 278–83. 23. R P Pendleton and M E Tuttle, Manual on Experimental Methods for Mechanical Testing of Composites, Society for Experimental Mechanics, Bethel, CT, USA, 1989. 24. T A Bogetti, J W J Gillespie and R B Pipes, ‘Evaluation of the IITRI compression test method for stiffness and strength determination’, Composites Science and Technology, 1989 32(1) 57–76. 25. D F Adams and E Q Lewis, ‘Influence of specimen gage length and loading method on the axial compression strength of a unidirectional composite materials’, Experimental Mechanics, 1991 31(1) 14–20. 26. D F Adams and E M Odom, ‘Influence of specimen tabs on the compressive strength of a unidirectional composite material’, Journal of Composite Materials, 1990 25(6) 774–86. 27. J M Hodgkinson, An Experimental Comparison of ASTM, BSI and CRAG Standard Test Methods for the Determination of Mechanical Properties of Composite Materials, The Centre for Composite Materials, Technical Report 90/02, Imperial College, London, 1990.

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6 Shear* W R BROUGHTON

6.1

Introduction

An intrinsically low resistance to shear deformation, particularly in material planes dominated by matrix properties, is a severe weakness in fibre-reinforced plastic composites. Relatively low values of shear stiffness and strength often compromise material performance, forcing designers to arrange laminate stacking sequences in order to maximise shear resistance. The resultant effect of shear property optimisation is that other mechanical properties are frequently compromised. Small tangential stresses can lead to severe reductions in the load bearing capacity of composite structures; hence the need for accurate methods for measuring shear properties. Considerable experimental and analytical effort has been expended in the development of in-plane and through-thickness (out-of-plane) shear test methods for the determination of shear modulus and strength of fibre-reinforced polymer composites. One of the principal difficulties in the development of a test method for the measurement of shear properties is the provision of a pure shear stress state in the specimen. Ideally, for quantitative shear measurements, the shear test method should provide a region of pure and uniform shear stress in the test section of the specimen throughout the linear and non-linear response regimes. This region should be one of maximum shear stress relative to all other regions of the specimen. In addition, a unique relationship should exist between the applied load and the magnitude of the shear stress in the test section. The difficulty of inducing pure shear increases with increasing anisotropy and inhomogeneity of the material. As these characteristics increase, the complex stress states arising at or near the loading zones become more dominant, particularly for continuous unidirectional laminates containing * Crown copyright

100

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high modulus and high strength fibres. In these materials, it is difficult to obtain adequate regions of uniform shear stress free of extraneous stress components within the specimen, even if the production of the specimen and test alignment are perfect. In addition, extraneous tensile and compressive stress components have a marked effect on the shear strength of these materials. Tensile stresses induce premature failure, whereas compressive stresses delay the onset of failure. The difficulties encountered in producing a state of pure shear in composite specimens have resulted in a limited number of these methods being incorporated into national and international standards. There is no universal method suitable for the accurate evaluation of the shear properties for the extensive range of material architectures encountered in composite technology. All the shear methods, standardised or otherwise, have physical and geometrical limitations. Most shear tests have been developed with the objective of maximising shear stress and minimising extraneous induced stresses. It is possible to measure the shear stress–strain response of a composite in the presence of non-shear stresses, provided the magnitude of the shear stress is considerably larger than the other stress contributions. Acceptable shear moduli measurements can be obtained from a range of test methods. Full characterisation of the shear properties of a composite lamina or laminate requires the measurement of shear modulus and shear strength in the 1–2, 1–3 and 2–3 planes. Because in-plane and through-thickness shear properties are not necessarily equal, test methods have been developed to induce both in-plane and through-thickness shear loading. Here, we are only concerned with in-plane shear test methods. In the assessment of shear test methods, consideration will be given to the shear properties attainable, shear and normal stress distributions in the test section, specimen fabrication and test apparatus requirements, data reduction procedures and data reproducibility.

6.2

Test methods

In this section six commonly used methods for the determination of shear properties are considered: • • • • • •

uniaxial tension of a ±45° laminate uniaxial tension of a 10° off-axis laminate two-rail and three-rail shear tests the V-notched beam (or Iosipescu) shear specimen twisting of a flat laminate torsion of a thin-walled tube.

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6.2.1 ±45° tension test The application of uniaxial tension to a balanced and symmetrical ±45° laminate is a relatively straightforward method for determining the inplane shear characteristics (modulus and strength) of continuous aligned fibre-reinforced systems. The method, widely used in the aerospace/defence industry, is available as BS EN ISO 14,129,1 which is a joint international (ISO) and European (EN) standard, and as ASTM D 3518.2 The test procedures described in these standards are based on ASTM D 3518 and utilise a 250 mm long rectangular specimen with width 25 mm and thickness 2 mm (see Fig. 6.1). It is recommended that for materials constructed with layers thicker than 0.125 mm, the laminate should consist of 16 layers (i.e. [±45]4S). The specimen is machined to the required size using diamond cutting equipment, for example, a circular wheel. The use of a liquid coolant such as water is recommended to prevent the build-up of heat in the test specimen, which could cause material damage. The surfaces and edges should be free from scratches, pits, sink marks and flashes. Edges should be ground parallel to remove machining defects. Providing failure does not occur within the grip region, specimens can be tested with or without end-tabs. End-tabs, if used, should be constructed from a cross-ply or fabric laminate fabricated in glass fibre/resin, or from the material under test, with the fibre axes of the fabric set at ±45° to the specimen axis. The end-tabs are adhesively bonded to the specimen with a high elongation adhesive and have a recommended length of 50 mm. This corresponds to an overall gauge length (between grips) of 150 mm. The tab material thickness should be between 0.5 mm and 2.0 mm, with a tab angle of 90°.

y Tab material orientation

150 Transverse strain gauge

45°

45°

25

45° 45°

Tab

Longitudinal strain gauge

Specimen

y

Jaws

50 250

6.1 Schematic of the ±45° tensile specimen.

x

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When a ±45° laminate is loaded in uniaxial tension, a biaxial state of stress is induced within each of the +45° and -45° lamina (i.e. layers).3,4 The normal stresses s11 and s22 in the lamina coordinate system depend on both the applied tensile stress sxx and the induced shear stress txy, whereas the shear stress t12 is related only to the applied tensile stress sxx, such that: s 11 =

s xx s xx s xx + t xy ; s 22 = - t xy ; t12 = ± 2 2 2

[6.1]

This analysis assumes that there is no interlaminar shear coupling. The corresponding in-plane lamina normal strains e11 and e22 and shear strain g12 are given by Equation [6.2]: e 11 = e 22 =

e xx + e yy ; g 12 = e xx - e yy 2

[6.2]

where exx and eyy are the normal strains parallel and perpendicular to the specimen axis, respectively. In order to determine the in-plane shear modulus, G12, strains need to be measured both parallel and perpendicular to the specimen axis using either strain gauges or extensometers. The usual approach when using strain gauges is to bond two separate gauges adhesively to the specimen as shown in Fig. 6.1. Alternatively, biaxial rosette gauges may be adhesively bonded to the specimen. The test speed given in the ISO standard is 2 mm min-1. The in-plane shear modulus of the unidirectional lamina, given by Equation [6.3]: G12 =

s xx t 12" - t 12' = 2(e xx - e yy ) g 12" - g 12'

[6.3]

is obtained from the initial slope of the shear stress–strain curve (t12 versus g12) over a strain range of 0.1–0.5%,1 as shown in Fig. 6.2. The specimen geometry has been selected to ensure that the shear modulus is unaffected by edge effects, end effects or the biaxial state of stress within individual laminae. In-plane shear strength, S12, is expressed as: S12 =

Pmax 2bh

[6.4]

where Pmax corresponds to the applied load at failure, and b and h are the width and thickness of the specimen, respectively. The ±45° tensile test provides an acceptable method for determining inplane shear modulus, but caution must be exercised in interpreting the ultimate shear strength and strain results.This is due to the fact that the laminae are in a state of biaxial stress and not pure shear. Normal stresses of a

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6.2 Typical shear stress–strain curve for the ±45° specimen.

similar magnitude to those of the shear stresses act along the shear planes, resulting in the onset of mixed-mode fracture. Multiple-ply cracking, fibre rotation and edge or internal delaminations occur prior to final fracture, with the onset of fracture being delayed due to the constraint imposed on the lamina by adjacent layers. True failure is difficult to determine, with most standards specifying the shear strength as corresponding either to the ultimate load generated during the test or to a specified strain level. It is recommended in the ISO standard that the test be terminated at g12 = 5.0%. The peak load at or before 5% strain is taken as the shear strength.

6.2.2 10° off-axis test The 10° off-axis tensile test is a method commonly employed for shear characterisation of fibre-reinforced polymer composites. The test consists of uniaxially loading a unidirectional laminate in tension with fibres oriented at 10° to the load axis (Fig. 6.3). A biaxial stress state is induced in the material’s principal coordinate system when subjected to uniaxial tensile load. The 10° angle was chosen to minimise the effects of longitudinal and transverse stress components s11 and s22 on the shear response. At an angle of 10° the shear strain approaches a maximum value.3–6 The in-plane normal and shear stresses and shear strain (in the material principal coordinate system) developed within the specimen in the absence of end constraints are given by Equations [6.5] and [6.6]5:

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45°

x

y Tab material orientation

150 Strain gauge rosette 2 1 1 2 3 Specimen

45°

25 Tab

10°

Jaws

y 50 250

6.3 Schematic of 10° off-axis specimen.

s11 = sxx cos2 q ;

s22 = sxx sin2 q ;

t12 = –12sxx sin 2q

g 12 = (e xx - e yy ) sin 2q + g xy cos 2q

[6.5] [6.6]

Substituting q = 10° into Equation [6.5] yields the relative magnitudes of the in-plane longitudinal, transverse and shear stresses along the 10° plane: s11 = 0.970sxx;

s22 = 0.030sxx;

t12 = 0.171sxx

[6.7]

where sxx is equal to the applied load, P, divided by the cross-sectional area, bh, of the specimen. A three-element rosette adhesively bonded at the centre of the specimen, as shown in Fig. 6.3, is used to measure the strains. The structural strains for such a rectangular rosette with three strain gauges (gauge 1 = 0°, gauge 2 = 45° and gauge 3 = 90° to the loading axis) are: exx = e1;

eyy = e3;

gxy = 2e2 - e1 - e3

[6.8]

The in-plane strain along the 10° plane is determined by substituting the structural axes strains from Equation [6.8] into Equation [6.6] and setting q = 10°. The resulting equation is: g12 = 1.879e2 - 1.282e1 - 0.598e3

[6.9]

Alternatively, the structural axes strains may be measured using a three-element 60° delta rosette (gauge 1 = 0°, gauge 2 = +120° and gauge 3 = -120° to the loading axis). The structural axes strains are given by Equation [6.10]: e xx = e 1 ; e yy =

2e 2 + 2e 3 - e 1 2(e 3 - e 2 ) ; g xy = 3 3

[6.10]

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Similarly, the in-plane strain along the 10° plane is determined by substituting the structural axes strains from Equation [6.10] into Equation [6.6] and setting q = 10°. The resulting equation is: g12 = 1.313e3 - 0.456e1 - 0.857e2

[6.11]

This test method is not registered either as an ISO or ASTM standard; thus there are no commonly used or agreed specifications for specimen dimensions and specimen preparation. A satisfactory approach would be to comply with Part 5 of the International Standard ISO 527.7 This international standard specifies ‘the test conditions for the determination of the tensile properties of unidirectional fibre-reinforced polymer composites’. Based on ISO 527-5, the 10° off-axis specimen would have a width of 25 mm, length 250 mm and thickness 2 mm (i.e. Type A). It is recommended that the 10° unidirectional coupon be tabbed in accordance with ISO 5275, identical to the procedure employed for the ±45° tension test. Specifications relating to specimen dimensions are contentious issues remaining to be resolved. The in-plane shear modulus of the unidirectional laminate is obtained from the initial slope of the shear stress–strain curve over a strain range of 0.05–0.25%.7 Finite element analysis indicates that the axial strain variation is very sensitive to out-of-plane bending and twisting eccentricities.5 This effect can be kept to a minimum by ensuring that the bending strains in the width and thickness are less than 3%, as specified in ISO 527-5. Tests are conducted at a speed of 1 mm min-1. The test has the advantages of adaptability to conventional tensile testing (including cyclic and environmental conditions), uniformity of throughthickness shear stress, no residual stresses and ease of manufacturing. However, as demonstrated above, it is necessary to measure three strains at a point and to transform stresses and strains to another coordinate system. Small orientation errors in machining the specimen angle and strain gauge alignment can produce large errors in shear measurements. This misorientation (recommended to be within ±0.5°) is not critical when measuring shear strain at failure, because strain peaks are relatively insensitive to small errors at a 10° load angle. The main concern with this test method is the non-uniformity of the stress field near the grips, which is caused by end constraints preventing rotation, thus inducing moments and shear forces at the ends. Using long specimens (aspect ratios of 10 or greater) promotes a state of uniform shear stress in the centre of the specimen and thus reduces the error in shear modulus caused by the end constraints. However, a complex correction factor is still required to calculate the true shear modulus.7 Failure of 10° off-axis specimens occurs due to the combination of transverse tensile and shear stresses. As a consequence, the method tends to

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underestimate the ultimate shear strength and strain. The onset of failure is catastrophic, with a single straight crack developing early, propagating rapidly across the gauge-section and separating the specimen into two sections. A recent development has been the use of oblique end tabs for testing these specimens.8,9 Numerical and experimental analyses have shown that although a state of homogeneous shear stress is produced, transverse tensile stresses are still present.

6.2.3 Rail shear test A third method for determining in-plane shear properties of fibre-reinforced polymer composites is the rail shear test. This test method is used extensively throughout the aerospace industry, with in-plane properties determined by imposing edgewise shear loads on the laminate using a tworail (Fig. 6.4) or three-rail fixture (Fig. 6.5). The two test configurations (i) two-rail shear and (ii) three-rail shear and associated test specimen geometries are specified in ASTM D 4255,10 a standard guide for testing in-plane shear properties of composite laminates. This standard guide covers the determination of in-plane shear properties of continuous and discontinuous aligned materials (0° and 90° orientations), symmetric laminates and randomly orientated fibrous laminates.

Tensile or compressive load

76 120.2 Fixture bolts

Specimen

25

Strain gauges 51 152 Rails

12.7

6.4 Two-rail shear fixture and specimen.

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Mechanical testing of advanced fibre composites Tensile or compressive load Centre rail slides through guide

Strain gauges

6.5 Three-rail shear fixture and specimen.

The two-rail shear test involves clamping the long sides of a rectangular specimen between two pairs of rigid steel loading rails, with the other sides remaining unconstrained (Fig. 6.4). The loading rails are usually bolted to the test specimen. A tensile force is applied to the rails, which induces an in-plane shear load on the specimen. ASTM D 4255 specifies a specimen length of 76 mm and a width of 152 mm. A strain gauge, adhesively bonded to the specimen at 45° to the longitudinal axis of the specimen, is used to measure shear strain. The shear strength, Sxy, and shear modulus, Gxy, can be calculated using the following equations: Sxy =

Pmax Lh

[6.12]

Gxy =

Dt xy DP = Dg xy 2LhDe 45

[6.13]

where Pmax is the ultimate failure load, L the specimen length along the rails and h the specimen thickness. The variables DP and De45 are the change in applied load and strain (for +45° or -45° strain gauge) in the initial linear region of the stress–strain curve. The three-rail (symmetric) shear test, developed to produce a closer approximation to pure shear, consists of three pairs of rails clamped to the

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test specimen, usually by bolts (Fig. 6.5). The two outside pairs of rails are attached to a base plate, which rests on the test machine. A third (middle) pair of rails are guided through a slot in the top of the base fixture. The middle pair of rails are usually loaded in compression rather than tension, since the former does not require fastening the base fixture to the test machine. Shear modulus is measured at the centre of both test sections using strain gauges bonded at 45° to the specimen’s longitudinal axis. The specimen width and length are 137 mm and 152 mm, respectively.10 The shear strength, Sxy, and shear modulus, Gxy, can be calculated using Equations [6.14] and [6.15]: Sxy =

Pmax 2Lh

[6.14]

Gxy =

Dt xy DP = Dg xy 4LhDe 45

[6.15]

where the variables have been defined previously. It is recommended that laminates be 1.27–3.17 mm (i.e. 0.050–0.125 inch) thick.10 Thin laminates tend to buckle at low loads, while thicker laminates may have shear strengths in excess of the rail clamping capacity. Specimen dimensions for both rail shear tests are shown in Figs. 6.4 and 6.5. Specimens are bolted to the rails using 9.5 mm bolts. The bolts are inserted through the specimen via 12.5 mm diameter drilled holes. The holes are oversized to ensure that the shear load is introduced into the laminate via frictional forces between the specimen and the steel loading rails. It is important that there is no bearing contact in the direction of loading between the bolts and the specimen. If the torque is too low, the specimen will slip and the bolts will begin to bear on the specimen, and if the torque is too high, then spurious failures may be induced by the high local through-thickness compressive stresses. The recommended torque on each bolt is 100 Nm, and the bolts may need to be retightened during loading. Specimen preparation and testing are time consuming and expensive. In reality, it is difficult to machine specimens to the required tolerances, and in many instances bearing contact initiates premature failure along the bolt line, rather than in the specimen centre. In addition, delaminations are commonly introduced during the drilling of holes. These defects act as stress raisers, adding further to the uncertainties in strength values measured using the two- and three-rail tests. The uncertainties associated with the results from this particular test were highlighted when the ASTM conducted round-robin tests; consequently ASTM D 4255 is only a guide.

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The existence of free edges causes the stress distribution in the laminate to deviate from an ideal shear state. Stress singularities exist near loaded corners, and axial and transverse stresses are also present. Numerical analysis has shown that the length to width ratio can have a major effect on stress distributions and is laminate dependent.3 Specimen dimensions, as specified in ASTM D 4255, ensure that a uniform shear stress distribution exists over a large region in the specimen centre, producing valid shear moduli values for all laminates, except those with an inherently high effective Poisson’s ratio (e.g. ±45° angle-ply). In these laminates, a non-uniform shear stress distribution exists with large normal stresses present at the edges. The two loading configurations are only suitable for shear moduli determination. Although the three-rail shear test provides a better approximation to pure shear, problems associated with the two-rail shear method (i.e. significant normal stresses and non-uniform shear stress distribution) are not eliminated. Large transverse tensile stresses present in the vicinity of the loaded corners invariably cause premature fracture in unidirectional laminates with fibres parallel to the rails (0° orientation). The onset of failure, in the form of longitudinal cracks, is often difficult to locate visually as the initiation site is obscured by the rails. This fibre orientation is associated with a large scatter in test data and low strength. Transverse (fibres perpendicular to the rails) and cross-ply (0/90) laminates fail over a wider region at comparatively high strains.3 Failure is associated with multiple-ply cracking, which is considered to be representative of subcritical failures observed in individual plies within laminates subjected to shear. It is worth noting that it is difficult to drill holes in unidirectional laminates without causing longitudinal splitting.

6.2.4 V-notched beam (Iosipescu) test The V-notched beam test, originally developed by Iosipescu11 for characterising the shear properties of metals, was subsequently adapted for use with fibre-reinforced plastic composites as ASTM D 5379,12 following experimental and analytical work conducted mainly by Adams and Walrath.13 The test method employs a double edge-notched, flat rectangular specimen, which is shown, together with what is often referred to as the ‘Wyoming’ test fixture, in Fig. 6.6. Two 90° angle notches with a notch root radius of 1.3 mm are cut at the edge mid-length with faces orientated at ±45° to the longitudinal axis, to a depth of 20% of the specimen width (i.e. 4 mm). The specimen length and width are 76 mm and 20 mm, respectively, with the thickness being between 3 and 4 mm, although greater thicknesses can be tested. Specimens with a thickness less than 3 mm require adhesively

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6.6 V-notched beam test fixture and specimen.

bonded tabs, typically 1.5 mm thick, to prevent out-of-plane bending or twisting, which may lead to premature failure. Local crushing, which can occur near the inner loading regions, is also avoided by the use of tabs. Test specimen dimensions may be reduced if required. Shear strain is measured by bonding two biaxial strain gauges, one on each opposite face of the specimen, to the centre of the specimen, in the area between notches. The strain gauges should have a gauge length of 1 mm or 2 mm, to keep within the region of uniform stress, and are aligned at ±45° to the longitudinal axis of the specimen. Although a special test fixture is required, testing is relatively straightforward. In principle, this procedure induces a state of pure shear stress at the midlength of an isotropic specimen, by the application of two force couples. A state of constant shear force is induced through the mid-section of the test specimen, with the induced moments cancelling exactly at the mid-length, thereby producing a state of pure shear at this location.3 Early finite element and experimental analyses suggested that there was indeed a uniform shear stress over most of the gauge section between the notch roots, despite the shear stress concentrations at these locations. The stress concentration was found to be a function of notch angle, depth and root radius and material orthotropy, which died rapidly on moving away from the notch tip. It was also claimed during the development of the standard14 that, although transverse normal stresses were developed in the test section, they were compressive and redistributed as inelastic failure (longitudinal cracking) occurred at the notch roots, leaving the test

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section essentially free of transverse normal stresses at loads approaching final failure. However, more recent investigations have demonstrated that the shear stress distribution in the test section of both isotropic and anisotropic specimens is not uniform.3,15–17 Furthermore, shear and normal stress distributions have been shown to be highly dependent on the orthotropy ratio Exx/Eyy, notch geometry and loading boundary conditions.The average shear strength, Sxy, and shear modulus, Gxy, can be calculated using Equations [6.16] and [6.17]: Sxy =

Pmax wh

[6.16]

G xy =

Dt xy DP = Dg xy whD(e 45 - e -45 )

[6.17]

where Pmax is the ultimate failure load, w is the distance between the notches and h is the specimen thickness. The variables DP, De45 and De-45 are the change in applied load and +45° or -45° normal strains in the initial linear region of the stress–strain curve. To minimise potential effects of out-ofplane movement or twisting of the specimen, it is recommended that the strain data used for determining shear modulus be the average of the indicated strains from each side of the specimen. Misalignment of as little as 1.4° from normal may cause a 6% difference in observed modulus between the two faces.18,19 Numerical studies15–17 show that for specimens with sharp notches, correction factors need to be employed to calculate the actual shear modulus value. ASTM D 5379, however, specifies a notch root radius of 1.3 mm in order to minimise the shear stress concentration at the notch roots, and thus promote a more uniform shear stress distribution along the notch-root axis. ASTM D 5379 does not specify the use of correction factors; however, the use of large radii is not entirely successful in promoting a uniform shear stress distribution. Various failure modes, shown in Fig. 6.7, may be encountered with the failure process being highly dependent on the microstructure of the material. In some cases, a mixed mode of failure has been observed. For example, in continuous unidirectional (longitudinal, or 0°) specimens, damage initiates at the notch roots with two symmetric cracks propagating parallel to the fibres on the opposite sides to the inner loading points. The shear stress concentration at the notch root is primarily responsible for crack initiation, with crack growth in the principal tensile stress plane being prevented by the aligned fibres. Axial splitting produces stress relief at the notch roots, resulting in a more uniform and symmetric shear stress distribution about the notch-root axis.15 Further loading causes these axial cracks to arrest and

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(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

6.7 Typical failure modes for V-notched beam test (* denotes unacceptable modes). (a) Unreinforced thermoplastic-shear yielding, (b) Unreinforced thermoset-brittle tensile*, (c) 0° continuous unidirectional, (d) 90° continuous unidirectional*, (e) woven fabric-intralaminar, (f) woven fabric-interlaminar, (g) ‘long’ fibre/thermoplastic-shear yielding, (h) ‘long’ fibre/thermoplasticbrittle tensile*, (i) sheet moulding compound (SMC), (j) chopped strand mat (CSM).

the formation of numerous short interfacial cracks in the gauge section. This last event produces final failure with the peak load being used to calculate shear strength. A more ideal shear stress state exists in the transverse or 90° specimens. The shear stress value is a minimum at the notch root and increases along the notch-root axis to a maximum value at the specimen centre. However, these specimens fail prematurely because fracture initiates by a combination of shear and transverse tensile stresses at the notch roots. Cracks propagate in an unstable manner along the notch-root axis, which is the path of

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least resistance. Transverse specimens invariably fail at significantly lower stresses than those measured for the corresponding longitudinal specimens. The failure mode for transverse specimens does not represent shear failure, and these specimens are therefore unsuitable for measuring shear strength; longitudinal specimens should be used in preference. A number of investigators, in particular Conant and Odom,19 have modified the recommended ASTM fixture in an attempt to prevent misalignment of the two fixture halves, to improve the accuracy of specimen centering relative to the jig and to provide lateral constraint to the specimen and wedges to prevent their displacement perpendicular to the plane of loading. Without doubt the major problem associated with the ASTM fixture is reliance on load application via the moving part of the jig, which is supported by a single off-set post and bearing arrangement. Such a system not only allows rotation (about the post) of the moving part of the jig relative to the fixed part but also assumes no deflection within the bearing itself. Such an assumption is not supported by experimental evidence, as there is clear movement visible to the naked eye, particularly at high loads. Conant and Odom19 introduced two linear bearings operating on shafts, each passing through both parts of the jig, constraining the fixture to linear motion in the plane of the specimen. The bearings were adjustable to obtain zero play, further preventing out-of-plane movement. A simpler arrangement could be provided by attaching the two sides of the basic Wyoming fixture within a four-bearing subpress.20

6.2.5 Plate-twist test This test method, which was initially developed to measure the shear modulus of plywood (ASTM D 3044),21 has proved to be satisfactory for measuring shear moduli ranging from 0.29 GPa (chopped glass-fibre reinforced polyurethane) to 88.2 GPa (steel). The test method is unsuitable for determining in-plane shear strength.22 In the plate-twist test, shown in Fig. 6.8, a square plate is supported on the two corners of one diagonal and load is applied at a constant rate to the corners of the opposite diagonal. The stress state induced in the plate is essentially pure shear. The total load is recorded as a function of the resultant displacement. The plate should be square or rectangular in shape with the diagonals being of equal length and the length to thickness ratio should be ≥35 to minimise through-thickness shear effects. This test method is unsuitable for materials which are not transversely isotropic or homogeneous through the section (e.g. multidirectional laminates including 0°/90° cross-plies). For these materials, the shear modulus produced under flexural loads is no longer equivalent to the in-plane shear modulus.

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6.8 Plate-twist test.

The shear modulus, G12, can be determined from the displacement of the loading points (DdP):22 G12 =

3DPabK 4 Dd p h3

[6.18]

and from the displacement at the plate centre (DdC): G12 =

3DPabK 8Dd c h3

[6.19]

where a and b are the plate edge dimensions, h is the plate thickness and DP is the change in load (total) for a change in displacement, d. A practical difficulty with the test has been the positioning of the loading points, which are normally in-board, rather than at the actual corner, as assumed in the analysis. This mispositioning leads to an error of several per cent in the shear modulus value. A correction factor, K, has been introduced into Equations [6.18] and [6.19] to account for in-board loading:23 2

K (r ) = 3r 2 - 2r - 2(1 - r ) ln(1 - r )

[6.20]

where r is the ratio of L, the test span diagonal length, and d, the plate diagonal length. The correction factor is relatively insensitive to variations in the Poisson’s ratio, n, over the range 0.25–0.40.22 The analytical solution as given by Equation [6.20] produces K values almost identical to those cal-

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culated by Sims et al.22 using a polynomial line fit to finite difference data (i.e. less than 1% discrepancy for r > 0.8). The plate twist method, which has recently become an international standard, (ISO 15, 31024), recommends a standard plate specimen 150 mm ¥ 150 mm and an in-board ratio of 0.95, with other plate dimensions being optional. The maximum thickness requirement for non-standard plate specimens should meet the requirement of 35h £ a £ b. The modulus is determined over the displacement range of 0.1h to 0.3h, with a maximum allowable plate deflection of 0.5 mm. There are many advantages in the use of a plate specimen, particularly for moulded plastics and fibre-reinforced plastic composites. For these materials, plate specimens more closely represent the properties of actual products than moulded-to-size dumbbell and beam specimens or hoop-wound tubes. As the technique is non-destructive (most shear methods result in the destruction of the test material during testing), a plate-twist specimen can also be sectioned into tensile or compression coupon specimens along the principal material directions to assess the material’s anisotropy. This guarantees that the shear modulus relates directly to any other property measured from the plate. An additional bonus is that the test results represent the shear response over a relatively large area, which means variations in microstructure across the plate are averaged.

6.2.6 Torsion shear of a thin-walled tube The torsion of a thin-walled circular tube is a method of directly applying shear load to fibre-reinforced plastic composites, and from an applied mechanics viewpoint it is the most desirable method for shear characterisation. In this test, an approximate state of pure shear stress is induced in a thin-walled circumferentially wound cylindrical tube subjected to pure torque about the longitudinal axis of the specimen. The shear stress is uniformly distributed around the circumference and along the specimen length. Because the wall thickness is small compared with the mean radius of the tube, the through-thickness shear gradient is negligible. The specimen should have a gauge length to diameter (L/D) ratio >1, and a wall thickness to diameter ratio (h/D) of 0.02, or less.3 This serves to promote a uniform shear stress state at the specimen mid-length and prevents either local or global shear buckling. ASTM D 544825 recommends thin-walled hoop-wound cylindrical specimens 140 mm long with a diameter of 100 mm and wall thickness of 2 mm. Specimens are adhesively bonded to close concentrically fitting circular end fixtures, which are inserted at each end of the specimen. The ends of the specimen are overwound with additional material and tapered to promote failure within the gauge length. The

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1.7– 3.5

225 10 15°

50

50

125

50

6.9 A thin-walled hoop-wound cylindrical specimen.

bond lengths at the ends should be 20 mm. The end fixtures attached to the specimen are mounted concentrically in the test machine, and a monotonic load is applied at constant torque speed of 2°/min. Axial stresses resulting from specimen shear deformation can be prevented by allowing free axial displacement. An example of a carbon fibre-reinforced epoxy specimen with tapered end reinforcement is shown in Fig. 6.9. Shear strain is measured by means of two bonded triaxial strain gauges (0°/45°/90°), diametrically opposite each other, at the centre of the specimen. The strain gauges have a gauge length of 6 mm. The longitudinal and transverse strain gauges are monitored to ensure there are no significant bending forces applied to the specimen during the test set-up and no bending loads present during the test. Data reduction is relatively straightforward, with the in-plane shear stress and shear modulus calculated using Equations [6.21] and [6.22]:3,25 t xy =

Gxy =

2TRo

(

4

p Ro - Ri

4

)

Dt xy Dt xy = Dg xy D(e 45 - e -45 )

[6.21]

[6.22]

where T is the applied torque, Ro the outer radial boundary and Ri the inner radial boundary of the cylinder. Shear strain is determined from the average of shear strains measured using the ±45° strain gauges. Failure initiates at the outer radius, with the in-plane shear stress at failure, Sxy, calculated by substituting the applied torque at failure into Equation [6.21]. The main disadvantage of this method is the cost and difficulty associated with tubular specimen fabrication and testing. Prohibitive material and fabrication costs and the need for specialised testing and gripping equip-

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ment have restricted the use of this test method. However, the method is frequently used to generate reference data for comparison with other test methods because the stress state within hoop-wound cylinders loaded in torsion approaches an ideal state of uniform shear.

6.3

Summary of test methods

The advantages and disadvantages of each test method are summarised in Table 6.1.

6.4

Comparison of data

A comparison of typical in-plane shear moduli obtained from a wide range of fibre-reinforced plastics tested using the plate-twist and the V-notched beam tests is shown in Table 6.2. As expected, the two sets of data are in general agreement, because the materials tested are essentially homogeneous in the through-thickness direction. In-plane shear modulus and ultimate failure stress (i.e. shear strength) data obtained from a variety of test methods for both unidirectional carbonfibre and glass-fibre composites are presented in Tables 6.3 and 6.4, with the coefficient of variation (%) shown in brackets. The results clearly show that the shear moduli measured using the ±45° tension and two-rail shear tests are consistently higher than the values determined with the V-notched beam test. The ±45° tension test consistently yields higher shear strength values than the other two methods.As a consequence of fibre scissoring, ultimate failure is delayed, with failure being mixed mode. However, damage in the form of ply cracking initiates at low strain levels, and therefore it is recommended that the test be terminated at g12 = 2.0%.

6.5

Recommendations and concluding remarks

The plate-twist test is capable of being used in conjunction with the Vnotched beam test to measure the shear properties of fibre-reinforced plastic composites. The range of materials which can be tested is diverse and not limited by the relative magnitude of property values. Testing is relatively straightforward, requiring only minimal instrumentation. The plate-twist is a non-destructive test allowing specimens to be re-used for further tests. Where material properties vary throughout a composite structure as a result of variations in fibre orientation and so on arising from the manufacturing process, the V-notched beam test can provide local values of shear moduli and in many cases the shear strength. The need to determine the

Advantages Shear modulus and strength obtainable Specimen preparation is straightforward Standard test equipment (no special loading jig) Data reduction is straightforward Can use for cyclic and environmental conditions ASTM and CEN/ISO standards Shear modulus and strength obtainable Additional in-plane elastic properties Specimen preparation is easy and economic Standard test equipment (no special loading jig) Uniform in-plane and through-thickness stress Can use for cyclic and environmental conditions Shear modulus and strength obtainable Compatible with most material types Stress state fairly uniform near specimen centre Data reduction is straightforward Can use for cyclic and environmental conditions ASTM ‘guide’ only

Test

±45° tension test

10° off-axis test

Rail shear test

Table 6.1. Advantages and disadvantages of shear test methods.

Large specimens/extensive preparation Specimens susceptible to machining defects Difficult to bolt/bond specimen to loading rails Special test fixture required Strain gauges required Large scatter in strength data

Only suitable for continuous aligned fibres Mixed-mode failure Three-element rosette required Data reduction is complex Sensitive to specimen/strain gauge misalignment No existing standard

Strain limit often required for strength Only suitable for continuous aligned fibres Special laminate layup required Strength dependent on number of layers Strain gauges or extensometers required

Disadvantages

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Advantages

Shear modulus and strength obtainable Compatible with most material types Small quantity of material required Data reduction is straightforward Suitable for use under environmental conditions ASTM ‘standard’ only

Shear modulus obtainable Compatible with most material types Stress state fairly uniform over entire specimen Easy and economic specimen fabrication Easy and economic testing and data reduction Can use for cyclic and environmental conditions ISO standard

Shear modulus and strength obtainable Compatible with most material types Stress state fairly uniform along specimen length Data reduction is straightforward Can use for cyclic and environmental conditions ASTM ‘standard’ only

V-notched beam test

Plate-twist test

Torsion of thin-walled tube

Large and expensive cylindrical specimens Extensive specimen preparation and testing Torsion facility and adhesively bonded grips Alignment fixture for specimen preparation Strain gauges required Non-uniform through-thickness shear stress

Not suitable for generating strength data

Accurate specimen machining required Special test fixture required Strain gauges required Non-uniform shear stress state ASTM test fixture not completely satisfactory Cannot be used under cyclic loading conditions

Disadvantages

120

Test

Table 6.1. (cont.)

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Table 6.2. Typical shear modulus (GPa) values. Material description

Plate-twist

V-notched beam

Chopped glass-fibre/polyurethane Polymethyl methacrylate (PMMA) Polyether ether ketone (PEEK) Glass-fibre random mat/polypropylene Glass-fibre chopped strand mat (CSM) Glass-fibre/polyester pultrusion Sheet moulding compound (SMC) Glass-fibre square weave fabric/epoxy Unidirectional XAS/914C carbon-fibre/epoxy Unidirectional AS4/3501-6 carbon-fibre/epoxy Unidirectional carbon-fibre/PEEK (APC-2)

0.29 1.20 1.30 1.69 2.16 3.04 4.80 5.00 5.08 5.40 5.84

— 1.56 1.14 — — 3.20 4.69 5.03 5.61 5.48 5.72

Table 6.3. Shear modulus (GPa) data for unidirectional fibre-reinforced systems (cv %). Test method

Carbon-fibre/epoxy

Glass-fibre/epoxy

Carbon-fibre/PEEK

V-notched beam ±45° tension Two-rail

4.31 (12.3) 4.83 (2.4) 4.75 (4.1)

5.86 (2.9) 6.99 (8.0) 6.79 (4.6)

5.19 (7.6) 6.57 —

Table 6.4. Shear strength (MPa) data for unidirectional fibre-reinforced systems (cv %). Test method

Carbon-fibre/epoxy

Glass-fibre/epoxy

Carbon-fibre/PEEK

V-notched beam ±45° tension Two-rail

50.3 (13.8) 115 (2.8) 67.9 (5.9)

90.9 (1.7) 167.4 (11.6) 85.4 (3.28)

50.0 (10.2) 58 —

failure mode occurring in each case is emphasised in Fig. 6.7. Further developmental work is required to eliminate specimen instability, and thus provide small front-to-back differences (1–2%) in shear strains and improved repeatability. The plate-twist and V-notched beam tests are complementary, offering designers and engineers the means of characterising the shear properties of an extensive range of composite materials.These two methods are relatively cost effective from both a fabrication and testing perspective, with data reduction being straightforward.

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Acknowledgements This chapter was written with the support of the Materials Measurement Programme, a programme of underpinning research financed by the United Kingdom Department of Trade and Industry. The author acknowledges the contributions of his colleagues Dr Graham Sims and Mr William Nimmo at the National Physical Laboratory, and Dr Paul Hogg, Queen Mary and Westfield College.

References 1. BS EN ISO 14,129: Fibre-reinforced Plastic Composites – Determination of In-plane Shear Modulus and Strength by ±45° Tension Test Method, 1997. 2. ASTM D 3518: ‘Standard test method for in-plane shear response of polymer matrix composite materials by tensile test of a ±45° laminate’, Annual Book of ASTM Standards, 100 Barr Harbor Drive, West Conshohocken, PA 19428, USA, Vol 15.03, 1997, 151–7. 3. S Chaterjee, D Adams and D W Oplinger, Test Methods for Composites, a Status Report. Volume III: Shear Test Methods, US Department of Transport, Federal Aviation Administration, Report DOT/FAA/CT-93/17, III, National Technical Information Service, Springfield, VA 22161, USA, June 1993. 4. R Byron Pipes, R A Blake Jr, J W Gillespie Jr, and L A Carlsson, Test methods, Delaware Composites Design Encyclopedia, Volume 6, eds L A Carlsson and J W Gillespie Jr, Technomic Publishing, Lancaster, PA, USA, 1990. 5. C C Chamis and J H Sinclair, ‘Ten-deg off-axis test for shear properties in fiber composites’, Experimental Mechanics, 1977 17(9), September, 339–46. 6. M-J Pindera, G Choksi, J S Hidde and C T Herakovich, ‘A methodology for accurate shear characterisation of unidirectional composites’, Journal of Composite Materials, 1987 21 1164–84. 7. ISO 527: Plastics – Determination of Tensile Properties. Part 5 – Test Conditions for Unidirectional Fibre-reinforced Plastic Composites, 1994. 8. F Pierron and A Vautrin, ‘The 10° off-axis tensile test: A critical approach’, Composites Science and Technology, 1996 56 483–8. 9. F Pierron and A Vautrin, ‘A new methodology for composite shear strength measurement using the 10° off-axis tensile test’, Proceedings of ECCM-7 (European Conference on Composite Materials), Volume 2, Institute of Materials, London, UK, Woodhead Publishing, May, 1996, 119–24. 10. ASTM D 4255: ‘Standard guide for testing in-plane shear properties of composite laminates’, Annual Book of ASTM Standards, 100 Barr Harbor Drive, West Conshohocken, PA 19428, USA, Vol 15.03, 1997, 199–208. 11. N Iosipescu, ‘New accurate procedure for single shear testing of metals’, Journal of Materials, 1967 2(3) 537–66. 12. ASTM D 5379: ‘Standard test method for shear properties of composite materials by the V-notched beam method’, Annual Book of ASTM Standards, 100 Barr Harbor Drive, West Conshohocken, PA 19428, USA, Vol 15.03, 1997, 235–47.

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13. D F Adams and D E Walrath, ‘Current status of the Iosipescu shear test method’, Journal of Composite Materials, 1987 21 494–507. 14. D W Wilson, ‘Evaluation of the V-notched beam shear test through an interlaboratory study’, Journal of Composites Technology and Research, 1990 12(3) 131–8. 15. W R Broughton, M Kumosa and D Hull, ‘Analysis of the Iosispecu shear test as applied to unidirectional carbon-fibre reinforced composites’, Composites Science and Technology 1990, 38 299–325. 16. H Ho, M Y Tsai and J Morton, ‘Numerical analysis of the Iosipescu specimen for composite materials’, Composites Science and Technology, 1993 46 115–28. 17. F Pierron, New Iosipescu Fixture for the Measurement of the In-plane Shear Modulus of Laminated Composites: Design and Experimental Procedure, Internal Report No. 940125, École des Mines de Saint-Étienne, Département Mécanique et Matériaux, France, January 1994. 18. E M Odom, D M Blackketter and B Suratno, ‘Experimental and analytical investigation of the modified Wyoming shear test fixture’, Experimental Mechanics, 1994 34(1). 19. N R Conant and E M Odom, ‘An improved Iosipescu shear test fixture’, Journal of Composites Technology and Research, 1995 17(1) 50–5. 20. J M Hodgkinson, Imperial College of Science, Technology and Medicine, London, UK, March 1999, private communication. 21. ASTM D 3044, ‘Standard test method for shear modulus of wood-based structural panels’, Annual Book of ASTM Standards, 100 Barr Harbor Drive, West Conshohocken, PA 19428, USA, Vol 4.10, 1998, 479–481. 22. G D Sims, W Nimmo, A F Johnson and D H Ferriss, Analysis of Plate-twist Test for In-plane Shear Modulus of Composite Materials, NPL Report DMM(A)54, 1992. 23. B Gommers, I Verpoest and P Van Houtte, ‘Further developments in testing and analysis of the plate twist test for in-plane shear modulus measurements’, Composites Part A, 1996 27 1085–7. 24. ISO 15,310: Fibre-Reinforced Plastic Composites – Determination of In-plane Shear Modulus by the Plate Twist Method, 1999. 25. ASTM D 5488: ‘Standard test method for in-plane shear properties of hoop wound polymer matrix composite cylinders’, Annual Book of ASTM Standards, 100 Barr Harbor Drive, West Conshohocken, PA 19428, USA, Vol 4.10, 1998, 248–259.

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7 Flexure J M HODGKINSON

7.1

Introduction

The use of flexural tests to determine the mechanical properties of resins and laminated fibre composite materials is widespread throughout industry owing to the relative simplicity of the test method, instrumentation and equipment required. It is also possible to use flexure tests to determine the interlaminar shear strength of a laminate (using a short beam), and this is dealt with in Chapter 8, and to investigate the properties of laminate faced sandwich beams with either honeycomb or foam cores. By careful design of the sandwich beam it is possible to assess not only the flexural and shear stiffness of the construction, but also the shear modulus and shear strength of the core, the tensile and compression moduli and strength of the facings, and to evaluate the bond between core and facings. Flexure may also be used to evaluate the interlaminar fracture toughness of laminates, as described in Chapter 9 of this book, and to assess the stiffness, strength and fatigue behaviour of more complex structures. In this chapter the discussion will be restricted to the flexural testing of simple laminated beams. There is a wide variety of standard test methods for flexure described by the National and International Standardization bodies. The details of the test methods recommended vary from one organisation to another, some being very precise, others allowing a wide degree of choice. Few of the available recommended test methods were developed specifically with high performance fibre-plastic laminated composites in mind, having been originally proposed for the mechanical testing of homogeneous solids. Amongst the exceptions here are those methods described by the American Society for Testing and Materials (ASTM),1 the Composites Research Advisory Group (CRAG)2 and the recently introduced International Standard.3 These organisations have all made some attempt to address the particular needs of these heterogeneous non-isotropic materials. Although it is frequently found that flexure tests give results which are very similar to those from other tests (tension and compression, for 124

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example) which are recommended for the acquisition of design data, it is generally recognised that test methods applying flexure as a means of loading do not produce results of design data quality. Data obtained from some flexure test methods have to be treated with caution, if not scepticism, because it is possible to achieve results which are a function of the method used, not reflecting in any way the properties of the material it was intended to measure. In general, flexure type tests are applicable to quality control and material selection where comparative rather than absolute values are required. As such, these types of test continue to be used widely because their relative simplicity allows a rapid assessment to be made with a minimum of fuss and technical expertise.

7.2

Three-point and four-point flexure tests

For flexure tests there is no involvement with end-tabs, or (normally) changes in the specimen shape, tests being conducted on simply supported beams of constant cross-sectional area. The two methods most usually used for the determination of flexural properties of laminates are the three-point and four-point tests illustrated schematically in Figs. 7.1 and 7.2, respectively. A flat rectangular specimen is simply supported close to its ends and either centrally loaded in three-point bending or by two loads placed symmetrically between the supports, giving four-point bending. Also shown in Figs. 7.1 and 7.2 are the shear force and bending moment diagrams related to the particular loading regimes. Clearly stress concentrations exist at the loading points but in four-point loading, between the inner loading points, there is a constant bending moment. Figure 7.3 shows the variation in normal stress, caused by bending moment, and shear stress, caused by shear force, assuming a rectangular specimen cross-section. In Figs. 7.1 to 7.3 the material properties are assumed to be uniform through the thickness because they are in unidirectional composites or isotropic materials. Under these circumstances the normal stress varies linearly from a maximum in compression on one surface to an equal maximum in tension on the other surface, passing through zero at the mid-plane, which is usually called the neutral axis. The maximum normal stress is given by Equation [7.1]: s=

6M bh 2

[7.1]

where M is the bending moment, with b and h being the specimen width and thickness, respectively. The distribution of shear stress is parabolic, with a maximum at the neutral axis and zero at the outer surfaces of the beam; the maximum value is given by Equation [7.2]:

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h

S L

Fs = P /2

Fs = P /2

Shear force diagram

M = PS/4

Bending moment diagram

7.1 Three-point flexure test, together with shear force and bending moment diagrams.

t=

3Fs 2bh

[7.2]

where Fs is the shear force on the specimen cross-section. The flexural response of the beam is obtained by recording the load applied and the resulting strain. The strain can be measured by bonding a strain gauge to the tensile surface of the beam, or by measuring the displacement at the centre of the beam and assuming that beam theory4 applies, so that strains can be calculated. The bending moment, M, is a function of the measured load and specimen geometry, so that the applied stress

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P

h Si So L

Fs = P /2

Fs = P /2

Shear force diagram

M = P(So - S i)/4

Bending moment diagram

7.2 Four-point flexure test, together with shear force and bending moment diagrams.

can be calculated from Equation [7.1] and the full stress–strain behaviour of the beam in bending can be obtained. The states of stress in specimens subjected to three- or four-point bending tests are somewhat different and may lead to differences in the results. The bending moment in a three-point bend test increases linearly from zero at the supports to a maximum under the central loading point, as shown in Fig. 7.1, whereas the shear force (and hence the interlaminar shear stress at the midplane) is uniform along the length of the beam. In four-point bending the bending moments increase linearly from zero at the supports to a maximum at the loading points and are constant between these points, as shown in Fig. 7.2. The shear force and interlaminar shear stress are zero

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Mechanical testing of advanced fibre composites sc

h

b

Cross-section

st

t

|sc|= |st|= 6M/bh2

t = 3Fs /2bh

Normal stress

Shear stress

7.3 Variation of normal stress and shear stress in a flexure test.

between the loading points, so that this central portion of the beam is subjected to a pure bending moment. From the point of view of the state of stress, the four-point test is the more desirable of the two methods but the three-point test is easier to carry out. The flexural strength is the stress on the surface of the specimen at failure, which should be accompanied by the breaking of fibres, rather than interlaminar shear. The strength is calculated using the maximum bending moment, corresponding to the failure load, in Equation [7.1], and assumes a linear stress–strain relationship up to failure. True flexural failure is encouraged by the use of a large loading span to specimen thickness ratio, because the span of the beam has no influence on the interlaminar shear stress but a large span results in a higher bending moment, promoting longitudinal failure. Unfortunately large span-to-thickness ratios produce large deflections, under load, which make it necessary to take account of horizontal forces developed at the supports when calculating the appropriate bending moment.

7.3

Comparison of recommended test methods

The aim here is to draw attention to some of the inconsistencies (and possible pitfalls when carrying out tests) which exist between some of the flexural test methods which have been published. It is clearly not possible to consider all of the national standards, so the comparison will be limited to those which give a good example of general recommended practice for the testing of fibre-reinforced plastics materials. These include those from the American Society for Testing and Materials (ASTM D 790M-93),1 the

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Composites Research Advisory Group (CRAG),2 BS 2782 method 10055 and ISO-14125.3 A detailed reading of these recommendations reveals that prior to the publication of ISO-14125 there was no agreement on virtually any aspect of the test method to be used between the three organisations. Areas of conflict include: specimen dimensions, span-to-thickness ratios, the use of three- or four-point loading arrangements, loading and support nose radii, loading rate, minimum overhang of specimen length beyond the support points and the calculations to be used when making allowance for large displacements.

7.3.1 Specimen dimensions and testing arrangement The ASTM and BSI specifications allow a wide freedom of choice in terms of specimen dimensions, as long as the cross-section is rectangular and specific span-to-thickness (S/h) ratios are adhered to. The ASTM specification allows a series of different S/h ratios (16 : 1, 32 : 1, 40 : 1 and 60 : 1) in both three- and four-point bending, BSI just one (16 : 1), and that in three-point loading only. ASTM offers two arrangements for four-point loading, with the loading points set at either 1/3 or 1/4 of the support span. The ASTM have attempted to satisfy the requirements of a range of industries with a number of reinforced materials in mind, whilst the BSI standard is restricted to textile glass-fibre reinforced plastics. On the other hand, CRAG, which is also restricted to the three-point loading arrangement, requires a particular (2 mm) laminate thickness, and specifies S/h ratios dependent on laminate layup and the type of fibre used. This is clearly aimed at high performance materials. Table 7.1 summarizes the dimensional possibilities for specimens within the ASTM, CRAG and BSI specifications. Table 7.2 gives the possibilities for support and loading nose radii, span-to-thickness ratios and loading (or strain) rate. The ASTM specification includes a series of tables which indicate the appropriate specimen width, length, support spans (and loading span for Table 7.1. Dimensional possibilities for flexure specimens in several specifications. Specification

Thickness (mm)

Width (mm)

Length (mm)

ASTM D790M BSI 2782 CRAG

1–25 1–50 2

10–25 15–80 10

50–1800 20 h 100

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Table 7.2. Possibilities for support and loading nose radii, span-to-thickness ratios and loading rate in several specifications. Specification

Support nose radius (mm)

Loading nose radius (mm)

Span-tothickness ratio

Strain rate (mm mm-1) or failure time

ASTM D790M BSI 2782 CRAG

3–1.5 h 2 3, 5

3–4 h 5 5, 12.5

16, 32, 40, 60 : 1 16 : 1 16, 20, 25, 40 : 1

0.01 and 0.1 0.01 Failure time 30–180 s

Table 7.3. Advice in the CRAG specification on S/h ratios for particular fibre types. Reinforcement

Fibre alignment to beam axis

Span-to-thickness ratio

Unidirectional carbon Unidirectional carbon Woven carbon Unidirectional glass Unidirectional glass Woven glass Woven Kevlar

0° 90° 0°/90° 0° 90° 0°/90° 0°/90°

40 : 1 25 : 1 25 : 1 20 : 1 20 : 1 20 : 1 16 : 1

four-point testing) and rate of crosshead motion (based on the strain rate of 0.01 mm mm-1) for the full range of specimen thicknesses and spanto-thickness ratios allowed. This is all very well but, given the range of possibilities, it is not clear under which set of conditions a particular type of material should be tested in order to obtain meaningful results. The CRAG document is far more specific and includes advice on material type, fibre alignment and appropriate span-to-thickness ratio given in Table 7.3. ISO-14125, perhaps understandably, appears to be an amalgamation of the previous three, although there were undoubtably influences from other national organisations in its drafting. It covers both three- and four-point (in this case only the 1/3 option is available) bending methods, tightens up on specimen thickness, length and width possibilities, is coherent in terms of loading and support nose radii and loading rate, and advises on what types of material should be tested under specific span-to-thickness ratios. Tables 7.4 and 7.5 give the specimen dimensional possibilities for three- and four-point bending tests, respectively, in this International Standard.

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Table 7.4. Recommended specimen dimensions for different material types for three-point flexure in ISO-14125. Material

Length (mm)

Span (mm)

Width (mm)

Thickness (mm)

Class Class Class Class

80 80 60 100

64 64 40 80

10 15 15 15

4 4 2 2

I II III IV

Class I: discontinuous fibre-reinforced thermoplastics. Class II: mat, continuous mat, fabric and mixed format reinforced plastic. DMC (dough moulding compound), BMC (bulk moulding compound) and SMC (sheet moulding compound). Class III: Transverse (90°) unidirectional composites. Unidirectional (0°) and multidirectional composites with 5 < E11/G13 ≤ 15 (for example, glass-fibre systems). Class IV: Unidirectional (0°) and multidirectional composites with 15 < E11/G13 ≤ 50 (for example, carbon-fibre systems).

Table 7.5. Recommended specimen dimensions for different material types for four-point flexure in ISO-14125. Material

Length (mm)

Support span (mm)

Loading span (mm)

Width (mm)

Thickness (mm)

Class Class Class Class

80 80 60 100

66 66 45 81

22 22 15 27

10 15 15 15

4 4 2 2

I II III IV

NB Classes as given in Table 7.4.

7.3.2 Calculations 7.3.2.1 Flexural modulus In each of the specifications the flexural modulus is defined in the same way, such that for a three-point bending test: Ef =

S3m 4bh3

[7.3]

where Ef is the flexural modulus, S is the support span, m is the slope of the load/deflection curve, with b and h being the width and thickness of the beam, respectively.

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As was mentioned previously, ASTM D 790 offers two options for the four-point flexure test. In the first the loading span is 1/3 of the support span, in the second it is 1/2 of the support span. ISO-14125 offers only the first of these options. The flexural modulus is given by Equations [7.4] and [7.5]: Option 1 Ef = 0.21

S3m bh3

[7.4]

Option 2 Ef = 0.17

S3m bh3

[7.5]

It can be seen from Equations [7.3]–[7.5] that the precise measurement of the support span and specimen thickness are crucially important, as they are both raised to the power 3. 7.3.2.2 Maximum stress The maximum stress at the outer surface of the beam in three-point bending is also defined in the same way by each of the specifications considered here, such that: s=

3PS 2bh 2

[7.6]

where s is the stress on the outer surface of the specimen and P the applied load. ASTM D 790, BSI 2782 and ISO-14125 each consider what correction should be applied to the stress equation if the beam experiences large deflections (greater than 10% of the support span). Table 7.6 shows the discrepancies which exist in these recommendations. CRAG makes no comment on a correction. It will be noted that whilst these corrections are similar, they are not precisely the same.

Table 7.6. Different ways of correcting for large deflections in a three-point bend test. Specification

Corrected stress equation

ASTM D790

s =

BSI 2782 and ISO-14125

3PS 2bh 2 3PS s = 2bh 2

6D 2 4hD ˆ Ê 1+ 2 - 2 Ë S S ¯ 2 4D ˆ Ê 1+ 2 Ë S ¯

D is the deflection of the beam at the centre of the support span.

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Table 7.7. Ways of correcting for large deflections in four-point bend tests. Standard

Corrected stress equation

ASTM D790 and ISO-14125 (loading span 1/3 of the support span)

s =

ASTM D790 (loading span 1/2 of the support span)

4.7D 2 7.04hD ˆ PS Ê 1+ 2 Ë bh S2 S2 ¯ 3PS Ê 10.9hD ˆ s = 14bh 2 Ë S2 ¯

The maximum stress at the outer surface of a beam tested in four-point flexure with the loading span 1/3 of the support span is given by both ASTM D 790 and ISO-14125 as: s=

PS bh 2

[7.7]

and in the case of ASTM, where the loading span can be 1/2 of the support span, the maximum stress is given by: s=

3PS 4bh 2

[7.8]

Again, corrections are recommended for large deflections and those given by both the ASTM and ISO documents are given in Table 7.7. It is, perhaps, interesting to note from Tables 7.6 and 7.7 that for the threepoint bend test correction the BSI standard has been adopted by ISO as opposed to that from the ASTM standard, whereas in the case of the fourpoint bend test ISO have been happy to adopt the ASTM correction.

7.4

Failure modes

Whilst a wide range of failure modes might occur under flexural loading, dependent on the particular test method used and the type or layup of material under test, these are broadly very similar for three- or four-point flexure tests. The types of failure likely to be observed are shown in Fig. 7.4, not all of which might be considered as acceptable flexural failures, those including evidence of interlaminar shear being particularly suspect. Certainly for specimens with axially aligned fibres one would not expect to see interlaminar shear accompanying failure, as this would suggest that the span-to-thickness ratio used in the test was too low.

7.5

Typical data

A number of investigations have been conducted at Imperial College into various aspects of the flexural behaviour of laminated composites.

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134

Mechanical testing of advanced fibre composites Tensile fracture of fibres

Tensile fracture of outer surface

Compression fracture of outer surface

Tensile fracture with interlaminar shear

Compression fracture with interlaminar shear

Interlaminar shear

7.4 Schematic of possible failure modes in three- and four-point flexural tests.

These were carried out over a number of years by different research students.

7.5.1 Programme 1 The first of these projects6 was a comparison of the three test methods1,2,5 referred to above (i.e. ASTM D 790, CRAG and BS 2782). At the time there was a general dissatisfaction with test methods for advanced fibre composite materials, and it was anticipated that the data from these three test methods might well be quite different. Since the choices of specimen shape and test arrangements are quite wide, and vary from standard to standard, a 2 mm thick laminate was decided upon (CRAG only allows this thickness); all other testing factors were followed for the particular standard being investigated. The material used was Ciba Geigy (now Hexcel) XAS/913 CFRP (carbon-fibre reinforced plastic), with unidirectional and a variety of other layups being tested. Here only the unidirectional data will be discussed; it is presented in Table 7.8, together with the other test parameters. In each case at least five specimens were tested. The results for flexural modulus are reasonably consistent, in the range

2 2 2 2 2 2 2 2

25

25

25

25

25

25

15

10

ASTM 3-point ASTM 3-point ASTM 3-point ASTM 3-point ASTM 4-point ASTM 4-point BSI 3-point CRAG 3-point

h (mm)

b (mm)

Method

40

16

30/60

20/60

60

40

32

16

S/h

100

50

150

150

150

100

80

50

L (mm)

5

2

3.2

3.2

3.2

3.2

3.2

3.2

Load roller radius (mm)

12.5

5

3.2

3.2

3.2

3.2

3.2

3.2

Support roller radius (mm)

5.0

1.0

12.0

13.3

12.0

5.3

3.4

0.9

Loading rate (mm mm-1)

59.0 ±5% 103.2 ±4.2% 101.7 ±4.4% 116.7 ±4.5% 132.4 ±7.7% 144.9 ±7.2% 73.7 ±7.0% 114.9 ±1.9%

E (MPa)

1370 ±4.1% 1440 ±3.2% 1490 ±7.3% 1560 ±6.2% 1607 ±6.5% 1441 ±6.7% 1460 ±5.3% 1720 ±6.4%

smax (MPa)

Table 7.8. Test conditions adopted for a comparison between different test methods and the flexural modulus and strength results obtained for XAS/913 CFRP.

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100–117 GPa, as long as the span-to-thickness ratio is greater than the 16 : 1 allowed under the ASTM and British Standards. At a span-tothickness ratio of 16 : 1 the elastic modulus measured is approximately onehalf of the correct value. Clearly such a low span-to-thickness ratio is inappropriate for these extremely stiff materials. On the other hand there is a suspicion that large span-to-thickness ratios may lead to somewhat higher strength values being recorded. Note here the somewhat higher values obtained with the CRAG specimens and the high span-to-thickness ratio ASTM specimens. It appears that the 16 : 1 span-to-thickness ratio is entirely satisfactory for the measurement of strength in these materials. Whilst it true that there are other influences at play in this series of experiments, for example differences in specimen width, overhang and load and support roller radii, by far the most important factor is the span-tothickness ratio used. One final observation is that the results from the four-point tests are not convincingly better than those from three-point tests. The flexural modulus is rather high in both cases examined here, although the strengths recorded are similar to those from three-point tests. Figure 7.5 shows typical failures for the unidirectional specimens tested under the various regimes of the programme. It should be noted that all of the three-point flexure specimens failed by complete and brittle fracture of the specimen, across the width, under the central loading roller, except those tested at a span-to-thickness ratio of 16 : 1. For these specimens there was evidence of damage under the central roller on both tension and compression surfaces; however, there was no complete fracture of the specimens. The four-point bend specimens also fractured in a brittle manner across their width – fractures which appear to have initiated under the central loading rollers, causing not only width-wise fracture but also interlaminar failures between these central rollers.

7.5.2 Programme 2 A second programme of three-point flexure tests7 involved three different CFRP materials from Hexcel: XAS/913, XAS/914 and HTA/6376.The layup tested in all cases was unidirectional, with both axial and transverse specimens being investigated. The tests were carried out according to the CRAG recommendations for specimen dimensions, roller diameters and testing rate. Five specimens were tested in each case. The results are shown in Table 7.9, where it can be seen that the flexural modulus and strength values for XAS/913 (axial) are very similar to those of the previous study using the CRAG test. It appears from these results that XAS/914 (axial) has a similar flexural modulus to that of XAS/913 (axial). This might be expected since the composite has the same fibre in

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7.5 Typical failures for unidirectional three- and four-point flexure specimens: (a) ASTM 3-point, 16:1; (b) ASTM 3-point, 32:1; (c) ASTM 3-point, 40:1; (d) ASTM 3-point, 60:1; (e) CRAG 3-point, 40:1; (f) BSI 3-point, 16:1; (g) ASTM 4-point, 1/4 points, 40:1.

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Table 7.9. Flexural modulus and strength data for several CFRPs with either axial or transverse unidirectional fibres. Material

Flexural modulus (GPa)

Flexural strength (MPa)

XAS/913 (axial) XAS/914 (axial) HTA/6376 (axial) XAS/913 (transverse) XAS/914 (transverse) HTA/6376 (transverse)

113.0 ± 2% 112.3 ± 2% 119.5 ± 5% 9.7 ± 11% 8.3 ± 22% 10.0 ± 5%

1642.5 ± 2% 1786.9 ± 2% 1924.8 ± 5% 99.8 ± 16% 83.0 ± 26% 109.1 ± 12%

each case, the resin having little influence on the modulus value. The strength of XAS/914 (axial) is, however, significantly greater, with the strength of HTA/6376 (axial) being greater still and with a slightly increased flexural modulus. The scatter in the axial data is quite low, but for the transverse data it is greatly increased. Given the degree of scatter in the flexural modulus data between the three materials, it would be difficult to suggest that there was much difference. Although the transverse strength data are subject to a similar degree of scatter, it does appear that the HTA/6376 material is superior to the other two. All of the fractures were brittle, across the width of the specimens, under the central loading roller.

7.6

Steel versus soft lined rollers

It has been mentioned previously that the loading rollers introduce a formidable stress concentration in flexure tests, even under four-point loading. A means of mitigating this effect is to line the rollers with a soft plastic or rubbery material, or even replace the steel rollers with plastic ones. This makes the specimen effectively useless for the measurement of flexural modulus unless a strain gauge is used, because there is significant contact deflection of the relatively soft roller material when load is applied. However, this approach does introduce the possibility of a more ‘realistic’ flexural failure. ISO 14125 allows this option, suggesting that ‘a thin shim, or cushion, between the loading member and the specimen may be used to discourage failure of the compressive face of the specimen’. What ISO actually proposes is that a 0.2 mm thick shim of polypropylene has been found to work well in this respect. Hexcel T300/913 CFRP specimens, 2 mm thick (150 mm long and 25 mm wide) with unidirectional axially aligned fibres, were tested8 in three- and

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four-point flexure according to ASTM D790. A first series of experiments investigated the effect in three-point loading (S/h of 60 : 1) of varying the diameter of the central steel loading pin, whilst keeping the steel support pin diameters constant at 6 mm. The results shown in Table 7.10 indicate, as might be predicted, that as the loading pin diameter is increased from 6 mm to 16 mm (all allowed in the standard for this thickness of material), the measured strength increases monotonically. A second series of experiments was carried out on specimens from the same 2 mm thick laminate, with specimens of the same size as the first series of experiments, in three-point loading (S/h 60 : 1) and both options of fourpoint loading allowed under the ASTM standard (in both cases the outer support span was 120 mm, with the inner loading span being either 60 mm or 40 mm). The support and loading rollers were always 6 mm in diameter (the only diameter allowed under the standard) and were either steel or plastic. The results are shown in Table 7.11. It is clear that the strength measured using the plastic pins is significantly higher in all cases. The failure modes were quite different, dependent upon whether the pins used were steel or plastic. When plastic pins were used no damage was noted on the compression side of the specimen, but multiple fibre failure occurred on the tension side in both three- and four-point loading, giving the surface a brush-like appearance, as shown in Fig. 7.6. Failure using the steel pins was catastrophic and occurred across the width, under the central loading pin(s), for three- and four-point loading arrangements, as noted previously.

Table 7.10. Influence of steel loading pin diameter on the flexural strength of T300/913 CFRP in three-point flexure. Pin diameter (mm) Strength (MPa)

6 1685

8 1726

10 1757

16 1766

Table 7.11. Flexural strength of T300/913 CFRP using steel and plastic loading pins. Experiment

Failure stress (plastic pins) (MPa)

Failure stress (steel pins) (MPa)

Three-point loading Four-point loading (1/2 span) Four-point loading (1/3 span)

1955 1640 1832

1685 1519 1590

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7.6 Brush-like appearance of fractured CFRP specimen tested using plastic loading and support pins in four-point loading.

7.7

Through-thickness flexure

Chapter 8 of this book covers test methods for the measurement of throughthickness elastic and strength properties of composite laminates. It does, however, seem more appropriate to introduce here a novel approach to through-thickness testing in flexure. Mespoulet9 designed a beam-type specimen, shown in Fig. 7.7, which consisted of a central region of composite machined from a 160-ply, 20 mm thick unidirectional laminate of Hexcel T300/914 CFRP, the composite being bonded to epoxy resin ‘arms’ in a jig into which the liquid epoxy was poured and allowed to cure. The length of the central composite section was 17 mm, and its cross-section was waisted by grinding to give 4 mm ¥ 4 mm at the centre and 8 mm ¥ 8 mm at the arms. The orientation of the fibres in the central region when under test could be in the 1–3 or 2–3 direction (i.e. not along the axis of the specimen), dependent upon how the specimen was orientated with respect to the loading jig. Eight specimens of were tested in four-point flexure with an outer span

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40 4¥4

8 8

specimen

epoxy

1.5

epoxy

15 80 100

7.7 Through-thickness flexure specimen. Dimensions are in millimetres.

of 80 mm and an inner span of 40 mm (i.e. at an effective span-to-thickness ratio of 20 : 1) to determine the through-thickness (1–3) failure stress, which was found to be 105 MPa. Specially designed in-plane transverse tension specimens in this same programme, testing thick laminates, gave a failure stress of 96.9 MPa. It should also be noted that in-plane transverse tension specimens from a 2 mm thick laminate of equivalent material (XAS/914), using the CRAG recommendations failed at 83 MPa (see Table 7.9).

7.8

Conclusions

Whilst it has to be admitted that data from flexure tests will always be viewed (with good cause) with a certain amount of suspicion, the test does provide a relatively straightforward, easy to use and economical technique for qualifying materials. This chapter has concerned itself with laminated beams of one sort or another; there are, however, a wide range of other types of beam and structure which the technique can be used for, with success. Even within the restricted remit of this book, the flexure technique has been shown to be a useful adjunct to the overall testing portfolio, finding use not only in the description of in-plane and out-of-plane laminate properties (both in this chapter), but also in shear behaviour (chapter 6) and interlaminar fracture behaviour (chapter 9). This is a testing technique which should not, and will not, be dismissed lightly.

References 1. ASTM D790M-93, ‘Standard test methods for flexural properties of unreinforced and reinforced plastics and electrical insulating materials’, American Society for Testing and Materials, Annual Book of ASTM Standards, Vol. 08.01, 1993. 2. P T Curtis (ed), CRAG Test Methods for the Measurement of the Engineering Properties of Fibre-reinforced Plastics, Royal Aircraft Establishment, Technical Report 88012, February 1988.

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3. International Standards Organisation (ISO-14125), Fibre Reinforced Plastic Composite – Determination of Flexural Properties, 1998. 4. A Morley, Strength of Materials, 9th Edition, Longmans, London, 1940. 5. British Standards Institute, BS 2782, British Standard Methods of Testing Plastics, Part 10, Glass reinforced plastics, Method 1005, Determination of Flexural Properties. Three Point Method, 1977. 6. N R Sottos, J M Hodgkinson and F L Matthews, ‘A practical comparison of standard test methods using carbon fibre reinforced epoxy’, Proceedings of the Sixth International Conference on Composite Materials and Second European Conference on Composite Materials, Imperial College, London, Elsevier Applied Science, 1987. 7. P Francotte, J M Hodgkinson and R Keunings, Experimental and Theoretical Analysis of the General and Micromechanical Behaviour of Composite Materials, Report of joint project between Imperial College and Université Catholique de Louvain, 1993. 8. R Grothaus, J M Hodgkinson and K Kocker,‘Interpretation of flexural tests using Weibull strength theory’, Proceedings of the 3rd International Conference on Deformation and Fracture of Composites, The Institute of Materials, Guildford, UK, March 1995, 269–76. 9. S Mespoulet, Through-thickness Test Methods for Laminated Composite Materials, PhD Thesis, Centre for Composite Materials, Imperial College, London University, UK, January 1998.

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8 Through-thickness testing* W R BROUGHTON

8.1

Introduction

Interlaminar (out-of-plane) stresses, combined with inherently low through-thickness (T-T) strength properties, especially in tension, are primarily responsible for damage initiation and eventual structural failure of layered composite materials. T-T properties of laminated composite are essentially matrix dominated and, as a result, are often significantly lower than the in-plane stiffness and strength properties of the material. There is also a tendency to associate interlaminar stresses with ‘thick’ sections; however, interlaminar stresses and strains may be induced in ‘thin’ laminates through the application of membrane loads (i.e. in-plane loads). Engineering structures are often unavoidably complex, consisting of a number of geometric features which induce interlaminar stresses and strains. High stress gradients are present in regions such as free edges (stress-free boundaries), curved edges (e.g. bolt holes), ply termination, thickness changes (e.g. ply drop-off or taper) and bolted or bonded joints. Until recently, the general tendency has been to use two-dimensional (2-D) (plane stress) analysis to evaluate structural response to three-dimensional (3-D) loading configurations. Three-dimensional finite element analysis, now in common use, frequently requires a full complement of in-plane and T-T properties, especially for those ‘difficult but real’ aspects of design where the composite, to perform its function, has to be shaped (e.g. flanged) and connected (e.g. bonded) to the remainder of the system. The need for T-T data poses a major problem; with the exception of shear, there are no recognised national or international standards available for generating reliable design data. As a consequence, designers and engineers rely on in-plane data or ad hoc tests to determine structural performance. This approach is clearly unsatisfactory, as the use of the data will result in either underdesigned or overdesigned structures.1–3 * Crown copyright

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Research has been undertaken worldwide into test methods and design procedures for in-plane properties of fibre-reinforced plastic composites. As a result, a supporting infrastructure of test methods is beginning to be established on an international basis, and these are discussed in other chapters of this book. Considerably less research and development of test methods suitable for the measurement of T-T properties has been undertaken, but there has been a continuing interest for many years and the available literature has been critically reviewed.1,2,4 This chapter evaluates the current status of test methods for measuring T-T properties under tensile, compressive and shear loading. Each method is examined in terms of the level of standardisation, elastic and strength properties obtained, material suitability, material thickness requirements, specimen fabrication, test apparatus, methods of data measurement and data reduction procedures. Consideration has also been given to both the practicality of using the test method in an industrial environment, in terms of ensuring ‘fitness for purpose’, and to the degree of uniformity of stress distributions throughout the test geometry. In most cases, the issue of test geometry and associated dimensions is still to be resolved.

8.2

General issues

A problem with many T-T test methods is the need to fabricate thick samples in order to machine specimens in the T-T direction. Fabrication of specimens with thicknesses of the order of 20 mm or greater is expensive and often difficult, with process induced stresses becoming increasingly important as the thickness is increased. Residual stresses, which are strongly influenced by processing history, can have a significant effect on the engineering properties of laminated structures by inducing warpage, fibre buckling, matrix microcracking and delaminations. Residual stresses arise from resin chemical shrinkage, as a result of curing and differences in thermal contraction between adjacent plies on cooling the laminate from the cure temperature. The net effect is that the residual strength properties of a laminate are likely to be diminished. The most familiar problem associated with processing thermoset-based composite systems is material degradation, induced through exothermic chemical reaction of the matrix. The risk of material degradation exists when the dissipation of liberated heat through thermal conduction is slow. In this case, the internal temperature may be elevated to levels that induce irreversible thermal damage. A second concern relates to the complex temperature and degree of cure gradients that develop in thick sections during the curing process. These gradients may induce a non-uniform state of cure through the laminate thickness. Non-uniform curing can produce poor con-

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solidation, leading to undesirable volume fraction gradients and entrapped volatiles or voids. Defects such as voids can significantly degrade matrix-dominated properties. Interlaminar shear strength diminishes by approximately 7% for each 1% increase in void content, for void contents in excess of 2%.5,6 Increasing the size (thickness) of a testpiece will lower the ‘apparent’ interlaminar shear and tensile strengths, as the number of critical flaws can be expected to increase with additional material. Thus, the detrimental effect of voids on interlaminar properties can be expected to be more evident when testing thick sections. The existence of size effects on interlaminar strength implies a need for exercising caution when using test coupon data as allowable design stresses (design allowables) for large composite structures, particularly where only a small volume of material is subjected to interlaminar tension. Interlaminar tensile data may result in a significant overestimation of structural strengths, especially if larger structures have higher levels of inherent defects than the test specimens.5 The assessment of test geometries for laminated composite materials would be incomplete without consideration being given to the influence of end and edge effects, and stress concentrations on stress uniformity. Saint Venant’s Principle, often neglected when developing mechanical test methods for measuring homogeneous isotropic elastic materials, is fundamental for determining a suitable gauge length, where a uniform stress and strain state are induced, and local effects caused by clamping of the specimen may be neglected. For fibre-reinforced plastics loaded along the T-T axis, the characteristic decay length over which the end effects are significant (greater than 1%) is, in general, smaller than for isotropic materials. The characteristic decay length can be determined in terms of geometric and material parameters.7 It should also be added here that, whereas the test methods discussed in this chapter may be suitable for the measurement of strength in unidirectionally oriented fibre-reinforced laminates, it does not follow that the same specimen shapes could measure the true strength for multidirectional materials, where the edge effects, evidenced by interlaminar stresses, are more severe. Stress concentrations at the specimen ends (loading zones) will often lead to premature failure in these regions. To ensure failure occurs within the gauge length, a number of tensile and compressive test methods employ waisted specimens, with the radius being either circular or elliptical. High stresses and strains can be expected at the intersection between the gauge length and the necking radius. These stresses will almost certainly induce premature failure in these zones. The use of large radii (20–30 mm) combined with plastic deformation of the composite should reduce the stress concentration to almost unity.

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A major problem of measuring T-T properties involves the testing of relatively thin laminates (<10 mm thick). To facilitate testing of thin laminates, two or more layers of the composite material may need to be bonded to form a sandwich construction. It is important that the positions of bondlines do not correspond to geometric features which act as stress concentrators and that material properties remain unaffected by the adhesive joints (i.e. similar properties to those of the integral/monolithic material).

8.3

Tensile test methods

This section provides an evaluation of direct and indirect loading configurations commonly used for measuring T-T tensile properties of fibrereinforced plastic composites. Test methods considered include: • • • • • •

square section block square section block with plain radius or elliptically waisted profile square section waisted block with a parallel gauge section I-section C-section closed ring.

The first three of these test methods are direct loading configurations, with the load introduction being via metallic end-loading bars.1,3,4 This approach assumes that loading bars can be successfully bonded to the specimens using commercially available adhesives, which may be the situation for thermoset resin-based systems, but is not in the case of fibre-reinforced thermoplastics. Difficulties encountered in transferring load to fibrereinforced thermoplastics have necessitated the development of the Isection for measuring T-T tensile strengths.8 Applied bending moments in sections of significant curvature can also produce direct T-T tensile stresses. Such bend test specimens include semicircular and semi-elliptical curved beams.9,10 Typical examples of bend specimens are the C-section and closed-ring specimens. These test geometries offer a means of determining the ‘apparent’ interlaminar tensile strength of ‘thin’ composite sections.

8.3.1 Square section block The simplest approach is to load a parallel-sided square block directly via adhesively bonded metallic loading bars with the tensile load applied along the T-T axis. This cross-sectional shape is preferable, as the geometry facilitates the measurement of lateral strains, which are required for the determination of Poisson’s ratios. Circular cross-sections are incompatible with lateral strain measurements for anisotropic materials.

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Reliable elastic property measurements can only be guaranteed when the state of stress over the entire gauge length is sufficiently uniform, and although T-T dimensions of 150 mm or greater (similar to the length recommended for in-plane tests) will facilitate this precondition, the cost of producing such thick laminates is usually prohibitive. Specimens with a large T-T dimension are also far more prone to process and machineinduced damage, so that residual strength can be expected to decrease with thickness. The use of short specimens with a length-to-width ratio of 2 : 1, or even lower4 where special precautions are taken to reduce end effects, should guarantee a relatively uniform stress state at the specimen midsection, making them suitable for elastic property determination. Short square section blocks when loaded in tension are only suitable for measuring elastic constants. Failure consistently occurs at the adhesive joints between the specimen and the metallic loading bars for all but the weakest materials, thus invalidating the strength data obtained. The results presented in Table 8.1 demonstrate that rectangular specimens 15 mm square, machined from 20 mm and 40 mm thick laminates, are capable of providing reliable elastic property data. Table 8.1 presents T-T test results from waisted and unwaisted specimens fabricated from unidirectional T300/924 carbon-fibre reinforced epoxy composite with a fibre volume fraction, Vf, of 60%. Work in 1998,4 including both finite element and experimental evidence on T300/914 unidirectional carbon/epoxy, reports that 6 mm square section specimens of thickness as low as 6 mm can also be used to determine elastic constants with an acceptable degree of accuracy, provided end effects and loading misalignments are minimised.

Table 8.1. T-T tensile properties of unidirectional T300/924 carbon fibre/epoxy.1 Test method

E33 (GPa)

n31

n32

S33 (MPa)

15 mm square block (40 mm thick) 15 mm square block (20 mm thick) 25 mm square, plain radius block waisted to 16 mm (40 mm thick) 25 mm square, radius waisted block with parallel-sided gauge section (38 mm thick)

9.9 ± 0.1

0.019 ± 0.002

0.55 ± 0.01

n/a

9.9 ± 0.4

0.020 ± 0.002

0.51 ± 0.01

n/a

n/a

n/a

n/a

78 ± 7

9.5 ± 0.1

0.020 ± 0.01

0.47 ± 0.01

71 ± 6

E33 = Through-thickness elastic modulus, n31 and n32 = axial and transverse through-thickness Poisson’s ratios, respectively by, S33 = through-thickness strength.

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A major disadvantage is in the number of strain gauges (four biaxial rosettes) required for the highest accuracy measurement of axial and transverse strains. A biaxial strain gauge with an active length of 2 mm is bonded to each face of the specimen at the mid-section, with gauges aligned parallel and perpendicular to the loading direction to measure axial and transverse strains, respectively. A nine channel data acquisition system is required to monitor and record strain measurements and applied load. Elastic moduli are obtained from the linear-elastic region of the stress–strain curve. The T-T elastic modulus is the average value of the four axial measurements. Poisson’s ratio values in the two transverse directions are the average values calculated from axial and transverse strain measurements for the two sets of opposing faces. Strain averaging accounts for possible bending strains caused by small deviations in specimen or load alignment. Strain gauge numbers could possibly be reduced if there was sufficient confidence in the quality and alignment of the specimen. Axial and transverse extensometers may also be used to measure the T-T elastic properties of 40 mm thick material. However, difficulty may be encountered in mounting these devices to the specimens. Specimens are usually machined roughly to size using a water-lubricated diamond wheel cutter and then surface ground to final size with a tolerance of ±0.1 mm, although ±0.01 mm is achievable and preferable. It is essential to ensure that all faces are flat and parallel to the opposite surface, and perpendicular to adjacent surfaces. Reusable stainless steel or aluminium loading bars are bonded to the ends of the specimen using a high strength, two part epoxy adhesive. Room temperature curing adhesives should preferably be used to avoid residual stresses at the adherend interface. The loading bars have their ends machined square to match the cross-section of the test specimen. Immediately before bonding, the adherend surfaces are lightly abraded and cleaned with a solvent (e.g. acetone). During the curing process the specimens need to be held in a gluing fixture to ensure proper alignment between the loading blocks and the loading axis, and to maintain pressure on the bonding surfaces. Specimens are usually left for at least 24 hours before testing to ensure that the adhesive is fully cured. Loading should be at a displacement rate of 1.0 mm min-1, with at least five specimens tested from each batch of material. The method is relatively straightforward, requiring no special loading fixture, unless the specimen dimensions are relatively small (e.g. 6 mm square specimens).3,4 Although such small specimens allow thinner laminates to be characterised, particular care is required during handling. Specimen fabrication is uncomplicated and economical, but care is needed to ensure that misalignment at both the fabrication and testing stages is minimised. Data reduction is straightforward, with the applied stress given by Equation [8.1]:

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P A

149 [8.1]

where P is the applied force and A the specimen cross-sectional area. The procedures for bonding of end-loading bars and axial load transfer to the specimen must be accurate; all sources of misalignment should be minimised. Small misalignments will induce bending, resulting in differential strains on opposing faces of the specimen. An offset of 0.1 mm in the loadline has been calculated to induce an error of ±10% between opposite faces of a block 12 mm in length and 6 mm square4 and a design of loading jig has been proposed, which ensures automatic correction for any misalignment in the load train.

8.3.2 Waisted block (circular and elliptical) As previously mentioned, short rectangular columns of uniform crosssection are unsuitable for generating T-T strength data, as failure invariably occurs at the specimen ends. An alternative approach is the use of waisted specimens which may be of circular or elliptical profile.1,3,4 The reduction in cross-sectional area promotes failure at the specimen mid-thickness. Using specimens with a large circular radius or elliptical fillet reduces the stress concentration in the vicinity of the fillet root. Examples of specimens with circular and elliptical profiles are shown in Fig. 8.1. The plain waisted

8.1 Waisted block specimens. (left) Circular or plain waisted, (right) elliptical.

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(or circular) specimen shown has a nominal T-T dimension of 40 mm, a fillet radius of 30 mm and 25 mm square ends. The gauge section is 32 mm long, with a cross-section approximately 16 mm square at the specimen midthickness.1 Similar but significantly smaller specimens, of both circular and elliptical profile, have also been developed;4 with a total length of 17 mm and 4 mm square gauge section of length as little as 2 mm, a carefully designed elliptically waisted specimen can give the true elastic and strength properties of fibre-reinforced/plastic matrix laminated composites. Specimens are machined to the required profile by wet grinding. Reusable stainless steel or aluminium loading bars are bonded to the ends of the specimen. The bonding procedure, loading configuration (Fig. 8.2) and test conditions are similar to those employed for rectangular block specimens. Specimens have a tendency to fail at the bondline between the composite and the loading bars when the interlaminar strength is higher than the tensile strength of the adhesive bond. Proper specimen design should effectively eliminate this possibility. Alignment is critical for lowfailure strain systems, as bending stresses produced through eccentric loading can result in premature failure. Care should be taken to minimise or eliminate the possibility of misalignment during bonding and testing. Mespoulet4 gives examples of successfully applied bonding arrangements and alignment jigs for carrying out tensile tests. Data reduction is simple, with the applied stress given by Equation [8.1]. T-T tensile failure should occur in a plane orthogonal to the loading direction at the specimen mid-thickness. Provided the adhesive joints have superior strength and fatigue performance to the composite material, the waisted block specimens could be used under cyclic loading conditions.

8.2 Typical T-T tensile loading configuration.

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Environmental testing could also be performed with the same provision that the adhesive joints can withstand the environmental conditions.

8.3.3 Waisted block with parallel-sided gauge section Test geometries suitable for measuring both tensile and compressive, T-T elastic and strength properties have been developed by the Defence Evaluation and Research Agency (DERA, Fort Halstead, UK) and Imperial College.1,4 These geometries both employ waisted rectangular specimens of as little as 17 mm in thickness, with a constant cross-section along the gauge length of the specimen (Fig. 8.3). In the case of the DERA specimen the overall thickness is 38 mm, with base dimension 25 mm square, reducing to a 12 mm long gauge section with a rectangular cross-section of 10 mm (2–3 plane) by 16 mm (1–3 plane) via large radii fillets (12 mm). This test geometry is intended to achieve an acceptable uniformity of stress, both along and across the specimen gauge length and to avoid significant stress concentrations adjacent to the gauge length. The Imperial College specimen4 is supported by finite element analysis which shows that the design is also acceptable for both elastic constant and strength determination. With a total thickness of 17 mm and ends 8 mm square, reducing via an elliptical waisting to a 2 mm long and 4 mm square gauge section, it aims to test unidirectionally reinforced material. For both specimens, preparation is identical to that employed for other waisted test geometries with reusable metallic loading bars bonded to the ends of the specimen. The loading configuration and test conditions (Fig. 8.4) are similar to those employed for short rectangular block specimens. For the highest accuracy, a biaxial strain gauge with an active length of 2 mm is bonded to each face of the specimen at the mid-section, with gauges

8.3 Waisted block (DERA) tensile specimen.

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8.4 Tensile loading of waisted specimen (courtesy of DERA, Fort Halstead, UK).

aligned parallel to and perpendicular to the loading direction. A data acquisition system is required to monitor continuously eight strain gauges and the applied load. In principle, the number of strain gauges could be reduced to avoid data replication, provided the induced bending loads are minimal. T-T tensile failure invariably occurs at the specimen mid-thickness, not in the vicinity of the fillet. Discounting the problem of misalignment, which can be managed by the use of suitably designed bonding and loading jigs, this test method is relatively straightforward to perform. Machining and instrumentation of specimens are, however, fairly labour intensive and expensive. Data reduction is simple, with the applied stress being given by Equation [8.1]. The main advantage is that the test geometry is suitable for producing a full stress–strain response under both tensile and compressive loading conditions and is potentially suitable for fatigue and environmental testing, provided the adhesive joints have strength and fatigue performance that is superior to the composite material and can withstand the environmental conditions.

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8.3.4 I-section specimen The bonding of loading bars to fibre-reinforced thermoplastics (e.g. glass-fibre reinforced polypropylene) is an extremely difficult task. Room temperature curing epoxy adhesives have been found to be unsatisfactory. It is recommended that surface treatments, such as corona discharge or flame treatment, be used. An alternative approach, developed at the National Physical Laboratory,8 uses an I-section specimen (Fig. 8.5), where the load is applied via the top and bottom flanges by two sets of hardened stainless steel stirrups. The inside surfaces of the flanges rest directly on the stirrup surfaces. This test geometry is particularly suited to testing relatively thin laminates (of the order of 20 mm thick). Specimens have a nominal width of 5 mm. The 10 mm gauge section is plain radius waisted, with a radius of curvature of 5 mm. The cross-section is 5 mm square at the specimen mid-thickness. The test is simple and economical, and there are no problems associated with alignment or adhesive bonding. A special loading fixture (loading stirrups) is required, but the overall costs involved are relatively low compared with bonded configurations. The flange thickness was found to be sufficient to ensure failure occurred within the gauge length. Ideally, the fillet radius should be larger, to minimise the high stresses and stress gradients in this region, but this is not practicable for 20 mm thick laminates.

8.3.5 C-section and closed ring specimens As previously mentioned, applied bending moments in sections of significant curvature can also produce T-T tensile stresses. Prime examples are

8.5 I-section tensile specimen.

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Region of delamination B A

A B

8.6 Closed ring specimen.

the closed ring and semicular (C-section) specimens (Figs. 8.6 and 8.7). These test geometries are only suitable for measuring T-T tensile strength. Specimens of both configurations can be sectioned from tubular structures and are representative of a number of structural features (e.g. bends and elbows). The two configurations are, however, only compatible with a limited range of materials, such as continuous aligned and multilayered laminates (including woven fabrics), where a clearly defined plane of failure exists. Indirect loading cannot be applied to discontinuous or random mat reinforced systems, because these materials tend to fail in transverse tension. Machining specimens is relatively inexpensive and straightforward; however, fabrication of the laminated sheet structure is moderately expensive when accounting for the initial costs of producing mandrels and moulding dies. The advantage of these methods is that the required laminate thickness is 10 mm or less. Materials are formed using a cylindrical mould (or mandrel), typically 50 mm in diameter. Specimens 20–25 mm wide are then sectioned from the cylinders. Two types of failure can occur, flexural failure involving the outer layers of the section and delamination failure near the specimen midplane (or radial neutral axis). Flexural failure involves tensile fracture and/or compressive failure at the appropriate surfaces. Caution is required when differentiating between the two modes of failure, because it is not unusual for flexural failure to be accompanied by delamination failure in the outer layers. The resultant failure mode is dependent upon the thickness-to-radius (h/R) ratio of the curved section, the fibre/matrix system and the layup configuration. Chandler et al.11 have predicted that a transition between delamination and flexural failure should occur at a critical thickness-to-radius ratio. Subsequent research indicates that the thickness

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for aligned and woven fabric C-sections with a radius of 25 mm should be 5 mm and 7.5 mm, respectively. These structures have a tendency to deform (i.e. straighten) during loading. In straightening, tangential tensile and interlaminar shear stresses are introduced into the curved structures. The influence of these stresses on the interlaminar tensile strength needs to be accounted for in the calculations. The use of thick specimens tends to reduce geometric deformation rather than eliminate the effect altogether. Low h/R ratios will often result in flexural failure and significant deformation prior to failure. Large structural deformation creates difficulties in measuring the onset of failure. Special loading fixtures are required for both test geometries. The fixtures are manufactured from hardened stainless steel to reduce grip wear due to frictional effects and to prevent environmental attack. Before a specimen is mounted, contact surfaces should be lubricated with graphite, or friction reducing inserts such as PTFE (polytetrafluoroethylene) should be used. A special test fixture for loading C-section specimens in tension has been designed and manufactured by DERA (Farnborough, UK). The fixture consists of a matching pair of loading arms which are held in the top and bottom grips of a test machine (Fig. 8.7). The specimen ends are clamped in each loading arm by tightening a central bolt. This secures the specimen between the ‘flat’ of the central mechanism and the load bar in the outer ‘yoke’. The test fixture is designed to induce simple bending within the specimen without introducing complicated off-axis end loads/moments or offset loads. In order to achieve this objective, the fixture allows free end rotation of the specimen whilst the load is applied. Shear components within the laminate are expected to cancel out, resulting in a ‘pure’ interlaminar tensile failure mode near the apex of the specimen.1 A major disadvantage of the use of indirect methods for inducing interlaminar tension is the considerable influence that combined stress states

8.7 C-section tensile fixture and specimen (courtesy of DERA, Farnborough, UK).

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have on structural deformation and failure. Failure mechanisms are often complex and the associated analysis is usually rather elaborate. These configurations are also prone to process-induced damage (e.g. poor compaction). Fractographic evidence suggests that mixed-mode failure containing both tensile and shear components occurs in preference to interlaminar tensile failure. Failure is caused by a combination of tensile and shear stresses in the vicinity of the specimen ends, a region of maximum stresses, and not along the mid-plane at the specimen apex.At present, there is insufficient evidence to support the use of either test method.

8.4

Compression test methods

The determination of in-plane compressive properties of fibre-reinforced plastic composites is particularly difficult, as explained in Chapter 5. The problems relating to T-T compression testing are also rather complex, with failure being dependent upon the specimen geometry, material microstructure and loading configuration. Ambiguities and uncertainties in the interpretation of fracture may result from competition between several failure mechanisms (e.g. interfacial failure, fibre microbuckling and plastic deformation) prior to final fracture. These mechanisms are often interactive, with progressive damage leading to local stress redistribution. As a result, the overall stress–strain state within a structure alters continuously with progressive failure. However, the loading arrangement itself is far simpler than for in-plane specimens. This section is essentially confined to the evaluation of the following waisted and unwaisted configurations: • • •

square section block square section waisted block with either a circular or elliptical profile square section waisted rectangular block with a parallel gauge section.

Details of suitable test specimen geometries are given in the section on T-T tension. Specimen preparation, instrumentation requirements and data reduction, using Equation [8.1], are similar to those for tension. However, caution needs to be exercised to ensure flatness and parallelism of both specimens and loading platens.

8.4.1 Square block The most basic approach is to load a rectangular block directly between two flat and parallel hardened steel platens, with the specimens located at the centre of the platens in closely fitting recesses (although these are optional), with the compressive load being applied along the T-T axis.12 A four-pillar die set is often used, as this ensures uniform loading to the ends of the specimen.There are no national or international standards avail-

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able, but International Standard ISO 60413 is a potential precursor.This standard specifies a method for the determination of compressive properties of plastics with the displacement rate (speed of testing) set in accordance with the purpose of the measurement (modulus or strength), the material specification (brittle or ductile) and the specimen length.A length-to-width ratio £0.4 is recommended to avoid the possibility of compressive buckling. This test geometry provides consistent and reliable elastic property data for both monolithic and layered (sandwich construction) materials, and is amenable to standardisation for this purpose as shown in Table 8.2, which gives data obtained for unidirectional T300/924 carbon fibre-reinforced epoxy (for a Vf of 60%). The rectangular block data presented in Table 8.2 were obtained from 15 mm square rectangular blocks, machined from 20 mm and 40 mm thick laminates. Elastic and strength properties were approximately the same for both T-T dimensions, meaning negligible end effects. The use of specimens with a length-to-width ratio of 2 : 1 should ensure a relatively uniform stress state at the specimen mid-section and prevent compressive buckling. Strength values were consistent to within ±10% and in reasonable agreement with the strength data obtained using

Table 8.2. T-T compressive properties of unidirectional T300/924 carbon fibre/epoxy.1 Test method

E33 (GPa)

n31

n32

S33 (MPa)

15 mm square block (40 mm thick) 15 mm square block (20 mm thick) Layered square block (40 mm thick) 25 mm square, plain radius block waisted to 16 mm (40 mm thick) 25 mm square, plain radius block waisted to 16 mm (20 mm thick) 25 mm square, radius waisted block with parallel-sided gauge section (40 mm thick) 25 mm square, radius waisted block with parallel-sided gauge section (20 mm thick)

10.0 ± 0.1

0.022 ± 0.001

0.52 ± 0.01

263 ± 3

9.9 ± 0.1

0.020 ± 0.001

0.56 ± 0.01

256 ± 6

10.0

0.02

0.52

258 ± 3

n/a

n/a

n/a

343 ± 7

n/a

n/a

n/a

344 ± 10

10.3 ± 0.2

0.020 ± 0.005

0.50 ± 0.01

297 ± 5

9.6 ± 0.4

0.018 ± 0.008

0.51 ± 0.03

283 ± 12

E33 = Through-thickness elastic modulus, n31 and n32 = axial and transverse through-thickness Poisson’s ratios, respectively, S33 = through-thickness strength.

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8.8 Failed fabric specimens: (left) DERA, (centre) plain radius, (right) square block.

the waisted block geometries. This test method is, however, unsuited to measuring T-T strength, as failure invariably initiates at the specimen ends, independent of material anisotropy and degree of homogeneity (see Fig. 8.8). The presence of stress concentrations in these regions causes premature failure, hence the lower strength value. This method is relatively insensitive to material flaws, such as porosity. Significantly smaller (6 mm square section, with a thickness of 6 mm) T300/914 carbon/epoxy specimens have been investigated,4,14 giving quite similar results to those in Table 8.2. Preparation and testing of the short block specimens are straightforward and economical, although care is required to ensure that the specimen ends are machined flat and parallel. The technique requires no special fixture. The use of a high precision die set ensures uniform axial loading. Commercial units are available at a reasonable price. As with the tensile test, a major drawback relates to the number of strain gauges required for the highest accuracy measurement of axial and transverse strain. The number of strain gauges could be reduced if there is confidence about the flatness and parallelism of the specimen and loading platens. Extensometers are not particularly suitable for measuring axial and lateral strains.

8.4.2 Waisted block (circular and elliptical) This relatively straightforward approach can be used to measure both T-T tensile and compressive strengths of monolithic and sandwich constructions. Testing can be considered uncomplicated, requiring no special fixture. The use of a high precision die set will ensure uniaxial loading over the entire specimen cross-section. Compared to rectangular blocks, specimen fabrication is expensive and labour intensive. As with tension, a large radius fillet (30 mm), or elliptical profile, reduces the stress concentration in the vicinity of the fillet root, although the stress state within the gauge length is less uniform than an equivalent sized rectangular prism.

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Consideration needs to be given to specimen dimensions in order to minimise end effects and avoid the possibility of compression buckling. A length-to-width ratio of 2 : 1, as used for the test geometry in Fig. 8.1, has proved to be satisfactory for an extensive range of composite materials. This test geometry may be scaled down by a factor of 2, with minimal effect on compressive strength. The results in Table 8.2 show that the influence of end effects increases slightly with reduction in thickness. Shear is the predominant cause of failure in all fibre-reinforced plastic composites, independent of the material microstructure or loading configuration. Failure is often instantaneous and catastrophic, resulting in diagonal and interlaminar cracking, with failure modes generally remaining unaffected by a reduction in specimen size. For 2-D woven fabrics, two orthogonal fracture planes can be observed at 45° to the T-T axis.

8.4.3 Waisted block with parallel-sided gauge section This versatile test geometry can be used to measure both T-T tensile and compressive elastic and strength properties.1,4,14 The specimens are subjected to direct compressive loading between two hardened steel parallel platens at a constant displacement rate (Fig. 8.9). The test geometry (Fig. 8.3) may be scaled down by a factor of 2, with minimal effect on either elastic property or strength data. It has been observed that the failure mode for most composites remains unaltered as a result of reducing specimen thickness. A reduction in specimen thickness to 15 mm or less makes handling (strain gauging and testing) more difficult. The accompanying

8.9 Compression fixture with DERA specimen (courtesy of DERA, UK).

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reduction in cross-sectional area has a tendency to induce compressive buckling, particularly for thermoplastic-based systems. Preparation and testing of these specimens are fairly expensive and labour intensive, considerable effort being required to machine specimens to size and to install strain gauges. Specimen preparation and instrumentation requirements and associated problems are similar to those encountered for tension. The technique requires no special fixture, although the use of a high precision die set ensures uniform axial loading. As with tension, a major drawback is in the number of axial and transverse strain gauges required. These could be reduced in number if there was sufficient confidence in the flatness and parallelism of the specimen and loading platens. Extensometers are not particularly suitable for measuring axial and lateral strains. Shear failure consistently occurs at the radius root, independent of the material microstructure. This is due to the presence of stress concentrations. Failure is usually instantaneous and catastrophic, with diagonal cracking occurring along the shear planes and between layers. Failure modes generally remain unaffected by a reduction in specimen size. Linear elastic finite element stress analysis1 has shown that for isotropic materials the stress concentration in the vicinity of the fillet is approximately 1.6. In contrast, the stress concentration at the mid-section of specimens with either a circular or elliptical profile is close to unity,1,4 provided the radius of curvature is large. This partially explains the lower strength values obtained using this test geometry. It is worth noting that plastic deformation and microdamage formation tend to reduce stress concentrations. Barrelling frequently occurs, resulting in failure of the adhesive bond between strain gauges and the composite, thus preventing the measurement of failure strains. Fibre-reinforced thermoplastics are particularly prone to this mode of failure.

8.5

Shear test methods

At a first glance, there appears to be a multitude of test methods of varying complexity for the evaluation of interlaminar shear properties. On closer inspection, the number of test methods that can be used effectively for TT shear characterisation is limited, with all techniques demonstrating deficiencies. A major difficulty is in producing a state of pure shear stress, particularly in the T-T direction. The problem is compounded by the impracticality of producing thick sections with similar dimensions to those employed for in-plane testing. This difficulty increases with material anisotropy and inhomogeneity. Additional problems associated with complexity and cost of specimen fabrication and testing and poor reliability of test data considerably reduce the number of test methods suitable for either

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quality control or design purposes. This section provides an overview of three test methods that are used extensively throughout the composite industry for evaluating T-T shear properties: • • •

short beam double-notch V-notched beam (Iosipescu).

The short beam and double-notch methods have been widely adopted for characterising the interlaminar failure resistance of fibre-reinforced plastic composites. Owing to their simplicity and the low costs involved in specimen fabrication and testing, the two methods are often used for quality control purposes. The V-notched beam test is suitable for determining both the in-plane and T-T shear moduli and shear strengths of most polymer matrix composites, provided a suitable shear failure occurs. Standards exist for all three methods: • • •

short beam, BS EN ISO 14,13015 double-notch, ASTM D 384616 V-notched beam, ASTM D 5379.17

The double-notch method, which consists of loading a non-symmetrically notched composite coupon in uniaxial tension or compression, is also included in BS 499418 and BS 6464.19 ASTM D 384616 specifies compressive loading, and the two BSI standards specify tensile loading.

8.5.1 Short beam The short beam method is one of the simplest tests to conduct and is used widely for measuring the ‘apparent’ interlaminar shear strength of continuous aligned and fabric-reinforced composites. The test consists of a short beam specimen of rectangular cross-section loaded in three-point bending so that an interlaminar shear failure occurs (Fig. 8.10). The specimen is supported by two cylindrical rollers which allow lateral motion, and the load is applied through a central roller located at the specimen midlength. The support and loading rollers are 6 mm in diameter. For aligned materials, the fibre axis is parallel with the length of the specimen. Flexure fixtures with an adjustable span facility can be purchased from test machine manufacturers or produced in-house at a relatively low cost. Tests are conducted at a displacement rate of 1 mm min-1 using standard mechanical test equipment. Specimen preparation is straightforward and only a small amount of material is required. The standard specimen thickness, h, is nominally 2 mm with a width, b, and overall length, L, of 10 and 20 mm, respectively.15 In accordance with the ISO standard, short beam specimens sectioned from

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Mechanical testing of advanced fibre composites P Fibre direction 3 1

P – 2

L – 2

L – 2

P – 2

8.10 Short beam loading configuration.

materials of non-standard thickness should have an overall length of 10 h and a width of 5 h. In all cases the loading span, S, is 5 h ± 0.3 mm. The small loading span-to-thickness (S/h) ratio has been adopted to increase the level of shear stress relative to the flexural stress in the test specimen to encourage interlaminar shear failure. Interlaminar shear failures are difficult to attain at S/h > 5. The four-point bend test has been considered as an alternative method. According to classical beam theory, the shear stress distribution in short beams loaded in three-point flexure is distributed parabolically through the specimen thickness. The stress is a maximum at the mid-plane and zero at the upper and lower surfaces. Finite element analysis has shown that the TT shear stress distribution is severely skewed near the load and reaction points and varies along the beam length. The maximum interlaminar shear stress, tmax, is in fact positioned between the mid-plane and the upper surface, close to the loading zone, and is larger than predicted by classical beam theory.20,21 Data reduction is straightforward, with the maximum interlaminar shear stress given as:15 t max =

3P 4bh

[8.2]

where P is the load applied by the central loading cylinder, with b and h being specimen width and thickness, respectively. The method is suitable for use with fibre-reinforced plastic composites, with both thermoset and thermoplastic matrices, providing an interlaminar shear failure is obtained. Interlaminar shear failure has been observed for aligned glass-fibre and carbon-fibre reinforced systems. Most other materials (e.g. chopped strand mat) tend to fail on the tensile face, with cracks propagating through the specimen thickness. The short beam test cannot give results which are acceptable as the absolute material shear strength, because failure is influenced by flexural

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and contact stresses. Failure frequently results from a combination of high shear and transfibril compression gradients present in the upper portion of orthotropic beams, near the concentrated central load. The surface under the central loading zone is subjected to compression, and the composite may undergo localised buckling. This effect will be particularly severe for aramid-reinforced composites, and thermoplastic-based systems, which have a low resistance to compression loading. It should be emphasised that the result obtained is not an absolute value. For this reason the term ‘apparent’ interlaminar shear strength is used to define the quantity obtained. Test results from different sized specimens, or from specimens tested under different conditions, are not directly comparable.15 Despite these difficulties, the simplicity of the test, combined with economic costs, has ensured its popular use for quality control and as a materials screening tool. The four-point bend arrangement has been considered as an alternative method, but test data have failed to demonstrate improved reliability. In conclusion, the short beam method is inappropriate for generating design data, although there has been a tendency to use the measurements as design allowables.

8.5.2 Double notch An alternative approach for measuring interlaminar shear strength is to apply uniaxial tensile or compressive load to a non-symmetrically notched specimen of rectangular cross-section. Various double-notch geometries have been suggested, including those specified in ASTM D 3846,16 BS 499418 and BS 6464.19 The specimen, shown in Fig. 8.11, is machined with two parallel offset notches, one on each face of the specimen, cut across the entire width of the specimen. The notches are equally spaced on either side of the specimen mid-length. A water-lubricated diamond cutting tool should be used to machine the notches. Failure of the specimen occurs in shear, along the mid-plane between the two notches. The main advantage of using the double-notch method is that relatively thin laminates (2.5–10 mm thick) can be tested. This advantage is counteracted by the difficulty encountered in accurately machining the notches to the required depth of half the specimen thickness (i.e. mid-plane). In principle, the entire load is transmitted by shear forces, distributed along the central plane between the notches. Linear-elastic stress analysis has shown that the shear stress distribution along the midplane between the notches is non-uniform, but tends to become more uniform as the notch separation increases.20 Shear stress concentrations exist at the notches. The T-T shear strength, Sxz, is given by Equation [8.3]:

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Pmax bL

[8.3]

where Pmax is the failure load, L the distance between notches and b the specimen width. T-T shear strength, as determined by the test method specified in ASTM D 3846,16 is measured by applying a compressive load to a double-notch specimen at a displacement rate of 1 mm min-1.The specimen must to be supported along its entire length to minimise out-of-plane deformation. Specimens are nominally 79.5 mm in length and 12.7 mm wide. The two parallel notches are 6.4 mm (0.25 in) apart and between 1 mm and 1.6 mm wide. Test specimen geometry and loading configuration are given in Figs. 8.11 and 8.12, respectively. The method specified in ASTM D 384616 is relatively straightforward to perform, requiring a support fixture of moderate cost. The method provides consistent strength data, with interlaminar failure regularly occurring along the mid-plane joining the two notches. T-T shear strength data is generally consistent with results obtained using the V-notched beam method. Specimen preparation and testing are relatively straightforward, although the quality of machining the notches has a significant effect on strength data. Notch depth must be accurately machined. Fractographic examination of the failure surfaces reveals shear dominated mixed-mode failure. BS 499418 specifies a method for tensile loading 3 mm thick double-notch coupons with an overall length of 200 mm and a width of 25 mm. The two notches are 12.5 mm apart and equidistant from the specimen mid-length. No particular details are available on the notch width. Since this structure is not laterally supported, the coupon bends. Without lateral support, this out-of-plane bending results in premature failure. Shear strengths using this

Notch depth is 1/2 specimen thickness

6.4 mm 36.3 mm

2.54 to 6.60 mm notch width 1.02 to 1.65 mm

10.0 mm 79.5 mm

8.11 Double-notch specimen for determination of T-T shear strength.

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8.12 Compression fixture with double-notch shear specimen.

method have been found to be lower than corresponding tests performed in compression. No allowances have been made in either the ASTM or BS standards to account for the non-uniformity of the stress distribution between the notches, the effect of bending or the local stress concentration at the fibre ends associated with the notch geometry. The close agreement between strength measurements, shown in Table 8.3, obtained using the doublenotch (ASTM D 3846)16 and V-notched beam shear tests for a wide range of materials indicates that the strength calculations do not need to be adjusted to account for stress concentrations present at the notches of double-notch specimens. Non-linear stress analysis conducted at the National Physical Laboratory has shown that the stress concentration at the notches is close to unity for an isotropic double-notch specimen loaded according to ASTM D 3846.16 This analysis would need to be extended to anisotropic solids in order to substantiate the experimental observation. Specimen alignment, as with all tests, can be regarded as critical to test performance.

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Table 8.3. Typical T-T shear properties. Material and test method

Gxz (GPa)

Gyz (GPa)

Sxz (MPa)

Syz (MPa)

UD carbon-fibre/epoxy Short beam Double notch V-notched beam

n/a n/a 5.3 ± 0.2

n/a n/a 2.9 ± 0.3

108 ± 6 75 ± 12 111 ± 2

n/a n/a 64 ± 9*

CSM Short beam Double notch V-notched beam

n/a n/a 1.64 ± 0.09

n/a n/a [1.64 ± 0.09]

13.4 ± 3.0* 38.3 ± 4.7 40.7 ± 1.7

[13.4 ± 3.0]* [38.3 ± 4.7] [40.7 ± 1.7]

2/2 twill glass-fibre fabric/epoxy Short beam Double notch V-notched beam

n/a n/a 4.12 ± 0.14

n/a n/a [4.12 ± 0.14]

52.5 ± 0.6* 64.9 ± 1.8 68.4 ± 0.9

[52.5 ± 0.6]* [64.9 ± 1.8] [68.4 ± 0.9]

Discontinuous glassfibre/nylon 66 Short beam Double notch V-notched beam

n/a n/a 1.68 ± 0.06

n/a n/a unavailable

18.6 ± 0.4* 66.4 ± 4.8 56.9 ± 3.6

[18.6 ± 0.4]* [66.4 ± 4.8] unavailable

Random glass-fibre mat/polypropylene Short beam Double notch V-notched beam

n/a n/a 1.04 ± 0.04

n/a n/a [1.04 ± 0.04]

14.2 ± 1.5* 18.1 ± 3.3 22.7 ± 0.8

[14.2 ± 1.5]* [18.1 ± 3.3] [22.7 ± 0.8]

[ ] assumed from material symmetry, * non-shear failure mode.

8.5.3 V-notched beam shear Details of test procedure, specimen geometry and preparation for this test method can be found in Chapter 6 on shear testing. Providing adequate material thickness is available (at least 10 mm), this method can be used to measure shear modulus and shear strength (Table 8.3) in all three material planes (i.e. X-Y, X-Z and Y-Z) for a diverse range of composite materials.22 T-T specimens are machined from 20 mm thick panels to the required dimensions according to ASTM D 5379.17 Differences between shear moduli, caused by out-of-plane deformation, could be as high as 10% for a batch of nominally identical specimens. To ensure maximum accuracy, shear modulus is determined from the average strain response of back-to-back biaxial rosettes. At present, the standard requires only one specimen from a batch to be tested in this manner, provided the amount of twist for this testpiece is no greater than 3% (for further details see Chapter 6 on shear testing).

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Table 8.4. Suitability of test methods for measuring T-T properties. Method

Elastic properties

Strength

Tension Plain short block Circular profile Elliptical profile DERA C-section I-section

Suitable Not applicable Suitable Suitable Not applicable Not applicable

Not suitable Suitable Suitable – needs further assessment Suitable Not suitable Suitable – needs further development

Compression Plain short block Circular profile Elliptical profile DERA

Suitable Not applicable Suitable Suitable

QA only Suitable Suitable – needs further assessment Suitable – thermoset systems only

Shear Short beam Double-notch V-notched beam

Not applicable Not applicable Suitable

QA only – continuous aligned laminates Suitable Suitable – caution on failure mode

8.5.4 Comparison of shear data A comparison of typical T-T shear modulus and shear strength data obtained from a wide range of composites is shown in Table 8.3. Default values are bracketed, where it is assumed the material is symmetric in the X-Z and Y-Z planes.

8.6

Concluding remarks

Table 8.4 summarises the suitability of each test method for measuring TT properties. The differences between tensile and compressive elastic property measurements are minimal, in view of the problems associated with correct alignment, stress non-uniformity and heterogeneity of the materials, the results are generally consistent (i.e. ±5% for elastic moduli and ±10% for strength). Owing to the ease of specimen preparation (i.e. no bonded loading bars) and testing, a user would be justified in conducting compression tests to produce the required elastic property data.

Acknowledgements This chapter was written with the support of the Materials Measurement Programme, a programme of underpinning research financed by the United Kingdom Department of Trade and Industry. The author acknowledges the contributions of his colleagues Dr Graham Sims and Miss Maria Lodeiro

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at the National Physical Laboratory, Dr Clive Messenger and Mr Matthew Hiley, Defence Evaluation and Research Agency at Farnborough, and Mr Robert Ferguson, Defence Evaluation and Research Agency, Fort Halstead.

References 1. W R Broughton and G D Sims, An Overview of Through-thickness Test Methods for Polymer Matrix Composites, NPL Report DMM(A)148, October 1994. 2. S Mespoulet, Through-thickness Test Methods for Laminated Composites – A Review, Centre for Composite Materials, Imperial College, London, UK, February 1995. 3. S Mespoulet, J M Hodgkinson, F L Matthews, D Hitchings and P Robinson, ‘A novel test method to determine the through-thickness tensile properties of long fibre reinforced composites’, Proceedings of Seventh European Conference on Composite Materials (ECCM-7), Institute of Materials London, UK, Volume 2, Woodhead Publishing, Cambridge, May 1996, 131–7. 4. S Mespoulet, Through-thickness Test Methods for Laminated Composite Materials, PhD Thesis, Centre for Composite Materials, Imperial College, London University, UK, January 1998. 5. N C W Judd and W W Wright, ‘Voids and their effects on the mechanical properties of composites – appraisal’, SAMPE Journal, 1978 January/February 10–4. 6. M R Wisnom and M I Jones, ‘Size effects in interlaminar tensile and shear strength of unidirectional glass fibre/epoxy’, Journal of Reinforced Plastics and Composites, 1996 15 January 2–15. 7. C O Horan and J G Simmonds, ‘Saint-Venant end effects in composite structures’, Composites Engineering, 1994 4(3) 279–86. 8. W R Broughton, ‘A critical evaluation of through-thickness test methods’, Proceedings of the Eleventh International Conference on Composite Materials, Australian Composite Structures Society Gold Coast, Queensland, Australia, ed M L Scott, Volume 25, Woodhead Publishing, Cambridge, July 1997, 894–904. 9. M Sumich, ‘Manufacture of composite test specimens for delamination studies’, Experimental Techniques, 1989 13 20–2. 10. C C Hiel, M Sumich and D P Chappell, ‘A curved beam test specimen for determining the interlaminar tensile strength of a laminated composite’, Journal of Composite Materials, 1991 25 854–68. 11. H W Chandler, A J Longmuir, S McRobbie, Y-S Wu and A G Gibson, ‘Tensile delamination failure of curved laminates of single and double-skinned construction’, Proceedings of the 2nd International Conference on Deformation and Fracture of Composites, UMIST, Manchester, UK, March 1993, Institute of Materials, published by IoM Communications Ltd, 1993, 16.1–10. 12. S Chaterjee, D Adams and D W Oplinger, Test Methods for Composites a Status Report, Volume II: Compressive Test Methods, US Department of Transport, Federal Aviation Administration, Report DOT/FAA/CT-93/17, II, National Technical Information Service, Springfield, VA 22161, USA, June 1993. 13. ISO 604: Plastics – Determination of Compressive Properties, 1993. 14. S Mespoulet, J M Hodgkinson, F L Matthews, P Robinson and D Hitchings, ‘The development of a through-thickness compression test for laminated CFRP’,

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15. 16.

17.

18. 19. 20.

21.

22.

169

Proceedings of the 4th International Conference on Deformation and Fracture of Composites, UMIST, Manchester, UK, March 1997, Institute of Materials, published by IoM Communications Ltd, 1997, 371–8. BS EN ISO 14,130: Fibre-reinforced Plastic Composites – Determination of Apparent Interlaminar Shear Strength by Short Beam Method, 1997. ASTM D 3846: ‘Standard test method for in-plane shear of reinforced plastics’, Annual Book of ASTM Standards, 100 Barr Harbor Drive, West Conshohocken, PA 19428, USA, Vol 8.02, 1998, 479– 81. ASTM D 5379: ‘Standard test method for shear properties of composite materials by the V-notched beam method’, Annual Book of ASTM Standards, 100 Barr Harbor Drive, West Conshohocken, PA 19428, USA, Vol 15.03, 1997, 235–47. BS 4994: Design and Construction of Vessels and Tanks in Reinforced Plastics, 1987. BS 6464: Reinforced Plastics Pipes, Fittings and Joints for Process Plants, 1984. S Chaterjee, D Adams and D W Oplinger, Test Methods for Composites a Status Report Volume III: Shear Test Methods, US Department of Transport, Federal Aviation Administration, Report DOT/FAA/CT-93/17, III, National Technical Information Service, Springfield, VA 22161, USA, June 1993. R B Pipes, R A Blake Jr, J W Gillespie Jr and L A Carlsson, ‘Test methods’, Delaware Composites Design Encyclopedia, Volume 6, eds L A Carlsson and J W Gillespie Jr, Technomic Publishing, Lancaster, PA, USA, 1990. W R Broughton, M Lodeiro and G D Sims, ‘Experimental validation of shear test methods for through-thickness properties’, Proceedings of Seventh European Conference on Composite Materials (ECCM7), Institute of Materials London, UK, Volume 2, Woodhead Publishing, Cambridge, May, 1996, 125–30.

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9 Interlaminar fracture toughness P ROBINSON AND J M HODGKINSON

9.1

Introduction

Laminated fibre-reinforced composites made of high strength fibres in a relatively weak matrix material are susceptible to delamination (i.e. separation of the layers). A typical quasi-isotropic carbon-fibre reinforced epoxy laminate has an in-plane tensile strength of 700–1200 MPa, dependent on precise layup,1 but the through-thickness tensile strength can be as low as 50 MPa and the through-thickness shear strength is also relatively low.2,3 It is clear therefore that through-thickness stresses in a component (see Fig. 9.1 for some possible sources) may give rise to the initiation of delamination if they exceed the through-thickness strength. The subsequent propagation of a delamination will, however, be controlled not by the through-thickness strength but by the interlaminar fracture toughness of the composite material. This chapter describes methods for measuring the interlaminar fracture toughness.

9.2

Terminology and typical values

9.2.1 Critical energy release rate Interlaminar fracture toughness of laminated composites is normally expressed in terms of the critical energy release rate, which is usually represented by the symbol Gc. The critical energy release rate is the energy consumed by the material as the delamination front advances through a unit area. The units commonly used for Gc are Joules per square metre or Newtons per metre. Interlaminar fracture toughness can be measured in each of the modes shown in Fig. 9.2 or in a combination of these modes. Typical values of interlaminar fracture toughness in modes I and II (GIc and GIIc, respectively) are given in Table 9.1 for a variety of carbon fibre and matrix types. In isotropic materials, toughness values (usually expressed in terms of the 170

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Interlaminar fracture toughness free edge

notch (hole)

ply drop

171

bonded joint

buckling

bolted joint

impact

pressure, p

delamination

delamination

9.1 Possible sources of delamination initiation caused by throughthickness stresses.

mode I

mode II

mode III

9.2 Schematic diagrams of the basic modes of crack loading, mode I (opening), mode II (shear), mode III (tearing).

critical stress intensity factor) are usually only quoted for the mode I case. For these materials the toughness is lowest in this mode, so that even if a crack is loaded to drive the growth in mode II, as shown in Fig. 9.3(a), the crack will deviate and grow in a direction which will be pure mode I, as shown in Fig. 9.3(b). In laminated composites, however, the delamination can be constrained to lie between the strong fibre-reinforced layers, so that it is possible to have delamination growth in all of the three modes shown in Fig. 9.2.

9.2.2 Relationship between energy release rate and stress intensity factor For metals and polymers, fracture toughness is often expressed in terms of the critical stress intensity factor, Kc. For linear elastic isotropic

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Table 9.1. Typical values of interlaminar fracture toughness for various materials. Fracture toughness (kJ m-2)

Material Fibre/matrix Mode T300/6376

Mode Mode Mode Mode Mode Mode Mode Mode Mode Mode Mode Mode Mode Mode Mode

XAS/913 T300/914 T800/924 AS4/PES

AS4/PEEK

I II II I II I II I II I II II I II II

(ELS) (ENF) (ENF) (ENF) (ELS) (ELS) (ENF) (ELS) (ENF)

Initiation

Propagation

0.27 0.60 0.65 0.28 0.66 0.14 0.72 0.22 0.44 0.80 1.23 1.29 1.68 1.74 1.82

0.27 — — 0.28 — 0.14 — 0.25 0.60 2.02 1.84 — 2.42 3.16 —

ELS = end-loaded split; ENF = end-notched flexure, * = eqoxy matrix; PES = polyether sulphone; PEEK = polyether ether ketore.

original crack

(a)

crack propagates in the pure mode I direction

(b)

9.3 Crack propagation in an isotropic material.

materials, KIc and GIc are related by the following expression for the plane strain case:4 GIc = K Ic 2

(1 - n 2 ) E

[9.1]

where E is the Young’s modulus and n the Poisson’s ratio. For a typical aerospace aluminium alloy with a KIc of 35 MPa m1/2, Equation [9.1] gives a GIc of 16 kJ m-2, which is considerably higher than the figures quoted in Table 9.1 for composite laminates and confirms their relative propensity to delaminate.

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9.2.3 Criteria for delamination growth To determine the load at which a delamination in a composite component will grow, it is necessary to assess the energy available for driving the delamination growth. This involves an analysis of the particular component to determine the energy release rate, represented by the symbol G. For simple cases closed form solutions for G are available,5 but for more complex cases finite element analysis is required to evaluate G.6 G, usually in its modal components, can be tested in some criterion involving the critical energy release rates for the particular material. For example, in a pure mode I case the delamination will grow if GI ≥ GIc. The equivalent test using the stress intensity factor approach would be KI ≥ KIc for growth.

9.2.4 Effect of increasing critical energy release rate and stress intensity factor A significant difference between the stress intensity factor and the energy release rate lies in their relationship to the applied load. For example, for a given linear elastic component with a given crack size, the load to cause mode I crack growth is directly proportional to the KIc value of the material. So, if a designer chooses a new material for the component which has twice the KIc of the original material, then the load to cause crack growth would be doubled, irrespective of whether the new material has different stiffness properties, these being incorporated within KIc. It follows from Equation [9.1] that for an isotropic material with the crack growing under plane strain conditions in mode I the critical load, Pc, will be proportional to: GIc E (1 - n 2 ) Thus doubling GIc, but keeping the stiffness characteristics unchanged, will produce a critical load increased by a factor of √2. However, if in choosing the new material, the stiffness characterisistcs are also changed, then the critical load will be changed according to the above proportionality relationship.

9.3

Overview of test methods and standards

There has been considerable research into the development of suitable test methods for the measurement of interlaminar toughness. Standards organisations such as the American Society for Testing and Materials (ASTM), the European Structural Integrity Society (ESIS) and the Japanese Industry Standards (JIS) have been evaluating some of the proposed methods.

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The test methods for measuring interlaminar fracture toughness generally involve beam-type specimens and have been developed almost exclusively for application to unidirectional laminates, with the delamination growth in the direction of the fibres. The strategy in all of these tests requires measurement of the load and applied displacement at which a delamination of known length grows. For some specimens the growth is stable, so that data can be collected at many points during the delamination growth. In other specimens the delamination growth is unstable, and the critical load and applied displacement can only be measured for the initial delamination length. From the load–displacement–crack length data it is then possible to determine the interlaminar toughness. For mode I the commonest test uses the double cantilever beam (DCB) specimen shown in Fig. 9.4. Test standards using this specimen have been produced by both JIS7 and ASTM8 and are limited to the testing of unidirectional laminates. Similarly, ESIS9 have published a protocol for DCB testing. Other methods for mode I testing include the width-tapered DCB10 and the wedge-driven test.11 For mode II there are two methods which have received most attention; these are the three-point loaded end-notched

End-block Laminate

h (ASTM) 2h (ESIS)

0 1 2 3 4 5 6 7 8 9101112

(a)

l1 B Crack length scale

l2 a L

(b)

0 1 2 3 4 5 6 7 8 9101112

l1

a

9.4 Double cantilever beam (DCB) specimen geometry, (a) end-blocks, (b) piano hinges.

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flexure (ENF) test, standardised by JIS,7 and the end-loaded split (ELS) as shown in Fig. 9.5. Both of these test methods are currently being evaluated in ‘round-robin’ trials by standards organisations, with ESIS9 having published a protocol for the ELS test. Other methods have also been proposed for measuring the mode II interlaminar toughness, and these include the centre-notched flexure (CNF) specimen12 and a version of the ENF specimen which is loaded in four-point flexure, the 4ENF.13 The JIS standard for mode II testing prefers the use of test machines which can accept feedback control so as to stabilise the delamination growth. However, there remains some concern over the variability of measured mode II toughness data and the dependence on delamination insert thick-

Pencil lead spacer

L

(a)

0

2h

1

2

3

4

5

6

7

Clamp on bearing

a

0

2h

1

2

3

4

(b)

a L

L

9.5 (a) End-loaded split (ELS) and (b) end-notched flexure (ENF) mode II test specimens, in their unloaded and loaded conditions.

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ness and the presence of any precracking (i.e. extension of the initial delamination prior to the test). The variability may be in part due to the nature of failure processes on the microscopic scale, which can include the development of inclined tension microcracks ahead of the delamination front which eventually coalesce by failure of the ligaments between them. Friction between the sliding surfaces may also contribute to the variation in values of GIIc determined by different data reduction methods.14 Tests investigating the dependence of measured toughness on insert thickness and precracking suggest that it may not be possible to establish a single value of GIIc which can be considered as a purely material property. In view of the difficulties surrounding the measurement of GIIc and observations that many failures in composite structures involve mixed mode I/II fracture, with the mode I component being dominant, it has been suggested that mode I and mixed mode I/II toughness data may prove to be most useful for the prediction of delamination failure of practical composite structures.15 This is not, however, a universally held view, with some researchers observing near-pure mode II fractures in realistic structural configurations.16,17 The usefulness of the mode II interlaminar toughness test is clearly still the subject of debate. The development of methods for measuring the interlaminar toughness in mode III is not as far advanced as for modes I and II. Although many proposals have been made,18 none has so far been found to be fully satisfactory. This is partly due to the difficulty of devising a specimen which achieves a pure mode III fracture and partly because the mode III interlaminar fracture toughness is believed to be higher than for the other two modes, so that delamination growth in real laminated components is expected to be controlled largely by the resistance in modes I and II. A test method currently being evaluated by ASTM is the edge cracked torsion (ECT) test19 shown in Fig. 9.6. In a real laminated component the delamination growth is likely to occur not in a single pure mode but as a combination of modes. There is therefore interest in measuring the interlaminar toughness during mixed mode crack growth. The development of mixed mode test methods has focused on mixed I/II modes, and the methods proposed include the fixed ratio mixed mode (FRMM) test method and the mixed mode bend (MMB) test which are illustrated in Figs. 9.7 and 9.8, respectively.

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177

W Edge crack

L

Lt

a B

9.6 Edge cracked torsion specimen. Dimensions in millimetres: L = 76.2, LT = 88.9, W = 31.75, B = 38.1. Clamp on bearing

0 1 2 3 4 5 6 7 8 9 10

2h

a L

9.7 Fixed ratio mixed mode (FRMM) test method. c

Fulcrum Saddle and yoke 0 1 2 3 4 5 6 7 8 9

a L

L

9.8 Mixed mode bend (MMB) test method.

10

2h

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9.4

Mode I testing

In the following sections the manufacture, test procedure and data reduction schemes for mode I interlaminar toughness are described, including recommendations made in the ASTM standard,8 the more recent of the two test standards for mode I and the ESIS protocol.9

9.4.1 Specimen manufacture and preparation In this section the manufacture of DCB test specimens for measuring the mode I interlaminar toughness is dealt with. Much of the description is also applicable to other beam-type test specimens used for measuring interlaminar toughness in mode II and mixed mode I/II. 9.4.1.1 The laminate and delamination insert As noted previously, interlaminar toughness test method development has focussed on unidirectional laminates. The starting point in the specimen production process is therefore the manufacture of a unidirectional laminate containing an initial delamination. The thickness of the laminate will normally be chosen to ensure that large deflection effects are not significant. To achieve a mid-plane delamination, the laminate will be made up of an even number of laminae and the typical thickness for a 60% volume fraction carbon-fibre composite is around 3 mm, with that of a 60% volume fraction glass-fibre composite being 5 mm. However, if the toughness is high, or other types of lower flexural modulus material are to be tested, the ASTM standard8 recommends that the thickness be chosen to satisfy the criterion: h ≥ 8.28

3

GIc ao E11

2

[9.2]

where h is the specimen thickness, GIc is the anticipated critical energy release rate, ao is the initial delamination length (measured from the load line) and E11 is the modulus of elasticity in the fibre direction. Satisfying this criterion effectively limits the opening displacement of the specimen arms at the onset of growth so as to ensure the initial load– displacement response is linear. However, during subsequent growth of the delamination the displacement may become large compared to the crack length, so that large displacement effects would need to be considered and allowance made for them in the data reduction process. Application of the above criterion requires prior knowledge of values of GIc and E11 for the material to be tested. Values of GIc for similar systems can usually be found in the literature or manufacturer’s data sheets. Alternatively, those given in Table 9.1 may provide a useful first estimate.

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An initial, or starter, delamination is introduced into the laminate during layup by including a thin non-stick film. The ASTM standard8 and ESIS protocol9 recommend that the film thickness should be no greater than 13 mm in order to simulate a sharp crack and cause a minimum disturbance to the laminate. Thicker films can give rise to a resin-rich zone at the tip of the film which may give a false initial value of the interlaminar toughness. The film should be chosen so as to be compatible with the cure temperature of the composite material. Early work made use of thin aluminium foil as insert material but polymer films are now recommended in an attempt, not entirely successful, however, to avoid problems with folding and crimping at cut edges and thermal mismatch. For epoxy matrix composites, cured at below 180°C, a thin fluoroethylene polymer film is suitable. For composites cured at higher temperatures (e.g. polyimide, bismaleimide and thermoplastics) a thin polyimide film should be used. When polyimide film is used it should be painted or sprayed with a mould release agent before insertion into the laminate. Silicon-based mould release agents may contaminate the laminate by migration through the individual layers. To prevent this it is advisable to bake the coated film at 130°C, subsequently handling the film carefully so that the layer of release agent is not damaged or removed. The film is placed at the mid-plane to give an initial delamination in the specimen of an appropriate length. For the DCB specimen, the ASTM standard8 recommends that the delamination front formed by the film should be 50 mm from the load line, with ESIS9 suggesting that the distance from the forward edge of the loading block (or piano hinge) to the film front should be at least 45 mm. For unidirectional laminates the film needs to be placed so that the delamination front is perpendicular to the direction of the fibres (i.e. the intended direction of delamination growth). It may be helpful to use a starter film which extends beyond the edges of the laminate, as this can aid location of the delamination front in the cured panel. Having laid up the laminate, incorporating the delamination-starter film, the panel is then cured according to the normal procedures for that material. Any deviations from the normal curing process should be noted because these may affect interlaminar toughness, since this is dependent on the matrix and matrix-to-fibre bond. Similarly checks on the cured laminate, including measurement of fibre volume fraction, void volume fraction and thickness, are recommended. A further quality check using a C-scan of the panel should also confirm the location of the starter film. 9.4.1.2 Specimen dimensions To mark out the specimen geometry on the panel, it is first necessary to locate the delamination front. If the starter film extends beyond the edges of the laminate, then the protruding strip of film may be used to mark the position of the delamination front. However, the film is often distorted or

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damaged at the edge of the laminate, and it is usually best to trim the panel on a diamond saw and then cut narrow strips from the fibre-direction edges of the panel; these strips can be totally delaminated by pulling apart by hand and the position of the delamination front marked on to the panel. From the delamination front line the rest of the panel can be marked out and specimens cut with the delamination front perpendicular to the specimen longitudinal direction. For DCB specimens the ASTM standard8 recommends that the specimen length, L, should be at least 125 mm and the width 20–25 mm. ESIS9 gives similar advice. At least five specimens should be tested. As usual, the geometry of the test specimens should be recorded. 9.4.1.3 Load introduction For the DCB specimen, and for some of the other test specimens, the next step is to provide some means of applying the load. Adhesively bonded end blocks or hinges, as shown in Fig. 9.4, can be used for this purpose. The geometry of these loading attachments is not prescribed in the ASTM standard8 or ESIS,9 except that they must be at least as wide as the test specimen. For the end blocks the distance from the loading pin centre to the mid-plane of the arm of the specimen (dimension l1 in Fig. 9.4) should be kept small to limit the change in lever arm caused by rotation of the block. The ASTM standard recommends that the distance l1 be chosen such that: l1 £

0.0434 h3 E11 h + 0.01 + a02 4 GIc

[9.3]

where h is the full laminate thickness and a0 the delamination length measured from the loadline. If the condition in Equation [9.3] cannot be satisfied, then end block corrections must be incorporated in the data reduction scheme. These end block corrections and data reduction schemes are discussed later. It is usually sufficient to lightly abrade (with sandpaper or grit blasting) and degrease the surfaces to be bonded. Bonding should follow immediately after surface preparation, and in most cases a cyanoacrylate adhesive is adequate; alternatively a tough room temperature cure adhesive can be used. The maximium load to be transmitted by the load attachments in the DCB test is relatively low and can be estimated by Equation [9.4]: Pmax =

B a

h3 E11GIc 96

[9.4]

where B is the width of the specimen and h is the full laminate thickness. The maximum force will clearly occur for the shortest delamination length (i.e. the starter delamination length) and so, if debonding of the end attach-

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ments does occur, one remedial strategy is to increase the starter delamination length. It is important that these loading attachments should be properly aligned on the specimen, preferably using some form of jig; otherwise the initial delamination growth may be non-uniform and consequently give a false value for the initial interlaminar toughness. After curing of the adhesive, any excess adhesive preventing opening of the starter delamination should be removed and, if hinges are used, their free action should be ensured. 9.4.1.4 Delamination measurement It is preferable to be able to take measurements of delamination growth during the test from both edges of the specimen. The edges are first coated with white water-based typewriter correction fluid, to aid in the visual detection of the crack tip, and then marked with a suitable scale. For the DCB specimen this involves marking a scale in 1 mm increments for the first 5 mm (ASTM)8 or 10 mm (ESIS)9 of growth from the starter delamination front and then in 5 mm increments for a further 20 mm (ASTM), or at least 40 mm (ESIS), with ESIS requiring that a final 5 mm should be marked at 1 mm intervals. The ESIS requirement for small scale increments at the end of the delamination growth is an attempt to counter the distorting effect that the close-packed data, obtained at the beginning of the test, can have on curve fitting conducted as part of the data analysis.20 The delamination length associated with each of the scale lines should be as measured from the loading line of the hinges, or a line joining the centres of the loading pins in the unloaded state (i.e. along the beam). In the ASTM standard it is noted that it may be difficult to locate the exact position of the starter delamination front. If this proves to be the case, the standard suggests that the specimen should be marked with sufficient 1 mm increments in the region of the starter delamination front so as to ensure that during the test the length of the starter delamination can be determined and growth data recorded at the next five 1 mm increment lines and then at the subsequent 5 mm increments. 9.4.1.5 Conditioning Specimens should be moisture conditioned in order to obtain baseline data at a uniform moisture content. One option is the fully dried condition, and this is recommended because the interlaminar fracture toughness of polymer matrix composites is sensitive to resin moisture content. The particular drying temperature and duration should be decided based on advice from the resin manufacturer, but for epoxies this might be 70°C in a vacuum oven until no weight loss is detectable. Conditioning should take place after

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the load blocks or piano hinges have been bonded to the specimen. Once fully conditioned, the specimens may be stored in a desiccator for, at most, 24 hours before testing. ASTM8 suggests the use of Procedure D in their Test Method D 5229M for drying laminates. Other conditioning procedures may be applied for the investigation of specific conditioning effects and ASTM suggests the use of their Standard Conditioning Procedure, which is Procedure C in ASTM Test Method D 5229M. This procedure gives the laminate the conditioning of a standard laboratory atmosphere (23°C and 50% relative humidity).

9.4.2 Test procedure The testing machine should be calibrated and be capable of being operated in displacement control mode with constant displacement rates in the range 0.5–5 mm min-1. The load sensing device should have an accuracy over the load range of interest of within ±1% of the indicated value. Crosshead separation may be used as a measure of opening displacement of the specimen provided that the deformation of the testing machine, with gripping fixture attached, is less than 2% of the opening displacement of the specimen. An X-Y plotter can be used to make a paper record of the load versus opening displacement during the test, or the data may be stored electronically for postprocessing. A means must also be provided for the load–displacement data to be ‘marked’ as the delamination front advances through each of the scale markings on the edge of the specimen. This could simply consist of marking the paper record of the load–displacement trace manually, or an event marker can be used to provide a ‘kick’ to the load axis which can later be related to the scale crack lengths. If the load–displacement data are being recorded electronically, then a signal from a hand-held event marker can also be recorded and again, after the test, these signals need to be interpreted in terms of the associated delamination lengths. The specimen is mounted in a fixture of the testing machine. The fixture either allows load to be applied to the pins inserted into the loading blocks attached to the specimen, or uses grips to hold the piano hinges. Either approach allows rotation of the specimen ends. Care should be taken to ensure that the specimen is aligned and centred and provision made for the free end of the specimen to be supported initially, in order to keep the beam orthogonal to the direction of the applied load. There are a number of acceptable ways of monitoring delamination growth. A travelling optical microscope with a magnification of no more than 70¥ (20–40¥ is generally sufficient) can be positioned on one side of the specimen, with a mirror being used to check for discrepancies from one side of the specimen to the other. Crack length gauges, bonded to the specimen edges, are another option. Perhaps the ideal is to use two charge

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coupled device (CCD) cameras, one on either side of the specimen, with suitable optics and adjustable mountings to enable the cameras to follow the advancing delamination tip. The cameras can be coupled to separate monitors, or to a monitor with split screen capability. Such a system allows full delamination growth monitoring capability on both sides of the specimen, without eye strain! Whatever means is used, it should be capable of pinpointing the delamination front with an accuracy of at least ±0.5 mm. The loads to be recorded during the test are generally rather low, with peak loads being in the range 100–200 N. It is, therefore, important that the output from the load cell be correctly ‘zeroed’ with any mounting fixture already in place, prior to inserting the specimen. Also, if there is any ‘play’ in the end block-to-loading pin-to fixture, or in the hinge, then it may be necessary to determine the displacement associated with the zero load by extrapolation from the linear portion of the load–displacement curve prior to delamination growth. At the start of the test the specimen is loaded at a constant crosshead speed of 0.5 mm min-1 (ASTM)8 or between 1 and 5 mm min-1 (ESIS),9 with load and displacement being recorded continuously. The delamination front at the end of the insert material should be observed on both sides of the specimen, and when the delamination initiates, the load–displacement record should be ‘marked’. Even in these opening mode I tests, the initiation of delamination growth is often difficult to detect, and for this reason the standards propose a number of ways, described later, for identifying GIc associated with initiation. Use of a low crosshead speed obviously helps identify initial movement of the delamination, as does appropriate illumination. Sometimes an unstable delamination growth is observed initially, hence the recommendation from ESIS9 that ten 1 mm increments be marked in the region of the insert front. As the delamination continues to grow, now in a stable manner, the load–displacement data are ‘marked’ as the delamination front passes the remaining 1 mm increment markers. At this stage the recommendations of ASTM8 and ESIS9 begin to diverge. ASTM suggests that the test continue past the first five 1 mm markers, possibly at an increased crosshead speed, with the load–displacement data being marked at each of the subsequent 5 mm increment markers. Checks should be made periodically on the opposite edge to see if delamination growth is uniform. If it is not, then the average should be recorded. The difference in delamination length between the two edges should not be greater than 2 mm; although there is no recommendation that the results from such specimens be discarded, this is the implication. When the delamination length has extended 25 mm from the original insert front, the specimen should be unloaded, with the unloading cycle also being recorded. ESIS,9 on the other hand, suggest that once data for five 1 mm delamination growth increments have been recorded (either after the initial stable initiation or five readings after the arrest of an unstable initiation), the

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specimen should be completely unloaded at a constant crosshead rate, which may be as high as 25 mm min-1. The delamination tip should then be marked on both sides of the specimen. If the difference is greater than 2 mm, asymmetrical loading of the specimen is likely to be the cause; ideally the cause should be identified and rectified before proceeding with subsequent tests. The specimen is then reloaded at the same crosshead rate as the initial loading, with the load–displacement data being marked as the delamination advances from what is now a ‘precrack’. The load– displacement data are marked as growth is initiated from the precrack and at each of the remaining 1 mm increment scale marks, then at the 5 mm increment marks and, finally, at the 1 mm increments over the last 5 mm of growth. The specimen is then unloaded at a constant crosshead rate. The relative merits of these different approaches to mode I testing are still being debated. The ASTM approach gives an initiation value from the insert. This value may be affected by a resin-rich zone at the delamination film front, but this is likely to be small for the recommended starter film thickness adopted in the standard. Propagation values may be increased owing to fibres bridging between the crack surfaces (fibre bridging), so that the initiation value is likely to be a lower bound. The ESIS approach also measures this insert initiation value but, in addition, gives information concerning delamination initiation from a mode I precrack. The initiation of growth from the precrack is also likely to be affected by fibre bridging, offering a degree of specimen stiffening.

9.4.3 Interpretation of test results The data acquired during the test are: the initial delamination length, ao (this can be confirmed after the test by separating the two arms of the specimen by hand); the various delamination lengths, a (where a = ao + the measured delamination length increments); the corresponding loads, P; and displacements, d.These, together with dimensions of the specimen (and endblock, if used), allow determination of the mode I fracture toughness of the material and the application of corrections where necessary. There are several ways in which initiation and propagation values of GIc may be determined from the data acquired, and these values may be used to generate a resistance curve, or R curve, by plotting the calculated G versus crack length, a, as shown in Fig. 9.9. GIc may be determined for testing from the starter film and from the mode I precrack, where available. 9.4.3.1 Methods for ascertaining delamination initiation It was mentioned earlier that the precise identification of delamination initiation by visual inspection can be notoriously difficult and, in any case,

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2500

G Ic (J m-2 )

2000

1500

1000

500

0 40

50

60

70

80

90

100

Crack length a (mm)

9.9 Typical R curve for mode I fracture. , propagation values; , deviation from linearity; , visual onset; , 5% offset.

is highly operator dependent. In order to obtain some degree of repeatability, three ways of relating points on the load–displacement curve to delamination initiation have been proposed: •

•

Initiation by visual observation (VIS): A visually observed initiation value for GIc can be calculated corresponding to the load and displacement at which the delamination is seen to grow from the insert on either edge of the specimen. Initiation determined by deviation from linearity (NL): Here GIc can be calculated using the load and displacement at the point of non-linearity of the load–displacement curve. The calculation assumes that the delamination begins to grow from the centre of the insert, within the specimen.21 It is noted in the ASTM standard8 that the NL value for GIc represents a lower bound and for brittle matrix composites is typically the same point at which delamination is observed to initiate at the specimen edges, see Fig. 9.10(a). However, for tough matrices a region of non-linear behaviour may precede visual observation of the initiation of delamination at the specimen edges, see Fig. 9.10(b).

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Mechanical testing of advanced fibre composites (a) MAX NL & VIS

5% Propagation markers

Force

Displacement

(b) MAX

Propagation markers

5% VIS NL Force

Displacement

(c) MAX NL & VIS

5% Propagation markers

Force

Displacement

9.10 Load–displacement curves for DCB tests, (a) brittle matrix, (b) tough matrix, showing stable crack growth, and (c) unstable crack growth.

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Initiation from 5% offset/maximum load (5%/MAX): This value of GIc may be calculated from the intersection values of the load–deflection curve with a line drawn from the origin and offset by a 5% increase in compliance from the original linear portion of the load–deflection curve, as shown in Fig. 9.10. If the maximum load occurs before the point of intersection, then the maximum load and corresponding displacement should be used to calculate GIc.

9.4.3.2 Identifying test data associated with propagation In addition to the data associated with initiation, determined as outlined above from either the insert or precrack, propagation values of GIc can be determined for each delamination length, load and displacement combination measured during delamination propagation. Under displacement control delamination growth is often quite stable, if not precisely steady. In fact, if GIc is constant (i.e. independent of crack length), then the growth in a DCB specimen under displacement control is always stable.5 However, growth can be unstable and this is characterised by one or more periods of no, or very slow, delamination growth followed by a rapid delamination, yielding sharp drops in the load–displacement graphs with virtually infinite slope, as shown in Fig. 9.10(c). It is usually impossible to record delamination length readings during unstable delamination growth, which is normally followed by arrest (i.e. no delamination growth) and a reloading phase which results in a local peak load when delamination growth restarts. If such ‘stick–slip’ behaviour is observed, the arrest points should be excluded from the analysis. 9.4.3.3 Data reduction The ASTM standard8 gives three methods for calculating GIc, and these have been evaluated by round-robin testing.22 The methods considered were: a modified beam theory (MBT), a compliance calibration (CC) and a modified compliance calibration (MCC). Since in the round robin, GIc values determined by the different methods differed by only 3%, it is clear that none is essentially superior. However, the ASTM standard points out that the MBT method yielded the most conservative values of GIc for 80% of the specimens tested and recommends the use of this method. ESIS9 offers only the MBT and MCC. These data reduction methods are described in the following sections, assuming that hinges have been used for applying the load and that there are no significant large displacement effects. Subsequently the corrections which should be applied to account for end blocks and large displacements are presented.

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188 9.4.3.3.1

Mechanical testing of advanced fibre composites Modified beam theory (MBT) method

The energy release rate for a DCB specimen in which the arms are considered to be clamped at the delamination front is given by simple beam theory to be: GI =

3Pd 2 Ba

[9.5]

By inserting into Equation [9.5] the values of load, P, and displacement, d, associated with growth at a particular crack length, a, the critical energy release rate, GIc, at that crack length can be determined. However, in practice, the arms are not perfectly built-in and rotation may occur at the delamination front. This rotational effect may be accounted for by treating the DCB as if it contained a longer delamination at each length, a + D, and so the mode I fracture toughness using this modified beam theory is calculated from Equation [9.6]:23 GIc =

3Pd 2 B(a + D)

[9.6]

D may be determined experimentally by plotting the cube root of compliance, C1/3, as a function of delamination length, a (the compliance is the ratio of displacement to the applied load, d/P). The values which should be used to generate this plot are the loads and displacements corresponding to the visually observed delamination onset and the propagation values. The extrapolation of a least squares fit through the data yields D as the negative of the intercept on the delamination length axis, as shown in Fig. 9.11. The intercept will normally be negative and so D will normally be positive. Typical values of D that have been determined5 for a 3 mm thick carbonfibre reinforced plastic (CFRP) specimen lie in the range 2.8–5.1 mm. In some cases the intercept turns out to be positive, and in these circumstances ESIS9 recommends that D should be set to zero. ASTM8 makes no recommendation concerning the sign of D but uses the modulus of D (i.e. |D|) rather than D in Equation [9.6]. However, if D does turn out to be negative, then the cause should be investigated; such a value could be produced, for example, if the crack lengths have been mistakenly measured from the end of the specimen rather than from the load line. In these circumstances the negative value of D would be valid and could be used in Equation [9.6] to produce valid GIc data. This approach also allows the determination of the flexural elastic modulus, E1f: 3

E1f =

64(a + D) P dBh3

[9.7]

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0.08

0.04

C

1/3

(mm

1/3

N

-1/3

)

0.06

0.02

0.00

-10

10

D = 4.55 mm

30

50

70

90

110

130

150

Crack length a (mm)

9.11 Determination of D for the modified beam theory.

Here, following the ASTM convention, h is the full laminate thickness. The values of EIf obtained should be delamination length independent; however, fibre bridging may increase the values determined. 9.4.3.3.2

Compliance calibration (CC) method (Berry’s method)24

This method makes use of the visually observed delamination onset and propagation values of d and P with the corresponding delamination lengths, a. The method assumes that the compliance, C, is proportional to an. A plot is constructed of log (C) versus log (a) and a least squares best fit line is drawn through the data. The exponent, n, is the slope of the line, as shown in Fig. 9.12. The mode I interlaminar fracture toughness is calculated from Equation [9.8]:25 GIc =

nPd 2 Ba

[9.8]

Typical values of n for the standard 3 mm thick CFRP specimen lie in the range 2.7–2.9 mm. (Note that simple beam theory gives n = 3.) In contrast to the modified beam theory, this approach is essentially a curve fitting process which does not directly address the mechanisms controlling the behaviour of the specimen. The value of n will change if the range of delamination lengths is changed, but for the crack length ranges normally used, GIc determined by this method is usually within a few per cent of that calculated using the modified beam theory.

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log C

190

Dy Dx

n=

Dy Dx

log a

9.12 Determination of n for the compliance calibration method.

9.4.3.3.3

Modified compliance calibration method

In this method the cube root of the compliance, C1/3, is assumed to be linearly proportional to the crack length, a, and the constant of proportionality is determined using a compliance calibration plot. By manipulating the algebra to produce an equation for G which does not explicitly involve the observed crack lengths, this method effectively includes the crack length correction achieved by the modified beam theory (MBT) method. The ASTM standard8 and the ESIS protocol9 differ slightly in the application of this data reduction method which uses all of the visually observed delamination onset and propagation data (although ESIS does allow the visually observed onset data to be omitted from the linear regression described below). In the ASTM method a plot is constructed of the delamination length normalised by specimen thickness, a/h, as a function of the cube root of the compliance, C1/3, as shown in Fig. 9.13. A least squares fit to the data gives a line of slope A1 and the mode I interlaminar fracture toughness is calculated from Equation [9.9]:26 GIc =

3 P 2C 2 3 2 A1 Bh

[9.9]

The ESIS9 approach is similar but uses slightly different nomenclature for the thickness, where h is now the half thickness of the laminate. The ESIS protocol recommends plotting the cube root of the product of the width and compliance (BC)1/3 versus the thickness-normalised delamination

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a/h

A1

C 1/3

9.13 Modified compliance calibration.

length, a/2h. The least squares slope of this line gives the coefficient, m. The mode I interlaminar fracture toughness is then given by Equation [9.10]: 2

GIc =

3m Ê P ˆ 2 3 (BC ) 4h Ë B ¯

[9.10]

Note that the ESIS protocol9 mistakenly refers to plotting (BC)2/3 in the text and omits a factor of 2h in the equation for GIc. 9.4.3.3.4

End block and large displacement corrections

If end blocks are used, these will stiffen the end portions of the specimen. Note that with hinges the stiffening effect is of no consequence, because this occurs outside the zone between the load line and the delamination front. As a test proceeds, the end blocks will rotate as the specimen deflects and so reduce the lever arm to the delamination front, reducing the displacement for a given load. In addition, if large displacements occur, then the deflection will be less than that predicted by small displacement theory owing to the shortening of the lever arm. For these reasons the measured displacement will be less than that which would occur if the loading were applied at the mid-plane of the arms and the displacement remained in the linear regime. An approximate correction factor, N, has been derived25 which can be applied to yield the corrected linear displacement, such that:

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Mechanical testing of advanced fibre composites d corrected =

d N

[9.11]

where d is the measured displacement and N is given by Equation [9.12]: 3

N = 1-

9 dl1 Ê l2 ˆ Ë a¯ 8 a2

2

Ï Ê l2 ˆ ¸ 9 Ê d ˆ Ì1 - Ë ¯ ˝ - Ë ¯ a ˛ 35 a Ó

2

[9.12]

where the term (l2/a)3 corrects for block rigidity ignoring the effects of 2 9 dl1 Ï Ê l 2 ˆ ¸ rotation; 1 Ì ˝ corrects for the change in lever arm caused by 8 a2 Ó Ë a ¯ ˛ rotation of the end block including a further correction for end block 2 9 Êdˆ rigidity; and corrects for the change in lever arm caused by large 35 Ë a ¯ displacements. See Fig. 9.4 for definitions of l1 and l2. The correction factor, N, can also be used to yield the corrected compliance. Recalling that the measured compliance C = d/P, then: Ccorrected =

C N

[9.13]

Clearly the second and third correction terms in N in Equation [9.12] could be applied when hinges are used, but the ASTM standard and ESIS protocol both recommend that N should be considered to be 1 for hinges. By correcting the displacements, or compliances, with the factor N and then using the corrected values in the data reduction schemes described earlier, the resulting GIc is that which would occur if the load measured for a given crack length had been applied at the arm mid-thickness position and the specimen had deflected in accordance with small displacement linear theory. In reality, when end blocks are used, the load is applied at a point significantly removed from the arm mid-thickness position and rotation at the end of the specimen will cause a shorter lever arm to the delamination front. Similarly large displacements will also cause the lever arm to be shorter than the crack length measured from the scale marked on the edge of the specimen. A factor, F, can be derived to account approximately for both of these effects, so that the actual lever arm (i.e. the corrected crack length) can be obtained25 from the crack length, a, measured from the scale on the edge of the specimen multiplied by √F: acorrected = a F

[9.14]

and 2

F = 1-

3 Êdˆ 3 Ê dl1 ˆ Ë ¯ 10 a 2 Ë a2 ¯

[9.15]

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2

3 Êdˆ 3 Ê dl1 ˆ corrects for large displacements and corrects for 10 Ë a ¯ 2 Ë a2 ¯ rotation of the end block. It can be shown that the energy release rate is proportional to the square of the moment at the delamination front,25 so that for a given load the GIc determined on the basis of small displacement theory and application of the load at the specimen arm mid-thickness position can be corrected to the true value by multiplying by F: where

GIc (corrected ) = GIc F

[9.16]

Again it can be noted that both correction terms in F can be applied when hinges are used for the load application and, in contrast to the recomendations for N, both the ASTM standard and ESIS protocol recommend that these terms should be used for hinges. Table 9.2 summarises the use of the N and F correction terms in the three data reduction schemes described earlier.

Table 9.2. Use of N and F correction factors in mode I data reduction schemes. Data reduction method

Use of N and F factors

Modified beam theory

(i) plot (C/N)1/3 versus crack length to determine the crack length correction, D 3P (d N ) F (ii) evaluate GIc from GIc = 2B (a + D ) (iii) the flexural elastic modulus can be 3 64P (a + D ) determined from E 1f = 3 (d N )Bh (i) determine n from a plot of log(C/N) versus log(a) nP (d N ) F (ii) calculate GIc from GIc = 2Ba ASTM: (i) determine A1 as the slope of a plot of (a/h) versus (C/N)1/3 23 3P 2 (C N ) (ii) calculate GIc* from GIc = F 2A1Bh ESIS: (i) determine m as the slope of a plot of (BC/N)1/3 versus (a/2h) 2 23 3m Ê P ˆ Ê BC ˆ (ii) calculate GIc from GIc = F 4h Ë B ¯ Ë N ¯

Compliance calibration method (Berry’s method)

Modified compliance calibration method

* Note that the application of the correction factors for GIc is given incorrectly in the ASTM standard.5

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The correction factors F and N usually produce only small corrections for 3 mm thick unidirectional CFRP specimens for the crack length ranges recommended. However, for longer crack lengths, or for other materials where the critical energy release rate is higher and/or the flexural stiffness is lower, these corrections can be more significant.

9.5

Mode II testing

As noted earlier, there have been many test methods proposed for measuring GIIc. These methods include the end-loaded split (ELS) test,5 the endnotched flexure (ENF) test5 and, more recently, the four-point end-notched flexure (4ENF) test.13 A test standard for a relatively complex stabilised ENF test has been produced by JIS.7 ASTM and ESIS have been conducting round-robin laboratory evaluations of other mode II test methods;27 ASTM have been investigating the ENF test, while ESIS have examined both the ENF and ELS methods. The ESIS protocol9 is for an ELS test for a unidirectional laminate. The following sections consider first the ELS test and then a number of variants of the ENF test.

9.5.1 ELS Test With this specimen, shown in Fig. 9.5(a), a lateral load is applied by the testing machine through a load block under displacement control at a constant rate. Delamination growth from a non-adhesive insert material or a mode I or mode II precrack at the laminate mid-plane is monitored so as to obtain delamination initiation and propagation readings at known positions on the load–displacement curves. Appropriate data reduction allows the determination of GIIc for initiation and propagation, which can be plotted versus the delamination length, a, as an R-curve. It should be expected that different initiation values of GIIc will be determined dependent on the type of starter crack and it is recommended that tests directly from the delamination film and following precracking should be performed, so as to obtain the most conservative value. 9.5.1.1 Specimens Laminate preparation is largely similar to that described earlier for the mode I DCB test specimens. If a starter film is to be used, it should be placed at the mid-thickness of the laminate prior to moulding. The starter film length in the specimen should be at least 50 mm from the load line so that the effects of the load block are reduced. The normal dimensions for the specimen are a width of 20 mm and overall length of 170 mm. The free length (i.e. the length measured from the

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load line at the loading block to the clamp) should be approximately 100 mm. For a 60% fibre volume fraction CFRP the laminate thickness should be 3 mm, and 5 mm for the same volume fraction glass-fibre reinforced plastic (GFRP). Although it is possible to use alternative specimen dimensions, ideally the width should be between 15 mm and 30 mm. An increase in length is not critical, but shorter specimens result in a small amount of delamination growth for investigation and too few data points for the analysis; care must be taken to ensure that the ratio, a/L, between the initial delamination length, a, and the distance from load line to clamp, L (see Fig. 9.5), is at least 0.55 in order to avoid unstable crack growth.5 Reducing the laminate thickness may result in specimens which are insufficiently stiff, so that delamination growth may occur only at large displacements, or failure of the specimen arms may occur instead of delamination growth. The ELS mode II test requires only one loading block, which is bonded to the specimen following the same procedure as that described for mode I DCB specimens. The position of the end of the delamination insert should be marked on both edges of the specimen and a thin layer of typewriter correction fluid painted onto both edges. Marks should be drawn on both edges every 1 mm from the tip of the delamination film for at least the first 5 mm and then every 5 mm up to 35 mm; subsequently marking should return to 1 mm intervals up to at least 40 mm.9 As for the mode I test, the crack lengths associated with each of these marks is as measured from the load line in the unloaded state. 9.5.1.2 Apparatus A tensile testing machine capable of giving a constant displacement rate of between 1 and 5 mm min-1 and equipped with a load cell accurate to ±1% is required; typical loads are in the 100N–200N range. A means of recording the complete load–displacement curve is required. A fixture is needed to introduce the load to the pin in the load block, allowing free rotation of the specimen end. A loading jig is also needed to clamp the remote end of the specimen, and this must allow for the horizontal movement of the specimen as the test proceeds. There are a number of alternatives: the end of the specimen may be clamped between rollers; the fixed clamp can be mounted on a fixture which allows horizontal movement through bearings (as shown in Fig. 9.5); or a fully fixed clamping arrangement can be used, together with a loading fixture which allows horizontal movement of the load point, so that the applied load remains vertical. This vertical load is normally applied to the load block by pulling up with the load block beneath the specimen, but it is also possible to invert the specimen and apply the load to the end block by pushing down.

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9.5.1.3 Test procedure 9.5.1.3.1

Elastic modulus determination

If the beam theory analysis is to be used to evaluate the data, it is necessary to obtain a value for the elastic modulus of the material from a threepoint bend test. The modulus value should be determined before delamination testing and on part of the specimen which does not contain the delamination film or precrack. Details for carrying out this test procedure are given in Chapter 7. 9.5.1.3.2

Mode II fracture test

The test parameters and data recording are basically the same as those described previously for mode I testing. Because these specimens do not open during the test, friction between the faces may be a problem, and to reduce this effect a thin film of PTFE, or a pencil lead, should be placed between the delamination faces at the load line (see Fig. 9.5), opening them slightly. The specimen is loaded at a constant crosshead rate in the range 1–5 mm min-1. For normal length specimens the low end of the speed range is suitable, but longer specimens can be tested at the higher end. The point of delamination initiation should be recorded on the load– displacement curve. Observation can be aided by optical microscope, or a CCD camera system, as described earlier for the mode I test, but even so the tip of the crack is difficult to track since there is no crack opening. Subsequent crack positions should be noted as the delamination passes each mark on the edge of the specimen. Normally loading should stop before the delamination tip reaches a point 10 mm from the clamp. The specimen is then unloaded, usually at a higher rate. Once removed from the jig, the specimen can be opened by hand in mode I. This reveals the final positions of the mode II delamination front on both edges of the specimen, since the surface features are generally quite different between mode I and mode II. If the difference between the two positions is greater than 2 mm, the results are suspect. 9.5.1.4 Data analysis As with the mode I test described previously, the data required for the analysis are the delamination length, a, together with the corresponding loads, P, and displacements, d. The same initiation values can also be determined, that is, deviation from linearity (NL), visual observation (VIS) and 5% offset or MAX. Propagation (PROP) values are also normally available, although in some materials the propagation may be unstable.

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Modified beam theory (MBT)

As with the mode I data reduction described previously, a correction for rotation at the delamination tip, D, must be introduced into the simple beam theory. The analysis immediately runs into problems: what value should this correction have? A method for determining D by experiment has been proposed which is similar to that described earlier for the mode I test. In this case (C - C0)1/3 is plotted against the crack length, a, where C0 is the compliance of a specimen without a delamination. Unfortunately there is an accuracy problem with this approach for mode II tests because it is now the difference between two compliances which is being plotted.28 There is some evidence28 to suggest that multiplying the value of D obtained from mode I tests by 0.42 gives a good approximation to the value of D corresponding to loading of the ELS specimen. In the absence of mode I test results on the same material the ESIS protocol suggests setting D to zero, although a theoretical estimate is available for D.25 The mode II fracture toughness is given by Equation [9.17]:9 GIIc

9P 2 (a + D II ) = 4 B 2 E1f h3

2

[9.17]

where P is the load, a is the delamination length, DII is the delamination tip rotation correction, B is the specimen width, E1f is the modulus of elasticity parallel to the fibre direction from a three-point bend test and h is the half-thickness of the specimen. Other equations are available for GIIc,28 for example excluding E1f but including P, a and d, analogous to Equation [9.6] for mode I. However, the support at the clamped end will not be absolutely rigid and corrections will need to be applied to d to allow for the effect of the support flexibility in addition to the other corrections discussed earlier for the mode I test. Equation [9.17] is based on small displacement theory and assumes the load to be applied at the specimen arm mid-plane. As for the DCB test, the correction factor, F, can be used for large displacements and end-block effects: GIIc (corrected ) = GIIc ◊ F

[9.18]

where GIIc is calculated from Equation [9.17] and: 2

È Êdˆ Ê dl1 ˆ ˘ F = Í1 - q 1 -q2 2 ˙ Ë ¯ Ë L ¯˚ L Î

[9.19]

in which d is the displacement, l1 is the distance from the centre of the load block to the mid-plane of the specimen arm to which the end block is attached and L is the free length of the specimen, see Fig. 9.5(a). The factors q1 and q2 are calculated from Equations [9.20] and [9.21]:

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4

È Ê aˆ Ê aˆ ˘ + 63 3Í15 + 50 Ë ¯ Ë L ¯ ˙˚ L Î q1 = 3 2 È Ê aˆ ˘ 20 Í1 + 3 Ë L ¯ ˙˚ Î 2

È Ê aˆ Í 1 + 3Ë ¯ L Ê Lˆ Í q 2 = -3 3 Ë a ¯Í Èa˘ Í 1 + 3Í ˙ Î ÎL˚ 9.5.1.3.4

˘ ˙ ˙ ˙ ˙ ˚

[9.20]

[9.21]

Experimental compliance method (ECM)

This alternative approach can be used if the loading and unloading load–displacement curves are both linear. The compliance, C, is plotted versus the cube of delamination length, a3, using only the VIS and PROP values. A least squares fit is obtained, the slope, m, of which can be used to determine GIIc from Equation [9.22]: GIIc =

3P 2 ma 2 2B

[9.22]

A correction factor, N, to account for end-block rigidity and rotation and large displacements has been derived25 for the ELS specimen to correct the measured compliance, as for the DCB specimen, but the ESIS protocol does not suggest that this should be used.

9.5.2 ENF test In its basic form the ENF test involves performing a three-point bend test on a specimen which contains a starter delamination at one end (see Fig. 9.5), where the total length of the specimen is some 150 mm and the width is 20 mm. As with the ELS specimen, the initial delamination may be extended from the insert by precracking, either in mode I, using the DCB configuration, or in mode II. To precrack the specimen in mode II the specimen can be positioned in the three-point bend fixture so that the delamination can only grow a few millimetres before reaching the central loading roller. This test has a relatively small zone of stable growth (simple beam theory predicts that for constant GIIc the delamination growth will be stable for a > 0.7 L), and this growth is likely to be affected by the central loading roller. The test is normally conducted in the unstable regime (a/L ª 0.5), yielding initiation data only. Equation [9.23] can be used to evaluate GIIc from the test data:5

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GIIc =

9P 2 (a + D 11 ) 16 B 2 E1f h3

199

2

[9.23]

The P values in Equation [9.23] are those associated with the NL, VIS and MAX/5% offset discussed earlier for mode I, although, as noted for the ELS test, detecting delamination growth visually can be difficult. It should be noted that the non-linearity due to large displacements in this specimen is of a softening form (rather than the stiffening form observed in the DCB) and can easily be confused with the non-linearity associated with the initiation of delamination growth. It is also possible to use an experimental compliance calibration approach. Compliance data can be determined before the toughness test is conducted by varying the position of the specimen in the bend fixture so that the compliance can be measured for a range of different delamination lengths encompassing the delamination length to be used in the toughness test. The cube of the compliance is then plotted against the delamination length and the slope, m, of the best fit straight line is used in Equation [9.24] to determine GIIc: GIIc =

3P 2 ma 2 2B

[9.24]

It is possible to stabilise the delamination growth in the ENF specimen so that propagation data can be collected. This can be achieved by using some form of feedback control rather than performing the test at a fixed crosshead displacement rate. Two such methods have been proposed for stabilised ENF (SENF) testing29 and form the basis of the JIS test standard.7 In one method, the relative shear displacement between the two arms of the specimen is controlled to increase at a constant rate. In the other method, a function involving both the crosshead displacement and the applied load is controlled to increase monotonically during the test. Both of these approaches require test machines that can accept feedback control, and this is likely to preclude widespread adoption of the SENF test. To achieve stable growth in an ENF-type test, but without the complexity of the SENF, it is possible to load the ENF specimen in a four-point bend test rig as shown in Fig. 9.14.13,30 With the delamination tip positioned between the inner loading rollers, the 4ENF test has a number of advantages over the more conventional ENF test. The delamination front will lie in a zone of pure moment, whereas in the three-point ENF (and in the ELS) there is also a shear force acting. It has been suggested13 that this reduces the friction problems associated with the other mode II tests, although there is still a compressive normal force acting between the arms of the specimen outside the central pure moment zone. Also, because the delamination front lies in the pure moment region,

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Specimen

Machine base

a L

9.14 4ENF testing arrangement.

the data reduction strategy is relatively simple. The compliance can be plotted against delamination length and the slope, m, of the best fit straight line found. If large displacements occur, then corrections similar to those presented earlier will be necessary. GIIc is then evaluated from Equation [9.25]: GIIc =

P 2m 2B

[9.25]

Note that Equation [9.25] does not involve the crack length, so that the nature of any R-curve will be directly reflected in the form of the load– displacement curve. So, for example, if GIIc is independent of crack length, then the load will reach a critical value and remain constant; if, however, GIIc increases with delamination growth, then so will the critical load. The 4ENF method is a relatively new proposal and is currently being investigated further.

9.6

Mixed mode I/II

Delaminations in real composite structures often grow in a combination of modes I, II and III, so that there is considerable interest in establishing mixed mode growth criteria.31,32 To support this, measurement of the delamination toughness at various mode ratios is required. Mixed mode I/II delamination behaviour has been under investigation for some time.27 Whilst there are a number of practical ways which may be used to induce a mixed mode response, there are two which have received

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a great deal of attention. These are the fixed ratio mixed mode (FRMM) and the mixed mode bend (MMB) tests.

9.6.1 FRMM test The basic form of FRMM specimen is essentially identical to the ELS specimen, discussed previously. It is, however, inverted when loaded, so that the loading block is above the specimen, with the testing machine acting in tensile mode, as shown in Fig. 9.7. In the FRMM case the ratio of mode I to mode II is very close to 4 : 3 throughout the test, which is carried out in the same way as the mode II ELS test, described earlier. The mode I and mode II contributions to the total mixed mode interlaminar critical energy release rate GI/IIc can be deduced from Equations [9.26] and [9.27]:5 G m Ic = F G

m

IIc

3P 2 (a + D I ) B 2 h3 E1f

2

9P 2 (a + D II ) =F 4 B 2 h3 E1f

[9.26] 2

[9.27]

where GI IIc = G m Ic + G m IIc

[9.28]

DI and DII are the crack length correction terms discussed in the earlier section on the ELS data analysis. F is the correction factor for large displacements and end-block effects, such that: 2

F = 1 - q1

Êdˆ Ê dl1 ˆ -q2 2 Ë L¯ ËL ¯

[9.29]

where 4

2

Ï Ê aˆ ¸ Ê aˆ + 130 + 15˝ 3Ì367 Ë L¯ Ó Ë L¯ ˛ q1 = 3 Ï Ê aˆ ¸ 20Ì7 + 1˝ Ó Ë L¯ ˛

[9.30]

and 2

Ê aˆ +1 L Ê ˆ Ë L¯ q2 = 3 3 Ë a¯ Ê aˆ 7 +1 Ë L¯ 7

[9.31]

By positioning the initial starter delamination away from the specimen midplane it is possible to achieve other mode ratios in the FRMM test,25 but

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then the two techniques for determining the mode separation (the local and global33 techniques) yield significantly different mode ratios. Evidence has been published which suggests that for some materials the global mode separation method is valid,34 but for others the local mode separation technique is the most suitable.35

9.6.2 MMB test The jig used for the MMB test method36 is shown in Fig. 9.8. It makes use of a specimen which is essentially identical to the DCB specimen described previously, but the jig allows the determination of the delamination fracture toughness at various ratios of mode I to mode II loading, from almost pure mode I to pure mode II. Forces to load the specimen are applied via end blocks (or piano hinges) at the delaminated end of the specimen and through rollers which bear on the specimen in the undelaminated region. The base of the jig is attached to the bottom specimen loading block and also supports the specimen near the opposite end with a roller, whilst a lever, attached to the top end block, also applies a downward force on the specimen centrally between the supports at either end of the specimen. By applying a downward load on the lever arm, as indicated in Fig. 9.8, the upper block is pulled upwards and a downward load is applied centrally to the specimen. To vary the mode mixture, the loading point position on the lever can be changed by varying the dimension ‘c’. It is also possible to adjust the mode ratio by moving the upper loading roller away from the central position.34 It is necessary to ensure that the load applied to the lever remains vertical throughout the test, and this is normally achieved by the use of a saddle and yolk arrangement. In order to reduce geometric nonlinear effects due to lever rotation, the lever should be loaded so that the position of the loading point is slightly above the mid-plane of the test specimen (approximately 15 mm). Load application to the lever and the specimen should allow sliding with a minimum of friction; this is generally achieved with roller bearings. The method of testing is basically the same as that described previously for the DCB and ELS specimens, load and displacement readings being taken and correlated with delamination position. It is recommended that the load point displacement be measured using a linearly variable displacement transducer (LVDT) rather than from the crosshead displacement, since this avoids the complexity of having to determine the compliance of the loading system separately for every lever length setting to be used. The desired mode mixture can be set by adjusting the relative positions

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of the lever loading roller and the loading saddle/yolk, such that the distance between them, c, from simple beam theory, is given by Equation [9.32]: GII ˆ GII GII ˆ 8 3Ê 1 + 3Ê 1 + 3 Ë Ë G¯ G G¯ c= L GII 39 -3 G

[9.32]

in which GI and GII are the mode I and mode II components, respectively, and G is the total energy release rate. This is reasonably accurate for most mode mixtures but becomes less so in the low mode II range owing to corrections that need to be made for crack tip rotation, when Equation [9.32] can be in error by up to 20%. The mixed mode interlaminar toughnesses GmIc and GmIIc can be obtained using Equations [9.33] and [9.34]: 2

for c > L 3 G m Ic =

P 2 (3c - L) (a + D) 16 BL2 E1f I

2

[9.33]

for c < L 3 G m Ic = 0 2

G m IIc =

3P 2 (c + L) (a + 0.42 D) 64 BL2 E1f I

2

[9.34]

where I is the second moment of area for one delaminated half of the specimen (Bh3/12) and L is the half-span length of the MMB test apparatus. These equations rely on delamination length corrections25,34 for laminate rotation at the delamination front. In this case Equation [9.35] is used to calculate D, the results of which have been shown to agree well with finite element predictions.37 D=h

E11 11G13

2

Ï Ê G ˆ ¸ Ì3 - 2Ë ˝ 1+ G¯ ˛ Ó

[9.35]

E11E22 , where E11 is the longitudinal modulus of elasG13 ticity measured in tension, E22 is the transverse modulus of elasticity and G13 is the out-of-plane shear modulus which may be assumed to be equal to the in-plane shear modulus G12 for a unidirectional composite. E1f in the Equations [9.33] and [9.34] is the flexural modulus of the laminate and can be determined from the initial load–displacement response but, if the crosshead displacement has been used, then a correction for the loading system compliance must be included. in which G = 1.18

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9.7

Multidirectional laminates

This chapter has so far largely concerned itself with the investigation of delamination growth in unidirectional laminates where the delamination is initiated between two plies of the same fibre orientation and the delamination front is constrained to grow in the fibre direction. A typical component will, however, be composed of a multidirectional laminate, and there is no reason to suppose that the location and direction of growth of a delamination would be constrained in such a manner. Delaminations may, for example, arise from manufacturing defects occurring between plies of any orientation, and delaminations from in-service damage, such as impact, normally occur between plies of different orientation. Whilst it is true that the unidirectional values of fracture toughness allow the ranking of different materials in their delamination resistance, if fracture mechanics is to be used to predict the growth of delaminations in multidirectional composite components, then the fracture toughness as a function of fibre orientation in the delaminating plies needs to be investigated.

9.7.1 Mode I Early published literature38–42 on mode I delamination growth in multidirectional laminates showed that the conventional DCB test produces complex fracture behaviour when examining interfaces other than that between unidirectional plies orientated parallel to the delamination direction. In laminates where the delaminating interfaces are not 0°/0°, a large degree of fibre bridging normally develops behind the propagating crack. This arises from the crack ‘jumping’ from the plane in which it was originally located by transverse cracking of an adjacent off-axis ply.43 When this occurs the crack tip bifurcates, leading to the development of significant fibre bridging, often of almost complete plies. One way of suppressing this behaviour is to use a delaminating film along both edges of a DCB specimen in addition to the normal starter crack film.44 A plan view of the mid-plane of the specimen used is shown in Fig. 9.15.

Edge delamination

9.15 Mid-plane plan view of side-delaminated specimen.

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In this work, multidirectional XAS/913 carbon/epoxy specimens were prepared with layups which were carefully designed to ensure that the laminate stiffness characteristics (i.e. the A-B-D matrix) of the two arms were identical, that all the laminate coupling effects (e.g. bend-twisting) were eliminated and that there was no curvature or in-plane shear distortion of the laminate (or half-laminate) caused by thermal stresses resulting from curing. (The ply-level residual stresses are, of course, still present and their magnitude in the delaminating plies may affect the measured interlaminar toughness.)45 Results using the conventional DCB specimen confirmed the observations of other researchers. Unidirectional specimens exhibited continuous stable crack growth at the intended interface and an essentially constant GIc with a crack length of 0.28 kJ m-2. Changing the fibre orientation of the delaminating plies to +45°/+45° and +45°/-45° resulted in fibre pullout, crack jumping, multiple delamination growth and considerable fibre bridging, as indicated on the fracture surface shown in Fig. 9.16(a). In edge-delaminated specimens with +45°/+45° and +45°/-45° mid-plane interfaces the crack tended to remain predominantly at the intended interface. The suppression of the complex combination of fracture modes is clearly seen in Fig. 9.16(b). The average GIc recorded for these interfaces was some 30% greater than that for the 0°/0° interface, whereas with no edge delaminations the increase was in excess of 100%. Despite the success of this edge delamination approach to the mode I testing of multidirectional laminates in XAS/91344 and T300/924,46 the unwanted fracture modes could not be fully suppressed in mode I tests on +45°/-45° interfaces in T800/924 laminates,47 as shown in Fig. 9.17. Investigation of lower angle +q°/-q° interfaces found that although reduction of the interface angle had an effect on the degree of fibre bridging, it was not

(a)

(b)

9.16 Fracture surfaces of (a) a conventional specimen and (b) an edge-delaminated specimen, for mode I DCB tests on a +45°/-45° interface in XAS/913.

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crack growth direction

9.17 Fracture surface of edge delaminated mode I DCB test on a +45°/-45° interface in T800/924.

eliminated entirely. The characteristics of the material system that dictate the success or failure of the edge delamination strategy are yet to be identified, but will include the fibre-to-matrix bond and, possibly, the fibre diameter. (T800 fibres are approximately half the diameter of XAS and T300 fibres.)

9.7.2 Mode II and mixed mode I/II Whilst it may not be possible to employ successfully the edge delamination approach to the mode I (or mode II) testing of all multidirectional interfaces and fibre/matrix combinations, there is evidence46 that it can work satisfactorily for 0°/q° interfaces under certain circumstances. The key is to reduce the tensile stresses in the q° ply caused by bending so that the delamination is inhibited from jumping through the q° ply. This condition can be satisfied in mode II (ELS) and mixed mode I/II (FRMM and MMB) by ensuring that the q° interface is in the lower arm of the specimen, when loaded as shown in Fig. 9.7, for the FRMM. It has been shown that for some materials, specimens can be tested in this manner without edge delaminations, provided the mode I component is sufficiently low.47

9.8

Conclusions

There is a degree of test method standardisation in place. At present this is restricted to national standards for unidirectional laminates. However, work is progressing on international standards to cover both modes I and II, mixed mode I/II test methods and even mode III. It is likely that these standards will be introduced in the next few years. There are many problems to be resolved, not least those surrounding the meaningful interlaminar toughness testing of multidirectional laminates, but considerable progress has been made in establishing specimen configurations, test procedures and data reduction schemes for the determination

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of the interlaminar toughness of laminated composites. The measured interlaminar toughness characteristics of a material system will not only enable it to be ranked against competing material systems, but will also allow prediction of delamination growth in real structures, which will have a major role in both initial design and in assessing the significance of any delamination damage occurring during service.

References 1. N R Sottos, J M Hodgkinson and F L Matthews, ‘A practical comparison of standard test methods using carbon fibre reinforced epoxy’, Proceedings of the Sixth International Conference on Composite Materials and Second European Conference on Composite Materials, Centre for Composite Materials, Imperial College, London, eds F L Matthews, N C R Buskell, J M Hodgkinson and J Morton, Elsevier Applied Science, 1987, Volume 1, 310–20. 2. S Mespoulet, J M Hodgkinson, F L Matthews, D Hitchings and P Robinson, ‘A novel test method to determine the through-thickness tensile properties of long fibre reinforced composites’, Proceedings of Seventh European Conference on Composite Materials (ECCM-7), Institute of Materials London, UK, Volume 2, Woodhead Publishing, Cambridge May 1996, 131–7. 3. S Mespoulet, Through-thickness Test Methods for Laminated Composite Materials, PhD Thesis, Centre for Composite Materials, Imperial College, London University, UK, January 1998. 4. J G Williams, Fracture Mechanics of Polymers, Ellis Horwood, Chichester, UK, 1984. 5. S Hashemi, A J Kinloch and J G Williams, ‘The analysis of interlaminar fracture in uniaxial fibre-polymer composites’, Proc Royal Soc A, 1990 427 173– 99. 6. D Hitchings, P Robinson and F Javidrad, ‘A finite element model for delamination propagation in composites’, Computers and Structures, 1996 60(6) 1093–1104. 7. JIS K7086, Testing Methods for Interlaminar Fracture Toughness of Carbon Fiber Reinforced Plastics, 1993. 8. ASTM D 5528-94a, ‘Standard test method for mode I interlaminar fracture toughness of unidirectional fibre-reinforced polymer matrix composites’, Annual Book of ASTM Standards, 100 Barr Harbor Drive, West Conshohocken, PA 19428, USA, Vol 15.03, 1997. 9. European Structural Integrity Society (ESIS), ‘Protocol for interlaminar fracture testing of composites (Mode I DCB – ISO CD 15024.2 and Mode II ELS – ESIS TC4 Version 95-11-10)’, Polymers and Composites Task Group, 1998. 10. I M Daniel, I Shareef and A A Aliyu, ‘Rate effects on delamination fracture toughness of a toughened graphite/epoxy’, in Toughened Composites, ed N J Johnston, ASTM STP937, 1987, 260–74. 11. A L Glessner, M T Takemori, M A Vallance and S K Gifford, ‘Mode I interlaminar fracture toughness of unidirectional carbon fiber composites using a novel wedge-driven delamination design’, in Composite Materials, Fatigue and Fracture, ed P Lagace, ASTM STP1012, 1989, 181–200.

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12. H Maikuma, J W Gillespie and D J Wilkins, ‘Mode II interlaminar fracture of the center notch flexure specimen under impact loading’, J Composite Materials, 1990 24 124–49. 13. R H Martin and B D Davidson, ‘Mode II fracture toughness evaluation using a 4-point bend end notched flexure test’, Proceedings, 4th International Conference on Deformation and Fracture of Composites, Manchester, Institute of Materials, published by IoM Communications Ltd, London, March, 1997, 243–52. 14. B R K Blackman and J G Williams, ‘On the mode II testing of carbon-fibre polymer composites’, Proceedings of the Twelfth European Conference on Fracture (ECF-12), Sheffield, ESIS, SIRIUS and University of Sheffield, eds M W Brown, E R los Rios and K J Miller, published by EMAS, Cradley Heath, UK 1998, 1411–6. 15. T K O’Brien, ‘Composite interlaminar shear fracture toughness, GIIc: shear measurement or sheer myth?’, NASA Technical Memorandum 110280, NASA Langley Research Center, Hampton, Virginia, USA. 16. E Greenhalgh and S Singh, ‘Investigation of the failure mechanisms for delamination growth from embedded defects’, Proceedings of the Twelfth International Conference on Composite Materials (ICCM-12), Paris, 1999, paper 341. 17. E Greenhalgh, B Millson, R Thompson and P Sayers, ‘Testing and fracture analysis of a CFRP wingbox containing a 150J impact’, Proceedings of the Twelfth International Conference on Composite Materials (ICCM-12), Paris, 1999, paper 340. 18. P Robinson and D Q Song, ‘The development of an improved mode III delamination test for composites’, Composites Science and Technology, 1994 52 217–33. 19. S M Lee, ‘An edge crack torsion method for mode III delamination fracture testing’, J Composites Technology and Research, 1993 15(3) 193–201. ASTM D30.06 Sub-committee on Interlaminar Properties, Mode III Interlaminar Fracture Task Group, Edge Crack Torsion Method, 1999. 20. A J Brunner, Interlaminar Fracture Testing of Unidirectional Composites, NATO Advanced Study Institute, Mechanics of Composite Materials, Portugal, July 1995. 21. T de Kalbermatten, R Jaggi, P Flueler, H H Kausch and P Davies, ‘Microfocus radiography studies during mode I interlaminar fracture tests on composites’, Journal of Materials Science Letters, 1992 11 543–6. 22. T K O’Brien and R H Martin, ‘Round robin testing for mode I interlaminar fracture toughness of composite materials’, ASTM Journal of Composites Technology and Research, Winter 1993 15(4) 269–81. 23. S Hashemi, A J Kinloch and J G Williams, ‘Corrections needed in double cantilever beam tests for assessing the interlaminar failure of fibre-composites’, Journal of Materials Science Letters, 1989 8 125–9. 24. J P Berry, ‘Determination of fracture energies by the cleavage technique’, Journal of Applied Physics, 1963 34(1) 62–8. 25. J G Williams, ‘The fracture mechanics of delamination tests’, Journal of Strain Analysis, 1989 24(4) 207–14. 26. K Kageyama and M Hojo, ‘Proposed methods for interlaminar fracture toughness tests of composite laminates, Proceedings of the 5th US/Japan Conference on Composite Materials, Tokyo, June 1990, 227–34.

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27. P Davies, B R K Blackman and A J Brunner, ‘Standard test methods for delamination resistance of composite materials: current status’, Applied Composite Materials, 1998 5 345–64. 28. Y Wang and J G Williams, ‘Corrections for mode II fracture toughness specimens of composite materials’, Composites Science and Technology, 1992 43(3) 251–6. 29. K Tanaka, K Kageyama and M Hojo, ‘Standardisation of mode I and mode II interlaminar fracture toughness tests for CFRP in Japan’, Proceedings, 2nd European Conference on Composite Materials – Testing and Standardisation, Hamburg, 1994. 30. R H Martin, T Elms and S Bowron, ‘Characterisation of mode II delamination using the 4-ENF’, Proceedings, 4th European Conference on Composite Materials – Testing and Standardisation, Lisbon, Portugal, Institute of Materials, published by IoM Communications Ltd, London 1998, 161–70. 31. E Greenhalgh, L Asp and S Singh, ‘Delamination resistance, failure criteria and fracture morphology of 0°/0°, 0°/5° and 0°/90° ply interfaces in CFRP’, Proceedings of the 5th International Conference on Deformation and Fracture of Composites, Manchester, Institute of Materials, published by IoM Communications Ltd, London, 1997, 43–52. 32. J R Reeder, Evaluation of Mixed-mode Delamination Failure Criteria, NASA TM 104210, 1992. 33. M Charalamides, A J Kinloch, Y Wang and J G Williams, ‘On the analysis of mixed-mode fracture’, International Journal of Fracture, 1992 54 269–91. 34. A J Kinloch, Y Wang, J G Williams and P Yayla, ‘The mixed mode delamination of fibre composite materials’, Composites Science and Technology, 1993 47(3) 225–37. 35. F Ducept, D Gamby and P Davies, ‘Mixed-mode failure criteria derived from tests on symmetric and asymmetric specimens’, Composites Science and Technology, 1999 59(4) 609–19. 36. J R Reeder and J H J Crews, ‘Redesign of the mixed-mode bending delamination test to reduce nonlinear effects’, Journal of Composites Technology and Research, 1992 14 12–9. 37. S Bhashyan and B D Davidson, ‘Evaluation of data reduction methods for the mixed mode bending test’, AIAA Journal, 1997 35 546–52. 38. A J Russell and K N Street, ‘Factors affecting the interlaminar fracture of graphite/epoxy laminates’, Proceedings of 4th International Conference on Composite Materials (ICCM-4), eds T Hayashi, K Kawata and S Umekawa, 1982, 279–86. 39. D J Nicholls and J P Gallagher, ‘Determination of GIc in angle ply composites using a cantilever beam test method’, Journal of Reinforced Plastics and Composites, 1983 2 2–17. 40. H Chai, ‘The characterisation of mode I delamination fracture in non-woven multidirectional laminates’, Composites, 1984 15 277–90. 41. W L Bradley, C R Corleto and D P Goetz, Fracture Physics of Delamination in Composite Materials, AFOSR-TR-88-0020, 1987. 42. A Laksimi, M L Benzeggagh, G Jing, M Hecini and J M Roelandt, ‘Mode I interlaminar fracture of symmetrical cross-ply composites’, Composites Science and Technology, 1991 41(2) 147–64. 43. S Singh and E Greenhalgh, ‘Micromechanisms of interlaminar fracture in

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44.

45.

46.

47.

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carbon-epoxy composites at multidirectional ply interfaces’, Proceedings of the 4th International Conference on Deformation and Fracture of Composites, Manchester, Institute of Materials, published by IoM Communications Ltd, London, 1997, 201–10. P Robinson and D Q Song, ‘A modified DCB specimen for mode I testing of multidirectional laminates’, Journal of Composite Materials, 1992 26(11) 1554–77. P Robinson, S Foster and J M Hodgkinson, ‘The effects of starter film thickness, residual stresses and layup on GIc of a 0°/0° interface’, Advanced Composites Letters, 1996 5(6) 159–63. S Foster, P Robinson and J M Hodgkinson, ‘Interlaminar fracture toughness testing of 0°/q° interfaces in carbon-epoxy laminates using edge delamination strategy’, Plastics, Rubber and Composites Processing and Applications, 1997, 26(10) 430–7. M S Hiley, ‘Delamination between multidirectional interfaces in carbon-epoxy composite under static and fatigue loading’, Proceedings, 2nd ESIS-TC4 Conference on Polymers and Composites, Les Diablerets, Switzerland, September 1999.

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10 Impact and damage tolerance P J HOGG AND G A BIBO

10.1

Introduction

Fibre-reinforced/plastic matrix composites owe their high specific basic mechanical properties (reduced probability of flaws in a fibre compared with the bulk material) to the synergistic behaviour of the fibre and resin. However, testing has shown that these materials are, in practice, sensitive to many aspects of in-service use for which it is difficult to provide design data. For example, impact-induced damage has been shown to reduce compression strength in continuous fibre systems. The types of composite material (short/random/continuous fibre with thermoset/thermoplastic matrices) and their applications (aerospace/automotive/civil/marine) vary widely, so that no single test can readily quantify the myriad of potential impact situations and their subsequent effect. This may in itself require further post-impact testing to measure the desired residual property (e.g. strength, stiffness, etc). The object here is to discuss the various impact test methods available, their relevance and the significant practical importance this experimental approach has contributed to the use of composite materials in industry. The emphasis is directed toward high performance composite materials, with a critical examination of the fundamental issues thought to be governing fracture and the potential for future impact testing to be simulated (virtual testing).

10.2

Impact testing

It is common to refer to the impact resistance of a material. However, this is an all-embracing term that can refer to many quite different aspects of a materials behaviour in a given structure. The impact ‘resistance’ of a composite may refer to the ability of the composite to withstand a given blow without any damage (i.e. the resilience); the maximum force necessary to rupture or separate a 211

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composite structure, irrespective of the preceding level of damage (the impact strength); the amount of energy that is absorbed by a given mass of the composite (the crush resistance); or perhaps the level of damage that a composite can sustain during impact loading without suffering undue reduction to some primary structural function after the impact event (damage tolerance). Impact loading is usually taken to mean the impact of either a projectile or the composite itself at speeds in the range 1–10 m s-1. This phenomenon has received the greatest attention to date, as out-of-plane impacts in this velocity range may have catastrophic consequences on the subsequent load carrying capability of the structure. Impacts in the speed range >100 m s-1 are termed ballistic events, while those at speeds >1000 m s-1 would be termed hypervelocity impacts. This chapter is restricted to impacts within the 1–10 m s-1 range. While testing within this speed range can present some practical difficulties, with respect to data analysis caused by vibration and noise, the complications induced by reflecting stress waves during the test are largely absent.1,2

10.2.1

Theoretical aspects

There are many theoretical aspects that must be considered for the correct interpretation (particularly if a plastics-based standard is being followed, the impact test may be instrumented) of experimental testing. The level of the impact blow (i.e. the impact energy or momentum) is varied in most test machines by varying the drop height of the striker, see Fig. 10.1. This has the effect of changing both the impact energy and the impact velocity simultaneously. An alternative approach would be to vary the mass of the striker, while keeping the velocity constant. Applying the physics of motion results in Equations [10.1] to [10.4], defining force F, velocity v, displacement x and energy E, respectively: dv dt

[10.1]

1 fdt M Ú0

[10.2]

F = Mg - f = M t

v = v0 + gt -

t t

x = v0 + t

1 2 1 gt fdt 2 M Ú0 Ú0 t

E = v0 Ú fdt + g Ú ftdt 0

0

[10.3] t

˘ 1 È fdt ˙ 2 M ÍÎÚ0 ˚

2

[10.4]

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Release mechanism

Impactor Measuring scale Guide

Specimen Velocity measurement & anti-multiple strike Impact support boundary conditions

10.1 Schematic diagram showing the essential elements of an impact test apparatus.

where v0 is the velocity at the point of impact. This allows the forces generated during a test, together with energy absorption and deflection, to be recorded. In cases such as this it is important that a reliable and accurate method for measuring the velocity at contact is employed because this parameter is required for the calculations of displacement and energy and, if incorrect, will generate erroneous results.3 In other cases where the test is uninstrumented, an alternative approach to determining energy absorption is to measure the rebound height. Where a post-impact property is being measured it is unusual for the test to be instrumented, although this may be specified in future in the emerging standards in this area. The signals generated by an instrumented striker may be noisy owing to excessive vibrations (from the machine, specimen or the striker itself) and it is possible with some test machines, and certainly with post-processing of the impact signal, to filter and smooth the curve. This has the effect of producing a force–time or force–displacement curve more similar to that generated during slow testing. It is generally agreed, however, by workers in the field that this process is extremely risky if the curves are to be inspected subsequently for signs indicative of fracture events. The filtering process cannot distinguish between spurious vibrations and genuine features on the curve that result from the fracture process, and much vital information can be lost through filtering.

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Experimental impact test methods

Unidirectional prepreg tape-based structures or components normally consist of relatively thin shell-like laminates; thus the majority of possible service impacts can be categorised as events involving thin monolithic shell structures. Added complications arise if the structure has a honeycomb core, as the skin/core interface bond may fail and, unlike the monolithic material, these are more difficult to inspect non-destructively. Damage caused by ballistic impact typically takes the form of a neat puncture and, whilst it still requires inspection to determine the spread of internal fracture, the damage is clearly visible.4 Consequently, the form of impact scenario that has attracted most experimental study has been based on low velocity/low energy and monolithic composite materials. The dropped tool on an aircraft wing, stones hitting the undershield of a car, a lifeboat hitting rocks, a fork-lift truck nudging the side of a portable building, can all be cited as possible examples of composite structures undergoing out-of-plane impact, albeit with a wide range of relative projectile–target masses, shapes and velocities. This class of impact event is usually simulated in tests by some form of falling weight or driven dart being impacted onto a simple square or circular plate. This approach will be discussed in more detail later. While the initial utilisation of composites was aerospace driven, the generalisation that all structures are thin is now an oversimplification and becoming increasingly untenable. Many large structures are now constructed from thick composites, and this has necessitated considerable activity in the testing arena in order to quantify out-of-plane through-thickness properties of composites. To date, the corresponding effort in impact testing of thick composites has not materialised. Some limited studies have been undertaken but, apart from empirical ballistic studies on thick composite armour, no systematic studies either of properties or test methods have been undertaken. Alternatively, an area that is currently receiving more attention is that of in-plane impact testing. This area is being recognised as important because of the rate sensitivity of the constituents of composite materials and their high specific energy absorbing capabilities (e.g. formula one cars).

10.2.3

In-plane impact testing

Typically, this might be the result of some high strain rate loading taking place in a remote part of a structure which results in a general transient membrane tensile stress being generated. This form of impact might be simulated in testing by the use of a Hopkinson bar apparatus to introduce a shock wave through a sample, or in some cases by the application of a

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high strain rate tensile force by servohydraulic machines.5 It is not always possible to generate a high strain rate tensile stress for a sustained period of time, and in some respects the transient loading and the tensile test at high strain rates, for practical purposes, are simply two extremes of what might be achieved. A body of high strain rate ‘tensile impact’ testing has been undertaken at Oxford in the UK.6–8 These tests do not introduce any new dimensions into testing by way of test geometry or fixtures; the only change relative to conventional tensile tests lies in the apparatus used to introduce the high strain rate, and the difficulties of recording accurate deflection (or strain) versus time data for the construction of the high strain rate stress–strain curves. The data generated from these tests may be regarded with the same significance as those used to generate design data, as they are capable of measuring a pseudo-material property. Another form of high strain rate in-plane loading that is becoming increasingly important is connected with the progressive crushing of composites, as might be engineered in crash conditions in vehicles and other energy absorbing structures.9–11 Crush testing involves compressive loading rather than tension, and the time duration and displacement involved in a crush test may be greater than in some drop weight impacts. The loading scenario is, however, a genuine impact event, as a crash involves a finite packet of energy and the collision of bodies at high speed. Although most research work in this field has been based on ad hoc test specimens, originally based on tubes, some progress has been made towards identifying standard test components and fixtures.

10.2.4

Out-of-plane impact testing

The application of an out-of-plane impact can be effected in a number of ways. Objects can be propelled towards a target specimen using pendulum strikers, falling weights, driven darts and fired sabots. Specimens can be simply supported, clamped, allowed to flex or be constrained, mounted on compliant fixtures or rigid frames. While variations in conditions will inevitably result in different forces, energy dissipation and fracture processes, it has been found that tests which produce similar stress states generate similar damage states.12 10.2.4.1

Flexed beam tests

The need to perform impact tests on metals and later on plastics was recognised before the advent of composites as engineering materials. It is not surprising that the first test methods explored for impact testing of composites were derived from the methods used successfully for these other materials. These included variations on the theme of Izod and Charpy impact tests,

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which use a swinging pendulum to strike a specimen which is in the form of a beam. The Izod specimen designed for metals consists of a beam clamped and struck as a cantilever, while the Charpy test developed for plastics has the beam simply supported and loaded in flexure by the pendulum striker. The Izod and Charpy tests both have provision for notched samples for use with tough specimens, see Fig. 10.2. These tests are very useful for the isotropic materials for which they were developed. In their simplest forms the pendulums are not instrumented and the datum recorded from each test is the energy absorbed by the specimen. This is measured by the angle through which the striker moves after it has impacted and fractured the specimen. The greater the swing of the pendulum after impact, the smaller the amount of energy absorbed. Similarly, impact energy supplied can be varied by adjusting the starting position of the pendulum, although in order to maintain a relatively constant velocity, it is usual to change the mass of the pendulum and keep everything else constant. The test can be instrumented in order to record force during the test, thereby allowing a record of the strength of the material under impact conditions to be obtained and, if the specimen is notched, the test can be used as a form of high rate fracture toughness test, see Table 10.1.13 In the general context of composite materials this form of test geometry is of limited value. The provision of a beam-type specimen is the first problem area. If the impact test is required to simulate the performance of a thin composite beam, then obviously the test is appropriate. However, it is unlikely that in service many reinforced thin beams will be manufactured from composite materials, unless the fibres are aligned along the beam. The test may well be suitable for ranking or providing a relative measure of variables in the construction of the material, such as interply adhesion, the role of toughening layers, different fibre types or resin types, for example, effec-

(a)

(b) Specimen Striker Notch Striker

Notch

10.2 Schematic representation of the Charpy (a) and Izod (b) impact equipment.

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Table 10.1. Charpy impact data for (a) longitudinally and (b) transversely reinforced unidirectional prepreg tape laminates (after Adams and Perry13). Composite

System (a) Carbon/epoxy Glass/epoxy Kevlar 49/epoxy Nylon/epoxy System (b) Carbon/epoxy Glass/epoxy Kevlar 49/epoxy Nylon/epoxy

Configuration

Maximum force (N)

Absorbed energy (J)

Normaliseda absorbed energy (kJ m-2)

unnotched notched unnotched notched unnotched notched unnotched notched

12 900 8 500 13 390 11 210 7 920 5 690 5 600 4 230

10.7 9.2 77 56 68 57 14.9 9.4

109 113 778 694 672 694 145 116

unnotched notched unnotched notched unnotched notched unnotched notched

778 512 676 689 445 338 436 276

0.5 0.3 1.1 0.9 1.4 0.9 0.5 0.5

5.0 3.6 10.9 11.3 13.0 12.6 5.5 6.7

NB typically an average of 3 specimens. a Normalised by dividing by the specimen cross-sectional area.

tively simulating a high speed bend test. This information is, however, peculiar to that test configuration. The impact test becomes something akin to a ‘materials’ or ply level property test with all of the complications of high strain rate testing (including vibrations, transient effects), and the data obtained cannot easily be used to predict or model the performance of more complicated (practical) laminates. Some useful studies performed using flexed beam tests were conducted by Marom et al.,14 which enabled the role of different fibres in hybrid composite structures to be investigated. Similarly, key work undertaken by Cantwell and Morton revealed the relationships between thickness and damage mechanisms for carbon-fibre composites, although this work relied on relatively thin and wide strips rather than on beams of the dimensions usually associated with flexed beam tests.15–18 The flexed beam test also imposes a uniaxial loading condition on the specimen. When composite structures, approximating to plates or shells in service, are impacted, the load almost inevitably involves a biaxial loading constraint. Consequently the failure modes exhibited by beam

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specimens, even if the beams are cut from laminates with a multiaxial fibre orientation, differ markedly from those exhibited by the majority of composite structures. Experience has also shown that in some cases multiaxial laminates in plate form develop damage which is not symmetric and which can propagate extensively within a plate before failure. Such behaviour cannot be reliably predicted on the basis of beam tests. While a place exists for beam-based impact testing in a laboratory context for the purpose of materials development, the test cannot be considered suitable for predicting the response of thin composite structures. It is probable, however, that as the interest in thick composites grows, Charpy or Izod-type tests, as applied to large sections of metal components, will be re-examined for correspondingly large composite beams. 10.2.4.2 Flexed plate impact testing Flexed plate impact tests typically comprise the impact of a projectile onto a plate-type specimen as shown schematically in Fig. 10.3. There are, however, no test methods that have been standardised specifically for the impact testing of long fibre composites. In many cases standards developed for plastics have been adapted for use with composites, and this often constitutes direct usage with no modification of geometry or specimen size. This configuration is often used to assess the ultimate load resistance of the material and its energy absorbing capabilities, or for studying the development and consequences of subcritical damage. In the first case it is usual to supply an impact with an excess of energy, such that the striker pene-

Impactor

Specimen

Boundary support condition e.g. 40 mm diameter ring

10.3 Schematic diagram of typical flexed plate impact geometry.

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trates the specimen without significant deceleration during the impact event. Typical force–time curves generated during excess energy impacts are shown in Fig. 10.4. The data produced in this way can be characterised using a number of parameters taken from the force–time (or force–displacement) curves. The most easily identifiable parameters are the peak force and the total energy absorbed by the plate. Neither of these parameters represents a material property. There is some indication that the peak force is determined by the strain to failure of the reinforcing fibres, coupled with the initial stiffness of the composite plate, and is independent of resin chemistry.19,20 Other features, such as energy to the peak force, or the force and energy at the onset of damage, may be obtained. The latter parameters are not always easy to identify, and in some cases no clearly defined load drop can be seen on the curve at deflections when cracking has begun. A reduction in the magnitude of the initial energy of the striker will result in a change in the force–time curves as shown in Fig. 10.5. During this process, the prominence of peaks associated with initial damage increases and, by sufficiently lowering the impact energy, it is possible to identify the onset of fracture quite clearly. For low energy impacts, the parameters such as peak force and absorbed energy are, on their own, not particularly helpful in the characterisation of the material behaviour. It is useful to be able to link absorbed energy or peak force to a damage parameter. The most widespread form of damage created during impact testing is delamination. Delaminations are also critical in the subsequent post-impact compression strength of a composite plate, as discussed in detail later, while the presence of fibre fracture is influential in terms of residual tensile strength.21 The area, or width, of the delaminations can be measured. For carbon-fibre composites this must be done using C-scan, or another non-destructive system, to image the delaminated area, as shown in Fig. 10.6, while for glass-fibre composites this zone can usually be seen with the naked eye. It may be noted that the force– displacement curves computed from the equations of motion are reasonably accurate up to the point at which the velocity of the striker falls to zero. Thereafter, significant errors may arise and the computed data are unreliable.22 The scatter generated during high energy testing is quite significant and overshadows most of the variations that may be present between different composite material systems. Table 10.2 presents data obtained for a series of test specimens drawn from one material and an equivalent set generated by individual specimens of many widely differing glass-fibre composites. The coefficient of variation of both data sets is very similar. A master plot can be constructed illustrating the similarity of most glass-fibre composite systems, as shown in Fig. 10.7. Similar plots can be

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Mechanical testing of advanced fibre composites (a)

8800

Force (N)

7040 5280 3520 1760 0.0

2.5

5.1

7.6

10.2

12.7

24.0

30.0

10.2

12.7

Time (ms) (b)

8800

Force (N)

7040 5280 3520 1760 0.0

6.0

12.0

18.0

Displacement (mm) (c)

100.0

Energy (J)

80.0 60.0 40.0 20.0 0.0

2.5

5.1

7.6

Time (ms)

10.4 Typical raw (unfiltered) data generated during a throughpenetration impact test on glass-fibre reinforced quasi-isotropic unidirectional prepreg tape. (a) Force–time, (b) force– displacement, (c) energy–time.

constructed for carbon-fibre composites, Fig. 10.8. The relative performance of carbon- and glass-fibre composites becomes clear on this form of plot. It should be noted that the data for the carbon-fibre systems are mean data points for different matrix systems (thermoplastic and thermoset). The data

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1850

(a)

Force (N)

1480 1110 740 370 0.0

1.3

2.6

3.9

5.2

6.5

2.4

3.0

5.2

6.5

Time (ms) (b)

1850

Force (N)

1480 1110 740 370 0.0

0.6

1.2

1.8

Displacement (mm) (c)

3.0

Energy (J)

2.4 1.8 1.2 0.6 0.0

1.3

2.6

3.9

Time (ms)

10.5 Typical raw (unfiltered) data generated during a low energy/low velocity impact test on glass-fibre reinforced quasi-isotropic unidirectional prepreg tape. (a) Force–time, (b) force– displacement, (c) energy–time.

for glass-fibre composites consist mainly of individual data points, apart from the SMC which is represented by mean data points. The behaviour of similar composites tested under low energy conditions is very different and is a function of resin chemistry, for a similar fibre

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Y scale / mm

Time / µs

% Areas

X scale / mm

10.6 C-scan showing the internal fractures induced by a low energy/low velocity impact on a triaxial [452,-452,06,-452,452]S carbon/epoxy unidirectional prepreg tape.

Absorbed energy (J)

200.0

150.0

100.0

50.0

0.0 0.0

50.0

100.0

150.0

200.0

Thickness (mm) ¥ fibre volume fraction (%)

10.7 Relationship between energy absorbed during throughpenetration versus thickness multiplied by fibre volume fraction for glass-fibre composites. , Random and woven glassfibre/thermoset resin; , sheet moulding compound (SMC); , random glass-fibre thermoplastic (GMT); , quasi-isotropic continuous glass-fibre reinforced polypropylene; , quasiisotropic carbon-fibre epoxy unidirectional prepreg tape (after Babic et al.).19

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Table 10.2. Data from through-penetration tests showing the scatter in the combined population and within a given material sample. Material

Maximum force (N)

GRP3 S1 9 200 GRP3 S2 15 300 GRP3 S3 14 400 GRP4 S1 800 GRP4 S2 15 300 GRP4 S3 11 000 GRP5 S1 8 000 GRP5 S2 16 100 GRP5 S3 13 400 GRP6 S1 8 200 GRP6 S2 15 300 GRP6 S3 10 400 GRP7 S1 8 600 GRP7 S2 16 900 GRP7 S3 11 200 GRP7 S4 4 750 GRP8 6 700 GRP9 5 900 Mean Stand. deviation Coefficient of variation (%)

Absorbed energy (J)

Normalised force [F ¥ (t ¥ Vf)]

Normalised energy [E ¥ (t ¥ Vf)]

85 136 115 78.1 150 100 766 138 99.3 66.8 118 83.2 76.1 174 84.3 42.6 65.5 45.9

101 103 119 87 98 99 91 92 104 92 101 86 93 115 97 81 92 92 97 9.6 9.9

0.93 0.91 0.95 0.82 0.96 0.90 0.75 0.87 0.77 0.75 0.78 0.69 0.82 — 0.73 0.73 0.90 0.72 0.82 0.09 10.9

GRP7 S4 Results from 6 specimens illustrating the variation within one material Mean Stand. deviation Coefficient of variation (%)

9.4 9.5 9.8

0.79 0.064 8.1

Vf = fibre volume fraction.

type.20,23–25 Considerable difference in behaviour, as measured by damage zones, is evident in Fig. 10.9. This shows the results for damage width versus impact energy for glass-fibre and carbon-fibre epoxy and carbon-fibre PEEK (polyether ether ketone) and Radel quasi-isotropic laminates. It should be noted that impact data generated using a particular test geometry and specimen size are not necessarily representative of the results generated using alternative test geometries even for identical materials. Changes in the relative size of striker, specimen, span and support conditions influence the distribution of tensile, compressive and shear stresses

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Absorbed energy (J)

200.0

150.0

100.0

50.0

0.0 0.0

50.0

100.0

150.0

200.0

Thickness (mm) ¥ fibre volume fraction (%)

10.8 Energy absorbed in through-penetration versus thickness multiplied by fibre volume fraction for carbon-fibre reinforced composites superimposed on master curve, from Babic et al.19 , Glass fibre; , carbon fibre.

50.0 Ring support diameter 40.0

Damage width (mm)

30.0

20.0

10.0

0.0 0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

Impact energy (J)

10.9 Extent of impact-induced delamination damage versus incident energy (ISO/DIN) in , quasi-isotropic carbon-fibre reinforced AS4/PEEK; , T650-42/Radel (thermoplastics); , a toughened epoxy (T800/924); and , glass-fibre reinforced epoxy (E-glass/914).

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throughout the thickness of the specimen and thereby influence the values obtained for the various test parameters. Equally, the same material with a different layup may result in different levels of damage, even when used with the same impact equipment. In other cases, impact tests have been standardised as part of a more extensive test method designed to study post-impact compression properties. According to the requirements of the user, the impact tests may be used to measure the ultimate resistance to rupture of the composite plate, or to induce some non-critical damage in the composite that may impinge on subsequent properties under a different loading regime (damage tolerance). There is no simple method for comparing results generated using different specimen geometries and layups, particularly if the impact event is designed to damage but not destroy the material. Specimens that have a relatively low flexural stiffness will tend to absorb a large quantity of any kinetic energy supplied by a projectile by elastic deformation.15,16,26 Thick specimens with a relatively high flexural stiffness over a short support span will, in contrast, suffer from contact deformation due to their stiffness; shear stresses will result in localised fracture before bending stresses become significant, Fig. 10.10.27

10.2.5

Standardisation of impact test techniques

Rationalisation of the various impact test methods currently being used is urgently required, since many researchers are repeating work and generating data that cannot be readily disseminated between groups because the data are generated by different impact apparatus (material for supports, boundary conditions, striker material and geometry, data acquisition and analysis). Dimensions of specimens and test supports for high energy or through penetration impact cited in the literature by numerous research groups are given in Table 10.3.28 The fibre layups used with these test configurations are of course variable according to the needs of a particular research or quality assurance programme. It is rare for testing to be performed on unidirectional plates, as this does not simulate any sensible practical application. Standard tests specified for plastics but commonly used for high energy impact testing of composites are included in Table 10.4.Again, the fibre construction or layup is not specified by the test standard. When an impact test is performed on a composite in order to measure the subsequent in-plane properties of the damaged composite, mainly in compression, the laminates are usually required to be quasi-isotropic layups. To some degree, in the absence of a specific test standard for impact, the test geometry adopted

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(a)

45 90 -45 0 45 90 -45 0 0 -45 90 45 0 -45 90 45

(b)

45 90 -45 0 45 90 -45 0 0 -45 90 45 0 -45 90 45

10.10 Schematic diagram of the damage induced by impact in (a) low span to thickness ratio specimens (shear); (b) high span to thickness ratio specimens (bending), after Cantwell and Morton.27

tends to be based on what commercial equipment is available. In the USA a preponderance of research groups utilise the test configuration that comes as standard in the instrumented impact test rig marketed by Dynatup, which consists of a hemispherical striker of diameter 16 mm and a non-specified support geometry; the test is usually undertaken with the specimen clamped. In contrast, much testing in Europe is performed to conform to the ISO/DIN standard for plastics – as many impact machines sold in Europe have been standardised using this geometry. The ISO/DIN standard does not require specimens to be clamped, and they are simply supported on a 40 mm steel support ring. Low energy non-penetrating impact testing is almost always undertaken in conjunction with subsequent post-impact testing which is usually based on compression tests. The tests are considered together below.

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Table 10.3. Various common drop-weight impact test geometries (from Wyrick and Adams28). Plate dimensions (mm)

Type of support and dimensions (mm)

Shape of impactor and diameter (mm)

Investigatorsa

300 ¥ 1000

100 diameter ring clamped 200 ¥ 800 clamped 152 apart clamped Only 80 sides clamped 127 ¥ 127 simply supported 140 ¥ 140 clamped 76 ¥ 127 not specified 76 ¥ 127 simply supported 28 apart simply supported 50 diameter ring not specified 100 diameter clamped 90 diameter clamped 50 diameter clamped

Hemisphere 12.7

Cantwell et al.

Hemisphere 15 and 30 Sphere 12.7

Levin Joshi and Sun

Hemisphere 20

Caprino et al.

Hemisphere 12.7

Dart 7.9

Wardle and Tokarsky Winkel and Adams Chaturvedi and Sierakowski Hirschbuehler

Sphere 15.9

Boll et al.

Hemisphere 5.5

Caprino

Hemisphere 12.5

Leach and Moore

Cantilever ball 25.4

Lal

Cantilever ball 25.4

Lal

Cantilever ball 25.4

Lal

300 ¥ 840 25 ¥ 305 80 ¥ 220 152 ¥ 152 150 ¥ 150 102 ¥ 152 102 ¥ 152 25 ¥ 150 75 ¥ 75 100 diameter 90 diameter 50 diameter

a

Flat cylinder 9.7

For reference details, see Wyrick and Adams.28

Table 10.4. Common impact test standards adopted for composites. Method

Impact velocity (m s-1)

Shape of impactor and diameter (mm)

Support conditions and dimensions (mm)

BS 2782

3.46

Hemisphere 12.7

ASTM D 3029-FA ASTM D 3029-FB ISO/DIS 6603/2

3.6 3.6 4.4

Hemisphere 15.86 Hemisphere 12.7 Hemisphere 20 and 10 options

50 I/D, 57 O/D ring, clamped if specimen less than 0.89 thick. 60 diameter or square specimen 76 I/D clamped 38.1 I/D clamped 40 I/D ring, clamping optional. 60 diameter or square specimen

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10.3

Damage tolerance – compression after impact (CAI) tests

Damage tolerance, as an aerospace design philosophy, may be summed up by the general requirements of the FAA’s (Federal Aviation Administration) FAR 25.571: ‘evaluation of the strength, detail design and fabrication must show that catastrophic failure due to fatigue, corrosion or accidental damage will be avoided throughout the operational life of the aeroplane’.29 Specific demands require a damaged structure to possess sufficient residual strength or stiffness for a specified set of flight conditions. Consequently, the susceptibility of composite materials to suffer damage from relatively minor impacts or other forms of in-service abuse is of major concern, particularly as this damage may not be visible on the surface at the site of impact on the material. The most deleterious form of internal damage that occurs within laminated composites after an impact is delamination. The presence of delaminations makes a composite susceptible to premature collapse during compression loading. The mechanisms thought to be the driving failure are sublaminate/ply buckling in the delaminated region and/or a mode I dominated crack growth, see Fig. 10.11.30–32 Tensile properties are less affected by this form of damage until higher energy impacts cause fibre fracture.21 Hence, a body of testing has evolved which seeks to assess the relative ability of different composite forms to withstand impact damage and subsequent in-plane compression loading.

10.11 Compression after impact failure in a quasi-isotropic carbonfibre reinforced unidirectional prepreg tape (T800/924) showing delamination propagation and ply buckling failure of a ‘thin film’ on a parent material.

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A compression test on a damaged specimen, which is usually a flat plate for convenience, measures the load at which a complex failure event takes place and may depend on ply layup, specimen width and many other factors. The test is clearly a component test and does not measure a material property, as such. It is accordingly extremely important to ensure that data generated in this field are compared on a sound basis, and the dimensions of specimens and test conditions must be consistent. The general philosophy that has been accepted is to perform an impact test at low energies on a flat plate which is then placed in some form of support fixture before being subjected to a compression test. Effectively two separate testing modes, the impact and the compression must be controlled and standardised if valid comparisons are to be made between materials and/or laboratories. Most test procedures that have evolved require a single plate to be cut to size and used for both the impact and compression phase of the test. In some cases, notably the CRAG (Composites Research Advisory Group)33 test method emanating from the UK, the specimen on which the impact is undertaken is not controlled. A large plate can be used, with multiple impacts being performed at different locations. The target plate is then cut to a specific size for the subsequent compression tests. Some test protocols and their derivatives have been developed that feature differing combinations of plates, impact support conditions, impacts and impact energies, all for the purpose of introducing the initial damage into a specimen prior to compression. These are listed in Table 10.5.33–37 After the impact has been performed, the damaged plate must be subject to compression. As it is usual to employ relatively thin plates for this test, it is important to ensure that any failures in the compression test result from a failure triggered by the impact damage. It is probable that undamaged thin sheets simply loaded in compression would buckle before suffering inplane compression failure. Consequently it is necessary to suppress this behaviour by employing antibuckling guides of some sort. In most tests the test plate is supported in a fixture which contains some guide constraint at the vertical edge of the plate, along with slots in the loading fixture for the plate at the top and bottom position.34–37 The CRAG test33 is different in that it allows for an antibuckling guide rail to be attached to the specimen, see Fig. 10.12, which may then be inserted into a conventional set of loading grips, or jaws, to hold the plate during compression.

10.4

Boeing test methods and related variants

The de facto standard test used worldwide is now the Boeing test method, which has become adopted as a testing guide by SACMA (SRM 2-888) and by Airbus (AITM 1.0010) with only minor modifications.35–37

3 (45/-45/0/90)nS

6.35 (45/0/-45/90)nS

4 to 5 (-45/0/45/90)nS

4 to 5 (-45/0/45/90)nS

4 (45/0/-45/90)nS

CRAG

NASA

Boeing

SACMA

Airbus

Tup: 16 dia Mass: 1–6 kg Energy: 9–40 J Support: 125 ¥ 75 clamped

Tup: 15.88 dia Mass: 5 kg Energy: open Support: 127 ¥ 76 clamped

Tup: 15.75 dia Mass: 4.5/6.8 kg Energy: open Support: 127 ¥ 76 clamped

Tup: 12.7 dia Mass: 4.5 kg Height: 0.61 m Energy: 27 J Support: 127 square/clamped

Tup: 10 dia Mass: open Height: 1 m Energy: open Support: 100 ring/clamped

Impactor tup and support conditions (mm)

End-tabs are recommended but other end grips accepted End loaded

End loaded

End loaded

End loaded

180 by 50 (cut to size post-impact) Damage width not to exceed 40 (254–318) ¥ 178 (cut to 127 post-impact)

152 ¥ 102 (cut to size before impact)

152 ¥ 102 (cut to size before impact)

150 ¥ 100 (cut to size before impact)

Loading arrangement

0.5 mm min-1

1.27 mm min-1

0.5 mm min-1

1.27 mm min-1

Adjust to give failure in 30–90 s

Loading rate

Compression after impact Specimen dimensions (mm)

SACMA = Suppliers of Advanced Composite Materials Association.

Material thickness and layup (mm)

Protocol

Table 10.5. Various industrial protocols for the measurement of residual compression strength.

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SCALE:

231

1cm

10.12 Schematic diagram showing a specimen and antibuckling fixture for compression testing (after Cantwell et al.).38

10.4.1

Impact test details

The impact fixture used for the Boeing test consists of a rectangular plate clamped to a loading plate with a rectangular cut-out using four spot clamps. The plate size is 4 in by 6 in (approximately 102 mm by 152 mm) and appears to have been selected to approximate the unsupported width of a composite wing skin between stringers. The required plate thickness is 0.2 in (5 mm). This is a fairly large specimen which consumes a lot of material. This is a problem for all testing laboratories, but it is a particular issue for those involved in materials development where quantities of experimental prepreg for testing may be limited. The same test plate is specified by SACMA. The impact is undertaken by dropping a striker onto the test plate. The striker does not need to be instrumented, and the method of introducing the impact is not rigidly controlled in the test specifications. For convenience, a Gardner-style impact apparatus (as used for early plastics testing) is suggested, since this rig may be available in many laboratories; a Dynatup 8200 series impactor is also suggested. The key feature, however, is that the striker must be equipped with a hemispherical tip of diameter 0.62 in (15.75 mm) and have a mass of 10–15 lbs (4.5–6.8 kg). The impact drop height is adjusted to provide the required impact kinetic energy. The original Boeing specification does not state a required impact energy

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level, but the SACMA Recommended Method specifies that energies of 1500 in-lb in-1 (6.67 J mm-1) thickness should be used. Airbus have converted the SACMA geometry to a metric equivalent and specified plates of 100 mm by 150 mm, with the thickness as close to 4 mm as is possible. This test method also differs slightly from the US approach in that a 16 mm diameter striker is used with specific energy levels defined in absolute terms (rather than adjusted for plate thickness) and corresponding to a range of impact masses: 1–3 kg for 9, 12, 16, 20 and 25 J impacts and 4–6 kg for 30 and 40 J impacts. Additional proposals to the Airbus (AITM 1.0010, Issue 2) specification have been made by British Aerospace Airbus, suggesting the use of instrumented strikers in order to identify a threshold force at which damage is generated in the plate, along with Cscanning of the impacted plate to measure the extent of damage. Some non-standard variations in the test method have been used in the past (ironically sometimes by Boeing), where the hemispherical indentor was rested on the specimen and was itself hit by a falling projectile. These effects were examined in a round-robin exercise undertaken in Japan.39 Energy losses in this arrangement were found to result in a reduction in damage and spurious improvements in the subsequent apparent residual compression strength on the order of 10–15%. The supporting frame used for the original Boeing impact test was constructed from a combination of plywood with a top plate of steel or aluminium. The SACMA variant specifies an aluminium support frame and the Airbus variant specifies a steel frame. The difference in the compliance of the test fixture introduced by these changes can also be considerable, and the amount of damage introduced into the plate for a given impact blow may be substantially reduced if the wooden hybrid frame is used.39 The support frame in all cases features a cut-out, which is 3 in by 5 in (75 mm by 125 mm for Airbus), over which the impact specimen is secured.

10.4.2

Compression test details

The impact plate is supported during an in-plane compression test in the Boeing fixture as shown in Fig. 10.13. The vertical sides of the specimen are restrained by antibuckling rails with knife edge supports. The plates fit into slots in the bottom of the main fixture and in the loading plate which sits on the top of the assembly. The height of the side supports are smaller than the plates such that, when the rig is assembled, a small part of the plate is unsupported (approximately 5 mm) by the antibuckling rails. This allows a maximum compressive strain of approximately 3.3% in the material during the test before excessive deflections mean the test has to be terminated before plate failure. The only other dif-

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Top plate

Test specimen

Support fixture

10.13 Boeing compression after impact jig.35

ficulty emerges when testing undamaged specimens in order to obtain a baseline property measurement. In these cases failure frequently occurs in the unsupported material, causing the undamaged compression strength to be of questionable value. The problem is to some extent eliminated in the Airbus variant of the test where the top plate is made to be the same size as the lateral gap between support rails. In this way the top loading plate is free to slide past the side rails, and the entire length of the test specimen can be laterally supported for the duration of the test. The Boeing and SACMA tests require the test plate to be equipped with four strain gauges mounted on the plate as shown in Fig. 10.14, two on each plate face. These are to ensure that the plate is mounted correctly in the fixture and that out-of-plane deformation does not occur before failure is triggered by the impact damage.

10.4.3

Compression after impact test data

The basic test data generated using the Boeing test and related standards can be presented as impact energy versus residual compression strength. The test can be used successfully to discriminate between laminates with different resins and fibres in order to gain an overall assessment of damage tolerance, as shown in Fig. 10.15 for laminates with brittle and tough resins. The trend in the aerospace industry has been to settle on one impact energy (per unit thickness of the specimen) and present the number generated as a CAI value for certification purposes. This is an approach that is

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Mechanical testing of advanced fibre composites Strain gauge locations (both sides) 4.0 1.0

1.0

1.0

6.0

Specimen centreline Impact location

Specimen centreline

10.14 Schematic diagram showing specimen geometry and position of strain gauges on the SACMA compression after impact coupon.36 All dimensions are in inches.

Residual compression strength (MPa)

500.0

400.0

300.0

200.0

100.0

0.0 0.0

10.0

20.0

30.0

40.0

Impact energy (J)

10.15 Residual compression strength data using the Boeing test plotted versus impact energy, showing the effect of damage saturation (damage to support boundary ratio of 1.0) and the effect of different resin systems on relative performance.44 , Resin A; , resin B; , resin C; , resin D; , resin E.

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fraught with problems. The test does not provide an absolute property value (design allowable); however, this test currently sets design strain limits. If the material is relatively brittle, cracking due to impact may extend to the edges of the plate, and when loaded in the compression fixture it is already effectively saturated. It is for this reason that plots of compression strength versus impact energy frequently indicate a levelling off of compression strength, see Fig. 10.15. This would not be the case if the plate size were increased or impact ranges were limited to minimise interactions with the support conditions. A further cause for concern is that a ranking of materials based on a single impact energy might change if a different reference impact energy level were selected.40–42 This is illustrated in Fig. 10.15, which shows some data generated on experimental and commercial resin laminates over a range of impact energies.

10.4.4

Miniature tests

The high cost of producing specimens for full size Boeing/SACMA/Airbus tests has prompted interest from many laboratories in producing a miniaturised version of the test.43 A variant developed by Hogg et al.44 was an attempt at providing a link between compression after impact test specimens and those widely used in Europe for excess energy impact tests according to ISO/DIN standards. The Hogg test specimen consists of a plate specimen 89 mm by 55 mm and 2 mm thick. Impact on the specimen is produced using an ISO/DIN impactor of diameter 20 mm (cf. 16 mm in the Airbus test), with the support geometry being a 40 mm diameter steel ring with clamping optional. The normal ISO/DIN test uses a 60 mm wide specimen. The impacted plates are supported during compression using a variable fixture resembling the larger Boeing fixture with the exception that instead of knife edge supports, the plates are being supported by slotted side bars. A similar specimen has been examined in Japan (50 mm by 80 mm) and included as part of a round-robin study of the test method. The results from both studies indicated a high degree of correlation between the miniaturised test specimens and the full scale Boeing tests, as shown in Fig. 10.16.44–46 One practical issue that must be allowed for when using the small fixture is that damage will tend to saturate the specimens at relatively low impact energies.

10.5

Data interpretation

The data generated by the compression after impact test, when presented in the manner of impact energy versus compression strength, link a test parameter from one test (impact energy) to a property measured in another

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Residual compression strength (MPa)

500 F-B-J S-B-J S-B-UK

F-T-J S-T-J S-T-UK

400

300

200

100

0 0

10

(a)

30

20

40

Impact energy (J)

Residual compression strength (MPa)

500 F-T-J F-B-J

400

F-T+B-UK 300

Boeing data

200

100

0 0 (b)

20

40

60

80

100

Damage width (mm)

10.16 Residual compression strength data from Hexcel (Boeing test), Hogg (miniature test) and Ilcewicz (Boeing test) plotted as a function of (a) impact energy; (b) damage width for full scale tests; (c) damage width for small scale tests.44–46 F (full scale), S (small scale), T (tough), B (brittle), J (Japan) and UK (United Kingdom).

(compression strength). This means that it is impossible to determine whether or not the relative performance of two laminate systems is controlled by their resistance to damage during impact, or the resistance to propagation of that damage during compression.

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Resdual compression strength (MPa)

500 S-T-J S-B-J S-T-UK S-B-UK

400

300

200

100

0 0 (c)

10

20

30

40

50

Damage width (mm)

10.16 (cont.)

In order to gain a better insight into the performance of the composite, it has become increasingly common to record the size of damage induced in the impacted specimen. For carbon-fibre laminates this has required the use of ultrasonic C-scan measurements, whereas for glass-fibre composites, transmitted light normally reveals the extent of damage. The damage measured in this way is delamination cracking, which is largely responsible for the reduction in compression strength of the material. Quasi-isotropic laminates, which are usually the material form examined in the test, generally produce damage zones that are globally circular, although these do in reality consist of lobed delaminations at a number of ply–ply interfaces, see Fig. 10.17. Studies of the composite laminates under compression have revealed that the delaminations propagate in a sideways direction prior to final failure of the plate, but never in the vertical direction, see Fig. 10.18. Based on these observations, Prichard and Hogg argued that a relevant damage parameter that could be used to assess impact resistance was the width of the delaminated area.42 Using this parameter, it was found that the impact and compression parts of the test could be separated. This has been applied to a set of data generated using a toughened epoxy laminate and two thermoplastic laminates (PEEK and Radel) based on similar fibres and with a quasi-isotropic layup.41 The initial data presented in the conventional fashion of residual compression strength versus impact energy are shown in Fig. 10.19. In Fig. 10.9 the damage width for both materials is shown plotted against impact energy; this reveals that the PEEK and Radel composites are much better than the toughened epoxy in resisting impact damage. Finally, in Fig. 10.20 the compression strength is plotted against

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10.17 Typical shape of an impact-induced delamination in a carbonfibre reinforced quasi-isotropic unidirectional prepreg tape (T300/914) laminate.

damage width. This is effectively a way of comparing the resistance of two laminates to damage propagation, irrespective of how difficult it was to generate that damage in the first instance. In this plot it is interesting to note that the performance of two distinctly different forms of resin chemistry, thermoset and thermoplastic materials, appears to be very similar. A broader survey comparing large and small specimens on the basis of both impact energy and damage width relative to residual compression strength shows that the results from both test methods give similar trends and that residual strength versus damage width results are numerically similar for both tests. When this exercise was undertaken, initially in Japan, it was concluded that the level of equivalence between the two sizes of test

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(a)

(b)

10.18 Quasi-isotropic glass-fibre reinforced unidirectional prepreg tape (E-glass/913) showing (a) the distribution of impact-induced delamination damage; (b) the propagation of delaminated regions.

was poor, but when more data were compared (using European as well as the Japanese generated data), the level of scatter became apparent, and it is clear that the agreement is good, see Fig. 10.16.45 The use of damage width as a damage parameter is extremely useful for quasi-isotropic laminates, but if the fibre layup in a specimen moves progressively away from such an arrangement, then the damage area

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Residual compression strength (MPa)

500

400

300

200

100

0 0

3

6

9

12

15

Impact energy (J)

10.19 Residual compression strength data versus impact energy for quasi-isotropic carbon-fibre reinforced () AS-4/PEEK, () T65042/Radel (thermoplastic) and () toughened epoxy (T800/924) generated using the miniature jig.41

Residual compression strength (MPa)

500

400

300

200

100

0 0

10

20

30

40

50

Damage width (mm)

10.20 Residual compression strength data versus damage extent for quasi-isotropic carbon-fibre reinforced () AS-4/PEEK, () T65042/Radel (thermoplastic) and () toughened epoxy (T800/924) generated using the miniature jig.41

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itself becomes asymmetric and difficult to quantify in this respect. Some angle ply layups result in slanted strips of delaminated material which are not amenable to this treatment. It should, however, be noted that the projected plan area superposition of delaminations, as measured by conventional C-scan, has been successfully correlated with residual strength.38 There is also an increasing interest in the aerospace field in composite laminates constructed from textile forms. Some of these forms, such as noncrimp multiaxial warp-knitted fabrics, can be used to generate laminates with quasi-isotropic layups and similar in-plane properties to prepreg materials based on unidirectional tape.47 However, when these fabric-based laminates are subjected to impact, the nature of the damage created changes slightly.48,49 The textile form makes the creation of large discrete delaminations more difficult. The area of damage generated in non-crimp fabrics may look similar to that created in prepreg tape laminates when viewed using a C-scan as shown in Fig. 10.21. However, if time of flight scanning is used, the damage is revealed to be more irregular, with pockets and regions of interply cracking that link up to form an irregular delamination. Consequently, the use of a physical parameter that represents a damage state becomes more difficult to define as the reinforcement architecture becomes increasingly complex (e.g. three-dimensional weaves), effectively suppressing delamination fractures.50,51 However, this may be compensated for by a reduced damage tolerance in tension, where an alternative and more suitable parameter may be defined.

10.6

Standardisation status

The compression after impact test procedures produces data with a relatively large degree of scatter as shown in the sets of experimental results in Figs. 10.7–10.9, 10.15, 10.16, 10.19 and 10.20. It is not clear at this time whether improving the test specification could result in a reduction in this scatter. Accepting the scatter inherent in the test has the advantage that the procedures are tolerant to variations in scale of specimen and minor factors such as impactor diameter. The marked effect of factors such as the compliance of the impact support frame and the way the specimen is actually struck means, however, that standardisation is very important, particularly given the role of impact testing in the certification of composites for aerospace applications. At present the only documented procedures are those developed by the aerospace companies, Boeing and Airbus, and the recommended methods of SACMA and CRAG. The Japanese standards body, JIS, is planning to introduce a standard in the near future based on the Boeing method but with a provision made for using a smaller test coupon for use in materials

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Y scale / mm

Depth/mm

% Areas

Calibrated depth: 0.5 mm

X scale / mm

Y scale / mm

Depth/mm

% Areas

X scale / mm

10.21 Representative time of flight C-scans showing the internal nature of impact (Boeing test) induced damage for (a) triaxial [452,-452,06,-452,452]S carbon-fibre reinforced unidirectional prepreg tape (T300/914); (b) triaxial [452,-452,06,-452,452]S carbon-fibre reinforced non-crimp fabric (T300/914) laminates.

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evaluation studies. ASTM has also been attempting to develop its own standard, based again on the Boeing/SACMA tests. It is also understood that ASTM are involved in the development of a quasi-static indentation test method, which has the intention of providing guidance for the study of impact damage resistance. The test would introduce damage in a more controlled manner than falling-weight tests and make use of a universal testing machine, rather than specialised equipment. Damage events would be associated with a critical force and the test could be used to screen materials for durability, or to put damage into a specimen for subsequent damage tolerance testing. There is, of course, no claim that a test of this type addresses such issues as wave propagation, vibrations in the specimen, time-dependent behaviour or inertia-dominated impact events, but the use of quasi-static testing has support in the research community.52,53

10.7

Future trends

The current situation relating to impact and damage tolerance testing of composites is plainly not satisfactory. The tests themselves produce data that can provide a useful and informative guide to the relative performance of different material systems. They do not at this time, however, provide any direct input into the design process. The performance of an aircraft structural part, in service after damage has been induced, may be inferred by reference to the compression after impact test, but cannot actually be predicted. The test methods currently used have allowed the mechanisms of impact damage and post-impact failure to be assessed, providing the industry with a realistic physical understanding of the processes involved. This in turn will allow more realistic modelling to be undertaken. In the long term, the wide variety of composite structures and the impact or damage events that can take place, the range of postimpact loading that can be imposed and the different criteria for failure mean that testing alone is unlikely to provide all the answers for a composites industry hoping to design better structures. It is instead inevitable that modelling will have to develop in such a way that the response of a composite structure to high strain rate loading with a specified force–time profile can be predicted in detail, such that the nature and level of damage sustained can be predicted and the propagation of that damage under subsequent loading can also be predicted until a failure point is reached. This form of modelling will require from the testing community a wealth of data not currently available. The dynamic properties of the fibre and resin, the various micromechanical strength parameters and their dependence on testing rate, the dependence of cracking on fibre architecture both in tape-based laminates and more complex textile-based materials will all

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be required. Most critically, physically sound failure criteria are needed that can predict local microfracture events under complex loading states, as a function of rate. In addition to a new range of experimental data, this approach will require a vast increase in the computing power available, although this is probably the only thing that it is reasonable to predict will actually materialise in the near future if current trends continue. In the short term, the research community is attempting numerous half-way measures using damage mechanics which effectively allow structures to be modelled such that a damaged zone is assigned reduced properties in a conventional structural analysis using finite element or other numerical methods to predict local stress states in damaged materials. Predicting the onset of failure is still problematic unless gross assumptions are made, or the situation being modelled is very well defined. This means that the design of composite structures to resist impact and to maximise damage tolerance will be dependent on testing of the type discussed in this chapter for some time to come.

References 1. W C Jackson and C C Poe, ‘The use of impact force as a scale parameter for the impact response of composite laminates’, Journal of Composites Technology and Research, Winter 1993 15(4) 282–9. 2. D Delfosse, G Pageau, R Bennett and A Poursartip, ‘Instrumented impact testing at high velocities’, Journal of Composites Technology and Research, Spring 1993 15(1) 38–45. 3. P Sjoblom, J T Hartness and T M Cordell, ‘On low-velocity impact testing of composite materials’, Journal of Composite Materials, 1988 22 30–52. 4. S V Potti and C T Sun, ‘Prediction of impact induced penetration and delamination in thick composite laminates’, International Journal of Impact Engineering, 1997 19 31–48. 5. G H Staab and A Gilat, ‘High strain rate response of angle-ply glass/epoxy laminates’, Journal of Composite Materials, 1995 29 1308–20. 6. J Harding and L M Welsh, ‘A tensile testing technique for fibre-reinforced composites at impact rates of strain’, Journal of Materials Science, 1983 18 1810–26. 7. Y Li, C Ruiz and J Harding, Modeling of the Impact Response of Fibrereinforced Composites, Technomic Publishing, Lancaster, PA, USA, 1991. 8. K Saka and J Harding, Behaviour of Fibre-reinforced Composites under Dynamic Tension, Oxford University Engineering Laboratory Report No. 1543/84, 1984. 9. D Hull, ‘A unified approach to the progressive crushing of fibre reinforced composites tubes’, Composites Science and Technology, 1991 377–422. 10. K E Jackson, J Morton, C M Traffanstedt and R L Boitnott, ‘Scaling of energy absorbing composite plates’, Proceedings, American Helicopter Society 48th Annual Forum and Technology Display, Vol 2, Washington, DC, AHS, 1992, 1431–40.

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11. J A Lavoie and J Morton, Design and Application of a Quasi-static Crush Test Fixture for Investigating Scale Effects in Energy Absorbing Composite Plates, NASA CR 4526, July 1993. 12. S N Kakarala and J L Roche, ‘Experimental comparison of several impact test methods’, Instrumented Impact Testing of Plastics and Composite Materials, ASTM STP 936, eds S L Kessler, G C Adams, S B Driscoll and D R Ireland, American Society for Testing and Materials, 1987, 144–62. 13. D F Adams and J L Perry, ‘Instrumented Charpy impact tests of several unidirectional composite materials’, Fibre Science and Technology, 1975 8 275–302. 14. G Marom, E Drukker, A Weinberg and J Banbaji, ‘Impact behaviour of carbon/Kevlar hybrid composites’, Composites, 1986 17 150–3. 15. W J Cantwell and J Morton, ‘Geometrical effects in the low velocity impact response of CFRP’, Composite Structures, 1989 12 39–59. 16. W J Cantwell and J Morton, ‘Comparison of the low and high velocity impact response of CFRP’, Composites, 1989 20 545–51. 17. J Morton and E W Godwin, ‘Impact response of tough carbon fibre composites’, Composite Structures, 1989 13 1–19. 18. W J Cantwell and J Morton, ‘Impact perforation of carbon fibre reinforced plastic’, Composites Science and Technology, 1990 38 119–41. 19. L Babic, C Dunn and P J Hogg, ‘Damage development and its significance in GRP subject to impact’, Plastics and Rubber Processing and Applications, 1989 12 199–207. 20. G A Bibo, D Leicy, P J Hogg and M Kemp, ‘High temperature damage tolerance of carbon fibre reinforced plastics: part I impact characteristics’, Composites, 1994 25 414–24. 21. E F Dost, S R Finn, J J Stevens, K Y Lin, and C E Fitch, ‘Experimental investigations into composite fuselage impact damage resistance and post impact compression behaviour’, Proceedings, 37th International SAMPE Symposium, Anaheim, CA, Vol. 32, SAMPE, Covina, CA, 1992, 1199–1212. 22. P Reed, ‘Mechanical properties and mechanical testing of polymers’, Handbooks of Polymer Science, ed G M Swallowe, Chapman and Hall, 1997. 23. K Srinivasan, W C Jackson and J A Hinkley, ‘Response of composite materials to low velocity impact’, Proceedings, 36th International SAMPE Symposium, San Diego, CA, SAMPE, Covina, CA, 1991, 850–62. 24. S M Bishop,‘The mechanical performance and impact behaviour of carbon-fibre reinforced PEEK’, Composite Structures, 1985 3 295–318. 25. K Srinivasan, W C Jackson, B T Smith and J A Hinkley, ‘Characterisation of damage modes in impacted thermoset and thermoplastic composites’, Journal of Reinforced Plastics and Composites, 1992 11 1111–26. 26. W J Cantwell and J Morton, ‘The influence of varying projectile mass on the impact response of CFRP’, Composite Structures, 1989 13 101–14. 27. W J Cantwell and J Morton, ‘Detection of impact damage in CFRP laminates’, Composite Structures, 1985 3 241–57. 28. D A Wyrick and D F Adams, ‘Residual strength of carbon/epoxy’, Journal of Composite Materials, 1988 22 749–65. 29. Anon, Federal Aviation Regulations Part 25, U.S. Department of Transportation, Federal Aviation Administration, 1993, Section 25.571, C22– 4.

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30. K N Shivakumar and J D Whitcomb, ‘Buckling of a sublaminate in a quasiisotropic composite laminate’, Journal of Composite Materials, 1985 19 2–18. 31. W-L Yin, ‘The effects of laminated structure on the delamination buckling and growth’, Journal of Composite Materials, 1988 22 502–17. 32. H Chai and C D Babcock, ‘Two-dimensional modelling of compressive failure in delaminated laminates’, Journal of Composite Materials, 1985 19 67–98. 33. P T Curtis (ed), CRAG Test Methods for the Measurement of the Engineering Properties of Fibre-reinforced Plastics, Royal Aircraft Establishment, Farnborough UK, Technical Report 88012, 1988. 34. Standard Tests for Toughened Resin Composites, NASA Reference Publication 1092 (revised edition), 1983. 35. Advanced Composite Compression Tests, Boeing Specification Support Standard, BSS 7260, 1986. 36. SACMA Recommended Test Method for Compression after Impact Properties of Oriented Fibre-resin Composites, SACMA Recommended Method, SRM 2–88. 37. Airbus Industrie Test Method Fibre Reinforced Plastics, Determination of Compression Strength after Impact, AITM 1.0010, Issue 2, 1994, 1–11. 38. W J Cantwell, P T Curtis and J Morton, ‘An assessment of the impact performance of CFRP reinforced with high-strain carbon fibres’, Composites Science and Technology, 1986 25 133–48. 39. K Tanaka and K Kageyama, Standardisation Study on Compression after Impact Test for CFRP’s in Japan, Proceedings of 2nd European Conference on Composite Materials – Composites Testing and Standardization, ECCM-CTS 2, Woodhead, Cambridge, 1994, 469–77. 40. J Brandt and J Warnecke, ‘Influence of material parameters on the impact performance of carbon-fibre-reinforced polymers’, High Tech – the Way into the Nineties, eds K Brunsch, H D Golden and C M Herkert, Elsevier Science Publishers BV, Amsterdam, 1986, 251–60. 41. G A Bibo, P J Hogg and M Kemp, ‘High temperature damage tolerance of carbon fibre reinforced plastics. Part II: Post impact compression characteristics’, Composites, 1995 26 91–102. 42. JC Prichard and PJ Hogg, ‘The role of impact damage in post-impact compression testing’, Composites, 1990 21 503–11. 43. P Sjoblom and B Hwang, ‘Compression-after-impact: the $50,000 data point’, Proceedings, 34th International SAMPE Symposium, Reno, NV, SAMPE, Covina, CA, 1989, 1411–21. 44. P J Hogg, J C Prichard and D L Stone, ‘A miniaturised post impact compression test’, Proceedings European Conference on Composite MaterialsComposites Testing and Standardisation, ECCM-CTS, Amsterdam, eds P J Hogg, G D Sims, F L Matthews, A R Bunsell and A Massiah, European Association for Composite Materials, Bordeaux, France, 1992, 357–70. 45. P J Hogg, G A Bibo and K Tanaka ‘A comparison of full-scale and miniaturised compression after impact tests’, Proceedings, 4th Japan International SAMPE Symposium, Tokyo, eds Z Maekawa, E Nakata and Y Sakatani, Japan SAMPE, Yokohama, 1995, Vol. 2, 907–14. 46. L B Ilcewicz, E F Dost and R L Coggeshall, ‘A model for compression after impact strength evaluation’, 21st International SAMPE Technical Conference, Atlantic City, NJ, SAMPE, Covina, CA, 1989, 130–40.

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47. G A Bibo, P J Hogg and M Kemp, ‘Mechanical characterisation of glass and carbon fibre reinforced non-crimp fabric’, Composites Science and Technology, 1997 57(9/10) 1221–41. 48. G A Bibo, P J Hogg, R Backhouse and A Mills, ‘Deformation mechanisms in fabric reinforced composites’, Proceedings, 10th International Conference on Composite Material, ICCM 10, Whistler, BC, Canada, eds A Poursartip and K Street, Cambridge, Woodhead, 1995, Vol 4, 317–24. 49. G A Bibo, P J Hogg, R Backhouse and A Mills, ‘Carbon fibre non-crimp fabric laminates for cost effective damage tolerant structures’, Composites Science and Technology, 1998 58(1) 129– 43. 50. G A Bibo and P J Hogg, ‘The role of reinforcement architecture on impact damage mechanisms and post impact behaviour – review’, Journal of Materials Science, 1996 31 1115–37. 51. J Brandt, K Drechsler, M Mohamed and P Gu, ‘Manufacture and performance of carbon/epoxy 3-D woven composites’, 37th International SAMPE Symposium, Anaheim, CA, SAMPE, Covina, CA, 1992, 864–77. 52. R B Bucinell, R J Nuismer and J L Koury, ‘Response of composite plates to quasi-static impact events’, Composite Materials: Fatigue and Fracture (Third Volume), ASTM STP 1110, ed T K O’Brien, American Society for Testing and Materials, Philadelphia, USA, 1991, 528–49. 53. P A Lagace, J E Williamson, P H W Tsang, E Wolf and S Thomas, ‘A preliminary proposition for a test method to measure (impact) resistance’, Journal of Reinforced Plastics and Composites, 1993 12 584–601.

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11 Fatigue* P T CURTIS

11.1

Introduction

Since the early 1980s the reduction of strength and the subsequent failure of materials subjected to cyclic loading has been addressed as one of the most fundamental problems of engineering materials. A satisfactory description of fatigue of materials, based on first principles, has not yet been achieved. Metallic materials, for instance, which are ductile in nature under normal operating conditions, are known to fail in a brittle manner when they are subjected to repeated loading. Because composite materials are regarded as having good fatigue resistance, they are in fact destined to be used in applications, such as in aircraft or other vehicles, in which the degradation of strength and life expectancy by fatigue processes is most likely. In general, the number of cycles to failure depends on a number of variables such as stress levels, stress state, mode of cycling, process history, material composition and environmental conditions. However, composites are, by nature, inhomogeneous and frequently anisotropic. The fatigue processes which reduce strength in these materials are generally very complex, involving the accumulation of many damage modes. This chapter explores the philosophy behind the development of methods for the fatigue testing of polymer composite materials. Methods for performing tests in the major loading regimes will be described, although in many cases there are no formal standards for fatigue testing of these materials. This is partly because of the difficulty in performing fatigue tests on polymer composites but also because it is only recently that standards have been developed for static testing, described in the other chapters of this book. As well as describing test methodology, consideration is given to the types (and indeed the suitability) of mechanical testing machines for measuring fatigue properties of polymer composites. In addition, some of the problems and pitfalls associated with fatigue testing are * Crown copyright

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Stress or strain

amplitude

1 cycle range

smax smean smin Note: R = smax

smin

Time

11.1 Typical applied stress–strain–time diagram.

described and techniques for avoiding, or minimising, their effects are discussed. Ways in which fatigue data are analysed and presented for polymer composites are discussed, so that it can be of most benefit. Finally, no fatigue test is really complete without a careful study of how damage develops during the fatigue test. The latter part of this chapter deals with how to apply inspection techniques to polymer composites in order to establish important information on fatigue damage development.

11.2

Basic test philosophy

Essentially any test method used for static testing has the potential to be used in fatigue; however, the fatigue environment is usually more demanding on both material and test technique. Problems which do not occur in static testing will almost certainly do so in fatigue loading. The main requirements for a fatigue test coupon are that it should fail in a manner similar to the material of the comparable structural component. Ideally, this should combine with ease of use and economy of preparation. The literature on composite fatigue behaviour contains many papers reporting work carried out on and comparing different coupon configurations for fatigue testing, in efforts to meet these requirements.1,2 Figure 11.1 shows a typical applied stress–strain–time diagram in a fatigue test. A cyclic stress is applied between predetermined maximum and minimum limits, the ratio of minimum to maximum stress being described as the R ratio. The mean stress, stress amplitude and cyclic frequency are also important parameters. The cyclic stress mode can be sinusoidal, triangular or whatever the user decides is most appropriate for the end application in mind.

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Most fatigue tests on composite materials have been performed in uniaxial tension–tension cycling. Tension–compression and compression– compression cycling are not commonly used, since failure by compressive buckling may occur in thin laminates and antibuckling guides are required. However, completely reversed tension–compression cycling can be achieved by flexural fatigue tests, although these are rarely representative of real-life loading regimes. A limited number of interlaminar shear fatigue and in-plane fatigue tests have also been performed. In the next sections typical test methods for these loading modes will be described.

11.2.1

Tensile tests

Tensile testing is probably the most common form of materials test. It is therefore essential that tensile tests in fatigue can be performed for polymer composites. The first requirement is to ensure that failures occur within the gauge length of the coupons and not be associated with grips, supports, antibuckling guides and so on. Coupon profiles have been varied in attempts to encourage such failures, ranging from waisting and cut-outs to simple parallel-sided coupons. Waisting usually ensures static failures at positions remote from the grips, but not necessarily in fatigue. Indeed, the plain parallel-sided specimen frequently yields the longest fatigue lives and the best all-round behaviour, although failures do occasionally occur at the grips. With care in preparation of the coupons and the use of end tabs, however, the incidence of failure close to the grips can be minimised. This is emphasised in Figs. 11.2 and 11.3. Figure 11.2 shows three gauge profiles tested statically and in fatigue. The static tests produced acceptable failures in all three cases, within the gauge section. In fatigue, however, the two waisted coupons both failed away from the waist and thus gave unacceptable results. The corresponding stress–life diagrams are shown in Fig. 11.3, where it is clear that the plain parallel-sided coupons gave the longest fatigue lives. It is recommended, therefore, that for most tensile fatigue testing, plain parallel-sided coupons should be used as the best compromise. If waisting must be used, then care should be taken to avoid disturbing the layup. Waisting is, therefore, usually restricted to across the width of coupons, as shown in Fig. 11.2. Waisting in the thickness will undoubtedly disturb the layup of the laminate, except for materials with all the fibres in the same direction. However, waisting even in such unidirectional material, with the fibres in the test direction, frequently leads to shear stress failure at the waists, resulting in delaminations which propagate in fatigue loading back to the grips where failure within the grips is triggered at reduced lifetimes, as depicted in Fig. 11.4.

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(a)

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(b)

11.2 Coupons with different gauge profiles tested: (a) statically, (b) fatigue.

900

Maximum stress (MPa)

800 700 600 500 400 300 –1 10

0

10

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10

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3

10

4

10

5

10

6

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Number of cycles

11.3 Stress–life plots for tensile fatigue coupons with different gauge profiles. S-N (stress versus number of cycles) curve of 0 ± 45° material in zero-tension loading, type 3 fibre, DX210 resin system. , 20 mm wide rectangular; , waisted specimens; , notched specimens; +, 10 mm wide rectangular. AFRP = aramid fibre-reinforced plastic.

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11.4 Schematic diagram showing delamination growth back to the grips in a unidirectional layup fatigue coupon.

11.2.2

Compression tests

Compression–compression and tension–compression fatigue testing are more complex than tensile loading, with the additional problem of stabilising the coupon during the compressive cycle. This requires that either short and, therefore, self-stable coupons should be used, or antibuckling guides are necessary to support the coupon. Short stable coupons, which may be parallel-sided or waisted, suffer from the disadvantage that the stress distribution in the free length may be affected by the restraint at the grips. Reduction of the specimen width to allow for this effect renders the edge stresses more critical. Such specimens are typically 10 mm wide with a free length of 10 mm and minimum thickness3 of 1.5 mm, as shown in Fig. 11.5. Long coupons are to be preferred, but when a compressive excursion is to be included in the fatigue cycle, it is necessary to provide supports to prevent buckling. No standard antibuckling guide exists, each test laboratory having developed its own devices. The main factor to consider when designing guides is that the free unsupported area of the specimen should be a maximum consistent with the requirement of preventing buckling,3 so as not to restrict any anticipated failure process. In addition, friction between the support and the specimen must be minimised, perhaps by the use of PTFE (polytetrafluoroethylene) tape on the contact surfaces. A typical device was shown in Fig. 10.12 in Chapter 10.

11.2.3

Flexural tests

Many laboratories use flexural fatigue testing as an alternative to axial fatigue, since it is easier to perform, requiring no supporting guides and generally significantly lower capacity testing machines. Flexural test methods used for static loading are generally suitable for fatigue, but care must be taken to minimise friction at the loading rollers. It is also necessary to introduce backing rollers on the reverse of the coupons if through-zero testing is intended.

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10

110

10

2

50 End plates 0.5–2.0 mm light alloy

11.5 Short plain parallel-sided compression fatigue test specimen.

11.2.4

Shear tests

Fatigue testing in shear loading is less common, but ought to be considered more widely than it is currently. The most commonly used shear technique is the interlaminar shear test.3 This can easily be modified for fatigue use by the introduction of backing rollers opposite the main rollers, particularly if the deflection is to be reversed in fatigue. A typical test arrangement is shown in Fig. 11.6(a). Alternative shear fatigue test methods used are also based on modifications to methods used for static testing. The tensile test on ±45° laminates induces shear along the fibres and has been used extensively as a static test for the characterisation of shear behaviour, as discussed in Chapter 6. It can also be used for the generation of shear fatigue data.3 Versions of the rail shear test (Fig. 11.6b), again widely used for static shear strength measurements, and discussed in Chapter 6, have also been used in fatigue. The rail shear specimen requires some modification for it to be suitable for fatigue tests; work with this type of specimen has shown that the fatigue lives obtainable are very dependent on the surface quality of the exposed edge of the coupon.4 Polishing the edge results in a significant increase in life, potential cracks presumably being removed. However, when small slots are

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11.6 Shear test specimens: (a) ILSS interlaminar specimen; (b) rail shear specimen.

introduced into the coupon ends, even longer lives are obtained. This is likely to be due to the failure zone being shifted from the coupon edge, where constraint and edge effects lead to complex stress fields, to a region where a simple shear stress field exists.

11.2.5

Biaxial fatigue testing

The test methods described above relate to uniaxial loading, where the material is stressed in a single direction. There is, however, considerable interest in loading materials in two independent directions, usually referred to as biaxial loading. Such loading arrangements cause many additional problems, usually associated with regions between the loading arms in the two directions, where stress concentrations can lead to premature failure. There are no ideal (or indeed standard) test methods for biaxial fatigue testing, but a method has been described5 which is effective for notched coupons. This approach is based on a cruciform testpiece but is not suited to plain unnotched specimens.

11.3

Machines and control modes

Most fatigue work is performed on servohydraulic test machines, which are generally simple to use and flexible in that any combination of test fre-

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quency and loading or straining mode can be used. They are, however, expensive and it is possible to use much cheaper constant displacement machines using an offset cam to perform fatigue tests. Vibration or resonance machines can also be used, although these usually operate at frequencies of 30 Hz and above, which may not always be suited to polymer composites, where these high frequencies can cause excessive heating to develop. A further key decision to be made is that of the controlling mode. Fatigue tests can be performed in load, position or strain control, although the test machine may not permit all modes to be used. Position control is the cheapest and most tried method, and requires the displacement to be cycled between preselected maximum and minimum values, independent of the load developed in the testpiece or, indeed, how the load may change as a result of damage developed during the test. In many applications a component will be required to sustain a cyclic load; thus load controlled fatigue may be more appropriate. This requires more sophisticated test machines, such as servohydraulic equipment, in which there is a feedback loop. This is essential so that, as the material is damaged in fatigue, greater displacements result, allowing the testpiece to support the applied load. Strain control is really a more controlled version of position control, which eliminates errors associated with movement within the grips or supports. In this approach a strain or clip gauge extensometer is attached to the coupon to monitor the strain, which is then used as the controlling parameter. There are difficulties associated with this method, as bonded strain gauges are usually themselves fatigue sensitive and care in selection is required. Attaching clip gauges in a fatigue test is also fraught with difficulty, since the knife edges tend to fret on the coupon, and cause damage, are damaged themselves or move during the test. A common remedy for these problems has been to bond grooved blocks onto coupons to locate the knife edges, but this all adds to the complication of the test. As a result, few laboratories choose to perform fatigue tests in strain control, load or position control being the most favoured control parameters. It is interesting to note here that composite materials exhibit a gradual softening, or loss of stiffness, under fatigue testing, due to the appearance of undetected microscopic damage. As a result, the strain in the specimen increases in load-controlled tests, whereas the stress decreases in straincontrolled tests. This softening effect is portrayed for these loading modes in Fig. 11.7. It follows that the cycles to failure may not always accurately represent the specimen life.This is the reason why many tests are performed until the specimen stiffness, or residual strength, decreases to a predetermined level.

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(a)

Stress or strain

Time (c)

(b)

Stress or load

Stress or load

Strain

Strain

11.7 Fatigue cycling under (a) stress or strain; (b) stress or load control; (c) strain control for polymeric composites.

11.4

Presentation of data

Data presented so far in this chapter have been in the form of stress–life diagrams or S–N curves, with a linear scale on the stress axis and a log scale for cycles, or life. This is the most widely used form of data presentation and provides a simple-to-interpret indication of how life is degraded by constant amplitude fatigue. Such diagrams show clearly whether a fatigue limit is reached at long lifetimes but does not describe the full behaviour of the material. For example, a single plot cannot show the effects of varying the R ratio (minimum to maximum stress). However, a master curve or Goodman diagram can. In this form of presentation the stress amplitude is plotted as the ordinate (y axis) and mean stress as the abscissa (x axis). Life information is displayed by showing different traces for fixed cycles to failure, such as 106 cycles. An example is given in Fig. 11.8. Such plots have proven to be a useful way to represent the full spectrum of fatigue behaviour and thus have found use as a guide in design. The excellent performance of polymer composites compared with metallics shows up well on such plots.

11.5

Monitoring fatigue damage growth

A key part of any investigative fatigue programme is the determination of fatigue damage development and failure processes. This is important in order to establish whether the test coupons are failing in a manner repre-

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Atternating stress (MN m–2) io n Compress –Tension

Stress

Alt. Alt. Mean

–1000

All oy

GF

R

P

RP

on si

Tita

AF

F

en –T

500

on si

C

Alum iniu m

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t

n Te

C C om om p pr res es si si on on

1000

niu mA lloy RP

–500 0 500 - Mean stress (MN M 2) +

1000

1500

11.8 Typical Goodman or master plot. CFRP is carbon-fibre reinforced plastic, GFRP is glass-fibre reinforced plastic, AFRP is aramid fibre-reinforced plastic.

sentative of the material, rather than from some artefact or problem associated with the test method. Such investigations also lead to a better understanding of how the material behaves and the likely performance in service. The monitoring of fatigue damage growth relies heavily on destructive and non-destructive testing methods, techniques which cannot be covered fully here. What is discussed, however, is how such techniques can be applied to the fatigue testing of composites, with some examples of the obtainable results. The inspection techniques can be destructive, like optical microscopy, or non-destructive, like ultrasonics. Some techniques are amenable to continuous inspection, such as thermography, or require interruption of the test, as is usually the case for X-radiography.

11.5.1

Microscopy

Optical microscopy is a technique available in most laboratories and can be particularly useful in the examination of damage at the edges of coupons and holes. The usual approach is to polish the edges of the coupon by conventional metallographic routes, followed by regular examination during the test. Ideally, the observations should be made without removal of the test coupon from the testing machine, but this is not always feasible. Alternatively, the technique can be used destructively by sectioning part-tested or failed coupons, mounting and polishing these by conventional routes for

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optical examination. One compromise is the ‘edge replication technique’, which relies on the application of a polymeric solution to the edge of the coupon during an interruption to the test. The dried film is removed, permitting the test to continue, and can be examined under a microscope to provide information on surface damage imprinted on the film. Examination of edges can be particularly valuable for interlaminar toughness tests, where crack length as a function of cycles is required. Double cantilever beam and edge-notched deflection tests are frequently used in fatigue and require little or no modification to work successfully. Another approach is to use a deplying technique. This relies on destroying the test coupon, or part of it, in a furnace at a temperature which is sufficiently high to carbonise the polymer matrix, but which leaves the fibres intact. The resulting debris can easily be separated into plies which carry information on their surfaces of delaminations and cracks, which can be enhanced by soaking the part in gold chloride solution prior to carbonisation (other volatile liquids can give similar results and are considerably cheaper); broken fibres are clearly identifiable. Although clearly destructive, this technique has proven to be powerful in studying damage in fatigue tested coupons. At the end of life, fractographic tools can be valuable in the evaluation of damage sequence. Fatigue testing of polymer composites frequently leaves characteristic features on the surfaces of failed coupons and components which can be used to determine the sequence of failure events or

11.9 Striations on the fracture surface of a fatigue-tested polymer composite.

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damage growth. Figure 11.9 shows a scanning electron micrograph of a typical fatigue failure; the striation markings thus revealed are often seen in the matrix of polymer composites, marking fatigue crack growth and arrest.

11.5.2

Ultrasonics

Ultrasonic C-scan is a non-destructive technique widely applied in fatigue testing programmes. The technique relies on measuring the attenuation of an ultrasonic beam passed through the specimen and relating this to damage present. The ultrasonic beam requires a transfer (or coupling) medium, which is usually water, and normally requires removal of the coupon from the fatigue testing machine to allow immersion in a tank of water. Techniques relying on water jetted at the specimen (and carrying the ultrasonic signal) are available and enable measurements to be made with the coupon mounted on the fatigue machine; but such an approach is potentially very messy to use around complex testing equipment, and is also expensive, probably beyond the budget of most laboratories. Ultrasonic inspection is particularly useful for the detection of interlaminar damage, such as edge cracks and delamination, and for the study of the growth of these types of damage in fatigue loading. Typical damage growth in a coupon, initially impacted and subsequently tested in compression fatigue loading, is shown in Fig. 11.10. Relatively new developments in ultrasonic testing techniques include highly sophisticated systems with computer analysis/enhancement of images which are portable enough to be used to inspect coupons in situ in an interrupted test. A typical example of such equipment is the ANDSCAN system, initially developed at DERA (Defence Evaluation and Research Agency), and now marketed by Wells Krautkramer.

11.10 Ultrasonic scans of impact damage and growth during the compressive fatigue of CFRP (carbon-fibre reinforced plastic).

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X-radiography

X-ray inspection of composites during fatigue loading is also a very useful technique. Since polymer composites are essentially transparent to X-rays, the technique usually relies on the introduction of an X-ray opaque penetrant into the damaged area of the composite as a liquid solution or suspension which fills cracks and delaminations, making them more clearly visible as shadows on X-ray film. The usual procedure is to remove the fatigue coupon from the test machine for inspection, but equipment is available which permits inspection within the fatigue machine. The technique is particularly suitable for the detection of in-plane damage, such as transverse cracks in 90° layers. It is therefore a complimentary approach to the ultrasonic technique. One note of caution is appropriate here. There is some evidence that the use of penetrants actually enhances the subsequent crack growth as well as the visibility of damage. As a result, attempts to use X-radiography as an interrupted technique are difficult, because under further loading, crack growth rates will be increased. It is recommended, therefore, that this technique be regarded as effectively destructive. Typical damage growth around a hole in a coupon loaded in tensile fatigue is shown in Fig. 11.11.

11.5.4

Thermography

What might be considered to be a somewhat more exotic technique is infrared thermography. This technique is, however, particularly well suited to the study of damage development during the fatigue loading of polymer composites. It has the advantage over most other methods in that inspection

11.11 X-radiograph of a notched coupon tested in tensile fatigue.

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11.12 Infrared thermogram of a ±45° CFRP tensile fatigue specimen, close to failure at 87 kcycles.

requires no interruption to the fatigue test. The resolution obtainable depends on the particular equipment, but is typically similar to that obtainable with ultrasonics, and rather less than can be achieved with X-radiography. Infrared thermography detects heat generated from two sources during a fatigue test: hysteresis, normally emanating from the resin or interface, and frictional heating as a result of differential movement at cracks. A typical thermogram is shown in Fig. 11.12 for a ±45° coupon tested in tensile fatigue and close to failure. Areas at elevated temperature are clearly visible close to the upper end-tab and near the centre of the gauge length. The hot area in the end-tab region indicates why damage, causing premature failure, often develops in fatigue close to the grips, which are subjecting the area to additional constraint. Once an area of damage has been detected using thermography, other higher resolution techniques, can be employed to examine the area in more detail.

11.6 11.6.1

Potential problems Stress concentrations

So far only plain coupon fatigue testing has been the main subject of discussion. In reality, tests must be performed on structural elements containing stress concentrating features, such as notches, holes, fasteners, impact

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damage and other imperfections. Fortunately it has been found that, in general, these stress concentrations have less effect on fatigue strength than they do statically. Dependent on the laminate configuration, these stress concentrations can reduce static tensile strength by as much as 50%. In fatigue, however, damage zones develop at stress concentrators, which can serve to reduce their magnitude; studies of damage development should this be a key part of any fatigue testing programme. Damage zones usually consist of cracks along the fibres within layers and interlaminar cracking between plies. Such mechanisms, as long as they do not damage fibres, can lead to increased strength. Further cycling results in some loss of strength, but typically, fatigue strength calculated on a net stress basis approaches that of the plain unnotched material after long lifetimes, resulting in fairly flat S–N curves.6–9 Consequently, it is not usually necessary to modify test procedures developed for plain coupons, as these are equally suited to coupons or elements containing stress raisers.

11.6.2

Frequency effects

Having discussed hysteresis heating effects in connection with infrared thermographic techniques, some reference should be made to frequency effects during the fatigue of composite materials. As a general rule, the test frequency should be chosen so as to minimise the hysteresis heating of the material. The source of this heating effect is hysteresis in the resin and, possibly, at the fibre/matrix interface. In some cases, where the reinforcing fibres are polymeric, these can also be a source of heating. Generally, laminates dominated by mainly continuous fibres in the test direction show lower strains and little hysteresis heating, and test frequencies of up to 10 Hz, or even more, can be suitable. Resin-dominated laminates, on the other hand, and those with few fibres in the test direction, show larger strains and marked hysteresis heating, and as a guide, frequencies should be limited to 5 Hz or less.10 Heating at damage sites, an alternative source of heating, may still occur and could cause local overheating. Ideally, the specimen temperature should be monitored during the test so as to ensure that such overheating does not occur. This is difficult without expensive thermography equipment, although the strategic positioning of thermocouples, the use of hand-held temperature sensors and the application of temperature-sensitive coatings are suitable alternatives, particularly when the site of the heating is known, such as when stress concentrators are present. The effect of frequency on properties, that is the effect of fatigue loading rate, is negligible for most continuous fibre composites when tested in the fibre direction, as long as hysteresis heating is not present. The main exception is glass-reinforced plastic (GRP), which has a significant rate

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effect; the greater the rate of testing, the greater the strength. It has been found11 that GRP can have a rate sensitivity of over 100 MPa per decade. The reasons for this are not entirely clear, although it has been suggested that it is due to the environmental sensitivity of the glass fibres, rather than any viscoelastic effect.12 Certainly, the effect has been found to change when the environment surrounding the glass fibres is changed. Testing composites with no fibres in the test direction, where the resin matrix has a viscoelastic behaviour, often results in significant rate effects. When collecting fatigue data on composite materials, the best policy is to carry out all fatigue tests at a constant rate of stressing,13 such that low load tests are performed at relatively high frequencies, whereas high load tests should be at low frequencies.

11.6.3

Edge effects

Edge-induced stresses can be a problem in many types of test, but especially so in fatigue. Some tests, such as those investigating interlaminar behaviour, may aim to maximise edge effects, but in fatigue tests the policy is usually to attempt to minimise edge-induced stresses and hence the damage that inevitably develops as a result of their presence. Both shear and normal stresses can develop at the coupon edges, these arising from the mismatch of properties between the plies, stresses being generated at the edges due to the inhibition of relative layer strains.14–16 The magnitude of these stresses changes with temperature, because the layers have different expansion coefficients, and also with moisture content, since the layers expand to different extents on absorbing moisture.17 The sign of the stresses may also change with external loading; for example, a laminate, though insensitive to edge effects in tension loading, may develop edge-induced damage in compressive loading. Layer stacking sequence is a critical variable, the magnitude of edge stresses varying greatly with the relative positions of the layers. Edge-induced damage, apparent in static loading, usually grows with increasing numbers of fatigue cycles. In the worst case the layers can become completely delaminated, leading to potential environmental attack, and certainly serious loss in compressive strength. The literature contains many theoretical treatments of edge-induced stresses,14–16 some allowing the approximate magnitude of the stresses to be calculated from elastic properties. Thus, the susceptibility of a laminate to edge effects may be determined before embarking on a fatigue test programme. Laminates known to be relatively insensitive to edge effects may, therefore, be selected for the work. In general, laminates with thin, evenly distributed layers lead to the lowest edge stresses for both tensile and compressive externally applied loads.

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Environmental effects

These are dealt with in more detail in Chapter 12, but some comments are pertinent here. The first problem to be tackled in this specialist area of polymer composite fatigue work is to decide how to perform the test. Fatigue tests are inevitably of a medium to long term nature, frequently lasting days or weeks. The possibility of coupons drying out during the period of the test must be considered. Room temperature tests generally lead to little change in moisture content (unless hysteretic heating is present), because the times involved for most materials to absorb or desorb significant quantities of moisture are long. The problem of coupon drying is particularly acute, however, when the fatigue test takes place at elevated temperature. Precautions must be taken to preserve the moisture content of the specimen. One possibility is to carry out the test in an environmental chamber, in which the temperature and humidity are controlled. This does, however, involve expensive equipment, which might be beyond the budget of many laboratories. Alternative approaches include enclosing the specimen in a polythene bag, in which a salt solution maintains the required humidity, or sealing the specimen totally by encapsulation.18,19

11.7

Fatigue life prediction

Since the early 1980s many damage growth models have been proposed. Sendeckyi20 has characterised them into three basic types: empirical fatigue, residual strength and stiffness reduction. Other models do exist, for example, actual damage mechanism based models. These, however, are based directly on observable damage and are difficult to apply quantitatively, owing to the complexity of the mechanisms involved.

11.7.1

Empirical theories

These theories have been developed to correlate particular sets of data. There are many different forms and their merit lies in their ability to predict performance. Typical of this class is the expression used by Mandell21 to relate fatigue performance to the ultimate static strength of the composite:

sa = suc - b log Nf

[11.1]

where sa is the applied stress amplitude, suc is the ultimate static strength, Nf is the number of cycles to failure and b is a constant. Typical values of b are 1.0420 for T300 carbon fibre in a ductile epoxy matrix and 1.2103 for the same fibre in a brittle epoxy matrix.22

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265

Residual strength degradation

Unfortunately for these theories it is not possible to assess the damage state of the laminate non-destructively with any degree of accuracy, as there is little established correlation between the results of non-destructive evaluation (NDE) and residual strength. Nevertheless, they have the merit of being based on measurable degradation behaviour, so they have some use as a predictive technique. Failure occurs when the reducing strength of the composite becomes equal to the applied stress. The models are usually based on an expression20 of the form: s r = s a [1 + (N f - 1) f ]

s

[11.2]

where sr is the residual strength, sa the applied stress amplitude, Nf the number of cycles to failure, with f and s being functions of the applied load ratio, R = smin/smax.

11.7.3

Stiffness degradation

These theories assume that damage in the laminate, whether caused by fibre fracture, matrix cracking or delamination, all cause a reduction in stiffness which can be used as an index of the rate and extent of damage growth. When sufficient damage has accumulated, the laminate fails. In order for life predictions to be made, a relationship must be established between the damage, D, its rate of accumulation with cycles, dD/dN, and the resultant life. Poursatip and co-workers23,24 proposed a model based on carbon fibre/epoxy laminates of layup [45°/90°/-45°/0°]s. They found that: dD Ê 1 dE ˆ = -2.857 Ë E o dN ¯ dN

[11.3]

where Eo is the original stiffness and dE/dN is the rate of stiffness reduction.

11.7.4

Damage accumulation

In variable amplitude stress loading, the total damage can be expressed by Miner’s linear cumulative damage rule:25 1= n

ni

ÂN m

=1

[11.4]

f

where ni is the number of cycles of a given stress range, Nf is the number of cycles to cause failure at that load and m is the number of stress range levels. Miner’s rule is used extensively to predict the fatigue performance of metals and has been used, with some success, with composites. However,

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according to Harris et al.,26 when the direction of stress changes within a fatigue test, as in mixed tension/compression cycling, the damage incurred is not predictable by a simple linear summation and actual lives are well below those that would be predicted from Miner’s rule.

11.8

Post-fatigue residual strength

The post-fatigue performance of a fibre-reinforced composite is studied by measuring the static strength and modulus after cycling it for various fractions of its total life to failure. Both static strength and modulus are reduced with increasing number of cycles. It has been reported27 that much of the static strength of a [0°/90°]s E-glass fibre/epoxy composite was reduced raidly in the first 25% of its fatigue life, which was then followed by a much slower rate of strength reduction until final failure. Reifsnider et al.28 observed an initial increase in the static strength of a [0°/±45°/0°]s boron fibre/epoxy laminate containing a central hole. This unique post-fatigue behaviour of a composite material was explained by means of a ‘wear-in/wear-out’ mechanism in damage development. The wear-in process takes place in the early stages of fatigue cycling. During this process, the damage developed locally around the central hole reduced the stress concentrations in the vicinity of the hole, resulting in increased strength. This beneficial stage of fatigue cycling was followed by the wearout process, which comprised large scale and widespread damage development leading to strength reduction. The residual strength of a composite, after a period of fatigue cycling, could be modelled as:

sresidual = su + swear-in + swear-out

[11.5]

where su is the ultimate static strength, swear-in is the change in static strength due to wear-in and swear-out is the change in static strength due to wear-out. The effect of wear-in is more pronounced at high fatigue load levels. Since fatigue life is longer at low load levels, there is a greater possibility of developing large scale damage throughout the material, so that the effect of wearout is likely to be more pronounced at low load levels.

References 1. J B Sturgeon, Fatigue Testing of Carbon Fibre Reinforced Plastics, Royal Aircraft Establishment, Farnborough, UK, Technical Report 75135, 1975. 2. P T Curtis and B B Moore, A Comparison of Plain and Double Waisted Coupons for Static and Fatigue Testing of Unidirectional GRP and CFRP, Royal Aircraft Establishment, Farnborough, UK, Technical Report 82031, 1982. 3. P T Curtis (ed), CRAG Test Methods for the Measurement of the Engineering Properties of Fibre Reinforced Plastics, Royal Aircraft Establishment, Farnborough, UK, Technical Report 88012, 1988.

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4. R J Butler, P M Barnard and P T Curtis, ‘The development of a satisfactory, simple, shear fatigue test for unidirectional E-glass epoxy’, ASTM STP 972, Composite Materials: Testing and Design, 1986, 227–40. 5. P A Tutton and K J Pascoe, The Effect of Specimen Geometry and Biaxial Loading on the Strength of Notched Carbon Fibre Composites, Cambridge University Engineering Department, Report under MoD agreement 2029/0153XR/MAT, 1982. 6. P T Curtis and B B Moore, ‘A comparison of the fatigue performance of woven and non-woven CFRP’, Proceedings of the 5th International Conference on Composite Materials, San Diego, CA, eds W C Harrigan, J Strife and A K Dhingia, The Metallurgical Society, Warrendale, PA, 1985, 293–314. 7. P T Curtis and B B Moore, A Comparison of the Fatigue Performance of Woven and Non-woven CFRP, Royal Aircraft Establishment, Farnborough, UK, Technical Report 85059, 1985. 8. D Schultz, J J Gerharz and E Alschweig, ‘Fatigue properties of unnotched, notched and jointed specimens of a graphite/epoxy composite’, ASTM STP 723, Fatigue of Fibrous Composite Materials, 1981, 31–47. 9. G Dorey, P Sigety, K Stellbrink and W G J t’Hart, Impact Damage Tolerance of a Carbon Fibre Laminate, Royal Aircraft Establishment, Farnborough, UK, Technical Report 84049, 1984. 10. P T Curtis, J Gates and C Margerison, The Selection of Cyclic Load Frequency for the Fatigue Testing of Fibre Reinforced Polymeric Composites, DERA, Farnborough, UK, Technical Report 93017, 1993. 11. C J Jones, R F Dickson, T Adam, H Reiter and B Harris, ‘The environmental fatigue behaviour of reinforced plastics’, Proceedings of the Royal Society of London A, 1984 396 315–38. 12. A G Metcalfe and G R Schmitz, ‘Mechanism of stress corrosion in E-glass filaments’, Glass Technology, 1972 13 5–16. 13. G D Sims and D C Gladman, A Framework for Specifying the Fatigue Performance of Glass Fibre Reinforced Plastics, National Physical Laboratory Report NPL-DMA(A) 59, 1982. 14. N J Pagano and R B Pipes, ‘The influence of stacking sequence on laminate strength’, Journal of Composite Materials, 1971 5 50–7. 15. P T Curtis, The Effect of Edge Stresses on the Failure of (0°,45°,90°) CFRP Laminates’, Royal Aircraft Establishment, Farnborough, UK, Technical Report 80054, 1980. 16. P T Curtis, ‘The effect of edge stresses on the failure of (0°,45°,90°) CFRP laminates’, Journal of Materials Science, 1984 19 167–82. 17. P T Curtis, Residual Strains and the Effects of Moisture in Fibre Reinforced Laminates, Royal Aircraft Establishment, Farnborough, UK, Technical Report 80045, 1980. 18. P T Curtis and B B Moore, The Effect of Environmental Exposure on the Fatigue Behaviour of CFRP Laminates, Royal Aircraft Establishment, Farnborough, UK, Technical Report 84027, 1984. 19. P T Curtis and B B Moore, ‘The effect of environmental exposure on the fatigue behaviour of CFRP laminates’, Composites, 1983 14 294–300. 20. G P Sendeckyi, ‘Life prediction in resin–matrix composite materials’, in Fatigue of Composite Materials, ed K L Reifsnider, Composite Materials Series, Vol. 4, Elsevier Science, Amsterdam, 1991, 431–83.

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21. J F Mandell, ‘Fatigue behaviour of fibre–resin composites’, in Developments in Reinforced Plastics 2, Properties of Laminates, ed G Pritchard, Applied Science, London, 1987, 67–108. 22. L L Lorenzo and H T Hahn, ‘Fatigue failure mechanisms in unidirectional composites’, Composite Materials: Fatigue and Fracture, ASTM STP907, 1986. 23. A Poursatip, M F Ashby and P W R Beaumont, ‘The fatigue damage mechanics of a carbon fibre composite laminate: I – Development of the model’, Composites Science and Technology, 1986 25(3) 193–218. 24. A Poursatip and P W R Beaumont, ‘The fatigue damage mechanics of a carbon fibre composite laminate: II – Life prediction’, Composites Science and Technology, 1986 25(4) 283–99. 25. M A Miner, ‘Cumulative damage in fatigue’, Transactions of the American Society of Mechanical Engineers – Journal of Applied Mechanics, 1945 12(3) A159–64. 26. B Harris, N Gathercole, M H Beheshty, J A Lee, B Grimm, H Reiter and T Adam, Fatigue Damage Growth and Life Prediction for Carbon Fibre Composites, Final Report on Research Agreement Number CB/FRN/9/4/2112097, DERA, 1996. 27. L J Broutman and S Sahu, ‘Progressive damage of a glass reinforced plastic during fatigue’, Proceedings, 24th Annual Technical Conference, Society of Plastics Industry, Washington, DC, Section 11-D, 1969. 28. K L Reifsnider, W W Stinchcomb and T K O’Brien, ‘Frequency effects on a stiffness-based failure criterion in flawed composite specimens’, Fatigue of Filamentary Composite Materials, ASTM STP636, 1977.

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12 Environmental testing of organic matrix composites G PRITCHARD

12.1

Introduction

The physical and mechanical properties of organic matrix fibre composites cannot be regarded as constant with time, as the circumstances of use can induce changes. This chapter is concerned with the nature of changes produced by the environment. The subject of internationally agreed standard test methods for assessing the environmental stability of composites is placed in the context of a wider discussion of the subject, designed to highlight the characteristics of useful test methods.

12.2

Why environmental testing?

It would be a mistake to assume that the properties of composite materials remain unchanged for ever. Ambient moisture, chemicals and radiation often cause changes in the microstructure or the chemical composition of materials, and these changes in turn cause a slow drift in such properties as modulus, strength and ultimate elongation. Typical consequences are: matrix swelling, fibre-resin debonding, matrix microcracking and chain scission. Chemical and other changes can occur. Sudden changes in properties are sometimes observed and spontaneous fracture is not unknown. Figure 12.1 illustrates these statements diagrammatically. A given property, such as strength, can sometimes decline so slowly during service life that it is simply not a factor in determining the product’s useful lifetime. Or the property can decline rather more quickly, shortening the useful life, and requiring some cautious checks on the material’s structural integrity as time progresses. Again, the strength can be fairly stable for a long time, but then fall suddenly, with no warning, before fracture occurs. As an illustration, unidirectional glass laminates can withstand immersion in dilute mineral acids such as sulphuric or hydrochloric acid in the absence of a tensile stress, but if both stress and acid are experienced 269

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Desired property

270

a b

Minimum acceptable property level c Time

12.1 Three ways in which material properties can change with time: (a) remaining acceptable throughout; (b) becoming unacceptable eventually; (c) catastrophic failure after time, e.g. through environmental stress cracking.

together, failure can occur quite suddenly.1 It is difficult to predict the timescale of environmental stress ruptures. These observations are obviously relevant to composites used in contact with liquids. Fibreglass boats have to last between 20 and 50 years, and like offshore oil installations, are exposed to salt water, ultraviolet radiation and repetitive wave action. But environmental degradation also has to be considered in composite parts in aircraft, where the chemicals are fuels, paint strippers, hydraulic fluids, brake fluids and runway de-icers. Other vehicles are also exposed to oils and fuels, and environmental degradation applies to storage tanks, road tankers, sewage pipes and chemical plants. There are implications for such diverse applications as building panels and printed circuitboard components.

12.3

Environmental threats to composites

Environmental degradation is caused chiefly by chemicals, temperature, microorganisms and radiation. It is sometimes aggravated by mechanical stress or electrical fields. Chemicals include all reactive substances, whether synthetic or natural, including water, oxygen, bleach, petrol, lubricants, detergents, cleaning solvents, acids, etching and oxidizing agents, and so on. In the world of glass and of polymers, water ranks as a fairly reactive chemical. High or fluctuating temperatures pose a threat to composites, and rapid changes in temperature can produce damage through thermal shock.2 Problems arise when a composite which contains absorbed moisture or some other liquid is suddenly heated quickly enough to drive off the liquid very rapidly. Similarly the whole electromagnetic spectrum of radiation

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must be considered: ultraviolet, visible, infrared, X-rays and gamma rays. For most purposes, ultraviolet and visible light are the most important. Ordinary sunlight has an adverse effect on some polymers, frequently causing discoloration and embrittlement. It is possible to protect against ultraviolet radiation (and against microorganisms) with suitable additives, so the performance of one commercial grade of a given generic polymer such as polyvinyl chloride is not necessarily a very useful guide to the behaviour of other grades of the same material which may contain different additives. We need to consider possible environmental effects before deciding what the design strain (or stress) of a structure should be. This means predicting what, if any, aggressive environment will be encountered, which in turn implies being familiar with the circumstances of use. It can be difficult enough for the laboratory-based scientist or engineer to form a reasonable estimate (unaided) of the year-round surface temperatures on a surface ship or an ordinary aircraft, which may serve in various climates. It is much more difficult to assess the likely stresses, temperatures and radiation levels on an experimental space platform, or the conditions applicable to a chemical reaction vessel subject to periodic overheating, or an oceanbed assembly in a remote part of the world, with unknown microorganisms present. Often, one agent initiates a degradation process, and another aggravates it, so both factors have to be present for anything to happen. Material reliability predictions therefore always have to be made in close consultation with the proposed user.

12.4

Standard tests

Environmental testing involves an assessment of a material’s properties and microstructure before and after exposure to some aggressive environment. The important considerations are: • • • • • •

careful characterisation and conditioning of the virgin composite material selection of a realistic environmental exposure regime which incorporates the significant factors operating during the useful life of the article control of the reproducibility of the exposure regime recognition and quantification of the most significant changes occurring in the composite during exposure statistical analysis cautious extrapolation in order to predict longer term behaviour. This is vital where a product such as a pipe or bridge may be in use for 30 or even 130 years. Obviously, laboratory testing cannot be carried out for even a fraction of that time.

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The chosen test procedure will depend on the motive for having any tests. The aim may be simply to compare the merits of two competing candidate materials, or to subject a single material to pass/fail criteria. It is these situations which will be discussed in the present chapter. More complicated procedures, containing an element of research and development, may be used where the objective is to find out what the principal mode of degradation is, or where the intention is primarily to improve the material. These procedures are outside the scope of this discussion. Composites are used in so many environments that it is not practicable to devise entirely appropriate international standard tests for all conceivable environmental scenarios. Standards can obviously be written in a generalised format to apply to any of a wide range of chemicals, but the prevailing temperature, stresses, test duration and specimen geometry, especially thickness, depend on the intended application. The test criterion frequently reduces to the achievement of a given percentage retention of specified mechanical properties after immersion in a standard environment under controlled conditions. These mechanical property retention tests are performed in accordance with ISO (International Standardization Organization) or ASTM (American Society for Testing and Materials) or similar standard methods. The immersion process itself raises a number of issues: whether both sides of a test panel should be immersed, whether specimens should be removed and cooled for periodic weighing, how to apply a stress at the same time as immersion in a liquid, and whether the test liquid or environment is itself stable over a period of time. There are a number of important national and international tests relating to the environmental performance of composite materials. There are also tests for the individual constituents of fibrous composites, such as the matrix resins, the fibre reinforcements and the chemically resistant linings of pipes, examples of which are given in Table 12.1. Some of these tests will be mentioned later. There are also some general recommendations. BS 4618, Recommendations for the Presentation of Plastics Design Data, Part 4: Environmental and Chemical Effects, has the following sections which are relevant to organic matrix composites: • • • •

Section 4.1 Section 4.2 Section 4.3 Section 4.4

Chemical resistance to liquids Resistance to natural weathering Resistance to colour change produced by exposure to light The effect of marine exposure.

Section 4.1 gives guidance about the various chemical reagents. The method of immersion is given as total immersion, whereas in practice tanks and pipes are exposed to their liquid contents on only one side. The effects

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Table 12.1. Examples of standard tests and specifications for environmental stability, relevant to reinforced plastics. ASTM D 543 ASTM C 581

BS EN 60068-2-45 ASTM C 582 ASTM G 20 ASTM D 3681 ISO 175 ISO 1776

Resistance of plastics to chemical reagents Determining chemical resistance of thermosetting resins used in glass-fibre reinforced structures intended for liquid service Basic environmental testing procedures: immersion in cleaning solvents Contact-molded reinforced thermosetting plastic (RTP) laminates for corrosion-resistant equipment Standard test method for chemical resistance of pipeline coatings Test method for chemical resistance of reinforced thermosetting resin pipe in a deflected condition Plastics: determination of the effects of liquid chemicals, including water Glass: resistance to attack by hydrochloric acid at 100°C

are usually similar, but with total immersion they are achieved much more quickly. Changes in dimensions and appearance after immersion are to be observed, together with changes in tensile, flexural, shear and impact strength. The stipulations for the impact test method and other mechanical tests leave scope for considerable variation. Section 4.2 deals with natural weathering, which is an obvious influence on all outdoor composites, but not usually much of a threat to functional viability, only to the aesthetic properties of the composite. The introduction to the standard warns that the results only give an indication of the likely behaviour of the material, and tests should preferably be long term (i.e. over several years), although even then the outcome may depend on the time of year at which the test programme was started. The method of exposure involves specimens mounted on racks facing south, with the specimen surfaces at 45° to the horizontal. There are provisions to eliminate interference from obstructions such as high rise buildings. Consideration is also given to specimen fixing or mounting. No copper should be used, because of the effect of copper ions on certain autocatalytic processes; aluminium, plastics or ceramic fixing materials are preferred. Timber backing is considered an undesirable specimen support, because it raises the specimen temperature too much. After exposure, the specimens are examined for biological attack before washing with soap and water, being machined into shape and subjected to any conditioning process required before the tests. Visual observations play a large part in the evaluation, but mechanical tests can be selected from the usual menu (tensile, flexural, shear strength, impact).

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Section 4.3 (on colour stability), is less important than the others for composite materials, although external building panels suffer from lightinduced changes in their original pigment colour if the wrong pigment is chosen, or if certain flame retardant additives are used. Section 4.4, the effect of marine exposure, is, perhaps, more relevant here. It does not specify actual tests, rather the general approach to be taken. The preamble identifies three types of marine exposure: (a) near the sea, (b) partially immersed and (c) totally immersed. It is pointed out that, unlike metals, most plastics are more severely affected by (a) than by (b), and least affected by total immersion. This is said to be because ultraviolet light is commonly considered more of a threat than water (a generalization which at best applies only to specific polymers and can certainly not be taken for granted with structural composite materials). Eight agents of marine degradation are listed: salt, water, sand, ultraviolet light, marine vegetation and microorganisms, marine pollutants and wave action. Thermosetting resin composites are not seriously affected by salt or sand, although in the very different context of aircraft, water erosion under high speed conditions can represent a more serious problem for brittle thermosetting resins than for the semicrystalline thermoplastics. Consider now ASTM C 581, mentioned already in Table 12.1. It illustrates some of the issues encountered during environmental testing. First, C581 is intended as a low-cost screening procedure and the results are fairly subjective. Second, it is not directed at advanced composites such as carbonepoxy and aramid laminates. Instead, it is a guide to the selection of a matrix material for process plant, effluent pipes and so on. Note that the term ‘advanced composite’, as used above, assumes that specific strength and modulus are the crucial properties that matter most to every user, whereas in many applications, environmental considerations are more important. Despite the title, the tests in C581 are not confined to the matrix resins. They are actually performed on chopped strand glass mat laminates. Testing resin and fibres separately would give no indication of resin–fibre interface quality and how it survives the environment. C581 deals with the changes induced by an environment on the Barcol hardness of a laminate and its appearance, flexural strength and flexural modulus. It also considers any change in the appearance of the immersion media. An introductory statement points out that the liquid medium may be hazardous. The test procedure specifies two plies of chopped strand mat, with two layers of a surfacing veil. The normal additives such as thixotropes, fillers or fire retardants are allowed. The control (i.e. the before-test value of the Barcol hardness) has to achieve a certain minimum, otherwise the resin would be considered undercured and unsuitable for chemical resistance work. Changes in appearance are recorded after visual inspection, without

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any objective spectroscopic or other instrumental technique. The guidance notes on the changes in mechanical properties point out that the rate of change of strength, modulus and hardness may be more significant than the absolute values (a typical test duration is about a year). The test procedures are simple enough, but the skills required to produce consistent and representative test laminates by hand layup with such constituents should not be underestimated. By the same argument, the test outcome may reflect the quality of the specimen fabricator. Finally, there are test methods and specifications applicable to finished or semi-finished articles, such as plastics or composite pipes and so on.These documents often contain sections dealing with chemical resistance. As an illustration, ASTM D 3262(88) concerns the short-time hydraulic failure of plastics pipe, tubing and fittings, but takes account of chemical considerations; for example, it includes a section 6.3.1: ‘Pipe specimens, when tested in accordance with 8.2.1, shall be capable of being deflected without failure at the 50 year strain level given in Table 4, when exposed to 1.0N sulfuric acid’. Specifications may, implicitly or explicitly, offer advice on materials selection. In ASTM D 3299(88), Standard Specification for Filament-wound Glass-fiber-reinforced Thermosetting Resin Chemically Resistant Tanks, it is said that fire-retardant agents may interfere with visual inspection of laminate quality, and should not be used on inner surfaces or interior layers, ‘unless their functional advantages outweigh the loss of visual inspection’.

12.5

Sample conditioning

Specimens are first conditioned to achieve a standard and reproducible initial state. This initial state may simply mean that the specimens are thoroughly dry, or that they have been held in a standard atmosphere such as 50% RH (relative humidity), or that some other prescribed treatment has been applied. One relevant standard is ASTM D 5229, Moisture Absorption Properties and Equilibrium Conditioning of Polymer Matrix Composite Materials; so also is BS 2782 Part 10, Method 1, 1977, Methods of Testing Plastics: Method 1004, Standard Atmospheres for Conditioning and Testing. Drying requires desiccation over a desiccant such as phosphorus pentoxide until constant weight is reached. The time taken to dry thick specimens can be considerable. Rapid drying at high temperatures to circumvent the need for lengthy specimen conditioning can introduce microcracks. The thermal history of a specimen can alter the crystallinity of a thermoplastic matrix, and since crystallinity has an enormous effect on solvent resistance, it is clearly necessary to ensure reproducible and standard laminate processing procedures prior to environmental testing.

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The main requirement of any conditioning operation is for the diffusion samples to be representative, completely dry and free of defects such as voids. In practice composites do contain voids, but they should be present at a reasonably low and consistent level, otherwise the quantity of liquid absorbed will be a function of void content. Ideally, preliminary material characterisation is advisable using scanning electron microscopy and ultrasonic C-scanning, if available. A series of papers by Thomason is relevant, discussing the characterisation of composite interfaces in connection with water resistance.3–5

12.6

Experimental approaches

Common procedures are: 1

2

Examination of the sample before and after immersion using optical and scanning electron microscopy (SEM) to detect any debonding or microcracks. If inspection before immersion is omitted, defects which were first noticed in immersed samples may appear significant until they are later discovered in the virgin material as well. Figure 12.2(a) shows an example of defects which developed after a period of environmental exposure. They are microcracks in glass-epoxy resins, formed after exposure to hot water, and observed under the SEM. Further prolonged exposure caused these fine cracks to become large enough to be visible to the naked eye, as shown in Fig. 12.2(b). The cracks were caused by residual hardener which dissolved in the water, producing osmotic cells and incidentally generated ammonia, which is harmful to glass fibres. These effects were originally reported by Kasturiarachchi and Pritchard.6 Measurement of the percentage retention of mechanical properties, such as tensile, shear or flexural strength. A reduction in shear strength, measured by the short beam method, the 10° off-axis tension method or rail shear, is usually attributable to interface breakdown, although matrix degradation is a possibility. Interface failure should also be reflected in a fall in the transverse tensile or flexural strength of unidirectional laminates. Changes in flexural properties are convenient to measure, because of the simple specimen geometry. Retention of compressive strength in the hot, wet state is another well established criterion of environmental durability in wet atmospheres.

Usually we consider whether the surrounding environment affects the composite. But the opposite can also be a concern. If containers manufactured from composite materials are used to store or transport food, drink or fuels, the testing programme may require an analysis to determine whether the contents have been contaminated as a result of leaching

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(a)

(b)

12.2 (a) Scanning electron micrograph showing fine cracks in a sample of glass/epoxy after exposure to hot water. (b) After prolonged exposure the cracks are visible to the naked eye.

of trace substances from the composite itself. In the case of drink, very tiny quantities can be detected by the sensitive palate. Gas–liquid chromatography is the first procedure to be considered for organic chemical constituents, preferably coupled with another technique such as Fourier transform infrared (FTIR) spectroscopy. Inductively coupled plasma emission spectrometry is also an appropriate technique, if trace elements are being sought. Tests on the fibre reinforcement can also be important. Glass fibres vary a great deal in their behaviour towards acids and alkalis.7 Individual filaments, or entire bundles, are immersed in an environment, and their tensile strength and modulus retention determined after specified periods. Single filament handling procedures require considerable practice in order to avoid damaging the specimens, especially if they are to be mounted in a liquid medium under stress. Glass fibres are attacked more

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Diameter remaining (%)

793K

813K 75

833K

50

853K 873K 25 20

60

100

140

Time (minutes)

12.3 Reduction in average diameter of a single high modulus carbon fibre, caused by heating in air at different temperatures. Eventually the fibre fractures, having oxidised preferentially at particular sites.9

seriously by acids which form insoluble mineral salts, such as calcium sulphate or aluminium oxalate, than by acids forming soluble salts.8 Thus oxalic and sulphuric acids are more aggressive media than nitric acid, at least below pH 1. If single carbon fibres are heated in air, they eventually fracture due to oxidation.9 This is relevant to the composite, because exposed fibre ends can be attacked at high temperatures. The decline in the average diameter of high modulus PAN (polyacrylonitrile) carbon fibres on heating in air at various temperatures is shown in Fig. 12.3. Close examination shows that the oxidation occurs selectively and locally as a result of the catalytic effect of trace impurities. The oxidation resistance is therefore dependent on the impurity profile.

12.7

Determination of sorption behaviour

The mass of liquid absorbed when a composite sample is immersed in a laboratory tank of liquid is usually determined by manual weighing, but automatic devices based on quartz springs, force transducers and electrical property measuring devices are sometimes used. The environment in which the samples are to be immersed needs to be defined. The chemical composition of some liquids (such as sodium hypochlorite or petrol) will change gradually during a long test, as a result

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of either decomposition or volatilization. Supplies therefore need to be refreshed frequently. Samples immersed in laboratory glass tubes can become difficult to identify after a time in an aggressive liquid, which changes their appearance and destroys surface markings. It is important to devise effective methods to overcome this problem, without scratching the samples. Numbered slots in inert specimen racks are better than using physically marked specimens. Suppose a sample of dry mass M0 increases in mass during immersion in a solvent, to reach Mt at time t. The usual assumption is that the amount of solvent absorbed is (Mt - M0). But if the sample is then dried, the new mass may be Md rather than M0. The reason would be that while sorption was occurring, some constituents of the sample itself were entering the liquid environment by a process of leaching. This is most noticeable with unsaturated polyesters and plasticised resins and can often be neglected with a more stable matrix. Where leaching occurs, the true liquid sorption at time t is given by Equation [12.1]: M s = 100Ê Ë

M t - Md ˆ M0 ¯

[12.1]

The original state of the sample will never be recovered, and a second sorption cycle is unlikely to be superimposable on the first. The sorption behaviour of resins changes rapidly with temperature as the glass transition temperature, Tg, is approached. It is unlikely that organic matrix composites will deliberately and knowingly be used within 15°C of the matrix Tg. However, sorption of a liquid lowers the Tg, so that the transition temperature has to be given a wider berth than 15°C if sorption is anticipated.

12.8

Lowering of Tg by absorbed liquids

The extent of the lowering of the Tg is very difficult to measure experimentally because the procedures involve heating a sample and this inevitably removes some of the absorbed liquid. It is essential to use a sample capable of retaining most of the absorbed liquid during heating for long enough to allow the property measurements to be made; errors are difficult to avoid. There are predictive equations, such as that of Kelley and Bueche,10 which estimate the change in the glass transition temperature as a result of absorbed liquid diluent: Tg =

a pn pTgp + a d (1 - n p )Tgd a pn p + a d (1 - n p )

[12.2]

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where Tg, Tgp and Tgd refer to the glass transition temperatures of the system, the polymer and the diluent, respectively. np is the volume fraction of polymer, with ap and ad being the volumetric expansion terms for the polymer and the diluent, respectively. McKague et al.11 used rapid heating methods to minimise loss of moisture during a study of the effect of water on Tg. They refined Equation [12.2] to give: Tg =

a gpn pTgp + a 1d (1 - n p )Tgd a gpn p + a 1d (1 - n p )

[12.3]

where ald and agp refer to the liquid and glassy volumetric expansion coefficients, respectively. Several widely differing values for the glass transition temperature of water have been used. McKague and co-workers used 4°C because it is the temperature at which the density is greatest. Carter and Kibler12 proposed that water absorption in epoxy resins is divided into bound and non-bound categories, with the proportion of each being temperature dependent. The implication is that below the Tg, many of the water molecules are more or less firmly held, whereas above the glass transition, most are free to move.

12.9 12.9.1

How do composites perform in adverse environments? The matrix

Few generalizations are completely safe, but the following points provide useful guidelines: • •

•

•

All organic matrix materials are permeable to moisture. Most organic matrix materials are permeable to a whole range of organic liquids, with a consequent reduction in matrix modulus, although semi-crystalline matrix resins are less permeable than amorphous ones. This observation means that the rate of cooling during processing of crystallisable thermoplastics such as PEEK (polyether ether ketone) and the degree of regularity of their chemical repeat units are very important for solvent resistance.13 All are poor at withstanding high temperatures. It is possible to predict from considerations of chemical structure whether one matrix will be more resistant to heat or radiation than another. This is a vital step in reducing the costs of material evaluation. Most resins are resistant to microorganisms, although the same cannot be said about some of the additives in thermoplastic polymers,

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• •

281

such as plasticisers, or about the adhesives and coatings which may be applied. Most matrix resins withstand dilute acids and alkalis better than light alloys or stainless steels would. Anions and cations do not diffuse easily, if at all, through uncracked resins.14 This is because of the large size of many ions, especially when solvated.

12.9.2

The reinforcement

Glass fibres are resistant to most chemicals and glass is the favoured material for containing chemicals during reactions, but it does not withstand strong alkalis and acids indefinitely. Flaws are initiated which can propagate under stress. Even hot water can cause glass fibres to lose their strength. Carbon fibres are resistant to almost all chemical reactions, notably to alkalis, non-oxidizing acids and steam below 1000°C, but they are vulnerable to oxidation and intercalation.15 The higher their heat treatment temperature and corresponding graphitic order, the better carbon fibres resist oxidation and the less well they withstand intercalation. Aramid and other thermoplastic fibres absorb moisture, unlike glass and carbon, and are affected by ultraviolet light, but in practice this is largely a surface effect.

12.9.3

The interface

The interface between fibres and resin can sometimes be broken by liquids, or possibly by thermal cycling. Hot water can break the bond between polyester resin and glass fibres. The breakdown can be observed under optical microscopy, and the reduced adhesion can sometimes be reflected in the smooth appearance of the fibre surfaces in a fractured specimen in a scanning electron microscope. It is also reflected in reduced transverse tensile strength and short beam shear strength. Interfacial breakdown is sometimes reversible on careful drying. Wherever environmental damage to the interface is expected, the best fibre surface treatment has to be applied. A matrix which has a high processing temperature will also require heat-resistant coupling agents for bonding to glass fibres.

12.9.4

Chemical reactions between composites and their environment

Some of the dangers are obvious. Carbon fibres undergo oxidation, glass is attacked by alkalis, and most resins are destroyed by alkalis and strong

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oxidizing acids. Having said that, chemical attack is rarely as severe a problem as might be imagined, simply because the dangers can be predicted and obviated. Even the much-quoted vulnerability of unsaturated polyester resins to hydrolysis is rarely a problem if the conditions recommended by the supplier are fulfilled. There can be degradation reactions involving frequently overlooked trace substances, such as unreacted hardener.

12.9.5

Physical changes caused by chemicals

Common chemicals such as water and solvents can cause physical effects, quite apart from any chemical reactions. These effects are chiefly dimensional changes, which can be undesirable in themselves, and which can lead to cracking or delamination. Solvents can also dissolve or leach out trace substances. The swelling process is usually accompanied by a reduction in the Young’s modulus through plasticisation, and by an initial rise in matrix strength, caused by relief of internal stresses, followed rapidly by a much larger fall. The elongation at break is frequently lowered. Short immersion times will usually produce changes only in the surface of the material.

12.9.6

Protective measures

The matrix offers some protection to the fibres against aggressive liquids, unless it becomes microcracked.16 If such protection is inadequate, a special surface layer may be used between environment and fibres. A very thick layer will simply have the effect of distancing the reinforcement from the aggressive medium. Protective layers can consist of tissues or veneers, made of special chemically resistant glass or polymer, embedded in a gelcoat, or they can be highly filled resin layers (see Fig. 12.4) or barrier films made of polymer, ceramic or metals.

12.9.7

Effects of mechanical stress

It has already been mentioned that stress can cooperate with an environment to produce sudden catastrophic failure by environmental stress cracking (ESC). This is chiefly a problem with glass fibres; carbon does not seem to be susceptible. Figure 12.5 shows in schematic form a procedure for the long term strain corrosion testing of buried sewage pipe.17 The sewage is simulated by using very dilute sulphuric acid. The composition of sewage in a pipe can, in practice, be altered by the presence of industrial effluent. Stress can alter the free volume of the matrix and therefore alter the amount of liquid absorbed.18 There can be substantially increased absorption in the vicinity of stress-induced damage around holes and notches.

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Surface tissue Chopped glass roving A

Chopped and filament wound glass in sand aggregate

B C

Chopped glass roving Surface tissue

12.4 Schematic cross-section of a GRP sewer pipe laminate: (A) protective, resin-rich outer layer, including chemically resistant polyester resin and special C-glass tissue, or a polymeric tissue, followed by a layer of about 30% w/w chopped glass, i.e. a relatively high resin content; (B) main structural laminate consisting of chopped roving, filament wound glass and quartz sand aggregate, together with anticorrosion grade polyester resin; (C) inner lining, similar to (A).

dilute sulphuric acid

12.5 End view of a pipe is shown. The pipe is placed under constant strain for a long time (typically several years), while filled with dilute sulphuric acid of pH about 1. A pipe joint may be included in the test section. The acid simulates sewage in its action on the pipe.

Figure 12.6 combines these effects, showing the effect of a compressive stress (defined here in terms of the strain) on the uptake of methylene chloride by carbon–PEEK. At first there is a reduced uptake with increasing applied strain, but later there comes a point when damage around holes increases the uptake dramatically.19 Creep and stress relaxation are very variable in polymers and are relatively low for those which are favoured in structural composites, but any

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Loge (% weight absorbed)

0.7

0.6

0.5

0.36% 0.4

0

0.2

0.4

0.6

0.8

1.0

Compressive strain (%)

12.6 Showing the amount of methylene chloride absorbed in 28 days at 23°C by carbon-fibre reinforced PEEK (quasi-isotropic APC-2, 32 plies), under compressive strain. As the strain increases, the free volume in the matrix decreases and the amount of solvent absorbed declines. After a certain strain level is reached, damage is caused around holes in the material. This causes an increase in solvent absorption.

tendency to these viscoelastic responses is accentuated by solvent uptake, because the absorbed molecules plasticise the matrix. Tests focus on either the effect of the environment on the long term deformation of the samples under load, or the possibility of creep rupture occurring. Such tests are normally individually designed to meet the requirements of the particular situation. As with all tests involving the simultaneous application of a sustained load and a potentially corrosive liquid, suitable apparatus is purpose built from corrosion-resistant materials, and ingenuity is needed to minimise testing costs.

12.10 Diffusion of liquids into composites 12.10.1

Qualitative considerations

Diffusion has great practical significance for composites. We need to know how much of a solvent diffuses into a composite material, how rapidly and to what extent. The amount of liquid absorbed is a useful but not an infallible indication of the magnitude of the change in mechanical properties.

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Diffusion of liquids into well-bonded composites occurs chiefly by activated diffusion, with very little contribution from wicking along fibres. The rate of diffusion is indicated by the diffusivity or diffusion coefficient. The presence of fibres means that the composite is anisotropic, and we have to deal with several different diffusion coefficients. The reason why diffusion parallel with the fibre direction in unidirectional laminates is usually faster than in other directions is probably simply a question of the simplicity of the diffusion path, although internal stresses cannot be entirely neglected.

12.10.2

Diffusion equations

The general principles of the mathematics of diffusion have been given by previous authors such as Crank and Park.20 The more recent account by Comyn21 also deals with the principles. It is not practicable to summarise the detailed arguments here, so only a few key equations will be mentioned. Fick’s first and second laws are given in Equations [12.4] and [12.5], and are generally considered as the starting point, although they are not obeyed by polymers unless certain conditions are met, including, the requirement that the rate of diffusion of the permeant is slow compared with the polymer segmental mobility. The first law states that: Q = -D

∂C ∂x

[12.4]

The second law introduces time as a parameter: 2 2 2 ∂C Ê∂ C ∂ C ∂ Cˆ =D + 2 + 2 2 Ë ∂x ∂t ∂y ∂z ¯

[12.5]

In these expressions Q is the rate of transfer per unit area of section (kg s-1 m-2), D is the diffusion coefficient (m2 s-1), C the concentration of diffusing material (kg m-3) and x the distance in the direction normal to the plane, with y and z referring to the other two directions. When considering the passage of water through a laminate for which the thickness is small in relation to its other two dimensions, it is possible to simplify Equation [12.5] by considering one direction (the x direction) only. This gives: ∂C ∂ 2C =D 2 ∂t ∂x

[12.6]

From these equations, more directly usable expressions can be obtained. Carter and Kibler12 give an expression for the mass of penetrant, Mt,

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absorbed as a function of time, in terms of the equilibrium absorption value M•. A commonly cited version of that expression is: Ê 8 Mt = M• Á 1 - 2 P Ë

n =•

Â n =0

2

1

(2 n + 1)

2

e

-P 2 D(2 n + 1) t ˆ ˜ h2 ¯

[12.7]

where Mt is the mass uptake by the material, M• is the mass uptake at equilibrium and h is the sample thickness. The curve corresponding to this equation can be divided into two parts, see Fig. 12.7(a). It is linear up to a weight gain of 0.6 Mmax, and it is possible to derive a useful expression for the linear section: 2

D=p

Ê h ˆ Ê (M 2 - M1 ) ˆ Ë 4 M• ¯ Ë ( t 2 - t 1 ) ¯

2

[12.8]

where D is the diffusion coefficient, t is time and M1 and M2 are any two mass uptake values corresponding with times t1 and t2, respectively. The diffusion coefficient can then be calculated. A material with classical Fickian behaviour will absorb a liquid as shown in Fig. 12.7(a). The diffusion of a liquid into a polymer matrix frequently, but not invariably, follows the Fickian relationship with time. The diffusivity can be calculated from the initial slope, and the amount of liquid sorbed in a given time can be deduced for different geometries. Fickian behaviour requires the initial linearity to be sustained until about 60% of the sorption has occurred. The sorption and desorption curves are superimposable, for constant diffusivity. Diffusion coefficients obey an Arrhenius relationship with temperature. Some of the many possible deviations from Fickian behaviour are shown in Fig. 12.7(b). Diffusion occurs even in the complete absence of microcapillary channels, as a consequence of the ability of sufficiently small molecules to travel through the free volume between the atoms of the organic phase by discrete jumps. Whether Fickian or anomalous diffusion occurs depends at least in part on the frequency of these solvent molecular jumps relative to the frequency of the macromolecular segmental motions of the resin. Both frequencies are temperature dependent. The solvent absorbed into glass- or carbon-fibre composites has to be accommodated in the matrix free volume, microvoids or debonded interfaces. Assuming that there is not an excess of voids or debonded interfaces, the majority of the diffusing substance is accommodated either in the preexisting free volume or in new matrix space created by swelling stresses. The time taken for swelling stresses to increase the available space depends on the nature of the polymer and can be considerable. Sometimes a plot of mass uptake against time, or the square root of time, shows a second

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Moisture absorption, M (%)

M max

M2

M1

t 11/2

t 21/2 Square root of time, t 1/2

(b)

Mass uptake, Mt

B A C

Square root of time

12.7 (a) Classical Fickian diffusion behaviour. (b) The three curves show departures from Fickian behaviour: (A) pseudo-Fickian, with a short linear portion and anomalous dependence on specimen thickness; (B) sigmoid; (C) two-stage, where equilibrium appears to have been achieved but further sorption occurs later.

plateau, as additional space for incoming permeant is eventually made available, as is shown in curve C of Fig. 12.7(b). This means that diffusion experiments which do not allow sufficient time for the second plateau effect to take place can be misleading about the final equilibrium solubility. Laminates which bear some relation to real materials are usually thick, and the diffusion process takes considerable time to complete. In the case of fibre-reinforced resins, where the second plateau also occurs, an alternative explanation has been mentioned by Morii et al.22 They suggest that glass filament bundles become gradually loosened through interface debonding. Another reason could be the progressive formation of

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microvoids through damage induced by chemical or physical processes, but this is uncommon. The free volume, and hence the diffusion coefficient, is increased by a tensile stress, reduced by a compressive stress and hardly changed by a flexural stress, since this involves both tensile and compressive modes in opposition to each other. In general, free volume increases with increasing temperature, but for polar polymers within certain temperature ranges, it is found to increase on cooling.23 Thus a lowering of the water temperature means an increase in water absorbed, even though the equilibrium, or maximum level, has already apparently been reached. This phenomenon occurs below Tg; the polymer retains its capacity to accommodate water, as a result of polar interactions acting to keep the structure like a rigid cage. The cage concept also explains why solvent uptake tends to be high with matrix resins of high Tg.

12.11 Classification of absorption categories A classification of absorption types, together with criteria for Fickian behaviour, is given by Marom24 and is summarised below. For Fickian diffusion: •

Both sorption and desorption curves are linear functions of the square root of time in the initial stage. • Beyond the linear portion, both absorption and desorption curves are concave to the abscissa. • The sorption behaviour obeys the film thickness scaling law, i.e. reduced sorption curves with an abscissa of t0.5/h are superimposable for films of different thicknesses. • When D is constant, the absorption and the desorption curves coincide over the entire range of t. • The temperature dependence of D can be expressed by the Arrhenius relation: Ê - E0 ˆ D = D0 exp Ë RT ¯

[12.9]

where the pre-exponential term, D0, is the permeability index, E is the activation energy of the diffusion process and R is the gas constant. Some anomalies in diffusion behaviour are: •

Pseudo-Fickian behaviour: the sorption and desorption curves when plotted against t0.5 show anomalously short initial linear portions, and/or the sorption curves depart from the film thickness scaling law.

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•

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Sigmoid behaviour: the sorption curves are sigmoid in shape, with a single inflection point at about 50% equilibrium sorption.The initial rate of desorption exceeds that of sorption, but desorption then becomes slower and the curves cross. Two-stage sorption behaviour: The initial uptake is rapid and a linear function of t0.5. The sorption curve then approaches a quasi-equilibrium, followed by a slow approach to a final true equilibrium.

In general, the mass of permeant absorbed is a function of time raised to a power n, which is 0.5 for Fickian diffusion, less than 0.5 for pseudo-Fickian behaviour, between 0.5 and 1 for anomalous diffusion, 1 for ‘Case 2’ diffusion and more than 1 for ‘super Case 2’ behaviour. (Both the penetrant molecules and the polymer molecules are in constant motion. The polymer molecules are too long to move as a whole; only segments or sections can move at a time. The mode is called Case 1 if the rate of diffusion of the penetrant molecules, that is, the frequency of the molecular jumps, is much less than the frequency of oscillation or relaxation of the segments of the polymer chain molecules. Case 2 is the opposite situation.)

12.12 Edge corrections In practice, the use of one-dimensional equations for Fickian diffusion into thick samples, such as structural composites, is common, but it can introduce significant errors. There are various ways to minimise such errors: First, use only very thin samples (this is not possible with most laminated materials), so that diffusion through the edges can be neglected by comparison with diffusion through the major surfaces. If the sample length and width are of the same order of magnitude and the thickness is smaller than either of the other two by two orders of magnitude, the true diffusion coefficient will lie within 5% of the measured diffusion coefficient and no correction is required.25 Second, use geometrical correction equations such as that attributed to Shen and Springer:26 h h Dt = Dm Ê 1 + + ˆ Ë w l¯

-2

[12.10]

where Dm is the diffusion coefficient from measured data, Dt is the true diffusion coefficient, h is the sample thickness, l is the sample length and w is the sample width. The method ignores diffusion through the perpendicular sample faces and treats diffusion through each pair of opposing surfaces additively. However, this assumption will only hold true for exposure times so short as to be experimentally useless, because there is increasing congestion at

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the corners of the specimen. Rothwell and Marshall27 have also addressed the problem. They do not assume that the interaction of the different sides can be neglected, but attempt to treat the three-dimensional diffusion case: 2 -2

È 3BW1 3C Ê W1 ˆ ˘ Dt = Dm Í A + ˙ 4 AW0 5 A 2 Ë W0 ¯ ˚ Î where

A = 1+

[12.11]

h h + w l

B=

h h h2 + + l w wl

C=

h2 wl

and W1/W0 is the fractional weight gain, below which data are used to fit a straight line. For short exposure times (when W1/W0 << 1) the edge correction factor reduces to that proposed by Shen and Springer. Third, follow Blickstad et al.,28 who discussed the correction of gravimetric data on moisture absorption in carbon-reinforced epoxy resins, and pointed out the need to use the three-dimensional solution to Fick’s equation. A similar method is proposed by Grayson25 in a paper that describes how a progressive numerical treatment is used to obtain the gravimetric data for a one-dimensional sample, which is then used to calculate the diffusion coefficient. The procedure for applying Grayson’s edge correction method is as follows: 1 2

Obtain a value of the diffusion coefficient, Dm, from the measured gravimetric data using Equation [12.8]. Use Dm and the sample dimensions to calculate an edge correction ratio, Rc, for each exposure time from the relationship: R=

F (h, D, t ) F (h, w, l , D, t )

[12.12]

where F(h,D,t) is the fractional weight gain as a function of time for the one-dimensional case, calculated from Equation [12.7], and F(h,w,l,D,t) is the three-dimensional fractional weight gain calculated from the three-dimensional equation. 3 Correct the measured gravimetric data by multiplying each measured fractional weight gain by its corresponding edge ratio.

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Obtain a new value of the diffusion coefficient, D1, from the edge corrected gravimetric data. Repeat steps 1–3 until the difference between Dn and Dn-1 is as small as desired. The subscript n is an integer that refers to the number of times the correction cycle has been applied.

As this process is repeated, the calculated value of the diffusion coefficient will approach that of a sample of thickness h, and infinite area. The disadvantage of this method is the lengthy iterative calculations required.

References 1. M A French and G Pritchard, ‘Environmental stress corrosion of hybrid fibre composites’, Composites Science and Technology, 1992 45 257–63. 2. Zhao Jiaxiang, Din Kunhe and Wei Jinxian, ‘The thermophysical and thermal shock resistance properties of carbon-carbon composites’, Proceedings of ICCM-6, London, eds FL Matthews, NCR Buskell, J M Hodgkinson and J Morton, Elsevier Applied Science, 1987, Volume 4, 394–400. 3. J L Thomason, ‘The interface region in glass fibre-reinforced epoxy resin composites: 1. Sample preparation, void content and interfacial strength’, Composites, 1995 26 467–75. 4. J L Thomason, ‘The interface region in glass fibre-reinforced epoxy resin composites: 2. Water absorption, voids and the interface’, Composites, 1995 26 477–85. 5. J L Thomason, ‘The interface region in glass fibre-reinforced epoxy resin composites: 3. Characterization of fibre surface coatings and the interphase’, Composites, 1995 26 487–98. 6. K A Kasturiarachchi and G Pritchard, ‘Scanning electron microscopy of epoxy-glass laminates exposed to humid conditions’, Journal of Materials Science, 1985 20 2038–44. 7. D Santrach and R Matzeg, ‘FRP corrosion resistance: the role of the glass fiber type’, Paper 1-A, 46th Annual Conference, Composites Institute, SPI, Washington, DC, 1991. 8. Q Qiu and M Kumosa, ‘Corrosion of E-glass fibers in acidic environments’, Composites Science and Technology, 1997 57 497–507. 9. G L Hart, The Chemical Stability of Carbon Fibres and their Composites, PhD Thesis, Kingston Polytechnic (now Kingston University), Surrey, UK, 1975. 10. F N Kelley and F Bueche, ‘Viscosity and glass transition temperature relationships for polymer-diluent systems’, Journal of Polymer Science, 1961 50 549–56. 11. E L McKague, J D Reynolds and J E Halkias, ‘Swelling and glass transition relations for epoxy materials in humid environments’, Journal of Applied Polymer Science, 1978 22 1643–54. 12. H G Carter and K G Kibler, ‘Langmuir type model for anomalous moisture diffusion in composite resins’, Journal of Composite Materials, 1978 12 118–31. 13. G Pritchard, ‘Anti-corrosion polymers: PEEK, PEKK and other polyaryls’, RAPRA Review, Report Number 80, RAPRA Technology, Shawbury, Shropshire, UK, 1995, Volume 7(8).

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14. B D Caddock, K E Evans and D Hull, Proceedings of the 2nd Conference on Fibre Reinforced Composites, Paper C25–86, Liverpool University, UK, Institute of Mechanical Engineers, Mechanical Engineering Publications, 1986. 15. G Pritchard, ‘The chemical reactivity of carbon fiber-reinforced composite materials’, Polymer-Plastics Technology Engineering, 1975 5(1) 55–81. 16. M A French and G Pritchard, ‘The fracture surfaces of hybrid fibre composites’, Composites Science and Technology, 1993 47 217–23. 17. R D Currie, ‘Manufacture, testing and installation of centrifugally cast pipes’, Pipecon: Conference on Large Diameter Glass Reinforced Plastic Pipes, Paper 12, Fibreglass Ltd/Amoco Chemicals SA, London, 1980. 18. A Fahmy and J C Hurt, ‘Stress dependence of water diffusion in epoxy resins’, Polymer Composites, 1980 1(2) 77–80. 19. G Pritchard and S J Randles, ‘The combined effect of mechanical stress and chemical environments on carbon-fibre reinforced PEEK laminates containing a circular hole’, Proceedings of ICCM-10, Whistler, BC, Canada, eds A Poursartip and K Street, Woodhead Publishers, Cambridge, UK, 1995, Volume 6, 265–72. 20. J Crank and G S Park, Diffusion in Polymers, London/New York, Academic Press, 1968. 21. J Comyn (ed), Polymer Permeability, London, Elsevier Applied Science, 1985. 22. T Morii, T Tanimoto, H Hamada, Z-I Maekawa, T Hirano and K Kiyosumi, ‘Relation between weight changes and bending properties of GFRP panels immersed in hot water’, Polymers and Polymer Composites, 1993 1(1) 37–44. 23. M J Adamson, ‘Thermal expansion and swelling of cured epoxy resin used in graphite/epoxy composite materials’, Journal of Materials Science, 1980 15 1736–45. 24. G Marom, ‘The role of water transport in polymer materials’, in Polymer Permeability, ed J Comyn, London, Elsevier Applied Science, 1985, Chapter 9. 25. M A Grayson, ‘An improved method of correcting diffusion coefficients from gravimetric data for edge effects’, Journal of Polymer Science, Part B, Polymer Physics, 1986 24 1747–54. 26. C H Shen and G S Springer, ‘Moisture absorption and desorption of composite materials’, Journal of Composite Materials, 1976 10 2–20. 27. W S Rothwell and H P Marshall, Analysis of Experimental Transport Data: Diffusion of Water in EPDM, LMSC-D566642, 1977. 28. M Blikstad, P O W Sjoblom and T R Johannesson, ‘Long term moisture absorption in graphite/epoxy angle ply laminates’, Journal of Composite Materials, 1984 18 32–46.

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13 Scaling effects in laminated composites C SOUTIS

13.1

Introduction

The implementation of composite materials in structural applications has involved the fabrication of costly prototypes and large scale experimental verification of certain design concepts. An alternative method of understanding and predicting the response of composite structures under a variety of loading conditions is through the use of scale model testing. Scale model testing requires that the relationships between the responses of the small scale model and full-size component be known so that the behaviour of the model can be used to predict the response of the full-size component. The relationships between the responses can be obtained through applied mechanics formulations. However, the presence of physical constraints can prevent the complete reproduction of certain responses in small scale models. Responses subject to such physical constraints or scaling conflicts include rate-dependent and notch-sensitive behaviours.1,2 Furthermore, the mechanics formulations are still evolving for advanced materials and may not provide the scaling relationships at the local material level necessary to relate all aspects of the response throughout the size range. The problem of designing, building and testing a scale model structure constructed of fibre-reinforced composite materials is a challenging one. Complications may arise from factors by which standard similitude laws cannot be satisfied. Such factors are fabrication, fibre diameter, fibre/matrix interface, ply interface and test method. If these limitations are ignored, one is left with two obvious scaling options for laminated composites:3,4 • •

ply-level scaling sublaminate-level scaling.

Ply-level scaling is achieved when a large scale laminate, with a given stacking sequence, is constructed from thick layers of the same fibre orientation, each built from a number of standard thickness plies. On the other hand, sublaminate-level scaling is achieved by the introduction of basic sub293

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laminates which are stacked together to form thicker laminates. For example, (+45/-45/0)S and (+454/-454/04)S are said to be scaled at a ply level, whereas (+45/-45/0)S and (+45/-45/0)4S are said to be scaled at a sublaminate level, where (+45/-45/0) is the sublaminate. In the following sections three approaches to scale-up law development are outlined, the applicability and limitations of the existing methods are summarised and practical application examples are presented.

13.2

Background

At least three approaches to a study of scaling are available. The first involves the use of dimensional analysis and similitude principles to define those non-dimensional groups of geometric and material variables which govern the response of scale models. The non-dimensional parameters may be derived either from the governing equations and boundary conditions or from the Pi theorem. Both techniques are described and the advantages and disadvantages of each are discussed by Baker et al.5 The Pi theorem is the more general method of the two and consists of identifying the important physical variables relevant to the problem under consideration. Each variable is represented dimensionally in terms of a fundamental set of units, typically either the force–length–time (F-L-T) system or the mass–length– time (M-L-T) system. From these parameters, an experimental programme can be defined using a number of scaled specimens to permit validation of the scaling parameters and to identify any scale effects or non-scaled behaviour. This approach has been successfully employed with composite structures in studies of transverse impact of beams,1 tensile strength4 and the static and dynamic responses of eccentrically loaded beam columns.6,7 A second approach is more mechanistic in nature; here, a scale effect is identified as a departure of the response from a known mechanics model, which occurs systematically with specimen size. In contrast to the similitude approach, the mechanistic approach permits selective scaling or the evaluation of the response as a subset of the material, and/or geometric parameters are varied. This approach may be preferred when there are many variables involved in characterising the response, and when it is desired to determine the sensitivity of the response to the change in individual variables.1 An obvious difficulty with this approach is the need to separate genuine scale effects from any inadequacies in the mechanics model being used. Finally, the scale effect in failure of composite structures can also be analysed using statistical methods, particularly Weibull distributions.8–10

13.3

Investigation of failure

Scale model testing is a practical and efficient alternative to full-scale testing for determining the structural response of most composite lami-

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nates. However, if the testing involves damage or failure of the structure, then the absolute size of the specimen will have a tremendous influence on the failure behaviour and ultimate strength of the structure. Composite materials are often used to build thin, high stiffness structures which routinely operate under large deflections and high design loads. If tests on subscale specimens are used to determine ultimate loads for these types of design, then the strength of prototype structures may be seriously overestimated owing to the scale effect in failure. A large difference in failure loads, strains and end-displacement ratios has been observed2 between scale models of an eccentrically loaded beam column, Fig. 13.1.The size effect in strength which is observed on the macroscopic level is the result of damage on the microscopic level which initiates within the laminate and develops in a particular manner under the applied load. The accumulation of damage and interaction of failure mechanisms eventually result in the ultimate failure of the structure. It was concluded2 that a detailed investigation of the effect of test specimen size on failure needs to be addressed on a material level before the phenomenon can be understood on the macroscopic level. Results of applying maximum stress, maximum strain and Tsai-Wu tensor polynomial failure criteria demonstrated that these criteria cannot predict a difference in strength based on the absolute size of the specimen, see Figs. 13.2 and 13.3. For the unidirectional layup, Fig. 13.2, the predicted strength is conservative, while for the cross-ply laminate the predicted load ratio at failure is higher than the experimentally observed values, Fig. 13.3. In Fig. 13.4 the load ratio is plotted as a function of the scale factor for several layups.2 If no scale effect in strength was present, then all of the data would fall on the line drawn at 1.0. The plot indicates that a scale effect is evident even between the full and 5/6 scale beams. The effect increases as the size of the beam decreases. The unidirectional laminates appear to be least sensitive to the effect in strength, although the effect is still observed. Other researchers10–12 have attempted to model the scale effect in strength of fibre-reinforced composites using either a statistical approach or a fracture mechanics model. These methods and their application to the eccentrically loaded beam column and uniaxially stressed laminates are discussed in the following sections.

13.3.1

Statistical approach

The application of statistical techniques for modelling the size effect in strength of brittle materials is based on the observation that these materials are flaw sensitive. Since the presence of imperfections can be described statistically in nature, it is reasonable to assume that larger specimens will exhibit a lower strength simply because the probability is higher that a strength-critical flaw, such as a void or crack, is present in the greater

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Top platen Upper hinge

Scaled beam specimen

Lower hinge Load platform Bottom platen

2/3 GL 1/2 GL 1/4 GL

Gauge length (GL)

Front view

Side view

Longitudinal strain gauge (back-to-back) Strain gauge rosette (back-to-back)

13.1 Schematic of front and side views of the eccentrically loaded beam column.2

volume of material. Basically, two approaches are available to model the size effect. The ‘weakest link’ theory assumes that a structure consists of a number of individual elements arranged in series. When one of these elements fails, the entire component fails. In contrast, the ‘bundle theory’ models a structure as a parallel arrangement of elements. When an element

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Unidirectional 1/4 and fullscale 0.8

Load/Euler load

0.6

0.4

1/4 Full

0.2

Analysis (failure location) 0.0 0.0

0.2

0.4

0.6

0.8

1.0

End displacement/length

13.2 Predicted failure location for unidirectional laminates.2

Cross ply 1/4 and full-scale 0.8

Load/Euler load

0.6

0.4 1/4 0.2 Full

Analysis (failure location)

0.0 0.0

0.2

0.4

0.6

0.8

1.0

End displacement/length

13.3 Predicted failure location for cross-ply laminates.2

fails, the load is redistributed among the remaining elements. Final failure occurs when all of the elements have failed. Weibull statistical theory has been applied to both the weakest link and bundle theories to develop mathematical models for predicting the scale effect in strength. The ultimate failure of individual carbon fibres and fibre bundles has been successfully modelled using Weibull statistics based on the weakest link theory.13 Sub-

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Normalised failure load

2.0

1.5

1.0

0.5 0.0

0.2

0.4

0.6

0.8

1.0

Scale factor

13.4 Normalised failure load ratio versus scale factor.2 +, unidirectional; ¥, angle ply; , cross ply; , quasi-isotropic.

sequently, this model has been applied by other researchers to investigate the scale effect in strength of composite test specimens. Statistical analysis has been used to explain the higher strength seen in composite specimens tested in flexure over those tested in uniaxial tension.9,10 Using Weibull theory, Bullock10 showed that the probability that a specimen containing a distribution of flaws throughout its volume could survive an applied stress distribution, s(x,y,z), is Equation [13.1]: m È ˘ s Ps = expÍ -Ú Ê ˆ dv˙ = e - l Î v Ë s0 ¯ ˚

[13.1]

where PS is the probability of survival, s0 is the characteristic ultimate strength of the unit or reference volume and m is the Weibull shape parameter. s0 and m are material properties; the characteristic strength has a probability of survival PS = e-1 = 0.37. The risk of failure, l, the exponent of e, is called the ‘stress–volume integral’. If smax is the maximum value of the applied stress through the component and v is the total volume, Equation [13.1] may be written in terms of dimensionless ratios14 as: m

ln 1 Ps = l =

Ê s max ˆ V Ê s ˆ Ë s 0 ¯ v Ú Ë s max ¯ v

m

dv V

[13.2]

The ratio, vc = s0/smax, is a safety factor referred to the characteristic strength of the reference volume and is called the ‘central safety factor’. The dimensionless variable s/smax is independent of the volume for an elastic analy-

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sis; that is, geometrically similar structures will have the same stress–volume integrals for any volume. Equation [13.2] can be written as: m

ln 1 Ps =

Ê 1ˆ V Ê s ˆ Ë vc ¯ v Ú Ë s max ¯ v

m

dv V

[13.3]

or 1

m

Ï 1 V Ê s ˆ dv ¸ m vc = Ì Ú Ë ¯ V ˝˛ Ó ln 1 Ps v v s max

[13.4]

Equation [13.3] states that for a specified central safety factor, stress distribution and volume, the probability of survival or the probability of failure Pf = 1 - PS may be calculated. According to Equation [13.4], for a specified safety level, the required central safety factor, vc may be calculated. 13.3.1.1

Design examples

13.3.1.1.1

Axial tension or compression

If a uniaxial force, F, is applied to a bar with cross-sectional area A, see Fig. 13.5, the stress in the bar is uniform: s = F/A = constant = smax and the probability of a failure is: È Ê 1ˆ Pf = 1 - exp ÍÎ Ë vc ¯

m

È v ˘ A1 ˘ ˙ = 1 - exp Í- m ˙ 1 ˚ Î vc ˚

[13.5]

P

A

l V

P

13.5 Reliability of a bar with a cross-sectional area, A, under tension.14

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Equation [13.5] can be used to illustrate the size effect. If two different volumes, V1 and V2, under uniform stress, have the same reliabilities (Ps1 = Ps2): m

m

È È Ê s1 ˆ ˘ Ês2 ˆ ˘ Ps1 = exp Í-V1 and Ps2 = exp Í-V2 ˙ Ë s0 ¯ ˚ Ë s 0 ¯ ˙˚ Î Î Ê s1 ˆ Ë s0 ¯

m

then

-V1

= -V2

or

s 2 Ê V1 ˆ m = s 1 Ë V2 ¯

Ês2 ˆ Ë s0 ¯

[13.6]

m

[13.7]

1

[13.8]

Assuming that the volume stressed V2 = 8V1 and m = 16, then, according to Equation [13.8], the strength of the bigger specimen will be reduced by more than 12% (that is, s2 = 0.878s1). Under uniaxial compression both the applied stress and the compressive strength of a reference volume are negative and the same relations apply. The ratio of strengths therefore depends on the relative volumes and the Weibull modulus, m, which is a measure of material variability and is approximately related to the coefficient of variation (CV) of individual specimen strengths by the relation m = 1.2/CV. A highly variable material will have a low value of m, and would be expected to give a high amount of scatter in specimen strengths and a large size effect. The theory therefore predicts a direct correlation between strength variability and size effect. Weibull theory satisfactorily explains the size effect in brittle materials; however, its application to composite materials is not entirely clear and special care should be taken when it is applied. Composites are not completely brittle materials, but are often able to sustain quite significant damage before final failure. 13.3.1.1.2

Three-point flexure

For the case of three-point bending loading conditions the stress distribution is non-uniform and Equation [13.1] is expressed as: m

È ˆ˘ 1 Êsf ˆ Ê Psf = exp Í-Vf Á 2 ˜˙ Ë ¯ s 0 Ë 2(m + 1) ¯ ˚ Î

[13.9]

where the subscript f is used to identify flexural loading. For two geometrically similar specimens (a model and a prototype) of volumes Vm and Vp the ratio of ultimate strengths for a given probability of failure is given by: 1

s m Ê Vp ˆ m = s p Ë Vm ¯

[13.10]

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Equation [13.10] is the same as that under uniaxial tension. The ratio of median failure stress in three-point flexure to that in tension is found by setting Pst equal to Psf in Equations [13.6] and [13.9]: 1

sf È 2 Vt ˘ m = Í2(m + 1) st Î Vf ˙˚

[13.11]

If two specimens of equal volume are tested in flexure and in tension, then by Equation [13.11], the flexural strength will be greater than the tensile strength by a factor:

[

s f = 2(m + 1)

1 2 m

]

st

[13.12]

using m = 16 then sf = 1.45st, the strength of the beam is 45% greater than that of the tension component owing to stress non-uniformity. Bullock10 applied the statistical analysis presented in Equations [13.1] to [13.12] to predict the strength behaviour of carbon-epoxy (T300/5208) composite specimens. Tests were conducted on fibre tows and tensile and flexural specimens to verify the analysis. An important finding from Bullock’s research is that the flaw-density exponent, m, which must be determined empirically, was found to be a material constant. For the T300/5208 the value of flaw-density exponent was found to be 24. Bullock showed good agreement between experiment and analysis and concluded that less expensive flexural specimens which are easier to test can be used to estimate ultimate tensile stresses of composite materials. While Bullock’s results show promise for predicting the ultimate strength of specimens which are tested under different conditions, the volume term was found to underestimate the actual volume effect for specimens of greatly different sizes. A limitation of the method includes the requirement that the flaw-density exponent be found empirically for each material system. Also, no data were presented to indicate how well the model would perform for laminates containing off-axis plies. The flaw-density exponent, m, would be most likely to be influenced by the laminate stacking sequence, especially for laminates in which failure mechanisms were matrix dominated and not governed by fibre fractures. The volumetric model given by Equation [13.9] was used by Jackson2 to predict the scale effect in strength observed in the failure response of eccentrically loaded beams, see Fig. 13.1. The flaw-density exponent was found empirically to be equal to 7.75 and was used in Equation [13.9] to predict the scale effect in tensile strength of AS4/3502 unidirectional and multidirectional laminates. As shown in Fig. 13.6, the volumetric ratio predicts the scale effect fairly well for the unidirectional and quasi-isotropic laminates. However, agreement between the volumetric ratio and the angle-ply and cross-ply laminates is not good. This is not unexpected, since the failure

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Normalised failure stress

5

4

3

2

1

0 0.0

0.2

0.4

0.6

0.8

1.0

Scale factor

13.6 Comparison of the volumetric ratio prediction of normalised failure tensile stress versus scale factor and experimental results.2 +, unidirectional; ¥, angle ply; , cross ply; , quasiisotropic; —, volumetric ratio.

mechanisms for the angle-ply and cross-ply laminates are characterised by transverse matrix cracking, but the flaw-density exponent was determined based on tests of unidirectional laminates which fail by fibre breakage. Obviously, the volumetric ratio is sensitive to the failure mode and should only be applied for laminates which exhibit similar failure mechanisms. In summary, results indicate that the Weibull statistical model based on the weakest link theory has been successful in predicting scale effects; however, it relies on empirical data to determine the Weibull shape and scale parameters. Also, the model lacks the sophistication needed to predict the difference in magnitude of the scale effect in strength for laminates which do not fail predominantly by fibre fracture.

13.3.2

Fracture mechanics theories

Elementary approaches to scaling indicate that under scaled loading conditions the stress state in the model is identical to that in the prototype, that is, stress scales as unity. Ideally, failure should occur at the same stress and strain levels for both the model and the full-scale specimens. However, as seen in the previous sections, deviations from this elementary approach to strength scaling are observed. Scale models constructed from brittle isotropic materials typically predict higher failure loads than the full-scale prototypes when the data are scaled up for comparison. Another explanation for this size effect in strength is based on the principles of linear elastic

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fracture mechanics (LEFM). A scaling conflict for stress is introduced when the critical stress intensity factor, Kc, is introduced in a dimensional analysis;11 the stresses in the region near a sharp crack in a body have been derived by Irwin15 and have the general form: s ij =

K fij (q ) 2pr

[13.13]

where K is the crack tip stress intensity factor (SIF), r and q are polar coordinates to locate a point in the stress field beyond the crack tip and fij is a non-dimensional function of the variable q; this crack tip stress field is independent of the loading. Thus, all cracks will have the same stress field and will only differ by the intensity factor, K, from one problem to the next. In the fracture mechanics approach, a critical SIF is defined as the parameter that governs the onset of unstable crack growth, rather than a maximum stress or strain at failure. Since composites often exhibit brittle fracture, it is reasonable to include a variable such as the critical SIF to model the fracture behaviour. The critical stress intensity factor is generally assumed to be a material property which is independent of loading conditions, initial crack geometry and size, or any other parameter. As such, Kc should have the same value for both the model and the prototype and, therefore, scale as unity. However, a dimensional analysis including the SIF as a variable4,6 requires that Kc be scaled in proportion to l1/2. Since this condition is violated when the geometric scale factor is 1, the stress at initiation of unstable crack propagation scales as l-1/2. Thus, the stress required to propagate a crack in a linear elastic model, sm,, will be greater by a factor l-1/2 than the stress needed to propagate a crack in a geometrically and constitutively (homologous stress–strain behaviour in the model and prototype systems) similar prototype, sp: sm =

sp l

[13.14]

where l is a geometric scaling factor (ratio of model to full scale dimension). According to Equation [13.14], the stress for crack propagation in a 1/4 scale structural model will be twice the value required for the full scale structure. Consequently, the model will appear twice as strong. Predicted failure stresses using this fracture model are shown in Fig. 13.7, along with tensile strength experimental data for several AS4/3502 carbonepoxy laminates.2 The fracture ratio tends to overpredict the scale effect in strength for the smaller scale unidirectional and quasi-isotropic laminates and underpredicts the effect for the angle-ply and cross-ply laminates. The cross-ply laminate response deviates from the fracture ratio model by the largest amount, especially for the smaller scale model specimens. In general,

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Normalised failure stress

5

4

3

2

1

0 0.0

0.2

0.4

0.6

0.8

1.0

Scale factor

13.7 Comparison of the fraction ratio prediction of normalised failure tensile stress versus scale factor and experimental results.2 +, unidirectional; ¥, angle ply; , cross ply; , quasi-isotropic; —, fracture ratio.

the fracture ratio is capable of predicting a scale effect in strength; but, like the volumetric model, the fracture model does not predict any variation in the scale effect owing to differences in laminate stacking sequence. Results presented in Fig. 13.7 show that a model which predicts the scale effects in strength, in order to be successful, must incorporate some measure of the failure mechanism of the laminate.

13.4

Practical application examples

The applicability of classical dimensional analysis principles in composite structural mechanics is assessed by examining two fundamental problems:16 • •

axial tension loading of a narrow laminate buckling of a narrow laminated plate

These problems are selected to highlight two important parameters in the scaling of composites layup and stacking sequence. These parameters are not relevant to the scaling of metallic structures but have significant effects in scaling of composites. The applicability of classical dimensional analysis is illustrated in the following examples.

13.4.1

Example 1: axial tension loading

Consider a 24-ply baseline laminate of 25 mm width and subjected to tensile loading along the 0° direction. The laminate stacking sequence is

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[±45/02/±45/02/±45/90/0]S, which gives a (42/50/8) distribution of plies. The lamina mechanical properties are: E11 = 129 GPa, E22 = 13 GPa, G12 = 5.9 GPa, n12 = 0.3, h = 0.13 mm and ef = 1.1%. The calculated Young’s modulus in the loading direction is Exx = 68.8 GPa. The strain response of the laminate can be approximated by: e=

P P = AEx nwhEx

[13.15]

where P is the applied load, n the number of plies, with h the ply thickness and w the laminate width. To scale down the laminate and simulate the strain response, two assumptions are made. First, it is assumed that symmetry of the laminate is maintained and second, that the orthotropy of the laminate is maintained throughout the scaling process. These assumptions ensure that Equation [13.15] holds true for all of the scaled-down laminates. Now consider the failure load Pf based upon the maximum strain criterion. Equation [13.15] becomes: Pf = nwhExef

[13.16]

The failure load calculated for the baseline laminate is 61.84 kN. For cases of constant modulus Ex, such as metals, the failure load would vary linearly with the cross-sectional area of the specimen. This is shown by the solid line in Fig. 13.8. However, for composite plates the modulus Ex is a function of the thickness (number of plies) and the layup. Scaling in thickness by adding or reducing the number of plies gives rise to a nonlinear relation-

Failure load (kN)

60

40

20

0

8

16

24

Laminate thickness (number of plies)

13.8 Tensile failure load of a narrow composite plate as a function of laminate thickness.16 Maximum strain criterion e = 0.011. Scaling down from 24-ply [(±45/02)2/±45/90/0]N laminate. denotes possible ply mix and stacking sequence for constant thickness.

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ship between the failure load and cross-sectional area. To illustrate this point, suppose that the laminate width is given a constant value of w = 25 mm while the number of plies is reduced. The failure loads will depend upon the type of plies (0, 45, 90) removed from the laminate. For example, if the baseline 24-ply laminate is reduced to 22 plies by removing two 0 plies, two 45 plies or two 90 plies, the corresponding failure loads are 79 kN, 91.7 kN and 89 kN, respectively. As the number of plies is reduced still further, the possible failure loads are found to lie in an envelope centred about the linear failure load versus cross-sectional area relationship as shown in Fig. 13.8.

13.4.2

Example 2: buckling of a narrow laminate

The second problem involves a narrow laminate under axial compressive load. The buckling load for an anisotropic plate of this kind with clamped ends and free edges is: 2

N cr = k

Ê 2p ˆ D Ë L ¯ 11

[13.17]

where L is the total length of the plate, D11 is bending rigidity in the loading direction and k is a constant equal to 1.0306 for the first buckling mode. For isotropic material: D11 =

Eh3 12(1 - n 2 )

[13.18]

From Equation [13.17], the scaling parameters to be considered in this case are L and D11. Because D11 depends on thickness, modulus and stacking sequence, this problem represents one higher level of complexity over Example 1. Consider the same 24-ply baseline laminate as in Example 1, with an unsupported length L = 76 mm. The axial bending rigidity of the plate is 204 N m. If the modulus is constant, as for metals, D11 varies with h3tot, where htot is the total thickness. When the thickness is reduced to 22 plies, the possible combinations of layup and stacking sequence, along with the associated bending rigidity and buckling load, are given in Table 13.1. Figure 13.9 shows the buckling load as a function of laminate thickness. The buckling loads for the composite laminate fall in an envelope centred about the solid curve, which is the buckling load versus thickness relationship for a constant modulus material. Figure 13.9 illustrates that scaling in composites, even for the simplest structural mechanics problem, involves more than dimensional parameters. Because of the multiplicity of possible laminate constructions, structural mechanics methods of analysis must be used to develop similitude rules.

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307

Table 13.1. Possible 22-ply laminates in Example 2. Layup

(45.5/45.5/9)

(36/55/9) (45/55/0)

Stacking sequence

Bending rigidity D11 (N m)

Buckling load Ncr (N m-1)

[45/02/±45/02/±45/90/0]s [±45/02/45/02/±45/90/0]s [±45/02/±45/02/45/90/0]s [±45/0/±45/02/±45/90/0]s [±45/02/±45/0/±45/90/0]s [±45/02/±45/02/±45/90]s [±45/02/±45/02/±45/0]s

177 163 156 140 151 156 156

800 738 705 635 682 706 707

Failure load (kN)

40

30

20

10

0 8

16

24

Laminate thickness (number of plies)

13.9 Buckling load as a function of laminate thickness.16 Scaling down from 24-ply [(±45/02)2/±45/90/0]S laminate. denotes possible ply mix and stacking sequence for constant thickness.

Similar results can be obtained for two-dimensional problems. The thickness, ply orientations and stacking sequence effects on bending of a rectangular composite plate under uniform lateral pressure is shown in Fig. 13.10, which demonstrates how the structural response deviates from the classical dimensional analysis results. The deviation is caused by the layup and stacking sequence effects on the plate rigidity parameters Dij. In comparing the results of the two-dimensional (2-D) problem with that of onedimensional (1-D), Fig. 13.10 shows a narrower band in the structural response. This is because the results of the 1-D problem are affected only by the axial bend stiffness D11, whereas the results of the 2-D problem are affected by all components of the in-plane mechanical properties. The overall effect of all four rigidity components (D11, D12, D22, D66) is less significant than that of a single component.

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Failure pressure qf

300

200

100

0

8

16

24

Laminate thickness (number of plies)

13.10 Failure pressure of a rectangular plate as a function of plate thickness.16 denotes possible ply mix and stacking sequence for constant thickness.

13.5

Specialised scaling techniques in composites

The previous section discussed the difficulties in direct application of the principle of similitude in composites. It was also shown that a scale model can be designed with the aid of structural mechanics. In this section, an analytical procedure to design scale models is presented. The procedure is similar to the one presented by Deo and Kan16 and McCullers and Neberhans17 and is demonstrated below. Consider an unstiffened composite cylinder of radius Rs, thickness hs and length Ls. The scaling parameters significant to buckling can be divided into three categories: (a)

Load parameters (load ratio, model/prototype) such that: Pr =

(N cr )m (N cr ) p

[13.19]

where Ncr is the buckling load per unit length around the cylinder circumference. (b)

Geometric parameters: Lm Lp

Length ratio

L=

Radius ratio

Rr =

Rm Rp

[13.21]

Thickness ratio

hr =

hm hp

[13.22]

[13.20]

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309

Property parameters: Modular ratio

Er =

Em Ep

[13.23]

Rigidity ratio

Dr =

Dm Dp

[13.24]

The load parameter Pr is a predetermined design factor for the model. The load requirement for the test model is usually higher than the actual structure. In the case where the exact buckling load of the structure is to be simulated, Pr = 1.0. The geometric and property parameters interact when buckling is considered. For composite structures, the property parameters are usually not unique because of the anisotropy of the materials. These parameters are also affected by the thickness parameter because of the ply orientations. Therefore, it is not possible to establish a simple scaling law for composite structures as discussed in the previous section. In this analysis, the scaled model is designed using an iterative procedure. The solution for symmetric buckling of an isotropic cylinder is first used to estimate the key scaling parameters. The buckling load of an isotropic cylinder with R >> h is given18 as: N cr =

2 1 2 (EDh) R

[13.25]

Based on this expression, the key scaling parameters can be written as: Rr = hr = Er = Dr =

1 1 2 (Er Dr hr ) Pr

(Rr Pr )

[13.26]

2

[13.27]

Er Dr

(Rr Pr )

2

[13.28]

hr Dr

(Rr Pr ) Er hr

2

[13.29]

Assuming that the test model is fabricated from the same material as the full-scale structure, then the Poisson ratios nm = np, and the stiffness (rigidity) ratio becomes: Dr = Erhr3

[13.30]

Equation [13.25] indicates that the length parameter is an arbitrary number if only buckling load is to be simulated. The length of the cylinder controls the buckling mode, but not the buckling load.

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For composite cylinders, the scale parameters are first estimated using Equations [13.26] to [13.30]. Then the following procedure is used: • Define the load requirement (Pr). • Select the radius and length ratio (Rr, Lr). Since length has no significant effect on the buckling load, assume Lr = Rr. • Maintain approximately the same axial Young’s modulus (Er = 1.0). • Estimate hr from Equations [13.27] and [13.30]: hr2 = PrRr. • Based on the estimated hr, determine the practical thickness of the model, hm; this practical thickness is determined based on the number of plies. • Determine the ply orientations; these should be similar to the full-scale structure in the initial estimate, because Er = 1.0. • Determine the laminate stacking sequence based on Dr given in Equation [13.29], taking into account the practical rules for laminate stacking sequence. • Conduct orthotropic buckling analysis to confirm Pr. • Perform iterations until the required Pr is obtained. The following numerical example illustrates this procedure:16 Consider a full-scale cylinder 1140 mm in radius and 640 mm in length. The cylinder is made from AS4/3501, 18-ply [±45/02/±45/90/0]s laminate with a thickness of 2 mm. A 1 : 5 subscale model with a load requirement of Pr = 1.5 is to be designed. For the full-scale cylinder buckling:

(N cr ) p = 77 N m

[13.31]

The required buckling load for the subscale model is:

(N cr )m = 115N m

[13.32]

The dimension requirement gives Rm = 228 mm, Lm = 127 mm and hr = (PrRr)1/2 = 0.548 or hm = 0.548 ¥ 2 ª 1.1 mm. For the material considered, a 9-ply laminate is required, which has nominal thickness of 1.1 mm. For Er = 1.0, the percentage distribution of 0°, 45° and 90° plies for the 9-ply laminate is either (33.3/55.6/11.1) or (44.4/44.5/11.1). A [±45/02/90/02/±45]T is chosen in this example. A 228 mm radius cylinder with this laminate results in a buckling load of 108 N m- or Pr = 1.4, which is below the load requirement of 1.5. Hence further iteration on the scale parameters is required. If the dimensional requirement (Rr = 0.2) can be changed, then the load requirement can be met by reducing the radius to 213 mm. With this radius the buckling load increases to 116 N m-1 or Pr = 1.51 > 1.5. The final values for the subscale model are Rm = 213 mm, Lm = 106.5 mm and hm = 1.1 mm. To further scale down the structure, a cylindrical panel instead of a sub-

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Scaling effects in laminated composites

p

Panel buckling load Ncr (kN m-1)

240

160

B = 12.07 cm

1.05Ncrc = 185.4 kM

(45/02/90/02/45)T SS edges

p cr

N Curved panel

For B ≥ 12.07 cm Ncrp is within 1.05Ncrc

B

Complete cylinder Ncrc = 176.6 kN

80 t

0

311

10

20

30

q

R

40

50

Panel width B (cm)

13.11 Effect of panel width on buckling load.16

scale cylinder can be considered. This requires determining the panel width (or central angle q), with all other parameters unchanged. Parametric studies indicate that for simply supported cylindrical panels, the panel buckling load, Ncrp is higher than that of a composite cylinder, Ncrc. However, the panel buckling load approaches the buckling load of a complete cylinder as the panel width increases. Beyond a minimum panel width, Ncrp is within 5% of Ncrc as shown in Fig. 13.11. The minimum width depends on the radius of the cylinder and can be determined analytically. For the example cylinder discussed here, the minimum panel width is 120 mm or central angle q = 32.4°. Figure 13.11 shows the effect of panel width on buckling load. It can be seen that the buckling load of the full-scale cylinder can be experimentally determined by testing a curved panel with a minimum width of 120 mm. It may be noted that although the buckling load of a complete cylinder can be simulated by a portion of a subscale cylinder (panel), the buckling mode is difficult to simulate.

13.6

Concluding remarks

Various analysis techniques have been presented and used to model scaling effects in composite laminates under static loading. A scale effect in strength is observed in unidirectional, angle-ply, cross-ply and quasiisotropic layups. In general, the failure loads and strains increase as the scale factor decreases. This implies that data generated from tests on scale model specimens will overestimate ultimate loads of prototype structures.

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Analysis of laminate failure using maximum stress, maximum strain and Tsai-Wu tensor polynomial criteria shows that these theories cannot predict the scale effect in strength. The scale effect cannot be explained by simple statistical models based on Weibull distributions of flaw densities and the weakest link approach, or by fracture mechanics models based on the critical stress intensity factor. Both of these approaches can predict a scale effect in strength, but do not account for variations in the magnitude of the scale effect caused by differences in laminate stacking sequences. The advantages and limitations of applying the principles of similitude to composite structures are summarised and illustrated by simple examples. An analytical procedure is formulated to design scale models for an axially compressed composite cylinder. Although the buckling load of the cylinder can be simulated by a curved panel (subscale cylinder), the buckling mode is difficult to simulate. The important point is that generalisations should not be made. There is always likely to be uncertainty over the question of validity of statistical methods or LEFM for any given case. Further information on scaling effects can be found in other recent works.19–24

References 1. J Morton, ‘Scaling of impact loaded fibre composites’, AIAA Journal, 1988 26(8) 989–94. 2. K E Jackson, ‘Scaling effects in the static and dynamic response of graphiteepoxy beam-columns’, NASA TM-102697, AVSCOM TR-90-B-006, July 1990. 3. T M Wieland, J Morton and J H Starnes Jr, ‘Scale effects in buckling, postbuckling, and crippling of graphite-epoxy Z-section stiffeners’, AIAA Journal, 1992 30(11) 2750–7. 4. S Kellas and J Morton, ‘Strength scaling in fiber composites’, AIAA Journal, 1992 30(4) 1074–80. 5. W E Baker, P S Westine and F T Dodge, Similarity Methods in Engineering Dynamics, Hayden Book Company, Rochelle Park, NJ, USA, 1973. 6. K E Jackson and E L Fasanella, ‘Scaling effects in the static large deflection response of graphite-epoxy composite beams’, NASA TM-101619, June 1989. 7. K E Jackson, S Kellas and J Morton, ‘Scale effects in the response and failure of fiber reinforced composite laminates loaded in tension and in flexure’, Journal of Composite Materials, 1992 26(18) 2674–705. 8. W Weibull, ‘A statistical distribution function of wide applicability’, Journal of Applied Mechanics, 1951 18 293–7. 9. C Zweben, ‘The effect of stress nonuniformity and size on the strength of composite materials’, Composites Technology Review, 1981 3(1) 23–6. 10. R E Bullock, ‘Strength ratios of composite materials in tension and flexure’, Journal of Composite Materials, 1974 8 200–6. 11. A G Atkins and R M Caddell, ‘The laws of similitude and crack propagation’, International Journal of Mechanical Sciences, 1974 16 541–8.

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12. A Carpinteri and P Bocca, ‘Transferability of small specimen data to full size structural components’, Composite Materials Response: Constitutive Relations and Damage Mechanisms, eds C Sih, G F Smith, I M Marshall and J J Wu, Elsevier Applied Science, London, 1988, 111–31. 13. F Lanza and H Burg, ‘Investigation of the volume effect on mechanical properties of various industrial graphites’, Proceedings of the 11th Biennial Conference on Carbon, Gatlinburg, Tennessee, 1973, 223–4. 14. R A Heller, ‘Size effects in brittle materials’, Periodica Polytechnica Series Mechanical Engineering, 1992 36(2) 135–52. 15. G R Irwin, ‘Analysis of stresses and strains near the end of a crack transversing a plate’, Journal of Applied Mechanics, 1957 54 361–8. 16. R B Deo and H P Kan, ‘Effects of scale in predicting global structural response’, First NASA Advanced Composites Technology Conference, NASA Langley Research Centre, Part 2, January 1991, 761–77. 17. L A McCullers and J D Neberhans, ‘Automated structural design and analysis of advanced composite wing models’, Composites and Structures, 1973 13 925–35. 18. S P Timoshenko and J M Gere, Theory of Elastic stability, McGraw-Hill Book Co, NewYork, 1961. 19. G Camoneschi, ‘The effects of specimen scale on the compression strength of composite materials’, Workshop on Scaling Effects in Composite Materials and Structures, NASA-CP-3271, ed K E Jackson, 1994, 81–100. 20. E C Edge, ‘Is there a size effect in composites’, Comments on designer’s corner by Carl Zweben, Composites, 1994 25(10) 956–7. 21. X Dao, L Ye and Y-W Mai, ‘Statistical fatigue life prediction of cross-ply composite laminates’, Journal Composite Materials, 1997 31(14) 1442–60. 22. M R Wisnom, J W Atkinson and M I Jones, ‘Reduction in compressive strain to failure with increasing size in pin-ended buckling tests’, Composites Science & Technology, 1997 57 1303–8. 23. S T Halliday, ‘Review of scaling and geometry effects on qusai-static mechanical properties of GRP marine laminates’, DERA/MSS/CR980367/1.0, August 1998. 24. J A Lavoie, C Soutis and J Morton, ‘Apparent strength scaling in continuous fibre composite laminates’, Composites Science and Technology, 2000 60(2) 283–99.

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14 Statistical modelling and testing of data variability L C WOLSTENHOLME

14.1

Introduction

Experimental data focus on a quantity of interest, termed the response variable. No two sets of data concerning a particular response variable are ever likely to be the same even when apparently collected under identical conditions. A certain amount of variation between any number of samples drawn from the same population is to be expected. Often, the objective is to identify factors, the explanatory variables, which influence the response, and this involves separating the variability in the data into that which is due to natural variation and that which may be due to these other factors. A principle of statistical testing of variability is that, under certain conditions, it is possible to put bounds on sample variation, with a certain probability. That is, a given percentage of the samples drawn from the same population will have a sample parameter, such as the sample mean, which lies between certain limits. The higher the probability, the further apart these limits will be. If a sample gives a value of the parameter which is outside this range, we are inclined to believe that the sample is not drawn from the specified population, but has responses influenced by some new factor. It is up to the experimenter to decide how to react to this information. When unusual variation is detected, it is important that the real reason for that variation is determined. It may be due to the use of different materials, but temperature, operator and machine are other possible explanatory variables.

14.2

Importance of looking at data plots

Some exploratory data analysis based on graphical methods is essential before proceeding to generate statistics which summarise the data. Many statistical tests rely on assumptions about the nature of the random variability in the data and, whilst some formal tests exist for this purpose, 314

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perfectly adequate assessment can often be made by eye using a suitable plot. Statistical computer packages and many spreadsheet packages will perform this task quickly and effectively. There is usually the facility to extract particular portions of the data and to examine them in every way possible. Plotting procedures are a way of revealing data structure and should be used before proceeding to formal analysis. Figure 14.1 shows carbon fibre strengths plotted against the log of fibre diameter. The plot shows a strong inverse linear relationship. If modelling the response, strength, is the objective, then the factor diameter could be an important element in the specification of the model parameters. Figure 14.2 shows a set of results from a low cycle fatigue experiment where the same material was used in experiments conducted at 14 different laboratories and reported by Thomas and Varma.1 A nominal strain level of 1.2% was set but the actual level was recorded in each case. Between one and three similar experiments were conducted at each laboratory, and each laboratory is indicated by a different symbol on the plot. There is some evidence of a relationship between cycles to fatigue life and strain level. Of more striking significance, however, is the clustering of results from individual laboratories at similar strain readings. Individual laboratories seem to produce very consistent results, but the results are markedly different between laboratories. There is a clear indication that a laboratory effect needs to be investigated. It could be that there were differences in material used at each site, though in this particular study it was found that similar laboratory effects were observed across different materials. So perhaps the experimental procedure or the equip-

Strength

5

4

3 1.9

2.0

2.1

2.2

Log fibre diameter

14.1 Carbon fibre data, strength versus log diameter.

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316

Mechanical testing of advanced fibre composites 8.0 lab1 lab2 lab4 lab5 lab6 lab7 lab9 lab13 lab14 lab15 lab16 lab18 lab19 lab20

Log cycles

7.5

7.0

6.5 1.125

1.150

1.175

1.200

1.225

1.250

1.275

Strain

14.2 Fatigue data, cycles to fatigue versus strain by laboratory.

ment used needs to be investigated. Ideally, possible explanatory variables should be identified before the experiment begins, but that may not be an easy task.

14.3

Basic statistics

The two principal features of any data set are (1) where the data are located on the scale of measurement and (2) to what degree the data are spread out. Common measures are: • •

central tendency: (arithmetic) mean, median – some kind of average value dispersion: standard deviation (sd), variance (sd)2, interquartile range.

It is important to differentiate between the true values of such parameters, which refer to the whole population (possibly infinite), and values yielded by a certain sample from that population. For example, we can call all the pebbles on a given beach, the population, and a bag of pebbles collected at random along the beach, a sample. Let a sample of values x1, x2, x3, . . . , xn be a simple random sample drawn from a population of x-values with mean, m, and standard deviation, s. The sample mean is given by Equation [14.1]: n

Âx

i

x=

i =1

n

[14.1]

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317

and the sample standard deviation, s, can be obtained from Equation [14.2]: n

s2 =

Â (x

2

i

- x ) (n - 1)

[14.2]

i=1

Population parameters are frequently unknown and are often estimated using the equivalent sample measures. This is written as: mˆ = x , sˆ = s (ˆ denotes estimate of ). It should be noted that these are point estimates and, as such, carry no indication of how close the estimate might be to the true value.

14.4

Distribution of sample statistics

The sample measures described above will be different from one sample to another, owing to the natural variability of data. It is possible to make statements about the way in which these measures behave. If a random variable X has mean mX = m and variance s 2X = s 2, then X , the mean of a sample of size n, has mean m X = m and variance s 2 X = s 2/n. The highly important central limit theorem states that for large n, the distribution of X is approximately normal, with mean m and variance s 2/n, independent of the distribution of X. It is only possible to define large within the observational context, but tens rather than hundreds of observations usually prove adequate. If X has a normal distribution, then X is exactly normal for all n. The normal distribution, shown in Fig. 14.3, is a symmetric bell-shaped distribution, centred on the mean m, with 95% of values lying within ±1.96s of m. The distribution may be denoted N(m, s 2). For testing purposes, all normal variates are converted to standard normal via the transformation Z = (X - m)/s. The variable Z has a mean 0 and variance 1 and 95% of the time -1.96 < Z < 1.96.

14.5

Testing for differences between samples

There are two classes of method: •

•

Parametric: assumptions are made about the populations from which the data are drawn, and usually depend on the normal distribution in some way. Non-parametric (or distribution free): no assumptions are made about underlying distributions. These methods are more versatile but, in general, slightly less powerful when applied to data for which the parametric assumptions are valid, and do not extend so easily to more complex modelling.

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Probable density function

0.4

N(0,1) t(15) t(5)

0.3

0.2

0.1

0.0 –3

t(5) t(15) N(0,1)

–2 –1 0 1 2 Number of normal sigma from the mean

3

14.3 Normal and t-distributions.

14.5.1

Parametric methods

14.5.1.1 Testing a single sample against a certain population In most parametric testing there are three important questions: (1) (2) (3)

Is the sample small or large? Is the population normal? Is the population variance known?

If the answer to (1) is ‘large’, then the answers to (2) and (3) have little material effect on the testing, because the central limit theorem applies and, if s2 is unknown, it can be estimated using Equation [14.2]. If the answer to (1) is ‘small’, then we can only proceed if the population yielding the sample can be assumed to be normally distributed. Further, the answer to (3) also becomes important because the distribution of the test statistic depends on it. In practice, most data under this heading fall into the small sample, population variance unknown category. In testing whether a sample has come from a certain population the null hypothesis is always that it has, and we look for evidence that it has not. An experiment may, for example, be investigating the effect of a new curing process. The statistical test starts by assuming that there is no effect and looks for evidence that there is, rather than assuming a difference and looking for evidence of no difference. It is rather like the principle of ‘innocent until proven guilty’ in a court of law. To test whether a large sample has come from a population with mean, m, we use the fact that:

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Statistical modelling and testing of data variability X - mX ª N (0, 1) sX

319 [14.3]

and therefore, if

(X - m) n s

< 1.96

[14.4]

the hypothesis that the sample comes from a population with mean, m, is accepted with 95% confidence. If the hypothesis were rejected, it would be a 5% level of significance. When s2 is unknown, it is estimated by s2. In the case of a small sample from a normal (or approximately normal) population,

(X - m) n

is only s N(0, 1) if s2 is known. It is far more likely that s 2 is unknown and has to be estimated, but in that case the sampling distribution of

(X - m) n

S assumes what is known as the Student or t-distribution. This is a symmetrical distribution, centred on zero. It takes a different shape for each value of its parameter n (known as the degrees of freedom) and tends to the standard normal distribution as n Æ • (see Fig. 14.3). In the single sample test, n would take the value n - 1 and 1.96 is replaced by a value in excess of 1.96. A set of statistical tables, such as those prepared by Neave,2 will provide all the critical values required in standard test procedures, but a few useful values from the standard normal and t-distributions are shown in Table 14.1. 14.5.1.2

A test involving two samples – do they come from the same population?

Consider two independent samples size n1 and n2, with sample means x 1 and x 2. Suppose the null hypothesis is that both samples come from a population with mean, m, and variance, s2. The test is based on the random variable X 1 - X 2 which has mean mX1 - mX2. Under the null hypothesis this mean is zero and has variance: s 2 X1 - X 2 = s 2 X1 + s 2 X 2 =

s2 s2 + n1 n2

[14.5]

For large samples X1 - X 2 ª N (0, 1) 1 1 s + n1 n2

[14.6]

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Table 14.1. Critical constants in tests based on the t and normal distributions. Confidence level (%) Level of significance (%) Degrees of freedom

95 5

99 1

1 2 3 4 5 6 7 8 9 10 15 20 25 30 40 50 Normal distribution values

12.71 4.30 3.18 2.78 2.57 2.45 2.36 2.31 2.26 2.23 2.13 2.09 2.06 2.04 2.02 2.01 1.96

t-distribution values 63.66 9.92 5.84 4.60 4.03 3.71 3.50 3.36 3.25 3.17 2.95 2.85 2.79 2.75 2.70 2.68 2.58

but is only so for small samples if the populations are normal and the population variance is known. If s2 is unknown, then it is estimated using a pooled estimate based on both samples: s2 =

(n1 - 1) s12 + (n2 - 1) s 22

[14.7]

n1 + n2 - 2

and for small normal samples the test is based on the t-distribution, using n = n1 + n2 - 2. Example 1: Samples of carbon fibres were collected from different parts of a 1000-fibre tow and gave the following data for their diameters measured in microns: • batch 1: n1 = 15 • batch 2: n2 = 13

x 1 = 7.641 x 2 = 7.371

s21 = 0.0718 s22 = 0.0751

Is there evidence of a significant difference in fibre diameter in different parts of the tow? We will assume that the populations are normal with equal variance, assumptions which will be examined later. The t-statistic is

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321

[14.8]

14 s12 + 12 s 22 giving t = 2.63. 26

The t-distribution with 26 degrees of freedom has 95% of values between ±2.056 and 99% of values between ±2.78. So, at a 5% level of significance, the null hypothesis that the samples come from the same population is rejected, but at a 1% level of significance the null hypothesis is not rejected. This would generally be regarded as a little inconclusive but depends on the practical consequences of such judgements.

14.5.1.3

Test for equality of variances

For samples from normal populations, the assumption of equality of variance may be tested using the F-distribution. Under the null hypothesis s 21 = s 22, s 21/s 22 ~ F(n1 - 1, n2 - 1). This distribution has two parameters, both called degrees of freedom, which vary the shape of the distribution. F-values are always greater than zero and, in general, the distribution has a long right-hand tail (i.e. is positively skew). Because of this asymmetry, the critical constants are not of a simple ±k form. Statistical tables generally only give the right-hand value, and the left-hand value is given by finding the reciprocal of F(n2 - 1, n1 - 1). In Example 1, s 21/s 22 = 1.036. This is compared with 1/F(14, 12) and F(12, 14) found in, say, Neave.2 At 95% confidence this yields the interval (0.31, 3.05), so the hypothesis of equality of population variances cannot be rejected. Where the assumption of equal population variances is in doubt, samples may be compared using the standardised difference: x1 - x2 s21 s 22 + n1 n2

[14.9]

Under the null hypothesis of equal population means, this statistic has an approximate t-distribution with degrees of freedom given by Equation [14.10]: n = ( s12 n1 + s 22 n2 )

2

[ s41 {n21 (n1 - 1)} + s24 {n22 (n2 - 1)}]

[14.10]

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Statistical packages such as Minitab3 include this version of the twosample test, but it is omitted in many basic statistics texts. An exception is Chatfield,4 which is a generally useful reference book. 14.5.1.4

Checking the normality assumption

Graphical inspection of the data should always precede formal analysis. The object here is to check whether the normal population assumption is tenable and to look for any unusual features of the data, for example, observations remote from the bulk of the data set (outliers). The latter might be perfectly valid but may, on the other hand, be due to recording error. Data displaying an approximately symmetrical bell shape are hoped for but can be fairly difficult to establish where there are only a small number of observations. The histogram is a popular plot but is of limited value for small samples. The boxplot is in many ways more useful as it highlights aspects of spread, symmetry and unusual observations. It shows the positions of quartiles (25%, 50%, 75% points), range and outliers and is useful for comparing samples. A plot focused more directly on the normal distribution is the normal plot. For each observation xi, a normal score, zi, is calculated and the {xi} are plotted against the {zi}. A facility to do this quickly and painlessly is available on packages such as Minitab. If the points lie approximately on a straight line, then the data conform well to a normal distribution. Figure 14.4(a) shows such plots for the data of Example 1 and have been produced using Minitab. More formal tests of normality are available. For example, the Shapiro– Wilk test5 is based on a measure of the linearity of the normal plot. So too is the Anderson–Darling test indicated in Fig. 14.4(b) and (c). The p-value quoted represents the probability that the data may have arisen by chance under the proposition of a normally distributed population. Only when the p-value is low, say <0.1, are we inclined to reject the normality assumption. It is known, however, that the data analysis techniques considered here are fairly robust (i.e. remain valid) to some departure from normality, so some form of visual impression is generally adequate and the most appealing.

14.5.2

Non-parametric methods

These usually involve ranking the data in order and using the rank numbers rather than the original data. This element of information loss explains why these methods are a little less powerful than parametric methods. The phrase, less powerful, means that slightly more convincing evidence is required to reject the null hypothesis. The appropriate measure of central tendency to test is the median rather than the mean.

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(a) Batch 1

Batch 2

7.0

7.5 Fibre diameter (mm)

8.0

(b) 0.999 0.99 Probability

0.95 0.80 0.50 0.20 0.05 0.01 0.001 7.2

7.7 Fibre diameter (mm)

8.2

(c) 0.999 0.99 Probability

0.95 0.80 0.50 0.20 0.05 0.01 0.001 7.0

7.2 7.4 7.6 Fibre diameter (mm)

7.8

14.4 Boxplots and normal plots for data from Example 1. (a) Boxplots, batches 1 and 2. (b) Normal plot, batch 1, average 7.64067, sd 0.267541, number of data 15, Anderson–Darling normality test A squared 0.241, p-value 0.7. (c) Normal plot, batch 2, average 7.37077, sd 0.273875, number of data 13, Anderson–Darling normality test A squared 0.185, p-value 0.887.

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14.5.2.1 Mann–Whitney test This test is the non-parametric equivalent of the two-sample t-test. It tests the hypothesis that the populations from which two independent samples are drawn have the same median. A favoured method of calculating the test-statistic U* is due to Wilcoxon. Both samples are combined and ranked together. Suppose samples 1 and 2 have n1 and n2 observations. The sum of the ranks of the observations in samples 1 and 2 are given by R1 and R2, respectively. As a check, R1 + R2 = –12 n(n + 1) where n = n1 + n2. U* is taken to be the smaller of U1 = R1 - –12 n1 (n1 + 1) and U2 = R2 - –12 n2(n2 + 1). For modest n1 and n2, statistical tables provide critical values of U*, and small values of U* count against the null hypothesis. Example 2: The raw data for this example are shown in Table 14.2, with appropriate ranks assigned to each observation. • •

U1 = R1 - –12 n1(n1 + 1) = 265 - –12 15(16) = 145 U2 = R2 - –12 n2(n2 + 1) = 141 - –12 13(14) = 50

The value of U* is therefore 50. For sample sizes 15 and 13 the critical value at 5% significance level is 61. Since 50 < 61, the hypothesis that the samples come from populations with the same median is rejected. For large samples, U1 and U2 are approximately normally distributed with mean –12 n1n2 and variance 1/12n1n2(n1 + n2 + 1), but there is little point in using non-parametric methods for large samples because the central limit theorem applies and parametric methods can be used to good effect. 14.5.2.2

Kolmogorov–Smirnov (K-S) test

This can be used for detecting differences of any kind between the populations from which two samples have been drawn. The two sample cumulative distribution functions (CDF) are compared: Table 14.2. Ranking the fibre diameter data. Sample

Observation

Rank

Sample

Observation

Rank

Sample

Observation

Rank

2 2 2 1 2 2 2 1 1

6.92 7.04 7.08 7.22 7.22 7.24 7.28 7.38 7.40

1 2 3 4.5 4.5 6 7 8 9

1 2 2 1 2 2 1 1 1

7.41 7.42 7.43 7.44 7.47 7.49 7.52 7.58 7.63

10 11 12 13 14 15 16 17 18

1 2 1 2 1 2 1 1 1 1

7.68 7.68 7.71 7.74 7.77 7.81 7.82 7.84 7.93 8.28

19.5 19.5 21 22 23 24 25 26 27 28

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Sample CDF

1.0

0.5

0.0 7.0

7.5

8.0

Fibre diameter

14.5 Cumulative frequency distributions for data of Example 1.

Sample CDF = p(x) =

number of observations £ x [14.11] number of observations in the sample

This produces a step function extending from 0 just below the smallest observation to 1 at the largest observation. The test statistic, D, is the largest vertical distance between the two functions (Fig. 14.5). Values are given in statistical tables which indicate whether D is large enough to reject the hypothesis that the samples come from the same population. For the data in Table 14.2 the value of D is 0.436 and the critical value at 5% significance is 0.492. At 10% significance the critical value is 0.446. The K-S test just fails to pick up a difference between the samples because the potential difference is specified so generally. The t-test and Mann– Whitney are better for detecting differences in average values, but K-S would be useful for detecting say, a difference in variance between nonnormal samples.

14.6

Comparing several samples simultaneously

Tests such as the t-test and Mann–Whitney can be extended to cover more than two samples. • •

Parametric: analysis of variance (ANOVA) Non-parametric: Kruskal–Wallis, Freidman

Here the discussion will be confined to parametric methods.

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Confidence intervals

An interval estimate of a parameter associated with a given level of confidence is called a confidence interval. The end-points of such intervals are confidence limits. A confidence interval for m in simple random sampling takes the form x ± (cs n ) , where the value of c is a percentage point from the appropriate sampling distribution of

(X - m) n

. S Given m samples, the usual approach is to assume that the m populations have equal variances and that these populations are normal. An estimate of the common variance may be constructed as: s2 =

(n1 - 1) s21 + (n2 - 1) s 22 + . . . (nm - 1) sm2 (n1 - 1) + (n2 - 1) + . . . + (nm - 1)

[14.12]

where ni, s 2i are the sample size and variance, respectively, for the ith sample. This is a generalisation of Equation (14.7); s2 is a weighted average of the individual sample variances and is thus a more reliable estimate of s 2. This estimate may be used to derive confidence intervals for the means of the populations, as above, and for other purposes. Example 3: The data in Table 14.3 concern the yield from a chemical reaction using three different catalysts, C1, C2, C3. It is of interest to know whether there is any difference in the performance of the catalysts. If the samples come from populations with approximately equal means, then the confidence intervals for the three population means will overlap to some degree. If some intervals do not overlap, then there is evidence, at some level of uncertainty, that the populations do not all have the same mean. Table 14.4 shows, for the data of Table 14.3, confidence intervals for each sample based on (1) the sample standard deviation and (2) the pooled standard deviation.

Table 14.3. Yield of a chemical reaction using three different catalysts. C1

C2

C3

2.5 3.6 3.2 2.7

2.6 3.1 3.0 2.5

2.4 2.9 2.8 2.3

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Table 14.4. 95% confidence intervals for the population mean of Example 3. Sample

n

Sample mean

Sample sd

C1 C2 C3

4 4 4

3.0 2.8 2.6

0.497 0.294 0.294

Sample C1 C2 C3 C1 C2 C3

Confidence interval (2.210, 3.790) (2.332, 3.268) (2.132, 3.068) (2.577, 3.423) (2.377, 3.223) (2.177, 3.023)

(1)

(2)

14.6.2

pooled sd = 0.3742

One-way analysis of variance (ANOVA)

This process combines the degree to which the confidence intervals overlap into a single measure which, under the null hypothesis of equal population means, has an F-distribution. The level of uncertainty is often expressed as a p-value, equivalent to the level of significance at which the null hypothesis would be rejected. It represents the probability that the degree of overlap, or rather lack of it, could have arisen by chance in samples from the same population. If the p-value is very small, say <0.05, then the hypothesis of equal means looks very unlikely. In this case, to discover where the differences might lie in particular, we have to go back to the confidence intervals. One-way ANOVA on just two samples is exactly equivalent to the two-sample t-test. Whichever set of confidence intervals is examined in Table 14.4, it is clear that there is insufficient evidence to suggest significant between-sample variation. The ANOVA calculation is based on taking the total variation among all observations and dividing it into within and between sample components. It is how large a proportion of the whole, taking into account the number of samples and the sample sizes, that is attributed to the betweensample variation which determines the conclusion. Table 14.5 is the ANOVA table for Example 3, and the p-value at 0.361 indicates no significant evidence that the mean yields differ amongst catalysts. This reflects the overlap of the confidence intervals. It should be noted that the same assumptions as for the t-test apply, namely normal populations and equal population variances, and whilst the sample standard deviations differ, they are not different enough for the latter assumption to be in serious doubt.

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Table 14.5. Analysis of variance (ANOVA) table. Source of variation

Degrees of freedom (DF)

Between samples Within samples Total

14.6.3

Sum of squares (SS)

Mean squares = SS/DF

F

p

2 9

0.32 1.26

0.16 0.14

1.14

0.361

11

1.58

Multiway analysis of variance

Inherent in the basic approach outlined above is the assumption that all data in any given sample have been collected under the same conditions. In practice this is not often the case. Identifying the conditions which are likely to influence results (i.e. the explanatory variables) is not easy, and unfortunately may be alighted upon after the experiment has been concluded. It may be discovered too late that potentially critical information has not been recorded. It is always better to acquire information which turns out to be redundant than to miss data which could be vital. For example, it may be thought that the measurement of a material property varies between testing laboratories, so an experiment is set up whereby several pieces from a large batch of a certain material are sent to each laboratory. Prior to the experiment it may have been assumed that all pieces of material have the same properties, but suppose this is not the case. A one-way ANOVA will not be able to separate material differences from laboratory differences. If, however, the sample material is ‘matched’ across laboratories, then the different effects may be separated, using two-way ANOVA. Example 3 continued: Suppose the experiments were in fact conducted at four different laboratories, the first measurement for each catalyst coming from laboratory 1, and so on. We will equate ‘catalyst’ here with ‘material’ and again test for differences between materials, but in the light of new knowledge about the testing environment. If there are l laboratories and m materials, and each laboratory makes a single measurement on each material, there will be n = ml measurements in total. Let yij denote the measurement made at laboratory i on material j, and ¯y the mean of all n observations. A measure of the total variation 2

among all observations is the total sum of squares, ssT = Â ( yij - y ) . ij

ANOVA divides this total variation into ‘between samples’,‘within samples’ and ‘residual’ variation. In the present context these contributions represent variation between laboratories, ssB, variation between materials, ssW, and

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Table 14.6. Two-way analysis of variance. Source of variation

Degrees of freedom (DF)

Sum of squares (SS)

Laboratories

l-1=3

ssB = mÂ (y i - y ) = 1.14

2

i

2

Materials

m-1=2

ssW = l Â (y j - y ) = 0.32

Residual

(l - 1)(m - 1) = 6

ssR = Â (y ij - y i - y j + y ) = 0.12

j

2

ij

Total

n - 1 = 11

2

ssT = Â (y ij - y ) = 1.58 ij

y = overall mean, y i = mean for laboratory i, y j = mean for material j.

‘left-over’ variation, ssR, which cannot be attributed to either of the main sources. Table 14.6 shows the breakdown for the data of Example 3. As before, if we assume that the responses have constant variance and are normally distributed, then, under the null hypothesis that there are no significant material or laboratory effects, the ratios (l - 1)ssW/ssR and (m - 1)ssB/ssR may be compared with the F-distribution and p-values calculated. For the results in Table 14.6 these F-ratios are respectively 19.0 and 8.0, indicating that there is a significant difference both between laboratories ( p-value <0.01) and between catalysts ( p-value <0.025). The earlier one-way ANOVA failed to detect these differences because laboratory differences were masking material differences. In Table 14.4 we noted that the estimate of the underlying variability was given by the pooled standard deviation, √ssR/(n - m - 1) = 0.3742. Here, the estimated variance ssR/[(l - 1)(m - 1)] = ssR/(n - m - l - 1). Taking the square root yields a standard deviation of 0.02. This much reduced value is the result of material and laboratory differences accounting for 92% of the variation in the results. The ‘left-over’ or unexplained variation, ssR, is now only 8% of the total, ssT.

14.6.4

The model

The model underlying the analysis is one where the expected response, E(yij) (e.g. material property measurement), is the sum of effects consisting of an overall mean value and departures from this average caused by the different effects: E ( yij ) = m + a i + b j

[14.13]

where ai is the effect due to the ith laboratory and bj is the effect due to the jth material. By definition, Sai = 0 and Sbj = 0.

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Table 14.7. Two-way analysis of variance with interaction. Source of variation

DF

SS

MS

Laboratories

l-1

mr Â (y i - y )

SS/(l - 1)

lr Â (y j - y )

SS/(m - 1)

r Â (y ij - y i - y j + y )

SS/[(l - 1)(m - 1)] SS/(n - lm)

F-ratio

i

Materials

m-1

j

Laboratory material Residual

(l - 1)(m - 1) n - lm

(y ijk - y ij ) Â ijk

Total

n-1

(y ij - y ) Â ijk

ij

yijk = kth observation for laboratory i and material j, y ij = mean of r replications for laboratory i and material j, n = lmr (and other terms as for Table 14.6).

The measured responses yij are assumed to vary around the expected value by some quantity eij: yij = m + ai + bj + eij

[14.14]

It is perhaps potentially misleading that eij is often referred to as the ‘error’. The term ‘random departure’ is a better description for this natural variation around the expected response. Fundamental to the model is the assumption that the {eij} are independent, with zero mean; and for the analysis using the F-distribution, a normal distribution with constant variance must also apply. Possible interaction effects between laboratories and materials may also be built into the model and assessed via replication of measurements, say each laboratory/material combination observed r times. The resulting ANOVA is given in Table 14.7, and it can be seen that for the case r = 1 it reduces to the form of Table 14.6.

14.6.5

Checking the model

Residual plots are an important complement to the calculations. Estimated responses are calculated from the fitted model. The residuals, the differences between the fitted and observed responses, may be plotted against the fitted values to provide a visual check on the model assumptions. Figure 14.6 shows the residuals for the two-way analysis of Example 3 against the fitted responses. The plot should show points scattered at random. If there is some form of pattern to the plot, then the model assumptions may be in doubt, and some rethink of the approach to the analysis is necessary.

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0.25

Residuals

0.15

0.05

–0.05

–0.15

–0.25 2.2

2.4

2.6 2.8 3.0 Fitted responses

3.2

3.4

14.6 Residual plot for analysis in Table 14.6.

14.6.6

Incomplete data

As we all know, real life does not always work out as planned. Standard multiway ANOVA assumes a perfectly balanced set of results; that is, the same number of results for each set of conditions. What if one experiment goes wrong? It may be possible to repeat it; but suppose the right kind of experimental material is not available, or the experiment is too long to repeat. One-way ANOVA is unaffected by this event, but multiway analysis of unbalanced data must be carried out by multiple regression using binary variables. This approach is not in essence different to ANOVA. Multiple regression on balanced data yields exactly the same results as ANOVA, but ANOVA is easier to use.

14.7

General linear model (GLM)

A regression model may be given by Equation [14.15]: yi = m + a1x1 + a2x2 . . . + alxl + b1z1 + b2z2 + . . . bmzm + ei

[14.15]

where yi is the ith observation, {xj} and {zk} are binary or indicator variables taking the value 0 or 1 dependent on whether or not the jth treatment (e.g. laboratory) or kth block (e.g. material) is present. The regression coefficients {aj} and {bk} are the treatment and block effects, respectively, where, as for Equation [14.14], Saj and Sbk are both zero. Differences between treatments will be determined by values of some aj which are different from zero and, similarly, differences between blocks will be

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determined by values of some bk which are different from zero. The judgement as to whether a coefficient is significantly different from zero depends on the assumptions made about the structure of the departures {ei}. We will assume that the {ei} have zero mean, constant variance and are normally distributed. Under these criteria, the estimated regression coefficients are normally distributed and p-values for testing zero effects may be assigned via an estimate of the residual variance and use of the tdistribution. Very small p-values suggest that the corresponding effects are non-zero. Wolstenholme and Crowder6 examined data from a study by Gould and Loveday7 concerning creep rate measurements made by different laboratories on samples from a number of different bars of the same batch of material. A one-way ANOVA was envisaged on the basis that differences would be related to laboratories only. However, it was apparent that there were also differences between bars. The experiment was unbalanced, so their analysis is based on Equation [14.15], with differences between laboratories and between bars indicated by the small p-values associated with some of the estimated regression coefficients. It is possible to have a combination of quantitative and binary variables. For example, Figure 14.2 shows that a model for cycles to fatigue failure might include a variable for strain as well as binary variables for laboratories. This can be represented by Equation [14.16]: y = m + q1w1 + q2w2 + . . . + a1x1 + a2x2 + . . . + ei

[14.16]

where the {xj} are binary variables associated with treatment effects, and wk are measurements of explanatory variables, such as strain, temperature, size or some function of such characteristics. Example 4: This is an interlaminar short beam shear test experiment. An experiment conducted at Imperial College8 investigated the effect of curing conditions on interlaminar shear stress. Six laminated carbon-fibre reinforced/epoxy panels were manufactured. Five were cured in a single autoclave cycle and placed at different stations on the autoclave table. Two were near the door of the autoclave, two were at the other end of the table near the internal fan and one was placed in the centre of the table. The sixth panel was cured separately using a pressclave. Ten samples, nominally of size ten, were cut from different areas of the panels. One panel had part of its surface abraded and one sample was drawn from this area. All specimens were nominally of the same dimensions but the width, w, and thickness, h, of each specimen was measured. The test was carried out in three-point flexure and the Zwick testing machine recorded the load (Pcrit) at which a delamination initiated. The apparent interlaminar shear strength (ILSS) is then calculated via the expression:

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Table 14.8. Data from interlaminar short beam shear test experiment. Sample

Number of specimens

Panel number

Position in autoclave

Surface finish

1 2 3 4 5 6 7 8 9 10

9 10 10 10 10 10 10 10 10 10

2 2 3 4 4 5 6 1 1 1

Fan end Fan end Fan end Door end Door end Centre — Door end Door end Door end

None None None None None None None None Abraded None

ILSS = 0.75

Pcrit wh

[14.17]

The ILSS values were measured according to the CRAG9 recommendation. A summary of the structure of the experiment is shown in Table 14.8. It has to be said at the outset that there are ways in which the design of the experiment could have been improved, using the same number of specimens. There is, for example, no means of assessing surface abrasion with reference to the heated press. The first step is to identify the response and explanatory variables. The obvious choice for the response variable is ILSS, but it is worth investigating whether Pcrit is more suitable. Factors to consider are whether these variables are approximately normally distributed, and the nature of the correlation with the explanatory variables. Quantitative explanatory variables might be width and thickness of specimen; qualitative explanatory variables might be type of curing process and situation within the curing process, and the existence of surface abrasion on the specimen. Another question to leave open is whether there is any benefit in keeping samples from the same panel separate. Clearly in the case of panel 1, surface abrasion is a separate factor but if, in general, there is little difference in samples from the same panel, more accurate assessment of influential factors will be achieved by an interpanel analysis, rather than an intersample analysis. Figure 14.7 shows boxplots for the sample ILSS and Pcrit values. The existence of some function of specimen size as a possible explanatory variable is responsible for the difference in these pictures. This will be explored presently. In the ILSS picture there is a clear indication that surface abrasion increases response. Further, there is some evidence that response in

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10

10

9

9

8

8

7

7 Sample

Sample

334

6 5

6 5

4

4

3

3

2

2

1

1 90 95 100 105 Interlaminar shear stress (MPa)

2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 Critical load (kN)

14.7 Boxplots for interlaminar short beam shear test data.

the autoclave is highest in the centre, where it is similar to the result for the heated press. The sample sizes are all fairly small and whilst there is some skewness in the sample distributions, there is little evidence of nonnormality in either Pcrit or ILSS. Neither do F-tests reject the hypothesis of equal variances, so for the purposes of the modelling described here, we can choose either Pcrit or ILSS as the response variable. The influence of variables other than the qualitative sample characteristics discussed so far needs to be examined. The data show considerable variation in specimen width and non-significant variation in specimen thickness, but it is thickness which is correlated with Pcrit. ILSS is not significantly related to either width or thickness. Figure 14.8 shows a series of plots investigating these potential relationships. The form of Equation [14.17] makes the cross-sectional area, wh, an obvious additional candidate for an explanatory variable. From the modelling point of view, any relationships need to be linear in nature. If ILSS is the response variable, it is clear that none of these size considerations need be included in the model, but if there were strong distributional arguments for choosing Pcrit, then either h or wh should be put into the model. Following from Equation [14.15], with ILSS as response variable, an appropriate model is one with {xj} representing curing position and z representing surface treatment. We cannot use a simple two-way ANOVA because the experiment is unbalanced, that is, there are unequal numbers of observations for each curing/surface combination. Using the sample number as curing level proves to be over-detailed for these data. There is little evidence of any real difference between samples cut from the same panel. Further, panels in similar positions in the autoclave perform in

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335

105

2.7

ILSS (MPa)

Critical load (kN)

2.8

2.6 2.5 2.4

100

95 90

2.3 2.2 9.0

9.5 10.0 Width (mm)

10.5

9.0

2.9

9.5 10.0 Width (mm)

10.5

105

2.7

ILSS (MPa)

Critical load (kN)

2.8

2.6 2.5 2.4

100

95 90

2.3 2.2 1.85

1.95 2.05 Thickness (mm)

2.15

1.85

2.9

1.95 2.05 Thickness (mm)

2.15

105

2.7

ILSS (MPa)

Critical load (kN)

2.8

2.6 2.5 2.4

100

95 90

2.3 2.2 18

19 20 21 Width ¥ thickness

22

18

19 20 21 Width ¥ thickness

22

14.8 Scatterplots for ILSS data: Pcrit and ILSS versus specimen width, thickness and width ¥ thickness.

similar fashion. Supporting statistical tests for the latter statements are not shown here. In the following model, the {xj} indicate the different positions under the column headed ‘Position in autoclave’ in Table 14.8. ILSS = m + a1x1 + a2x2 + a3x3 + a4x4 + b1z1 + b2z2 + e

[14.18]

A summary of a GLM analysis performed by Minitab is shown in Table 14.9. [Computation note: the difference between SeqSS and AdjSS is

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Table 14.9. General linear model fitted to ILSS data. Factor

Levels

Position Surface

4 2

1 (pressclave) 1 (not abraded)

Source

DF

Analysis of variance for ILSS Seq SS Adj SS Adj MS

Position Surface Error Total

3 1 94 98

193.70 292.19 776.03 1261.92

161.62 292.19 776.03

Coeff m

2 (door) 2 (abraded)

3 (fan)

P

53.87 292.19 8.26

6.53 35.39

0.000 0.000

sd

t-value

P

98.6790

0.5833

169.16

0.000

a1 a2 a3 a4

1.0838 -0.7697 -2.1858 1.8628

0.7394 0.4869 0.5256 0.7394

1.47 -1.56 -4.16 2.52

0.146 0.122 0.000 0.013

b1 b2

-3.0218 3.0218

0.5079 0.5079

-5.95 5.95

0.000 0.000

9

8 Log cycles

4 (centre)

F

Term Constant Position 1 2 3 4 Surface 1 2

Values

7

6

5 –0.5

0.0 Log strain

14.9 Interlaboratory low cycle fatigue data.

0.5

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Standardised residuals

2.5 1.5 0.5 –0.5 –1.5 –2.5 –3.5 5

6

7

8

9

20

26

Fitted responses

Standardised residuals

2.5 1.5 0.5 –0.5 –1.5 –2.5 –3.5 1

5

10

15

Laboratory

14.10 Residual plots for GLM fitted to low cycle fatigue data.

explained in the Minitab Reference Manual and is not important for the discussion here.] The very low p-values in the analysis of variance table indicate very significant effects in varying the curing condition and in the presence of surface abrasion. The p-values associated with the coefficients {aj} show that results are markedly lower for samples near the fan and highest in the centre of the autoclave. There is some evidence that response is higher than average in the heated press but not significantly so. Surface abrasion increases the response markedly and is the most significant result regardless of whether the model is based on ILSS or Pcrit. Example 5: This is a low cycle fatigue test. The data illustrated in Fig. 14.2 are part of a larger data set involving tests at 0.6%, 1.2% and 2.0% strain levels, covering 15 laboratories. The complete data set is shown in Fig. 14.9. Log of cycles to failure and log strain are shown to be linearly related and

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Table 14.10. General linear model fitted to low cycle fatigue data. Factor

Levels

Values

Lab

15

1 16

2 18

4 19

5 20

6 26

7

9

13

14

15

Analysis of variance for log cycles Source

DF

Seq SS

Adj SS

Adj MS

F

P

lg strain Lab Error Total

1 14 92 107

85.7069 12.8781 2.8214 101.4065

78.5126 12.8781 2.8214

78.5126 0.9199 0.0307

2560.14 30.00

0.00 0.00

Term

Coeff.

sd

t-value

P

Constant lg strain

7.481 -1.871

0.01992 0.03697

375.48 -50.60

0.000 0.000

Lab 1 2 4 5 6 7 9 13 14 15 16 18 19 20 26

0.371 0.379 -0.130 0.198 0.271 0.271 -1.033 -0.114 0.017 0.310 0.047 -0.469 -0.359 -0.236 0.477

0.07510 0.06460 0.06054 0.06078 0.07556 0.05741 0.08421 0.05740 0.05732 0.07533 0.06911 0.05099 0.05740 0.05740 0.09711

4.94 5.86 -2.14 3.26 3.59 4.73 -12.27 -1.99 0.29 4.12 0.68 -9.20 -6.25 -4.10 4.91

0.000 0.000 0.035 0.002 0.001 0.000 0.000 0.050 0.772 0.000 0.500 0.000 0.000 0.000 0.000

are therefore suitable choices for response and quantitative explanatory variables. Further, from Fig. 14.2, binary variables {xj} for laboratory effects should be included. So, following from Equation [14.16], the model to be fitted is: log(cycles) = m + q log(strain) + a 1 x1 + a 2 x2 . . . + a 15 x15 + e

[14.19]

Table 14.10 shows the results of fitting Equation [14.19] to the data of Fig. 14.9.The analysis of variance table shows a highly significant linear relationship between log(cycles) and log(strain) and significant differences between laboratories. The t-values for the laboratory coefficients show that laboratories 1, 2, 7, 15, 26 give markedly higher measurements than average, and laboratories 9, 18, 19, 20 give markedly lower measurements. Figure 14.10 shows residual plots for this analysis where the residuals have been standardised. This converts the distribution of the residuals to one which

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not only has zero mean, but a standard deviation, one. Under the normality assumption there should be approximately 5% of residuals outside the interval [-1.96, 1.96]. In this example, some 10% of observations have large residuals, but the plot against fitted responses does not show any particular pattern. When we plot the residuals against individual laboratories, some quite sharp differences in variability show up, for example between laboratories 19 and 20. However, although some model deficiencies may exist, the essence of the conclusion is preserved, namely that laboratories do differ quite substantially. As with multiway ANOVA, interaction terms may be built into a regression model, but in the examples considered here there are too few replications to estimate these effects. Or, to put it another way, there are too few residual degrees of freedom available to spread over the possible laboratory/material interactions. Care is needed in constructing a regression model to ensure that the model is not overburdened with variables, and to avoid the presence of correlated variables. Both features lead to poorly estimated regression coefficients. Further reading may be found in, for example, the classic reference for regression analysis by Draper and Smith.10

References 1. G B Thomas and R K Varma, in Harmonisation of Testing Practice for High Temperature Materials, eds M S Loveday and T B Gibbons, Elsevier, London, 1992. 2. H R Neave, Elementary Statistics Tables, Routledge, London, 1994. 3. Minitab Release 10 Xtra, Minitab Inc., USA, 1995. 4. C Chatfield, Statistics for Technology, 3rd edition, Chapman and Hall, London, 1983. 5. S S Shapiro and M B Wilk, ‘An analysis of variance test for normality (complete samples)’, Biometrika, 1965 52 591–611. 6. L C Wolstenholme and M J Crowder, ‘Materials metrology: statistical analysis of data’, in Materials Metrology and Standards for Structural Performance, eds B F Dyson, M S Loveday and M G Gee, Chapman and Hall, London, 1995. 7. D Gould and M S Loveday, The Certification of Nimonic 75 Alloy as a Creep Reference Material, CRM 425, Commission of the European Communities, Luxembourg, 1990. 8. J M Hodgkinson and A Talby, Influence of Autoclave and C-Scan Position on the Performance of Composites, Final year project report, Department of Aeronautics, Imperial College, London University, UK, 1992. 9. P T Curtis (ed), CRAG Test Methods for the Measurement of the Engineering Properties of Fibre-reinforced Plastics, Royal Aircraft Establishment, Farnborough, UK, Technical Report 88012, 1988. 10. N R Draper and H Smith, Applied Regression Analysis, 3rd edition, Wiley, New York, 1998.

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15 Development and use of standard test methods* G D SIMS

15.1

Introduction

This chapter reviews the development and validation of new standard test methods and documents the current initiatives related to the mechanical testing of advanced composite materials – in particular, the standards and test methods being developed for international use by the International Standards Organisation (ISO) and the provision of EN standards in support of the Single European Market (EU) by the Comité Européen de Normalisation (CEN) are covered. ISO standards are not mandatory, and alternative national standards were previously published related to national conditions. However, for CEN member countries, mainly EU and EFTA (European Free Trade Area) countries, it is mandatory to publish any approved EN standard as their national standard and withdraw any existing national or international standard of the same scope. It is agreed that where ISO has published, or has work in progress on a standard of the required scope, the ISO document will be considered for reballoting as a CEN document. In general, CEN looks towards ISO for the basic test methods, while CEN is more concerned to provide product and technical specifications (e.g. as covered by EU directives) in support of the Single European Market. The main concern in this book is the mechanical testing of composite materials (i.e. consolidated material), but it should be noted that test methods and specifications are also needed to characterise fibres, matrices and unconsolidated preimpregnates. Test methods are also required for electrical and thermal properties, for environmental, chemical and ageing resistance and for toxicity and processing properties (e.g. tack). Thermal and electrical properties can be anisotropic, in a manner similar to the mechanical properties. This chapter mainly covers composite materials containing continuous fibres in an organised or oriented layup. These materials include unidirec* Crown copyright

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tionally oriented preimpregnates, multidirectional preimpregnates and fabric reinforcement. Although balanced fabric materials (equal warp and weft fibres) can be tested using conventional methods, oriented fabrics or hybrid combinations of unidirectional fibre plus fabric materials need test methods appropriate to their higher anisotropy. Most of these materials are pressed at elevated temperatures from prepregs to achieve consolidation and cure for thermoset matrices, but similar types of properties can be found through the wet fabrication process of thermoset filament winding and pultruded rods, or from equivalent thermoformed systems with thermoplastic matrices. Other groups of composite materials may contain mat reinforcement in either a thermoset matrix (i.e. conventional hand or sprayed lay-up GRP, or glass reinforced plastic), or the normally filled resin-based sheet moulding compounds (SMC), or a thermoplastic matrix, such as the more recently introduced glass mat thermoplastics (GMT). As these materials are generally (unless they include aligned fibres) almost isotropic in-the-plane, standard ‘plastics’ type dumb-bell or wide strip specimens can be used.The main characterisation problem is the assessment of the point-to-point variations in properties that can occur in these materials.

15.2

Development of test methods

Most test methods originate in industrial companies as a means of controlling and measuring specification parameters and material performance. Academic and government research establishments also develop new test methods and are frequently involved in research to improve them. A method recommended by a trade body, a group of companies or a government body may result from these in-house developed methods. These recommended methods will be offered to national standards bodies to be considered for submission to ISO or CEN, or more rarely now for publication as a national standard. Standards published internationally by ISO or CEN require the support of the national delegates of the appropriate member countries. More details of these bodies are given later. The measured materials properties are used for several purposes, including: • • • • • •

materials specification materials development materials selection design data product development quality assurance

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non-destructive evaluation research.

Once a method has been prepared from whatever source, the normal route for a standard to be developed is that it is tabled in a national committee, which will consider whether its submission should be supported for publication as an international standard. Within the ISO system the draft will then pass through the stages outlined below (slightly different stages for CEN or parallel CEN/ISO votes).

15.2.1

New work item (NWI)

The drafted test method and the proposal justifying the ‘industrial’ need for the standardisation of the method are circulated by the relevant national standard technical committee to its members for comment. If approved for submission to ISO, the draft with the completed case for the new work item (NWI) is prepared. ISO then undertakes a ballot of all voting countries in that work area to determine, first, if there is support for the proposed topic and, second, if the attached draft is acceptable at either committee draft (CD) or draft international standard (DIS) ballot stage. A good quality draft obtaining wide support can be advanced by this latter assessment. If the new topic is approved, then it will be assigned to a working group (WG).

15.2.2

Committee draft (CD)

Normally, the draft proposed initially will form a working draft not circulated outside the committee. Either a project leader will be appointed to lead the work or a small task force will be formed that will work on the draft until it has consensus or majority support for submission to public ballot and comment at the CD level. As this is the primary vote for technical changes, it would be preferable to undertake a five or six months’ long ballot as in the CEN system rather than the current three-month ballot in ISO.

15.2.3

Draft international standard (DIS)

Providing the CD ballot receives more than 75% approval from countries with voting rights for the subject area (i.e. ‘p’ members) and not more than 25% negatives from all countries (includes also observer ‘o’ counties), the draft can be progressed to DIS status. Normally, the CD ballot comments will be discussed at the working group level and responses agreed with the project leader. The project leader then prepares ‘a disposition of comments’ showing each country’s comments, the response and any intended modifi-

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cations to the text. This information is then presented with the revised text for the DIS five-month ballot.

15.2.4

Formal draft international standard (FDIS)

The review of ballot voting and comments is repeated so that a final twomonth ballot can be undertaken. At this stage and at the DIS stage only editorial changes are expected. If technical changes are required following voting, a CD-2 or DIS-2 draft would be prepared at an earlier stage for reballot. If there are no negative votes at the DIS ballot and the ballot is not in parallel with CEN, then there is no requirement to undertake the FDIS ballot. In order to speed up the standards making process to meet industrial timescales and requirements, it is now necessary in proposing a NWI to submit a good working draft and a proposed project leader. Other countries voting in support must also nominate their technical expert to work on the standard. In addition, NWIs are only allowed to exist on the work programme for five years and an optimum development time is 44 months. This timescale does not really allow repeat ballots (e.g. CD-2 or DIS-2) and highlights the need for well developed documents at each stage. The CEN approval system is similar but uses prEN to designate a draft European standard. CEN timescales are also a little different, as are the joint parallel processing voting schedules. Progress of an NWI is accelerated if validation has been undertaken prior to submission, so that the precision clause can be completed as discussed below.

15.3 15.3.1

Validation of test methods Procedures

As noted above, standard test methods are used at several stages of the product development, certification, manufacturing and supply process, which places increased legal importance on the reliability of the test method. Typical occasions when data obtained for a material or product properties could be used in a legal manner are: • • • •

a dispute regarding material supply a dispute regarding free trade a product liability case a major failure investigation.

Consequently, standard bodies, such as ISO, require that new or revised methods are experimentally validated and their precision is determined.

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Although this requirement has been given increased prominence with the arrival of EN standards, it was previously a requirement that a ‘precision’ clause be included in standards.1,2 The validation data are normally obtained by a responsible body (e.g. a standards committee) planning a series of tests to be conducted according to a draft standard by various establishments, normally ten or more. This round, robin (RR) testing involves the supply of nominally identical material to all the participants who carry out the tests according to the laiddown procedure. The measured data and required test report are sent to the organiser of the RR, who analyses all the reported data according to the procedure set out in, for example, ISO 57251 and ASTM E691.2 ISO 57251 provides detailed guidance on the running of an interlaboratory (round-robin) trial to determine the precision statement for inclusion in the published standard. The number of participants in an experimental round-robin exercise depends on the number of ‘levels’ (e.g. materials) used. Normally, for four to six materials, eight to ten participants would be appropriate. The difficulty for composites is the wide and endless range of materials that can be, and are, produced. The need is to select ‘generic’ materials that are covered by the standard, represent different primary variations and represent the major volume, commercial or legal interests. Care should then be used when applying the precision data to materials with significant differences, and additional checks should be undertaken by the user of the standard in these cases by, for example, back-to-back comparison using one of the ‘generic’ materials. ASTM E691-792 is similar to ISO 5725 except that it requires explanations for the occurrence of outlier data prior to elimination, in addition to data being identified as outliers by statistical procedures. In ASTM standards there is reference to ‘bias’ in addition to ‘precision’. However, in most cases there is no reference value for comparison in order to determine bias. The precision of a test method is determined from an assessment of both the repeatability (r) and reproducibility (R) of the method. Repeatability is defined in the standard as ‘the value below which the absolute difference between two single test results obtained under repeatability conditions may be expected to lie within a probability of 95%’. •

•

Repeatability conditions refer to measurements made by the same method, by the same laboratory, by the same operator, on the same equipment, within a short period using identical test material. The reproducibility is similarly defined using the same methods but different laboratories, different operators, different equipment and identical test material.

For a destructive test the requirement for identical material to be used in the evaluation cannot be met; consequently the repeatability and repro-

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Table 15.1. Reasonably understandable definition of repeatability and reproducibility. Repeatability

Reproducibility

The difference between two single test results found on identical test material by one operator using the same apparatus within a short time interval will exceed the repeatability on average not more than on in twenty instances of the norma and correct operation of the method.

The difference between two single and independent results found by two operators in different laboratories on identical test material will exceed the repeatability on average not more than one in twenty instances of the normal and correct operation of the method.

ducibility values determined also include the material variability, which reinforces the need to use representative materials with low intrinsic variability. The repeatability and reproducibility standard deviations are the standard deviations giving the dispersion of test results obtained under the respective conditions. Although these standards define the procedure to be used to measure the precision, the actual values that are acceptable are decided by the expert committee responsible for drafting the standard in question. Essentially, the precision of the test method should be commensurate with its intended purpose (i.e. it should meet a fitness for purpose criterion). Some standards already include such data (e.g. ASTM D790).3 However, standards normally indicate that data are not available through the wording: Clause 11 Precision The precision of this test method is not known because inter-laboratory data are not available. When inter-laboratory data are obtained, a precision statement will be added with the next revision. Clauses indicating the existence of data are less common. An unusual example is given above in Table 15.1.4 The expression that data from one test in 20 tests will lie outside the precision range is a more easily understood and practical interpretation of the 95% confidence limits.

15.3.2

Validation data

Some examples of recent round-robin validations are available.5 The data provided in Table 15.2 are from a round-robin on the manufacture of a test panel for specimen preparation. The procedure used now forms an input into the revision of ISO 1268, a multipart standard at CD ballot in 1998

122 GPa 7.96 GPa 1780 MPa 151 MPa

6.81 GPa 0.58 GPa 246 MPa 39.9 MPa

2.44% 5.43% 3.41% 10.0 MPa

Repeatability r

(NB E = flexuredmodular in 11 or 22 direction, S = flexural strength similarly).

2 mm

69.3% 67.1% 69.2% 104 MPa

Fibre Weight Fraction Inter-laminar shear strength Flexure properties E11 E22 S11 S22

1 mm 2 mm 5 mm 2 mm

Mean

Property and panel thickness

2.0 2.6 4.9 9.4

1.4 2.5 1.5 3.4

sd of r /Mean (%)

31.3 GPa 1.89 GPa 321 MPa 56.0 MPa

8.44% 6.54% 4.35% 22.4 MPa

Reproducibility R

Table 15.2. Precision data for specimens taken from plates manufactured using autoclaves at eight sites.5

9.1 8.5 6.4 13.2

4.4 3.5 2.2 7.6

sd of R /Mean (%)

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covering all composites process routes. Part 4 deals with the aerospace preimpregnates materials most relevant to this text. The validation data are for a single batch of low-bleed carbon-fibre/epoxy preimpregnate, delivered directly to eight sites, manufactured at three thicknesses using autoclaves under the time/pressure conditions specified by the manufacturer and then tested using a range of mainly quality assurance (QA) test methods at a single site. The results of this validation exercise are given in Table 15.2. As expected, the R values are greater than the r values.

15.4

Sources of standards and test methods

The principal sources of standards and recommended methods are briefly reviewed below, together with their main characteristics and output.

15.4.1 • •

• • • • •

International Standards Organisation (ISO)

There are 167 member countries worldwide. Composites are principally covered by the Technical Committee (TC) 61(Plastics)/ Sub-Committee (SC) 13(Composites) within six working groups (WG) (TC61/SC13/WG 14, 16, 20). Some tests for all plastics that are prepared in other SCs within TC61 apply to composites. A comprehensive series is available for glass fibres and their secondary products (mats, fabrics, woven roving and yarns). Set of standards for carbon fibres has been published. Test panel manufacture is being prepared in ten parts to cover all current process routes (new methods can be added). Laminate test methods were published in 1997–2000 to cover all present and future fibres and matrices that meet the requirements of the standard.

15.4.2

Comité Européen de Normalisation (CEN)

It is mandatory to publish in all European countries, including Iceland. 15.4.2.1 • •

General series

The plastics work area CEN TC249 with composites sub-committee (SC2) was established in 1990. The same convenor and secretariat (AFNOR) as ISO TC61/SC13 committee provide excellent liaison and cooperative working as envisaged under the Vienna agreement.

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•

•

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A similar structure to ISO has been established to aid joint drafting/ validation exercises for composites. There are working groups on all fibres (specification and test), two active on composites materials, one each at the sub-component product level (pultrusions) and composite material test methods. The main interest is the development of specification standards, which is complemented by the support and adoption by CEN of ISO test methods. 150 plus ISO test methods for plastics being balloted as CEN standards on a straight yes/no acceptance require German language versions to add to existing English and French versions.

15.4.2.2 Aerospace •

•

• • • • •

European aerospace series is prepared by the trade federation Association Européen des Constructeurs de Material Aerospatiale (AECMA). Initially, there were fibre specific mechanical and physical test methods leading to duplicate methods with unwarranted differences in the same method for similar fibres (e.g. carbon, glass and aramid). Scope is limited to aerospace. Test methods are normally not experimentally validated but accepted on a consensus basis. Some standards are not in agreement with current practice owing to a long gestation period. Modulus is measured at set load levels (cf. strain levels in all other series of standards). The Airbus Industries Test Methods (AITM) proposed 6000 series has special drafting and voting arrangements.

15.4.3

EN-ISO Vienna agreement

The Vienna Agreement on sharing of the work load between ISO and CEN allows either organisation to lead work items, with agreed responsibilities for consultation and timescales. A parallel voting procedure is used, so that the approved document becomes both a CEN and an ISO standard, or one or other if not agreed by both ISO and CEN. Depending on the lead organisation, different responsibilities apply. For CEN led work, the project leader must take care to consult fully with non-CEN countries. For ISO led items, ISO must work quickly to match the fast development of standards required in Europe. However, faster development of standards is also an increasing requirement in ISO. For composites, liaison is easily accomplished in the field of composite materials, as

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the ISO and CEN Sub-Committee Chairman and Secretariat (AFNOR) are the same and many of the leading ISO WG members and convenors are also CEN convenors.

15.4.4

International prestandardisation research – VAMAS

One aim of the VAMAS (Versailles Project on Advanced Materials and Standards) is to avoid the need for protracted harmonisation on existing standards, through collaborative international prenormalisation research. The programme is chaired alternately by the UK (NPL) and the USA (NIST). The overall objective is to promote trade in high technology products through international collaboration in prestandards research. This generates the technical basis from which common accepted standards and specifications for advanced materials can be developed.The initiative is supported by the G7 countries (i.e. Canada, France, Germany, Italy, Japan, UK, USA and the EU, with Russia becoming the eighth member). Other countries can apply to participate in individual projects. It is the intention of this initiative that the technical work conducted should result in a recommended procedure that would be supported by all the VAMAS member countries to produce an agreed international standard test method and that the VAMAS work should provide the necessary validation evidence. Examples of current activities in 2000 included: •

•

•

•

Fatigue (ISO 13,003) – data obtained in a VAMAS fatigue round-robin5 have been used to support a French proposal dealing with tensile and flexural fatigue testing. Fracture toughness – VAMAS has run an intercomparison of four competing Mode II methods from Japan, USA and Europe in order to recommend to ISO the preferred method(s) to be standardised. Compression-after-impact (CAI) – It was agreed that the programme would look fundamentally at the general design requirements for measuring material impact resistance related to damage tolerance in structures before, if appropriate, working on standardisation of the currently developed CAI test. Interfaces – A round-robin on measurement of ‘interface’ mechanical strength is being run by NIST. This work area anticipates future needs, since interfaces are particularly important to the behaviour and performance of composite materials, but there are no established test methods or standards.

15.4.5

National standards

The principal national committees contributing to composite test methods standardisation are given below. Increasingly national standards in Euro-

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pean countries will be replaced as a consequence of the mandatory publication of EN standards. (a)

(b)

(c)

(d)

(e)

(f)

UK – British Standards Institution (BSI) • PRM/42 committee provides UK vote on the general engineering series for fibres and composites at CEN and ISO and produces BSI standards in this area. • ACE/64 committee provides UK vote on AECMA/CEN aerospace series. • PRM/21 provides UK vote on general plastics test methods including ISO revisions • A comprehensive series of plastics test methods are available (BS 2782), which are being replaced dual numbered by ISO or CEN standards. Japan – Japanese Industrial Standards (JIS) • An early series of glass-fibre/resin standards was provided, with a later series of carbon-fibre test methods. • Initially related to ASTM methods, followed by Japanese developments but now implementing ISO standards. • English translations are available for at least four standards for carbon-fibre reinforced plastics. USA – American National Standards Institute/American Society for Testing and Materials (ANSI/ASTM ) • ANSI provides the secreteriat for TC61 and provides the official USA vote, while ASTM provides the specialist composites input based on the D30 committee activities. • ASTM has published many fibre and laminate test methods; they are not fibre-type specific, but a fibre modulus greater than 20 GPa is required. • Some carbon-fibre specific standards are provided for tensile properties, resin flow, gel time and for basic fibre and yarns. • Use of standards is not limited to the aerospace industry. Germany – Deutsches Instut for Normung (DIN) • Laminate tests are available in the aerospace series, with some fibre specific methods. • Fibre property methods are available, especially for textiles and glass fibres. • There is a full range of general plastics test methods. France – Association Français de Normalisation (AFNOR) • There are comprehensive series of methods and specifications for glass fibres and glass-fibre based systems. • Drafting has concentrated on glass-fibre resin prepreg properties. Italy – Ente Nazionale Italiano di Unificazione (UNI)

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15.4.6

351

Glass-fibre standards are available; carbon-fibre versions are being drafted. There is an extensive series of methods for glass-fibre reinforced thermoplastics pipes. No laminate test methods are available.

Trade and other groupings

(a)

Suppliers of Advanced Composite Materials Association (SACMA) recommended methods (USA)6 • Well prepared, fibre non-specific set of laminate test methods is available. • Methods are based on ASTM standards where possible but some revisions (e.g. reduced range of specimen sizes) undertaken. • New methods have been proposed for preparation as ASTM standards. (b) Composites Research Advisory Group (CRAG) recommended methods (UK)7 • Methods are recommended by UK grouping of defence establishments and aerospace industry companies. • There are three reports following work started in 1982 and completed in 1988. • A coherent and consistent set of test methods for all fibre (textile fibre diameter) types and continuous formats (unidirectional, multidirectional and fabric) is recommended. • There are individual test requirements sensitive to fibre type, orientation and so on, where technically required. • These methods were adopted by the Advanced Composites Group of the British Plastics Federation (now the Composites Group) and proposed to BSI as the basis for national and international standards, but delayed by lack of experimental evidence for validation. (c) European Structural Integrity Society (ESIS) ESIS has been active in many areas and in particular on fracture toughness studies for polymers and composites, with several round robins aimed at validation of the draft test methods produced. It submitted the drafts for both Mode I fracture toughness tests for polymers and for delamination in composites and provided one of the Mode II methods currently being compared in the VAMAS project on behalf of ISO. In addition, many other groups and bodies exist, such as the European Space Agency (ESA), USA National Aeronauticals and Space Administration (NASA), USA Department of Defense (DoD) and the Military

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Engineering Society for Advancing Mobility, Land, Sea, Air and Space Handbooks, and so on, that publish or have interests in test methods for composites.

15.5

Harmonisation of composite test methods

Several factors have prompted the drive for international harmonisation of composite test methods over the last few years. Principally, these are: • • • •

The internationalisation or globalisation of supply, manufacturing and user industries The need to reduce the cost of all testing, particularly when expensive jigs are required earlier availability of a comprehensive and validated database The need for increased traceability of test methods and data.

As noted in the previous section, a large number of initiatives on composite materials test methods were being pursued worldwide, in response to the strong demand for test methods for advanced composites. The test methods have been found through experience to be generally reliable and repeatable, but a detailed review showed that there was an absence of full validation to show the site-to-site reproducibility.8 A detailed assessment of the test method specifications9 in these initiatives showed that most had similar philosophies and a large degree of technical similarity. This similarity, together with the increasing international aspect of the advanced composites industry, highlighted below, supported the harmonisation of these test methods. Several of the initiating bodies were cooperating informally in the harmonisation of test methods, so that it was likely that their validation exercises could be used to support the new or revised international (ISO) standards. ASTM had an international task force, with overseas members, working on the comparison of test specifications following the lead taken on behalf of the Advanced Composites Group of the British Plastics Federation.10 The international aspects are illustrated by the following factors: •

• •

Many of the major supply companies are international, with plants and associated companies in Europe, Japan and the USA, a trend aided by recent mergers and acquisitions. Subcontracted work crosses most boundaries, including the Atlantic and Pacific Oceans, in both directions. Major products such as aeroplanes are sold and operated worldwide, with a specialist task force entitled the Commercial Aircraft Composite Repair Committee (CACRC) involving worldwide representa-

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Table 15.3. Recommended international test methods equivalent to CRAG methods. Property and method Tensile properties – unidirectional – fabric/multidirectional Compression properties Flexural properties Interlaminar shear strength In-plane shear properties Notched (hole) tensile strength Notched (hole) compressive strength Bearing properties – pin – bolt Fracture toughness – Mode I – Mode II Fatigue properties Fibre, resin and void fractions – glass fibre – carbon fibre Density of plastics Hot/wet conditioning Out-gassing Coefficient of linear expansion

•

Recommended method

CRAG number

BS EN ISO 527-5 and -1 BS EN ISO 527-4 and -1 BS EN ISO 14126 BS EN ISO 14125 BS EN ISO 14130 BS EN ISO 14129 ISO NWI (UK draft)/ASTM D 5766 ISO NWI (UK draft)/ASTM D 6484 ISO NWI (UK draft) prEN 6037 ASTM D 5961 ISO 15024 ISO NWI proposal from VAMAS (see text) ISO/CD 13003

300, 301

ISO 1172/ISO 7822 ISO 14127 ISO 1183 prEN 2823 ESA-PSS-01-722 ISO 11359-3

400, 401 200 100 101 303 403 700

600

500 1000

800 902 802 801

tion from all sectors of the supply, aircraft manufacture and user interests. Other products, such as automobiles, process plant, access engineering (ladders, walkways, handrails), are also produced and sold on a worldwide basis.

The aerospace industry dominates the advanced composite market and thus the material specifications and test methods. However, it is agreed in general that the material properties themselves define the data and test method requirements for critical applications and that these will be similar for both aerospace and non-aerospace use. Hence, it is likely that a common series of test methods can be developed (cf. BS 18 Method for tensile testing of metals, which includes aerospace materials11) acceptable to both groups of users. A further coincident incentive to harmonisation of standards was the increasing demand from users and designers for extensive data for design

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Table 15.4. Standards organisations and other bodies. Acronym

Title

ACE/64 ACG AECMA AFNOR ASTM BPF BSI CEN CEC CFMA CRAG DIN DoD ESA ESIS ETAC

Aerospace series – Reinforced Plastics Committee at BSI (UK) Advanced Composites Group of BPF (UK) Association Européen des Constructeurs de Material Aerospatiale Association Français de Normalisation (France) American Society for Testing and Materials (USA) British Plastics Federation (UK) British Standards Institution (UK) Comité Européen de Normalisation Commission of the European Communities Carbon Fibres Manufacturers Association (Japan) Composites Research Advisory Group (UK – Ministry of Defence) Deutsches Instut fur Normung (Germany) Department of Defense (USA) European Space Agency European Structural Integrity Society (was EGF) European Trade Association of Advanced Composite Materials Suppliers European Free Trade Association International Standards Organisation Japanese Industrial Standards (Japan) Ministry of Defence (UK) Fibres for reinforcements and test methods for composites, BSI Committee Plastics – mechanical properties, BSI Committee Suppliers of Advanced Composite Materials Association (USA) Versailles Project on Advanced Materials and Standards

EFTA ISO JIS MoD PRM/42 PRM/21/-/3 SACMA VAMAS

calculations (e.g. in finite element analysis packages), together with an increasing concern over the cost of testing and qualifying materials. Although there is a great similarity between different versions of the same test, there are detailed differences which have poorly, if at all, understood influences on the data recorded. For example, while most compression test methods for unidirectionally reinforced material use a plain strip specimen (normally tabbed), there are a multitude of loading/support jigs and associated specimen aspect ratios which yield different results.12 At the same time basic questions remain about the compression failure mode, how it should be measured, the influence of macro- and microbuckling, and so on, so that it still needs to be established if any individual method is appropriate to the prediction of service performance under compression loads. The new BS EN ISO 14,126 standard, and its equivalent ASTM method D3410, concentrate on the quality of the test by limiting the specimen bending regardless of the test jig.

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Development and use of standard test methods

15.6

355

Recommended mechanical test methods

As noted previously, the specifications for the most commonly used test methods for advanced composites have been found to be similar and harmonised standards have been published. It is informative to consider the original list of CRAG recommendations, as being the most complete and integrated series to assess the progress over the last few years. Table 15.3 shows the test methods from CRAG7 with the current equivalent recommendation from the ISO, CEN or ASTM series. Some methods do not have equivalents in the official standards system. For example, there is no official standard for the measurement of porosity using ultrasonics (CRAG number 1001), although work at NPL (National Physical Laboratory) supported by DERA (Defence Evaluation and Research Agency) has led to procedures aimed at establishing the technique itself on a firmer and traceable basis.13 The data requirement supporting ‘background information on environmental effects’ (CRAG number 900) is covered by several ISO and EN test methods. It is clear from the information presented in this chapter that the requirements for a comprehensive and consistent series of standard test methods for advanced composites are being developed from the available recommended methods by cooperative action within the international bodies such as ISO, CEN and, for supporting research, VAMAS and ESIS. This approach is drastically reducing (1) the number of standards to be produced, (2) the chances of confusion and (3) the costs of qualification testing and the cost of introducing new materials. A coherent set of test methods will also increase the designer’s confidence in these materials by providing a larger and more reliable source of property data. Table 15.4 identifies standards organisations and other bodies interested in test methods, and Appendix A gives their contact points.

References 1. ISO 5725, 1986; BS 5497: Precision of Test Methods, BSI (London), 1987. 2. ASTM E 691-92: ‘Standard practice for conducting an interlaboratory study to determine the precision of a test method’, Annual Book of ASTM Standards, Section 14, General Methods and Instrumentation, Vol 14.02, 1992. 3. ASTM D 790M-93: ‘Standard test methods for flexural properties of unreinforced and reinforced plastics and electrical insulating materials’, Annual Book of ASTM Standards, Section 8, Plastics, Vol 8.01, 1994. 4. ISO 1924-2: ‘Paper and board – Determination of tensile properties – Part 2: Constant rate of elongation method’, 1995. 5. G D Sims, ‘Validation results from VAMAS and ISO round robin exercises’, Tenth International Conference on Composite Materials, Whistler, Vancouver, BC, Canada, eds A Poursartip and K Street, Woodhead, Cambridge, UK, Vol 4, 1995, 195–202.

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356

Mechanical testing of advanced fibre composites

6. SACMA Recommended Methods, SACMA, 1600 Wilson Boulevard, Suite 1008, Arlington, VA 22209, USA. 7. P T Curtis, CRAG Test Methods for the Measurement of the Engineering Properties of Fibre Reinforced Plastics, Royal Aircraft Establishment, Farnborough UK, Technical Report Technical Report 88012, 1988. 8. G D Sims, Standards for Polymer Matrix Composites. Part I – Assessment of CRAG Test Data, NPL Report DMM(A)6, 1990. 9. G D Sims, Standards for Polymer Matrix Composites, Part II – Assessment and Comparison of CRAG Test Methods, NPL Report DMM(A)7, 1990. 10. G D Sims, Development of Standards for Advanced Polymer Matrix Composites – a BPF/ACG Overview, NPL Report DMM(A)8, 1990. 11. BS 18: Method for Tensile Testing of Metals (Including Aerospace Materials), 1987. 12. F L Matthews, E W Godwin and G Rueda, ‘Mechanical testing and relevance of standards’, Institute of Mechanical E Conference on Designing with Composites, London, 1989. 13. W R Broughton, M J Lodeiro and G D Sims, Validation of Procedures for Ultrasonic Inspection of PMCs: UK Round Robin, NPL Report CMMT(A)179.

Bibliography – selected ISO standards BS EN ISO 527 – Part 1 BS EN ISO 527 – Part 4

BS EN ISO 527 – Part 5

BS EN ISO 14125 BS EN ISO 14126 BS EN ISO 14129

BS EN ISO 14130

ISO 13003 ISO 15024

ISO 15310 ISO 1268

Plastics – Determination of tensile properties – General principles. Determination of tensile properties – Test conditions for isotropic and orthotropic fibre-reinforced plastic composites. Plastics – Determination of tensile properties – Test conditions for unidirectional fibre-reinforced plastic composites. Fibre-reinforced plastic composites – Determination of flexural properties. Fibre-reinforced plastic composites – Determination of the in-plane compression strength. Fibre-reinforced plastic composites – Determination of the in-plane shear stress/shear strain, including the inplane shear modulus and strength, by the ±45° tension test method. Fibre-reinforced plastic composites – Determination of the apparent interlaminar shear strength by the shortbeam method. Fibre-reinforced plastics – Determination of fatigue properties under cyclic conditions. Standard test method for mode I interlaminar fracture toughness Gic of unidirectional fibre-reinforced polymer matrix composites. Fibre-reinforced plastic composites – Determination of in-plane shear modulus by the plate twist method. Fibre-reinforced plastics – Test plates manufacturing methods. Part 1: General conditions.

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Development and use of standard test methods ISO 1172 ISO 10352 ISO 7822 ISO 14127 ISO 10350-2 ISO 11359-2

357

Textile glass-reinforced plastics – Determination of loss on ignition. Fibre-reinforced plastics – Moulding compounds and prepregs. Determination of mass per unit area. Textile glass-reinforced plastics – Determination of void content. Determination of the resin, fibre and void content for composites reinforced with carbon fibres. Plastics – Acquisition and presentation of comparable single point data. Part 2: Long fibre-reinforced plastics. Plastics – Thermomechanical analysis (TMA). Part 2: Determination of coefficient of linear thermal expansion and glass transistion temperature.

Appendix A – Contact details for standards organisations 1. International Standards Organisation (ISO) – standards available from national bodies. 2. Comité Européen de Normalisation (EN) – standards available from European national bodies. 3. British Standards Organisation (BSI), 2 Park Street, London WIA 2BS, UK. 4. Association Français de Normalisation (AFNOR), Tour Europe, La Défense, Cedex 7, 92080-Paris, France. 5. Deutsches Institut fur Normung e.V (DIN), Postfact 1107 D-1000, Berlin 30, Germany. 6. American Society for Testing and Materials (ASTM), 100 Barr Harbor Drive, West Conshohocken, PA 19428, USA; [Plastics (Vol. 8.01, 8.02, 8.03) Composites (Vol. 15.3)]. 7. Japanese Industrial Standards (JIS), Standards Department, Agency of Industrial Science and Technology, Ministry of International Trade and Industry, 1-3-1 Kasumigaseki, Chiyoda-ku, Tokyo, Japan. 8. Ente Nazionale Italiano di Unificazione (UNI), Piazza Armando Diaz 2, 1 20123, Milano, Italy. Latest information and hot-links on standards available from Composite Group Web Pages at NP (www.npl.co.uk/cog/index.html)

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Index

analysis of variance, 22 anti-buckling guide, 87, 229, 231–2, 250, 252 Arrhenius, 286, 288 autoclave, 37–9, 41, 90, 332– 4, 337, 347 Barcol hardness, 274 barely visible damage, 32 beam, 17, 26–7, 29, 31, 116, 124, 127–8, 130 short, 17, 27, 29, 161–3, 166–7 v-notched, 101, 110–11, 113, 118, 120–1, 161, 164–7 Bending moment diagram, 125–6 bias, 344 buckling, 157, 159–60, 163, 250, 304, 306–12 macro-, 85, 96, 354 micro-, 76, 156, 354 ply, 228 sublaminate, 228 Celanese (fixture) jig, 77, 79–83, 85–6, 93 central limit theorem, 317–18, 324 tendency, 316, 322 chain scission, 269 charge coupled devices, 182, 196 committee draft, 342–5 compliance calibration, 187, 189–90, 193, 198–9 compression, 8, 16–17, 21, 24–5, 29, 33, 40, 51, 75, 78, 87–92, 94–6, 109, 116, 124 after impact, 228, 230, 349 post-impact, 225 confidence, 319, 320–1, 326–7 limits, 21, 23, 326 control load, 255–6 position, 255 strain, 255–6 creep, 7, 13, 33, 63, 283, 332 rupture, 7, 22, 30, 33, 284 critical energy release rate, 170, 173, 178, 188, 193–4, 201–2

stress intensity factor, 171, 173, 303 cyclic, 2, 119–20, 150, 248–9, 255 damage accumulation, 265 mechanics, 244 parameter, 219, 237, 239 subcritical, 218 tolerance, 32–3, 212, 225, 228, 233, 241, 243–4, 349 data acquisition, 50, 62, 152, 225 analysis, 196, 212, 225 interpretation, 235 reduction, 64, 101, 117, 119–21, 144, 148, 150, 152, 156, 162, 176, 178, 180, 187, 190, 192–3, 197, 200, 206 delamination, 15, 59, 104, 109, 144, 154, 170–207, 219, 228, 237–8, 241, 250–1, 258–9, 282, 332, 351 deply, 258 design allowables, 145, 235 diffusion, 276, 284–9 coefficient, 285–91 equations, 285 direct loading, 76, 78 dispersion, 316 draft international standard, 342–3 drilling, 39 dry cutting, 39, 69 ductility, 6, 7, 24 edge delamination, 205–6 end block, 174, 180, 183, 187, 191–2, 197–8, 201–2 end-tab, 27, 40–1, 44, 51, 57–60, 62, 65–6, 71–3, 76, 84–6, 89, 91–2, 94, 102, 107, 261 environment(al), 2, 30, 34, 62, 106, 119–20, 151–2, 155, 263– 4, 269–72, 276–9, 282, 284, 340, 355 conditioning, 181–2 hot/wet, 29, 276, 353 stress cracking, 270, 282

359

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360

Index

testing, 269, 274–5 threats, 270 explanatory variable, 314, 316, 333–4, 338 extensometer, 53–5, 63, 71, 103, 119, 148, 158, 160, 255 failure mode, 67, 71, 89–90, 112–14, 121, 133–4, 217, 354 fatigue, 7, 22, 30, 152, 184, 228, 248, 315, 336–8, 349, 353 biaxial, 254 compression-compression, 250, 252 damage development, 249, 256 flexure, 250, 252, 349 limit, 256 resistance, 248 shear, 253 tension-compression, 250, 252, 266 tension-tension, 250 test coupon, 249 fibre bridging, 184, 188, 204–5 buckling, 76, 96, 144 Fick(ian), 285–90 finite element analysis, 106, 111, 143, 160, 162, 173, 203, 244, 353 flexure, 8, 24, 26–7, 124 four point, 87, 125, 127, 130, 133, 163, 199 three point, 17, 26, 125–6, 130, 132, 136, 161–2, 198, 300–1 fracture mechanics, 302–3, 312 fracture toughness, 6, 18, 25, 29, 33, 124, 188, 204, 216, 349, 351, 353 gauge length (section), 25, 56–7, 63, 67, 71–2, 85, 87, 89, 91–2, 102, 107, 111, 113, 116–17, 145, 147, 150–1, 153, 158–9, 250 glass transition temperature, 279–80 Goodman diagram, 256–7 honeycomb, 87, 124, 214 Hopkinson bar, 214 ICSTM jig, 79, 82, 85, 93– 4, 96, 97 impact, 7, 31, 32, 273 ballistic, 212, 214 boeing, 229–36, 241–3 charpy, 215–18 compression after, 228, 230, 233–5, 241, 243 damage, 211, 228–9, 233, 237, 243 dynatup, 226, 231 energy, 212, 223–4, 229–40 flexed beam, 215–17 flexed plate, 218 gardner, 231 hypervelocity, 212 in-plane, 214 instrumented, 212

izod, 215–18 out-of-plane, 212, 214–15 post-, 211, 213, 219, 225–6, 243 resistance, 7, 33, 211, 237, 243, 349 strength, 212 test(ing), 211–18, 227–31 test methods, 225 through penetration, 222–3, 225 velocity, 212, 217 interface, 8–9, 15, 17, 204–5, 262, 276, 281, 293, 349 interlaminar failure, 156, 162 fatigue, 250 fracture toughness, 170–81, 258 stresses, 143, 145, 155, 162 tensile strength, 146, 150, 155 interquartile range, 316 ITRII jig, 79–81, 85–7, 94 laminate production, 36, 84, 90 mean, 314, 316–19, 322, 324, 326–7, 329, 346 stress, 249, 256 value, 20–2 median, 20, 316, 322, 324 microcrack(ing), 176, 269, 275–6, 282 mixed mode, 29, 104, 112, 118–19, 156, 164, 176, 178, 200–1, 206 mode i, 170–85, 188–9, 194, 196–8, 200–6, 228, 351, 353 mode ii, 170–8, 194–203, 206, 351, 353 mode iii, 171, 176, 200, 206 mode separation, 202 modified beam theory, 187–90, 193, 197 modulus, 7–8, 16–17, 47, 49, 53, 67, 75, 90, 92, 95–7, 102, 112, 116, 269, 305, 310, 348, 350 compression, 25, 92–3, 124 elastic, 6–7, 24, 51, 64–5, 71, 167, 196–7, 203 flexural, 25–6, 131, 134–5, 138, 178, 188, 203, 274 secant, 64–5 shear, 13–16, 25–6, 100–24, 166–7 tangent, 65 tensile, 15–16, 25–8, 33, 43, 47, 124, 277 multi-directional, 58–9, 73, 87–8, 91–2, 114, 145, 204–6, 341, 351, 353 new work item, 342–3 non-crimp fabrics, 241–2 non-destructive, 116, 118, 214, 219, 265, 342 normal distribution, 317, 319–20, 322, 330 open hole, 29 out-of-plane, 100, 111–12, 114, 141, 143, 164, 166, 233

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Index parallel-sided, 44, 72, 250–3 parametric, 317, 322, 324–5 pattern, 41 permeability index, 288 plane strain, 173 Poisson’s ratio, 13, 25, 47, 54–5, 65, 110, 115, 146, 148, 172, 309 pooled distribution, 320 population, 20, 314, 316–21, 324–7 precision, 343–6 precrack(ing), 176, 184, 194, 198 press-clave, 37–8, 90, 332, 336 probability, 21, 298, 300, 314, 322–3, 327 quality assurance, 4, 225, 341, 347 control, 4, 30, 39, 125, 161 quasi-isotropic, 67, 93, 170, 220–8, 237– 41, 298, 301– 4, 311 radiation, 270–1 repeatability, 88, 121, 344–6 reproducibility, 88, 101, 344–6, 352 residual strength, 219, 228, 232–7, 240–1, 255, 264–6 stresses, 58, 106, 144, 148, 205 resistance curve, 184–5, 200 response variable, 314, 333– 4, 338 round robin, 76–7, 110, 116, 175, 187, 232, 235, 344–5, 349, 351 Saint Venant’s Principle, 13, 25, 57, 145 sandwich, 85, 87, 124, 157–8 scale effect(s), 294–7, 301– 4, 311–12 model, 293–5, 302, 308–10 scaling, 293–4, 305 scrim cloth, 41 shear, 2, 13, 15, 17, 24, 26–7, 33, 76–8, 81, 87, 90, 93, 100–1, 108, 110–13, 116–18, 121, 159 buckling, 116 coupling, 103 failure, 160–1 force diagram, 125–6 interlaminar, 6, 9, 16–17, 25, 29, 33, 87, 124, 128, 133– 4, 145, 161, 163, 353 pure, 100–1, 103, 109, 111, 114, 116, 160 rail test, 101, 107–10, 118, 121, 253– 4 wyoming fixture, 110 significance, 319–21 span/thickness (depth) ratio, 17, 27, 128–30, 133, 136, 141, 162 specimen (sample) bow-tie, 44–5 configuration, 206 c-section, 146, 153, 167 design, 2, 46, 73, 107

361

dog-bone, 44–5 double cantilever beam, 174, 178–81, 186, 188, 194, 195, 197–9, 202, 204, 205 double-notch, 161, 166 dumbbell, 116, 341 edge cracked torsion, 176–7 edge delaminated, 204–6 end-loaded split, 172, 175 194–5, 198–9, 201–2, 206 end-notched flexure, 172, 174–5, 194, 198–9, 253– 4, 258 fabrication, 101, 117, 120, 144, 148, 160, 161 fixed ratio mixed mode, 176–7, 201, 206 geometry, 15, 164, 272 i-section, 146, 152, 167 manufacture, 39, 178 mixed mode bend, 176–7, 201–2, 206 ±45° tensile, 101–6, 118–19, 253 plate-twist, 114–16, 118, 120, 121 preparation, 36, 67, 76, 83, 109, 119, 161, 164, 178, 345 production, 89–90 10° off-axis, 101, 104–7, 119 stacking sequence, 15–16, 19, 26, 62, 100, 263, 304–8, 310, 312 standard deviation, 20–1, 71, 316–17, 326, 329, 339, 345 statistical analysis, 271, 298 approach, 295 strain-gauge, 25, 36, 41, 52–3, 55–6, 62, 84–5, 90, 95, 97, 103, 105–9, 111, 117, 119–20, 126, 148, 151–2, 158–60, 233– 4, 255 strain measurement, 53, 62 strength, 6–7, 21, 24, 28, 33, 45, 68–9, 73, 75–6, 92–3, 95, 97, 102, 110, 119–20, 269 compression(ive), 25, 75–6, 78, 87, 90, 93, 97, 159, 211, 300 flexural, 25, 128, 135, 138, 273– 4, 276, 301 shear, 15, 44, 59, 95, 100–1, 103– 4, 107–8, 112–14, 118–21, 124, 164, 166–7, 273, 276 tensile, 15, 25, 27, 29, 43– 4, 47, 59, 69–70, 75, 145, 273, 276–7, 353 through-thickness, 147, 153, 158, 161 stress amplitude, 249, 256 relaxation, 7, 283 stress-life diagram, 250–1 stress-strain curve, 64, 89, 91, 103–4, 106, 108, 112 stress-strain-time, 249 Student’s t, 21–2, 319–21 tension, 8, 13, 15, 17, 26–7, 40, 43 test(ing) apparatus, 144 equipment, 50, 101, 117, 119, 161 jig, 2

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362

Index

machine, 2, 25, 32, 50– 4, 59, 62–3, 68, 90–1, 117, 182, 194–5, 199, 212–13, 248, 254, 332 thermal shock, 270 thermography, 257, 260, 262 through-thickness, 7, 52, 57–9, 62, 72, 81, 100–1, 106, 109, 114, 118–20, 214 compression, 156 flexure, 140 shear, 160–1, 163– 4, 170 tensile, 146, 170 testing, 143 time dependent, 7, 13, 243 thoughness, 7, 171 transverse sensitivity, 41, 55 strength, 138 tube (cylinder) filament wound, 18–19

hoop wound, 116–18 thin-walled, 101, 116, 120 ultrasonic, 39, 84, 257, 259–60, 276, 355 VAMAS, 349, 351, 354–5 variance, 20–1, 316–21, 324–7, 330, 332, 334 Vienna agreement, 347–8 viscoelastic, 7, 13, 63, 263, 284 volume fraction, 8–9, 14, 16–18, 34, 62, 179, 195 waisted(ing), 44, 57, 72, 85, 87, 145, 153, 156 block, 149, 151, 156, 158 Weibull, 294, 297–8, 300, 302, 312 Wheatstone bridge, 55 x-radiography, 257, 260