Oxide Scale Behavior in High Temperature Metal Processing

Michal Krzyzanowski, John H. Beynon, and Didier C. J. Farrugia Oxide Scale Behaviour in High Temperature Metal Process...

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Michal Krzyzanowski, John H. Beynon, and Didier C. J. Farrugia

Oxide Scale Behaviour in High Temperature Metal Processing

Michal Krzyzanowski, John H. Beynon, and Didier C. J. Farrugia Oxide Scale Behaviour in High Temperature Metal Processing

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A Comprehensive Reference

Michal Krzyzanowski, John H. Beynon, and Didier C. J. Farrugia

Oxide Scale Behaviour in High Temperature Metal Processing

The Authors Dr. Michal Krzyzanowski University of Shefﬁeld Department of Engineering Materials Mappin Street Shefﬁeld S1 3JD United Kingdom

All books published by Wiley-VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate. Library of Congress Card No.: applied for

Prof. John H. Beynon Swinburne University of Technology Faculty of Engineering & Industrial Sciences P.O. Box 218 Hawthorn, VIC 3122 Australia Dr. Didier C.J. Farrugia Swinden Technology Center Corus Research, Dev. & Techn. Moorgate, Rotherham South Yorkshire S60 3AR United Kingdom

British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliograﬁe; detailed bibliographic data are available on the Internet at http://dnb.d-nb.de. © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Cover © Flying-Tiger, fotolia All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form – by photoprinting, microﬁlm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not speciﬁcally marked as such, are not to be considered unprotected by law. Composition Toppan Best-set Premedia Limited Printing and Bookbinding betz-Druck GmbH, Darmstadt Cover Design Schulz Graﬁk-Design, Fußgönheim Printed in the Federal Republic of Germany Printed on acid-free paper ISBN: 978-3-527-32518-4

V

Contents Preface

IX

1

Introduction

2

A Pivotal Role of Secondary Oxide Scale During Hot Rolling and for Subsequent Product Quality 7 Friction 8 Heat Transfer 12 Thermal Evolution in Hot Rolling 17 Secondary Scale-Related Defects 20 References 24

2.1 2.2 2.3 2.4

1

3 3.1 3.2 3.3 3.4 3.5

Scale Growth and Formation of Subsurface Layers 29 High-Temperature Oxidation of Steel 32 Short-Time Oxidation of Steel 36 Scale Growth at Continuous Cooling 41 Plastic Deformation of Oxide Scales 45 Formation and Structure of the Subsurface Layer in Aluminum Rolling 57 References 62

4

Methodology Applied for Numerical Characterization of Oxide Scale in Thermomechanical Processing 67 Combination of Experiments and Computer Modeling: A Key for Scale Characterization 67 Prediction of Mild Steel Oxide Failure at Entry Into the Roll Gap as an Example of the Numerical Characterization of the Secondary Scale Behavior 68 Evaluation of Strains Ahead of Entry into the Roll Gap 69 The Tensile Failure of Oxide Scale Under Hot Rolling Conditions 73 Prediction of Steel Oxide Failure During Tensile Testing 80 Prediction of Scale Failure at Entry into the Roll Gap 89

4.1 4.2

4.2.1 4.2.2 4.2.3 4.2.4

Oxide Scale Behaviour in High Temperature Metal Processing. Michal Krzyzanowski, John H. Beynon, and Didier C.J. Farrugia Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-32518-4

VI

Contents

99

4.2.5

Veriﬁcation Using Stalled Hot Rolling Testing References 103

5

Making Measurements of Oxide Scale Behavior Under Hot Working Conditions 105 Laboratory Rolling Experiments 105 Multipass Laboratory Rolling Testing 112 Hot Tensile Testing 115 Hot Plane Strain Compression Testing 127 Hot Four-Point Bend Testing 135 Hot Tension Compression Testing 140 Bend Testing at the Room Temperature 143 References 146

5.1 5.2 5.3 5.4 5.5 5.6 5.7

6 6.1 6.2 6.3 6.4 6.5

7 7.1 7.2 7.3 7.4

8 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8

Numerical Interpretation of Test Results: A Way Toward Determining the Most Critical Parameters of Oxide Scale Behavior 149 Numerical Interpretation of Modiﬁed Hot Tensile Testing 150 Numerical Interpretation of Plane Strain Compression Testing 156 Numerical Interpretation of Hot Four-Point Bend Testing 158 Numerical Interpretation of Hot Tension–Compression Testing 164 Numerical Interpretation of Bend Testing at Room Temperature 171 References 175 Physically Based Finite Element Model of the Oxide Scale: Assumptions, Numerical Techniques, Examples of Prediction 179 Multilevel Analysis 179 Fracture, Ductile Behavior, and Sliding 183 Delamination, Multilayer Scale, Scale on Roll, and Multipass Rolling 189 Combined Discrete/Finite Element Approach 195 References 203 Understanding and Predicting Microevents Related to Scale Behavior and Formation of Subsurface Layers 207 Surface Scale Evolution in the Hot Rolling of Steel 207 Crack Development in Steel Oxide Scale Under Hot Compression 211 Oxide Scale Behavior and Composition Effects 215 Surface Finish in the Hot Rolling of Low-Carbon Steel 226 Analysis of Mechanical Descaling: Low-Carbon and Stainless Steel 230 Evaluation of Interfacial Heat Transfer During Hot Steel Rolling Assuming Scale Failure Effects 244 Scale Surface Roughness in Hot Rolling 250 Formation of Stock Surface and Subsurface Layers in Breakdown Rolling of Aluminum Alloys 255 References 263

Contents

9 9.1 9.2 9.3 9.3.1 9.3.1.1 9.3.1.2 9.3.1.3 9.3.2 9.3.3 9.3.4 9.3.5 9.4 9.4.1 9.4.2 9.4.3 9.4.4 9.4.4.1 9.4.4.2 9.4.4.3 9.4.4.4 9.4.4.5 9.4.4.6 9.4.4.7 9.4.4.8

9.4.5 9.4.6 9.5 9.5.1 9.5.2 9.5.3 9.5.4 9.5.5 9.5.6 9.6

Oxide Scale and Through-Process Characterization of Frictional Conditions for the Hot Rolling of Steel: Industrial Input 271 Background 271 Brief Summary of the Main Friction Laws Used in Industry 278 Industrial Conditions Including Descaling 286 Rolling 286 Inﬂuence of Roll Gap Shape Factor 286 Inﬂuence of Pass Geometry and Side Restraints 293 Inﬂuence of Friction and Tension on Neutral Zone 294 Inﬂuence of High-Pressure Water Descaling 299 Inﬂuence of Oxide Scale During Rolling 305 Comparison of Processing Conditions Between Flat and Long Products 307 Summary 308 Recent Developments in Friction Models 308 Mesoscopic Variable Friction Models Based on Microscopic Effects 308 Anisotropic Friction 319 Application to Wear 320 Sensitivity and Regime Maps 321 The Effect of Draft on the Coefﬁcient of Friction 325 The Effect of Roll Velocity on the Coefﬁcient of Friction 326 The Effect of Roll Velocity on the Coefﬁcient of Friction Including the Effect of the Thickness of Secondary Scale, hsc 326 The Effect of Interpass Time on the Coefﬁcient of Friction for a Range of Secondary Oxide Scale Thickness 327 The Effect of Thickness of Secondary Oxide Scale on the Coefﬁcient of Friction 328 The Effect of Roll Radius Rr (Effectively Contact Time) on the Coefﬁcient of Friction 329 The Effect of Roll Surface Roughness on the Coefﬁcient of Friction with Consideration of the Interpass Time 329 The Inﬂuence of Roll Surface Roughness and Secondary Oxide Scale on the Coefﬁcient of Friction 330 Macro- and Micromodels of Friction 332 Implementation in Finite Element Models 334 Application of Hot Lubrication 336 The Effect of Stock Surface Temperature on COF for Different Lubricant Flow Rates 339 The Effect of Lubricant Flow Rate on COF 340 The Effect of Interstand Time, for the Purpose of Secondary Scale Growth, on COF Under Lubrication 340 The Effect of Reduction on COF Under Lubrication 341 The Effect of Roll Speed on COF Under Lubrication 342 Summary of Effect of Hot Lubrication 342 Laboratory and Industrial Measurements and Validation 343

VII

VIII

Contents

9.6.1 9.6.1.1 9.6.1.2 9.6.1.3 9.7 9.7.1 9.7.2 9.7.3 9.8

Typical Laboratory Experimental Procedure 343 The Effect of Contact Force and L/hm Ratio on COF 347 The Effect of Scale Thickness on Friction 347 The Effect of Lubrication on Friction 347 Industrial Validation and Measurements 354 Beam Rolling Example 354 Strip Rolling 355 Inverse Analysis Applied to the Evaluation of Friction 356 Conclusions and Way Forward 358 References 360 Index

367

IX

Preface The authors’ interest in oxide scale behavior during high-temperature metal processing began with a desire to have more accurate descriptions of friction and heat transfer during thermomechanical processing. This was needed for their modeling work on both microstructure evolution and shape changes, particularly for hot metal rolling operations. The evolution of microstructure is a major component of the research of the Institute for Microstructural and Mechanical Process Engineering: The University of Shefﬁeld (IMMPETUS) in the UK, where Michael Krzyzanowski and John Beynon worked closely together. The research within IMMPETUS spans ferrous and nonferrous metals, particularly the important structural alloys of aluminum, iron (stainless and carbon steels), magnesium, nickel, and titanium. The boundary conditions describing the effects of thermal and mechanical loads on the metal are crucial for accurate prediction of the details of metal ﬂow and the operating temperature ﬁelds. However, the research into these boundary conditions quickly revealed that the oxide scale on the hot metal would need to be treated as a detailed material in its own right, and not just a homogenous layer with nominal properties, traditionally described as a single friction or heat transfer coefﬁcient. Thus began a major research effort to understand how oxide scale performs under the severe operating conditions that are typical of industrial metal forming at elevated temperatures, with their combination of large plastic deformations, often at high speeds, with sharp temperature gradients, all changing quickly with time. At the same time, Didier Farrugia, based at Corus’ Swinden Technology Centre nearby, was leading modeling activity into both microstructure evolution and shape changes. He became interested in extracting practical and simple algorithms for friction and heat transfer from the detailed research being undertaken in the university. He and his Marie Curie Fellows, Christian Onisa whose contribution to Chapter 9 has been invaluable and Quiang Liu, concentrated on friction in the hot rolling of long steel products and aligned their research with IMMPETUS. A long partnership with the University of Shefﬁeld resulted, whereby the detailed research has been guided by the needs of industry, and the industry models have beneﬁted from the insights gleaned during the research. Collaboration with other companies, particularly in steel and aluminum, also helped accelerate the progress of the research. These productive relationships were Oxide Scale Behaviour in High Temperature Metal Processing. Michal Krzyzanowski, John H. Beynon, and Didier C.J. Farrugia Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-32518-4

X

Preface

aided by a seamless combination of techniques to tackle the various problems, bringing together computer-based models, laboratory experiments, and industrial trials and data. It is striking that work that began with a focus on being able to quantify friction and heat transfer more accurately, quickly evolved into a much richer ﬁeld of investigation into surface quality. The greater understanding of how oxide scale performs under these severe operating conditions has allowed the evolution of surface quality to be much better understood, including the important issue of how to control the surface quality, not just predict it. This book is underpinned by the essential output from this work, enhanced by extensive reference to the excellent work of others in this ﬁeld. It is the authors’ desire that this book will inspire yet more people to take up this vital ﬁeld of research for both its inherent intrigue and industrial importance. The authors are indebted to colleagues from the Institute for Microstructural and Mechanical Process Engineering: The University of Shefﬁeld (IMMPETUS), UK, where the main research results presented in this publication were obtained and to Corus Research, Swinden Technology Centre, in UK. They would also like to acknowledge the outstanding role of regular meetings and invaluable discussions with industrial partners; it was the guidance that effectively led this research over many years. Finally, the authors would like to express their appreciation to their various employers who allowed them some of the time needed to write this book. For the rest of the time we thank our partners. January 2010

Michal Krzyzanowski, Shefﬁeld, UK John Beynon, Melbourne, Australia Didier Farrugia, Rotherham, UK

1

1 Introduction Since all practical metal-working operations are conducted using equipment that is open to the atmosphere, oxidation of the metal surface is inevitable and, for high-temperature operations, of major signiﬁcance. This oxidation is unwelcome since it represents a loss of metal and usually has to be removed at the end of the operation. Less obvious is the inﬂuence that the oxide scale has on the metalworking operation, in terms of forces and temperature, surface quality of the ﬁnished product once the scale has been removed and on the degradation mechanisms acting on the tools. These effects are fully appreciated by the metals industry, which has achieved a great deal to develop operations that cope with the oxidation problem by making their processes consistent, so that scale removal and surface quality are reasonably reproducible from piece to piece. However, such consistency is difﬁcult to achieve with new operations, where the alloy or forming operation has not been trialed. It remains the case that the inﬂuence of oxide scale on processing conditions and product quality are variable, even under the best of conditions. If this situation is to improve, then the understanding and quantiﬁcation of oxide scale behavior has to improve signiﬁcantly. This can be achieved through a combination of detailed physical observation and computer-based modeling of both laboratory tests and factory operations. This book summarizes current work dealing with oxide scale behavior during high-temperature metal processing. Two main structural metals are considered, aluminum and steel, the latter easily dominating in terms of tonnages worldwide. The main industrial operation considered is rolling, which itself dominates forming operations. Although these are the main examples in the book, there is much of generic importance that can be applied to other forming operations, notably forging. The oxidation of metals has been investigated over many years, with the complexity of different types and structure of oxide, different degrees of adherence to the metals, and variable integrity of the oxide scale according to the alloy, atmosphere, and heating conditions that are employed. Less well understood is the way deformation alters the oxide scale and how that altered scale itself affects the deformation process. This is a complicated topic because of the inaccessibility of the interface between hot metal and the forming tool, which greatly restricts the ability to measure directly what is happening, particularly under industrial conditions. As a result, deduction based on partial evidence has Oxide Scale Behaviour in High Temperature Metal Processing. Michal Krzyzanowski, John H. Beynon, and Didier C.J. Farrugia Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-32518-4

2

Introduction

become the main method for understanding the behavior of oxide scale under hot working conditions. More recently, this has been supplemented by computerbased modeling to help interpret the observations and to predict behavior in other circumstances. Even the basic properties of the oxide scale are poorly deﬁned under hightemperature industrial processing conditions because the circumstances are usually far removed from laboratory conditions where relatively well-controlled experiments can be conducted. More realistic laboratory testing has its own problems of measurement access, so computer-based models are needed to analyze the test results so that “pure” material properties can be extracted for later application to industrial processes. This industrial application in turn requires a computer-based model so that the material properties can be inserted into a realistic description of the details of the stock-oxide-tool system. Even this chain of events is complicated by the need for several different types of laboratory test, each one contributing an element of the behavior that can be built up into a full description of the detailed complexity of the industrial operation. There are two main domains where understanding oxide scale behavior matters. First, the operating conditions of friction and heat transfer, particularly at the interface between stock and tool, need to have the oxide scale included in the modeling if accurate predictions of these important boundary conditions are to be achieved. This has profound implication in changing the tribological conditions in the contact area between the product and the tool as well as initiating degradation mechanisms such as wear and thermal fatigue on the tool. Accuracy in these boundary conditions is a requirement of most metal-forming modeling, where operating forces and temperatures are being calculated. Traditionally, single and approximate coefﬁcients are used for friction and heat transfer. In many circumstances this can be accurate enough, but there are many other situations where more accuracy is needed, particularly in operations involving large areas of contact and long contact times with the tool, where friction and heat transfer will inevitably play a larger role. It is important to assess the need for detailed modeling before embarking on the assembly of such detailed information: both analytical and computer-based models can assist this preliminary assessment. The second main domain, where detailed knowledge of the oxide scale matters, is in the surface quality of the formed product. This applies particularly for metal rolling, where a high-quality surface ﬁnish is normally required, such as sheet metal for white goods (e.g., refrigerator cases) and plate for yellow goods (e.g., earth-moving equipment). At high temperatures, the oxide scale may be sufﬁciently ductile to deform along with the underlying hot metal. In this case, the surface of the metal is as smooth as the surface of the roll or die. However, in many cases the oxide is not hot enough to ﬂow plastically, fracturing instead, such as steel at less high temperatures and aluminum throughout the hot working temperature range. In this case, the underlying hot metal can extrude up through the cracks to make contact with the tool. As well as sharply changing the local friction and heat transfer conditions, once the metal has been “descaled,” these extrusions become protrusions, or bumps, on the metal surface, degrading the

Introduction

metal’s smooth appearance. A more subtle effect concerns the ease of descaling, which may be affected by the thermomechanical processing conditions, which can make the oxide difﬁcult to remove. Given that the metal-forming operation is run to optimize the shape change and microstructural reﬁnement in the metal, changing the operating conditions to facilitate better control of the oxide scale is still rare. It is hoped that as understanding of oxide scale behavior improves, enabling good predictions of behavior during hot forming operations, an element of process control for surface quality will be introduced as standard. For the researcher, there remains a wealth of issues to be investigated into the behavior of oxide scale in high-temperature metal processing. Although this book lays down much guidance and presents many data, it is very clear to the authors that much needs to be done before an acceptable level of insight has been achieved across the range of commonly formed alloys. This is largely because the chemical composition of the alloy plays a major role in the behavior of the oxide scale. In addition to the major differences between alloy groups (aluminum alloys, carbon steels, and stainless steels) within these groups, particularly in carbon steels, small compositional changes have a large inﬂuence on oxide scale behavior, as will be discussed in this text. Although some inroads have been made to analyze and quantify the effect of composition, many more measurements need to be made. For the industrialist, the approach presented in this book opens the door to much more quantiﬁed insight into the complicated world of oxide scale, which for many years has relied on observations with too little underpinning theory. There is much to be gained from embracing the computer-based modeling approach, informed by measurements in the laboratory and factory, in achieving better quality products more reliably. Applications for this approach abound, across ferrous and nonferrous alloys, ﬂat and long product rolling, and open- and closeddie forging. Although most of the book is devoted to the underpinning research, the metals and conditions reported are all industrially relevant and informed by current and anticipated practice. This makes the transfer of the research results to actual industrial practice relatively straightforward, as illustrated in the ﬁnal chapter. The technical content of this book begins in Chapter 2 where the crucial role of the secondary oxide scale for hot rolling and subsequent descaling operations is highlighted. This chapter gives an introduction to friction, heat transfer, and scalerelated defects, thereby encompassing the main areas of inﬂuence of the oxide scale. As with the remainder of the book, friction and heat transfer information in the literature is presented in terms of relevance to industrial hot working operations. The third chapter is devoted to high-temperature oxidation and the formation of subsurface layers. High-temperature oxidation has been studied extensively for some time, although mainly for applications where critical components are submitted to prolonged high temperature in service, which requires a protective oxide scale. This ﬁeld of research and domain of application is only brieﬂy described in this chapter. The main focus of the chapter is to describe the complexity of oxides

3

4

Introduction

forming on carbon steels and aluminum alloys under industrial conditions, including the constraint of short times and the effect of concurrent deformation. This results in more complicated oxide structures than are observed for metals simply oxidized in furnaces. The chapter closes with the particularly complicated case of subsurface layers formed in aluminum alloys, which can leave the metal prone to later ﬁliform corrosion. The methodology for quantitative characterization of oxide scale behavior in metal-forming operations is discussed in Chapter 4. This is illustrated by an important example, namely the prediction of oxide scale failure at entry into the roll gap. This is a crucial location for deformation of the scale, which can have considerable inﬂuence on its behavior in the roll gap and also on subsequent forming passes and descaling operations. The investigations that are reported illustrate how vital it is to make precise measurements of the most critical parameters of scale deformation and failure under hot working conditions for good accuracy in the subsequent modeling. A range of recently developed laboratory-based experimental techniques, each providing a partial insight, is discussed in Chapter 5. The wide range of experimental methods presented in this chapter illustrates the complexity of the behavior of oxide scale in hot forming operations, including descaling, whereby so many tests are needed to build up sufﬁcient evidence to understand the ﬁne details of events under industrial conditions. Interpretation of such experimental results is often accompanied by serious difﬁculties due to inhomogeneities in the tests, very small measured loads and other various disturbances. Sometimes the measured data cannot be directly applied to mathematical modeling of the scale-related effects. For such cases, application of a physically based ﬁnite element model to provide numerical analysis of experimental results becomes a necessity. Several examples of such numerical interpretations are discussed in Chapter 6 for various laboratory techniques. It is worth highlighting the value of the ﬁnite element method in such modeling, with its capacity to encompass a wide range of phenomena and allow them to interact to provide realistic, coupled solutions to complicated problems. The main assumptions, numerical techniques, and experimental veriﬁcations of the physically based model for oxide scale failure under hot rolling conditions are presented in Chapter 7. The chapter opens with the challenging issue of dealing with a wide range of length scales that are pertinent to these solutions. The analysis usually needs to go no ﬁner a level than the microstructural scale of the order of microns, but this has to be tackled within a macroscale operation about ﬁve orders of magnitude larger, around a meter. To address this large range while continuing to encompass much of the details of the metal-oxide-tool interaction, as well as oxide microstructure, requires ingenuity if tolerable computation times for the modeling are to be maintained. Most of the modeling complexity is at the microscale, such as the range of failure modes for oxide scale, including brittle and ductile fracture. The ﬁnite element method can tackle these issues, as well as multiple sequences of deformation, common to industrial practice. The

Introduction

chapter closes with a new method which combines discrete and ﬁnite elements, which appears to be particularly well suited to complicated patterns of metal ﬂow and oxide fracture without the need to guess beforehand where the fracture might occur. Chapter 8 illustrates how advanced modeling can be used for prediction of micro events related to the oxide scale behavior on the surface of hot metal being rolled, including the formation of subsurface layers and how these events inﬂuence both the rolling process and the quality of the rolled product. This chapter discusses the important topic of the inﬂuence of minor changes in chemical composition on the behavior of oxide scale on carbon steels; an inﬂuence that is surprisingly large. Preliminary investigations attempting to provide a scientiﬁc rationale for the effect of chemical composition are presented based on simply binary alloys. Although well removed from the complicated industrial alloy compositions, there are clear indications how such compositions should be tackled in future research. Surface quality also features strongly in this chapter, beginning with the problematic issue of roll pick-up, whereby oxide scale detaches from the stock surface and is carried round by the roll to embed a surface defect in the following stock surface. Descaling is also discussed, particularly room temperature descaling by bending of the metal, and what can be done during the preceding hot rolling to make this process more efﬁcient. The chapter closes with a discussion of the formation of subsurface layers in aluminum rolling during breakdown rolling, which appears to be the root cause of ﬁliform corrosion. As mentioned earlier, the whole book is approached from the viewpoint of industrial metal processing conditions. Thus the research reported is usually conducted under industrial or near-industrial conditions. Nevertheless, the laboratory investigations are just that, and there will always remain a need to translate that work into terms that relate directly to industrial practice. Chapter 9 provides this vital industrial input. After an introduction to industrial practice, particularly focused on long product rolling, the ways friction is normally characterized during industrial rolling are summarized. Chapter 9 then goes through a range of important industrial conditions, such as the inﬂuence of rolling geometries and descaling operations. Rolling geometry is particularly important for long product rolling, which is much more three-dimensional than ﬂat rolling. The chapter then presents a new way of taking some of the ﬁne details presented earlier in the book and creating a more representative and accurate friction law for use in industry. This is not a trivial exercise, but it is a pioneering development in the translation of the complexity observed into practical friction descriptions. It also includes anisotropic friction and the effect on roll wear. Creating such models is the ﬁrst step, but knowing what to include and what to exclude requires a quantiﬁed appreciation of the sensitivity of the process to the detail. This is addressed next in Chapter 9, including the important addition of hot lubrication, which is used in long product rolling for complex sections and rails, though much less in ﬂat rolling. As with so much modeling that feeds off practical measurements, the shortcomings of the modeling are revealed and the chapter includes further off-line measurements to

5

6

Introduction

provide greater insight into factors such as the effect of lubricant ﬂow rate. It is important to validate such modeling with industrial measurements, and these are presented for both beam rolling and strip rolling with carbon steels, including mention of how inverse analysis can be used with industrial data. The chapter closes with a discussion of the lessons learnt from the work presented in this book for improving industrial practice and argues the need for yet more research.

7

2 A Pivotal Role of Secondary Oxide Scale During Hot Rolling and for Subsequent Product Quality An important role of the oxide scale in determining friction and heat transfer during thermomechanical processing, as well as the quality of the formed product, arises from its pivotal position on the interface between tool and workpiece, at the heart of a complex set of events. The oxide scale can deform plastically or fracture, behavior that will have a considerable impact on the interaction between tool and workpiece, and on the surface ﬁnish of the formed product. In the hot strip mill, the slab is brought to the temperature in the reheating furnace and discharged for rolling. To break the primary scale, the slab is passed through a slab descaler before the reversing roughing mill. Between successive rolling passes a secondary scale is formed, which is further removed by high-pressure water jets before the subsequent passes during reversing rolling or before the strip enters the tandem ﬁnishing mill. This secondary scale grown after passing the ﬁrst slab descaler, its characterization and behavior under hot rolling conditions, is the main topic of this publication. In the hot rolling of long products, especially for a bar mill, the lack of space between the furnace and the ﬁrst rolling stands means that installation of a scale breaker is difﬁcult. Therefore, removing the primary scale was relied on box passes, on the ﬁrst or two stands. The introduction of steel qualities having a thin adhesive oxide scale meant that a new method of removing the scale had to be implemented. Since the 1950s, hydraulic power descaler is used for spraying the steel surface with jets of water at high pressure leading to breakup and removal/ﬂushing of the scale. Principles of the descaling of long products follow similar patterns to the ﬂat rolling, except that clearances can be reduced and fewer nozzles can be used to remove the oxide scale around the billet/bloom perimeter. Typical pressure is up to 200 bars (three to four pumps) with impingement of 1 to 2 MPa. There are new systems on the market these days, such as rotary headers, working at pressure in excess of 400 bars. Most of the long product mills have lower accumulator water/air with lower capacity pumps than strip mills. The strain imposed on the metal surface when the strip enters the roll gap, which arises because of drawing in of the stock by frictional contact with the roll, produces longitudinal tensile stresses on the metal surface ahead of contact with the roll. It is important to know whether this kind of stress results in oxide failure.

Oxide Scale Behaviour in High Temperature Metal Processing. Michal Krzyzanowski, John H. Beynon, and Didier C.J. Farrugia Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-32518-4

8

2 A Pivotal Role of Secondary Oxide Scale During Hot Rolling and for Subsequent Product Quality

One reason is that the thermal conductivity of the nonfractured oxide scale is a factor of about 10–15 less than that of the steel [1] and the fractured scale can enable direct contact of hot metal with the cold tool, due to extrusion of the hot metal through fractured scale up to the cool roll surface [2]. Aluminum oxide is also a good thermal insulator and similar effects have been observed during the hot rolling of aluminum alloys [3]. The behavior of steel’s oxide scale passing through a sequence of hot rolling stands is complex and not a well understood process. In spite of the signiﬁcant effort that has been made during the recent years towards understanding and predicting this behavior, it still remains a research topic. At higher temperatures, there have been indications that the oxide/ metal interface is weaker than the oxide itself, and sliding of the nonfractured oxide raft is observed during uniaxial tension of an oxidized specimen [4]. The location of the plane of sliding is determined by the cohesive strength at different interfaces within the metal/inhomogeneous oxide and by the stress distribution when delamination within the scale takes place. Both fracture and sliding will produce sharp changes in heat transfer and friction in the roll gap. The size and shape of these oxide islands and the subsequent metal ﬂow around them are likely to depend on the alloy, the hot working conditions – such as load, speed, and temperature – and the previous scale deformation. The complexity of events between stock and tool in hot (or warm) working immediately becomes evident. An additional point of consideration is the demand for increasingly small ﬁnal thicknesses of the hot rolled steel strip, approximately 1.2 mm during conventional rolling and 0.8–1.0 mm for ultrathin hot rolled strips produced on mini-mills using endless rolling technology. Not only does this emphasize the importance of the surface, given how much of it there is, but in such extreme conditions, the formation of oxide-related defects can affect the structure of the subsurface layers of the metal within the strip.

2.1 Friction

Off-line mathematical models are widely used in the rolling industry for the development of draft schedules in their product and process design. When modeling hot rolling, the resulting grain distribution, the retained strain, the amount of recrystallization, and precipitation can all be calculated. To a large extent, the accuracy of this modeling depends on the appropriate formulation of the boundary conditions, which can be as sophisticated as the models themselves. The boundary conditions are often expressed in terms of the coefﬁcient of friction and the coefﬁcient of heat transfer. In 1997, Roberts commented that of all the variables associated with rolling, none is more important than friction in the roll bite [5]. Since the trend in modern strip rolling is to produce thinner strips of higher strength metals, the control of friction in the roll bite is the most important variable, according to Yuen et al. [6].

2.1 Friction

The usual choice of friction coefﬁcient is the Coulomb–Amonton deﬁnition (or just “Coulomb” for brevity), μ = τ / p, which is the ratio of the interfacial shear stress τ to the interfacial pressure p. There is a view that this coefﬁcient of friction may not be the best description of interfacial phenomena in between the roll and the roll metal [7]. For example, in ﬂat rolling the normal pressure p may increase signiﬁcantly beyond the material’s ﬂow strength. The interfacial shear stress, τ, may also increase but it cannot rise above the metal’s yield strength in pure shear; this imbalance leads to unrepresentative ratios. The problem may be overcome by the use of the Tresca friction factor instead. The friction factor, m, is deﬁned as the ratio of the interfacial shear stress to the metal’s ﬂow strength, k, in pure shear, m = τ / k. Nevertheless, the Coulomb friction coefﬁcient is widely used and understood by engineers in the metal forming and the ﬂat rolling industry, and is also often used in the mathematical modeling. There are different formulas for the friction coefﬁcient in hot rolling proposed by various authors, which attempt to take account of operating conditions such as temperature. Those by Roberts (1983), by Geleji, quoted by Wusatowski in 1969, Rowe (1977) and also some later results published by Munther and Lenard (1997), Yu and Lenard (2002) and by Fedorciuc-Onisa and Farrugia (2003–2004) are presented below. Roberts gave an increasing relation between the coefﬁcient of friction and the temperature T [8]:

μ = 2.7 × 10 −4 T − 0.08, for T (°F)

(2.1)

It can be rewritten for T in °C as follows:

μ = 4.86 × 10 −4 T − 0.07136

(2.2)

Roberts combined the data from experimental 84 inch (2.13 m) and 132 inch (3.35 m) wide 2-high hot strip mills obtained for well-descaled strips. Geleji’s formula indicates the opposite trend with respect to the inﬂuence of temperature [9]:

μ = 1.05 − 0.0005T − 0.056ν

(2.3)

where T is the temperature in °C and ν is the rolling velocity in m/s. The relation was obtained for steel rolls by applying an inverse method matching the measured and calculated roll forces. For doubled poured and cast rolls the formula for the friction coefﬁcient is slightly different:

μ = 0.94 − 0.0005T − 0.056ν

(2.4)

and it changes again for ground steel rolls:

μ = 0.82 − 0.0005T − 0.056ν

(2.5)

These relations, indicating a decreasing friction coefﬁcient with increasing temperature, accord with the experimental results obtained by Rowe [10]:

μ = 0.84 − 0.0004T

(2.6)

9

10

2 A Pivotal Role of Secondary Oxide Scale During Hot Rolling and for Subsequent Product Quality

Equation (2.6) was obtained for temperatures higher than 700 °C. A comparison of the friction coefﬁcients obtained using formulas (2.1)–(2.6) indicates that the relations can give large differences for different rolling temperatures and therefore may not be completely reliable. The evolution of secondary oxide scale and its failure during hot rolling and interpass cooling with respect to its thickness, composition, ductile/brittle behavior, and thermal properties, play a signiﬁcant role in affecting the tribological behavior. In 1984, Felder characterized oxide scale behavior during hot rolling as being highly inﬂuenced by the temperature [11]. He deﬁned H, the ratio of the scale thickness h to the scale thickness thermally affected by the contact with the tool ht, as follows: H=

h = h × (6ac Δt )−0.5 ht

(2.7)

where ac is the thermal diffusivity of the oxide scale and Δt is the contact duration. According to Felder, there are three different tribological regimes related to the ratio. The ﬁrst one is for H > 2 when the oxide scale is insigniﬁcantly cooled by the cold roll surface. For this regime, the scale can be characterized as ductile, softer than the metal and strongly adherent to the metal surface. The friction is then described by the Tresca friction factor, which is not sensitive to the pressure and the contact time. For the second regime, when H < 0.05, the oxide scale is considered to be signiﬁcantly cooled due to contact with the roll; it is then harder than the metal and can be considered as quasirigid. The scale is brittle, has a low adherence, and can be considered as abrasive. The Coulomb friction coefﬁcient, proportional to the shearing and not very sensitive to the contact time, is applied for this regime. In between these two extremes, for 0.05 < H < 2, the friction behavior can become a complicated function of the contact time and pressure. In 1997, Munther and Lenard combined the data from rolling samples on a laboratory rolling mill with different oxide scale thicknesses at various temperatures [12]. Experimentally measured data, such as the roll separating force, torque, and forward slip, coupled with ﬁnite element analysis led to the determination of the friction coefﬁcient. They found that the friction coefﬁcient increased with increasing reduction and decreasing temperature, and it increased with decreasing velocity and decreasing scale thickness (Figure 2.1). They put the experimental evidence of the effect of the scale thickness on the friction coefﬁcient into the following formula:

μ = 0.369 − 0.0006hexit

(2.8)

where hexit is the scale thickness at the exit from the roll gap. Li and Sellars reported that the forward slip increases signiﬁcantly with the scale thickness for the same reduction [13]. The forward slip was measured for a relatively wide range of oxide scale thickness, 20–670 μm, during their experimental hot rolling of steel. They attributed the change in the forward slip to the variations of the scale temperature and, as a result, to changes in the roll/scale contact conditions. The real contact area between rolls and the oxide scale will be less for a thick

2.1 Friction 0.6

Coefficient of Friction

0.5

Red. = 25% red. Roll Velocity = 170 mm/s AISI 1018

0.4

0.3

0.2

0.1 1.59 mm 0 700

800

0.29 mm

0.015mm

900 1000 Temperature (°C)

1100

Figure 2.1 Inﬂuence of the rolling temperature on the friction coefﬁcient for 25% reduction, 170 mm/s rolling speed and different oxide scale thicknesses, 1.59, 0.29, and 0.015 mm [12].

scale than for a thin one under similar contact pressure. This is because the oxide scale ﬁlls the valleys of the roll surface asperities during a rolling pass. A smaller contact area means an easier relative movement between the roll and the oxide scale that, coupled with a low surface oxide temperature, should lead to a high forward slip. For a similar scale thickness, the measured forward slip for a higher reduction was larger than that measured for the lower reduction. The lubrication behavior of the thin oxide scales described above is in agreement with the load and torque measurements made by El-Kalay and Sparling during laboratory hot rolling of mild steels [14]. A decrease in the friction coefﬁcient as a result of the temperature increase in the roll gap was noticed by Ekelund in 1927 during hot rolling of carbon steels [15]. This effect can also be related to the lubrication behavior of the “soft” oxide scale. During multipass hot rolling of long products, the magnitude of the coefﬁcient of friction within the roll bite varies due to the complicated pressure-slip variations along and across the interface between the proﬁled roll and stock. While the Coulomb friction models consider the shear stresses to be functions of the normal stress or yield stress, other models like the Norton model have constructed the shear stresses as functions of the relative velocities between the surfaces. A new Coulomb–Norton-type friction model for long products and bar sections has been developed recently at Swinden Technology Centre (Corus RD&T, UK) [16]. Among other assumptions, the model takes into consideration some complex interactions at the stock–roll interface due to the presence of secondary oxide scale, as has been discussed above. The different modes of oxide scale failure, such as through-

11

12

2 A Pivotal Role of Secondary Oxide Scale During Hot Rolling and for Subsequent Product Quality

thickness cracking and scale sliding, depending on the temperature and steel composition, have been implemented into the mathematical model. The friction force occurs either between the roll surface and oxide scale; or between the roll surface, the oxide scale fragments, and eventually fresh steel extruded through the scale gaps depending on the relative magnitude of the shear stresses inside the scale layer and at the oxide scale/stock interface. The coefﬁcient of friction is a function of the contact force fNormal, the sliding velocity vrel, the stock temperature T, the roll surface roughness Ra, and the factor Hsc, which depends on the state of the secondary oxide scale at the roll gap: − log

μ = k1Hsc

( )a tan ⎛ R 1200 T

⎜⎝

Tk3 1200 a

⎞ log (1 + f Normal ) ⎟⎠ log (k2 + vrel )

(2.9)

where k1, k2, and k3 are constants established experimentally. The factor Hsc is a function of the thickness of the secondary scale hsc, the thermal diffusion coefﬁcient ac, and the contact time Δt; thus, Hsc = hsc (6ac Δt )−0.5

(2.10)

The model has been implemented as a VFRIC subroutine in the commercial ABAQUS/Explicit ﬁnite element code and used to represent the effect of each variable on the coefﬁcient of friction [17]. For example, an increase in the roll velocity results in a reduction of the coefﬁcient of friction, particularly at relatively low temperature when bonds formed between metal and oxide scale are weak. It was also found that the thickness of the secondary oxide scale alters the inﬂuence of the roll velocity due to its capacity to lubricate the interface in the ductile (“sliding”) regime (Figure 2.2). In the case of rolling with a thin oxide scale (about 10 μm), assuming that the temperature is above the sliding ductile transition (see Sections 4.2.2 and 4.2.3, for instance, or Section 6.1 for a detailed explanation of this transition), an increase of the roll velocity should lead to the corresponding decrease of the coefﬁcient of friction. For rolling with thicker scales (about 80 μm) the effect becomes negligible. Although the aim is to reduce the secondary scale thickness, some decrease in friction could be achieved by secondary scale growth to compensate for the negative effect of rolling with lower roll velocities (Figures 2.7c and d). In practice, the operational parameters act simultaneously and the model highlights the circumstances where the friction coefﬁcient may achieve its undesirable values, indicating the need for the introduction of lubricant, such as a water–oil emulsion, when extreme conditions are reached. Recent enhancement of the friction model with a lubrication component now allows the same type of predictive analysis when lubricant is applied during hot rolling [18].

2.2 Heat Transfer

In thermomechanical processing (TMP) the thermal history of the workpiece has a profound inﬂuence on the ﬁnal properties of the product. There is strong indus-

2.2 Heat Transfer hH (μm) 0.5

0.5

80

c)

0.3

0.2 0

μ1200(fn) 0.3

1·104

5000

0.2 0

1.5·104

Contact force, F n (N)

0.5

T=930°C

a)

0.3

1.5·104

b)

μ930(fn) 0.4 μ1200(fn) 0.3

0.2 0

1·104

5000

Contact force, F n (N)

0

1·104

0.5

T=1200°C

μ1200(fn)

5000

Contact force, F n (N)

μ930(fn)0.4

10

d)

μ930(fn) 0.4

μ930(fn) 0.4 μ1200(fn)

7

1.5·104

0.2 0

5000

1·104

1.5·104

Contact force, Fn (N) ωr (rad/s)

20

Figure 2.2 Effect of the roll velocity on the friction coefﬁcient for different thicknesses of the oxide scale, hsc; roll radius 152.5 mm; draft 8 mm; roll roughness 1.5 μm [17].

trial need for more accurate, predictive, computer-based models of the TPM of metals. These models are handicapped by the inadequate deﬁnition of two boundary conditions, friction and heat transfer. Radiation to the environment, convection to descaling and backwash sprays, and heat conduction to the work rolls have been considered to be the main modes of heat loss during hot strip rolling. The complexity of the interface between tool and stock makes measurements very difﬁcult. The direct measurement of friction and heat transfer is impractical for most industrial hot metal-forming operations, and even for many conducted in the laboratory. The difﬁculties of making laboratory measurements, combined with the complexity of the tool–stock interface, result in a wide range of reported values for the heat transfer coefﬁcient (HTC), Table 2.1 [19]. In the absence of detailed insight and with a lack of fundamental understanding of the mechanism of heat transfer at a moving interface, most modelers assume a simple description, or an average value, of the heat transfer coefﬁcient. It has been observed that the contacting points between two surfaces serve as paths of lower resistance for heat ﬂow in comparison to adjacent regions where heat

13

14

2 A Pivotal Role of Secondary Oxide Scale During Hot Rolling and for Subsequent Product Quality Table 2.1 Measured heat transfer coefﬁcient (HTC) between roll and stock for the hot rolling

of steel and aluminum. Steel

Aluminum

HTC (kW/m2 K)

Reference

HTC (kW/m2 K)

Reference

10–50 15 15–20 19–22 100–350 200–450

[20] [21] [22] [23] [24] [25]

2–20 5–50 10–260 18–38 23–81 200

[26] [27] [28] [29] [30] [31]

transfer occurs by conduction through air gaps [32]. Thus, it was assumed that the link between friction and heat transfer at the interface is the fraction of the total area, εA, that involves direct contact. It was postulated that the real contact area depends on both the interfacial pressure, p, and the shear strength, k, in the real contact zone: p=

mc ε A k μf

(2.11)

where mc is an empirical constant within the range of 0 to 1 and μf is the friction coefﬁcient at the interface [33]. Based on experimental results [34], it was concluded that the variation in the HTC with reduction, rolling speed, and lubrication observed through pilot mill tests on 316 L stainless steel could be explained on the basis of the inﬂuence of these rolling parameters on actual contact area. As expected, the interface heat transfer coefﬁcient increases during rolling because the real area of contact between two surfaces under applied load increases with higher pressure. The inﬂuence of other factors, such as roll reduction, rolling temperature, roll speed, roll and rolled material and their roughness, can be related to their effect on the roll pressure distribution through the roll gap. It has been found that the average HTC is linearly related to mean pressure (Figure 2.3) [35]. The relationship presented in Figure 2.3 can be used to determine the magnitude of the HTC in industrial rolling from an estimate of the rolling load. According to the estimation, the heat losses to the work rolls during rough rolling (i.e., shortly after the stock leaves the reheating furnace) can be more than 30%. This shows the signiﬁcance of accurately characterizing the interface HTC in the roll bite. The application of lubricants or the presence of oxide scale introduces an additional thermal resistance between the roll surface and the material. During strip rolling, for example, the scale layer that is adhered to the surface of the metal strip attempts to elongate in the rolling direction with the same ratio as the substrate driven by the shear stresses generated in the substrate. In many cases, with increased reduction and decreased rolling temperature, through-thickness cracks will appear with different widths and lengths oriented mostly perpendicular to the

2.2 Heat Transfer

Heat Transfer Coefficient (kw/m2 K)

300 Low-carbon steel (0.05%C)

250

Stainless Steel (304L)

200 Microalloyed Steel (0.025%Nb) 150 Best fitting line 100 50 0 5

10

15

20 25 30 35 Mean Pressure (kg/mm 2)

40

45

Figure 2.3 Inﬂuence of the mean roll pressure on the average heat transfer coefﬁcient during hot rolling of low carbon, stainless, and microalloyed steels [35].

rolling direction. This will lead to extrusion of fresh hot steel through the gaps forming within the scale under the inﬂuence of the roll pressure. As a result of such extrusion, a direct contact between the relatively cold roll and the hot strip metal surface can be established. This type of scale behavior was observed in the hot rolling of both aluminum [3] and steel [2]. Based on the experimental observations of oxide scale behavior, analysis of real contact area and thermal resistance, combined with experimentally derived interfacial HTC values, a physical model has been developed by Li and Sellars to represent the heat transfer during hot steel rolling [13]. According to the model assumptions, the heat transfer within the roll gap consists of two parallel heat ﬂow systems: through the oxide scale, called a “two-layer” zone, and directly between the roll/fresh metal interface, a “one layer” zone. Thus, the total thermal resistance over the entire apparent contact area is expressed as follows: Aa As Aox = + Re Re 1 Re 2

(2.12)

where Aa, As, and Aox are the overall apparent contact area, and the apparent areas occupied by the extruded fresh steel and by the oxide scales in the roll gap, respectively. The effective interfacial HTC, Ce, can be derived from Equation (2.12) as Ce = Ce1α s + Ce 2 (1 − α s )

(2.13)

where Ce1 and Ce2 are HTCs for the “one layer” and “two layer” zones, respectively; αs is the area fraction of the gaps formed from the through-thickness cracks at the interface and ﬁlled with fresh metal. The area fraction is deﬁned as αs = As/Aa. In order to obtain the effective interfacial HTC for the entire rolling pass, it is

15

16

2 A Pivotal Role of Secondary Oxide Scale During Hot Rolling and for Subsequent Product Quality

therefore necessary to obtain not only the HTC components for the individual contact zones and thermal barriers, but also to know the mean area fraction of the fresh steel in the roll gap. The mean area fraction of the fresh steel extruded through the gaps within the oxide scale can be obtained approximately as [13] 2 1 ⎞ α s = Δh ⎛ + ⎝ 3ho 8R ⎠

(2.14)

where Δh is the absolute reduction in the thickness, ho is the initial slab thickness, and R is the roll radius. The equation for the interfacial heat transfer coefﬁcient (2.13) can be rewritten depending on HTCs for the individual contact zones and thermal barriers as Ce = Cb1α s +

C oxCb2 (1 − α s ) C ox + Cb2

(2.15)

where Cb1, Cb2, and Cox are the HTCs for the partial contacts at the “one layer” and the “two layer” zone, respectively, usually called contact conductance, and Cox is the HTC through the oxide scale. The coefﬁcient Cox can be approximately obtained for a given oxide scale thickness δox and the scale thermal conductivity kox by using the following equation: C ox =

kox δ ox

(2.16)

No systematic analysis has been found for quantitative variations of the conduct conductance with surface, interface, and deformation conditions during metalforming operations. However, it has been shown that the contact conductance is related to the apparent contact pressure, pa, and the hardness of the softer contacting material, HV, in addition to the surface roughness and thermal conductivity of two contacting solids under normal static contact conditions [36–38]. Assuming the above-mentioned equation and also the relationship between the degree of real contact and the dimensionless contact pressure obtained on the basis of experimental measurements and mathematical analysis by Pullen and Williamson [39] and later by Mikic [40], Li and Sellars established an exponential relationship between the contact conductance and the contact pressure during hot rolling [13]. They assumed the same contact and heat transfer states at the scale layer/tool interface for forging and rolling. According to them, the contact conductance for a “two-layer” zone Cb2 during hot steel rolling can be calculated by using the same equation developed earlier for hot forging of steel, namely Cb2 = A

kh 2 Rar

B ⎡1 − exp ⎛ −0.3 pa ⎞ ⎤ ⎢⎣ ⎥ ⎝ HVox ⎠ ⎦

(2.17)

where A and B are empirical constants, whose values are 0.4 × 10−3 and 0.392, respectively; Rar is the roll asperity height; kh2 is the harmonic mean of the thermal conductivity of the oxide scale kox and the steel roll kr and is determined by 1 ⎛1 1 = + ⎞ 2 kh 2 ⎝ kr kox ⎠

(2.18)

2.3 Thermal Evolution in Hot Rolling 400

300

scale: ~30 mm ~250 mm

Reduction: ~18.9% ~38.9% 250 IHTC (kw/m2 K)

IHTC (kw/m2 K)

300 200 150 100

200

100 50 0 0

600 200 400 Initial oxide scale thickness (mm)

800

0

0

10

a

20 30 Rolling reduction (%)

40

50

b

Figure 2.4 Interfacial heat transfer coefﬁcient for steel hot rolling with initial temperature around 1000 °C derived for different scale thicknesses (a) and rolling reduction (b) [13].

The Vickers hardness of the oxide scale HVox is considered to vary with the surface temperature of the oxide scale Toxs according to the following equation developed on the basis of available experimental data [41]: HVox = 7075 − 538 Toxs

(293 K ≤ Toxs ≤ 1273 K )

(2.19)

Equation (2.17) can be replaced by the following for low pressures: Cb2 = A

B kh 2 ⎛ p 0.3 a ⎞ . Rar ⎝ HVox ⎠

(2.20)

For a “one layer” zone and for the rolling conditions where the initial rolling temperature is around 1000 °C, the scale thickness is within 25–700 μm, the rolling reduction is between 10 and 50%, and the corresponding average rolling pressure is between 130 and 200 MPa, then the contact conductance can be calculated using Equations (2.17) and (2.20), where the constants A and B are set to 0.405 and 1.5, respectively. Figure 2.4 illustrate changes of the interfacial HTC derived for the different scale thicknesses and rolling reductions. As can be seen, the interfacial HTC decreases dramatically once the scale thickness increases because of the relatively poor thermal conductivity of the oxide scale. At the same time, the interfacial HTC increases rapidly with rolling reduction. This is physically consistent with the variation of the real contact area and the high contact conductance in the fresh steel zone that dominates the overall high values of the HTC at the interface during steel rolling, even though the area fraction of the fresh steel zone is less than that of the oxide scale for rolling passes with a reduction of less than 50%.

2.3 Thermal Evolution in Hot Rolling

The surface temperature of the strip experiences large variations as it passes through the mill. Hydraulic descaling of the oxide from the steel surface sets up

17

2 A Pivotal Role of Secondary Oxide Scale During Hot Rolling and for Subsequent Product Quality

Temperature (°C)

1200

Predicted

1100 Measured

Distance From Surface (mm) Surface 0.45 0.89 Centerline Surface

1000 900 800

500

0

5

10

15

Stand 4 Stand 3 Stand 2

Descale Sprays

600

Stand 1

700

Backwash Sproy

Temperature (°C)

18

20 25 Time (s)

30

35

40

Figure 2.5 Comparison of model predictions with measured temperatures during industrial hot rolling of 0.34% C steel rolled to a ﬁnished gage of 3.56 mm [34].

large thermal gradients thorough the thickness. Figure 2.5 illustrates the surface temperature evolution in the ﬁnishing mill at Stelco’s Lake Erie Works in Canada. The small downward spike in surface temperature that is calculated to occur after the two initial large spikes that are related to descale sprays is due to a set of backwash sprays situated before entry to the ﬁnishing mill. The next four sharp drops represent the four ﬁnishing stands. In spite of a signiﬁcant chilling effect due to the contact with the work rolls, the effect is limited to a thin surface layer and the surface temperature recovers rapidly in the interstand regions due to recalescence by the heat within the body of the metal being rolled. Li and Sellars applied mathematical modeling to examine the evolution of the secondary oxide scale during multipass hot rolling of a plain carbon steel strip at the British Steel (now CORUS) Port Talbot works in the UK [42]. They considered two models of the secondary oxide scale growth, according to a “scale deformation” or “scale cracking” model. The ﬁrst model assumes that the oxide scale undergoes only plastic ﬂow during hot rolling and that the integrity of the scale remains the same as before rolling. According to the second model, oxide scale growth after a rolling pass is started from different places. In the scaled zones the oxide grows from the existing scale in a way similar to model one, while in the cracked zone, the scale grows faster on the freshly created steel surface. The average thickness of the oxide scale is then calculated at any stage after the rolling passes. Figure 2.6 illustrates the temperature changes calculated for a sequence of 12 hot rolling passes. After reheating to around 1250 °C in the reheating furnace, the slab is discharged and passed through a roughing descaler to break the primary oxide

2.3 Thermal Evolution in Hot Rolling center

Temperature (°C)

1,200

center

mean

mean

surface

1,000 800

surface

1st descaling

RP2 RP3

600 0

2nd descaling

RP1

(a) roughing mill 20

40

F7 F1

RP4 RP5

F2

F5 F6 F3 F4

(b) finishing mill

60 80 Time (s)

100

120

125

130 Time (s)

135

140

35

120 100

scale deforming scale cracking no rolling effect

scale deforming scale cracking no rolling effect

30 25

80

20

60

RP1

40

RP3

F2

RP4

F3

RP5

20 0 0

15

RP2

F1

(a) roughing mill 20

40

60 80 Time (s)

100

120

F4 F5 F6 F7

10 5

(b) finishing mill 125 130 Time (s)

135

0 140

Oxide scale thickness, mm

Oxide scale thickness, mm

Figure 2.6 The temperature changes of the front end of the plain carbon steel strip predicted for 12-pass hot rolling based on the industrial rolling schedule [42].

Figure 2.7 The secondary oxide scale thickness predicted for 12-pass hot rolling based on an industrial rolling schedule; ﬁve roughing passes followed by seven ﬁnishing passes [42].

scale. The broken scale is then removed by high-pressure water jets. A secondary oxide scale is formed on the exposed slab surface during multipass reverse rolling in the roughing mill. The secondary scale is then removed by another hydraulic descaling operation just before the strip enters the 7-stand tandem ﬁnishing mill. The evolution of the secondary oxide scale thickness computed for the industrial process is shown in Figure 2.7. It can be seen that both the rolling operation and scale deformation patterns have signiﬁcant inﬂuence on the scale thickness. This is in spite of the strong sensitivity of the scale growth to the surface temperature of the strip and interpass delay time. When the scale is broken, the average thickness of the oxide scale before secondary descaling is about 16% higher than that when the scale deforms in a ductile manner. The rapid scale growth in the freshly exposed steel areas contributes signiﬁcantly to the scale thickness. Figure 2.8 illustrates the evolution of oxide scale thickness computed for three constant interfacial HTCs for the front end of the slab during roughing rolling. The average thickness of the oxide scale is reduced with an increase in the interfacial HTC.

19

140

IHTC 20 kW/m2 K 100 kW/m2 K 300 kW/m2 K

120 100

no rolling effect

80 60 40

scale deforming

20 0

20

40

60 80 Time (s)

100

Oxide scale thickness, (mm)

2 A Pivotal Role of Secondary Oxide Scale During Hot Rolling and for Subsequent Product Quality Oxide scale thickness (mm)

20

(a) 120

140

IHTC 20 kW/m2 K 100 kW/m2 K 300 kW/m2 K

120 100

no rolling effect

80 60 40

scale cracking

20 0

(b) 20

40

60 80 Time (s)

100

120

Figure 2.8 The secondary oxide scale thickness predicted for the front end of the slab during roughing rolling and the different interfacial heat transfer coefﬁcients assuming the scale deformation (a) and the scale cracking (b) model [42].

Temperature 26% Sliver 17%

Scale defects 30%

Scratches 27%

Related to descaling 26% Others Relatede to rolls 35% 21% Related to temperature 18%

Figure 2.9 Yield drop in the hot-rolled steel sheet. Note that about 30% of yield drops are related to the oxide scale [43].

It has to be noticed that the “scale deformation” model can principally be applied to low reduction hot rolling with very thin and hot scale layers. In many other rolling conditions, “plastic” deformation of the oxide scale is impossible. The surface temperature of the oxide scale, which is in contact with the cold roll surface, is low and the scale is brittle. As a result, a number of through-thickness cracks perpendicular to the rolling directions appear in the secondary scale, which would lead to the “scale cracking” model.

2.4 Secondary Scale-Related Defects

The scale-related defects on the product ﬁnish are chronic defects. They have a great impact on a hot-rolling operation. According to some observations made at Kimitsu Works, Nippon Steel Corporation and compiled by the Iron and Steel Institute of Japan, approximately 30% of yield drops can be related to the scale defects (Figure 2.9) [43].

2.4 Secondary Scale-Related Defects Table 2.2

Classiﬁcation of the main scale marks.

Defect

Reason

Explanation

Flaky scale

High temperature in ﬁnishing rolling

Originated from blistering and rolling-in of the secondary scale generated between stands

Sand-like scale

Roll surface degradation

Originated from satin-like roughening of the roll surface at the ﬁnishing stand and the rolled-in secondary scale

Meteor-like scale

Roll surface degradation

Originated from meteor-like roughening at the ﬁnishing stand and rolled-in secondary scale

Spindle-shaped scale

Imperfect descaling

Originated from imperfect descaling in roughing and localized rolling in of the remaining scale

Red scale

Silicon scale

Originated from imperfect descaling due to melting to above the eutectic point in the reheating furnace and wedge-like inclusions of fayalite into the underlying metal

Some changes in operational conditions can lead to the generation of different patterns on the surface of the product. The appearance of these new patterns causes confusion and demands for clariﬁcation and countermeasures. However, insufﬁcient understanding of defect generation mechanisms combined with some shortcomings in operating conditions and control factors results in the lack of necessary control in hot rolling operations. At present, there is no unanimous classiﬁcation of the product defects related to the presence, deformation, and failure of oxide scale during hot metal-forming operations. As an example of such an approach, classiﬁcation of the main scalerelated marks made on the basis of data compiled by the Iron and Steel Institute of Japan is presented in Table 2.2 [43]. It is difﬁcult to distinguish origins and mechanisms of the product defects that can be related directly to the secondary oxide scale. This is partly because degradation of the work rolls contributes to the formation of the defects. The roll material undergoes high surface temperature ﬂuctuations that induce deterioration of the roll work surface by fatigue and surface oxidation. The roll surface is very important for the surface quality of the rolled product. As has been shown [44–46], the roll surface progressively deteriorates during a production campaign. At the beginning, the oxide layer on the roll surface decreases by wear. In the course of the rolling campaign, small pits can be observed on the roll surface. The pit number progressively increases and there may be peeling around them, followed by the formation of “comet tails” that eventually leads to “banding” when 100–300 μm

21

2 A Pivotal Role of Secondary Oxide Scale During Hot Rolling and for Subsequent Product Quality Banding

Friction coefficent m

22

0.30 0.29 0.28 0.27 0.26 0.25 0.24 0.23 0.22 0.21 0.20

Roll oxidation Comet tails New oxide layer

Roll degradation 0

50

100 Strip number

150

200

Figure 2.10 Effect of roll evolution and the number of rolled strips on the friction coefﬁcient during hot rolling [44].

thick oxide scale can be removed from the roll surface together with some roll material. Pitting, thermal cracks, and peeling can also appear during the wear stage. However, these latter defects, in terms of the strip surface quality or friction, are not as signiﬁcant compared with the initiation of comet tails and banding. Figure 2.10 illustrates the inﬂuence of the roll surface evolution on the friction coefﬁcient. In different cases, the maximum of the friction coefﬁcient is reached with different strip numbers [44] but it is always reached as banding appears. “Streak coating” is a banded condition caused by nonuniform adherence of the roll coating to a work roll. It can be created during hot or cold rolling [47, 48]. If generated in the hot rolling process, it is also called “hot mill pick-up.” A streak on the sheet surface in the rolling direction can also be caused by transfer from the leveler rolls. This phenomenon is also quite common in aluminum hot rolling. The formation of secondary oxide scale can be considered as a useful phenomenon for its contribution as a thermal barrier between the hot strip and cold work roll during a rolling operation. However, the scale undergoes deformation and failure during the process. The scale fragments cannot always be fully removed by a descaling operation. Moreover, the residues can also be transferred to the roll surface then embedded into the surface layer of the strip under the pressure of the degraded work rolls. These events would lead toward so-called rolled-in-scale defects on the strip surface [49]. The embedding depth can reach 20 μm and can affect signiﬁcant areas of the strip surface (Figure 2.11). The oxide particles embedded into the metal surface can be removed during a subsequent descaling procedure but they leave a rough surface. Cold rolling can smooth out the surface again, if the roughness is not signiﬁcant. Otherwise the metal sheet will present surface depressions. Those particles that are not totally removed during the descaling operation and remain on the strip are particularly harmful in subsequent processing and use.

2.4 Secondary Scale-Related Defects Secondary scale

Degraded work roll

Scale/substrate interface perturbation a Work roll

Descaling residue

Secondary scale

Oxide incrustation b

Figure 2.11 Schematic representation of the printing effects due to degraded rolls (a) and descaling residues (b) [47].

Secondary scale

Crack

Oxide reformation

Work-roll

Oxide Crack opening embedding

Substrate extrusion

Work-roll

a

Oxide reformation

Secondary scale

Buckling

Oxide embedding

Substrate extrusion b

Figure 2.12 Schematic representation of the oxide scale embedding due to fragmentation (a) and buckling (b) at entry into the roll gap [47].

If the oxide scale is fragmented at the entry into the roll gap due to cooling or longitudinal tension, hot metal will extrude into the crack openings under the roll pressure (Figure 2.12a) changing the proﬁle of the metal surface after the rolling pass. If the oxide/scale interface is relatively week, it can lead to the local buckling followed by embedding into the metal surface (Figure 2.12b). According to Tominaga, some rolled-in scale defects can be inﬂuenced by growth stresses within the secondary scale [49]. Blistering can occur when the

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2 A Pivotal Role of Secondary Oxide Scale During Hot Rolling and for Subsequent Product Quality Between Stands

Entrance’ of Stand

Growing Secondary Scale

Growing Stress

Sticking Stress

Scale Growing Stress

Strip

Blistering

Growing Stress

Sticking Stress Blister

a

b

Roll Bite

Exit of Stand

Destruction and Stack of Scale

Scale Defect

Roll c

d

Figure 2.13 Schematic representation of the consecutive stages of scale defect formation due to blistering when the scale/metal interface is “weak” [49].

scale/metal interface is relatively week (Figure 2.13). In such cases, “growing stresses” can exceed “sticking stresses” and blisters can be developed. Then, the blisters are embedded into the surface layer of the metal during hot rolling, which would lead to the formation of scale-related defects. This mechanism is more pronounced for the rolling at high temperatures when the probability of blistering is high and that would occur during rough rolling rather then at the ﬁnishing stands because of the temperature differences (Figure 2.6). Oxide scale-related defects, in spite of having a signiﬁcant impact on metalforming operations, remain inadequately understood because of the complexity of physical events behind them. Insufﬁcient understanding of the defect formation mechanisms coupled with a limited capacity to monitor and control operating conditions has led to the situation when more research and technological solutions are needed.

References 1 Krzyzanowski, M., Beynon, J.H., and Sellars, C.M. (2000) Analysis of secondary oxide scale failure at entry into the roll gap. Metallurgical and Materials Transactions B, 31, 1483–1490. 2 Li, Y.H., and Sellars, C.M. (1996) Evaluation of interfacial heat transfer and friction conditions and their effects on hot forming process. Proceedings of

37th MWSP Conference, ISS, vol. 133, pp. 385–393. 3 Ball, J., Treverton, J.A., and Thornton, M.C. (1994) Evaluation of the effects of stresses in hot rolling mills on oxide ﬁlms on aluminium. Lubrication Engineering, 50, 89–93. 4 Krzyzanowski, M., and Beynon, J.H. (1999) The tensile failure of mild steel

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oxides under hot rolling conditions. Steel Research, 70, 22–27. Roberts, C.D. (1997) Mechanical principles of rolling. Iron and Steelmaker, 24, 113–114. Yuen, W.Y.D., Popelianski, Y., and Prouten, M. (1996) Variations of friction in the roll bite and their effects on cold strip rolling. Iron and Steelmaker, 23, 33–39. Lenard, J.G. (2002) An examination of the coefﬁcient of friction, in Metal Forming Science and Practice (ed. J.G. Lenard), Elsevier, Oxford, pp. 85–114. Roberts, W.L. (1983) Hot Rolling of Steel, Marcel Dekker, New York. Wusatowski, Z. (1969) Fundamentals of Rolling, Pergamon Press, Oxford. Rowe, G.W. (1977) Principles of Industrial Metalworking Processes, Edward Arnold, London. Felder, E. (1985) Interactions cylindremétal en laminage, rapport CESSID, Session Laminage, Centre de Mise en forme des Matériaux, Ecole des Mines de Paris. Munther, A., and Lenard, J.G. (1997) A study of friction during hot rolling of steels. Scandinavian Journal of Metallurgy, 26, 231–240. Li, Y.H., and Sellars, C.M. (1996) Modelling deformation behaviour of oxide scales and their effects on interfacial heat transfer and friction during hot steel rolling, in Proceedings of 2nd Int. Conf. on Modelling of Metal Rolling Processes (eds J.H. Beynon, P. Ingham, H. Teichert, and K. Waterson), The Institute of Materials, London, UK, pp. 192–206. El-Kalay, A.K.E.H.A., and Sparling, L.G.M. (1968) Factors affecting friction and their effect upon load, torque, and spread in hot ﬂat rolling. Journal of the Iron and Steel Institute, 206, 152–163. Ekelund, S. (1927) Några Dynamiska Förhållanden vid Valsning (Some Dynamic Relationships in Rolling), Jernkontorets Annalen, 111, 39–97. Fedorciuc-Onisa, C., and Farrugia, D.C.J. (2003) Simulation of frictional conditions during long product hot rolling, in Proceedings of the 6th

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ESAFORM Conference on Material Forming (ed. V. Brucato), Salermo, Italy, pp. 763–766. Fedorciuc-Onisa, C., and Farrugia, D.C.J. (2004) Through process characterisation of frictional conditions for long product hot rolling. Steel Grips, 2, 331–336. Liu, Q., Fedorciuc-Onisa, C., and Farrugia, D.C.J. (2006) Through process characterization of frictional conditions under lubrication for long product hot rolling. Proceedings of Steel Rolling 2006 – 9th International & 4th European Conferences, Paris, June 19–21, CD-Rom. Beynon, J.H. (1999) Modelling of friction and heat transfer during metal forming, in Proceedings of KomPlasTech’99 (eds A. Piela, F. Grosman, M. Pietrzyk, and J. Kusiak), 17–20 January, Szczyrk, Akapit, Krakow, pp. 47–54. Chen, B.K., Thomson, P.F., and Choi, S.K. (1992) Temperature distribution in the roll-gap during hot ﬂat rolling. Journal of Materials Processing Technology, 30, 115–130. Timothy, S.P., Yiu, H.L., Fine, J.M., and Ricks, R.A. (1991) Simulations of single pass of hot rolling deformation of aluminium alloy by plane strain compression. Materials Science and Technology, 7, 255–261. Semiatin, S.L., Collings, E.W., Wood, V.E., and Altan, T. (1987) Determination of the interface heat transfer coefﬁcient for non-isothermal bulk forming process. Journal of Engineering for Industry – Transactions of the ASME, 109, 49–57. Pietrzyk, M., and Lenard, J.G. (1989) A study of thermal mechanical modelling of hot ﬂat rolling. Journal of Materials Shaping Technology, 7, 117–126. Hlady, C.O., Samarasekera, I.V., Hawbolt, E.B., and Brimacombe, J.K. (1993) Heat transfer in the hot rolling of aluminium alloys, in Proceedings Int. Symp. on Light Metals Processing and Applications; 32nd Annual Conf. of Metallurgists (eds C. Bickert, R.A.L. Drew, and H. Mostaghaci), CIMM, Quebec City, PQ, Canada, pp. 511–522.

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2 A Pivotal Role of Secondary Oxide Scale During Hot Rolling and for Subsequent Product Quality 25 Hlady, C.O., Brimacombe, J.K., Samarasekera, I.V., and Hawbolt, E.B. (1995) Heat transfer in the hot rolling of metals. Metallurgical and Materials Transactions B, 26, 1019–1027. 26 Malinowski, Z., Lenard, J.G., and Davies, M.E. (1994) A study of heat transfer coefﬁcient as a function of temperature and pressure. Journal of Materials Processing Technology, 41, 125–142. 27 Pietrzyk, M., and Lenard, J.G. (1989) A study of boundary conditions in hot/cold ﬂat rolling, in Proceedings of the Int. Conf. Computational Plasticity: Models, Software and Applications (eds D.R.J. Owen, E. Hinton, and E. Onate), Pineridge Press, Wales, pp. 947–958. 28 Chen, W.C., Samarasekera, I.V., and Hawbolt, E.B. (1992) Characterisation of the thermal ﬁeld during rolling of microalloyed steels. Proceedings of the 33rd Mechanical Working and Steel Processing, Conf. Proc. XXIX, USA, Iron & Steel Soc., pp. 349–357. 29 Stevens, P.G., Ivens, K.P., and Harper, P. (1971) Increasing work-roll life by improved roll-cooling practice. Journal of the Iron and Steel Institute, 209, 1–11. 30 Murata, K., Morise, H., Mitsutsuka, M., Haito, H., Kumatsu, T., and Shida, S. (1984) Heat transfer between metals in contact and its application to protection of rolls. Transactions of Iron and Steel Institute of Japan, 24, B309. 31 Sellars, C.M. (1985) Computer modelling of hot working processes. Materials Science and Technology, 1, 325–332. 32 Samarasekera, I.V. (1990) The importance of characterizing heat transfer in the hot rolling of steel strip. Proceedings of the Int. Symp. on the Mathematical Modelling of the Hot Rolling of Steel, 29th Annual Conference of Metallurgists, CIMM, Hamilton, ON, Canada, 1990, Pergamon Press, New York, NY, pp. 145–167. 33 Wanheim, T., and Bay, N. (1976) A model for friction in metal forming processes. Annals of the CIRP, 27 (1), 189–194. 34 Devadas, C., Samarasekera, I.V., and Hawbolt, E.B. (1991) The thermal and

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metallurgical state of steel strip during hot rolling: part I. characterization of heat transfer. Metallurgical Transactions A, 22, 307–319. Chen, W.C., Samarasekera, I.V., and Hawbolt, E.B. (1993) Fundamental phenomena governing heat transfer during rolling. Metallurgical Transactions A, 24, 1307–1320. Cooper, M.G., Mikic, B.B., and Yovanovich, M.M. (1969) Thermal contact resistance. International Journal of Heat and Mass Transfer, 12, 279–300. Yovanovich, M.M., and Schneider, G.E. (1976) Thermal Constriction Resistance Due to A Circular Annular Contact, AIAA Paper 76-142, American Institute of Aeronautics and Astronautics, New York. Williamson, M., and Majumdar, A. (1992) Effect of surface deformations on contact conductance. Journal of Heat Transfer-Transactions of the ASME, 114, 802–810. Pullen, J., and Williamson, J.B.P. (1972) The contact of nominally ﬂat surfaces. Proceedings of the Royal Society London, A327, 159–173. Mikic, B.B. (1974) Thermal contact conductance: theoretical considerations. International Journal of Heat and Mass Transfer, 17, 205–214. Samsonov, G.V. (1973) The Oxide Handbook, IFI/Plenum, New York. Li, Y.H., and Sellars, C.M. (1997) Effect of scale deformation pattern and contact heat transfer on secondary oxide growth, Proceedings of the 2nd Int. Conf. on Hydraulic Descaling in Rolling Mills, October 13–14, 1997, Cavendish Conf. Centre, London, UK (ed. ), The Institute of Materials, London, pp. 1–4. Yoshida, K. (2005) Inﬂuence of scale properties on surface characteristics of steels, in The Iron and Steel Institute of Japan (ed.), pp. 3–4. Y. Kondo (English translation). Uijtdebroeks, H., Franssen, R., Sonck, G., and Van Schooten, A. (1998) On-line analysis of the work roll surface deterioration. La revue de métallurgie-CIT, 95 (6), 789–799. Uijtdebroeks, H., Franssen, R., Vanderschueren, D., and Philippe, P.M.

References (2002) Integrated on-line work roll surface observation at the SIDMAR HSM. Proceedings of the 44th MWSP Conf. Proc., Orlando, September 2002, Vol. XL, pp. 899–908. 46 Beverley, I., Uijtdebroeks, H., de Roo, J., Lanteri, V., and Philippe, J.M. (2001) Improving the Hot Rolling Process of Surface-Critical Steels by Improved and Prolonged Working Life of Work Rolls in the Finishing Mill Train, EUR 19871 EN, European Commission, Brussels.

47 Picqué, M.B. (2004) Experimental Study and Numerical Simulation of Iron Oxide Scales Mechnical Behaviour in Hot Rolling, PhD thesis, Ecole Des Mines De Paris, Paris, France. 48 Garcia-Villan, M. (1998) Défaut calamine ﬁnisseur, Raport de Stage Université de technologie de Compiègne/Sollac (USINOR). 49 Tominaga, K. (1995) Prevention of secondary scale defect at H.S.M in Mizushima Works. Camp ISIJ, 8, 1242–1247.

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3 Scale Growth and Formation of Subsurface Layers Oxide scale growth is a process that cannot be ignored in the high-temperature processing of metals. The typical conventional semicontinuous hot strip mill comprises a primary descaler, reheat furnace, a reversing roughing mill, a coil box or delay table, a secondary descaler, a multistand tandem ﬁnishing mill, and a down-coiler [1, 2]. A preheated slab is reduced in thickness considerably by the roughing mill to become a so-called transfer bar, which is then rolled in smaller increments to the ﬁnal strip thickness by the ﬁnishing mill. The strip surface temperature is in the range of 1000–1100 °C at entry to the ﬁnishing mill and within the range of 840–920 °C at the exit from the last ﬁnishing stand. The oxide scale on the transfer bar is removed by a hydraulic descaler as the strip passes through just in front of the ﬁnishing mill. After the descaling, oxide scale grows back and is deformed at each stand while the bar is progressively rolled through the ﬁnishing mill into a thin strip. The oxide scale continues to grow on the strip surface during cooling on the run-out table, primarily between the exit from the ﬁnishing mill and the start of water sprays. The time available for scale growth during and after ﬁnishing rolling is usually very short, normally less than 30 s. The strip temperature decreases during rolling, and the cooling rate can vary from strip to strip, and also along the length of the same strip. The scale thickness can reach 20–100 μm before entering the ﬁnishing mill and is reduced to 5–12 μm at the exit [2–4]. The typical scale structure at the time of coiling is three layered: a surface hematite (Fe2O3), an intermediate magnetite (Fe3O4), and an inner wüstite (FeO) layer [5]. The coiling temperature of the hot-rolled strip is within the range 500–740 °C. Once coiled, the strip cools slowly due to the relatively small surface area. Strip edges are usually slightly thinner (∼0.1 mm) than the inner parts of the strip, which allows better access of air to these regions. As a result of the oxygen supply, additional scale can form around the edges during coiling. The thickness of this scale increases with increasing coiling temperature and decreasing cooling rate [5, 6]. In particular, a thick hematite layer develops within 10–20 mm of the edges. The scale at the edges essentially consists of two layers, an outer hematite and an inner magnetite layer. The scale adheres well to the steel and no macro- or microseparations are visible under optical or scanning electron microscopes. This scale is difﬁcult to remove by the conventional pickling process. Oxide Scale Behaviour in High Temperature Metal Processing. Michal Krzyzanowski, John H. Beynon, and Didier C.J. Farrugia Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-32518-4

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3 Scale Growth and Formation of Subsurface Layers Hematite Fe2O3 Magnetite Fe3O4

Fe3O4 + Fe3O4 /Fe + FeO

Steel Figure 3.1 Schematic illustration of the oxide scale formed across the width of a hot-rolled strip (after [5]).

The scale structures developed at different locations across the width of a hotrolled strip are schematically illustrated in Figure 3.1 [5]. The ﬁnal structure depends on the coiling temperature. For strips coiled at lower temperatures, such as 500–520 °C, the scale structure at the edge regions is three layered, with an outer hematite layer, an intermediate magnetite layer, and an inner layer comprising a mixture of magnetite and iron. For strips coiled at 600 °C and above it becomes essentially a two-layered structure with an outer hematite layer and an inner magnetite layer. The wüstite layer, initially present in the scale, is largely oxidized to magnetite during cooling. The total scale thickness and the thickness of the hematite layer increased with coiling temperature. Further oxidation of the steel substrate at the strip-center regions can take place at the expense of the higher oxides because of the lack of an oxygen supply. The hematite layer is consumed ﬁrst, followed by the consumption of the magnetite layer during further oxidation. The wüstite layer is then transformed into a mixture of magnetite and iron due to proeutectoid and eutectoid reactions. Some wüstite can be retained until room temperature, particularly for strips coiled at high temperatures, such as 720–740 °C. The wüstite layer becomes more homogeneous through the scale thickness and relatively rich in iron during cooling from the high coiling temperatures. It is known that wüstite rich in iron is more stable than wüstite rich in oxygen. Therefore, a larger amount of wüstite can be retained to room temperature in the center regions. Metallic iron particles have also been observed on the surface of samples taken from the center regions of a strip [5]. There were several mechanisms proposed for this phenomenon. According to one, the metallic iron particles were formed by the reduction of the scale as a result of a reducing atmosphere between the strip wraps, in conjunction with both crack development within the scale and a small amount of steel surface decarburization. They may also be formed as part of the eutectoid reaction product, with the preferential precipitation of iron particles along the wüstite grain boundaries. The grain boundaries are usually the channel for fast solid phase diffusion and iron would prefer to diffuse along these channels, which would lead to iron enrichment at the wüstite grain boundaries. The enriched iron would precipitate prior to the onset of the Fe3O4–Fe eutectoid reaction at temperatures below 570 °C.

3 Scale Growth and Formation of Subsurface Layers

The typical mild steel secondary oxide scale is signiﬁcantly different from that observed on aluminum, and should be considered separately. The oxide formed on hot-rolled aluminum alloys is of considerable interest to the aluminum industry because of the effect of the ﬁne subsurface layers on product quality, such as subsequent ﬁliform corrosion resistance [7, 8]. The work rolls exert a normal load and a shear stress on the surface of the work piece, causing severe shear deformation of the near-surface region compared to the bulk microstructure during rolling. This results in the development of a surface layer, a few microns thick, which has different morphological, optical, microstructural, and electrochemical properties compared with the bulk. The surface layer can control many important properties such as corrosion resistance, adhesion, and optical appearance, and hence it is important to understand both its electrochemical behavior and microstructural details. High shear processing of aluminum alloys signiﬁcantly transforms the surface microstructure. Hot rolling is particularly effective due to asperity contact between the sheet surface and the work rolls under the boundary lubrication conditions that can prevail in the latter stages of the hot rolling operation. Subsequent cold rolling, under hydrodynamic lubrication, smears out and reduces the thickness of the transformed layers. Although the layers are characterized by an ultraﬁne grain size, it is not only this or the magnesium oxide that promotes surface reactivity and susceptibility to corrosion [9]. The main contributing factors to the electrochemical reactivity of the surface layer are differences in intermetallic particle distribution and solid solution content. The break-up of primary intermetallic particles can result in a higher density of cathodic sites in the surface layer. It has been concluded that the more signiﬁcant effect is the preferential nucleation and growth of dispersoids in the surface layers during heat treatment due to the inﬂuence of strain [10]. The presence of the ultraﬁne grained surface layers on the aluminum sheet after rolling is a relatively recent ﬁnding. However, the surface layers developed by sliding wear, grinding, or machining have been known for many years [11–13]. They were even believed to be amorphous metal. More recent studies have revealed the redistribution of the intermetallic particles in the deformed surface layer, and these particles were concluded to be the main controlling factor of the corrosion susceptibility. The dispersoid density depends on the level of manganese supersaturation in a solid solution. Although most of the available iron is already out of solid solution, the dispersoids are of the α-AlMnSi type. Preferential precipitation can be prevented by reduction of the level of manganese solid solution prior to hot rolling. The reduction of the manganese level in the alloy or a suitable homogenization treatment prior to hot rolling can be appropriate for this reason. It is important for continuously cast alloys where the levels of supersaturation are higher in the as-cast state and where there may be no formal homogenization step. This detrimental effect of manganese on ﬁliform corrosion resistance is distinct from the beneﬁcial effects of manganese in reducing the susceptibility to pitting corrosion [14]. High-temperature oxidation has been studied extensively, mainly for the cases of components for high-temperature service where oxide scales provide protection

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3 Scale Growth and Formation of Subsurface Layers

[15, 16]. The main deﬁnitions and obtained ﬁndings can also be applied to oxide scale formation under conditions relevant to hot metal processing.

3.1 High-Temperature Oxidation of Steel

According to the Fe–O equilibrium phase diagram, the following three kinds of oxides exist at temperatures higher than 570 °C: wüstite (FeO), magnetite (Fe3O4) and hematite (Fe2O3) [17]. However, the diagram represents only equilibrium conditions while, in hot working, circumstances can be greatly affected by kinetics. The typical morphology of the oxide scale formed on low-carbon steel at hot rolling temperatures is illustrated in Figure 3.2. Generally, three types of scale can be distinguished with low, middle, and high porosity [18]. The extent of porosity depends closely, but not exclusively, on the temperature at which the oxide scale was grown. Different types of the scale morphology have been observed, namely duplex or the one comprising three different layers of scale. The relative thickness of each layer varies. Typically, the inner layer has a large number of evenly distributed small pores. Iron oxidation consists mainly of the outward diffusion of iron ions and the inward diffusion of oxygen [19]. Such an inner layer is most

Figure 3.2 SEM photographs showing cross-sections of the oxide scale formed on mild steel: (a) different sublayers and voids; (b) relatively big void in the middle of the oxide scale.

3.1 High-Temperature Oxidation of Steel

probably formed due to inward transport of oxygen along grain boundaries. In contrast, the larger crystals of the outer layers are formed as a result of outward diffusion of metal cations through the oxide layer. As a result, large voids about 1 mm in length can develop, as shown in Figure 3.2b. It has been shown that the formation of wüstite and magnetite is controlled mainly by the outward diffusion of metal cations, while hematite is formed mainly due to the inward diffusion of oxygen [20]. The thickness ratios of hematite, magnetite, and wüstite layers at high temperatures can deviate depending on the oxidation conditions. However, the typical values are at about 1:4:95. The predominance of wüstite is due to the diffusion coefﬁcient of iron in wüstite is much higher than that in magnetite and the diffusion coefﬁcients of oxygen and iron in hematite are extremely small [21–26]. The relative thicknesses of the hematite and magnetite layers increase below 650 °C, but the wüstite layer is still the major component of the scale above 580 °C [27, 28]. At temperatures below 570 °C, wüstite is not stable and the scale becomes two layered with a thick inner magnetite and a relatively thin outer hematite layer. The scale structure may deviate from the above “classic” structure due to the separation of the scale from the iron substrate, resulting in lower oxidation rates and thicker magnetite and hematite layers [29]. Normally, the following three types of oxidation rates are observed in high temperature oxidation: parabolic, linear, and intermediate [30, 31]. Oxidation obeys a parabolic rate law when the rate controlling step is diffusion within the oxide. If the rate controlling step is either the metal surface or the phase boundary interface reaction, then the oxidation is described by a linear law. The logarithmic or exponential rate can represent the initial stages of oxidation or low-temperature rate. The presence of alloying elements in steel also signiﬁcantly modiﬁes the full range of oxides that might be possible at a particular temperature. Because of the presence of various alloying and impurity elements in steel, the oxidation behavior and the developed scale structure are more difﬁcult to interpret than simple iron oxidation. Carbon, for instance, can facilitate or hinder the transport of diffusing ions, thereby increasing or decreasing oxidation [32, 33]. Carbon diffuses to the scale/metal interface and reacts with iron oxide, evolving CO gas and creating gaps. In high carbon steels at high temperatures, through-thickness cracks can occur in the scale due to gas pressure in the gaps, allowing access to the core for air and, hence, increasing the oxidation rate. If there are no cracks formed in the scale, the stabilized gaps can hinder the outward diffusion of iron ions and decrease the oxidation rate. As has been summarized in a review on high-temperature oxidation, the main effect of alloying elements less noble than iron on the oxidation, such as aluminum, silicon, and chromium, is the formation of a protective layer at the scale/ metal interface enriched in alloying elements [34]. For such steels, the initial oxidation kinetics are parabolic and then deviate from the parabolic law as the protective layer, rich in alloying elements, is established. However, aluminum, as an alloying element, can increase the temperature of wüstite formation and thus can contribute toward oxidation resistance [35]. Among these three elements, silicon acts as the most protective element, and chromium the least. Nickel and copper are more

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34

3 Scale Growth and Formation of Subsurface Layers

noble elements than iron and should be rejected at the scale-base metal interface. In addition, the iron matrix of such alloys is selectively oxidized [36]. However, nickel, for instance, does not diffuse rapidly into the core since the diffusion coefﬁcient of nickel in iron is low. Instead, its concentration at the interface becomes higher than that in the bulk of the metal. For example, Fe–Ni alloy containing only 1.0 wt.% Ni and oxidized in oxygen at 1000 °C exhibited signiﬁcant nickel enrichment at the surface, about 70 wt.% [37]. The selective oxidation of iron and concentration of nickel in the thin surface layer result in interpenetration of the oxide scale and metal that produces an additional mechanical oxide–metal bond which increases the oxidation resistance. If the diffusion coefﬁcient of the alloying element is higher than the oxidation rate, the concentration of the element increases, mainly within the bulk rather than at the surface of the metal. However, some of these elements, for instance copper in the iron alloy containing 2 wt.% Cu, can concentrate at the surface promoting formation of the interlocked scales similar to those formed on nickel alloys [38]. Manganese can substitute for iron in wüstite and magnetite [39]. It has also been observed that manganese together with silicon can combine with iron oxide to develop iron-manganese-silicate in the oxide scale of the silicon killed steels [40]. Generally, the oxidation of carbon steels is slower than that of iron. The oxidation kinetics and scale structure exhibit signiﬁcant deviations from the classical oxidation kinetics and scale structure observed for pure iron. For instance, the scale thickness reaches a maximum at a temperature within the range 980–1060 °C during long-term oxidation (2 h, which is long in industrial terms). Thereafter, the scale thickness decreases with increasing oxidation temperature for the same time [41–43]. The effect is assigned to the loss of scale/steel adhesion coupled with blistering of the scale when the steel is oxidized at very high temperatures. It has been assumed that it is the formation of carbon monoxide (CO) or carbon dioxide (CO2) at the scale/metal interface that is responsible for the loss of adhesion between the scale and the steel substrate [44]. Other elements, such as silicon, manganese, and phosphorous, may also affect the oxidation rate and scale structure that develops. The microstructure of oxides has not been well described. The results of an application of electron backscattered diffraction (EBSD) to the detailed investigation of microstructure and microtexture of oxide scale formed on pure iron, low carbon, and Si steel have been reported relatively recently [45, 46]. Based on the Kikuchi diffraction patterns, image quality (IQ) maps coupled with orientation imaging maps (OIM) were analyzed to describe both the orientation and shape of grains forming in wüstite, magnetite, and hematite layers. Despite different texture and grain size of the metal substrate, wüstite exhibited a columnar cell structure with a nonrandom crystallographic texture with the scale growth direction being normal to the sample surface for all specimens. Magnetite was identiﬁed as a cubic cell-type microstructure having a 〈001〉//GD texture (GD stands for the growth direction of oxide normal to the sample surface) while hematite formed as a very thin wedge shape layer on the top of the oxide scale. At the interface between wüstite and pure iron, small granular-type grains of wüstite are observed

3.1 High-Temperature Oxidation of Steel

[010] FeO

111

Fe a

max 15.06 12.00 7.30 4.44 2.70 1.64 1.00 0.61 min 0.00

Initial stage

101

001 [010] b

c

111 max 24.52 19.00 10.54 5.85 3.25 1.80 1.00 0.55 min 0.00

Grain growth stage

50.00 µm = 50 steps 001

35

101

Figure 3.3 The IQ map and the GD inverse pole ﬁgures (IPFs) of the wüstite layer: (a) the microstructure of the initial stage and (b) the grain growth stage; (c) IPF at the initial stage and (d) at the growth stage [46].

(Figure 3.3) [46]. No crystallographic relationship between substrate texture and iron oxide texture was established in this research. It seems that the microstructure of oxide scale layers depends mainly on the content of alloying elements rather than microstructure of the substrate. For example, silicon has a strong effect on the microstructure of the oxide scale layer in high temperature oxidation. It allows the formation of a mixture of wüstite and fayalite (Fe3SiO4) on the substrate surface covered by the relatively thick hematite layer having a bamboo-type microstructure during oxidation of 2 wt.% Si steel at 950 °C. The same oxidation of steels containing 0.4 and 0.98 wt.% of Si allowed instead the formation of magnetite, wüstite, and the composite of wüstite and SiO2. The wüstite layer comprises columnar cells grown from the substrate, but the interface between wüstite and substrate shows a different, more complex structure. A thin layer of tiny grains at the wüstite/substrate interface is observed. Details of such microstructure can be revealed by the IQ maps but not by the secondary electron or backscattered image. These grains are wüstite, as analyzed by indexing Kikuchi patterns. They are roughly granular in shape with longer axes parallel to the substrate surface. No special orientation relationship has been observed between these grains and the substrate. It can be speculated that these wüstite grains are formed in the initial stage of high-temperature oxidation. Assuming that the growth rate for wüstite grains formed in the initial stage of

d

36

3 Scale Growth and Formation of Subsurface Layers Fe2O3

Fe2O3

Fe3O4

Figure 3.4

The IQ map of the magnetite/wüstite interface for pure iron [45].

oxidation is low, it can be concluded that iron diffusion at high temperatures through the initial oxide layer is very fast. The grains that formed ﬁrst are left alone. It is possible that carbon or other alloying elements may be concentrated at the interface. This is the case for both low-carbon and 0.4% Si steels. The silicon content is also high at the wüstite/metal interface. Based on the Kikuchi diffraction patterns, IQ and OIM maps also allow the observation of details of the microstructure at the interface between magnetite and wüstite following the high-temperature oxidation of iron [45]. The magnetite layer was observed to have a cubic cell structure (Figure 3.4). The hematite layer was located in the shape of a sharp edge. It was unexpected that hematite can be grown with a certain angle to the magnetite grains. It can be explained by some sort of stress relief at the interface. The origin of this stress is the difference of the thermal expansion coefﬁcient between magnetite and hematite. The formation of particular oxide phases depends on the conditions and the atmosphere used for oxidation.

3.2 Short-Time Oxidation of Steel

Most of the research results on the oxidation of steel discussed in the previous section were based on long-time oxidation. However, the time available for secondary and tertiary oxidation during the hot rolling of steel, that is, after primary and secondary descaling, is much less than that concerns classical oxidation studies. Details of steel oxidation under conditions that are more relevant to hot rolling are discussed next, based on studies related to oxidation at elevated temperatures within a very short time [47–50]. Two sweeping actions were observed when monitoring the surface morphology of low-carbon steel during oxidation within the ﬁrst 30 s at 880 °C and 1050 °C [48]. It was assumed that the two were the result of phase transformations. Wüstite was transformed to magnetite during the ﬁrst stage and the magnetite was transformed to hematite during the second. Another possibility was that the magnetite was transformed to pseudomagnetite (a slightly crystallographically distorted magnetite) during the ﬁrst sweeping action that was subsequently reduced back to wüstite during further growth following the formation of a ﬁnal stable magnetite during the second sweeping action. Another study

3.2 Short-Time Oxidation of Steel

Figure 3.5 Average thickness of the oxide scale grown on a steel sample during 60 s oxidation exposure at different temperatures [47].

found that a layer of wüstite formed on pure iron during short-time oxidation at 1200 °C [26]. The layer was smooth after 30 s of exposure then, after 210 s, it was transformed into a single-phase irregular wüstite. It has been concluded that during short-time oxidation, up to 480 s at a temperature within the range 950– 1150 °C, a single layer of wüstite invariably developed on ultralow-carbon steel in dry air [49, 50]. The results were supported by monitoring the oxide scale structure at different stages in a laboratory simulation of ﬁnishing rolling, cooling, and coiling of steel [51]. Using high-temperature X-ray diffraction, it was found that wüstite grows ﬁrst after secondary descaling, that is, during the start of tertiary scale formation. Magnetite is formed after a longer time. A series of experiments have been carried out to examine the oxidation of lowcarbon, low-silicon steel in ﬂowing air within 30–60 s in the hot rolling temperature range [47]. The observed oxidation kinetics are illustrated in Figure 3.5 and it was assumed that only wüstite formed within the oxide scale. It is just the target temperatures that are indicated in Figure 3.5 because there is a rapid increase in surface temperature within the ﬁrst few seconds once the oxidation reaction has started due to the sudden heat release. The temperature of the metal surface was registered by a thermocouple that was spot welded in the middle of the sample surface. The rapid increase in surface temperature was observed in all cases. The highest temperature reached was about 20–25 K above the target temperature. For shorter reaction durations (<12 s), the sample temperatures were all above the target within the reaction durations. But for longer durations, the sample temperature was ﬁrst raised to 20–25 K above the target, then lowered to about 20–25 K below and then quickly returned to close to the target temperatures. After holding at the required temperature, the sample was cooled sharply to room temperature at a preset rate by introducing into the furnace

37

3 Scale Growth and Formation of Subsurface Layers 1230 Target: 1180°C 0.75 mm thick steel

1210 Temperature (°C)

38

1190 1170 1150 1130

Switch from 1110 nitrogen to air flow 1090 6 sec

12 sec

18 sec

1070

42 sec

60 sec

30 sec

24 sec

1050 0

10

20

30

40

50

60

70

80

90

Time (s) Figure 3.6 Variation of the surface temperature of the sample taken from a 0.3-mm-thick cold-rolled steel strip during oxidation for different times. The dimensions of the sample were 90 mm in length and 27 mm in width [47].

signiﬁcant gas ﬂow through small holes arranged evenly on a circular inlet. A typical example of the measured surface temperature is presented in Figure 3.6. Parabolic plots of the weight-gain data obtained at different temperatures within the range 850–1180 °C are illustrated in Figure 3.7 [47]. The slightly positive deviation at the 12 s data point (Figures 3.7a and b) is the result of higher average surface temperature caused by the release of the heat of formation of the oxide. The authors used the following parabolic equation to describe the kinetics data at 850 °C:

( ) W A

2

= k pt + C

(3.1)

where (W/A) is the weight gain per unit area, t is the duration of isothermal holding at the target temperature, and C is a constant. This yields the parabolic rate constant for the early stage reaction at 850 °C of kp = 1.368 × 10−5 kg2 m−4 s−1. A rate constant derived from the data obtained for 300 to 1800 s oxidation at 850 °C is 30% below the rate constant derived from the data obtained within 60 s oxidation, that is, kp = 0.968 × 10−5 kg2 m−4 s−1. It is similar to that obtained by the same authors for longer term oxidation of the same steel at 850 °C, that is, kp = 1.023 × 10−5 kg2 m−4 s−1) [52]. The oxide scales formed at 850 °C on most of the samples are generally uniform and smooth, excluding the front surface of the sample which was oxidized for 6 s, which had a small center region at the lower part of the sample appearing slightly rougher than in the surrounding areas and on other samples. A thermocouple was spot-welded at the middle of the front sample surface for temperature measurement and control. The inserted thermocouple affected gas ﬂow on the side where the thermocouple was welded. The oxidation kinetics exhibited at the target temperature of 900 °C appeared to be initially parabolic, similar to those at 850 °C, but then slowed to approach a

3.2 Short-Time Oxidation of Steel

Figure 3.7 Parabolic plots of oxidation kinetics determined as the weight-gain data for the steel samples oxidized at 850 °C (a, b), 900 °C (c), 1000oC (d), 1100 °C (e), and 1180 °C [47].

linear rate law with a rate constant kp = 3.978 × 10−4 kg cm−2 s−1 at longer exposure times, such as 18–60 s. Nearly the entire front surface and at the bottom-center region of the back surface of the sample, oxidized for 6 s, had an appearance similar to the “rough”-scale patch observed on the front surface of the sample oxidized at 850 °C for the same time. The microstructures of these regions were also similar, exhibiting an undulating, or saw-tooth-like, topography. The oxide

39

40

3 Scale Growth and Formation of Subsurface Layers

scale surface became ﬂat and smooth after longer exposure time. Bubble-like blisters were also observed to start forming at an exposure time of 12 s on the back surface and at an exposure time of 24 s on the front surface of the sample. The formation of blisters appeared to change the reaction kinetics. The time when the blisters started to form coincided with the time when the oxidation rate started to deviate from seemingly parabolic to linear. The experimental samples were taken mostly from a 0.75-mm-thick cold-rolled steel strip. For comparison purposes, some experiments were conducted using samples taken from a 0.3-mm-thick cold-rolled steel strip. The oxidation kinetics at the target temperature of 1000 °C are close to the parabolic behavior apart from the initial 6 s, where oxidation rates of the thinner steel were consistently lower than those of the thicker one (Figure 3.7d). Linear regression of the kinetics data against Equation (3.1) yields the parabolic rate constant of 9.137 × 10−5 kg2 m−4 s−1 for the 0.75-mm-thick steel and 8.275 × 10−5 kg2 m−4 s−1 for the 0.3-mm-thick steel. The oxide scales were compact without blister formation, in either the smooth or rough areas. However, after oxidation for 30 s, some scale around the edge began to spall off after cooling to room temperature. It was also observed that, initially, the entire surface was nearly completely occupied by the rough scale. This roughscale region became smaller with longer exposure time and the rate of shrinking of this rough-scale region on the back surface appeared to be faster than that on the front. The patterns of shrinkage of the rough-scale areas were also different on the two surfaces. Similar kinetics patterns were observed for the two different steels at the target temperature of 1100 °C (Figure 3.7e). Many blisters were observed around the edges on the back side of the samples for both steels at an exposure time of 60 s. Linear kinetics were observed for oxidation at 1180 °C (Figure 3.7f). The rate constant changed at about 24 s from a more rapid initial rate to a slower stage. The linear rate constants are compared in Table 3.1. Both sides of the steel samples were occupied by the “rough”-scale area within the ﬁrst 24 s. For more than 30 s of exposure, the smooth-scale areas initially formed at the edge regions and spread gradually toward the center region on the front surface and more rapidly on the back surface. Many small blisters were seen to form in the smooth areas around the front edges and on nearly the entire surface of the back surface at an exposure duration of 60 s. Blisters were not observed at the rough-scale regions. Microscopic examination of the “rough”-scale areas revealed the undulating, saw-teeth like, pattern on the scale surface (Figure 3.8) [47]. The scale–steel interface was perfectly ﬂat. Some oxide grains appeared to grow faster than others, with the protruding grains appearing to be larger and sharper. The surface of the smooth scale area was ﬂat in its cross-sections. In the blister-free scales, the entire scale layers were occupied by wüstite with some magnetite precipitates in them regardless of whether the surface was “rough” or smooth, granular or ﬂat. Magnetite did not form a continuous layer in any of the observed adherent scales. The scale structure of the blistering area was different comprising primarily magnetite and some retained wüstite.

3.3 Scale Growth at Continuous Cooling Table 3.1

Oxidation rate constants obtained for the different target temperatures (after [47]).

Target temperature (°C)

850 (18–60 s) 900 1000 (0.75 mma) 1000 (0.3 mm) 1100 (0.75 mm) 1100 (0.3 mm) 1180 (0.75 mm) 1180 (0.75 mm) a

41

Short-term steel oxidation rate

Long-term iron oxidation rate

Linear rate (kg m−2 s−1)

Parabolic rate (kg2 m−4 s−1)

Parabolic rate (kg2 m−4 s−1)

– 3.98 × 10−4 –

1.37 × 10−5 –

1.44 × 10−5 2.95 × 10−5 1.05 × 10−4

–

8.28 × 10−5

2.28 × 10−3 2.21 × 10−3 2.76 × 10−3 2.10 × 10−3

9.14 × 10−5 (6–24 s) (6–30 s) (6–18 s) (30–60 s)

2.70 × 10−4 (24–42 s) 2.22 × 10−4 (24–42 s) – –

1.05 × 10−4 3.10 × 10−4 3.10 × 10−4 – –

The ﬁgure indicates the thickness of the sample.

3.3 Scale Growth at Continuous Cooling

Scale growth and its structure development have been investigated during continuous cooling of low-carbon steels from different temperatures at different cooling rates [2, 53]. Strip samples 1.5–2 mm thick were heated in pure nitrogen or reducing (5 vol.% H2 in N2) atmosphere to the start of cooling temperature, held at the target temperature to achieve uniform temperature distribution and then cooled to room temperature at rates ranging from 5 to 60 K/min in ambient air or in ﬂowing air. Fine blisters were observed on those samples cooled from 1150 °C and above; however, blister-free scales were observed on those samples cooled from 1050 °C and below. The average scale thickness on each sample was calculated from the weight gain of the sample, and plotted against the start of cooling temperature (Figure 3.9). The scale thickness on the low-silicon steel samples (0.006 wt.% Si) increases rapidly with the start of cooling temperature. Scales formed on thicker samples were thicker because of the lower cooling rates. A relatively high level of silicon (0.2 wt.% Si) in the steel reduced the scale thickness noticeably, particularly at higher temperatures. The formation of a fayalite (Fe2SiO4) layer at the interface was thought to be responsible for the thinner scale formation. It was found that the scale thickness increases with lower cooling rate. The scale structures were very similar, comprising a thin layer of hematite on the surface, a relatively thick intermediate magnetite layer, and a thick inner wüstite layer at cooling rates from 15 to 60 K/min. Magnetite precipitates were found in the wüstite layer for cooling rates of 10 to 60 K/min. A magnetite–iron eutectoid layer formed near the magnetite layer, while a wüstite layer containing magnetite precipitates was observed at the inner region when the cooling rate was reduced to 5 K/min.

42

3 Scale Growth and Formation of Subsurface Layers

Figure 3.8 SEM images of the oxide scale surface from different areas after the short-time oxidation: (a) “rough” scale from the sample oxidized at 1000 °C for 12 s; (b) “rough” scale from the sample oxidized at 1180 °C for 24 s; (c) transition area between “rough” and smooth scale from the sample oxidized at 1100 °C for 24 s; (d) transition area between “rough” and smooth scale from the sample oxidized at 1000 °C for 12 s; (e) smooth scale from the sample oxidized at 1180 °C for 24 s [47].

It is nearly impossible to suppress the formation of Fe3O4 precipitates inside the wüstite layer growing on iron during continuous cooling [54]. Even water quenching does not prevent the precipitation of Fe3O4 inside the wüstite at the oxidation temperature above 980 °C. The proeutectoid phase only formed at the region adjacent to the magnetite phase, where oxygen is supersaturated after oxidation upon

3.3 Scale Growth at Continuous Cooling

Figure 3.9

Scale growth on low-carbon steel strip under continuous cooling conditions [53].

cooling. No iron precipitates are observed at the region adjacent to the substrate, indicating that the very low iron-supersaturation level does not provide sufﬁcient driving force for iron precipitation. Any supersaturated iron would probably diffuse to the nearby substrate [55]. Decomposition of wüstite has been the subject of many studies [54, 56–58]. Most focused on the phase-transformation behavior of wüstite during isothermal holding and only a few considered the structures developed under continuous cooling conditions [59–62]. Different scale structures are observed for different combinations of start of cooling temperature and cooling rate under continuouscooling conditions. The structures range from those containing primarily retained wüstite with some proeutectoid precipitates as a result of rapid cooling, to those containing a mixture of magnetite and metallic iron as a result of very slow cooling. During continuous cooling, proeutectoid magnetite is formed at the beginning. The transformation starts at temperatures above 570 °C, and continues to grow, forming new precipitates at temperatures below 570 °C. This is followed by magnetite precipitation at the wüstite/steel interface, forming a magnetite seam. The ﬁnal transformation product is the lamellar magnetite–iron eutectoid. The amount of retained wüstite decreases with lower cooling rate. The authors categorized the scale structures into three types. Type I is the scale containing primarily retained wüstite and proeutectoid magnetite precipitates at the region near the magnetite layer. Type II scale contains magnetite precipitates near the magnetite layer and also near the substrate. Type III scale contains a mixture of magnetite precipitates in the region near the magnetite layer, magnetite precipitates adjacent to the substrate, iron–magnetite eutectoid, and retained wüstite. The conditions for the formation of various scale types are illustrated in Figure 3.10 [59].

43

3 Scale Growth and Formation of Subsurface Layers 900

Simulated Coiling Temperature (°C)

44

800 Type I 700 Type II 600

Type III

500 Type I 400

Type I-II Type II

300

Type II-III Type III

200 100 1

2

5 20 10 Strip Cooling Rate (K/min)

60

100

Figure 3.10 Schematic diagram illustrating the conditions for the formation of different scale types depending on the cooling temperature and cooling rate [59].

Fe2O3 Fe3O4 FeO+Fe3O4 precipitates

Fe3O4 seam Steel substrate 10 µm Figure 3.11

The typical structure of type II scale formed during continuous cooling [59].

The microstructure of the type II oxide scale is shown in Figure 3.11. As has been mentioned, a magnetite seam is formed at the wüstite/iron interface just before the onset of the 4FeO → Fe3O4 + Fe eutectoid reaction. High cooling rates can suppress the formation of this layer (Figure 3.10). Various mechanisms have been proposed to explain the formation of the magnetite seam [59, 63, 64].

3.4 Plastic Deformation of Oxide Scales

3.4 Plastic Deformation of Oxide Scales

The effects that oxide scale produces during rolling depend on both the properties of the scale itself and the properties of the scale metal interface. It has been pointed out that the scale can damage the surface of steel when the rolling conditions make it hard and brittle [65]. The conditions that affect the deformation and fracture behavior of oxide layers have been analyzed, pointing to elastic and plastic properties, adhesion and toughness [15, 66]. Various authors have conducted compression [26, 67] or tension tests [18, 68, 69] on oxidized samples with scales comprising mainly wüstite that were able to sustain high amounts of plastic deformation before breaking. Other authors [65, 70–74] have carried out hot rolling tests with a wide variety of scale thickness. The conclusions drawn from these works seem to indicate that thin scale layers behave plastically at high temperatures when the deformation is limited to low reductions. Results of high-temperature tests conducted on ultralow carbon steel in plane strain compression have been reported [75]. The tests were conducted in a chamber that was designed to control the oxidation, allowing obtaining scales having different thicknesses. Measurement of the oxide scale thickness clearly exhibited plastic behavior of the scale. The thickness of the oxide layer as a function of the reduction in height of the sample, assuming an initial thickness of 20 μm, is illustrated in Figure 3.12. The dashed line corresponds to equal deformation in steel and the oxide layer. These results are in agreement with observations made by other authors, as can be seen in Figure 3.13 where the reduction in the oxide scale height measured by optical means is plotted together with similar results obtained by other authors

Final scale thickness (µm)

20

15

10

5

0

0

20

40 60 Specimen reduction (%)

80

Figure 3.12 Change of the thickness of the oxide scale as a function of reduction in plane strain compression testing [75].

45

3 Scale Growth and Formation of Subsurface Layers 80

60 Scale reduction (%)

46

40

20 Temperature (°C) 950 1050 This work Filatov et al. 0

0

20 40 60 Specimen reduction (%)

80

Figure 3.13 Reduction of the oxide scale and the underlying steel sample after plane strain compression at high temperatures [75]; data from [74, 75] are plotted together for comparison.

for the temperature range 950–1050 °C. The high plasticity exhibited by the oxide scale can be explained assuming ductile behavior of its main constituent, wüstite. It has been shown that wüstite is able to sustain high values of strain [18, 26, 67–69]. The behavior of the scale layer at temperatures ranging from 650 °C to 1050 °C can be characterized as brittle, mixed, or ductile, based on its integrity (Figure 3.14). The oxide scale exhibits ductile behavior when it is deformed at temperatures above 900 °C, although the ductility range can be extended by limiting the amount of deformation [75]. These observations are of interest for hot rolling of steel strip in continuous mills. Normally, the reduction applied in the ﬁrst stands at temperatures above 950 °C is more than 40%, whereas in the last stands, the reduction is limited due to load or shape constraints. Relatively few reports exist that describe the mechanical behavior of oxide scale on steels at high temperatures. However, such information on the deformation behavior of different types of oxides on steels is needed by the rolling industry, as well as data on scale adhesion and oxide fracture toughness. A quantitative knowledge of the mechanical properties of oxide scales at rolling temperatures can provide a signiﬁcant improvement of sheet quality. The mechanical properties of oxide scales formed on mild steel were investigated in four-point-bend tests at 800, 900, and 1000 °C in dry air, humid air (7–19.5 vol.% H2O), and laboratory air at different deformation rates [76]. Deformation curves for metal/oxide composites have obtained by bend tests of oxidized specimens with different scale-thickness values, which were achieved by preoxidation in the testing machine. After mechan-

3.4 Plastic Deformation of Oxide Scales 80 B M O

Krzyzanowski et al. Filatov et al. Suárez et al.

Reduction (%)

60

40

20 Brittle

0 500

600

Mixed

Ductile

700 800 900 Temperature (°C)

1000

1100

Figure 3.14 Plastic behavior of the oxide scale as a function of temperature and reduction [75]; data from [18, 74, 75] are plotted together for comparison.

ical testing the scale/substrate thickness values were measured by optical microscopy. Depending on the remaining metal thickness, the change of load resulting only from the deformation of the steel substrate was calculated for the oxidized specimens. The rate of load change due to the deformation of the oxide scale was calculated by subtracting the steel–substrate curve from the original curve of the oxidized specimen. Numerical analysis based on the ﬁnite element method supported the experimental technique in order to assess the strain in the cross section of the specimen. The four-point-bend tests were conducted in oxidizing atmospheres with different water-vapor contents and in a nonoxidizing atmosphere (argon with a titanium-getter) with two displacement rates of 0.5 mm/min and 5.0 mm/min, corresponding to strain rates in the oxide of 2.4–5.2 × 10−5 s−1 and 2.4–5.3 × 10−4 s−1, respectively. A very thin oxide scale, less than 2 μm, had formed on the surface of the specimens even under the “nonoxidizing” environmental conditions. Longer preoxidation times led to higher oxide-thickness values and higher loads. Figure 3.15 shows typical experimentally obtained load–displacement curves. The load corresponding to the deformation of the underlying metal was calculated on the basis of the cross-section ratios measured by optical microscopy. Subtracting this curve from the measured one led to the load-displacement curve of the oxide scale. As can be seen, the oxide scale exhibits plastic deformation at this high temperature. The maximum load due to the deformation of the oxide scale was calculated to be around 20 N. The stress–displacement curves calculated for the metal and for the oxide scale are illustrated in Figure 3.16. The stress levels are similar, but the oxide scale shows a lower slope in the elastic range, that is, an apparently lower elastic

47

48

3 Scale Growth and Formation of Subsurface Layers

Figure 3.15 Load–displacement curves for the oxide scale and the underlying metal at 900 °C, the dew point (DP) of 40 °C and the displacement rate 5 mm/min [76].

Figure 3.16 Stress–displacement curves calculated for the oxide scale and the underlying metal at 900 °C, the dew point (DP) of 40 °C and the displacement rate 5 mm/min [76].

modulus than the metal. The load–displacement curve obtained at 1000 °C is shown in Figure 3.17. It has to be noticed that a reduction of the deformation rate and the higher temperature led to a lower load of the composite and the difference in load between the oxide and the underlying metal was lower due to the higher oxide/metal thickness ratio. The stress–displacement curves calculated for this temperature are shown in Figure 3.18. It can be seen that the maximum stress in the oxide scale of 17 N is nearly twice lower than in the case of 900 °C despite the deformation rate being 10 times higher during the measurement. An increase in the average oxide stress values with decreasing temperature has been obtained for all the measured values of the maximum oxide stress

3.4 Plastic Deformation of Oxide Scales

Figure 3.17 Load–displacement curves for the oxide scale and the remaining metal at 1000 °C, the dew point (DP) of 40 °C and the displacement rate 0.5 mm/min [76].

Figure 3.18 Stress–displacement curves calculated for the oxide scale and the remaining metal at 1000 °C, the dew point (DP) 40 °C and the displacement rate 0.5 mm/min [76].

(Figure 3.19). The stresses measured for the higher deformation rate are more than that in the case of the slow deformation rate at the same temperature for all these cases. Varying the water-vapor content or the scale thickness did not appear to lead to any systematic change in the mechanical behavior of the oxide scale. It has been shown by the same authors that decreasing the strain rate by a factor of 9–10 was followed by a decrease in the average oxide ﬂow stress by 20–35% (Figure 3.20). As a ﬁnal stage of the research [76], the normalized shear stresses (σs/μ, where μ is the elastic shear modulus) were calculated from the measured average oxide stresses using the following equations and inserted into the deformation

49

50

3 Scale Growth and Formation of Subsurface Layers

Figure 3.19 The average oxide scale ﬂow stress obtained for different oxide scale thicknesses, temperatures, deformation rates, and water-vapor contents [76].

Figure 3.20

The average oxide scale ﬂow stress obtained for different strain rates [76].

mechanism map for wüstite created by Frost and Ashby [77] assuming that FeO forms the largest part of the oxide scale (Figure 3.21):

γ = ε × 3

(3.2)

σs = σ

(3.3)

3

⎛ T − 300 TM dμ ⎞ μ = μ0 × ⎜ 1 + × ⎟ ⎝ TM μ0dT ⎠

(3.4)

80 0

50 0

DYNAMIC RECRYSTALLISATION

10–4

7 × 10–5 1/s

POWER LAW CREEP

40 0

Shear strain rate

(s–1)

7 × 10–4 1/s

TEMPERATURE (°C)

60 0

10–2

x - 0.05 d - 10 µm • ILSCHNER ET AL (1964)

90 0

WUSTITE Fe1-xO

10 00

1

SHEAR STRESS AT 20°C (MN/m2) 10 100 0 0 11 13 00 12 00

1

70 0

3.4 Plastic Deformation of Oxide Scales

LATTICE DIFFUSION

LATTICE DIFFUSION

10–6

30 0

DIFFUSION FLOW

–8

10

BOUNDARY DIFFUSION

10–10 10–5

3×10–5

10–4 3×10–4 10–3 Normalised shear stress

3×10–3

PLASTICITY

CORE DIFFUSION

10–2

T = 1000°C T = 900°C

Data from the present project

T = 800°C Figure 3.21 Schematic diagram illustrating the ﬂow stress dependence on temperature for Fe1−xO. The data from [76] are superimposed on to the diagram from [77].

where σ and ε are, respectively, the measured average oxide stress and strain rate; σs and γ are, respectively, the shear stress and the shear strain rate; μ and μo are the shear moduli; and T is the temperature. The shear moduli were calculated using the following:

μFeO, 1273 K = 4.58 × 10 4 MPa μFeO, 1173 K = 4.68 × 10 4 MPa

(3.5)

μFeO, 1073 K = 4.78 × 10 4 MPa The measured results are in relatively good agreement with the original map data in spite of the map corresponding to one particular grain size and atomic disorder for wüstite, while the investigated oxide scales were a combination of FeO, Fe3O4,

51

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3 Scale Growth and Formation of Subsurface Layers

and Fe2O3. It was therefore concluded that an extrapolation to higher deformation rates corresponding to the hot-rolling process along the lines deﬁned by the map data is plausible. The deformation behavior discussed above was related mainly to the primary oxide scale. An interesting observation has been made by other authors comparing the deformation behavior of primary and secondary oxide scales during hot rolling [78]. The primary scale deformed by 26% when the steel sample reduction was only 16%. When the sample was deformed by 34% the primary oxide scale was subjected to 57% reduction. The scale thus exhibited plastic behavior and was deformed more than the underlying steel sample. These rolling tests were carried out at approximately 1000 °C. After rolling, the samples were transferred into a cooling box with a nitrogen atmosphere with a ﬂow rate of 20 l/min. The other tests were carried out on the samples where the primary oxide scale was manually removed by tapping and the secondary scale allowed to grow. The samples were heated for 145–160 min before the removal of the primary scale. The secondary scale thickness was about 30 μm and the X-ray diffraction tests revealed that there were three components in the secondary oxide layer: hematite, magnetite, and wüstite. Magnetite exhibited its strongest presence at diffraction angles, 2θ, of 30.1, 35.5, 57.1, and 62.6°. However, hematite revealed its signiﬁcant presence at 33.1, 35.7, 49.5, and 54.2° even though it was shadowed by magnetite (Figure 3.22). The interface between the secondary scale and the substrate became rougher than for the primary scale and after bulk reduction of the sample by 16%, the scale thickness was reduced from 29.5 to 24 and 24.2 μm at the rolling speeds of 0.24 and 0.72 m/s, respectively. In other words, 16% bulk reduction resulted in the secondary scale thickness reduction of about 14% and the rolling speed did not have a measurable effect on the secondary scale thickness (Figures 3.23 and 3.24).

Figure 3.22 steel [78].

X-ray diffraction results for the secondary oxide scale grown on a low-carbon

3.4 Plastic Deformation of Oxide Scales

Figure 3.23 Effect of the rolling reduction on the thickness of the primary and secondary oxide scales [78].

Figure 3.24 scales [78].

Effect of the rolling speed on the thickness of the primary and secondary oxide

As can be seen from Figure 3.23, the bulk reduction does not have a signiﬁcant effect on the thickness of the secondary oxide scale. This can be explained by the total scale thickness being so small that the difference in the scale thickness caused by the deformation could be well compensated by oxidation while the sample was delivered to the cooling box. The results of the tests have also revealed that the

53

54

3 Scale Growth and Formation of Subsurface Layers

Figure 3.25

Effect of the rolling reduction on the surface roughness [78].

holding time of the samples signiﬁcantly affects the secondary scale thickness. The thickness of the scale grown during 55 to 70 min heating time (Figure 3.23) was less than half the value for the scales that were produced in 145–160 min (Figure 3.24). This shows that the thermal history of the steel in the reheating furnace affects the oxide scale thickness even after descaling. The behavior of the oxide scale during hot rolling is reﬂected in the change of the surface roughness of the rolled product. The results presented in Figure 3.25 show that the bulk deformation signiﬁcantly affects the surface ﬁnish of the oxidized sample surface [78]. It has been found that the surface roughness decreases when the oxide scale is thick and the bulk deformation increases. Initially, for a steel surface with primary oxide scale, the surface roughness increased with reductions up to 16%. A signiﬁcant decrease was then observed with the further reduction. The surface roughness of the descaled surfaces decreased when the reduction increased from 8 to 25%. However, the decrease is diminished with a further increase of the deformation. As can be seen in Figure 3.25, the ability of the reduction to improve, that is, reduce, the surface roughness is limited for the thin oxide scale. The tests have also revealed that the effect of the rolling speed on the surface roughness is more complex. The roughness of both the descaled and nondescaled surfaces increased with the rolling speed for the case of 55–70 min heating. At the same time, it was decreased with increasing rolling speed when the sample heating time was 145–160 min. The following study clearly showed that both γ-Fe3O4 above 800 °C and FeO above 700 °C are capable of plastic deformation while plastic ﬂow was not discernible for α-Fe2O3 [69]. Two types of plasticity were observed during the study. For type I plasticity, typical for γ-Fe3O4 at 800–1100 °C, the stress increased with increasing strain; this type of plasticity was classiﬁed as work hardening. Type II

3.4 Plastic Deformation of Oxide Scales

plasticity was classiﬁed as steady-state deformation and was observed for FeO at 1000–1200 °C. The mechanism of type I plasticity for oxides is explained as dislocation glide or grain boundary sliding [79]. The γ-Fe3O4 specimen that showed type I plasticity was investigated and its dislocations were examined by transmission electron microscopy (TEM) after extending in tension by up to 50% at a strain rate of 2.0 × 10−4 s−1 at 1000 °C. Burgers vectors of two representative dislocations were investigated by varying the reﬂection vector (g vector) of the incident electron beam for determination of the slip system in the oxide. As can be seen from Figure 3.26, g vectors for disappearing dislocations are g 1 = [111 ] and g 2 = [ 022 ] . The Burgers vector of dislocation A was determined to be [111 ] from the following equations: g 1 ⋅ bA = 1 ⋅ hA + ( −1) ⋅ k A + ( −1) ⋅ l A = 0 g 2 ⋅ bA = 0 ⋅ hA + ( −2) ⋅ k A + ( −2) ⋅ l A = 0

(3.6)

where bA = (hA kA lA) is the Burgers vector of the dislocation A. The Burgers vector of dislocation B, [011], was determined in a similar way from the following equation: g 3 ⋅ bb = 0 ⋅ hB + ( −2) ⋅ kB + 2 ⋅ lB = 0

(3.7)

g 4 ⋅ bB = 1 ⋅ hB + ( −1) ⋅ kB + 1 ⋅ lB = 0 The crystalline structure of γ-Fe3O4 is spinel, that is basically FCC, and the most probable closed-packed plane for the dislocation gliding is considered {111}. The primary slip system of γ-Fe3O4 oxide is believed to be {111} 110 and type I plasticity observed for this oxide is believed due to the dislocation glide presumably along the above slip plane. The same main slip system is considered also for FeO oxide at high temperatures [79, 80]. Dislocation glide is much easier for cubic-type crystals, such as γ-Fe3O4 and FeO, than for other crystal systems, such as α-Fe2O3. The lattice constant can also inﬂuence the dislocation mobility. The smallest lattice constant of 0.43 nm is for FeO oxide compared with both 0.84 nm for γ-Fe3O4 and a = 0.50 nm (c = 1.37 nm) for α-Fe2O3 oxides. The dislocation is more mobile for smaller lattice constants because of the Peierls stress. Hence, the presence of type I plasticity in the oxides at high temperatures can be explained by the crystalline structure and the lattice constant. For FeO tested above 1000 °C, and for γ-Fe3O4 tested at 1200 °C, steady-state deformation, that is, type II plasticity, has been observed [79]. Generally, the mechanism for type II plasticity in the oxide scale is due to either dislocation climb (dislocation creep) or diffusion creep (Nabarro–Herring creep, Coble creep) [79, 81]. According to the Ashby map [82], the steady-state deformation of FeO corresponds to the regime of dislocation climb where the strain rate is expressed by the following equation:

ε = A ×

( μ)

D ⎛σ⎞ ×⎜ ⎟ kT ⎝ μ ⎠

n

(3.8)

55

56

3 Scale Growth and Formation of Subsurface Layers

Figure 3.26 Determination of burgers vector in γ-Fe3O4 crystal after the tensile test of up to 50% strain at 2.0 × 10−4 s−1 and 1000 °C [69].

where A is a material constant, D is the effective diffusion coefﬁcient, μ is the shear modulus, k is the Boltzmann constant, T is the absolute temperature, σ is the stress, and n is the stress exponent. The stress exponents are within the range of 3 to 4 for plastic deformation due to dislocation climb [81]. At the same time, the stress component value of 4 has

Saturated Stress (MPa)

3.5 Formation and Structure of the Subsurface Layer in Aluminum Rolling

10–1 1000 °C

1200 °C 1 10–5

10–4 10–3 Strain Rate (s–1)

10–2

Figure 3.27 Saturated stress of the FeO oxide scale measured for a range of strain rates at 1000 and 1200 °C [69].

been reported elsewhere [69, 83] favoring the conclusion that the type II plasticity observed for FeO is dominated primarily by dislocation climb. Type II steady-state plasticity by dislocation climb was observed for FeO tested with strain rate varying between 6.7 × 10−5 s−1 and 2.0 × 10−3 s−1 at 1000 °C and 1200 °C (Figure 3.27). The diffusion of point defects is important for this type of deformation since dislocation climb is assisted by the ﬂow of point defects into dislocations. The diffusion coefﬁcients for the three types of oxide, FeO, γ-Fe3O4, and α-Fe2O3, at 1000 °C are 9 × 10−8, 2 × 10−9, and 2 × 10−15 cm2 s−1, respectively [69]. Thus the ﬂow of point defects facilitates dislocation climb for FeO, enabling the steady-state deformation at 1000 °C, since the diffusion coefﬁcient of FeO is the largest among the three oxides. This type of deformation was not observed for γ-Fe3O4 tested below 1100 °C. The contribution of the diffusion of point defects to dislocation climb is much less for this oxide than for FeO. The authors hence concluded that dislocation climb cannot support plastic ﬂow sufﬁciently, and hence dislocation glide can be considered as dominating for γ-Fe3O4 deformed below 1100 °C.

3.5 Formation and Structure of the Subsurface Layer in Aluminum Rolling

The formation of the surface and subsurface layers in the hot rolling of aluminum ﬂat products depends on a range of factors, particularly on the tribological conditions at the roll/stock interface. A highly deformed subsurface layer of the stock is produced by high shear during hot rolling due to the asperity contact between stock and work rolls [9]. It is believed that the friction conditions between roll and workpiece, such as position of the neutral zone, roughness of the rolls, and roll speed, are extremely important for the ﬁnal structure and thickness of the

57

58

3 Scale Growth and Formation of Subsurface Layers Metal grains (0.04–0.2 µm in size) Continuous oxide layer

Oxide particies (2.5–50 nm in size)

A

B

Boundary between the subsurface layer and the bulk

Volds

Bulk matal grains Inclusions

Figure 3.28 Schematic representation of the surface layer of a hot-rolled aluminum alloy including microcrystalline oxides mixed with ﬁne grained material and a continuous

surface thin oxide layer. A is the thickness of the continuous oxide layer, 25–160 nm, and B is the thickness of the mixed subsurface layer, 1.5–8 μm [84].

subsurface layers and the subsequent effect on ﬁliform corrosion.1) It is interesting that similar layers induced by cold rolling do not enhance ﬁliform corrosion rates to the same extent as by hot rolling. According to Fishkis and Lin [84], the surface region of a hot-rolled aluminum alloy is characterized by a surface layer of continuous oxide 25–160 nm thick, and a subsurface layer of about 1.5–8 μm thickness (Figure 3.28). The subsurface layer is complex and consists mainly of ﬁne grained metal with a grain boundaries pinned by small (about 3–30 nm) crystalline and amorphous oxides. The type and properties of the oxides depend on the stage of the process. MgO, γ-Al2O3, MgAl2O4 and amorphous Al2O3 were observed at the start of the process, while only MgO was found at the end. Grain growth in this subsurface layer was retarded by Zener pinning by the small oxide particles. It has been noticed that the presence of a highly magnesium-enriched surface oxide, formed during high-temperature heat treatment, did not signiﬁcantly inﬂuence the loss of ﬁliform corrosion resistance for alloys with a composition based on alloy AA3005 [85]. It was concluded that the most signiﬁcant microstructural feature inﬂuencing ﬁliform corrosion suscep1) Filiform corrosion is a thread-like form of corrosion that occurs under organic coatings on ﬁnished aluminium products.

3.5 Formation and Structure of the Subsurface Layer in Aluminum Rolling

59

5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0

Mg Remainder AI

Fe Mn Cr

0

0.5 1 1.5 2 2.5 Depth below surface (µm) a)

Amount (wt%)

Amount (wt%)

tibility is redistribution of intermetallic particles in the subsurface layer. The redistribution led to ﬁner intermetallic particles with an associated increase in density compared with the initial state. The evolution of the microstructure and the chemical distribution in the heavily deformed subsurface layers is subject to current research. There arise many difﬁculties in performing this investigation on industrial material, such as obtaining samples at various positions along the process route and lack of knowledge of key variables such as roll roughness, state of lubrication, and the degree of material transfer from the stock to the roll. The importance of high subsurface shear induced by the rolling process has been highlighted [9]. At the same time, the relative importance of the microstructure and of the second phase particle volume fraction and size distribution is difﬁcult to assess. Other authors emphasize the importance of intermetallic precipitation arising from the enhanced Mg levels near the surface [7, 85]. Laboratory simulations of the industrial reheating and breakdown rolling of the Al–Mg–Mn aluminum alloy AA3104 allowed for both characterization of the stock surfaces and subsurface layers and production of the specimens with surface features, microstructure of the subsurface layers and susceptibility to ﬁliform corrosion that were similar to industrially prepared metal [86]. The general appearance of the distribution of selected elements at the surface of the industrially rolled transfer bar, obtained using glow discharge optical emission spectrometry (GDOES), is similar to that obtained for the laboratory rolled samples (Figures 3.29a and b). The microstructure of the subsurface layer of the industrially rolled material exhibited the same features as those produced in the laboratory rolled sample (Figures 3.30a and b). A ﬁne-grained structure with grain boundaries pinned by small oxide particles is characteristic for both cases. The depths of the subsurface layers were approximately 2 μm for the industrially rolled material and 3 μm for the laboratory specimen, and both revealed a sharp interface with the substrate.

3

5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0

Mg Remainder AI

Fe Mn Cr

0

0.5 1 1.5 2 2.5 Depth below surface (µm) b)

Figure 3.29 Metallic element distribution as a weight percentage of the total metal content in the subsurface layer obtained for the industrially rolled transfer bar (a) and for a laboratory rolled sample of the aluminum alloy AA3104 [87].

3

60

3 Scale Growth and Formation of Subsurface Layers

Figure 3.30 The focused ion beam (FIB) image of the subsurface layer of the industrially rolled transfer bar (a) and the laboratory rolled sample (tilt angle 63o) (b) of the aluminum alloy AA3104 [86].

Rolling dircction (a)

(b)

Figure 3.31 Morphologies of ﬁliform corrosion ﬁlaments on the rolled surfaces of painted aluminum AA3104 specimens: (a) industrially rolled transfer bar; (b) laboratory rolled material [86].

In both industrial and laboratory rolled materials, the depth of raised magnesium content correlated well with the observed thickness of the subsurface particle layer in each case. The morphologies of the ﬁliform corrosion ﬁlaments on the rolled surfaces of samples taken from the industrially rolled and laboratory rolled specimens are shown in Figures 3.31a and b, respectively. The direction of subsequent ﬁliform growth tended to be parallel to the rolling direction in both cases.

3.5 Formation and Structure of the Subsurface Layer in Aluminum Rolling 40

Mg (Wt%)

30

Reheated only

20

Reheated and laboratory rolled

10 0

0

1

2

3

Depth (µm)

Figure 3.32 Distribution of magnesium at the surface of aluminum alloy AA3104 following laboratory processing [86].

It can be seen that the ﬁliform corrosion susceptibilities of the rolled surfaces for both cases are also similar. The main success of this work is that it provides a methodology for the production of laboratory rolled surfaces with characteristics similar to those seen in industrially hot-rolled aluminum. The simulation of the industrial breakdown rolling can act as a basis for further investigations of the evolution of the subsurface layer. Examination of the processed samples using GDOES revealed that reheating induced signiﬁcant Mg enrichment in the surface and near surface regions and that Mg diffusion and oxidation continued throughout the reheating. The rate of oxidation decreased with time during the reheating process. As can be seen in Figure 3.32, the level of Mg in the near-surface regions of the rolled specimen was an order of magnitude less than that observed in the reheated specimens (it peaked at about 40 wt.%, ignoring the presence of oxygen). This redistribution of Mg is partly responsible for the formation of the subsurface layers, since Mg reacts with the oxygen to produce MgO and MgAl2O4 particles that provide the Zener pinning, stabilizing the ﬁne-grained surface structures. The scale of the subgrains in the laboratory specimens (about 50–350 nm) was similar to that found in the transfer bar. Inspection of the work roll surfaces after the test indicated that, under the rolling conditions used, the fall in Mg content arose mainly due to the removal of some of the thin oxide layer by abrasion and adhesion to the work roll surface. Some of the surface material is known to be transferred from the stock to the roll, leaving a surface coating of the aluminum alloy on the roll. The coating and the morphology of the work roll surfaces would therefore be expected to have a signiﬁcant effect on the evolution of the subsurface layers. Moreover, the deformation process increases the surface area, which inevitably dilutes the Mg by the introduction of fresh metal. This is not offset by additional Mg diffusion toward the surface during rolling as there is too little time between reheat and completion of the rolling pass for that to occur to a signiﬁcant degree. Further, a small amount of Mg (as oxides) was intermixed into the subsurface layer by deformation during rolling. It is thought that the mechanisms which led

61

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3 Scale Growth and Formation of Subsurface Layers

to the deformation and mixing of the oxide particles into the subsurface layer arose from slip at the roll/stock interface and the action of roll surface asperities on the stock surface. In both the industrially and laboratory rolled samples, the depth of raised magnesium content correlated well with the observed thickness of the subsurface particle layer [87]. An interaction between the stock and work roll surfaces can take place under conditions of forward and backward slip, or as a combination of sticking, forward and backward slip during a rolling process. It is considered that under conditions of forward and backward slip, the asperities on the work roll surface would determine the morphology of the stock surfaces by a combination of plowing and machining of the material surface. The ﬁnish on the work roll surfaces would be imprinted on the stock surface under sticking conditions. Hence, the ﬁnal stock surface morphology could be the result of either one of these rolling conditions, or a combination of both, and the morphology of the stock surfaces should reﬂect the morphology of the work roll surfaces. This remains the subject of further research.

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3 Scale Growth and Formation of Subsurface Layers 37 Wulf, G.L., Carter, T.J., and Wallwork, G.R. (1969) The oxidation of Fe–Ni alloys. Corrosion Science, 9, 689–701. 38 Hammar, B., and Vannerberg, N.G. (1974) The inﬂuence of small amounts of chromium and copper on the oxidation properties of iron. Scandinavian Journal of Metallurgy, 3 (3), 123–128. 39 Rawers, J.C., Oh, J.M., and Dunning, J. (1990) Oxidation behaviour of Mn and Mo alloyed Fe-16Ni-(5-8)Cr-3.2Si-1.0Al. Oxidation of Metals, 33 (1/2), 157–176. 40 Saunders, S.R.J., Monteiro, M., and Rizzo, F. (2008) The oxidation behaviour of metals and alloys at high temperatures in atmospheres containing water vapour: a review. Progress in Materials Science, 53, 775–883. 41 Upthegrove, C. (1933) Scaling of Steel at Heat-Treating Temperatures, Engineering Research Bulletin, No. 25, University of Michigan, The George Banta, Menasha, Wisconsin. 42 Grifﬁths, R. (1934) The blistering of iron oxide scales and the conditions for the formation of a non-adherent scale. Journal of the Iron and Steel Institute, 130, 377–388. 43 Siebert, C.A., and Upthegrove, C. (1935) Oxidation of a low carbon steel in the temperature 1650 to 2100 °F. Transactions of the American Society for Metals, 23, 187–224. 44 Siebert, C.A. (1939) The effect of carbon content on the rate of oxidation of steel in air at high temperatures. Transactions of the American Society for Metals, 27, 752–757. 45 Kim, B.K., and Szpunar, J.A. (2002) Anisotropic microstructure of iron oxides formed during high temperature oxidation of steel. Materials Science Forum, 408–412, 1711–1716. 46 Szpunar, J.A., and Kim, B.K. (2007) High temperature oxidation of steel; new description of structure and properties of oxide. Materials Science Forum, 539–543, 223–227. 47 Chen, R.Y., and Yuen, W.Y.D. (2008) Short-time oxidation behaviour of low-carbon, low-silicon steel in air at 850–1180 °C: I. Oxidation kinetics. Oxidation of Metals, 70, 39–68.

48 Melfo, W.M., and Dippenaar, R.J. (2007) In situ observations of early oxide formation in steel under hot-rolling conditions. Journal of Microscopy, 225, 147–155. 49 Suárez, L., Bourdon, G., Vanden Eynde, X., Lamberigts, M., and Houbaert, Y. (2007) Tertiary scale behaviour during ﬁnishing hot rolling of steel ﬂat products. Advances in Materials Research, 732–737. 50 Suarez, L., Petrov, R., Kestens, L., Lamberigts, M., and Houbaert, Y. (2007) Texture evolution of tertiary oxide scale during steel plate ﬁnishing hot rolling simulation tests. Materials Science Forum, 550, 557–562. 51 Bolt P.H. (2004) Understanding the properties of oxide scales on hot rolled steel strip. Steel Research International, 75 (6), 399–404. 52 Chen, R.Y., and Yuen, W.Y.D. (2006) Oxidation of a low carbon, low silicon steel in air at 600–920 °C. Materials Science Forum, 522/523, 77–85. 53 Chen, R.Y., and Yuen, W.Y.D. (2003) Review of the high temperature oxidation of iron and carbon steels in air or oxygen. Oxidation of Metals, 59 (5/6), 433–468. 54 Gleeson, B., Hadavi, S.M.M., and Young, D.J. (2000) Isothermal transformation behavior of thermally-grown wüstite. Materials at High Temperatures, 17 (2), 311–319. 55 Talekar, A., Chandra, D., Chellappa, R., Daemen, J., Tamura, N., and Kunz, M. (2008) Oxidation kinetics of high strength low alloy steels at elevated temperatures, Corrosion Science, 50, 2804–2815. 56 Shiraiwa, T., Araki, T., Fujino, N., and Matsuno, F. (1971) Non-metallic inclusions in rimmed steel. Sumitomo Metals, 23 (2), 202–211. 57 Ilschner, B., and Mlitzke, E. (1965) The kinetics of precipitation in wüstite (Fe1−xO). Acta Metallurgica, 13 (7), 855–867. 58 Hachtel, L., and Human, A. (1995) Scale structure and scale defects on hot strip. Praktische Metallographie, 32 (7), 332–344.

References 59 Chen, R.Y., and Yuen, W.Y.D. (2000) A study of the scale structure of hot-rolled steel strip by simulated coiling and cooling. Oxidation of Metals, 53 (5-6), 539–560. 60 Rolls, R., and Arnold, F.V. (2004) The structure and adhesion of oxide scales on Fe–Ni–Mo and Fe–Cr–Mo alloys. Materials and Corrosion, 23 (10), 886–893. 61 Chen, R.Y., and Yuen, W.Y.D. (2005) Examination of oxide scales of hot rolled strip products. ISIJ International, 45 (1), 52–59. 62 Fontana, M.G. (1987) Corrosion Engineering, 3rd edn, McGraw-Hill, New York. 63 Smuts, J., and De Villiers, P.R. (1965) Scale on heat-treated hot-rolled steel plate. Journal of the Iron and Steel Institute, 204, 787. 64 Baud, J., Ferrier, A., and Manenc, J. (1978) Study of magnetite ﬁlm formation at metal-scale interface during cooling of steel products. Oxidation of Metals, 12 (4), 331–342. 65 Yu, Y., and Lenard, J.G. (2002) Estimating the resistance to deformation of the layer of scale during hot rolling of carbon steel strips. Journal of Materials Processing Technology, 121, 60–68. 66 Schütze, M. (1994) An approach to a global model of the mechanical behaviour of oxide scales. Materials at High Temperatures, 12, 237–247. 67 Matsumo, F. (1980) Blistering and hydraulic removal of scale ﬁlms of high temperature. Transactions ISIJ, 20, 413–421. 68 Hidaka, Y., Anraku, T., and Otsuka, N. (2002) Tensile deformation of iron oxides at 600–1250 °C. Oxidation of Metals, 58 (5–6), 469–485. 69 Hidaka, Y., Anraku, T., and Otsuka, N. (2003) Deformation of iron oxides upon tensile tests at 600–1250 °C. Oxidation of Metals, 59, 97–113. 70 Li, Y.H., and Sellars, C.M. (1996) Modelling deformation behaviour of oxide scales and their effects on interfacial heat transfer and friction during hot styeel rolling, in Proceedings of Second Int. Conf. Modelling Metal Rolling Processes (eds J.H. Beynon, P. Ingham, H. Teichert, and K. Waterson),

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Institute of Materials and Mining, London, pp. 192–206. Munther, P.A., and Lenard, J.G. (1999) The effect of scaling on interfacial friction in hot rolling of steels. Journal of Materials Processing Technology, 88, 105–113. Krzyzanowski, M., Sellars, C.M., and Beynon, J.H. (2002) Characterisation of oxide scale in thermomechanical processing of steel, in Proceedings of Int. Conf. on Thermomechanical Processing: Mechanics, Microstructure & Control, 23–26 June 2002 (eds E.J. Palmiere, M. Mahfouf, and C. Pinna), University of Shefﬁeld, Shefﬁeld, UK, pp. 94–102. Boelen, R., Thomson, P.F., and Brownrigg, A. (2002) Controlled oxidation rolling, in Proceedings of Int. Conf. on Thermomechanical Processing: Mechanics, Microstructure & Control, 23–26 June 2002 (eds E.J. Palmiere, M. Mahfouf, and C. Pinna), University of Shefﬁeld, Shefﬁeld, UK, pp. 103–108. Filatov, D., Pawelski, O., and Rasp, E. (2004) Hot-rolling experiments on deformation behaviour of oxide scale. Steel Research International, 75, 20–25. Suárez, L., Houbaert, Y., Vanden Eynde, X., and Colás, R. (2009) High temperature deformation of oxide scale, Corrosion Science, 51, 309–315. Echsler, H., Ito, S., and Schütze, M. (2003) Mechanical properties of oxide scale on mild steel at 800 to 1000 °C. Oxidation of Metals, 60 (3/4), 241–269. Frost, H.J., and Ashby, M.F. (1982) Deformation-Mechanism Maps, Pergamon Press, London. Sun, W., Tieu, A.K., Jiang, Z., and Lu, C. (2004) High temperature oxide scale characteristics of low carbon steel in hot rolling. Journal of Materials Processing Technology, 155–156, 1307–1312. Stringer, J. (1970) Stress generation in growing oxide ﬁlms. Corrosion Science, 10, 513–543. Manenc, J., and Vagnard, G. (1969) Etude De L’oxydation D’alliages Fer-Carbone. Corrosion Science, 9 (12), 857–862. Stringer, J., and Hed, A.Z. (1971) The oxidation of Ni-7.5%Cr and Ni-7.5%Cr-

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2.5%Sm2O3 at 900 and 1100 °C. Oxidation of Metals, 3 (6), 571–576. Ashby, M.F. (1972) A ﬁrst report on deformation, mechanism maps. Acta Metallurgica, 20 (7), 887–897. Reppich, B. (1967) Plastic deformation of iron (II) oxide. Physica Status Solidi, 20 (1), 69–82. Fishkis, M., and Lin, J.C. (1997) Formation and evolution of a subsurface layer in a metal working process. Wear, 206, 156–170. Afseth, A., Nordlien, J.H., Scamans, G.M., and Nisancioglu, K. (2002) Filiform corrosion of AA3005 alumin-

ium analogue model alloys. Corrosion Science, 44, 2543–2559. 86 Frolish, M.F., Krzyzanowski, M., Rainforth, M.W., and Beynon, J.H. (2006) Oxide scale behaviour on aluminium and steel under hot working conditions. Journal of Materials Processing Technology, 177, 36–40. 87 Frolish, M.F., Walker, J.C., Jiao, C., Rainforth, W.M., and Beynon, J.H. (2005) Formation and structure of a subsurface layer in hot rolled aluminium alloy AA3104 transfer bar. Tribology International, 38, 1050–1058.

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4 Methodology Applied for Numerical Characterization of Oxide Scale in Thermomechanical Processing 4.1 Combination of Experiments and Computer Modeling: A Key for Scale Characterization

The procedure for quantitative characterization of oxide scale behavior in thermomechanical processing is schematically illustrated in Figure 4.1. The approach is based on a combination of experiments under appropriate operating conditions and computer modeling for interpretation of the test results, and then implementation of the obtained physical insight into the ﬁnite element model for detailed prediction. Application of the advanced mathematical model to a metalforming operation allows for detailed prediction of the micro events related to oxide scale failure at the tool/workpiece interface that leads to better understanding of mechanisms responsible for a chosen technological effect that is under investigation. It can be heat transfer or friction in hot rolling, or descalability of particular steel under appropriate technological conditions. These numerical experiments with the advanced physically based model give a basis for evaluating a technological impact of the particular model assumptions. Sometimes, the assumed mathematical model is overcomplicated and can include assumptions which are not necessary, or less pronounced, for the particular case under investigation. Such numerical analysis enables model reduction while predicting a desired technological effect with a desired level of accuracy and, at the same time, for a reasonable computation time. Such model adjustment is a necessary stage because the use of the full, complex oxide scale model for prediction of a technological operation is not always justiﬁed, particularly because of long computational times. The following sections give an example of the use of this methodology for one particular case, namely the prediction of the scale failure at entry into the roll gap. The probability of oxide failure at this location is sufﬁciently high for practical interest. The zone of entry into the roll gap is important for the current rolling pass, taking into account that hot metal can extrude through any gaps between the fractured scale fragments under the roll pressure. Should a direct contact between the hot metal and the cold roll surface happen, it signiﬁcantly inﬂuences

Oxide Scale Behaviour in High Temperature Metal Processing. Michal Krzyzanowski, John H. Beynon, and Didier C.J. Farrugia Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-32518-4

68

4 Methodology Applied for Numerical Characterization of Oxide Scale Conventional measurements

Finite element modelling

Microcopies (SEM, BEI, EBSD)

Tensile testing, Compression testing

Interpretation of test results

Structure of surface layer; Statistical features

Physically based model Mechanics, Physics & Chemistry + Statistics, Phenomenological assumptions

Detailed understanding of events

Adjustment of the model for technological operation

BETTER PREDICTION

Figure 4.1 Schematic representation of the method applied for numerical characterization of oxide scale in the thermomechanical processing of steel.

both heat transfer and friction at the roll/stock interface [1]. The appropriate consideration of the effects of scale failure ahead of entry into the roll gap is particularly important for the establishment a comprehensive constitutive equation for the interfacial heat transfer coefﬁcient and for friction.

4.2 Prediction of Mild Steel Oxide Failure at Entry Into the Roll Gap as an Example of the Numerical Characterization of the Secondary Scale Behavior

Attention paid to the entry zone has resulted in different approaches over recent years, such as experimental observations, numerical modeling, and analytical consideration [2–5]. It has been shown that the surface oxide scales exhibit different behavior at entry into the roll, such as deformation with the parent steel or cracking and delamination from the steel surface before rolling, strongly dependent on scale thickness and structure, cooling time before the rolling pass, rolling temperature, reduction, and speed. These parameters determine the stresses developed within the scale and also the strength of the scale and the scale/metal interface. Generally, the observations have shown that the different crack patterns observed in the scale arise from the stress distributions rather than from temperature gradients. Flat rolling of the steel gives rise to signiﬁcant tensile loading of the free metal surface layer around the roll gap. As was indicated earlier [2], at entry into the roll gap the tensile stresses may be well above the yield stress of steel during hot ﬂat rolling.

4.2 Prediction of Mild Steel Oxide Failure at Entry Into the Roll Gap as an Example

Figure 4.2 The longitudinal component of the total strain predicted using the elastic roll and elastic plastic stock model (ε = 0.2); only the symmetrical upper half is shown.

4.2.1 Evaluation of Strains Ahead of Entry into the Roll Gap

The ﬁrst stage is devoted to numerical evaluation of the inﬂuence of the main technological parameters that might affect the longitudinal tensile strains in the stock surface ahead of contact with the roll. The basic ﬁnite element model conﬁguration can be seen in Figure 4.2. The stock was assumed to be elastic–plastic while the roll had elastic mechanical properties. The mechanical properties were assumed to be similar to those used in hot rolling models [6, 7], and the reduction was 20%. A mixture of isoparametric, arbitrary quadri- and trilateral plane strain elements was used for the modeling. Bilinear were used where the strains tend to be constant throughout the element, and biquadratic interpolation functions were used to represent the coordinates and displacements in the stock model. Analytical and discrete boundary formulations were used when nodes of the roll and stock have come into contact. The analytical formulation creates a spline through the nodes on the outside surface instead of piecewise linear lines for the discrete procedure, which improves the accuracy of the contact description. Numerical modeling of the friction at the workpiece/tool interface has been simpliﬁed to the Coulomb friction model. Further details of the mathematical model can be found in [8]. As follows from the sensitivity analysis, the aspect ratio ho/L calculated on the basis of the projected length of contact determined numerically, Lfe, always exceeds that obtained using the single analytical formula for L: L = R (ho − h f )

(4.1)

where ho and hf are the thickness of the stock before and after the rolling pass, respectively. The difference is related to bending of the stock surface ahead of entry into the roll gap. This bend is less for lower friction coefﬁcients, which was

69

4 Methodology Applied for Numerical Characterization of Oxide Scale

simulated better using a bilinear interpolation function rather than biquadratic one. The sensitivity of the numerically determined projected length to the characteristic element size indicates that the ﬁnite element mesh should be reasonably ﬁne at the area of the contact for appropriate simulation of the stock surface shape at the entry. At the same time, the calculated longitudinal component of the total strain did not exhibit signiﬁcant sensitivity to any of the parameters apart from application of the tri-lateral elements (Figures 4.3 and 4.4). This type of element seems to be less appropriate for application in the next stage of the analysis. Thus, quadrilateral plane strain elements and bilinear interpolation functions were chosen for studying the effect of different roll gap aspect ratios and the friction coefﬁcients on the tensile strain ahead of contact with the roll. Along with the tensile strain ahead of contact with the roll, the curvature of the stock surface just before the roll bite also plays a signiﬁcant role in oxide scale failure. The curvature of the bending can be calculated as a radius of a circumfer-

0.16

Longitudinal component of total strain

70

0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 0

0.1

0.2

0.3

0.4

0.5

0.6

Friction coefficient

quad 4; 1.25x1.5 mm; 0.00085 s; 1 mm/s quad 4; 0.31x0.35 mm; 0.00085 s; 1 mm/s tria; 1.25x1.5 mm; 0.00085 s; 1 mm/s quad 8; 1.25x1.5 mm; 0.00085 s; 1 mm/s quad 4; 1.25x1.5 mm; 0.00085 s; 0.5 mm/s quad 4; 1.25x1.5 mm; 0.0017 s; 1 mm/s quad 4; 1.25x1.5 mm; 0.000425 s; 1 mm/s

Figure 4.3 Longitudinal component of the total strain predicted at the stock surface at the moment of the ﬁrst contact with the roll for different friction coefﬁcients and the following numerical parameters: element type, element size, time increment, and relative sliding velocity, respectively.

4.2 Prediction of Mild Steel Oxide Failure at Entry Into the Roll Gap as an Example

Figure 4.4 Schematically illustration of calculation a curvature radius, Rcon, ahead of the roll contact as the circumference radius crossing the three points with the xi, yi coordinates.

ence crossing the three points (Figure 4.4) and solving the following equation system with regard to M, N, and L: x12 + y12 + Mx1 + Ny1 + L = 0 x22 + y22 + Mx2 + Ny2 + L = 0

(4.2)

x32 + y32 + Mx3 + Ny3 + L = 0 where (x1, y1), (x2, y2), and (x2, y2) are coordinates of the corresponding points determined numerically. The radius Rcon is then deﬁned by 2 Rcon = 0.25 (M 2 + N 2 − 4L )

(4.3)

Figure 4.5 illustrates the tensile strain and the radius of the surface stock curvature calculated at the moment of contact with the roll when a steady state in the rolling simulation was reached. The radius of the curvature shows signiﬁcant scatter. This can be explained by the discrete nature of the representation of the coordinates and displacements in the stock model producing exaggerated errors in Rcon. The tensile strains were near yield strain, assumed to be 0.02, when the aspect ratio and the friction coefﬁcient were low (both = 0.1) for all three model types. With an increase in the aspect ratio, the tensile strain grew faster for the cases where the friction coefﬁcient was larger for all model types: perfectly plastic, elastic– plastic and elastic–plastic with hardening. A trend for the radius of the surface stock curvature calculated at the moment of contact with the roll is difﬁcult to discern due to the scatter. The scatter can be decreased by statistical averaging of the data. It has also been shown that the radius of the curvature was nearly the same for different friction coefﬁcients when the aspect ratio was 0.1. In contrast to the tensile strain, which was about the same for all model types at a friction

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4 Methodology Applied for Numerical Characterization of Oxide Scale

e max 0.18

a

0.16 0.14 0.12 0.1 0.08 0.06

Fric coeff. 0.5

0.04

Fric coeff. 0.3

0.02

Fric coeff. 0.1

0 0

0.2

0.4

0.6

0.8

1

1.2

Rcon, mm 35

b

30 25 20 15 10 5 0 0

0.2

0.4

0.6

Aspect ratio

0.8

1

1.2

ho/L

Figure 4.5 Longitudinal component of (a) the total strain εmax and (b) the radius of the stock surface curvature Rcon predicted at the stock surface at the moment of the ﬁrst contact with the roll for different aspect ratios and friction coefﬁcients assuming an elastic–plastic stock and a roll radius of 68.3 mm.

coefﬁcient of 0.1, the radius of the curvature at the same low friction coefﬁcient was different, being smallest for the perfectly plastic model, at about 0.06–0.1 mm, and largest for the elastic plastic with hardening case, at about 13–14 mm. Generally, the longitudinal component of total strain ahead of contact is higher when the roll radius is increased for the corresponding aspect ratio. The roll radius chosen for the next case, Rroll = 354 mm, corresponds to industrial conditions (708 mm work roll diameter for tandem ﬁnishing stand F7, Port Talbot Hot Strip Mill, Corus, Wales). Similar to the laboratory conditions (68.3 mm roll radius), growth of the tensile strain was faster for the cases with larger friction coefﬁcients. The dependence of the tensile strain on the friction coefﬁcient is less for low aspect ratios.

4.2 Prediction of Mild Steel Oxide Failure at Entry Into the Roll Gap as an Example

A formula (4.4) has been developed on the basis of the numerical results obtained for the elastic–plastic stock to evaluate the longitudinal strain component ε at entry into the roll gap for the given friction coefﬁcient μ and the aspect ratio ho/L during rolling of ﬂat products with 40% reduction:

( ) μ )( )

( ) ( )

ε = ( 0.157 + 0.128 μ )

ho h − 0.063 o L L

2

ε = (0.318 + 0.177

ho h − 0.187 o L L

2

for Rroll = 68.3 mm (4.4)

for Rroll = 354 mm

Figure 4.6 illustrates the lines representing the strains obtained using Equation (4.4) plotted together with the points obtained numerically using the ﬁnite element modeling. When the oxide/metal interface is strong the longitudinal strain in the stock surface ahead of contact with the roll will be transmitted to the oxide scale that might result in its failure. As follows from Equation (4.4), this type of oxide failure in tension is more likely to occur during rolling with high aspect ratios, such as 0.6–0.8, rather then small ones, 0.1–0.2. The small aspect ratios are more typical for industrial ﬂat rolling conditions while laboratory rolling usually takes place under the aspect ratio within the range of 0.6–0.8. As can be seen from Figure 4.6, the tension ahead of entry into the roll gap for the industrial conditions is signiﬁcantly less than during the laboratory trials, decreasing the probability of oxide failure under industrial conditions. At the same time, the curvature of the stock surface at the moment of contact with the roll is another reason for oxide failure in this area due to breaking in bending. The radius of the curvature is less for rolling with low aspect ratios and bending is particularly sharp for the perfectly plastic material. For elastic–plastic material the radius of the curvature is higher than that for the case of rolling perfectly plastic material. Thus, for industrial rolling of ﬂat products, failure of the oxide scale due to bending can be expected to be more pronounced than the failure due to longitudinal tension ahead of entry into the roll gap, which is more signiﬁcant for laboratory rolling conditions with higher aspect ratios. 4.2.2 The Tensile Failure of Oxide Scale Under Hot Rolling Conditions

It is now clear that as the stock enters the roll gap, it is drawn in by frictional contact with the roll, which is moving faster than the stock surface at entry. This produces a longitudinal tensile stress in the stock surface ahead of contact with the roll. Thus, the aim of this stage is to study the inﬂuence on the scale behavior of this tensile loading just before roll contact at the upper or lower faces. Tensile test equipment limits the variation of the test parameters in its ability to approximate hot rolling conditions. Apart from results presented in the section above, the results from several hot strip mills were also used to provide baseline conditions for testing [9–11]. The thermal history of the slab has shown that the

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4 Methodology Applied for Numerical Characterization of Oxide Scale

e max 0 .1 6 0 .1 4

a

Typical industrial conditions

0 .1 2 0 .1 0 0 .0 8 0 .0 6

Typical laboratory conditions

0 .0 4 0 .0 2 0 .0 0 0 .0

0.2

e max

0 .4

0 .6

Aspect ratio

0 .8

1 .0

1 .2

ho/L

0.22 0.20

b

Typical industrial conditions

0.18 0.16 0.14 0.12

Typical laboratory conditions

0.10 0.08 0.06 0.04 0.02 0.0

0.2

0.4

Aspect ratio

0.6

0.8

1.0

ho/L

Figure 4.6 Longitudinal component of the total strain εmax obtained using Equation (4.6) plotted together with the points predicted numerically at the stock surface at the moment of the ﬁrst contact with the roll for different aspect ratios and friction coefﬁcients (0.1, 0.3, and 0.5) assuming the elastic–plastic stock, with a roll radius of (a) 68.3 mm and (b) 354 mm.

difference between the scale surface and the scale/steel interface is signiﬁcant, about 100 °C, before the ﬁrst descaler and becomes smaller, 30–50 °C, when a much thinner secondary oxide scale is formed. However, the surface temperature changes during contact between the rolls and the slab are very signiﬁcant. The surface temperature of the slab decreases by as much as 250–350 °C, due to descaling water, but remains within temperature limits of 600–1200 °C. The deformation of a slab in the roll gap is inhomogeneous, both along the length and through the thickness. The lowest strain is attained at the center and the highest at or near the surface. The maximum strain rate is found at the

4.2 Prediction of Mild Steel Oxide Failure at Entry Into the Roll Gap as an Example

entrance to the roll bite just under contact with the rolls. Very high strain rates of more than ﬁve to ten times the nominal strain rate are reached just beneath the surface because of redundant shearing and the highest strains and strain rates take place at the region where oxide fracture is most likely to occur. The following parameter variations were chosen for the hot tensile test program: temperature: 830–1150 °C, thickness of the scale: 10–300 μm, strain: 1.5–20%, and strain rate: 0.02–4.0 s−1. Cylindrical tensile specimens, of 6.5 mm diameter and 20 mm length in the gage section, were prepared from mild steel. The steel grade 070M20 had a typical mass content of 0.17% C, 0.13% Si, 0.72% Mn, 0.014% P, 0.022% S, 0.06% Cr, 0.07% Ni, 0.11% Cu, <0.02% Mo, <0.02% V. The specimens were oxidized to the desired extent in the tensile rig just before starting the tensile testing. Excluding intermediate cooling was desirable because it could cause spalling of oxide scales. Two different modes leading to oxide spallation were observed in the tests. The ﬁrst mode is generally accepted for tensile failure at up to 600 °C [12]. In this mode it is assumed that there is a strong interface between metal and oxide, but a relatively weak oxide. Failure begins by through-scale shear cracking followed by initiation of a crack along the scale–metal interface that might result in spallation (Figures 4.7a and b). The initiation of cracking along the oxide–metal interface is shown in Figure 4.8, showing a scanning electron micrograph (SEM) of the crosssection of the oxide scale about 15 μm thick after oxidizing and testing at 830 °C. The through-thickness cracks are formed with the crack spacing approximately uniform. The variations might be due to the random distribution of voids and pre-existing cracks within the scale [13]. It is also possible that there is a small temperature change along the axis of the specimen that might have an inﬂuence on the properties of the scale. The second mode of oxide spallation corresponds to the interface being weaker than the oxide scale and was observed at higher temperatures (Figures 4.7c and e). In this mode the oxide scale was slipping along the interface throughout elongation under the uniaxial tensile load after spallation at the upper end of the specimen gage length. As can be seen in Figures 4.7d and f, it may result in spallation of the whole oxide raft after cooling. Such behavior of the scale may be explained by assuming that slipping between oxide scale and metal occurred when the stress from deformation exceeded that necessary for viscous ﬂow without fracture at the scale–metal interface, but did not exceed the critical level for through-thickness fracture of the scale under these conditions. Generally, the two modes leading to oxide spallation were observed for the range of parameters of this testing program. The ﬁrst mode (strong interface and weak oxide) was observed at 830 °C for 1.5–2.0% strain and 0.1–0.2 s−1 strain rate. The second mode (strong oxide and weak interface) was observed at 900–1150 °C. Visible sliding of the oxide scale raft has been observed during elongation at these temperatures. No through-thickness scale cracks were observed for scales 30– 60 μm thick after testing at 1000 °C with 2.0–5.0 strain at strain rates of 0.2 and 2.0 s−1. In these cases, due to ductile behavior of the oxide scale, the strain was insufﬁcient for failure at the ends of the specimen gage section. Increasing the

75

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4 Methodology Applied for Numerical Characterization of Oxide Scale

a

b

c

d

e

f

Figure 4.7 Oxide scale on the tensile specimen after testing at (a) 2% strain, 0.2 s−1 strain rate, 830 °C temperature, 3000 s oxidation time; (b) 2% strain, 0.2 s−1 strain rate, 830 °C temperature, 1500 s oxidation time; (c) 5% strain, 0.2 s−1 strain rate, 900 °C temperature, 800 s oxidation time; (d) 20% strain, 0.2 s−1 strain rate, 900 °C temperature, 300 s oxidation time; (e) 5% strain, 2.0 s−1 strain rate, 1150 °C temperature, 100 s oxidation time; (f) 20% strain, 0.2 s−1 strain rate, 1150 °C temperature, 100 s oxidation time.

strain rate up to 4.0 s−1 resulted in a through-thickness crack in the middle part of the specimen. For thicker scales, about 175 μm, tested under the same conditions, sliding of the nonfractured raft took place. The observations have also shown that oxide scales formed at 1150 °C delaminated more readily than more homogeneous scales formed at 900 °C. These outer layers were displaced along the interface within the oxide scale during elongation of the tensile specimen at 1150 °C. The most important conclusion that can follow from these test results is that the oxide scale cannot be assumed both to be perfectly adhering during tensile loading, in the sense of sliding, and to be fully brittle. The two limit modes are strongly inﬂuenced by the temperature, strain and strain rate (Table 4.1). Detailed

4.2 Prediction of Mild Steel Oxide Failure at Entry Into the Roll Gap as an Example

77

Figure 4.8 Scanning electron micrograph showing the zone of crack initiation along the oxide/metal interface after through-thickness cracking after testing in tension at 830 °C temperature, 2.0% strain, 0.2 s−1 strain rate and after 100 s oxidation time.

Table 4.1 State of the oxide scale after the hot tensile test for the different temperature, strain, strain rate, and oxidation time.

Temperature, (oC) 830

900

975

1150

Strain (%)

Strain rate (s−1)

Oxidation time (s)

Result

1.0 1.5 2.0 2.0 2.0 2.0 1.5 2.0 10.0 20.0 10.0 10.0 5.0 5.0 5.0 5.0 5.0 2.0 5.0 5.0 10.0 5.0 5.0

0.2 0.2 0.1 0.2 2.0 4.0 0.2 0.2 0.2 1.0 2.0 3.0 0.2 2.0 4.0 0.2 4.0 0.2 0.2 4.0 0.2 0.2 4.0

1500

Irregular cracks Through-thickness cracks Through-thickness cracks, spallation Through-thickness cracks, spallation Through-thickness cracks, spallation Through-thickness cracks, whole spallation No through-thickness cracks No through-thickness cracks Sliding during tension, no cracks Sliding during tension, no cracks Sliding during tension, no cracks Sliding during tension, no cracks No cracks No cracks Through-thickness crack in the middle Sliding during tension, no spallation Sliding during tension, no spallation No through-thickness cracks Sliding during tension, delamination Sliding during tension, delamination Sliding during tension, delamination Sliding during tension, no spallation Sliding during tension, delamination

300

100 100 100 800 800 100 100 100 100 800 800

78

4 Methodology Applied for Numerical Characterization of Oxide Scale

macro- and microscopic observations of the scales after the tests also allow determination of the morphology and understanding detailed failure mechanisms. Generally, three types of scales were distinguished during the test program with low, middle, and high porosity (Figure 4.9). The extent of porosity depends closely, but not exclusively, on the temperature at which the oxide scale was formed. It

Figure 4.9 Optical micrograph showing the cross-section of the oxide scales grown at (a) 830 °C for 1500 s; (b) 900 °C temperature for 300 s; (c) 1150 s for 100 s.

4.2 Prediction of Mild Steel Oxide Failure at Entry Into the Roll Gap as an Example

has been shown that the failure strains are strongly dependent on measured composite void size [14]. There are different types of fracture surfaces in the oxide scales observed (Figure 4.10). These were duplex or consisted of three different layers of grains and the thickness ratio between the layers varied. The inner layer had a large number of evenly distributed small pores. Usually, the whole thickness of the oxide layer had spalled during tension at 800 and 900 °C, according to either the ﬁrst or the second model of spallation described above. The interface between the small equiaxed grains of the inner layer and the large grains of the outer layer is a potential location for delamination within the oxide scale. The scale formed at 1150 °C was nonhomogeneous. The preceding mixture of air with nitrogen did not result in changes of homogeneity. At 1150 °C, delamination within the oxide layer took place during tensile loading. The separated outer scales were very porous and much thicker than the nonseparated oxide layer, which was usually 3–8 μm thick (Figure 4.11). These thin scales have no pores and tightly adhere to the metal surface, even after relatively large strains. Normally, at

Figure 4.10 Scanning electron micrographs showing different types of fracture surfaces in oxide scales formed at (a, b) 975 °C for 800 s; (c) 975 °C for 100 s; (d) 830 °C for 3000 s.

79

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4 Methodology Applied for Numerical Characterization of Oxide Scale

Figure 4.11 Scanning electron micrograph of the cross-section of the surface layer of the specimen showing delamination within the oxide scale after testing in tension at 1150 °C, 10% strain; 0.2 s−1 strain rate, and 100 s oxidation time.

temperatures below 850–900 °C, cracks occur perpendicular to the direction of the principal tensile stress (Figure 4.12). The through-thickness penetration and smooth crack surfaces show that it is an essentially brittle process of unstable crack propagation for the temperature region up to about 850–900 °C. These lower temperature experiments have not shown the stable crack growth that could indicate that the scale has a signiﬁcant amount of ductility. If the defects or microcracks in the oxides are small relative to the dimensions of the oxide scale, then linear elastic fracture mechanics can be applied for the temperature region up to 850–900 °C. At higher temperatures, about 900–1200 °C, usually the interface is weak enough to allow sliding of the nonfractured oxide raft, and the location of the plane of sliding is determined by the cohesive strength at different interfaces and the stress distribution. 4.2.3 Prediction of Steel Oxide Failure During Tensile Testing

The mathematical model used for prediction of steel oxide failure during tensile testing is composed of two parts. The ﬁrst is a macrocomponent computing the strains, strain rates, and stresses in the specimen during the hot tensile test. This is then linked to the microlevel model of the oxide scale failure during the test. Both components of the model are rigorously thermomechanically coupled, and all the mechanical and thermal properties were included as functions of temperature. The MARC ﬁnite element code was used to simulate metal/scale ﬂow, heat transfer, viscous sliding, and failure of the oxide scale during hot tension of axisymmetric samples.

4.2 Prediction of Mild Steel Oxide Failure at Entry Into the Roll Gap as an Example

Figure 4.12 Scanning electron micrograph showing the cross-section of the oxide scale grown at 830 °C for 300 s (a) and at 1150 °C for 100 s (b) after testing in tension at 830 °C, 2.0% strain, and 0.2 s−1 strain rate.

Figure 4.13 illustrates the basic model setup assuming axial symmetry about the specimen central axis. The model enables the calculation of the distributions of velocities, strain rates, strains, stresses, and temperature in the oxidized deformation zone in the middle part of the specimen. Normally the experiments were carried out using position control [15]. Thus, applying the displacements at the ends of the sample simulates the tensile loading in the model. All parameters necessary for heat transfer calculation were introduced as functions of the temperature T (in °C) on the basis of available experimental data [16, 17]. The properties of the steel were then calculated from the following formulas:

81

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4 Methodology Applied for Numerical Characterization of Oxide Scale

Figure 4.13 conditions.

Tensile test model – schematic representation of FE mesh and boundary

c p = 422.7 + 48.66 exp ( 0.319 × 10 −5 × T ) for T ≤ 700 °C c p = 657.0 + 0.084 (T × 10 −3 )

−24.6

for T > 700 °C

λ = 23.16 + 51.96 exp ( −2.02519 × 10 −3 × T ) ρ = 7850 (1 + 0.004 × 10 −6 × T 2 )

(4.5)

−3

where cp, λ, and ρ are the speciﬁc heat, thermal conductivity, and density, respectively. The mechanical properties of the steel were assumed to be similar to those used in rolling models [18, 19]. The ﬂow strength in the hot deformation process was introduced as a function of temperature, strain, strain rate, and carbon content

4.2 Prediction of Mild Steel Oxide Failure at Entry Into the Roll Gap as an Example

using Shida’s equations [20]. In order to avoid unnecessary complexities in this macrocomponent of the model, the induction heating was simulated by assuming a temperature distribution along the surface layer. Using this assumption, the temperature was deﬁned along the metal boundary surface as a function of both time and position, which was veriﬁed by radiation pyrometry. The energy balance for the boundary surface was expressed as

λ

∂T = α (Ta − T ) ∂n

(4.6)

where n is a coordinate normal to the surface, α is the heat transfer coefﬁcient, and T and Ta are the boundary surface and the ambient temperature (°C), respectively. The surface of the specimen was subjected to gas cooling and the following coefﬁcient of radiative heat transfer was speciﬁed for this surface:

(

α = 1.2 − 0.52

)

T T 4 − Ta4 5.675 × 10 −8 1000 T − Ta

(4.7)

Heat transfer through the grip contact surface was modeled by means of a heat transfer coefﬁcient assuming αgr = 30 W/m2 K. The incremental procedure was used to solve the nonsteady-state coupled problem. The oxide scale is simulated as consisting of scale fragments joined together to form a scale layer of 10–100 μm thickness covering the whole gage length of the specimen at the beginning of tensile loading. The length of each scale fragment was several times less than the smallest spacing of through-thickness cracks observed in the experiments. Each fragment was 0.47 mm in length and consisted of 40–75 four-node, isoparametric, arbitrary quadrilateral axisymmetric elements for the modeling. Fewer elements were used nearer the gage shoulders. For the scale to be adherent to the metal surface at the beginning of the elongation, a loading equivalent to the atmospheric pressure was applied to the scale throughout the heating stage. The scale and the metal surface were assumed to be adherent when they were within a contact tolerance distance, taken to be 1 μm. Tangential viscous sliding of the oxide scale on the metal surface was allowed, arising from the shear stress τ transmitted from the specimen to the scale in an analogous manner to grain-boundary sliding in high-temperature creep [21]:

τ = ηvrel

(4.8)

where η is a viscosity coefﬁcient and νrel is the relative velocity between the scale and the metal surface. The viscous sliding of the scale is modeled using a shearbased model of friction such that

ηvrel = −mkY

( )

v 2 arctan rel t π c

(4.9)

where m is the friction factor; kY is the shear yield stress; c is a constant taken be 1% of a typical vrel which smoothes the discontinuity in the value of τ when stick/ slip transfer occurs; and ¯t is the tangent unit vector in the direction of the relative

83

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4 Methodology Applied for Numerical Characterization of Oxide Scale

sliding velocity. The calculation of the coefﬁcient η was based on a microscopic model for stress-directed diffusion around irregularities at the interface and depends on the temperature T, the volume-diffusion coefﬁcient DV, and the diffusion coefﬁcient for metal atoms along the oxide/metal interface δSDS, and the interface roughness parameters p and λ [22]:

η=

kTp 4 4 Ωλ (δ SDS + 0.8 pDV ) 2

(4.10)

where k is Boltzmann’s constant, Ω is the atomic volume, p/2 is the amplitude, and λ is wavelength. It was assumed for the calculation that the diffusion coefﬁcient along the interface was equal to the free surface diffusion coefﬁcient. It was assumed in the model that spalling of the scale could occur along the surface of the lowest energy release rate, which can be either within the scale or along the scale/metal interface. A ﬂaw will continue to grow under a stress if its energy release rate G exceeds the critical energy release rate Gcr. The strain energy release rate is equal to the J-integral both for linear and nonlinear elastic material behavior [23]. The possibility of calculation of the J-integral is an option in the model. The lack of data for the J-integral as a function of crack length for the oxide scale and the availability of experimental data showing that through-thickness cracking is an essentially brittle process of unstable crack propagation for the test parameters favor the assumption of linear elastic fracture mechanics (LEFM) for the model. Assuming the opening of the through-scale crack due to applied tension loading perpendicular to the crack faces (tensile mode), the critical failure strain εcr may be used as a criterion for the through-thickness crack occurring [12] 12 2γ (T ) ⎞ ε cr = ⎛⎜ 2 ⎟ ⎝ F πE (T ) c ⎠

(4.11)

where γ is the surface fracture energy, E is Young’s modulus, F takes values of 1.12, 1, and 2/π for a surface notch of depth c, for a buried notch of width 2c, and for a semicircular surface notch of radius c, respectively. Assuming γ = K2/2E, where K is the stress intensity factor, the critical strain and stress can also be expressed in terms of the K-factors. There is a possibility of through-scale failure due to shear deformation in the oxide. Assuming that the stress intensity factor related to the fracture due to shear loading parallel to the crack faces (plane shear mode) exceeds the corresponding value for the tensile mode, which as a rule is justiﬁed, the following criterion for the shear failure in the oxide was chosen:

ε crsh = 2ε cr

(4.12)

where ε is the critical strain for shear fracture in the oxide scale. Using (4.11) and (4.12), the normal and tangential separation stresses were calculated in the model using the deformable–deformable contact procedure implemented in the MARC code. Once contact between a node and a deformable surface is detected, a tie is activated. The tying matrix is such that the contacting node can slide along the surface, be separated or be stuck, according to the general contact conditions. sh cr

4.2 Prediction of Mild Steel Oxide Failure at Entry Into the Roll Gap as an Example Table 4.2 Thermal and mechanical properties of the oxide scale and interface used for calculation.

Parameter

Function

Reference

Density (kg/m3)

ρ = 5.7 × 103

[24]

Speciﬁc heat capacity (J/kg deg)

cp = 674.959 + 0.297T − 4.367 × 10−5T for T ∈ 600–1100 °C

[24]

Thermal conductivity (W/m K)

λ = 1 + 7.833 × 10−4T for T∈ 600–1200 °C

[24]

Young’s modulus (GPa)

E = Eoxo (1 + n (T − 25)) n = −4.7 × 10−4; Eoxo = 240 GPa;

[25]

Poisson’s ratio

ν = 0.3

[26]

Heat transfer coefﬁcient at the oxide/metal interface (W/m2 K)

α = 30 000

[7]

Surface diffusion coefﬁcient times effective surface thickness (m3/s)

δSDS = δSDoS exp(−QS / RT) δSDoS = 1.10 × 10−10 m3/s; QS = 220 kJ/mole

[27]

Volume (lattice) diffusion coefﬁcient (m2/s)

DV = DoV exp(−QV / RT) DoV = 1.80 × 10−4 m2/s; QV = 159 kJ/mole

[27]

Stress intensity factor (MN m−3/2)

K = ao + a1T + a2T2 + a3T3 + a4T4 + a5T5 for 20–820 °C ao = 1.425; a1 = −8.897 × 10−3; a2 = −8.21 × 10−5; a3 = 3.176 × 10−7; a4 = −5.455 × 10−10; a5 = 3.437 × 10−13

[28]

A summary of thermal and mechanical properties of the oxide scale used for the calculation is given in Table 4.2. It has been shown using high-temperature tensile testing that for the mild steel at temperatures around 850–870 °C there were indications of transfer from the through-scale crack mechanism of oxide failure to the slipping of the nonfractured oxide raft. In terms of the model, this means that the separation stress within the oxide scale is less than the separation stress at the oxide/metal interface at temperatures up to 850 °C, and exceeded by it above 870 °C (Figure 4.14). Although the direct measurement of the separation stresses using an experimental technique appears impossible, the available data about the transition temperature range seem to be sufﬁcient for modeling the changes in oxide failure observed during hot tensile testing. It was assumed that the scale deforms elastically such that the possible forms of stress relaxation were fracture, viscous sliding along the interface, and spallation. At temperatures up to 850 °C and at strain rates within the investigated interval, the contribution of viscous sliding is negligible. Through-thickness cracks develop from pre-existing defects located at the outer surface of the oxide layer (Figure 4.15a). Precise analysis of the stress distribution within the oxide layer was

85

4 Methodology Applied for Numerical Characterization of Oxide Scale 850 oC

870 oC within the oxide scale

Separation stress

86

for the oxide–metal interface

temperature

Figure 4.14 Schematic representation of the effect of temperature on the separation stresses of the scale/metal system assumed for modeling.

Figure 4.15 Distribution of the εx strain component predicted in the tensile specimen after testing at 2% strain, 0.2 s−1 strain rate for the scale thickness 67 μm, and different temperatures (a) 830 °C and (b) 900 °C.

4.2 Prediction of Mild Steel Oxide Failure at Entry Into the Roll Gap as an Example

not the aim in this case but with a changed ﬁnite element mesh it is possible to make such calculations. In general, the critical failure strain calculated from Equation (4.11) can vary for the given temperature depending on both the parameters of the defects and the surface fracture energy, γ. It has been shown that the length c can be calculated as an effective composite value made up of the sum of the sizes of discrete voids whose stress ﬁelds overlap [28]. An attempt to calculate the surface energy from ﬁrst principles provided an opportunity to deduce values of the stress intensity factor for comparison with those found experimentally [29]. The formation of tensile cracks through the thickness of the oxide scale produces considerable redistribution of the stress within the scale and also at the oxide/metal interface. Figure 4.16 depicts the noncracked oxide scale fragment before tension and after through-thickness crack formation

Figure 4.16 Distribution of the σx stress component predicted in the tensile specimen during testing at 5% strain, 0.2 s−1 strain rate for the scale thickness 67 μm, and the temperature 400 °C. (a) before cracking; (b) after tension.

87

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4 Methodology Applied for Numerical Characterization of Oxide Scale

Figure 4.17 Distribution of the εx strain component predicted in the tensile specimen during testing at 5% strain, 0.2 s−1 strain rate for the scale thickness 67 μm, and the temperature 400 °C. (a) Before cracking and (b) after tension.

at the end of the test. The stress concentration visible at the crack zone near the interface can lead to the onset of cracking along the interface. The in-plane stress cannot transfer across the crack and becomes zero at each of the crack faces. By symmetry it reaches a maximum value midway between the cracks. Similarly, within the scale fragment the strain distribution signiﬁcantly relaxes the level of deformation of the oxide scale compared with the surface layer of the metal (Figure 4.17). The formation of the crack through the thickness of the oxide scale develops shear stresses at the interface (Figure 4.18). At low temperatures in the absence of relaxation by viscous sliding, these stresses have a maximum at the edges of the cracks. Relaxation of shear stresses can occur by interface cracking and spallation of the scale fragment when the strain increases. At higher temperatures the interface sliding due to stress-directed diffusion can have a signiﬁcant role in relaxation of the shear stresses. Figure 4.15b shows the simulation result of another mode of oxide scale failure that has been observed experimentally for the mild steel in the temperature range 870–1200 °C. In this case, the oxide scale has spalled from the metal surface and sliding along the oxide/metal interface is at its maximum. In places, small areas

4.2 Prediction of Mild Steel Oxide Failure at Entry Into the Roll Gap as an Example

Figure 4.18 Distribution of interfacial shear stress after tension predicted in the tensile specimen during testing at 5% strain, 0.2 s−1 strain rate for the scale thickness 67 μm, and a temperature of 400 °C.

of adhered scale were observed, during modeling, in the regions of relatively low temperature and deformation. The spalled parts of the scale cool faster than the nonspalled fragments because less heat is transferred from the hot metal. The oxide scale data used allow the main physical phenomena to be taken into account in presenting the model capabilities. Nevertheless, an understanding of the processes that control oxide scale behavior at high temperature is far from clear. A detailed discussion is beyond the scope of this publication, but important factors that interact with the present discussion can be highlighted. These mostly concern the parameters determining adherence and fracture of the oxide scale in the high-temperature range. Absolute values for fracture energy and diffusion parameters at the oxide/metal interface are difﬁcult to deﬁne even though the literature shows that much effort has been expended in trying to determine them. Nevertheless, the data so far obtained allow for the next, ﬁnal stage of this particular analysis, namely, prediction of mild steel oxide failure at entry into the roll gap. 4.2.4 Prediction of Scale Failure at Entry into the Roll Gap

The mathematical model used in this stage has been developed on the basis of the approach described in the previous section and validated for the modeling of oxide scale failure during tensile testing. The model comprises a macrolevel that computes the strains, strain rates, and stresses in the specimen during hot ﬂat rolling (Figure 4.19) and a microlevel to model oxide scale failure (Figure 4.20).

89

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4 Methodology Applied for Numerical Characterization of Oxide Scale

Nodes Elements

12123 - 22789 10402 - 18356

Elastic Roll Radiative Cooling

Oxide scale raft

Elastic–Plastic Stock (Half Section) Figure 4.19 setup.

Macro part of the hot ﬂat rolling model – schematic representation of the model

Figure 4.20 Micro part of hot ﬂat rolling model – schematic representation of FE mesh and boundary conditions.

4.2 Prediction of Mild Steel Oxide Failure at Entry Into the Roll Gap as an Example Table 4.3

Main oxide scale model assumptions.

Assumption

Equation

Stress-directed diffusion of metal atoms around interface irregularities controls the rate of viscous scale sliding

Vrel =

1 τ η

[21]

v rel =

1 k −1 τ τ η

[21]

Dislocation creep in addition to diffusional ﬂow of atoms can circumvent interface irregularities Critical strain for through-thickness crack depends on fracture surface energy, Young’s modulus, the shape and position of the void, and the composite void size The viscosity coefﬁcient depends on the temperature, atomic volume, the diffusion coefﬁcients, and the interface roughness

2γ εc = F 2 πEc

η=

kTp2 8Ω (δDs + λDV 4 π )

Reference

[12]

[22]

The different modes of oxide scale failure are predicted by taking into account already discussed main physical phenomena, as summarized in Table 4.3. Both components of the ﬁnite element (FE) model are rigorously thermomechanically coupled. Thus, all the mechanical and thermal properties are included as functions of temperature. The commercial MARC K7.2 FE code was used for solving the nonsteady-state two-dimensional problem of the metal/scale ﬂow, heat transfer, viscous sliding, and failure of the oxide scale during hot rolling. Since the area of interest, where the oxide failure is considered, is localized at the entry to the roll gap and with the aim of limiting the model size, only an elastic sector of the roll above the roll gap and a small oxide scale raft on the strip surface were considered. To mimic the effect of the long continuous oxide scale on the stock surface, the rear end of the scale is ﬁxed to the metal surface using rigid ties. The speciﬁc heat, thermal conductivity, and density of the mild steel, necessary for heat transfer calculation, were introduced on the basis of available experimental data [17, 30]. The mechanical properties were assumed to be similar to those used in rolling models [7, 10]. The ﬂow strength in the hot deformation process was introduced as a function of temperature, strain, strain rate, and carbon content using Shida’s equations [20]. The radiative cooling of heated surfaces was simulated by prescribing the energy balance for the boundary surface. The oxide scale is simulated as consisting of scale fragments joined together along the metal surface to form a continuum scale layer. The length of each scale fragment was less than that observed in the hot rolling laboratory tests to allow sensitivity of the model to crack spacing. Each model fragment consisted of 272 four-node, isoparametric, arbitrary quadrilateral plane strain elements. It has to be noted that the length of scale fragment, type of element used, and their number for the scale fragment mainly depend on the

91

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4 Methodology Applied for Numerical Characterization of Oxide Scale

conditions being analyzed. The scale and metal surface were assumed to be adherent when they were within a contact tolerance distance, taken to be 1 μm. To allow for contact between the metal and the oxide scale fragments to form a continuous scale layer on the stock surface, atmospheric pressure is applied to the scale fragments as a boundary condition. The available experimental data showed unstable crack propagation for the test conditions when through-thickness oxide scale cracking occurred, favoring the assumption of linear elastic fracture mechanics for the model. A critical failure strain was used as the criterion for the throughthickness cracking and was applied perpendicular to the crack faces. Assuming that the critical failure strain related to the fracture due to shear loading parallel to the crack faces exceeds the corresponding value for the tensile mode, the normal and tangential separation stresses were calculated in the model using the deformable–deformable contact procedure implemented in the MARC code. Tangential viscous sliding of the oxide scale over the metal surface was allowed when the scale and the metal surface were adherent. The viscous sliding arose as a result of the shear stress transmitted from the underlying metal to the scale in a manner analogous to grain-boundary sliding in high-temperature creep [21]. This kind of sliding is different from frictional sliding of the separated scale fragment when separation stresses are exceeded. As can be seen in Figure 4.21, which illustrates model predictions of the longitudinal stress component within the cross-section of the stock, hot ﬂat rolling gives rise to signiﬁcant tensile loading of the free metal surface layer around the roll gap at both entry and exit. These zones are areas where the probability of tensile

Figure 4.21 Distribution of the stress component in the rolling direction (σx) predicted in the cross-section of the roll gap in the absence of the oxide scale.

4.2 Prediction of Mild Steel Oxide Failure at Entry Into the Roll Gap as an Example

Figure 4.22

Distribution of temperature predicted in the cross-section of the roll gap.

oxide failure is highest. The zone of entry into the roll gap is important from the point of view of the current rolling pass because hot metal can extrude through any cracks under the roll pressure, thereby enhancing both heat transfer and friction. The longitudinal tension at the exit from the roll gap could produce further oxide scale failure because the temperature at the interface has dropped to about 800 °C (Figure 4.22), which is the temperature range for brittle oxide scale behavior. This additional failure, if it happens, is reﬂected on the micro events at the interface for the subsequent rolling passes or on the quality of the surface of the ﬁnal rolled product. The present analysis pays attention mainly to two key technological hot rolling parameters which have an inﬂuence on the secondary oxide scale failure at the entry into the roll gap, namely, the temperature and the oxide scale thickness. The initial stock temperature is probably the most crucial factor for oxide scale failure and the most variable in commercial rolling practice. Apart from the direct inﬂuence on the extent of tangential viscous sliding and adherence of the scale, the surface fracture energy and Young’s modulus, which are reﬂected in the model criteria for through-thickness cracking and spallation, there is evidence of the inﬂuence of temperature on the morphology of the oxide scale and the formation of voids. The scale formed at 1150 °C was nonhomogeneous and delamination within the oxide layer took place during tensile loading [15]. The observations have shown that oxide scales formed at 1150 °C delaminated more readily than more homogeneous scales formed at 900 °C. The outer layers displaced along the interface within the oxide scale during elongation of the specimen. The separated outer scales are very porous and much thicker that the nonseparated oxide layer, which was usually 3–8 μm thick. The temperature also has a signiﬁcant effect on the oxide growth kinetics [31, 32] contributing to the thickness of the scale growth between rolling passes. The secondary scale grows faster on the newly exposed

93

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4 Methodology Applied for Numerical Characterization of Oxide Scale

metal surface after passing through a descaler. However, the secondary scale thickness usually does not exceed 150 μm [9, 11]. The numerical approach developed for the oxide scale modeling allows for the formation of nonhomogeneous oxide scale. Nevertheless, to avoid unnecessary complexities in this microcomponent of the model, a homogeneous scale 100 μm thick and containing voids has been assumed for the numerical analysis. A sequence of through-thickness crack formation can be seen in Figure 4.23 showing different increments of the nonsteady-state modeling corresponding to different moments of time for the oxide scale raft entering the roll gap. Throughthickness cracks develop from the pre-existing defects located at the outer surface of the oxide layer, where the critical strain for failure has been reached. It reaches a maximum value approximately midway between the cracks. Within the scale fragment the in-plane stress cannot transfer across the crack and becomes zero at each of the crack faces. Thus the level of longitudinal stresses within the oxide scale is signiﬁcantly relaxed compared with the surface layer of the metal (Figure 4.24).

Figure 4.23 Distribution of the strain component εx predicted for different time moments of scale raft entering into the roll gap at an initial temperature of 800 °C. Here the scale raft consists of 10 fragments.

4.2 Prediction of Mild Steel Oxide Failure at Entry Into the Roll Gap as an Example

Figure 4.24 Distribution of the σx stress component predicted at the moment of entering into the roll gap at an initial temperature of 800 °C. Note the crack (crack N 2 in Figure 4.23), which has opened up in the oxide scale ahead of contact with the roll.

At low temperatures, in the absence of relaxation by viscous sliding, relaxation of stresses can only occur by cracking and spallation of the scale fragment when the strain increases. At higher temperatures interface sliding can have a signiﬁcant role in relaxation of the transmitted stresses (Figure 4.25). The level of longitudinal stresses at the stock surface layer for the higher stock temperature is less than that for the lower one but, as can be seen from Figures 4.24 and 4.25, the relaxation of the oxide scale stresses relative to the metal surface layer is visible in both cases. The difference is that through-thickness cracks at the entry into the roll gap have not occurred in the higher temperature range, so the scale would enter the roll gap without cracks. In this case, stress relaxation within the scale takes place by sliding along the oxide/metal interface. The approach developed and described earlier [15, 33], combining the hot tensile measurement and FE modeling, allows for determination of these transitional temperature ranges for a particular steel grade. Although viscous sliding becomes easier at high temperature, the shear stress at the oxide/metal interface will eventually lead to the separation of the scale from the metal. To mimic the effect of a long continuous oxide scale on the stock surface, in the model the rear end of the oxide scale raft has been ﬁxed to the metal surface using rigid ties. The relative velocity between the oxide scale and the metal surface increases as the scale comes to the entry into the roll gap and reduces when the ﬁxed end of the scale comes up to the zone of longitudinal deformation (Figure 4.26). At the moment of entering the roll gap, the roll comes

95

4 Methodology Applied for Numerical Characterization of Oxide Scale

Figure 4.25 Distribution of the stress component σx predicted at the moment of entering into the roll gap at an initial temperature of 1100 °C. At this elevated temperature, there is no cracking of the oxide scale.

0.002

Relative velocity, m/s

96

Scale contact with the roll

0.001 0 -0.001

0

0.05

0.1

0.15

0.2

0.25

0.3

-0.002 -0.003 -0.004 -0.005 -0.006

Time, s Figure 4.26 Relative velocity between the oxide scale and the metal surface predicted for the time of entering the roll gap for the following parameters: scale thickness = 0.1 mm, stock thickness = 25 mm, temperature = 1100 °C, roll speed = 30 rpm, and reduction = 20%. The oxide scale raft is ﬁxed to the metal surface at the rear end.

into contact with the scale and drags it into the roll gap. Since the roll surface is moving faster than the metal surface at entry, the relative velocity could be signiﬁcantly decreased and it could even change sign, depending on at which oxide surface, bottom or top, the friction force is greater.

4.2 Prediction of Mild Steel Oxide Failure at Entry Into the Roll Gap as an Example

It has to be noted that the criteria for oxide failure in the model have been developed in terms of crack propagation rather than initiation of ﬂaws. For oxide scale on a free metal surface, such as at entry into the roll gap, the underlying elongating metal transmits an increasing stress to the oxide scale as rolling proceeds. Thus, even after through-thickness crack formation, the elongating substrate allows the transmission of the stress to each pre-existing void in the oxide scale, thus making crack initiation not the limiting process. This assumption has been implemented into the model based on the experimental observations of the present and other authors [26]. Although the model allows for the assumption of a spectrum of strain values as criteria for crack generation and spalling, just one level of critical strain has been chosen for this analysis. As can be seen in Figure 4.27a, if the oxide scale is thin enough, it could enter the roll gap without cracks, as a continuous layer, even at a relatively low temperature. This kind of behavior is typical for the thinnest scales. Although the scale on mild steel at 700 °C can be considered as brittle, crack generation, in terms of the model, is a size-dependent concept. The stress sufﬁcient for the pre-existing crack propagation increases as the crack size decreases. The pre-existing cracks for the thin scales, which mimic the scale ﬂaws, are less than those for thicker scales. Reducing them, the lower limit could be reached when the stress for crack propagation eventually exceeds the yield stress assumed for the oxide scale. The oxide scale will then be able to deform in a ductile manner and not fail by through-thickness cracking. This is known in the literature as the comminution limit of the material [34]. The results of modeling favor the conclusion, which is important from the technological point of view, that for a particular steel grade and the rolling parameters, there is a lower limit of the oxide scale thickness, beneath which the scale enters the roll gap without through-thickness cracks. If the oxide thickness is greater than the lower limit mentioned above, the crack pattern at entry into the roll gap is sensitive to the scale thickness (Figures 4.27b and c). In the low-temperature range when the interface is strong, relaxation occurs by the formation of through-thickness cracks at a sufﬁciently high strain within the scale layer. Although there will be some small relaxation of stresses because of viscous sliding, it seems likely that crack generation will be negligibly affected because adherence at the oxide/metal interface prevents the scale from slipping. The increase of the oxide scale thickness results in redistribution of the cracks. This is inﬂuenced by the critical criteria for separation within the oxide scale and the oxide/metal interface [33, 35]. In spite of the lack of direct data about the separation criteria making determination of the effect problematic, the modeling results have shown that the crack spacing tends to increase for thicker oxide scales at entry into the roll gap. To clarify the difference between the failure behavior of the thinnest (30 μm) and the thickest (300 μm) oxide scale in the lowtemperature range, the results of prediction are plotted together in Figure 4.28. Fixing the rear end of the oxide scale raft to the metal surface makes observation of the effect easier. The thinnest scale neither cracks at the zone of longitudinal tensile stresses before the entry into the gap, nor cracks at the moment of the roll

97

98

4 Methodology Applied for Numerical Characterization of Oxide Scale

Figure 4.27 Distribution of the strain component εx predicted at the moment of entering into the roll gap for the different thicknesses of the oxide scale: (a) 0.03 mm thickness; (b) 0.1 mm thickness; (c) 0.3 mm thickness.

gripping. This is in contrast to the thickest oxide scale, which fractures into islands at the moment of contact with the roll. From these results, the conclusion is reached that if the initial rolling temperature is in the low-temperature range, in terms of the mode of oxide scale failure, and the oxide scale thickness exceeds its comminution limit when the scale could fail only in ductile manner, the longitudinal tensile stress at entry into the roll gap can favor through-thickness cracks in the scale. The breaking up of the scale by bending at the moment of the roll gripping can contribute additionally to failure in this temperature range.

4.2 Prediction of Mild Steel Oxide Failure at Entry Into the Roll Gap as an Example

Figure 4.28 Distribution of the strain component εx predicted at the moment of entering into the roll gap for the different thicknesses of the oxide scale assuming that the oxide scale raft ﬁxed to the metal surface at the left end. (a) 0.03 mm thickness, time with respect to the beginning of calculation – 0.2788 s; (b) 0.3 mm thickness, simulation time = 0.272 s; (c) 0.3 mm thickness, simulation time = 0.2788 s.

4.2.5 Veriﬁcation Using Stalled Hot Rolling Testing

It is evident from the preceding discussion that, for the hot rolling of mild steel, the area of entry into the roll gap can be the source of through-thickness cracks, depending to a signiﬁcant extent on the initial rolling temperature and oxide scale thickness. Stalled hot rolling tests have been conducted with the aim of verifying the main points of the discussion based on the numerical analysis. Figure 4.29 illustrates results from one test. Using furnace oxidation with the gas protection at 1150 °C for 15 min allowed a scale layer of about 300 μm thickness to be grown that smoothly covered the specimen surface. The oxidized specimen was then cooled to 700 °C, with the aim of reaching the low-temperature range for a

99

100

4 Methodology Applied for Numerical Characterization of Oxide Scale

Figure 4.29 Oxide scale on the strip after testing (a) and thermal history of the strip (b) during a stalled hot rolling test. Furnace temperature for oxidation with gas protection 1130 °C; oxidation time 15 min (scale thickness around 250–300 μm); initial rolling temperature 700 °C.

relatively strong oxide/metal interface and weak scale, and rolled to a reduction of 30%. The thermal history (Figure 4.29b) shows two steps down in temperature: the ﬁrst, during the rolling pass, and the second, smaller, due to the contact with the roll during the reverse roll movement. Several zones could be observed after testing (Figure 4.29a). The nondeformed zone with the initial slightly blistered oxide scale is visible on the far left of the image in Figure 4.29a. Next is the zone of entry into the roll gap where the central noncracked and the lateral cracked areas can be distinguished. This central area is the most relevant to the ﬂat rolling conditions modeled above because conditions nearest to plane strain prevail. The sides were inﬂuenced by three-dimensional deformation ﬁelds at the edges of the specimen. The zone of the arc of contact with the roll reﬂects the semicircular shape of the crack pattern formed at the edges of the oxidized specimen before the gap, together with small cracks between the larger circular cracks. The central part of the arc consists of the many horizontal cracks with the small crack spacing similar to that, which resulted from the small cracks formed at the edges between

4.2 Prediction of Mild Steel Oxide Failure at Entry Into the Roll Gap as an Example

Entry into the roll gap

A B

B

C

C Rolling direction

Figure 4.30 Secondary electron image showing the oxide scale on the strip at the zone of entering into the roll gap during a hot stalling rolling test. The full width zone is shown on the left side of the ﬁgure with details around points a, b, and c on the right side.

the semicircular lateral cracks. It favors the assumption that these horizontal cracks have been formed at the moment of the scale contact with the roll. The crack spacing for both types of cracks, formed before and at the moment of entering, had widened at the exit from the roll gap where extensive longitudinal tensile stresses form at the stock surface layer. Figure 4.30 shows the SEM image of the oxide scale at the zone of entry into the roll gap where three areas described above are marked and shown separately on the right. It can be clearly seen that the oxide scale at the central area B has been broken at the moment of roll contact, backing up the numerical prediction made using FE modeling for the same parameters (Figures 4.28b and c). The results have been placed together in Figure 4.31 for better comparison. The additional cracks at the lateral areas A and C appeared after the moment of roll gripping can serve as evidence that breaking of the oxide scale at the moment of contact with the roll can contribute to the crack pattern formed on the free scale before entering due to longitudinal tensile stresses. Although the developed model needs more reliable data, particularly for oxide scale and oxide/metal interface properties, at this stage of its development it has allowed predictions to be made which are in good agreement with available experimental results of stalled hot rolling tests. In combination with the hot tensile testing, which gives the necessary information about the temperature ranges for

101

102

4 Methodology Applied for Numerical Characterization of Oxide Scale

Figure 4.31 Oxide scale on the strip (a) predicted and (b) observed in the middle of the top strip surface at the moment of entering into the roll gap.

the two modes of oxide scale failure, the model can be used for an analysis of failure of the oxide scale at entry into the roll gap for the particular steel grade and for the particular rolling conditions. The research reported in this chapter is an example of how the methodology, which is based on a combination of techniques, can allow materials to be characterized in circumstances where standard methods of measurement are not feasible or adequate on their own. Detailed ﬁnite element analysis using a physically based oxide scale model is a crucial aspect of the approach and takes a central place in the method. The main aim of the measurements is to upgrade the FE model with data that are more speciﬁc for the particular oxide scale under investigation and are crucial for the analysis. This mechanical testing coupled with microscopic observations of the morphological features of the scale and interface allows for more realistic numerical formulation of the problem and, as a result, for more adequate prediction. The microscopic observations using scanning electron microscopy, backscattered electron imaging, and electron backscattered diffraction analysis of scales grown under different conditions during mechanical testing allow for conﬁguration of the model so that it precisely reﬂects the characteristic morphological features such as different oxide layers, voids, and roughness of the interfaces. About 20 different model parameters describing the properties of the oxide scale and the scale/metal interface have separate inﬂuences on the results of prediction. The model is also used to determine the most critical parameters of the scale failure. One of them is temperature for the change of mechanism from the through-thickness crack mode to the sliding mode of scale failure in tension. The oxide scale model is generic, developed to be independent of any technological process, and represents a numerical approach that can be applied to many metalforming operations where precise prediction of oxide scale deformation and failure plays a crucial role.

References

References 1 Li, Y.H., and Sellars, C.M. (1996) Modelling deformation behaviour of oxide scales and their effects on interfacial heat transfer and friction during hot steel rolling, in Proceedings of 2nd International Conference on Modelling of Metal Rolling Processes, December 9–11, 1996 (eds J.H. Beynon, P. Ingham, H. Teichert, and K. Waterson), The Institute of Materials, London, pp. 192–206. 2 Pawelski, O. (2001) Spannungen und Formänderungen in der elastischen Zone am Walzspalteinlauf, in Walzen Von Flachprodukten (ed. J. Hirsch), Wiley-VCH Verlag GmbH, Weinheim, pp. 38–44. 3 Li, Y.H., and Sellars, C.M. (2001) Behaviour of surface oxide scale before roll bite in hot rolling of steel. Materials Science and Technology, 17 (12), 1615–1623. 4 Krzyzanowski, M., Beynon, J.H., and Sellars, C.M. (2000) Analysis of secondary oxide scale failure at entry into the roll gap. Metallurgical and Materials Transactions, 31B, 1483–1490. 5 Krzyzanowski, M., and Beynon, J.H. (2002) Oxide behaviour in hot rolling, in Metal Forming Science and Practice (ed. J.G. Lenard), Elsevier, Amsterdam, pp. 259–295. 6 Lenard, J.G., Pietrzyk, M., and Cser, L. (1999) Mathematical and Physical Simulation of the Properties of Hot Rolled Products, Elsevier, Amsterdam. 7 Pietrzyk, M., and Lenard, J.G. (1991) Thermal-Mechanical Modelling of the Flat Rolling Process, Springer, Heidelberg, Berlin. 8 Beynon, J.H., and Krzyzanowski, M. (2003) Tensile strains ahead of entry into the roll gap. Steel Research, 74 (5), 277–284. 9 Chen, W.C., Samarasekera, I.V., Kumar, A., and Hawbolt, E.B. (1993) Mathematical modelling of heat ﬂow and deformation during rough rolling. Ironmaking and Steelmaking, 20 (2), 113–125. 10 Fletcher, J.D., and Beynon, J.H. (1996) Relating the small scale thermotribo-mechanics in hot strip rolling

11

12

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to the global deformation behavior, in Proceedings of 2nd Int. Conf. Modelling of Metal Rolling Processes, 9–11 December 1996, The Institute of Materials, London, UK, pp. 202–212. Li, Y.H., and Sellars, C.M. (1997) Effects of scale deformation pattern and contact heat transfer on secondary oxide growth, in Proceedings of 2nd Int. Conf. on Hydraulic Descaling in Rolling Mills, October 13–14, 1997, The Institute of Materials, London, UK, pp. 1–4. Schütze, M. (1995) Mechanical properties of oxide scales. Oxidation of Metals, 44 (1/2), 29–61. Nicholls, J.R., Evans, H.S., and Saunders, S.R.J. (1997) Fracture and spallation of oxides. Materials at High Temperatures, 14 (1), 5–13. Nagl, M.M., Evans, W.T., Hall, D.J., and Saunders, S.R.J. (1994) An in situ investigation of the tensile failure of oxide scales. Oxidation of Metals, 42 (5/6), 431–449. Krzyzanowski, M., and Beynon, J.H. (1999) The tensile failure of mild steel oxides under hot rolling conditions. Steel Research, 70 (1), 22–27. Boyer, H.E., and Gall, T.L. (eds) (1985) Metals Handbook, Desk Edition, ASM, Metals Park, OH, USA. Devadas, C., and Samarasekera, I.V. (1986) Heat transfer during hot rolling of steel strip. Ironmaking and Steelmaking, 13 (6), 311–321. Fletcher, J.D., and Beynon, J.H. (1996) Heat transfer conditions in roll gap in hot strip rolling. Ironmaking and Steelmaking, 23 (1), 52–57. Fletcher, J.D., Talamantes-Silva, J., and Beynon, J.H. (1998) The inﬂuence of the roll gap interface conditions on subsequent surface ﬁnish, in Proceedings Modelling of Metal Rolling Processes: Symposium 8, March 1998, The Institute of Materials, London, UK, pp. 50–59. Shida, S. (1974) Effect of carbon content, temperature and strain on compressive ﬂow stress of carbon steels. in Hitachi Res. Lab. Report, Tokyo, Japan, pp. 1–9.

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4 Methodology Applied for Numerical Characterization of Oxide Scale 21 Riedel, H. (1982) Deformation and cracking of thin second-phase layers on deformation metals at elevated temperature. Metal Science, 16, 569–574. 22 Raj, R., and Ashby, M.F. (1971) On grain boundary sliding and diffusional creep. Metallurgical and Materials Transactions B, 2 (4), 1113–1127. 23 Bakker, A. (1983) An analysis of the numerical path independence of the J-integral. International Journal of Pressure Vessels and Piping, 14 (3), 153–179. 24 Ranta, H., Larikola, J., Korhonen, A.S., and Nikula, A. (1993) A study of scale-effects during accelerated cooling, in Proceedings 1st Int. Conf. ‘Modelling of Metal Rolling Processes’, The Institute of Materials, London, UK, pp. 638–649. 25 Morrel, R. (1987) Handbook of Properties of Technical and Engineering Ceramics, HMSO, London. 26 Robertson, J., and Manning, M.I. (1990) Limits to adherence of oxide scales. Materials Science and Technology, 6, 81–91. 27 Swinkels, F.B., and Ashby, M.F. (1981) A second report on sintering diagrams. Acta Metallurgica, 29, 259–281. 28 Hancock, P., and Nicholls, J.R. (1988) Application of fracture mechanics to failure of surface oxide scales. Materials Science and Technology, 4, 398–406.

29 Jacucci, G. (ed.) (1986) Computer Simulation in Physical Metallurgy, vol. 21, Elsevier, Amsterdam. 30 Bauccio, M. (ed.) (1993) Metals Reference Book, 2nd edn, ASM International, Materials Park, OH. 31 Sheasby, J.S., Boggs, W.E., and Turkdogan, E.T. (1984) Scale growth on steels at 1200 °C: rationale or rate and morphology. Metal Science, 18, 127–136. 32 Ormerod, R.C. IV, Becker, H.A., Grandmaison, E.W., Pollard, A., Rubini, P., and Sobiesiak, A. (1990) Multifactor process analysis with application to scale formation in steel reheat systems, in Proceedings Int. Symp on Steel Reheat Furnace Technology (ed. F. Mucciardi), CIM, Hamilton, ON Canada, pp. 227–242. 33 Krzyzanowski, M., and Beynon, J.H. (1999) Finite element model of steel oxide failure during tensile testing under hot rolling conditions. Materials Science and Technology, 15 (10), 1191–1198. 34 Kendall, K. (1978) The impossibility of comminuting small particles by compression. Nature, 272, 710–711. 35 Beynon, J.H., and Krzyzanowski, M. (1999) Finite-element model of steel oxide failure during ﬂat hot rolling process, in Proceedings Int. Conf. Modelling of Metal Rolling Processes 3, London, December 13–15, 1999, The Institute of Materials, IOM Communications, London, UK, pp. 360–369.

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5 Making Measurements of Oxide Scale Behavior Under Hot Working Conditions Making observations of oxide scale behavior under industrial conditions is extremely difﬁcult and is not much easier in the laboratory. Standard methods of measurement on their own are not adequate for this purpose. A single experiment has yet to be found that is capable of representing the full range of phenomena. Instead, a range of techniques, each providing a partial insight, has been developed by different authors. Some of them are brieﬂy summarized in this chapter.

5.1 Laboratory Rolling Experiments

It has been shown during laboratory hot rolling of low carbon steel slabs that different thicknesses and structures of the oxide scales result in signiﬁcantly different states of the oxidized slab surface after the deformation, ranging from a continuous oxide scale layer adhering to the metal surface to severely cracked scales with signs of metal extrusion through the gaps in the scale under the roll pressure [1]. Different thicknesses and structures of the oxide scales resulted in different crack width, crack spacing and extent of fresh steel ﬂow through the gaps during hot rolling, as a function of temperature and rolling reduction. The direct measurement of scale temperature within a secondary oxide scale proved to be difﬁcult because of the signiﬁcant temperature gradient across the scale thickness during conventional hot rolling tests. In hot “sandwich” rolling, two slabs welded together at the leading edge are angled apart during furnace reheating with cracked natural gas protection to allow the formation of a thin oxide scale on the surfaces. After reheating, the slabs are closed together with the two scale layers trapped between the slabs, which can then be rolled at different temperatures and reductions [2]. A schematic representation of the “sandwich” hot rolling test is illustrated in Figure 5.1. The temperature gradient across the oxide scale between the slabs is negligible during hot rolling and the temperature history can be reliably measured by means of an inserted thermocouple, in contrast to conventional rolling, where the surface oxide scale undergoes severe chilling by the roll. As can be seen in Figure 5.2, the scale behavior during hot “sandwich” rolling of plain carbon steel is strongly sensitive to rolling temperature and reduction. Two Oxide Scale Behaviour in High Temperature Metal Processing. Michal Krzyzanowski, John H. Beynon, and Didier C.J. Farrugia Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-32518-4

5 Making Measurements of Oxide Scale Behavior Under Hot Working Conditions

Slab Roll

Oxide scale

Roll Slab Thermocouple

Figure 5.1

Schematic representation of the “sandwich” hot rolling test.

60 50 Rolling reduction, %

106

mixed region

40 cracking

30 20 no cracking

10 0 550

650

750

850

950

1050

o

Rolling temperature, C Figure 5.2 Oxide scale behavior during hot sandwich rolling of C-Mn steel slabs; scale thickness ∼100 μm, rolling speed of 0.14 m/s [3].

extreme cases were observed during the rolling tests: ﬁrst, circumstances where the scale exhibited no cracking, and second, where scale cracks, oriented transverse to the rolling direction, appeared after the rolling pass. It was concluded that during the conventional hot rolling at low rolling speed, which is more typical for laboratory rolling conditions and industrial plate rolling, the scale chilling during the rolling pass is signiﬁcant and the scale temperature can easily fall below the critical level for scale cracking, even though the bulk temperature of the slab remains above that level. The contact time with the rolls for industrial hot strip rolling is much shorter because the rolling speed is signiﬁcantly higher, and the

5.1 Laboratory Rolling Experiments

oxide scale can remain at high temperatures during the rolling pass, exhibiting no cracks after rolling. In a conventional rolling process, both cracking and deformation of the surface scales are observed on hot rolled steel slabs that had been rolled completely through the roll gap. However, metal deformation in the roll gap is a transient and accumulated process during which the rolling reduction and metal ﬂow speed vary continuously from the entry to exit plane according to the roll speed and the deformation zone geometry as deﬁned by the roll diameter, slab thickness, and reduction. The scale behavior in a roll pass is also a transient process, and the scale deformation and cracks observed after hot rolling are only the ﬁnal results. Therefore, to obtain a complete understanding of the scale behavior during hot rolling, it is important to know the scale behavior before the roll bite and its variation in the roll gap. It is impossible to obtain such information using conventional rolling tests. For this reason, a stalling test procedure has been developed as an alternative approach to examine the behavior of surface scales before entry into the roll gap [4]. In the hot stalling tests, the steel slabs have their broad surfaces ground to the same ﬁnish and cleaned of any contaminants. Each steel slab is placed in the furnace and reheated for necessary time with or without cracked natural gas protection at different furnace temperatures to allow the formation of oxide scale layers of desired thickness and structure. The slab is placed on its edge in the furnace such that the broad surface is not in contact with any part of the furnace chamber. This procedure ensures uniform growth of scale on both broad surfaces [5]. After oxidation, the slab is air cooled outside the furnace to the desired temperature, in this case 900, 1050, 1100, or 1150 °C, and is then rolled in the laboratory mill to a chosen reduction. In order to achieve stalling during testing, the rolling mill is stopped when approximately one-third to one-half of the slab length has passed through the roll gap by switching off the power supply. This technique allows a partially rolled state to be developed in the second half of the slab. A low roll speed is used for all tests in order to reduce the time required to stop the mill. In the laboratory Hille 50 rolling mill, for instance, the testing speed was 10 rev/ min (Figure 5.3), corresponding to a rolling speed of 0.07 m/s. The mill is switched over to rotate in the reverse direction immediately after the stopping to expel the partially rolled slab, thereby minimizing local overheating of the rolls. The variations of the rolling load, the roll speed, and the slab temperature measured using the LabVIEW data acquisition system in a typical hot stalling rolling test carried out using the laboratory Hille 50 rolling mill are presented in Figure 5.4 [4]. It illustrates the starting points of roll biting, mill power switch-off, reverse roll rotation, and complete expulsion of the partially rolled slab from the roll gap. The slab temperature is measured by using a K-type thermocouple inserted into the center of the slab. After hot rolling, the steel slab was cooled to room temperature in air. Macro- and microstructural observations of the surface can be carried out at room temperature to examine the cracking and deformation behavior of the oxide scales. The major advantage of hot stalling is that it allows close examination of the hot scale behavior before the roll bite under the combined conditions of scale temperature and other rolling variables.

107

5 Making Measurements of Oxide Scale Behavior Under Hot Working Conditions

Laboratory Hille 50 rolling mill at the University of Shefﬁeld, UK.

80

900 temperature

60 load (half)

850

40 20 0 1506

A

1508

B C roll speed 1510

1512

D

800

Slab temperature (°C)

Figure 5.3

Rolling load (kN) and speed (rpm)

108

1514 750

–20 Time (s)

A start rolling; B power switch-off; C start reverse rotation of rolls; D complete expulsion of partially rolled slab Figure 5.4 An example illustrating variations of data measured during hot stalling rolling of steel at 900 °C with 20% reduction [4].

5.1 Laboratory Rolling Experiments

The state of the oxide scale at entry into the roll gap after hot stalling under different reductions at the same rolling temperature of 900 °C is shown in Figure 5.5. The temperature was measured at the slab center. The observed scale layers are thin and compact, and initially well adhered to the parent steel after reheating in the furnace with a controlled gas atmosphere. Signiﬁcantly different behavior is observed in the scales during hot stalling. The rolling parameters for the test are presented in Table 5.1. As can be seen in Figure 5.5a, no cracks are visible in the scale before and during rolling at 10% reduction. The scale layer adheres to the parent steel from entry to exit plane, except some round scale blisters that are formed either during reheating in the furnace or during air cooling outside the furnace. About 3 mm wide wave in the rolling direction is observed in the scale just before the roll bite when the rolling reduction of the steel increases to 20% (Figure 5.5b). The wave is similar to the viscous wave reported by other authors [6]. The width of the delaminated viscous band reaches about 4.6 mm when a higher 40% reduction is applied during the rolling (Figure 5.5c). As can be seen from Figures 5.5b and c, such separation of the oxide scale from the hot steel surface is followed by its brittle cracking at the moment of the roll biting. This is because the separation might inﬂuence a

Figure 5.5 State of the oxide scale at entry into the roll gap observed for the steel slab after the hot stalling rolling tests carried out at the rolling temperature of 900 °C under different reductions (Table 5.1). The scale thickness is approximately 20 μm. [4]. Table 5.1 Parameters of the hot stalling rolling test related to Figure 5.4 [4].

Reduction (%)

Reheating temperature (°C)

Air cooling time (s)

Roll bite angle (°)

10 20 40

976 947 975

45 23 39

10.7 15.2 21.5

109

110

5 Making Measurements of Oxide Scale Behavior Under Hot Working Conditions

drop of the scale temperature and the scale becomes brittle enough to be broken under the deformation. In attempting to reduce the concomitant thermal effects and to simulate the behavior of oxide scale during rolling at low temperatures when the low carbon steel scales exhibit signiﬁcantly brittle behavior, a brittle lacquer can be applied on the surface of lead slabs, which are then rolled at room temperatures [7]. In this type of testing, pure lead slabs are coated with lacquer layers of various thicknesses, about 10–110 mm, on the broad surfaces. The coating is formed by single or repeated spraying of the clear liquid lacquer. The acrylic lacquer is the same as that used for protection of dry transfer marking and electrical circuits in electronic devices, for example, type RS 569-307. This lacquer exhibits brittle fracture behavior at room temperatures. The specimens need at least 24 h to dry and set following application of the coating. The coated lead slabs are rolled to the required reductions, such as 10, 20, 30, and 50%, at a low, steady speed. The general rolling procedure is the same as that described above for hot stall rolling of steel. In order to release the partially rolled specimen, the top roll was raised to provide a faster response than could be achieved by reversing the rotation of the rolls. This procedure is possible for lead slab rolling where the rolling loads are relatively low. It also avoids any effects of reverse rotation on the appearance of the lacquer. The lacquer mimics a brittle oxide scale on a hot working metal (lead has a low melting point so is hot worked at room temperature) but without temperature gradients. For the relatively thick scales (about 100 μm) the crack patterns of the oxide scales and the lacquers are similar (Figure 5.6). The cracking behavior of the oxide scales at temperatures when they are brittle can be further understood by this ambient rolling of the lead slab with brittle lacquer coatings. In the central area of the slab surface, the cracks produced are narrow, with no visible full extrusion of fresh metal into the gaps.

Figure 5.6 State of (a) the oxide scale on steel and (b) the lacquer on lead at entry into the roll gap observed after the stalled rolling tests; (a) rolling temperature = 900 °C, reduction = 20%, initial scale thickness = 50 μm; (b) rolled at room temperature, reduction = 12%, initial lacquer thickness = 105 μm (after [4]).

5.1 Laboratory Rolling Experiments

In contrast, near the edge of the slab, the cracked pieces are much larger and curved, and the major cracks are ﬁlled with extruded metal (Figure 5.7). The parameters of this stalling rolling test are presented in Table 5.2. The similar crack and lacquer patterns suggest that the wide cracks observed at the edges of the slab arise mainly because of spread and cracking in the edge areas before entry into the roll gap, while the effect of a temperature gradient across the slab width is secondary. The hot stalling experiments using oxidized steel slabs, combined with the cold stalling using lead slabs coated with brittle lacquer, are able to provide an effective and reliable means for studying the surface scale behavior during hot rolling, both

Figure 5.7 State of the lacquer layer after cold stalling rolling of the lead slabs with different geometry: Ho ≈ 11.3 mm (a, b, and c) and Ho ≈ 6.4 mm (d, e, and f); other rolling parameters are given in Table 5.2 [4].

111

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5 Making Measurements of Oxide Scale Behavior Under Hot Working Conditions Table 5.2 Parameters of the cold stalling rolling test related to Figure 5.7 [4].

Photo (Figure 5.7)

Rolling reduction (%)

Lacquer thickness (μm)

Initial slab width (mm)

a b c d e f

11.2 29.7 50.4 16 30 49

88 91 64 90 86 84

46 46 46 55 55 44

before and after the roll bite, when the scale is subjected to further deformation and failure within the arc of contact under the roll pressure. This cannot be achieved by conventional rolling experiments.

5.2 Multipass Laboratory Rolling Testing

The main aim of this type of testing is to investigate the behavior of the oxide scale during multistage deformation at high temperatures under the complex loading conditions found in the rolling processes. The testing allows for evaluation of the phase distribution within the oxide scale formed under secondary oxidation conditions and determination of the morphological changes related to the speciﬁc rolling deformation. During the multistage laboratory rolling testing, it is also possible to measure and trace the oxide scale defects found in the initially nondeformed scale, thereby establishing their inﬂuence on the behavior of the scale during the subsequent deformation stages. The mechanism of the oxide scale failure is complicated even during a single rolling pass since it depends on many technological parameters. Multipass laboratory rolling allows for observation and establishment of additional features of scale failure that are directly related to multistage deformation. The surface ﬁnish can also be evaluated for its relationship with the oxide scale failure during the deformation process. A combination of multipass laboratory rolling with other experimental techniques described in this chapter seems to be the most effective laboratory tool for understanding and characterizing the scale behavior during hot rolling. Multipass rolling tests were carried out using a recently upgraded, fully instrumented Hille 50 mill [8]. The roll gap during the tests was adjusted either manually or electronically through the worm gearing from 0 to 35 mm. The rolling parameters are shown in Table 5.3. Two different types of the rolling samples were used in the testing program (Figure 5.8). The sample shown in Figure 5.8a was used for the initial analysis during the full length rolling tests. A relatively small section, 15 × 50 × 8 mm, with the oxide scale in the nondeformed state was left at the end of each specimen for

5.2 Multipass Laboratory Rolling Testing Table 5.3

Parameters of the laboratory hot rolling testing [8].

Oxidation temperature (oC)

800

Oxidation time (s) Reduction (%) Rolling speed (mm/s)

900 20 70

1000 3000 40 360

900 20 70

3000 40 140

50 360

200

15 50

50

1.5 D 10 10.5 ++ 200

2

1.5 D 25

25

25

17 8

a Figure 5.8

113

30

60

70 b

Two types of the rolling specimens used for the multipass hot rolling testing [8].

comparison. Thermocouples for monitoring temperature were placed 2 mm beneath the upper surface and at mid-thickness in the specimen. The sample shown in Figure 5.8b was used for the stalling tests. The thermocouples were placed 2 mm beneath the upper surface at different sections of the sample to register the differences in the temperature history under the different deformation conditions. The upper surface of each sample was ground with 400 grade silicon carbide (SiC) paper, cleaned using an industrial degreaser, and rinsed with water and alcohol before testing. For a given steel grade, scale failure during hot rolling depends mostly on the temperature, scale thickness, and the rolling reduction [9, 10]. Hence, the parameters of the rolling program were chosen to cover both modes of scale failure at entry into the roll gap, that is, brittle and ductile. The oxidation conditions were selected for brittle behavior of the scale at 800 °C and ductile behavior at 1000 °C. The oxidation times were chosen to produce different scale thicknesses at the same oxidation temperature and to observe their behavior under similar rolling conditions. The samples were heated in an electrical resistance furnace without a protective atmosphere to the oxidation temperature. After initial oxidation, they were extracted from the furnace and subjected to a small predeformation, about 0.8% reduction, in the rolling mill with the aim of breaking and removing the primary oxide scale. The same samples were then re-introduced into the furnace and reoxidized for different times, Table 5.3. The oxidation was followed by two

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5 Making Measurements of Oxide Scale Behavior Under Hot Working Conditions

Figure 5.9 A specimen after the hot stalling two pass rolling test; three sections are visible: one part not deformed and the others reduced by one or two rolling passes [8].

different sets of rolling campaign. During the ﬁrst, the full length of the sample was passed through the roll gap in two deformation stages. The stalling rolling tests were performed during the second set, when the rolling mill was stopped while the sample was still in contact with the rolls. The advantage of the stalling tests was that different deformation conditions were obtained on the same sample with the same thermal history and oxidation conditions. For two-pass rolling, both deformations were made in the same rolling direction, with the same strain and the roll speed. In the two-pass stalling tests, the rolls were ﬁrst stopped when the sample were deformed about 75% of its original length before the rolls were separated and the sample removed. The roll speed and separation were adjusted for the second pass and the sample was deformed around half the length rolled after the ﬁrst stage of deformation. Figure 5.9 illustrates the shape of the sample after the stalled twopass rolling test after cooling in air from the rolling temperature. The rate at which the test was brought to the stalling condition did not inﬂuence the morphological features observed along the arc of contact, such as the scale failure and the formation of partial and through-thickness extrusions of hot metal into the cracks. Figure 5.10 illustrates different features at the scale–metal interface. The cracks formed from the initial contact with the roll during a previous deformation are widened and the underlying metal surface is exposed to the atmosphere. This allows the formation of a new thin oxide scale, as shown in Figure 5.10a. As the sample moves inside the arc of contact, the scale fragmentation becomes more evident. The damaged small scale fragments at the upper areas of the scale cross-section can be observed in Figures 5.10c and d. The throughthickness metal extrusion is shown in Figure 5.12b, where the relatively thin oxide scale failed during the ﬁrst deformation stage followed by the metal extrusion into the widening gap during the second deformation, allowing the direct contact of the hot metal with the roll surface. Local extrusions are also observed toward the exit from the roll gap, and exhibit heavy scale fragmentation at the upper areas of the scale cross-section (Figures 5.10c and d). The multipass hot rolling testing is also allowed statistical information about crack spacing and crack width after different stages of scale failure to be gathered. Figure 5.11 illustrates an example of such information for both deformation stages. The data can be used to analyze the inﬂuence of the rolling parameters on oxide scale failure.

5.3 Hot Tensile Testing

Large scale fragments

Scale formed after scale cracking

50 µm

a

Through thickness metal extrusion

100 µm

b

Scale fragmentation

Partial metal extrusion

c

50 µm

Partial metal extrusion

50 µm

d

Figure 5.10 Cross-section of the surface layer, illustrating different aspects of the oxide scale failure under the second deformation stage in the multipass hot rolling testing [8]; see the text for detailed explanation.

5.3 Hot Tensile Testing

As has been discussed, when a slab enters the roll gap, it is drawn in by frictional contact with the roll, which moves faster than the stock at that point. This inevitably produces a longitudinal tensile stress in the stock surface ahead of contact with the roll. It is this tensile stress that can lead to fracture of the scale prior to roll contact, and therefore the uniaxial tensile test can provide much valuable information on the behavior of the oxide scale that is relevant to hot rolling conditions. Some details of this testing method are discussed in this section. The testing equipment used for the tensile testing is shown in Figure 5.12. Initially, the dynamic characteristics of the tensile test machine were assessed to determine the maximum strain rate. The maximum crosshead rate for the test machine was about 80–100 mm/s. Thus, the maximum strain rate for this kind of test on the equipment available may not exceed 4–5 s−1 [10]. Figure 5.13 illustrates the results of elongation of the tensile specimen as a function of time for different strain rates. Good agreement with a linear increase in length was observed for low strain rates. For the fastest tests, at strain rates of 2.0–4.0 s−1, slight nonlinear

115

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5 Making Measurements of Oxide Scale Behavior Under Hot Working Conditions

Figure 5.11 The crack spacing and the crack width measured in the failed oxide scale after one and two deformation stages [8].

Figure 5.12

Equipment used for hot testing of the oxide scale in tension.

5.3 Hot Tensile Testing 1.4

elongation, mm

1.2 1 0.8 0.6 0.4 0.2 0 640.9

640.95

641

641.05

641.1

641.15

641.2

641.25

641.3

time, s

Figure 5.13 Elongation of the tensile specimen as a function of time for 5.0% strain and different strain rates [10].

movement of the crosshead took place at the beginning and the end of the test. Thus, the following parameter variations were chosen for the hot tensile test program: temperature: 830–1150 °C, thickness of the scale: 10–300 μm, strain: 1.5–20%, and strain rate: 0.02–4.0 s−1. These tensile tests revealed two types of accommodation by the oxide scale of the deformation of the underlying steel substrate [10]. At lower temperatures, the oxide scale fractured, usually in a brittle manner, with the through-thickness cracks triggering spallation of the oxide scale from the steel surface. At higher temperatures, the oxide scale did not fracture; rather it slid over the steel surface, eventually producing delamination of the scale. By assuming the transition temperature range, when the separation load within the scale fragments is less than the separation load at the oxide/metal interface at low temperature and exceeded by it at high temperature, it is possible to model transfer from one oxide scale failure mechanism to another. The testing technique described next is mainly used for evaluation of the transition temperature range. Round tensile specimens, having 6.5 mm gage diameter and 20 mm gage length, were prepared from mild steel. The steel grade 070M20 had a typical mass content of 0.17% C, 0.13% Si, 0.72% Mn, 0.014% P, 0.022% S, 0.06% Cr, 0.07% Ni, 0.11% Cu, <0.02% Mo, <0.02% V. The specimens were oxidized to the desired extent in the tensile rig just before starting the test. The vertical cylindrical induction furnace (with a working chamber 32 mm in diameter and 40 mm in height) was used for the heating (Figure 5.14). Excluding intermediate cooling is desirable because it could cause spalling of oxide scales. Air was used for high-temperature oxidation of the steel. Generally, the tensile test included the following stages: heating, 120 s; stabilizing of temperature in inert atmosphere, 300 s; oxidation, between 100 and 3000 s (depending on temperature and desired oxide thickness); gas change stage, 120 s; tension , up to 40 s; and cooling, 900 s. The principal effect of the nitrogen on the oxidation is dilution of other effective air species, such as O2 and H2O. The

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5 Making Measurements of Oxide Scale Behavior Under Hot Working Conditions

Ceramic cap Quartz tube Specimen Induction coil Nitrogen and air inlet

Nitrogen and air inlet

Figure 5.14 Details of the specimen in the furnace used for its heating and oxidation during testing in tension.

nitrogen was used for all stages as an inert atmosphere except for the oxidation stage. The slow cooling was necessary to prevent oxide fracture due to the strains which might result from thermal stresses arising from mismatch of the thermal expansion coefﬁcients of the oxide and substrate. Each sample was placed in the grips so that a small tensile load of 0.06 kN was applied during heating and the oxidation stage to eliminate the effects connected with backlash in the grips and thermal expansion. The system was switched over from load to position control at the end of the gas change stage just as tensile testing began and changed back to load control during cooling after testing. After cooling, the samples were sectioned to determined oxide thickness and crack patterns using macro and microscopic examination. These techniques provided detailed information of the failure processes. How this information can be used to provide insight into the behavior of the oxide scale during hot rolling has been described in Chapter 4. The temperature of transition between these two types of failure was sharp and very sensitive to steel chemical composition. It has been demonstrated experimentally that small differences in chemical content can be the reason for different modes of scale failure in tension [11, 12, 13]. The effect is so signiﬁcant that it will be discussed in detail in the following chapters in terms of the effect of the chemical composition of the underlying steel on oxide scale evolution and scale adhesion. A modiﬁcation to the tensile test was developed in an effort to measure directly the loads involved in these two types of failure [14]. The technique has signiﬁcant potential in terms of determining the most critical parameters for the modeling of scale failure and also for investigating the inﬂuence of different alloying elements on scale/metal adhesion at high temperatures. The aim of the modiﬁed hot tensile tests is twofold: determination of the temperature ranges for modes of oxide scale failure and evaluation of separation loads for scale failure in tension. Round tensile specimens for determination of failure modes of 6.5 mm gage diameter and 20 mm gage length are ground to a 1000 grit surface ﬁnish with SiC

5.3 Hot Tensile Testing

Figure 5.15 Drawing of the tensile specimen (left) and schematic representation of the two halves of the specimen (right) used for evaluation of the separation loads responsible for scale failure [14].

paper. Each specimen has a hole from one end for a thermocouple allowing temperature measurement during the test. Specimens for evaluation of the separation loads responsible for scale failure have the same shape and quality of the surface before oxidation but were cut in two equal parts pushed together before the test (Figure 5.15). To prevent transverse movements during tension a ceramic pin is inserted into an axisymmetrical hole, 1.5 mm in diameter and 5 mm long, in both halves of the specimen. The surfaces have to match each other accurately to prevent oxidation of the end faces between the halves. The specimens were oxidized to the desired extent in the tensile rig immediately before starting the test, just as for the normal tensile test described above. To measure the strain for any test the gage length should be taken into consideration, which is not obvious for the test when oxidation takes place between two separated parts of the specimen. The strain parameter is replaced by a ﬁxed length separation of the grips, equal for all tests. Each part of the sample is placed in the grips so that a small compression load is applied during heating and the oxidation stages. The system is switched over from load control to position control at the end of the gas change stage to allow measurement of load during tension. The procedure for the measurement of the separation loads includes several stages (Table 5.4). A small compressive load is applied during heating and oxidation stages to allow a continuous scale layer on the cylindrical side of the specimen to be obtained and to prevent oxidation on the ﬂat faces where the two halves join. The contact between the hot steel parts inevitably results in some bonding between them. The separation load is increased when the compression load is increased during the time necessary for heating and oxidation of the specimen. At the same time, too small a compression load does not ensure proper contact between the two parts of the specimen during heating and oxidation stages, so the optimal compression has to be chosen for all tests (Table 5.4, stage 1). The separation load measured without oxidation has to be registered for all tests as a background (Table 5.4, stage 2). During testing with oxidation (Table 5.4, stage 3), the separation load arising

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5 Making Measurements of Oxide Scale Behavior Under Hot Working Conditions Table 5.4 Measurement procedure for evaluation of the separation loads in the oxide

scale–metal system including different stages [14]. Stage of the procedure

Evaluation

1

Testing without oxidation for different compression loads

Effect of bonding

2

Testing without oxidation under the chosen compression

Separation load (bonding)

3

Testing with oxidation

Separation load (scale + bonding)

4

Subtraction of separation loads obtained in stage 2 from that obtained in stage 3

Separation load (scale)

Figure 5.16 Two different modes of oxide scale failure in tension during measurement of separation loads: (a) through-thickness crack development and (b) sliding along the oxide/ metal interface; the fragment of scale beneath was detached after the test [14].

from both oxide scale and bonding is measured. To separate the oxide scale effect from any background resulting from bonding and friction of the ceramic rod with the inside of the specimen, the results obtained in stage 2 are subtracted from the results obtained in stage 3. This is the ﬁnal stage of the testing procedure (Table 5.4, stage 4). The ﬁnal states of the oxide scale after testing are illustrated in Figure 5.16. The ﬁrst mode corresponds to the strong interface between the oxide scale and metal relative to the oxide scale and failure occurs by through-thickness cracking. In this case the separation load within the oxide scale is registered. The second mode

5.3 Hot Tensile Testing

relates to the interface being weaker than the oxide scale, which results in sliding of the oxide scale raft along the oxide/metal interface. The tangential separation force is registered in this case. The oxide scale clearly grew to form a continuous layer around the cylindrical surface of the specimen before the tension stage. Scanning electron microscopy after testing and cooling of the specimens has shown that the scale layer is continuous in the transverse direction but does not always have the same thickness around the circumference. An increase of oxidation time is desirable for improving homogeneity of the scale along the circumference, but this is not always feasible when investigating thin scales that may be typical of industrial practice. Figure 5.17 illustrates the level of loads causing

Figure 5.17 Loads registered during two modes of oxide scale failure in tension: (a) through-thickness crack and (b) sliding along the interface; ◊, testing with oxidation; ⵧ, testing without oxidation; 䉱, subtraction of ⵧ from ◊ [15].

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5 Making Measurements of Oxide Scale Behavior Under Hot Working Conditions

failure of the oxide scale for both temperature ranges. As mentioned earlier, to eliminate an inﬂuence of bonding between the two halves of the specimen and friction between the ceramic rod and specimen, the results of testing with the same parameters but without oxidizing, that is, in an effectively inert atmosphere of nitrogen, were subtracted from measured loads for the oxidized specimens. The measured critical shear load for causing separation of the scale along the scale/ metal interface at high temperature range can be seen in Figure 5.17b. The location of the plane of sliding is determined by the lowest cohesion strength at different interfaces and the resulting stress distribution. The measured loads are recalculated in terms of strain energy release rate to be introduced into the scale model (Chapter 6). Following the tensile technique described above, a comparative test program was carried out by different authors using both round and ﬂat specimens, to see if the shape of the tensile gage section had an inﬂuence on the results [8, 16]. The oxide scales on the surface of both shapes of specimen after tension exhibited the same crack pattern when the deformation conditions were the same. The throughthickness cracks developed in the scale in the direction perpendicular to the direction of tension. However, the crack pattern was changed and was not directional when the specimen was heated and cooled without tension. Figure 5.18 shows the state of the scale on the surface of the round, ﬂat undeformed, and ﬂat deformed specimens with different numbers of cracks in the oxide scales. The ranges of gage section, width/height ratio, and average crack spacing in the tests were 0.18–0.49 and 1.2–5.0 mm, respectively. The purpose of the next hot tensile testing technique is the investigation of the deformation of the surface oxide scale by determining the strain–stress curves and observing the failure behavior of the iron oxide scales at elevated temperatures. Tensile testing of pure FeO, γ-Fe3O4, and α-Fe2O3 was performed using this technique at 600–1250 °C under controlled gas atmospheres [17]. Although the strain rates of 2.0 × 10−3–6.7 × 10−5 s−1 achieved in these tests are relatively low in comparison to those observed in industrial practice, they do allow for investigation of mechanical properties, deformation, and fracture behavior of the iron oxides at elevated temperatures. The equipment for the tensile testing included 100 kgf (981N) tensile tester, gold-image infrared heater, quartz reaction chamber, gas control system, and observation unit with CCD camera (Figure 5.19). The system is designed to avoid reaction between the oxide specimens (α-Fe2O3, γ-Fe3O4, and FeO) and the ambient gas atmosphere that maintains the oxide composition during the high-temperature tensile testing. The specimens of iron oxide for tensile testing were prepared by complete oxidation of 99.99% pure iron specimens. The dimensions of the specimen before oxidation are shown in Figure 5.20. The specimens were oxidized at 1250 °C for 2 h, cooled to 600 °C over 15 min, and were tested in tension at strain rates in the range 6.7 × 10−5 to 2.0 × 10−3 s−1. The procedure is illustrated schematically in Figure 5.21. The gas atmospheres for producing various types of iron oxide at 1250 °C were each different. For instance, an atmosphere of 10 vol.% H2O–20% O2–bal. N2

5.3 Hot Tensile Testing

Round specimen:1 ∅6.5 mm Strain: 0.02 Strain rate: 0.2 s–1 Number of cracks: ~20

Specimen thickness: 3 mm Tension was not applied

Specimen thickness: 5.4 mm Strain: 0.0125 Strain rate: 0.13 s–1 Number of cracks: 3

Specimen thickness: 3.5 mm Strain: 0.014 Strain rate: 0.14 s–1 Number of cracks: 12

Specimen thickness: 2 mm Strain: 0.012 Strain rate: 0.12 s–1; Number of cracks: 16

10 mm Figure 5.18 State of the oxide scale on the gage section of the tensile specimen; in all cases the oxidation temperature was 830 °C [16].

(calculated partial pressure of oxygen, PO2 , of 2 × 10−1) was used for producing α-Fe2O3. An atmosphere of 10 vol.% H2O–0.05% O2–bal. N2 (PO2 of 5 × 10−4) was used for obtaining γ-Fe3O4 and one with 10 vol.% H2O–3% H2–bal. N2 (PO2 of 1 × 10−10) was used for growth of FeO. The gas mixture, being controlled during the entire experiment, was introduced to the reaction chamber from the very beginning of the oxidation to the end of the tensile test. X-ray diffraction of respective specimens after oxidation was used to conﬁrm the formation of iron oxide, Figure 5.22. As can be seen from Figures 5.22a and c, the iron specimens were fully transformed into α-Fe2O3 and FeO during oxidation. Although some negligible inclusions of α-Fe2O3 and FeO were registered during γ-Fe3O4 formation, it can be

123

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5 Making Measurements of Oxide Scale Behavior Under Hot Working Conditions

Figure 5.19 Schematic representation of the testing equipment for determining strain–stress curves and observing the failure behavior of iron oxide scales at elevated temperatures [17].

Figure 5.20

Drawing of the specimen for hot tensile testing [17].

Figure 5.21

Temperature history of the specimen for hot tensile testing [17].

5.3 Hot Tensile Testing (a)

a–Fe2O3

Intensity (cps)

1000

0

(b)

g –Fe3O4

1000

0

(c)

FeO

1000

0 10

20

30

40

50

60

70

80

90

100

2q (°) Figure 5.22 X-ray diffraction patterns of the specimens with different oxides, (a)–(c), after preoxidation at 1250 °C for 2 h. (a) PO2 = 2 × 10 −1; (b) PO2 = 5 × 10 −4 , and (c) PO2 = 1× 10 −10 [17].

Figure 5.23 Optical micrographs of the cross-section of the tensile specimens with different oxides after oxidation at 1250 °C for 2 h. (a) PO2 = 2 × 10 −1; (b) PO2 = 5 × 10 −4 ; and (c) PO2 = 1× 10 −10 [17].

concluded that γ-Fe3O4 was also the predominant oxide (Figure 5.22b). Crosssections of the test specimens after oxidation are shown in Figure 5.23. The oxidized specimens had a larger cross-section than that of the original iron specimens. The white box in Figure 5.23a indicates the original cross-section of the iron test specimen before oxidation. Pores were observed in the oxides and the porosity, estimated by density measurements, was around 30%. The original crosssectional area of the oxidized specimen of 2 mm2 was assumed for stress calculation with a Pilling–Bedworth ratio (PBR) of around 2 for Fe-oxide, as reported

125

5 Making Measurements of Oxide Scale Behavior Under Hot Working Conditions

elsewhere [18]. Transmission electron microscopy (TEM) was conducted for a specimen after a tensile deformation at a strain rate of 2.0 × 10−4 s−1, fractured at 50% strain at 1000 °C, in order to determine the Burgers vector of γ-Fe3O4 deformed at elevated temperature. The thin foil specimen for TEM observation was prepared by sputtering Ar ions at the center of the tensile-deformed γ-Fe3O4 specimen. Stress–strain curves obtained for α-Fe2O3, γ-Fe3O4, and FeO oxide specimens deformed in tension at various temperatures are shown in Figure 5.24. Plastic behavior was not obviously exhibited for α-Fe2O3 at 1150–1250 °C (Figure 5.24a). For γ-Fe3O4, plastic deformation was observed at temperatures above 800 °C, and at 1200 °C stress saturation occurred. The mechanism of plastic deformation might have changed at 1200 °C and 110% elongation was obtained at 1200 °C for this oxide (Figure 5.24b). For FeO oxide, plastic deformation is observed above 700 °C. This oxide exhibited “steady-state deformation” above 1000 °C, and 160% elonga-

(a) a-Fe2O3

Stress (MPa)

40

30

20

1200 °C 1150 °C 1250 °C

10

0

0

5 10 Strain (%)

(b) g –Fe3O4 30

(c) FeO

700 °C (2.0 MPa, brittle-fracture at 2.0%)

25 800 °C

20

900 °C 15 1000 °C 1100 °C 1200 °C

10 5 0

15

35 30 Stress (MPa)

35

Stress (MPa)

126

600 °C (brittle-fracture at 1.5%)

25 20

700 °C

15

800 °C

10

900 °C 1000 °C 1200 °C

5 0

20

40

60

80 100 120

Strain (%)

0

0

40

80 120 Strain (%)

Figure 5.24 Stress–strain curves obtained for different oxides during tensile testing at various temperatures at a strain rate of 2.0 × 10−4 s−1 [17].

160

5.4 Hot Plane Strain Compression Testing

tion was achieved at 1200 °C (Figure 5.24c). The authors suggested that the steadystate deformation resulted from either dynamic recovery due to dislocation climb (dislocation creep) or diffusion creep (Nabarro–Herring creep or Coble creep). This large, 160%, elongation at 1200 °C was unexpected since only 2–15% elongation was reported for this oxide in earlier studies. This is probably due to extremely pure grain boundaries that minimize fracture of the oxide scale.

5.4 Hot Plane Strain Compression Testing

Most of the experimental devices used to study the oxide scale behavior during hot plane strain compression testing are designed to oxidize the surface of steel samples for a short time, sometimes for a few seconds. Usually, the device consists of a chamber that is installed within the frame of a test machine, so that the specimen can be deformed immediately after oxidizing. The atmosphere within the chamber is controlled to be an inert or a controlled oxidizing atmosphere. A schematic diagram of one such experimental setup is shown in Figure 5.25 [19]. The material used to construct this device was mica because it is nonﬂammable and isolating material, and mechanically stable at the test temperatures. It does not react with the oxide or the gas atmosphere. The chamber comprised three main parts. Both the upper and bottom parts had an elongated oriﬁce allowing the tool to deform the specimen, while the middle part secured the sample on top of four small alumina rods. The central part had two drilled holes for two 9 mm quartz tubes that supply the gases. The two quartzs tubes were also drilled to allow for the gas ﬂowing into the chamber and the upper tool. The test begins with ﬂushing the chamber with nitrogen at 14 nl/min (i.e., ﬂow in l/min but converted to standard air conditions of 1.013 25 bar absolute, 0 °C and

Tool

Steel sample

Tube

Tube Figure 5.25 Schematic diagram of the chamber illustrating the position of the steel sample, the gas feeding tubes, and the upper tool [19].

127

128

5 Making Measurements of Oxide Scale Behavior Under Hot Working Conditions Valves for gas control

D A

E C B

D A: Chamber. B: Gas tubes. C: Induction coil. D: Tools. E: Robot

a

b

Figure 5.26 Photographs of the robot designed to hold the chamber and the ancillary equipment (a) and the complete test rig for deforming the oxide scale in plane strain compression [19].

0% relative humidity). The specimen is heated to 200 °C at 22 °C/s using induction heating. This temperature is held for 120 s before heating the sample further to the test temperature at a rate of 42 °C/s, allowing 20 s at the end of the heating for homogenization of the temperature within the sample. At the end of the heating phase, nitrogen is replaced by dry air to oxidize the sample for the required time. The atmosphere is than changed back to nitrogen to stop further oxidation. The time required to replace the gas was estimated to be less than 0.1 s. The trials were conducted at temperatures ranging from 950 °C to 1150 °C for up to 480 s. Figure 5.26 illustrates the testing rig developed for the oxidation and deformation, including a robot to control the gas atmosphere within the chamber. The chamber, induction coil, and ancillary equipment for gas control were mounted on the robot to assure its position within the testing frame. The temperature during testing was recorded and controlled by the chromel–alumel thermocouple (type K) installed in the center of the specimen. Preliminary trials were carried out with up to six thermocouples, ﬁve of them spot welded to the surface of the sample (Figure 5.27). Then tests were carried out in a routine way by placing the samples into a furnace. Details of the experimental setup and the obtained testing results can be found elsewhere [20]. Another reported plane strain compression test designed for studying the behavior of the oxide scale under high-temperature-forming conditions consists of upsetting a strip between two ﬂat dies (Figure 5.28). Again, oxidation of the steel strip samples is achieved in situ by allowing a temporary oxidative atmosphere inside the protective glass vessel. The oxidation temperature was 900 °C in all reported tests. This temperature is close to that found at entry to the ﬁnishing hot strip mill. The oxidation time was varied to achieve oxide thicknesses between 10 and 100 μm. The system was then brought up or down to the deformation temperature. After stabilizing at required tempera-

5.4 Hot Plane Strain Compression Testing 1200

1060

a 1000

1040

d

Temperature (°C)

1020

800

600

400

b f

1000 980 960 200

e c 50 240

280

35

d

e c

5.9

200

0

0

100

200

f

b

a

300

400

Time (s) Figure 5.27 Temperature recorded by the thermocouples inserted into the specimen. The temperature in the testing region (surrounded by dashed lines) is shown magniﬁed [19].

Figure 5.28 Schematic representation of the plane strain compression testing rig designed for studying oxide scale behavior under hot metal-forming conditions (a) and the implemented testing procedure (b) [21].

129

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5 Making Measurements of Oxide Scale Behavior Under Hot Working Conditions

Figure 5.29 Cracked oxide scale on the side of the plane strain compression indentation (smooth die) after testing under the following parameters: strain, 0.4; strain rate, 1 s−1; temperature, 900 °C; oxide scale thickness, 50 μm. (a) Enlarged view of the circled area in (b); the white bar is 1 mm long. [21].

ture, the test was performed in a fraction of a second. After the test, the specimen was allowed to cool down to room the temperature in a nitrogen atmosphere. This test allows observation of crack formation under the plane strain compression. Figure 5.29 shows a typical top view, with an array of cracks perpendicular to the major ﬂow direction x, very similar to cracks opening before the rolling bite [4]. They run through the oxide thickness, with a uniform density. Their origin is not the oxide bending ahead of the bite but probably the ﬂow of the underlying metal transmitting tensile stress to the oxide scale. The authors suggest that it might also be due to punching by roughness peaks on the die [21]. It has also been found during this test that occasionally cracks may not be normal to the surface. Figure 5.30 illustrates the case where oblique cracks, followed by rotation of fragments, have arisen near the edge of a die. The same pattern has been observed on hot rolled strips [22]. This proves the relevance of this phenomenon, tentatively attributed to the presence of a signiﬁcant shear stress (die edge/friction) which induces rotation of the principal axes. Another phenomenon that is possible to investigate in this test is interface waviness due to the tool roughness printing, particularly when rolls are severely worn. The results show that the oxide surface reﬂects the roll roughness to a large extent, indicating plastic deformation of the oxide scale. Bending of the sample in the ﬂank of a grooved die can represent the “roll banding” defect, that is, peeling of an orthoradial strip of roll oxide. As can be seen in Figure 5.31a, this bending can result in normal, through-thickness crack formation that has been bifurcated along the interface. The die groove is oriented in the die width direction, equivalent to the rolling direction. Such a crack would thus be longitudinal, contrary to those shown in the ﬁgure. Delamination within the oxide scale observed after the test is shown in Figure 5.31b. Lines of pores found in the oxide scales, parallel to the interface, may be the origin of such defects.

5.4 Hot Plane Strain Compression Testing

Figure 5.30 Oblique cracks observed near the plane strain compression test die edge (top) and on a rolled strip (bottom) [21, 22].

Figure 5.31 Interfacial delamination observed (a) on the ﬂank of a groove and (b) within the oxide layer after the plane strain compression test [21].

An innovative technique based on the measurement of contact electrical resistance in plane strain compression testing of aluminum has been developed, looking at how metal-to-metal contact is established, whether oil can penetrate the microcracks in the oxide scale, and how fast the transfer ﬁlm develops [23]. By using an anodized oxide layer about 12 μm thick on the strip surface, the details of the contact can be investigated by visual observation of the oxide layer break-up and by monitoring the electrical resistance across the interface between the tool and the strip. Neither of these observations is possible with the much thinner airgrown natural oxide layer normally present on aluminum, which is typically 2–3 nm thick. Taken in conjunction with friction measurements, these observations can give valuable insight into the conditions at the interface. The way in which a thick anodized oxide layer breaks up during rolling is similar to that seen in air-grown layers [24, 25]. However, quantitative differences have been observed between anodized and as-received aluminum strips during plane strain compression testing using ﬂat punches, with the transfer layer growth slower for the anodized layer [26]. It may be that localized fracture of the anodized oxide layer outside the edge of the indentation, observed in similar plane strain compression testing with ﬂat punches, causes a reduction in the area of newly generated metal surface in contact with each punch and so slows the growth rate of the transfer layer. Comparing these results with industrial practice may be handicapped by differences in the mechanical behavior of the anodized layer compared with industrial scales. Nevertheless, the behavior of the anodized samples is qualitatively

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5 Making Measurements of Oxide Scale Behavior Under Hot Working Conditions

Figure 5.32 Schematic representation of the test setup allowing measurement of contact electrical resistance in plane strain compression testing of aluminum [27].

similar to that found for the as-received strip, giving reasonable conﬁdence in applying the lessons learnt from experiments with anodized layers to industrial conditions with air-grown oxide on aluminum. The methodology for measuring electrical resistance in plane strain compression testing is discussed below. The methodology, among other phenomena, allows for investigation of the inﬂuence of oxide break-up on boundary lubrication and transfer layer build-up. The experimental setup is shown in Figure 5.32. The specimen is indented by punches on both sides of the strip. Instead of the ﬂat punches normally used for plane strain compression testing, cylindrical steel punches (grade EN31) with diameter 25.4 mm are used to minimize the disturbance to the electrical resistance measurements from edge effects. The punches are polished to a mirror ﬁnish (0.05 μm root mean square roughness). The load is applied to one of the punches with a closing velocity between 0.05 and 0.5 mm/min. A Tufnol die holder was used to keep the tools well aligned during the compression test, and to insulate them from the Instron testing machine. A maximum load of typically 24 kN was applied to give a strip reduction of around 25%. For each series of tests this maximum load was kept constant. The electrical resistance R between the two punches (effectively the sum of the contact resistances at the interfaces between the strip and each of the punches) was measured using the electrical circuit shown in Figure 5.33. The DC power supply of 5 V was rectiﬁed. Values of 1 kΩ and 10 Ω were chosen for the reference resistors R0 and R1, respectively, to ensure that the electric potential across the sample was below 50 mV during the tests. According to the manufacturer, the electrical breakdown strength of the oils used in these experiments was about

5.4 Hot Plane Strain Compression Testing

Figure 5.33 Electrical circuit used to measure electrical resistance during the plane strain compression testing; R is the contact resistance; R0 and R1 are the reference resistances [27].

10–20 MV/m. An input of 50 mV across the sample would avoid the electrical breakdown of oil ﬁlms thicker than 2 nm at both interfaces. The output voltage was recorded and the resistance is given by the following equation: V 1 1 = i − R V0R0 R1

(5.1)

The results of the testing at a loading velocity of 0.05 mm/min on a sample under dry conditions are illustrated in Figure 5.34a. The reduction is measured by means of a clip gage. The reduction and resistance are shown as a function of loading time, with the zero time set at an arbitrary load of 0.3 kN. The test continues until a maximum load of 20 kN and a ﬁnal reduction of about 20% are reached. At the beginning of the test the electrical resistance is tens of MΩs, which is off the scale of the graph in Figure 5.34. It then drops suddenly to a few ohms at a reduction of about 10% and then gradually to a nominal zero resistance. It was found by optical microscopy that fresh metal extruded through microcracks in the oxide layer (Figure 5.34c). It can also be seen from the ﬁgure that the crack spacing decreases outward from the center of the indent. A similar phenomenon was observed in cold rolling by the same authors [24]. In the following test, loading is held constant at the point when the electrical resistance drops sharply. The electrical resistance falls slightly as the load is held constant and the reduction stays effectively unchanged (Figure 5.34b). Optical microscopy revealed that metal extruded through just one line of cracks near the center of the indent (Figure 5.34d). These observations support the hypothesis that metal-to-metal contact between the fresh aluminum metal and the tool surface occurs in a stepwise manner as metal extrudes through successive cracks, depending on the mechanisms of cracking and extrusion [24]. In the plane strain compression, it is expected that the ﬁrst crack occurs at the edges of the indent due to a bending effect that is similar to that observed at the entry to a rolling pass (Figure 5.35a). As indentation proceeds, this crack will open up, while more cracks form further out from the center of the indent as it widens

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0.1

400 600 Time (s)

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0 c 0.5

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5 Making Measurements of Oxide Scale Behavior Under Hot Working Conditions

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Load held 0.2 Reduction

10 0 0

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400 Time (s)

Reduction

Electrical resistance (Ω)

134

Center of indent

0.1 600

800

0

150 μm d

Figure 5.34 Variation of the electrical resistance with time (a, b) and optical micrographs of the surfaces under dry conditions (c, d) during plane strain compression testing after full load of 20 kN (20% reduction) (a, c) and when the test was interrupted at 12 kN (10% reduction) (b, d) [27].

(a)

Punch

Oxide Cracks

Substrate

(b)

Extrusion Figure 5.35 Schematic illustration of (a) crack initiation through the oxide scale and (b) metal extrusion through the opening cracks during plane strain compression [27].

5.5 Hot Four-Point Bend Testing

(Figure 5.35b). The crack spacing decreases toward the edge of the indent because bending of the top surface is more severe with increasing entry angle. The crack formed nearest to the center of the indent is the preferred location for the ﬁrst metal-to-metal contact. Normally, during plane strain compression testing using ﬂat punches, the ﬁrst crack occurs at the edge of the indentation and gradually moves away from the indent with increasing deformation.

5.5 Hot Four-Point Bend Testing

The deformation behavior of oxide scales at hot metal-forming temperatures can also be investigated using high-temperature four-point bending. Such tests were carried out at temperatures from 800 to 1000 °C with different displacement rates and water vapor contents [28]. The four-point-bend test equipment used for this purpose is illustrated in Figure 5.36. The bending ﬁxtures can be placed in the center of the vertical tube furnace between the outer columns of almost any universal test machine for tensile or compressive testing. The test machine used in this program, an Erichsen 490, allowed displacement rates between 0.01 and 5.00 mm/min with a maximum load of 20 kN. The mechanical data are measured by a load cell located in the upper cross-head of the machine and a strain gage to measure the cross-head movement. The quartz-tube test chamber is airtight at the

Figure 5.36 Schematic representation of the equipment for hot four-point-bend testing of oxide scales [28].

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5 Making Measurements of Oxide Scale Behavior Under Hot Working Conditions

Figure 5.37 Schematic representation of the specimen designed for hot four-point-bend testing of the oxide scale [28].

lower end and the process atmosphere can be controlled during oxidation and mechanical testing. The upper part of the test chamber has a small slit between the push rod and the chamber ﬂange, which serves as the gas outlet. The temperature is measured near the specimen by a Pt–Rh–Pt thermocouple. Oxidation of the specimens is performed within the apparatus without intermediate cooling before conducting the tests. The four-point-bend ﬁxtures were manufactured from alumina because of its excellent hardness and high-temperature strength. The test specimen was designed to apply a deﬁned compressive-stress state in the metal/oxide system (Figure 5.37). All surfaces of the specimen that are irrelevant for the mechanical testing of the oxide scale were protected against oxidation by an aluminide diffusion coating produced by a pack-cementation process. The upper surface was ground in the middle part over a length of 20 mm to a depth of 0.5 mm after the pack-cementation process. In this way, the iron oxide scales can grow during oxidation only on this surface. The oxide scales can easily spall during the fourpoint-bend testing when they are under compressive stresses that exceed a critical value, which is not desirable for the experiment. In order to suppress buckling or decohesion of the oxide scale under compression during the test, the sharp edges were introduced as stress supporting shoulders on the sides of the ground area. In order to obtain the mechanical behavior of the steel substrate that can be further used as a datum for the evaluation of the mechanical behavior of the oxide scales, the load–displacement curves were ﬁrst measured using unoxidized specimens in an inert atmosphere. Argon in the presence of a titanium getter near the specimen was used to absorb the remaining oxygen in the atmosphere. The tests were then performed under the same parameters using the oxidized specimens. Subtracting the results obtained for the unoxidized specimens from those with oxide scales led to measurement of the mechanical properties of the oxide scale (Figure 5.38). This is similar to the subtraction technique that has been applied for determination of the separation loads within the oxide scale/metal system during the modiﬁed hot tensile testing described above [14]. The four-point-bend tests were thus performed with the oxide scale supported on a metal substrate, which is different to those with free-standing oxide scales described above for hot

5.5 Hot Four-Point Bend Testing

Figure 5.38 Schematic representation explaining obtaining of the load–displacement deformation curves for oxide scale during hot four-point-bend testing [28].

tensile testing [17]. This seems to be an important aspect when trying to extrapolate the laboratory results to practical conditions of the steel-rolling process. At Arcelor Research, the four-point-hot bend testing procedure has been developed on a Zwick 1474 tension–compression machine and performed under controlled atmosphere, temperature, and humidity cycles (Figure 5.39) [29]. The procedure was designed to mimic the conditions encountered in a rolling mill. The material is heated in nitrogen up to 900 °C; then air with 15% H2O is introduced for 4–8 min depending on the desired oxide thickness. The atmosphere is then changed to nitrogen again and the material is brought down to the testing temperature. The deformation is performed within the range of 600 to 900 °C. The chemo-thermomechanical treatment produces a 70- to 100-μm-thick oxide layer consisting of more than 95% FeO. The oxide scale is only formed on the lower side of the specimen undergoing tension. The other side is protected by a 1- to 2-μm-thick Cr/Cr2O3 layer. Similar to other methods [14, 28], a reference test is performed on an unoxidized sample before testing of the oxidized samples. The dimensions of the specimens are 50 mm length, 8 mm width and 1 mm thickness. The bending is applied through four 2.5 mm radius alumina rolls, the upper (central) ones 20 mm apart, the lower ones 40 mm apart. The usual ram velocity was 1 mm/min (0.0167 mm/s) but tests at 20 mm/min (0.333 mm/s) and 200 mm/ min (3.33 mm/s) have also been performed. The procedure leads to relatively small imposed plastic strain (<5 × 10−3) and strain rate ( 7 × 10 −5 s−1 < ε < 1.4 × 10 −2). The force–displacement curve is continuously recorded during the testing. The central deﬂection is measured by an alumina pin connected to a LVDT transducer. The whole system is enclosed in a silica vessel ﬂooded by the controlled gases. On occasion, an acoustic emission (AE) device is added; the transducers are located on the deﬂection measurement pin, in the cold section of the rig. The force–deﬂection curves obtained during testing at 600 °C are shown in Figure 5.40. The lower curve corresponds to a nonoxidized sample. It can be seen

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5 Making Measurements of Oxide Scale Behavior Under Hot Working Conditions

Figure 5.39 Schematic representation of the hot four-point-bend testing facilities for obtaining the load–displacement deformation curves for oxide scale [29].

5.5 Hot Four-Point Bend Testing

Figure 5.40 The force–deﬂection curves registered during the hot four-point-bend testing [29].

that the oxidized specimens are stiffer due to the additional 70-μm-thick oxide layer. The two oxidized samples (marked as test nos. 3 and 4 in this and also in Figure 5.41) exhibit rather different loads for the same test conditions. However, it has been shown that both curves converge at higher strain and the difference between them relates to the adhesion of the oxide scale to the alumina rolls of the testing rig increasing the stiffness of the system and causing higher initial slope rather than to the properties of the oxide scale. The interpretation of the test includes determination of the critical stress for transverse fracture. This requires identiﬁcation of the time of ﬁrst cracking and then evaluation of the corresponding stress in the oxide layer. Evaluation of the stresses in the oxide scale requires numerical modeling [30] and this is the subject of the next chapter, while the ﬁrst time cracking was identiﬁed using acoustic emission. As can be seen in Figure 5.41, acoustic emission events start at the very end of the initial linear (elastic) part of the force–deﬂection curve at the beginning of plastic deformation. The major load drops in test no. 4 are connected with events of much higher energy, such as spalling of large pieces of oxide at the roll/sample contact and the small transverse cracks are hidden by these much larger perturbing oxide spallings. That is why only those tests with a smooth load deﬂection curve are retained for analysis of the stress–strain relation and of the critical cracking stress. While the tests with rough curves, perturbed by adhesion of the oxide scale to the aluminum rolls, are avoided in the analysis. Protection of the roll/ sample contacts by lubrication or an antiseizure product can improve the testing procedure. The authors concluded that the transverse fracturing of interest starts

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Figure 5.41 Acoustic emission curves registered during the hot four-point-bend testing superimposed with the force deﬂection curves from Figure 5.40; (a) test no. 3; (b) test no. 4 [29].

at the beginning of plastic deformation of the steel substrate, at the transition from the linear to the nonlinear part of the load–deﬂection curves. The critical fracture stress is determined numerically at this point where only the Young’s moduli of the steel and the oxide are necessary for the computation.

5.6 Hot Tension Compression Testing

It has been mentioned that an open gap in the oxide scale may enable the steel underneath to extrude up under the inﬂuence of the roll contact pressure. Once such hot steel makes direct contact with the roll, the local friction, and heat transfer conditions can be expected to change dramatically. A hot tension/compression

5.6 Hot Tension Compression Testing

Stage 2 - Compression Stage 1 - Tension

Cracks in the oxide scale Figure 5.42

Schematic representation of the hot tension–compression test (after [31]).

testing technique has been developed to make direct observations of such extrusion under controlled laboratory conditions [31]. Figure 5.42 shows the main scheme of the tension–compression test. A tensile sample with a rectangular cross-section is used to produce a ﬂat specimen with through-thickness cracks in the surface scale in the same way as during hot tensile testing of cylindrical specimens. The central section is then cut and compressed between tool steel anvils to observe extrusion up through the open crack. This technique was developed further to investigate the behavior of a range of crack openings [32]. The specimens were prepared from mild steel while the compression tool was made from high speed steel M2. The diameter of the compression tool was a few millimeters larger than the specimens in order to achieve a better contact during the test (Figure 5.43). The gage section of the specimens was a parallelepiped with dimensions of Z × 11 × 20 mm, where Z varied between 2 and 5.5 mm (Figure 5.43). The surfaces of the gage section prepared for oxidation were ground with 1200 grade SiC paper. The specimens had holes drilled axi-symmetrically for thermocouples. The compression tool was polished after each test. This operation is essential to avoid an undesirable oxide scale building up on the tool surface and to obtain the repeatability of the required test conditions. The tensile stage of the testing is carried out under a small tensile load applied early to avoid the effects connected with backlash in the grips during heating and cooling. Also, being under load control during the heating and cooling stages prevented stresses arising due to thermal expansion and shrinkage. Nitrogen was used for heating as an inert atmosphere, during cooling and when the specimen was deformed in tension, while air was used for high-temperature oxidation. During the compression stage, the top compression tool is situated as far as possible outside the heating coil to maintain the relatively low temperature. The slab imitation specimen is placed inside of the induction-heating coil for heating and oxidation. Both the tool and the specimen were placed in the vertical inductive furnace, which consisted of a cylindrical quartz glass, a ceramic base, and lid described earlier for hot tensile testing (Figure 5.14). The experiment schedule

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8.0

12.0 11.0

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120.0 48.5 Figure 5.43 Specimen geometry for hot tension–compression testing with a variable thickness of the central section (after [31]).

Nitrogen

Heating 120 s

Air

Deformation ~3 s

Stabilisation

Oxidation

Gas change

300 s

100–3000 s

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Cooling 900 s

Figure 5.44 Schematic representation of the experimental schedule for hot tension– compression testing (tension stage) (after [31]).

included ﬁve stages (Figure 5.44). The system was switched from load control to position control just before and changed back immediately after the deformation. The following conditions were applied for the tensile stage of the tests: elongation of 0.2–0.3 mm (equivalent to a strain of 0.012–0.015) and strain rate of 0.12– 0.15 s−1. The slow, controlled cooling for about 15 min to 100 °C was the ﬁnal stage of the experiment. The compression stage schedule is similar to the tension part but omits an oxidation stage unless it is needed for studying the scale growth behavior after the scale failure in tension. Figure 5.45 is a photograph of the specimen inside the induction furnace before and after the compression stage. The oxide fragments from the sample can be picked up by the tool under speciﬁc conditions. The sticking phenomenon was observed, for instance, during testing at 870 °C with an oxide scale about 50 μm thick. The oxide scale, initially adhered to the specimen, can be pulled away by the tool surface but this is highly sensitive to temperature. In such way, the tensilecompression test can be used to investigate a “roll pick up effect” (Figure 5.46).

5.7 Bend Testing at the Room Temperature

Figure 5.45 The specimen inside of the induction coiled furnace (a) before and (b) after the compression stage in hot tension–compression testing (after [31]).

Figure 5.46 Scanning electron micrographs of cross-sections of a specimen after compression illustrating (a) a fragment of oxide scale near extruded metal and (b) an uneven metal surface after the scale was picked up by the tool (after [31]).

An important surface quality defect stems from the pick-up by the roll of oxide scale from the steel surface, which usually occurs in small patches which then come back around on the roll surface and indent into the following metal [33]. The roll pick-up effect is also connected to deformation and failure of the oxide scale during the rolling pass. The fragmented scale can be partly spalled from the stock surface, inevitably reducing the scale/steel separation force. For these reasons, the effect should be considered together with the hot rolling and modeled assuming that scale failure can arise during hot rolling [34].

5.7 Bend Testing at the Room Temperature

Coiled steel rod produced by hot rolling for subsequent wire drawing inevitably possesses an oxidized surface. The oxide scale must be removed before the ﬁnal

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Figure 5.47. Schematic representation of a cantilever bending test (after [16]).

drawing operation to ensure a good surface ﬁnish in the ﬁnal product. The amount of scale formed is dependent on the rolling conditions, particularly the billet reheating temperature, which determines the rolling temperature, the laying temperature, and the cooling rate. Understanding the scale removal mechanism is important for optimization of industrial mechanical descaling conditions when bending, tension, and compression at room temperature are operational factors inﬂuencing scale spallation. The technique based on cantilever and constrained testing was developed to investigate oxide failure and spallation during mechanical descaling by bending at room temperatures [35]. The cantilever bending test procedure for assessing descalability is illustrated in Figure 5.47. A 300 mm length rod specimen was cut from the coil, with an initial curvature from the coil diameter of about 1 m. It was then held horizontally at one end in a vice, and a load was applied to the other end to bend the steel rod in the direction that increased the original curvature. The convex side of the specimen formed a zone of longitudinal tension at the metal surface layer, while the opposite, concave side had longitudinal compressive stresses at the metal surface layer along the length of the rod. With bending of the rod, the oxide scale on the tensile and compressive sides of the rod surface underwent continuous cracking and removal along the length of the rod. Once part of a circle with a constant radius was formed in the bent part of the rod, releasing the loaded end stopped the bending. Because of the gradation of deformation, there was always a region on the rod where the oxide scale had undergone initial cracking, crack development, or complete scale removal from the rod surface (after brushing). Before and after the test, the curvatures of the tensile surface and the compressive surface of the specimen were measured and used to evaluate the critical strain for scale cracking and scale removal. Constrained bending tests around cylinders were applied to observe the scale behavior after uniform strain (Figure 5.48). To simulate industrial bending around

5.7 Bend Testing at the Room Temperature

Figure 5.48

Schematic diagram of a constrained bending test (after [16]).

a pulley, 300 mm long rod specimens were cut from the coil with an initial curvature from the coil diameter of about 1 m. One end of the specimen and a cylinder were ﬁxed in a vice, and the other end of the specimen bent around the cylinder. A series of cylinders, with diameters 51, 74, 92, 102, 143, 160, 180, and 215 mm, were used in the constrained bending tests. Again a region is formed on both sides of the specimen where, with decreasing cylinder diameter, the oxide scale underwent progressive descaling, forming a zone of initial through-thickness cracking, a zone of signiﬁcant cracking with evidence of spallation, and a zone of complete scale spallation from the rod surface after brushing following bending. After testing, the oxide scales were examined macro- and microscopically using a Minolta X-700 single lens reﬂex (SLR) camera and a scanning electron microscope (SEM, Jeol JSM-6400). These techniques provided detailed information on the failure processes. Cross-sections were mounted in a low viscosity resin, and then ground and polished for microscopic examinations. The fracture surface of the oxide scale was gold plated for SEM investigations. Figure 5.49 illustrates the descaling process under gradually increasing strain during the cantilever bending test. As the strain increased, scale spallation developed progressively. The scale began to crack at a relatively small bending strain. New through-thickness cracks were formed midway between the initial cracks and also developed in new parts of the rod surface as the strain increased. The process of cracking developed until scale fragments spalled from both tensile and compressive sides of the rod surface. There are different techniques for evaluating strains during the bending tests, such as scriber, shadowgraph, or scanner method. However, numerical modeling

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Figure 5.49 Stages of descaling under gradually increasing strain in the cantilever bending test (after [16]).

based on application of the ﬁnite element method is probably the most precise and powerful method nowadays for investigation of spallation with delamination within the multilayered oxide scale. The application of the modeling approach for numerical interpretation of the test results is described in later chapters.

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scales by inverse analysis of a hot four point bending test, in Proc. 5th Int. ESAFORM Conf. on Material Forming, April 14–17, 2002, Akapit, Krakow, pp. 187–190. Trull, M. (2003) Modelling of oxide failure in hot metal forming operations. Ph.D. Thesis, University of Shefﬁeld, Department of Engineering Materials, Shefﬁeld, UK. Krzyzanowski, M., Suwanpinij, P., and Beynon, J.H. (2004) Analysis of crack development, both growth and closure, in steel oxide scale under hot compression, in Materials Processing and Design: Modelling, Simulation and Applications, NUMIFORM 2004, vol. 712 (eds S. Ghosh, J.C. Castro, and J.K. Lee), American Institute of Physics, Melville, NY, pp. 1961–1966. Beverley, L., Uijtdebroeks, H., de Roo, J., Lanteri, V., and Philippe, J.M. (2001) Improving the hot rolling process of surface-critical steels by improved and prolonged working life of work rolls in the ﬁnishing mill train, EUR 19871 EN, European Commission, Brussels. Krzyzanowski, M., Trull, M., and Beynon, J.H. (2005) Roll pick-up investigations – experimental and modelling, in Proceedings 11th Int. Symp. on Plasticity and its Current Applications: PLASTICITY ‘05, Kauai, Hawaii, USA, January 3–8, 2005 (eds A.S. Khan, and A.R. Khoei), Neat Press, Fulton, Maryland, USA, pp. 106–108. Krzyzanowski, M., Yang, W., Sellars, C.M., and Beynon, J.H. (2003) Analysis of mechanical descaling: experimental and modeling approach. Materials Science and Technology, 19 (1), 109–116.

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6 Numerical Interpretation of Test Results: A Way Toward Determining the Most Critical Parameters of Oxide Scale Behavior The main aim of the measurements is to upgrade the ﬁnite element model with data reﬂecting properties that are more speciﬁc for the particular oxide scale under investigation and are critical for the analysis. This mechanical testing, coupled with microscopic observations of the morphological features of the scale and interfaces, allows for more realistic numerical formulation of the problem and, as a result, for more adequate prediction. Many model parameters describing properties of the oxide scale and the scale–metal interface have separate inﬂuences on the results of prediction of scale failure during deformation in metal-forming operations. One of the most important factors is the temperature for the change of mechanism from through-thickness crack mode to sliding mode of scale failure in tension. As discussed in Chapter 4, in terms of model parameters, this means the temperature where separation loads at the oxide/metal interface are becoming less than the separation loads within the scale fragments (Figure 4.14). This favors sliding of the scale along the weakest interface during tension applied to the underlying steel. Two modes of sliding are possible at elevated temperatures. First, tangential viscous sliding of the oxide scale on the metal surface occurs when the shear stress transmitted from the specimen to the scale exceeds that necessary for viscous ﬂow without fracture at the scale/metal interface. Second, separation of the whole scale raft from the metal surface can occur when the energy release rate exceeds its critical level, resulting in fracture along the interface. The second mode of sliding of the detached oxide scale was dominant in the tensile tests. By modeling the conventional hot tensile test, it is possible to determine the transition temperature [1]. The details of the numerical interpretation of the tensile test can also be found in Chapter 4. The separation loads, measured during modiﬁed hot tensile testing, seem to be the critical parameters for scale failure (Section 5.3). They depend on the morphology of the particular oxide scale, the scale growth temperature, and are also very sensitive to the chemical composition of the underlying steel. These loads are relatively small, making their measurement particularly difﬁcult. Application of the modeling to provide numerical interpretation of experimental results signiﬁcantly improves accuracy in determining the separation loads. The method has been developed for low-carbon steel oxides, which show both brittle failure at lower temperatures and signs of ductile fracture at higher temperatures. Numerical Oxide Scale Behaviour in High Temperature Metal Processing. Michal Krzyzanowski, John H. Beynon, and Didier C.J. Farrugia Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-32518-4

150

6 Numerical Interpretation of Test Results

interpretation of the test results can assist in determining these most critical parameters of the scale behavior.

6.1 Numerical Interpretation of Modiﬁed Hot Tensile Testing

The mathematical model for oxide scale, based on the application of the ﬁnite element method, has been described in detail in Chapter 4 (Section 4.2.3) and is used here, coupled with the hot tensile testing, to determine the critical parameters for characterizing scale failure. The macro-parts of the model that compute the temperature, strain, strain rate, and stress in the tensile specimen during testing are adjusted according to the conﬁguration of the tensile test (Figure 6.1). The micropart of the model is related to the oxide scale. The oxide scale model is positioned on the gage section of the specimen and is validated during the procedure. Each fragment of the oxide scale model consists of a mixture of isoparametric, arbitrary quadri- and trilateral axisymmetric elements. The contact tolerance distance between each scale fragment and the scale/metal interface is decreased to about 0.5 μm. As follows from the hot tensile testing results, the oxide scale during tension can fail in two modes: through-thickness crack mode and sliding mode. Usually, the scale consists of several layers having different morphology, phase content, and, as a result, different properties. For multilayer steel scales, in addition Macro hot tensile test model Grip cooling

R a d i a t i v e Ux = -f(t)

Induction heating

c o o l i n g Ux = f(t)

Grip cooling

Uy = 0 Left part Oxide scale

Right part

Micro oxide scale model

Left part

Right part

Oxide/Oxide Interface

Oxide/metal Interface

Separation

Viscous sliding and separation Left part

Right part

Figure 6.1 Schematic representation of the ﬁnite element mesh and the model set-up for simulating modiﬁed hot tensile testing.

6.1 Numerical Interpretation of Modiﬁed Hot Tensile Testing

to through-thickness cracking, delamination within the nonhomogeneous oxide scale can occur. Such delamination can take place between the oxide sublayers having signiﬁcantly different grain sizes. Large voids, otherwise called blisters, usually situated between oxide sublayers, can act as sources of multilayered oxide delamination. To be able to predict such behavior, the oxide scale model comprises different sublayers having different thermomechanical properties (Figure 6.2). The main assumption of the model and the implemented properties of materials are discussed elsewhere [2–4]. The temperature dependence of Young’s modulus of the different steel oxide scale layers is calculated from the following equations [5, 6]:

(

E ox = 151.504 1 −

)

T − 300 GPa for FeO 5476.66

(6.1)

o Gox = 55.7 GPa Tm = 1643 K ν ox = 0.36

(

E ox = 209.916 1 −

)

T − 300 GPa for Fe2O3 9200

o Gox = 88.2 GPa Tm = 1840 K ν ox = 0.19

Figure 6.2 Scanning electron micrograph (a) and details of the ﬁnite element mesh (b) representing the cross-section of the three-layer steel oxide scale.

(6.2)

151

152

6 Numerical Interpretation of Test Results o where Gox is the shear modulus at 573 °C, Tm the melting point, and νox is Poisson’s ratio. The porosity dependence of Young’s modulus of the scales can be taken into account as [7, 8]: o E = E ox exp ( −bp )

(6.3)

where E is the modulus of the fully compact solid, p the porosity, and b ≈ 3. Small pores reduce Young’s modulus, while large pores act as ﬂaws or stress concentrators and weaken the material toward fracture. The MSC/MARC commercial ﬁnite element code has been used to simulate metal/scale ﬂow, heat transfer, viscous sliding, and failure of the oxide scale during hot rolling assuming the plane strain condition. Releasing nodes was organized using user-deﬁned subroutines in such a way that the crack length is determined based on the increment number; then, according to the crack length, the boundary conditions are deactivated by calling a routine for a speciﬁc node number. Figure 5.16 shows the ﬁnal states of the scale after testing. The ﬁrst mode corresponds to the strong interface between the oxide scale and metal relative to the oxide scale, and failure occurs by through-thickness cracking. In this case, the separation force within the oxide scale is registered. The second mode relates to the interface being weaker than the oxide scale, which results in sliding of the oxide scale raft along the oxide/metal interface. The tangential separation force at the oxide/scale interface is registered in this case. Before the tension phase, the grown oxide scale formed a continuous layer around cylindrical side of the specimen, which cracked across after applying tension. Observations made after the testing and cooling the specimens using scanning electron microscopy have shown that the layer was continuous in the transverse direction but did not always have the same thickness along the circumference. The separation loads characterizing the scale failure are relatively small, making their measurement particularly difﬁcult. Another difﬁculty of the hot tensile test is that the oxide scale failure takes place in the middle at the edges of the specimen join where the local nonhomogeneity in temperature, stress, and strain distributions can complicate their measurement. However, the nodes, where the reaction forces are registered, are at the ends of the specimen, relatively far away from the place where the failure occurs (Figure 6.1). Application of the ﬁnite element model to provide numerical analysis of the experimental results signiﬁcantly improves the accuracy of the determined separation loads. As an example of the numerical analysis in the lower temperature range, Figure 6.3 illustrates the strain around the area of crack formation in the scale, while the load predicted as a reaction force at different points of the specimen head during the scale failure is shown in Figure 6.4. The distribution of the tensile stress component around the crack shows the typically brittle nature of the fracture. The reaction force, shown for two points in the specimen head and related to the separation loads at the crack, shows steep growth followed by abrupt decrease to zero when the crack occurred. The difference, observed between the predicted loads along the edge, shows the importance of determining the place of contact with the grips during the test. o ox

6.1 Numerical Interpretation of Modiﬁed Hot Tensile Testing

Time 0.0072 s

Time 0.009 s

Time 0.0108 s

Time 0.0117 s

Figure 6.3 Distribution of longitudinal strain component (εx) predicted during throughthickness crack formation in the oxide scale during hot tensile testing at 800 °C, 0.2 s−1 strain rate, and 100 μm scale thickness.

Reaction force x, N

290 240 190 140 90 40 -10 0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

Displacement, mm (x 2) Figure 6.4 Reaction force at the head of the specimen predicted during through-thickness crack formation in the oxide scale during hot tensile testing at 800 °C, 0.2 s−1 strain rate, and 100 μm scale thickness.

153

6 Numerical Interpretation of Test Results

Figure 6.5 illustrates the same information but for 1150 °C when the oxide scale fails in sliding mode. As can be seen from Figure 6.5a, the failure of the oxide scale occurs along the scale/metal interface,in such a way that the tangential separation load is registered at the specimen ends. The predicted reaction force increases less steeply at the lower temperature (Figure 6.5b) and decreases then gently before dropping down to zero, hence showing some signs of ductility at high temperatures.

1.900e–002

1.665e–002

1.430e–002

1.195e–002

Time 0.09 s

Time 0.018 s

Time 0225 s

Time 0.0279 s

9.600e–003

7.250e–003

4.900e–003

2.550e–003

2.000e–004

a 140 120

Reaction force x (N)

154

100 80 60 40 20 0 0

0.005

0.01

0.015

0.02

Displacement mm (x 2)

0.025

0.03

0.035

b

Figure 6.5 Failure of the oxide scale in tension in sliding mode predicted for the temperature 1150 °C, strain rate 0.2 s−1, scale thickness 100 μm: (a) distribution of longitudinal strain component (εx); (b) reaction force.

6.1 Numerical Interpretation of Modiﬁed Hot Tensile Testing

Matching the predicted and measured loads at the head of the specimen gives the possibility to determine the separation loads within the scale or at the scale/ metal interface, which can then be implemented in the model for the oxide scale failure prediction. The method has been developed for low-carbon steel oxides. As an example, Figure 6.6 illustrates measured and predicted loads for the same test parameters for low-carbon steel with increased Si content and failed in throughthickness mode at 975 °C. The subtracted load curve (Figure 6.6a, black points) and predicted separation loads (Figure 6.6b, upper curve) are in good agreement at the point situated closer to the axis of the specimen. The thicker the oxide scale, the bigger is the difference between data registered with and without oxidation. Increasing the oxidation time improves the resolution of the measurement and, as a result, the accuracy of determination of the separation loads for the oxide scale. However, thick scales are not always desirable when investigating secondary or tertiary scales in practice. 0.8 0.7 0.6

Load, kN

0.5 0.4 0.3 0.2 0.1 0 -0.1 0

0.5

1

1.5

2

2.5

3

3.5

4

-0.2

Cross-head displacement, mm

a

Reaction force x, N

240 190 140 90 40 -10 0

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 Cross-head displacement, mm (x 10-2)

b Figure 6.6 Measured (a) and predicted (b) reaction force during through-thickness oxide scale crack formation during hot tensile test predicted for 975 °C, 0.2 s−1 strain rate, and 800 s oxidation time. (a) Three curves are plotted: (◊) testing with oxidation; (ⵧ) testing without oxidation; (䉱) subtraction of ⵧ from ◊.

155

156

6 Numerical Interpretation of Test Results

6.2 Numerical Interpretation of Plane Strain Compression Testing

The Forge2005® FEM software has been used for the interpretation of the plane strain compression test [9]. It is thermomechanically coupled FEM software with an updated Lagrangian, (V, p) formulation. Three-node P1+/P1 triangles are used to discretize both the oxide layer and the metal strip. The master/slave technique was used to manage the contact between the deformed metal and the oxide. Elasticviscoplastic behavior was assumed for the metal and the oxide scale while the tools were assumed to be rigid bodies. Several developments have been made by the authors to standard contact and friction descriptions implemented in the commercial software for modeling the physical phenomena during deformation of the scale–metal system [10]. The inequalities and threshold conditions in the (normal) nonpenetration condition and the (tangential) stick–slip friction are relaxed and treated by a penalty technique and a regularization method, respectively. The master/slave technique is used to avoid spurious oscillations during a contact between the deformable bodies. Penetration δ of a point of the slave body 2 into the master body 1 generates the following force Fp: Fp = −K p δ − d0

+

(6.4)

where d0 is the tolerance and 〈x〉 means that the force is generated only if x > 0. Kp is chosen to be sufﬁciently large to prevent signiﬁcantly large penetration above d0. The threshold frictional condition is replaced by the following: +

τ = τ c (ai ) F [(V2 − V1 ) t ]

(6.5)

where F is a continuous and differentiable function such that F(0) = 0, F′(0) ≠ ∞ and F → 1 as [(V2 − V1)t] → ∞ –. The function F is described as follows: F (x ) =

x K r2 + x 2

(6.6)

where Kr is a small regularization parameter. An adequate choice of Kr preserves the stick–slip transition. Thus, sliding, Equation (6.5), sticking ((V2 − V1) t = 0), and also combinations of these two contact options are available. The contact and friction conditions are valid for a whole interface between two bodies during the simulation. The oxide scale is adherent at the beginning of each simulation and bilateral sticking contact is selected. Transition has been introduced for each node individually between bilateral and unilateral contact based on the critical stress criterion σadh. As can be seen from Figure 6.7a, it is equivalent to unilateral contact with adhesion:

(V2 − V1 ) n ≥ 0, σ n ≤ σ adh (ai )

[(V2 − V1 ) n ][σ n − σ adh ] = 0

(6.7)

6.2 Numerical Interpretation of Plane Strain Compression Testing

Figure 6.7 Schematic representation of the normal (a) and tangential (b) stress– displacement relations [10].

The thick lines represent the traditional unilateral contact. The vertical thin line is the bilateral contact. The transition is reversible; the bilateral contact is imposed again until σn > σadh, if the contact is resumed during the calculation. In the case of the sticking and sliding friction, the tangential critical stress τcrit is introduced (Figure 6.7b). The dashed line is the contact penalty technique on which the bilateral to unilateral transition can be added, as shown by the vertical, dot–dash line. Arrows follow a typical separation (Figure 6.7a) or stick–slip process (Figure 6.7b). The sticking contact breaks down at τ = τcrit and is regularized by the large elastic spring constant bringing the tangential stress to the level given by the friction law that is also regularized, (V2 – V1) t = 0 ⇔ τ = 0. This extension has some resemblance to the cohesive zone models used by the authors for crack propagation modeling. This technique is also used to facilitate a smooth numerical simulation of the coating delamination [11]. The present model [10], however, has abrupt transitions and zero fracture energy, which is suitable for brittle materials and interfaces. A simple stress-based fracture criterion has been assumed for modeling of the through-thickness cracks within the oxide scale during the test simulation:

σ tt = σ crit (T )

(6.8)

A crack is created when the criterion is reached at a given surface node perpendicular to the oxide scale layer directly from the interface to the external surface. The nodes are then doubled on this line and the body is separated into two. The through-thickness crack development predicted for the oxide scale during plane strain compression testing at 1000 °C is illustrated in Figure 6.8. The critical fracture stress for the oxide was chosen as 200 MPa. The friction factor between the die and the oxide layer was selected as m = 0.08. The oxide–metal interface was assumed to be perfectly adherent. The oxide and the metal yield stresses are given by, respectively,

157

158

6 Numerical Interpretation of Test Results

a

b

Figure 6.8 Modeling of the through-thickness crack formation during plane strain compression testing [10].

σ (MPa ) = 69 exp0.00299 T (K ) ε 0.223 ( 3ε )

0.159

0.09 3340 ⎞ 0.22 σ (MPa ) = 8.5 exp ⎛⎜ ε ( 3ε ) ⎝ T (K ) ⎟⎠

(6.9) (6.10)

The cracks formed either around the die edges (Figure 6.8a), due to the stress singularity, or at the asperity tops (Figure 6.8b). The critical tension is reached when the ﬂow of the underlying metal shears the interface and transmits the strain to the oxide. In another simulation with periodic roughness covering, the whole die width (Ra = 0.3 μm) reported by the same authors [10], cracks appeared periodically. However, the wavelength was much larger than the corresponding roughness wavelength.

6.3 Numerical Interpretation of Hot Four-Point Bend Testing

The deformation behavior of oxide scale at hot metal forming temperatures can also be investigated using elevated temperature four-point-bend testing. Tests have been carried out at temperatures ranging from 800 to 1000 °C with different displacement rates and water vapor contents [12]. For modeling this test, the authors assumed ideal elastic–plastic behavior of the material at the high temperatures. The stress was assumed constant with increasing strain and the stress level depends on the strain rate. Another assumption was the symmetric behavior under tensile and compressive loading. The specimen deformed elastically until the stress in the outer ﬁber reached the ﬂow stress σF, met,max for the given strain rate ε1 . The specimen deforms plastically in the outer plane after exceeding the strain emet,el. Due to the decreasing strain rate, the ﬂow stress decreases with increasing distance from the outer plane due to the decreasing strain rate, depending on the relation between ﬂow stress and strain rate. The ﬂow stress is reached at the whole cross-section for the very large strains, such as εmet → ∞. The resulting bending moment can be calculated from the following equation:

6.3 Numerical Interpretation of Hot Four-Point Bend Testing

Figure 6.9 Schematic representation of the stress distribution in the four-point-bend specimen for εmax = 2εel [12].

hmet 2

Mb,met = 2bmet

∫

σ ( y ) ydy

(6.11)

0

where σ(y) is the stress distribution at the cross-section of the bending specimen, y is the distance from the neutral plane, bmet is the width of the bending specimen, and hmet is the thickness of the metal substrate. The following equation was derived by assuming that a decrease in the strain rate εF ,met ,max by a factor of 10 lowers the maximum ﬂow stress σF,met,max linearly by a certain percentage, referred to as B:

σ F ,met σ F ,met ,max

=

(

B ⎛ ε met ⎞ B ⎜⎝ ⎟⎠ + 1 − 0.9 εF ,met ,max 0.9

)

(6.12)

Assuming the stress distribution at the specimen for εmax = 2εel illustrated in Figure 6.9, it can be expressed as follows: B ⎛ δ ⎞⎤ y ⎡ σ ( y ) = σ F ,max ⎢1 − ⎜1 − ⎟⎥× ⎣ 0.9 ⎝ hmet 2 ⎠ ⎦ δ

0≤y ≤δ

B ⎛ δ ⎞⎤ h ⎡ σ ( y ) = σ F ,max ⎢1 − ⎜⎝ 1 − ⎟⎠ ⎥ δ ≤ y ≤ 2 hmet 2 ⎦ ⎣ 0.9

(6.13) (6.14)

where δ is the maximum of the elastic region in the cross-section. From Equations (6.11), (6.13) and (6.14) one can ﬁnd δ

B ⎛ 2δ ⎞ ⎤ y Mb,met = 2bmetσ F ,met max ∫ ⎡⎢1 − 1− ydy ⎝ hmet ⎠ ⎥⎦ δ ⎣ 0.9 0 + 2bmetσ F ,met ,max

hmet 2

∫ δ

(6.15)

⎡1 − B ⎛ 1 − 2y ⎞ ⎤ ydy ⎣⎢ 0.9 ⎝ hmet ⎠ ⎦⎥

which results in

(

) (

)

2 2 B δ2 B B hmet ⎡h ⎤ Mb,max = 2bσ F ,met ,max ⎢ met 1 − − 1− + 0.9 6 0.9 0.9 12 ⎥⎦ ⎣ 8

(6.16)

159

6 Numerical Interpretation of Test Results

1.6 1.4 1.2 1.0 0.8

Plastic 1.2

0.6

1.0

0.4 B=0 B=0.2 B=0.33 B=0.5

0.2 0.0

0

2

(dε/dt)/σF,max

Mb,met / Mb,met,el, (Fmet/Fmet,el)

160

0.8 B=0

0.6 B=0.2

0.4 0.2 0.0 0.0

4 6 εmet,max / εmet,el

B=0.5 0.2

B=0.33 0.4 0.6 0.8 (dε/dt)/(dε/dt)max

8

1.0

10

Figure 6.10 Schematic representation of the material behavior in four–point-bend testing for the different ﬂow stress–strain rate dependences [12].

Equation (6.16) is solved for different elastic portions of the specimen cross-section δ, and for the different ﬂow stress–strain rate dependencies 0 < B < 0.5. This leads to the schematic representation of the load–strain curves illustrated in Figure 6.10. The tests conducted in the protective atmosphere lead to the load-displacement curves of the nonoxidized metal that are used as “zero-lines.” For these specimens, the stresses and strains in the outer plane are described by only two parameters, the ﬂow stress σF,met,max and the ﬂow strain εF,met,max and, hence, the Young’s modulus Emet assuming ideal elastic–plastic behavior of the pure metal. The ﬂow stress can be calculated analytically by assuming the material behavior for the different ﬂow stress–strain rate dependences illustrated in Figure 6.10. The authors used the following equations for calculating the ﬂow stress in the outer plane:

σ F ,met ,max =

1 Fmax .met l 6 2 C 2 2 bhmet

(6.17)

where Fmax,met is the maximum load, l is the roller spacing between the inner and outer ﬁxtures, bmet is the specimen width, hmet is the specimen height, and C is the factor obtained from Figure 6.10. The strain rate-ﬂow stress factor B is calculated from the following relation: B = 1−

Fmet ,max,2 Fmet ,max,1

(6.18)

6.3 Numerical Interpretation of Hot Four-Point Bend Testing

Figure 6.11 Schematic representation of the ﬁnite element mesh for the four-point-bend test specimen model [12].

Parameter C is then estimated from Figure 6.10 for the given value of the parameter B. Finite element modeling is used for the calculation of the ﬂow strain εmet,el in this testing. It has been shown that the strain in the outer plane depends only on the roller displacement and the geometry of the bend specimen, but does not depend on the Young’s modulus of the material in the elastic region of the deformation curve. The ﬂow strain of the outer plane εmet,el is obtained by inserting the respective roller displacement for 1/C of the measured maximum load into the ﬁnite element model. The ﬁnite element mesh for the specimen model is illustrated in Figure 6.11. The strain corresponding to the displacement of 2 mm and scale thickness of 880 μm was evaluated to be 0.8% at the oxide/metal interface and 1.7 % in the outer plane using the ﬁnite element model (Figure 6.14). The stress–strain curves illustrated in Figure 6.12 were obtained using the strain value of the outer plane as a basis. An inverse analysis method based on the ﬁnite element method can also be used to determine the constitutive equation parameters for steel and oxide, as reported elsewhere [13]. The authors used the developed inverse analysis technique for the interpretation of the experimental load-deﬂection curves obtained in hot fourpoint-bend testing described in Section 5.4 [10]. The details of the numerical technique can also be found in [14]. The fully automatic parameter identiﬁcation module has been written at CEMEF and then adapted for the purpose of identiﬁcation of steel and oxide mechanical parameters. The applied inverse method con¯ such that the direct model answer Mc sists in ﬁnding the set of parameters P approaches closely the experimental values Mexp: Q (M c (P ) , M exp ) = min Q (M c (P ) , M exp ) P ∈P

(6.19)

¯ is the set of admissible physical parameters and Q is the cost function. where P The cost function, quantifying the difference between calculated and experimental values, was chosen as

161

162

6 Numerical Interpretation of Test Results

Figure 6.12 The stress–strain curves obtained for the oxide scale during four-bend testing using ﬁnite element modeling for interpretation of the test results [12].

s

Q = ∑ βi (Miexp − Mic )

2

(6.20)

i =1

where β is the weight coefﬁcient deﬁned as

βi =

1

(6.21)

(Miexp )

2

This cost function allowed the use of Gauss–Newton algorithm neglecting the second order terms. A deterministic iterative method (gradient type) was used for the minimization of the cost function. The ﬂowchart for the automatic minimization is illustrated in Figure 6.13. Using both the above numerical technique and the load-deﬂection curves obtained for the nonoxidized sample, the following constitutive parameters have been indentiﬁed for the low-carbon steel containing (in wt%) 0.05 C, 0.25 Mn, 0.011 S, 0.015 Si, and 0.035 Al:

σ = K ε n ε m

(6.22)

where σ is the von Mises equivalent stress. K = 307 MPa s−m, n = 0.152, m = 0.1. As seen in Figure 6.14, good agreement has been reached between the experimental results and prediction using the numerical technique. In the absence of transverse cracks during deformation at high temperatures, such as 900 °C, the oxide scale was assumed to be an elastic–viscoplastic material. The Young’s modulus of the scale depends on the temperature [15] according to:

E oxide

⎧175 GPa ⎪⎪164 GPa ≈⎨ ⎪153 GPa ⎪⎩141 GPa

at 600 °C at 700 °C at 800 °C at 900 °C

(6.23)

6.3 Numerical Interpretation of Hot Four-Point Bend Testing

Figure 6.13 Automatic minimization ﬂowchart used for the identiﬁcation of the steel and oxide mechanical parameters [14].

Figure 6.14 Comparison between experimental and predicted load–deﬂection curves using the constitutive equation (6.22) with the identiﬁed parameters for different temperatures [10].

163

164

6 Numerical Interpretation of Test Results

Figure 6.15 Hardness ratio between oxide scales and their respective steel substrates for different temperatures [10].

The following equation was analyzed for the identiﬁcation of Kox, nox, and mox parameters describing the plastic behavior of the scale:

σ (MPa ) = K ox ε nox ε mox

(6.24)

The same numerical technique, based on the inverse analysis and ﬁnite element simulations, has been applied for the identiﬁcation of parameters. An example is presented in terms of the oxide-to-steel yield stress ratio, or ratio of Vickers hardness numbers Hv(ox)/Hv(steel) (Figure 6.14). The ratio depends strongly on the temperature and strain rate. One of the advantages of using the hardness ratio is that it can be compared with results obtained by hardness testing [16] (Figure 6.15). Ex-LC stands for the low-carbon steel with the same content used in the testing (see Equation (6.22) for the constitutive equation). It was found that the hardness ratio is close to 3 within the 600–800 °C temperature range, and decreases to about 1 at around 1000 °C. It conﬁrms the “lubricating” role of the iron oxides at high temperatures [17].

6.4 Numerical Interpretation of Hot Tension–Compression Testing

The hot tension–compression testing technique has been described in Section 5.5 and enables the analysis of crack formation and subsequent metal extrusion through the crack openings under controlled laboratory conditions [18]. Heat transfer and inhomogeneous strain–stress distributions within the specimen have a signiﬁcant impact on the ﬁnal results and were subjected to numerical analysis using the ﬁnite element method [19, 20]. High-temperature tensile–compression tests were simulated using the commercial code MSC.Marc 2000, MSC.Mentat 2000. Taking into consideration the available experimental results [2, 21], it was assumed for the modeling that the tensile stresses on the surface of the gage

6.4 Numerical Interpretation of Hot Tension–Compression Testing

a Points of the temperature registration

b Figure 6.16 Temperature distribution predicted within the gage section of the 2-mm thick specimen when the center of the gage section (a) and the cylindrical part is heated (b) (after [19]).

section are transmitted to the oxide scale causing their through-thickness failure. A thermomechanically coupled 3D model was developed assuming two alternative gage section thicknesses, 2 and 4 mm, and a temperature range of 800–880 °C. By assuming symmetry, only 1/8th of the specimen was modeled. As mentioned in Section 5.5, induction heating was used for heating the specimens. The minimum sizes of the steel specimens should be limited in order to be effectively heated up to the testing temperatures due to variation of the magnetic properties. The specimen with 2-mm thick gage section had insufﬁcient thickness to be heated effectively, and modeling of the temperature distribution within the specimens allowed for the relevant adjustments so as to obtain a desirable even temperature distribution in specimens of both thicknesses that were in good agreement with the thermocouple measurements (Figure 6.16). A thermomechanical model is always sensitive to the temperature-dependent material properties. These properties should be carefully selected and adjusted accordingly, if necessary. For instance, Figure 6.17 illustrates the stress distribution in the longitudinal tensile direction on the surface of the samples with two different thicknesses of the gage section during tensile loading. The difference in the maximum value of stress is mainly due to the stress–strain sensitivity to the temperature. The temperature inside the induction furnace was lower for the 2-mm model, namely 800 °C on the surface of the specimen in the center of the gage section. The gage section of the 4-mm model had the higher temperature, as seen in Figure 6.16, such as 880 °C. The stress history in the center of the gage section surface is shown in Figure 6.18a. The experimental and modeling results show a good agreement for both specimens, with the 2- and 4-mm thick gage sections. Figure 6.18b shows the corresponding strain distributions for the same models with elastic and plastic

165

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6 Numerical Interpretation of Test Results Comp 11 of Stress, MPa

a 75 70 65 60 55 50 45 40

Y

Gage thickness 4 mm

X Z

b

Gage thickness 2 mm

Figure 6.17 Distribution of longitudinal tensile stress predicted on the surface of the specimens having different thickness of the gage section (a) 2 mm and (b) 4 mm, but the same temperatures at the thermocouple. Total tensile strain is 0.015, and the strain rate is 0.2 s−1 [19].

strains shown separately. The elastic strain was the same at any point of the gage section, while the plastic strain varied from the center to the edge. Nevertheless, the strain distribution was nearly identical for both 2- and 4-mm thick samples during the testing. Sliding of the oxide scale along the scale metal interface was not observed during testing. Hence, the oxide scale was assumed to adhere to the metal surface in the modeling. A crack was assumed to develop in the oxide scale perpendicular to the direction of the maximum principal stress if the maximum principal stress in the material exceeded a certain value, σcr. The critical stress for cracking σcr was calculated according to the following equation using the available experimental data for the stress intensity factor KIC:

σ cr = 0.7 K IC

d

(6.25)

where d is the scale thickness [22, 23]. The crack formation does not develop a gap within the ﬁnite element mesh in this modeling approach. It was assumed that the material loses all load-carrying capacity across the crack unless tension softening is included. Calculations of the cracking strain are implemented in the MSC.Marc ﬁnite element code [24, 25]. It is assumed in the model that the total strain can be decomposed into an elastic component and a cracking component. Figure 6.19 illustrates the consecutive stages of the crack initiation and development during tension of the specimen with a 4-mm-thick gage section at 850 °C. The stress distribution before the second crack occurs is shown in Figure 6.19b and also the stress relaxation zone where the ﬁrst crack appeared. As can be seen from Figure 6.19, cracking happens at the region with maximum stresses. The ﬁnal crack pattern of the specimen with a 2-mm gage section tested at 750 °C is shown in Figure 6.20. The crack pattern was similar to that observed experimentally. The numerical approach allows for the analysis of the crack pattern formation depending on the deformation parameters and the scale–metal properties.

6.4 Numerical Interpretation of Hot Tension–Compression Testing

Figure 6.18 History plots illustrating evolution of the equivalent stress at the center of the gage section (a), the elastic and plastic strain (b) predicted at different places in the gage section for a strain rate 0.15 s−1 [19].

The values of the stress intensity factor, KIC, vary widely [26]. Hence, a sensitivity analysis is necessary for the validation of the cracking behavior of the oxide scale for accurate simulation. At high temperatures, the oxide scale exhibits ductile behavior and calculation of the strain energy release rate for the modeling of scale failure subject to the calculation of J-integral rather than KIC factor. However, the evaluation of the stress intensity factor at the testi conditions is very important for modeling cracking in the oxide scale. The high-temperature compression phase of the test is not a plane strain test. The 3D ﬁnite element simulation can also assist in the accurate stress–strain evaluation during this phase of testing. It has been shown numerically that the maximum of the equivalent plastic strain is situated not at the area of the contact, but in the middle of the specimen. Some

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6 Numerical Interpretation of Test Results

Com 11 of Cracking Strain 0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0

a

Com 11 of Stress, MPa 800 720 640 560 480 400 320 240 160 80

b

Comp 11 of Cracking Strain 0.2 0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04

c

0.02 0 Figure 6.19 Consecutive stages of though-thickness crack development within the oxide scale during the tension phase of testing at 850 °C. Cracking strain at the ﬁrst crack initiation (a), stress distribution after the ﬁrst crack (b), and appearance of the second crack (c), KIC = 12 MN m−3/2 (after [19]).

6.4 Numerical Interpretation of Hot Tension–Compression Testing 0.03

Comp 11 of Cracking Strain

0.027 0.024 0.021 0.018 0.015 0.012 0.009 0.006 0.003 0

a

b

Figure 6.20 Crack pattern on the oxide scale predicted at 750 °C and for KIC = 4 MN m−3/2 (a) and observed during the testing in tension (b) (after [19]).

specimens, especially at temperatures higher than 970 °C, tend to be bent. The ﬁnite element modeling should be used to check and adjust any related differences in the stress–strain behavior of the specimens during the compression phase. As it has been mentioned in Section 5.5, the tension–compression technique was developed further to investigate the behavior of a range of crack openings [27]. In most cases, the scale enters the roll gap not as a continuous layer but as a fragmented layer having relatively small or large through-thickness gaps formed at the entry zone. The scale pattern within the roll gap undergoes further development under the high roll pressure. It is the purpose of this analysis to investigate the crack development in the steel oxide scale under compressive loading at high temperatures by modeling the scale behavior using a physically based oxide scale model. Such a model allows for a detailed numerical analysis of the microevents at the tool/workpiece interface and will be discussed in detail in the Chapter 7. The model is generic, developed independently of any particular technological process, and represents a numerical approach that can be applied to many metalforming operations, where precise prediction of oxide scale deformation and failure plays a crucial role. The width of the gap between scale fragments changes under compression because of sliding and deformation of the oxide scale and metal extrusion through the gap. Results of the hot compression test modeling have revealed that the sizes of the ﬁnal gaps depend on many parameters, the ﬁrst being the initial gap width before the compression (Figure 6.21). The initial temperature was 1000 °C, while the initial scale thickness was 100 μm. The cracks with initial widths smaller than 135 μm were closed when reduction reached 15%, while those initially wider than 200 μm increased. The cracks having an initial width between these critical values remained unchanged or slightly decreased in width. The change in crack width during reduction can be explained by sliding along the metal surface at high temperatures when the scale/metal interface is relatively weak [1]. Further investigation allowed for an assumption

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6 Numerical Interpretation of Test Results 350 300 250

Gap width, mm

170

200 150 100 50 0 0

5

10

15

20

25

30

35

40

Reduction, %

Figure 6.21 Change of the gap in the oxide scale during compression predicted for different initial gap widths (after [27]).

a

c

b

d

Figure 6.22 Scanning electron micrographs of the cross-section of the compressed specimen (a, c) and the results of ﬁnite element modeling illustrating the formation of the surface proﬁle during compression (b, d) with closure of the gap (a, b) and metal extrusion through the gap (c, d) (after [27]).

that there are two critical initial gaps for the oxide scale at the high temperature range. The ﬁrst one is the critical gap width below which the gap can be closed. The second one is the width above which the gap is increased during compression. Between these critical values, the gap becomes smaller than the initial size. The details of this investigation are of signiﬁcant technological importance and will be discussed later in this book. The scanning electron micrograph shown in Figure 6.22a illustrates a cross-section of the oxide scale after compression at 1000 °C. A

6.5 Numerical Interpretation of Bend Testing at Room Temperature

clearly visible hump, resulting from metal extrusion through the gap formed within the oxide scale during the tensile stage, can be seen at the scale/metal interface. It has to be noted that it is only part of the oxide scale left on the metal surface. The outer part of the scale was spalled after the compression and was transferred to the surface of the upper part of the compression tool. The results indicate the following mechanism for the surface proﬁle formation. The gap width, 110 μm, formed after the tension phase, is below the critical width for a 100-μmthick oxide scale. The modeling results indicate that for a reduction of more than 20%, the proﬁle of the interface should be similar to that shown in Figure 6.22b. After spallation of the uppermost layer, only the thinnest (10 μm) oxide scale layer still adhered to the metal surface. Figure 6.22c illustrates the cross-section of the interface where the upper part of the oxide scale was spalled just before the compression test, leaving a scale layer of about 20 μm thick and a gap width of about 80 μm. According to the modeling results, this gap should be ﬁlled with extruded metal under the reduction of 38%. Figure 6.22d shows satisfactory agreement with the experiment.

6.5 Numerical Interpretation of Bend Testing at Room Temperature

The technique based on cantilever and constrained testing developed to investigate oxide failure and spallation during mechanical descaling by bending at room temperatures was described in Section 5.6 [28]. The details of the oxide scale modeling approach used for the analysis of multilayer oxide scale failure are described in the next chapter. For multilayer oxide scales, in addition to throughthickness cracking, delamination within the nonhomogeneous oxide scale can occur. Such delamination can take place between the oxide sublayers having signiﬁcantly different grain sizes. Large voids, otherwise called blisters and usually situated between oxide sublayers, could act as sources of multilayered oxide delamination. To predict such behavior, the oxide scale model comprises various sublayers having different mechanical properties. The inhomogeneity of scale morphology is a reason for the cessation of crack propagation within the scale near the stock surface, as observed during experimental investigation of hydraulic descaling at elevated temperatures [29]. Two models are used for the analysis. The ﬁrst has a relatively coarse ﬁnite element mesh and large number of scale fragments (Figure 6.23). It is used to evaluate crack spacing during bending. This enabled the critical length for detailed analysis to be evaluated, with the aim of decreasing the computation resources. The second model included one or two oxide scale fragments (solid or multilayer) (Figure 6.24). This model had a reﬁned ﬁnite element mesh around the scale, allowing more precise calculation of crack propagation. Both models used for the descaling analysis comprised a macrolevel model that computed the strains, strain rates, and stresses in the specimen during bending and a microlevel model to determine the oxide scale failure. Oxide scale failure is predicted taking into

171

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6 Numerical Interpretation of Test Results Oxide scale fragments

300 mm length and 5.5 mm diameter steel rod

Rigid body Fixed end

Free end

Figure 6.23 Schematic representation of the ﬁnite element mesh and model N1 setup used for numerical interpretation of the bend test [28].

account the essential brittleness of the process at room temperature. For opening of a through-scale crack in the tensile mode, owing to applied tension loading perpendicular to the crack faces, a critical failure strain εcr is used as the criterion for the occurrence of through-thickness cracking [6]: 2γ (T ) ⎞ ε cr = ⎛⎜ 2 ⎝ F πE (T ) c ⎟⎠

12

(6.26)

where γ is the surface fracture energy, E is Young’s modulus, T is the temperature, and F takes values of 1.12 for a surface notch of depth c, 1 for a buried notch of width 2c, and 2/p for a semicircular surface notch of radius c. The critical strain can also be expressed in terms of fracture toughness by substituting γ = K2/2E into Equation (6.26), where K is the stress intensity factor. Assuming that the stress intensity factor relating to fracture in the plane shear mode owing to shear loading parallel to the crack faces exceeds the corresponding value for the tensile mode, a criterion for shear failure in the oxide was chosen as

ε crsh = 2ε cr where ε crsh is the critical strain for shear fracture in the oxide scale.

(6.27)

6.5 Numerical Interpretation of Bend Testing at Room Temperature 300 mm length and 5.5 mm diameter steel rod Rigid body

Fixed end

Free end Oxide scale

Figure 6.24 Schematic representation of the ﬁnite element mesh and model setup for model N2 used for numerical interpretation of the bend test [28].

For the case of the bending test for descalability, the mechanical properties of the oxide scale used for the modeling were determined at room temperature as follows: Young’s modulus, E = 130 GPa (FeO), E = 208 GPa (Fe3O4), E = 219 GPa (Fe2O3); Poisson’s ratio, ν = 0.36 (FeO), ν = 0.29 (Fe3O4), ν = 0.19 (Fe2O3); and the critical stress intensity factor, KIC = 1.7 MN m−3/2 [26, 30]. The commercial MARC K7.2 FE code was used for solving the nonsteady-state 2D problem of the metal with oxide scale ﬂow and failure during testing. The tensile stress–strain properties of the steel rod were measured before the testing and were introduced into the model. Figure 6.25 illustrates oxide scale failure in a through-thickness crack mode owing to tension at the convex side of the bend specimen. It is assumed in the model that the scale deforms elastically. Generally, for the elastic scale model, the possible forms of stress relaxation could be fracture, viscous sliding along the interface, and spallation. At room temperature, the contribution of viscous sliding is considered to be negligible [31]. Through-thickness cracks develop from preexisting defects located at the outer surface of the oxide layer. The critical failure strain can vary depending on the parameters such as the size of the defect and the surface fracture energy. It has been shown that the length of the defect c, Equation (6.23), can be calculated as an effective composite value made up of the sum of the sizes of discrete voids whose stress ﬁelds overlap [26]. The formation of tensile cracks through the thickness of the oxide scale produces considerable redistribution of the stress within the scale and also at the oxide–metal interface. Stress

173

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6 Numerical Interpretation of Test Results Cracks

Outer surface

Oxide scale

a Oxide scale

b

Steel rod

Figure 6.25 Through-thickness cracks on the convex surface of a steel rod after bending, scanning electron micrograph (a) and prediction (b) [28].

concentration around the crack tip near the scale/metal interface can lead to the onset of cracking along the interface. The in-plane stress cannot transfer across the crack and becomes zero at each of the crack faces. By symmetry, the in-plane stress reaches a maximum value midway between the cracks. As a result of the cracks, the in-plane strain within the scale fragment is signiﬁcantly relaxed compared with the longitudinal strain of the attached metal layer. The formation of a crack through the thickness of the oxide scale creates shear stresses at the scale/ metal and scale/scale interfaces. These stresses have a maximum value at the edges of the cracks. Relaxation of the shear stresses at low temperatures, in the absence of relaxation by viscous sliding, can only occur by interface cracking and spallation of the elastically deformed scale fragment when the strain exceeds the critical level. Generally, spallation occurred at the scale–metal interface, but occasionally, as can be seen from Figure 6.26a, a thin inner layer remained attached to the steel and spallation occurred by delamination within the scale. This was modeled by having a multilayer scale with a more ductile inner layer (Figure 6.26b), which closely simulates the observed behavior. The mechanism of oxide scale spallation for the opposite, concave side of the steel rod, where longitudinal

References

SEM image

a

Model prediction Inc. 20

Inc. 40

Inc. 80

b

Figure 6.26 Scanning electron micrograph of electric arc furnace steel rod layer at 830 °C (a); model prediction for given time increments (Inc.) during progressive bending (b) [28].

compression stresses developed, was different. It is discussed in the following chapters. Concluding this section, it has to be noted that the numerical interpretation provides a means for quantiﬁcation of the test results applicable for the analysis of mechanical descaling.

References 1 Krzyzanowski, M., and Beynon, J.H. (1999) Finite element model of steel oxide failure during tensile testing under hot rolling conditions. Materials Science and Technology, 15 (10), 1191–1198. 2 Tan, K.S., Krzyzanowski, M., and Beynon, J.H. (2001) Effect of steel composition on failure of oxide scales in tension under hot rolling conditions. Steel Research, 72 (7), 250–258. 3 Krzyzanowski, M., Beynon, J.H., and Sellars, C.M. (2000) Analysis of secondary oxide scale failure at entry into the roll gap. Metallurgical and Materials Transactions, B31, 1483–1490.

4 Krzyzanowski, M., and Beynon, J.H. (2000) Modelling the boundary conditions for thermomechanical processing – oxide scale behaviour and composition effects. Modelling and Simulation in Materials Science and Engineering, 8 (6), 927–945. 5 Morrel, R. (1987) Handbook of Properties of Technical and Engineering Ceramics, National Physical Laboratory, HMSO Publications, London. 6 Schütze, M. (1995) Mechanical properties of oxide scales. Oxidation of Metals, 44 (1–2), 29–61. 7 Rice, R.W. (1977) Microstructure dependence of mechanical behaviour of ceramics, in Treatise in Materials Science

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8

9

10

11

12

13

14

15

16

17

18

and Technology, vol. 11 (ed. R.K. MacCrone), Academic Press, New York, pp. 199–381. Birchall, J.D., Howard, A.J., and Kendall, K. (1981) Flexural strength and porosity of cements. Nature, 289, 388–390. Grenier, C., Bouchard, P.-O., Montmitonnet, P., and Picard, M. (2008) Behaviour of oxide scales in hot steel strip rolling. International Journal of Material Forming, 1, 1227–1230. Picqué, B., Bouchard, P.-O., Montmitonnet, P., and Picard, M. (2006) Mechanical behaviour of iron oxide scale: experimental and numerical study. Wear, 260, 231–242. Abdul-Baqi, A., and van der Giessen, E. (2002) Numerical analysis of indentation-induced cracking of brittle coatings on ductile substrates. International Journal of Solids and Structures, 39, 1427–1442. Echsler, H., Ito, S., and Schütze, M. (2003) Mechanical properties of oxide scales on mild steel at 800 to 1000 °C. Oxidation of Metals, 60 (3/4), 241–269. Picqué, B., Favennec, Y., Paccini, A., Lanteri, V., Bouchard, P.O., and Montmitonnet, P. (2002) Identiﬁcation of the mechanical behaviour of oxide scales by inverse analysis of a hot four point bending test, in Proceedings of the 5th ESAFORM Conference (eds M. Pietrzyk, Z. Mitura, and J. Kaczmar), Akapit, Krakow., pp. 187–190. Picqué, B. (2004) Experimental study and numerical simulation of iron oxide scales mechnical behaviour in hot rolling, Ph.D. thesis, Ecole des mines de Paris, France. Rice, R.W. (2000) Mechanical Properties of Ceramics and Composites – Grain and Particle Effects, Basel, Marcel Dekker, New York. Vagnard, G., and Manenc, J. (1964) Etude de la plasticité du protoxyde de feret de l’oxyde cuivreux. Mémoires et études scientiﬁques de la revue de métallurgie, 61 (11), 768–776. Luong, L.H.S., and Heijkoop, T. (1981) The inﬂuence of scale on friction in hot metal working. Wear, 71, 93–102. Trull, M., and Beynon, J.H. (2003) High temperature tension tests and oxide

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27

scale failure. Materials Science and Technology, 19, 749–755. Trull, M. (2003) Modelling of oxide failure in hot metal forming operations, Ph.D. Thesis, University of Shefﬁeld, Shefﬁeld, UK. Krzyzanowski, M., Trull, M., and Beynon, J.H. (2002) Numerical identiﬁcation of oxide scale behaviour under deformation – a way for reﬁning of contact simulation in metal forming operations, in Euromech 435 Colloquium “Friction and Wear in Metal Forming” FWMF June 18–20, 2002, Valenciennes, LAMIH, Université de Valenciennes et du Hainaut Cambrésis, Valenciennes, France, pp. 95–102. Krzyzanowski, M., and Beynon, J.H. (1999) The tensile failure of mild steel oxides under hot rolling conditions. Steel Research, 70 (1), 22–27. Thouless, M.D. (1990) Crack spacing in brittle ﬁlms on elastic substrates. Journal of American Ceramic Society, 73 (7), 2144–2146. Schütze, M. (1990) Plasticity of protective oxide scales. Materials Science and Technology, 6, 32–38. Simons, J.W., Antoun, T.H., and Curran, D.R. (1997) A ﬁnite element model for analysing the dynamic cracking response of concrete, Presented at 8th International Symposium on Interaction of the Effects of Munitions with Structures, McClean, Virginia, SRI International, Menlo Park, CA, 94025. Simons, J.W., Kirkpatrick, S.W., Klopp, R.W., and Seaman, J.W. (1999) Methods for modelling damage in ﬁnite element calculations, in Proceedings of the International Seminar on Numerical Analysis in Solid and Fluid Dynamic, Osaka University, Japan, pp. 79–86. Hancock, P., and Nicholls, J.R. (1988) Application of fracture mechanics to failure of surface oxide scales. Materials Science and Technology, 4, 398–406. Krzyzanowski, M., Suwanpinij, P., and Beynon, J.H. (2004) Analysis of crack development, both growth and closure, in steel oxide scale under hot compression, in Materials Processing and Design: Modelling, Simulation and Applications,

References NUMIFORM 2004, vol. 712 (eds S. Ghosh, J.C. Castro, and J.K. Lee), American Institute of Physics, Melville, New York, pp. 1961–1966. 28 Krzyzanowski, M., Yang, W., Sellars, C.M., and Beynon, J.H. (2003) Analysis of mechnical descaling: experimental and modeling approach. Materials Science and Technology, 19 (1), 109–116. 29 Nakamura, T., and Sato, M. (1994) Descalability on reheated steel slabs at

high temperature. Tetsu-to-Hagan, ISSN 0021-1575 CODEN TEHAA2, 80 (3), 237–242. 30 Robertson, J., and Manning, M.I. (1990) Limits to adherence of oxide scales. Materials Science and Technology, 6, 81–91. 31 Riedel, H. (1982) Deformation and cracking of thin second-phase layers on deformation metals at elevated temperature. Metal Science, 16, 569–574.

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7 Physically Based Finite Element Model of the Oxide Scale: Assumptions, Numerical Techniques, Examples of Prediction Detailed ﬁnite element analysis using a physically based oxide scale model is a crucial aspect toward the understanding and prediction of scale behavior during metal-forming operations. As discussed in previous chapters, the model has been applied to the numerical interpretation of the test results to acquire valuable physical parameters related to the scale deformation and failure. Providing it is validated, the model can also be used for detailed modeling of the micro events during technological operations. By doing this, it is possible to distinguish the most appropriate assumptions critical to the simulation of a particular process, while at the same time avoiding less important, unnecessary complications in the modeling, hence saving computational resources. This stage of numerical analysis gives a basis for the reduction of the oxide scale model for engineering applications. The upgraded oxide scale model is usually a part of a more complex ﬁnite element model, and the reduction or adjustment of the model for a particular technological operation is a ﬁnal stage toward accurate prediction. The model has been developed gradually by closely linked combination of laboratory testing and measurements, rolling tests, microstructural investigations, coupled with ﬁnite element analysis of the observed experimental phenomena. The oxide scale model is generic, developed without reference to any particular technological process, and represents a numerical approach that can be applicable to many metal-forming operations where precise prediction of oxide scale deformation and failure plays a crucial role [1].

7.1 Multilevel Analysis

Ideally, the oxide scale model should be included into and run simultaneously with a macro model representing either a technological operation or a testing procedure. However, the thickness of the secondary oxide scale, usually about 10–100 μm, is relatively small with regard to the macro model and such coupling can cause serious numerical difﬁculty. Reﬁning the ﬁnite element mesh near the roll–stock interface to be able to place the oxide scale can evoke a nonpositive stiffness matrix due to the large time increment (Figure 7.1). Oxide Scale Behaviour in High Temperature Metal Processing. Michal Krzyzanowski, John H. Beynon, and Didier C.J. Farrugia Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-32518-4

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7 Physically Based Finite Element Model of the Oxide Scale

Figure 7.1 Hot rolling 2D ﬁnite element modeling. Note that the execution is stopped at the entry of the reﬁned (10 times) mesh area due to the nonpositive stiffness matrix.

Figure 7.2 Hot rolling 2D ﬁnite element modeling. The time increment was decreased relative to the case shown in Figure 7.1 (15 times). Note that the execution is stopped at the entry due to the penetration of the elements.

Decreasing the time increment can result in the penetration of the relatively large ﬁnite elements of other contact areas of the macro model, as shown in Figure 7.2. Penetration of the small size ﬁnite element into the relatively large one during the contact is a typical fault in the numerical analysis. The ﬁnite elements should have similar sizes at the contact regions and the increment load should be adequate for the element sizes being in contact to avoid the numerical obstacles. It becomes difﬁcult to satisfy the above criteria in a single model. That is why the oxide scale model is usually a meso-part of a more complex macro ﬁnite element model. Corresponding linking of modeling scales is a necessary stage for the prediction of scale behavior during modeling of both mechanical testing and technological operations. When quality of surface ﬁnish is the subject of the numerical analysis or ﬁne mechanisms of formation within a surface layer of few microns thickness is under consideration, the oxide scale model has the capacity to include very ﬁne features such as multilayer scale, voids, or a complicated proﬁle of the scale/metal interface. To link macro and meso scales of modeling, the model can be reduced to a small segment at the stock–roll interface (Figure 7.3). The boundary conditions for the small segment, such as temperature and displacement history, are taken from the macro model, as shown in Figure 7.4. The ﬁnite element mesh near the interface is then reﬁned as required. The origin of coordinates is changed by tying it to one of the segment nodes and, ﬁnally, the oxide scale fragments are introduced to the metal surface. This procedure allows for the consideration of the ﬁne morphological features of the scale and the

7.1 Multilevel Analysis

Figure 7.3 Linking of macro and meso scales of modeling: 1 – macro model run; 2 – reduction to characteristic meso level; 3, 4 – ﬁnite element mesh reﬁnement near the interface; 5 – change of the origin of the coordinate system and placement of the oxide scale.

Figure 7.4 Schematic representation of the ﬁnite element mesh near the roll/stock interface (a, b) and the boundary conditions transferred from the macro level to the boundary node of the meso level model (c–e).

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7 Physically Based Finite Element Model of the Oxide Scale

scale/metal interface while, at the same time, reducing the number of elements under consideration [2]. The approach also enables a thin ﬁlm to be introduced on the roll surface, which can be deﬁned as oxide scale. After implementing the boundary conditions for the small segment, taken from the corresponding nodes of the macro model, changing the origin of the coordinate system by tying it to one of the segment nodes, reﬁning the FE mesh near the interface, and introducing the oxide scale fragments at the surface of the stock (and the roll, if necessary), the model is ready for the demands of the numerical analysis. Figure 7.5 illustrates use of the model for analyzing the surface state during a hot ﬂat rolling pass. Such model adjustment maintained the advanced level of interface complexity, but at the same time, the number of elements did not exceed 9000, which kept the computational time within several hours, rather than weeks for the full model equivalent, if it could run to completion at all.

Figure 7.5 Temperature distribution predicted at the moment of scale entering the roll gap. Note: (a) additional scale failure at the moment of roll gripping; (b) void closure within the scale under the roll pressure; (c) uneven stock surface near the place of the pre-existed void (arrow) [2].

7.2 Fracture, Ductile Behavior, and Sliding

7.2 Fracture, Ductile Behavior, and Sliding

The oxide scale is simulated as comprising numerous scale fragments joined together to form a scale layer 10–100 μm thick, covering the representative raft length of about 20–50 mm (Figure 7.6). The crack spacing is a predictable parameter in the model. To be able to reﬂect the real crack pattern observed during the hot rolling pass (Figure 7.7), the length of each oxide scale fragment is chosen to be less than the smallest spacing of cracks observed in the experiments. The predicted crack spacing should be insensitive to the sizes of the scale fragments. Normally, they are chosen randomly, enabling prediction of representative crack spacing and distribution of cracks along the length of the raft due to both longitudinal tension and contact with the roll (Figure 7.8). Oxide scale failure is predicted by taking into account the main physical phenomena such as stress-directed diffusion, fracture and adhesion of the oxide scale, strain, strain rate, and temperature. The main mathematical assumptions of the

Figure 7.6 Schematic representation of the oxide scale ﬁnite element model consisting of the scale fragments joined together to form a continuous scale layer.

1 mm

Crack spacing

Figure 7.7 Scanning electron micrograph showing the oxide scale crack pattern formed after the hot rolling pass.

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7 Physically Based Finite Element Model of the Oxide Scale

Figure 7.8 Hot strip rolling model: representation of the ﬁnite element mesh, initial oxide scale with randomly distributed pre-existing cracks (a) and equivalent total strain predicted within the cross-section of the strip after the ﬁrst rolling pass for the different pre-existing crack spacing (b and c); strip thickness 1 mm; oxide scale thickness 100 μm; reduction 30%.

Figure 7.9 SEM image showing the cross-section of the oxide scale grown at 830 °C (a) and at 1150 °C (b), then failed due to tension under 0.02 strain, 0.2 s−1 strain rate at 830 °C.

model related to oxide scale and properties of materials have been described in Sections 4.2.3 and 4.2.4 (Tables 4.2 and 4.3). It was assumed that spalling of the scale could occur along the surface of lowest energy release rate, which can be either within the scale or along the scale/metal interface. A ﬂaw will continue to grow under a stress if its energy release rate G exceeds the critical energy release rate Gcr. The availability of experimental data exhibited that through-thickness cracking is an essentially brittle process of unstable crack propagation for the majority of cases (Figure 7.9). It favors the assumption of linear elastic fracture

7.2 Fracture, Ductile Behavior, and Sliding

mechanics for the model, which is acceptable for the prediction of scale failure for such cases. Assuming the opening of the through-scale crack due to loading applied perpendicular to the crack faces (tensile mode), the critical failure strain εcr may be used as a criterion for through-thickness cracking occurring [3]: 2γ (T ) ⎞ ε cr = ⎛⎜ 2 ⎝ F πE (T ) c ⎟⎠

12

(7.1)

where γ is the surface fracture energy, E is Young’s modulus, F takes values of 1.12, 1, and 2/π for a surface notch of depth c, for a buried notch of width 2c, and for a semicircular surface notch of radius c, respectively. Assuming γ = K2/2E, where K is the stress intensity factor, the critical strain and stress can also be expressed in terms of the K-factors. There is a possibility of through-scale failure due to shear deformation in the oxide. Assuming that the stress intensity factor related to the fracture due to shear loading parallel to the crack faces (plane shear mode) exceeds the corresponding value for the tensile mode, which as a rule is justiﬁed, a criterion for the shear failure in the oxide is chosen as follows:

ε crsh = 2ε cr

(7.2)

where ε crsh is the critical strain for shear fracture in the oxide scale. Tangential viscous sliding of the oxide scale on the metal surface is allowed, arising from the shear stress τ transmitted from the specimen to the scale in a manner analogous to grain-boundary sliding in high-temperature creep [4]:

τ = ηv rel

(7.3)

where η is a viscosity coefﬁcient and νrel is the relative velocity between the scale and the metal surface. The viscous sliding of the scale is modeled using a shearbased model of friction such that

ηv rel = −mkY

( )

v 2 arctan rel t π c

(7.4)

where m is the friction factor; kY is the shear yield stress; c is a constant taken to be 1% of a typical vrel which smoothes the discontinuity in the value of τ when stick–slip transfer occurs; and –t is the tangent unit vector in the direction of the relative sliding velocity. The calculation of the coefﬁcient η was based on a microscopic model for stress-directed diffusion around irregularities at the interface and depends on the temperature T, the volume-diffusion coefﬁcient DV, the diffusion coefﬁcient for metal atoms along the oxide/metal interface δSDS, and the interface roughness parameters p and λ [5]:

η=

kTp 4 4 Ωλ (δ SDS + 0.8 pDV ) 2

(7.5)

where k is Boltzmann’s constant, Ω is the atomic volume, p/2 is the amplitude, and λ is the wavelength of the roughness. It was assumed for the calculation that the diffusion coefﬁcient along the interface was equal to the free surface diffusion

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7 Physically Based Finite Element Model of the Oxide Scale

coefﬁcient. Tangential viscous sliding of the oxide scale over the metal surface due to the shear stress transmitted from the steel is allowed when the scale and the metal surface are adherent. This kind of viscous sliding is different from the frictional sliding of the separated scale fragment when separation stresses are exceeded. The ﬁnite element model is rigorously thermomechanically coupled, and all the mechanical and thermal properties are included as functions of temperature. The radiative cooling of heated surfaces was simulated by prescribing the energy balance for the boundary surface. The scale and metal surface were assumed to be adhering when they were within a contact tolerance distance. The tensile tests carried out at high temperatures revealed two types of accommodation by the oxide scale of the deformation of the underlying steel substrate (Figures 7.10a and b) [6]. At lower temperatures, the oxide scale fractured, usually in a brittle manner, with the through-thickness cracks triggering spallation of the oxide scale from the steel surface. At higher temperatures, the oxide scale did not fracture, rather it slid over the steel surface, eventually producing delamination of the scale. By assuming the transition temperature range, when the separation load within the scale fragments is less than the separation load at the oxide/metal interface at low temperature and exceeded by it at the high temperature, it is possible to model transfer from one oxide scale failure mechanism to another (Figure 7.10c).

Figure 7.10 Two different modes of oxide failure observed in hot tensile testing of lowcarbon steel at (a) 830 °C and (b) 900 °C. (c) Schematic representation of the effect of temperature on separation loads for the scale/metal system deduced from the testing.

7.2 Fracture, Ductile Behavior, and Sliding

The most critical parameters for scale failure have been measured during both tensile and modiﬁed hot tensile testing and depend on the morphology of the particular oxide scale, scale growth temperature and, very sensitively, the chemical composition of the underlying steel [7, 8]. The oxide model is validated during the procedure detailed in Section 6.1. Matching the predicted and measured loads allows the strain energy release rate to be determined, which is a critical parameter for the prediction of crack propagation within the scale or along the scale/metal interface. In some cases, steel oxides can show both brittle failure at temperatures below about 800 °C and signs of ductile fracture at higher temperatures (Figures 7.11 and 7.12). At high strain rates, the failure can become brittle in spite of high temperatures (Figure 7.11c). Experimental observation of the ductile fracture within the oxide scale favors the important conclusion that the model should be able to accommodate both types of failure. For the former, the critical strain for the failure is implemented in the model, while the J-integral is used as a parameter corresponding to the strain energy release rate for the consideration of ductile scale failure. Path independence of the J-integral can be used for the nonelastic material behavior [9, 10]. Provided that the actual elastic–plastic material behavior resembles this nonlinear elastic behavior, the J-integral can also be used to evaluate the stress and strain ﬁeld near the cracks in an elastic–plastic material. Determination of the crack length is based on the increment number and deactivation of the separation forces based on the crack length and J-integral value. It has been assumed that no-singularity modeling near the crack tip is applicable, with a quarter-point node technique and only one contour for the J-integral speciﬁed for each interface (Figure 7.13).

Figure 7.11 SEM image showing cross-section of the steel oxide scale after failure in tension at 800 °C and 0.2 s−1 strain rate (a); at 1050 °C and 2.0 s−1 strain rate (c). Prediction of through-thickness brittle crack formation during hot tensile testing (b).

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7 Physically Based Finite Element Model of the Oxide Scale

Figure 7.12 SEM image showing cross-section of the steel oxide scale after failure in tension at 1050 °C and 0.05 s−1 strain rate (a). Prediction of through-thickness ductile crack formation during hot tensile testing (b).

Oxide/metal Interface Viscous sliding and separation

Oxide/Oxide Interface Separation

Figure 7.13 Schematic representation of the interfaces within the oxide–metal model where separation is assumed.

In the virtual crack extension method, only derivatives of elements of the inverse Jacobian J−1 and of the determinant of the Jacobian [ J ] are involved (where the symbols have their usual meaning):

δW e =

⎛

∫ ⎜⎝Wδ

Vo

J + σ ijδ J −jk1

∂u i [ J ]⎞⎟ dV 0 ∂ηk ⎠

(7.6)

This numerical method, comprehensively described elsewhere [9], appeared to be easy to apply for the simulation of crack propagation along the interfaces. The MSC/MARC commercial ﬁnite element code was used to simulate metal/scale

7.3 Delamination, Multilayer Scale, Scale on Roll, and Multipass Rolling

ﬂow, heat transfer, viscous sliding, and failure of the oxide scale during hot rolling, assuming the plane strain condition. The release of nodes was organized using user-deﬁned subroutines in such a way that the crack length is determined based on the increment number. Then, according to the crack length, the boundary conditions are deactivated by calling a routine for a speciﬁc node number.

7.3 Delamination, Multilayer Scale, Scale on Roll, and Multipass Rolling

The morphology of the oxide scale can be quite complicated. Generally, different types of fracture surfaces in the oxide scale are related to the duplex or three different layers of grains, and the model should reﬂect these peculiarities. The microscopic observations using scanning electron microscopy (SEM), backscattered electron imaging (BEI), and electron backscattered diffraction (EBSD) allow for the conﬁguration of the ﬁnite element model to reﬂect precisely the characteristic morphological features, such as different oxide sublayers, voids, roughness of the interfaces, the proportion of each layer at different temperatures, oxidation times, and steel composition (Figure 7.14). The big voids, otherwise called blisters, usually situated between oxide sublayers, could act as sources of multilayered oxide delamination. To predict such a behavior, the oxide scale model comprises three sublayers, each having different mechanical properties (Figure 7.15). Temperature

Figure 7.14 Capturing the morphological features of the oxide scale and reﬂecting them in the ﬁnite element model: schematic representation.

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7 Physically Based Finite Element Model of the Oxide Scale

Figure 7.15

Schematic representation of the multilayer oxide scale model setup.

dependence of Young’s modulus of the different oxide scale layers was calculated from the following equations [11, 12]: o (1 + n (T − 25)) E ox = E ox

(7.7)

where n = −4.7 × 10−4; o = 240 GPa (for the oxide scales on iron); E ox

T is the temperature in °C.

(

E ox = 151.504 1 −

)

T − 300 GPa for FeO 5476.66

(7.8)

G = 55.7 GPa Tm = 1643 K ν ox = 0.36 o ox

(

E ox = 209.916 1 −

)

T − 300 GPa for Fe 2O3 9200

(7.9)

G = 88.2 GPa Tm = 1840 K ν ox = 0.19 o ox

The inner layer has a large number of evenly distributed small pores. The porosity dependence of Young’s modulus of the scales can be taken into account as [13, 14]: o E = E ox exp ( −bp )

where

(7.10)

7.3 Delamination, Multilayer Scale, Scale on Roll, and Multipass Rolling o E ox is the modulus of the fully compact solid, p is the porosity, b ≈ 3. Small pores reduce Young’s modulus, while large pores act as ﬂaws or stress concentrators and weaken the material toward fracture.

Table 7.1 illustrates Poisson’s ratio for the different oxide layers. The plasticity of the scale is assumed to be about 130 MPa at 1050 °C [15]. The oxide scale model can be placed on the roll surface of the macro model. The thermomechanical properties of the roll oxide scale are different from those assumed for the stock oxide scale. The roll scale works as an additional thermal barrier between the roll and the stock, affecting the stock scale failure within the roll gap (Figure 7.16). It was shown in the experiments [8, 16] that the oxide/metal interface becomes weaker at high temperatures, supporting the model assumption that there is a transition temperature range, such that once it has been exceeded, the separation loads at the oxide/metal interface become less than the separation loads within the oxide scale (i.e., between the scale fragments) (Figure 7.10c). For low-carbon steels, the transition temperature range is situated between 800 and 900 °C. The transition is very sensitive to the chemical content of the underlying steel though. Comparing the temperature history at different points across the stock/roll interface predicted for the cases with and without the roll oxide scale, Table 7.1

Poisson’s ratio for the different scale layers assumed for the modeling

FeO

Fe3O4

Fe2O3

Reference

Note

0.36 0.3

0.29

0.19

[4] [14]

Single crystal at room temperature Data used for modeling of rolling

Figure 7.16 Differences in crack opening of the stock scale within the roll gap predicted for (a) not oxidized and (b) oxidized roll. The differences are related to the temperature changes at the interface.

191

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7 Physically Based Finite Element Model of the Oxide Scale

T (˚C) 1100

rolling1

MARC

Roll 1

900 800

2

3

Scale on stock 2

3 4

1 20 2.55

Time (s)

3.332

Stock

Figure 7.17 Temperature history predicted for different points at the stock/roll interface assuming the roll not to be oxidized.

and illustrated in Figures 7.17 and 7.18, one can see that the presence of the roll scale, as a thermal barrier, increases the temperature of the interface between the stock and the oxide scale. The increase in temperature can be so signiﬁcant that it can exceed the transition temperature range, as shown in Figure 7.18 (points 4 and 5), making this interface weaker than the roll scale/stock scale interface (points 2 and 3). As seen in Figure 7.19, the weak stock/oxide scale interface supports the conditions for the transfer of the stock oxide scale to the roll surface, enabling simulation of the effect known as “roll pick-up” (Figure 7.19). The possibility of roll pick-up prediction and control is very important from a technical point of view, as the effect can lead either to the deterioration of the surface quality or to the improvement of the descalability [17, 18]. The advanced, physically based, ﬁnite element model developed during a single rolling pass can be extended to provide the basis for detailed numerical investigations of the roll/stock interface behavior during multipass hot rolling operations. An additional point of concern for the modeling can arise when the thickness of the strip is reduced. The possibility of a cooperative relationship between the formation of oxide scale related defects at the upper and lower faces has been noticed, and the formation of shear zones within the thin steel strip has been demonstrated numerically during preliminary research [19]. The observed effect is more pronounced for thin or ultrathin hot rolled strips, like 0.8–1.0 mm thickness, and with relatively thick oxide scales (a situation that one would try to avoid in industrial practice). The oxide scale should be placed on both the upper and lower faces of the strip for modeling of this circumstance. The following consecu-

7.3 Delamination, Multilayer Scale, Scale on Roll, and Multipass Rolling

rolling1

T (˚C) 1100 900

MARC

600 608 616 624 632 640 648 656 664 672 640 680 688 696 704 712 720 728 736 744 752 760 648 768 776 784 656 664 672 680 688 696 704 712 720 728 736 744 752 760 632 768 776 784

800

Roll 5 4

1

640 648

656 664

656

672 680 688 696 704 712

720 728 736 744

752 760 768 776 784

712 720 728 736 744 752 760 768 776 784 664 672 680 688 696 704

3

2 3

2

648 640

4 680

688

696

672 656

632

704

712 720 728

784 736 744 752 760 768 776

1

20

2.55

Scale on stock

5

664

648 600 608 616 624

Scale on roll

Stock

640 632

Time (s)

3.332

Figure 7.18 Temperature history predicted in different points at the stock/roll interface assuming an oxidized roll.

Figure 7.19 Prediction of the scale failure at exit from the roll gap. Note the scale fragment transferred to the roll surface, that is, pick-up.

tive stages are recommended for the modeling, namely simulation of the combined hot compression–tension test followed by a multipass hot rolling modeling of the steel strip having the same thickness. Longitudinal tension is added as a technological parameter that is relevant to coupled tandem rolling. Initially, the single oxide scale fragments are introduced on both the upper and lower faces of the specimen model undergoing compression, followed by consecutive application of tension applied perpendicular to the direction of the compression (Figure 7.20). Application of the tension after the initial compression is simulated, reﬂecting the longitudinal stress taking place during both the conventional and endless rolling technology [20]. This is followed by the introduction of the single oxide scale fragment on both top and bottom surfaces of the strip and, ﬁnally, a continuous oxide layer can be introduced on both strip surfaces (Figure 7.21).

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7 Physically Based Finite Element Model of the Oxide Scale

ux = 0

Compression

Plane of symmetry

194

Tool 1 Top scale

0.5 ÷ 2 mm

Tension

Bottom scale Tool 2 uy = 0

Figure 7.20 Schematic representation of the compression model setup with consecutive tension perpendicular to the compression direction.

Rigid rolls Elastic plastic strip

Guide rolls Rolling pass 1

Rolling pass 2

Rigid roll

Rigid roll Oxide scale Rolling direction Figure 7.21 Schematic representation of the multipass hot rolling model setup with the continuous oxide scale introduced on both strip surfaces.

7.4 Combined Discrete/Finite Element Approach

Figure 7.22 Modeling of two-pass hot rolling: distribution of equivalent plastic strain (a) and distorted elements (b) within the cross-section of the strip after consecutive rolling passes; strip thickness 1 mm; scale thickness 0.1 mm.

The modeling results exhibited that the oxide scale after the ﬁrst rolling pass enters the second rolling pass having been deformed, fragmentized and partly spalled from the metal surface. These effects are progressively increased during the second rolling pass. It was also observed that the formation of the scale-related shear zones within the strip volume takes place mainly during the second rolling pass (Figure 7.22b). The distorted elements were determined as elements having internal angles that deviated from 90° by more than 15°. The scale-related shear zones remain within the strip volume after spallation of the scale fragments. A single scale fragment remaining on the strip surface after the ﬁrst rolling pass can inﬂuence the formation of the shear zones during consecutive rolling passes. Longitudinal tension contributes to the formation of the observed shear zones. More work, particularly experimental, is needed to characterize the scale-related effect of shear zone formation that has been demonstrated numerically. It is important because there are experimental prerequisites that the shear deformation should lead to the formation of shear zones in the metal’s microstructure [21].

7.4 Combined Discrete/Finite Element Approach

The complex behavior of the stock/roll interface in thermomechanical processing, including the oxide scale, presents a rich variety of phenomena of great technological importance and the models should reﬂect different scales of consideration. The modeling approach discussed earlier has already reached the advanced level. However, prediction of physical phenomena, which are taking place during the high-temperature metal processing in different scales at the same time, becomes

195

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7 Physically Based Finite Element Model of the Oxide Scale

very difﬁcult using traditional ﬁnite element techniques. Effectively, the numerical problem becomes a matter of discrete rather than continuum numerical analysis even assuming today’s level of understanding of physical events at the interface. Assuming potential inclusion of the grain structure of the oxide scale, lubrication and generation of abrasive particles into the system, and mechanical intermixing at the surface sublayers, application of traditional ﬁnite element techniques for precise modeling of these events all at the same time becomes impossible. An alternative approach is to use the latest combined discrete and ﬁnite element analysis technology. Combined methods encompass approaches for linking solid continuum models with discrete element methods to simulate multiscale and multiphase phenomena [22, 23]. These approaches have enormous potential to get the solutions for a wide range of problems or groups of problems on different length scales that may occur during material processing. This creates a need for the development of the next-generation models, which will support the design and control of hot rolling and descaling processes, accounting for various physical phenomena occurring at the stock/roll interface and subsurface layers of the rolled materials. The numerical method described in this section is a combined method. It combines two different scales of modeling, such as macro and meso, and it also combines ﬁnite element analysis of a continuum with a discrete element dynamic method applied for the simulation of mesoscale phenomena. The approach uses both the discrete element method at mesoscale to reach the necessary precision, and the ﬁnite element method at macroscale to save the computational resources. Although some models for studying micromechanics of materials should wait until computer power and material database become sufﬁcient, the focus is now on the development of this combined methodology [24, 25]. For example, it has been shown in Figure 4.30 (Section 4.2.5), illustrating the scanning electron micrograph of the entry zone into the roll gap, that the central and lateral areas can be distinguished on the oxidized surface at the entry zone. The central area is the most relevant to the ﬂat rolling conditions modeled above. The sides are inﬂuenced by three-dimensional deformation ﬁelds at the edges of the specimen. The zone of the arc of contact with the roll reﬂects the semicircular shape of the crack pattern formed at the edges of the oxidized specimen before the gap, together with small cracks between the larger circular cracks, while the central part of the arc consists of the many horizontal cracks with the small crack spacing. Although, two-dimensional modeling approach reﬂects the oxide scale’s pattern of failure over the central area at the moment of roll contact, application of the developed numerical technique for the predictions at the sides of the stock is fraught with difﬁculties mainly because the potential crack passes within the three-dimensional ﬁeld, which cannot be known a priori. For solving this problem, a new combined modeling approach based on multiscale ﬁnite element and discrete element numerical analysis has been developed. Figure 7.23 schematically illustrates the multiscale ﬁnite element model setup. The modeling is reduced to representative cells at the stock–roll interface.

7.4 Combined Discrete/Finite Element Approach

Figure 7.23 Schematic representation of the multiscale combined ﬁnite/discrete element model setup with a macro ﬁnite element model.

The three-dimensional representative cells are chosen near the central area and at the edges of the stock where the deformation conditions are different. The design of the representative cell is based on the possible inputs from the experimental studies. The sizes of the cells should be chosen depending on both the tasks of the numerical analysis and length scale of the predicted failure of the oxide scale. A critical issue is the interaction from one scale of modeling to another. This can be done in different ways using the latest ﬁnite and discrete element analysis technology [26]. Load histories for the cell are taken from the macro model (Figure 7.24). The oxidized face of the three-dimensional representative cell is deformed during the analysis under loading, as shown in Figure 7.24a, transferring the deformation to the two-dimensional oxide scale model, which is based in this case on discrete dynamic element analysis (Figure 7.24b). Figure 7.24a illustrates the results of the crack propagation assuming brittle behavior of the oxide scale mimicking failure of the low-carbon steel oxide scale at the lower temperature range when the scale metal interface is relatively strong, allowing no movement between the metal surface and the scale. The starting point for the modeling at the meso level is a continuum representation of the solid oxide scale by ﬁnite elements. A fracturing criterion is speciﬁed through a constitutive model assuming Rankine and Rotating Crack formulation

197

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7 Physically Based Finite Element Model of the Oxide Scale

Figure 7.24 Schematic representation of (a) the interpolation of the boundary conditions transferred from the macro model to the representative cell and (b) consecutive stages of oxide scale failure predicted using discrete analysis.

designed for modeling the tensile failure of brittle materials [26]. The tension failure surface is determined as the follows: g=

t + Δt

σ i − t + Δt f t

(7.11)

where σi is the principal stress invariants, ft is the tensile strength of the material, t is the time, and Δt is the time increment. The Rotating Crack formulation is based on assuming an anisotropic damage evolution by degrading the elastic modulus E in the direction of major principle stress invariant:

σ nn = E d ε nn

(7.12)

where Ed = (1 – ω) E, ω is the damage parameter, and nn is the local coordinate system associated with the principal stresses (Figure 7.25). The damage parameter depends on the fracture energy of the oxide scale. The adopted constitutive model predicts the formation of the failure band within a single element or between elements. The load-carrying capacity across such localized bands decreases to zero as damage increases until eventually the energy needed to form a discrete fracture is released. The topology of the mesh is updated, leading to the fracture propagation within a continuum and resulting in the formation of a discrete element. This evolution process is continued until either the system comes to equilibrium or up to the time of interest (Figure 7.26) [27]. The latest discrete element, three-dimensional model of the oxide scale showing failure of the scale at the entry into the roll gap is illustrated in Figure 7.27. The oxide scale model comprises three layers representing FeO + Fe2SiO4 (the bottom

7.4 Combined Discrete/Finite Element Approach snm ft

Softening Associated with Micro-fracturing Unloading with damage E Ed enm

Figure 7.25

Softening for Rankine and Rotating Crack formulations.

Figure 7.26 Schematic representation of the formation of the failure band and fracture propagation in brittle materials embedded into ELFEN 2D/3D ﬁnite element/discrete element numerical modeling package (after [27]).

Figure 7.27 The discrete element three-dimensional model of the oxide scale (a) before and (b) after the deformation transmitted from the surface of the representative cell during rolling at the entry into the roll gap [24].

layer), the dense FeO (the middle layer), and the mixture of Fe2O3 and Fe3O4 (the top layer). The scale layers are assumed to be adherent when they are within a contact tolerance Ltol. Tangential viscous sliding arose from the shear stress transmitted from the specimen surface to the scale and between scale layers. The calculation of the viscous sliding coefﬁcient is based on a microscopic model for the

199

200

7 Physically Based Finite Element Model of the Oxide Scale

Steel 1

Steel 2 Figure 7.28 Oxide scale after stalled hot rolling. Note through thickness crack formation for both steel grades, but crushing of the oxide scale around crack faces with steel 2. Steel 1: 0.19 wt% C, 0.79 Mn, 0.18 Si, 0.14 Cu, <0.01 Nb. Steel 2: 0.18 wt% C, 1.33 Mn, 0.36 Si, 0.08 Cu, 0.041 Nb.

stress-directed diffusion around irregularities at the interface and depends on the temperature, the volume-diffusion coefﬁcient, the diffusion coefﬁcient for metal atoms along the oxide/metal interface, and the interface roughness parameters in the same way as was discussed in Section 7.2. Apart from cracking and delamination of the oxide scale layer, the approach allows for the generation of abrasive particles to be accounted for during the rolling pass that can take place around the brittle cracks. This type of scale failure has been observed experimentally and it is sensitive to the chemical content of the underlying steel (Figure 7.28). The oxide scale debris at the roll/stock interface can signiﬁcantly affect friction and heat transfer during metal processing, and the numerical technique enables the relevant predictions to be made. Although particle models for studying the micromechanics of materials should wait until computer power becomes sufﬁcient, the recent work is an example of experimentation with the methodology [25]. The model is developed in two-dimensions to keep the computational resources reasonably small. The macro model setup including three consecutive rolling passes under plane strain conditions is illustrated in Figure 7.29. The model enables calculation of the distributions of velocities, strains, strain rates, stresses, and temperature around the representative

7.4 Combined Discrete/Finite Element Approach

1.52 mm

Element size 0.2 mm Representative cell 1.64mm × 0.44mm

Figure 7.29 Schematic representation of the macro model setup illustrating transfer from the macro to meso level [25].

Figure 7.30 Schematic representation of the meso model setup illustrating the representative cell together with the transition zone [25].

deformation zone near the surface of the rolled material, in such a way to allow the load histories to be taken for the representative cell. The mechanical and thermal properties of the material were assumed to be similar to those used in rolling models. Figure 7.30 schematically illustrates the representative cell together with the transition zone. The meso model consists of a large number of bodies that interact with each other. Each individual discrete element is of a general shape and size. The discrete elements can be introduced into the model as a set of rigid bodies. They can also be deformable and are discretized into ﬁnite elements to analyze deformability and diffusion [22]. The basic assumption of the discrete analysis is that a solid material can be represented as a collection of particles or blocks interacting among themselves in the normal and tangential directions. The motion of each element is governed by Newton’s law as

201

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7 Physically Based Finite Element Model of the Oxide Scale

miui = Fi + Fidamp , Iiω = Hi + H idamp

(7.13)

where u is the element centroid displacement in a ﬁxed coordinate frame; ω is the angular velocity; m is the element mass; and I is the moment of inertia. Vectors F and H are, respectively, the resultant of all forces and moments applied to the ith element due to external load, contact interactions with neighboring blocks and other obstacles. The contact forces between two blocks are decomposed into normal and tangential components and obtained using a constitutive model formulated for the contact. A quasistatic state of equilibrium of the assembly of blocks is achieved by applying the nonviscous-type damping necessary for kinetic energy dissipation: Fidamp = −α t Fi

u i ωi , H idamp = −α r H i u i ωi

(7.14)

where α t and α r are damping constants for translational and rotational motion, respectively. Initial bonding for the neighboring particles can also be assumed. The main assumption of the ﬁnite element method is that the continuum domain is discretized with ﬁnite elements. Combining discrete and ﬁnite element methods involves the treatment of contacts between discrete particles/blocks and ﬁnite element edges. Similar to the case of contact between two spheres, the contact force between the sphere and external edge of a ﬁnite element is decomposed into normal and tangential components and generally can include cohesion, friction, damping, heat generation, and exchange [28]. To obtain continuity in transferring mechanical and physical variables between discrete and ﬁnite element zones, a transition zone can also be introduced between those domains. The idea of the transition zone is that the domain is discretized and governed by both the discrete and ﬁnite element methods [29]. In this zone, the thickness of which can be adjusted to obtain the necessary level of smoothness, the location of the discrete elements is constrained by the location of the relative ﬁnite element nodes. It allows the continuity of the displacements, strains, and stresses in the domain. The algorithm for the transient dynamic problem involving both discrete and ﬁnite elements includes cyclic consecutive computation of the nodal velocities, nodal displacements, nodal pressures, updating the nodal coordinates, checking the frictional contact forces, and updating the residual force vector. It has been realized by using both MSC Marc and ELFEN commercial software. The critical time step for the entire calculation is taken as the critical time step for the discrete analysis, which is much smaller than the one for the ﬁnite element analysis. Assuming a constant temperature T, the transfer processes within the thin subsurface layer can be described by the system of diffusion and the motion Equations (7.13)–(7.15) for particles integrated in time using a central difference scheme:

(

)

∂ ⎛ ∂ ∂C ∂ C ⎞ dC D (T ) + ⎜ D (T ) ⎟ = ∂y ⎝ ∂x ∂x ∂ y ⎠ dt C = C ( x , y , t ) ; 0 ≤ x ≤ L x ; 0 ≤ y ≤ Ly ; t > 0

(7.15)

References

Figure 7.31 Displacement of the discrete element particles/blocks in X (longitudinal) direction predicted in the subsurface layer during the hot rolling of aluminum.

where D(T) is the diffusion coefﬁcient, C is the concentration, and t is the time. In such a case, the amount of substance transferring across the area, governed by the system of Equations (7.13)–(7.15), is expected to be signiﬁcantly different from what it should have been by following the assumption that only diffusion processes were responsible for the transfer, depending on the extent of mechanical mixing in the area. As an example, Figure 7.31 illustrates the prediction of the mechanical mixing on the meso level taking place in the thin (a few microns thick) surface layer of aluminum alloy during hot rolling. The numerical analysis of physical phenomena responsible for the formation of the thin stock surface layer during the hot rolling of aluminum alloys provides the opportunity to link technological parameters, with the ﬁne mechanisms taking place within the surface layer at the meso level, such as diffusion, churning, and mechanical mixing coupled with heat transfer.

References 1 Krzyzanowski, M., and Beynon, J.H. (2006) Modelling the behavior of oxide scale in hot rolling. ISIJ International, 46 (11), 1533–1547. 2 Krzyzanowski, M., Sellars, C.M., and Beynon, J.H. (2002) Characterisation of oxide scale in thermomechanical processing of steel, in Proceedings of Int. Conf. on Thermomechanical Processing: Mechanics, Microstructure & Control, June 23–26, 2002 (eds E.J. Palmiere, M. Mahfouf, and C. Pinna), University of Shefﬁeld, Shefﬁeld, UK, pp. 94–102.

3 Schütze, M. (1995) Mechanical properties of oxide scales. Oxidation of Metals, 44 (1–2), 29–61. 4 Riedel, H. (1982) Deformation and cracking of thin second-phase layers on deformation metals at elevated temperature. Metal Science, 16, 569–574. 5 Raj, R., and Ashby, M.F. (1971) On grain boundary sliding and diffusional creep. Metallurgical Transactions, 2A, 1113–1127. 6 Krzyzanowski, M., and Beynon, J.H. (1999) Finite element model of steel

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7

8

9

10

11

12

13

14

15

16

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oxide failure during tensile testing under hot rolling conditions. Materials Science and Technology, 15 (10), 1191–1198. Krzyzanowski, M., and Beynon, J.H. (2000) Modelling the boundary conditions for thermomechanical processing – oxide scale behaviour and composition effects. Modelling and Simulation in Materials Science and Engineering, 8 (6), 927–945. Tan, K.S., Krzyzanowski, M., and Beynon, J.H. (2001) Effect of steel composition on failure of oxide scales in tension under hot rolling conditions. Steel Research, 72 (7), 250–258. Bakker, A. (1983) An analysis of the numerical path dependence of the J-integral. International Journal of Pressure Vessels and Piping, 14, 153–179. De Lorenzi, H.G. (1981) 3-D elastic– plastic fracture mechanics with ADINA. Computer & Structures, 13, 613–621. Morrel, R. (1987) Handbook of Properties of Technical and Engineering Ceramics, National Physical Laboratory, HMSO Publications, London. Echsler, H., Ito, S., and Schütze, M. (2003) Mechanical properties of oxide scales on mild steel at 800 and 1000 °C. Oxidation of Metals, 60 (3/4), 241–269. Rice, R.W. (1977) Microstructure dependence of mechanical behaviour of ceramics, in Treatise in Materials Science and Technology, vol. 11 (ed. R.K. MacCrone), Academic Press, New York, pp. 199–381. Birchall, J.D., Howard, A.J., and Kendall, K. (1981) Flexural strength and porosity of cements. Nature, 289, 388–390. Ranta, H., Larkiola, J., Korhonen, A.S., and Nikula, A. (1993) A study of scale-effects during accelerated cooling, in Proc. 1st Int. Conf. on ‘Modelling of Metal Rolling Processes’, September 1993, London, UK, The Institute of Materials, London, UK, pp. 638–649. Krzyzanowski, M., and Beynon, J.H. (1999) The tensile failure of mild steel oxides under hot rolling conditions. Steel Research, 70 (1), 22–27. Beverley, L., Uijtdebroeks, H., de Roo, J., Lanteri, V., and Philippe, J.-M. (2001) Improving the hot rolling process of surface-critical steels by improved and

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prolonged working life of work rolls in the ﬁnishing mill train, EUR 19871 EN. European Comission, Brussels. Krzyzanowski, M., and Beynon, J.H. (2004) Improvement of surface ﬁnish in steel hot rolling by optimal cooling ahead of entry into the roll gap: numerical analysis. Proceedings of International Conference on Materials Science & Technology, MS&T ’04, September 26–29, 2004, New Orleans, Louisiana, USA, pp. 77–87. Krzyzanowski, M., and Beynon, J.H. (2005) Simulation of oxide scale failure during multipas hot rolling and related product defects. Informatyka w Technologii Materiałów, 5 (3), 19–25. Nikaido, H., Isoyama, S., Nomura, N., Hayashi, K., Morimoto, K., and Sakamoto, H. (1997) Endless hot strip rolling in the No. 3 hot strip mill at the chiba works. Kawasaki Steel Technical Report, No. 37, pp. 65–72. Harren, S.V., Déve, H.E., and Asaro, R.J. (1988) Shear band formation in plane strain compresssion. Acta Materialia, 36 (9), 2435–2480. Munjiza, A. (2004) The Combined Finite-Discrete Element Method, John Wiley & Sons, Inc., New York. Cook, B.K., and Jensen, R.P. (eds), (2002) Discrete element methods: numerical modelling of discontinua, in Proceedings of the 3rd Int. Conf. on Discrete Element Methods, September 23–25, 2002, Santa Fe, American Society of Civil Engineers, New Mexico. Krzyzanowski, M., and Rainforth, W.M. (2008) Aspects of FE/discrete multiscale modelling of stock surface and subsurface layers in hot rolling, in Proceedings of the 14th International Symposium on Plasticity & its Current Applications (eds A.S. Khan, and B. Farokh), Kona-Hawaii, January 3–8, 2008, NEAT Press, Maryland, USA, pp. 280–282. Krzyzanowski, M., and Rainforth, W.M. (2009) Application of combined discrete/ ﬁnite element multiscale method for modelling of Mg redistribution during hot rolling of aluminium. Computer Methods in Materials Science, 9 (2), 271–276.

References 26 ELFEN 2D/3D Finite Element/Discrete Element Numerical Modelling Package, Version 3.0, Swansea, Rockﬁeld Software Ltd., UK. 27 Yu, J.A. (1999) Contact interaction framework for numerical simulation of multi-body problems and aspects of damage and fracture for brittle materials, Ph.D. thesis, Swansea, University of Wales Swansea, UK. 28 Oñate, E., and Rojek, J. (2004) Combination of discrete element and ﬁnite element methods for dynamic

analysis of geomechanics problems. Computer Methods in Applied Mechanics and Engineering, 193, 3087–3128. 29 Tang, Zh., and Xu, J. (2006) A combined DEM/FEM multiscale method and structure failure simulation under laser irradiation, in Proceedings of the Shock Compression of Condensed Matter – 2005 (eds M.D. Furnish, M. Elert, T.P. Russell, and C.T. White), American Institute of Physics, New York, pp. 363–366.

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8 Understanding and Predicting Microevents Related to Scale Behavior and Formation of Subsurface Layers Research the behavior of oxide scale on a metal surface during different kinds of deformation at elevated temperatures has mostly been motivated by a desire to better understand the microscopic events at the tool/workpiece interface that could inﬂuence heat transfer, friction, descalability, and surface ﬁnish during hot rolling operations. Direct observations of oxide scale behavior under industrial hot working conditions is very difﬁcult, while it is not much easier in the laboratory. Any single experiment is not capable of representing the full range of phenomena taking place during this high-temperature processing. Hence, a range of techniques have been developed, each providing a partial insight. The experimental results have been interpreted numerically; then a physically based numerical model of the rolling operation has been developed and used to simulate the process. Detailed ﬁnite element analysis allowed for the consideration of scale evolution and also for detailed understanding of the microevents both during testing and technological operations. Some results obtained by this complex investigation are presented in this chapter. After relevant adjustment of the mathematical model, it gives a basis for better prediction of the technological operation providing corresponding design criteria.

8.1 Surface Scale Evolution in the Hot Rolling of Steel

The evolution of a steel’s secondary oxide scale during hot rolling starts the moment it enters into the roll gap (Figure 8.1) [1]. The scale is then subjected to further signiﬁcant changes both within the roll gap under the roll pressure and at the exit zone followed by its failure during hydraulic and mechanical descaling operations. Important surface-quality defects may arise when the oxide scale is removed after hot rolling or when small patches are picked up by the roll and come back around on the roll surface to be indented into the following metal. As the stock is drawn into the roll gap by friction, a small amount of tensile deformation is produced ahead of contact with the roll. It is this tensile deformation, coupled with bending at the moment of gripping with the roll, that can induce cracking in the oxide scale at this entry zone [2]. The simple uniaxial tensile test Oxide Scale Behaviour in High Temperature Metal Processing. Michal Krzyzanowski, John H. Beynon, and Didier C.J. Farrugia Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-32518-4

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8 Understanding and Predicting Microevents

T °C

Crack due to longitudinal tension

Crack due to bending at the roll bite Entry into the roll gap

1030

Exit from the roll gap

931 865

766 700 Extruded metal

Oxide scale

Gaps

Figure 8.1 Temperature and crack distribution at the oxidized stock/roll interface during hot rolling [1].

can thus provide much valuable information on the behavior of oxide scale that is relevant to thermomechanical processing [3, 4]. Such tests revealed brittle scale fracture at lower temperatures triggering through-cracks, as shown in Figure 8.1, with possible spallation of the oxide scale from the steel surface. However, at higher temperatures, the oxide scale did not fracture, rather it slid over the steel surface, eventually producing delamination of the scale. The temperature of transition between these two types of failure was found to be sharp and very sensitive to steel chemical composition [5]. Since the oxide scale conducts heat at a much lower rate than the underlying metal, steep temperature gradients can be developed across the scale thickness. This leads to thicker scales having a cooler outer surface compared to thin scales. Thin scales can thus remain hot and deform in a ductile manner along with the steel substrate as the stock is drawn into the roll gap. The cooler outer surfaces can initiate fracture more easily, even well ahead of roll contact. Much thicker scales can withstand higher forces and may not crack until subject to the additional force due to bending as the stock ﬁrst meets the roll. An open gap in the oxide scale may enable the steel underneath to extrude up under the roll contact pressure, as can also be seen in Figure 8.1. Once such hot steel makes direct contact with the roll, the local friction and heat transfer conditions can be expected to change dramatically. Figure 8.1 illustrates the gap patterns typically formed in the oxide scale while entering into the roll gap and at the roll gap. The gaps have different lengths because of their different origin. Some relatively big gaps are formed from through-thickness cracks developed at the entry zone due to longitudinal tensile strain in that area. Others, usually small gaps, are formed due to bending at the roll bite. The small gaps can become even narrower during passage through the roll gap. The gap between scale fragments is changed under the roll compression because of sliding and deformation of the oxide scale

8.1 Surface Scale Evolution in the Hot Rolling of Steel T, °C Before deformation 999.7

Scale fragments

Tool

959.7 Specimen 919.7 Initial width 100 μm

Initial width 250 μm

879.8 After deformation 839.8

Tool

799.8 Specimen 759.8

719.8

Figure 8.2 Crack closure of a small crack (initial crack width 100 μm) and crack widening of a big crack (initial crack width 250 μm) predicted during compression at 38% reduction. The initial temperature = 1000 °C; initial scale thickness = 100 μm; and strain rate = 3.6 s−1.

and metal extrusion through the gap. Crack closure eliminates or reduces the metal extrusion and improves the product’s surface ﬁnish. It has been shown that among the main factors inﬂuencing the degree of metal extrusion during compression are the temperature and the initial width of the gap [6]. The scale slides at high temperatures making the initial gap smaller or closed. However, if the initial gap is relatively big, the gap width is increased during the deformation (Figure 8.2). This effect is discussed in detail in the following section. The inﬂuence of the temperature is so signiﬁcant that even a thin oxide ﬁlm on the roll surface can inﬂuence crack closure and opening because it changes the temperature at the scale/metal interface. The observations using scanning electron microscopy (SEM), backscattered electron imaging (BEI), and electron backscattered diffraction (EBSD) allow for conﬁguration of the ﬁnite element model to reﬂect precisely the characteristic morphological features, such as different oxide sublayers, voids, roughness of the interfaces, the proportion of each layer at different temperatures, oxidation times, and steel composition. The oxide scale on the surface of carbon steel may comprise two or three oxide types, be porous, have large scale voids, and have a crystal size with the same order as that of scale thickness. Not surprisingly, it is often insufﬁcient to treat such a material as a homogeneous isotropic layer. One aspect of

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8 Understanding and Predicting Microevents

Figure 8.3 The different states of multilayer scale evolution predicted during hot rolling modeling: (a) development of a through-thickness crack in the oxide layer entering the roll gap, (b) delamination within the scale at the moment of roll gripping, and (c) crack arrest before reaching the metal surface within the roll gap due to the temperature gradient.

this microstructure, when dealing with the oxide scale ahead of roll contact, is the presence of different layers within the oxide scale. Figures 8.3a and b show that the gripping by the roll may well encourage the delamination of the oxide scale together with an opening up of a through-thickness crack, starting at the outer surface of the scale. Cracks through the oxide scale can also occur due to roll pressure within the roll gap [7]. The cracking starts at the outermost oxide scale layer and propagates inward to the relatively hot surface of the stock. Crack propagation within the roll gap can be stopped at the thin oxide sublayer situated near the stock surface (Figure 8.3c). This phenomenon, as has been shown numerically, was also discussed by other authors, observing experimentally similar cessation of crack propagation within the scale [8]. This type of cracking is more typical for multilayer steel scales that come under the roll either as a continuous layer without throughthickness cracks or when the average crack spacing can be described as signiﬁcantly large, so as to assume scale continuity. Cracking through such scales starts at the uppermost oxide scale layer, which is situated close to the cold surface of the roll, and propagates inward to the relatively hot surface of the stock. The uppermost scale layer is much cooler due to contact with the cold roll, which has encouraged its brittleness. The temperature gradient across such scales is so signiﬁcant that it can change the conditions for crack propagation within the scale and the cracks may not occur in a through-thickness manner as found at the entry into the roll gap when the temperature is more uniform across the scale thickness. Since the oxide scale may be severely damaged by rolling, it is appropriate to consider how this damage contributes to the subsequent descaling. By applying moving boundary conditions that represent a water jet impact in terms of both pressure and cooling, it is possible to model hydraulic descaling operations [9].

8.2 Crack Development in Steel Oxide Scale Under Hot Compression

Figure 8.4 Scale failure predicted at the exit from the roll gap. Note the transfer of the scale fragment to the roll surface and partly lifted scale fragment remained on the stock surface.

Since all mechanical properties of the model are thermally sensitive, including thermal expansion/contraction, such water jet impact inevitably introduces considerable stresses around the oxide scale. It has been shown that the oxide scale fragment that is least attached to the steel stock is removed at the ﬁrst stage of descaling. The other scale fragments were removed in a progressive sequence according to their degree of attachment. By analyzing the reaction forces in the model during the descaling phase, it is possible to evaluate the mechanical and thermal impact that is necessary for descaling purposes. An important surfacequality defect stems from the pickup by the roll of oxide scale from the steel surface, usually in small patches which then come back around on the roll surface and indent into the following metal (Figure 8.4) [10]. A further surface defect may arise when the oxide scale is removed after hot rolling. If the scale had been fractured and the metal had extruded up through the gaps, then these extrusions become protrusions, and will need to be cold rolled to smooth the surface again.

8.2 Crack Development in Steel Oxide Scale Under Hot Compression

As discussed in the previous section, in most of the cases the oxide scale enters the roll gap not as a continuous layer but as a fragmented layer having relatively small or large through-thickness gaps formed at the entry zone (Figure 8.1). The scale pattern within the roll gap undergoes further development under the high roll pressure. Modeling the scale behavior using a physically based oxide scale model coupled with different experimental techniques for the veriﬁcation of the modeling results enabled the analysis of crack development in the oxide scale under the compression at elevated temperatures. The gaps between the scale fragments have different lengths because of the different origin. Some relatively big gaps are formed from through-thickness cracks developed at the entry zone due to longitudinal tensile strain in the area. Others, usually small gaps, are formed due to bending at the roll bite. The small gaps can become even narrower while passing through the roll gap. They are not ﬁlled with metal during the rolling pass while the big gaps can be ﬁlled with extruded hot metal, sometimes enabling direct contact with the roll surface. The width of the gap between scale fragments changes under compression because of sliding and deformation of the oxide scale and metal extrusion through the gap.

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8 Understanding and Predicting Microevents

Results of hot compression test modeling have revealed that the sizes of the ﬁnal gaps depend on several parameters, the ﬁrst being the initial gap width before the compression; it has been brieﬂy discussed in Section 6.4 in relation to the numerical interpretation of the scale behavior in hot tension–compression testing. The change of the gap in the oxide scale during compression predicted for the different initial gap width is illustrated in Figure 6.23. The initial temperature was 1000 °C, while the initial scale thickness was 100 μm. The cracks with initial widths less than 135 μm were closed when reduction reached 15%, while the cracks initially wider than 200 μm were increased. The cracks with an initial width between these critical values remained unchanged or slightly decreased in width. The change in crack width during reduction can be explained by sliding along the metal surface at high temperatures when the scale/metal interface is relatively weak [11]. At low temperatures, when the interface for this steel is strong enough to sustain the shear stresses inﬂuenced by the reduction, the crack width is changed to a lesser extent, mainly due to deformation. As can be seen (Figure 8.5), the scales initially having the same thickness, 100 μm, and the same initial gap width, exhibited different behavior during compression showing no tendency to be closed at the temperature of 700 °C. It can be assumed that there are two critical initial gaps for the oxide scale at the high-temperature range. The ﬁrst one is the critical gap width below which the gap can be closed. The second one is the width above which the gap is increased during compression. Between these critical values, the gap becomes smaller than the initial size (Figure 8.6). These opposite tendencies for the scale gap closure and opening during compression can be explained by the tangential loads arising from the compressed metal extruded up to the roll surface at the both edges of the scale fragment. They are more pronounced at higher temperatures. At lower temperatures, the scale/metal interface is stronger and produces shear loads of opposite sign that makes sliding of the scale raft more

180 160 140

Gap width (mm)

212

120

initial temperature 700 oC

100 80 60 40

initial temperature 1000 oC

20 0 0

5

10

15

20

25

30

35

Reduction, % Figure 8.5 Change of the gap in the oxide scale during compression predicted for different initial temperatures (after [6]).

8.2 Crack Development in Steel Oxide Scale Under Hot Compression 350

Gap becomes bigger

Gap width, mm

300

250

200

Gap becomes smaller 150

100

50

Gap closed 0 0

50

100

150

200

250

300

350

Initial gap width, mm Figure 8.6 Predicted relationship between initial and ﬁnal gap in the oxide scale during compression (after [6]).

difﬁcult. Increasing the compression strain rate results in the closure of the small gaps at higher reduction. The results also exhibit the absence of the second critical width, above which the gap is increased under the compression with the higher strain rate. The higher strain rates make the viscous sliding more difﬁcult. It can be explained by taking into account that tangential viscous sliding of the oxide scale on the metal surface arises from the shear stress transmitted from the specimen to the scale. It was modeled using a shear-based model of friction, described in Section 7.2, in an analogous manner to grain-boundary sliding in high-temperature creep [12]:

η vrel = −mkY

( )

v 2 arctan rel t c π

(8.1)

where η is a viscosity coefﬁcient, νrel is the relative velocity between the scale and the metal surface, m is the friction factor, kY is the shear yield stress, c is a constant taken to be 1% of a typical vrel which smoothes the discontinuity in the value of τ when stick/slip transfer occurs, and ¯t is the tangent unit vector in the direction of the relative sliding velocity. The calculation of the coefﬁcient η was based on a microscopic model for stress-directed diffusion around irregularities at the interface and depends on the temperature T, the volume-diffusion coefﬁcient DV, the diffusion coefﬁcient for metal atoms along the oxide/metal interface δSDS, and the interface roughness parameters p and λ (Section 7.2). The thicker oxide scale has shown gap closure at a higher initial gap than the thinner one (Figure 8.7). It supports the assumption that the tangential loads arising from compressed metal extruded up to the roll surface at the both edges of the scale fragment initiate the sliding of the scale along the interface. The thin scale exhibits a reduced tendency to be closed due to the sliding. Shorter scale rafts have shown a better ability to slide under the deformation. This is illustrated in Figure 8.8. Before compression, both scale rafts had the same initial gap width (200 μm), initial temperature

213

8 Understanding and Predicting Microevents 180 Initial scale thickness 50 µm

160

Gap width (mm)

140 Initial scale thickness 100 µm

120 100 80 60 40 20 0 0

5

10

15

20

25

30

35

40

Reduction (%)

Figure 8.7 Change of the gap in the oxide scale during compression predicted for different initial scale thicknesses and 1000 °C temperature (after [6]).

250

200

Gap width, mm

214

4 fragments scale raft 150

100

50

2 fragments scale raft 0 0

10

20

30

40

50

Reduction, %

Figure 8.8 Change of the gap in the oxide scale during compression predicted for different scale lengths (after [6]).

(1000 °C), and the initial scale thickness (100 μm). At 35% reduction, the gap width became four times shorter than the initial size for the shorter scale rafts, while the longer scales allowed for signiﬁcant metal extrusion through the gap, resulting in its widening, which starts at 15% reduction. The experimental veriﬁcation using hot tension–compression testing described in Section 5.5 conﬁrmed the modeling predictions. The through-thickness cracks were produced in the oxidized ﬂat section of the specimen during the tensile stage. This section was then subjected to uniaxial compression during the second stage. The low-carbon steel specimens were oxidized directly in the testing rig using an induction heating system. The details of this veriﬁcation can be found in Section 6.4.

8.3 Oxide Scale Behavior and Composition Effects

215

Summarizing the results, it can be concluded that the pre-existing gap formed between scale fragments while entering the roll gap might be changed during further compressive deformation during the rolling pass because of sliding and deformation of the oxide scale and metal extrusion through the gap. It can lead to crack closure that eliminates or reduces the metal extrusion and improves the product surface ﬁnish. Among the factors inﬂuencing the degree of metal extrusion is temperature because the scale slides at high temperatures making the initial gap smaller or closed. For the initial width of the gap, there are two critical initial values. The ﬁrst is the critical gap width below which the gap can be closed at high temperature and the second is the width above which the gap width is increased. Between these critical values, the gap becomes slightly smaller than the initial one. The thickness of the scale is also a factor because the thicker the oxide scale, the larger the both critical initial gaps. The length of the scale raft is also important because the shorter the fragment of the oxide scale, the easier it is to slide. Finally, the strain rate is another factor because an increase in the strain rate results in the closure of the small gaps at higher reduction.

8.3 Oxide Scale Behavior and Composition Effects

Initially, some peculiarities of scale growth kinetics, morphology, and mechanisms of failure that could be attributed to different chemical contents have been established for several steel grades: mild, Si–Mn, Mn–Mo, and stainless steels using hot tensile testing for the temperature conditions similar to those of hot rolling (Table 8.1) [3, 4]. Using ﬁnite element modeling, an evaluation of the inﬂuence of the most critical parameters has been undertaken. Appropriate upgradation of the model parameters allowed the repetition of experimentally observed phenomena. One of the most important physical factors affecting oxide scale behavior during hot metal-forming operations is scale adhesion. Further analysis using different model iron alloys exhibited a correlation that supports the key role of chemical composition for the solid scale/solid metal adhesion. There are indications that the main assumptions made for available solid scale/melted metal adhesion models can be applied to solid oxide/solid metal systems.

Table 8.1

Chemical content of steels used for the analysis (wt%).

Element

C

Si

Mn

S

P

Cr

Ni

Cu

Mo

Nb

Mild steel 1 Mild steel 2 Si–Mn steel Mn–Mo steel Stainless steel

0.19 0.18 0.57 0.34 0.025

0.18 0.36 1.90 0.23 0.47

0.79 1.33 0.79 1.28 1.44

0.03 0.01 0.008 0.039 0.034

<0.005 0.025 0.01 0.022 0.031

0.05 0.03 0.18 0.17 18.4

0.07 0.02 0.08 0.12 9.2

0.14 0.08 0.16 0.17 0.26

<0.02 <0.02 <0.02 0.24 0.47

<0.01 0.041 – – –

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8 Understanding and Predicting Microevents

The main differences in the chemical content of the chosen steel grades are in the silicon, manganese, and molybdenum contents, and also relatively high contents of Cr and Ni for the stainless steel. All steel grades included Cu within 0.16–0.26 wt%. The rates of oxidation were determined measuring the scale thickness in the middle region of the sample away from ends. For the two mild steels, the parabolic character of oxidation had been established for oxide growth in air. The prediction of scale thickness δox was made using the parabolic rate constant kp for iron oxidation on the basis of compiled experimental data [13]:

δ ox2 = δ ox2 0 + k p tox

(

k p = 5.053 × 10 −4 exp −

)

20419 ( m2 s ) T

(8.2)

where tox is the oxidation time and T the temperature. This agrees reasonably well with the measurements of oxide thickness. The different alloying elements of the steel have an inﬂuence on the oxidation rate in reheat environments. A more complex equation for the prediction of the scale thickness has been developed [14]. It has been shown that silicon could partially inhibit scale growth or contribute to thicker scales by inhibiting the healing of surface cracks. Copper, in combination with nickel, may decrease the amount of scale formed, but in combination with other alloying elements, it may encourage scale growth or might have no effect at all. Manganese, at up to 1.75 wt.%, can contribute to thickening of the scale. Nickel tends to increase the thickness of the scales by forming its own oxides when carbon is also present, while in combination with other elements, the formation of nickel oxides is retarded. However, the effect of steel chemistry on the scale thickness, for the chosen two mild steels, should be more pronounced for the longer times of oxidation that are typical for reheating process, but not for the secondary oxide scale growing during the short periods between subsequent descaling operations. Thus, the differences in chemical content for the low-carbon steels used in this investigation have not produced signiﬁcant differences in oxide scale thickness for the chosen time periods. Generally the morphology of the scales and the oxide/metal interface observed were not distinguishable from the types that have been described earlier in this book. However, for a given temperature of oxidation, the two mild steels revealed signiﬁcant differences. The ﬁrst was the amount of porosity in the scale, illustrated in Figure 8.9. It also indicates different crystal sizes in the oxide scale. Each appears to comprise three layers, although the relative thickness of each layer is different for the two steels. The inner FeO layer has a large number of evenly distributed small pores. The middle, dense FeO layer has the largest grains for both the steels. The outer layer consisted mainly of fractions of magnetite and hematite. The interface between the magnetite and dense FeO layer was the area of formation of relatively large pores. It was observed that adherence of the inner porous layer with the metal surface was more for steel 2 than for steel 1. This results in relatively easier delamination within the oxide scale along this layer for steel 2 during descaling before SEM observation (Figure 8.9c). This suggests that

8.3 Oxide Scale Behavior and Composition Effects

a

b

c

d

Figure 8.9 Scanning electron micrographs showing the cross-section of oxide scales formed at 975 °C for 800 s (a, c) and at 1150 °C for 800 s (b, d). a, b = mild steel 1; c, d = mild steel 2 (see Table 8.1 for the chemical content) (after [5]).

there should be a difference in the mechanical properties of the oxides and oxide/ metal interface for these steel grades. The difference in oxide grain sizes and porosity for the two mild steels was also observed. The larger grains of the middle oxide layer had relatively larger but more infrequent pores grown on mild steel 1 at the temperature range below 975 °C (Figures 8.9a and c). The corresponding layer of mild steel 2 has a large number of more evenly distributed smaller pores. It was opposite at higher temperatures; relatively larger oxide grains were observed for mild steel 2 (Figures 8.9b and c). It is supposed that the relative strength of oxide changes with temperature. Mild steel oxides had the highest oxidation rate out of the chosen ﬁve steel grades throughout the temperature range 783–1200 °C. At 855 °C and 800 s oxidation time, the oxide scale formed on the surface of the mild steel was more than 25 μm thick, while Mn–Mo oxide scale was about 5 μm thick, Si–Mn scale thickness was less than 5 μm, and stainless steel did not show any visible oxide layer on the surface of the specimen under these conditions (Figure 8.10). The low oxidation rate at this temperature for Mn–Mo and Si–Mn steel can be explained by the presence of manganese and silicon, which act as the deoxidizers. It is known that up to 1.75% Mn promotes scale growth at high temperatures [15]. Silicon and molybdenum act as inhibitors of the scale growth process [16], resulting in thinner scales for these steels. While molybdenum helps to build up the resistance against

217

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8 Understanding and Predicting Microevents

a

b

c Figure 8.10 Scanning electron micrographs showing the cross-section of the oxide scale formed on the surface of (a) Mn–Mo (scale fracture surface), (b) Si–Mn (scale fracture surface), and (c) stainless steel (specimen cross-section) after tensile testing; (a) T = 855 °C, tox = 800 s; (b) T = 1200 °C, tox = 800 s; and (c) T = 1074 °C, tox = 800 s (after [4]).

oxidation in Mn–Mo steel, a detrimental effect was observed due to the formation of volatile MoO3-type oxide, which ruptured the oxide ﬁlm and allowed access to atmosphere oxygen [16]. This could be one of the reasons for obtaining a slightly thicker scale for Mn–Mo steel compared with Si–Mn steel. For stainless steel, the oxide ﬁlm formed at low temperatures, 783–912 °C, was very thin and observed as temper colors. The ﬁlm became thicker and more opaque at higher temperatures and became optically visible as an oxide scale at an oxidation temperature of 1074 °C and above (Figure 8.10c). It is well known that chromium inhibits scale growth at high temperatures [15]. The 316L stainless steel contains 18.4% chromium and it resulted in the highest resistance to oxidation. The stainless steel scales tightly adhered to the metal surface even after the application of 5% strain. The scales usually consisted of several different layers of grains and separation under the inﬂuence of deformation took place along the weakest interface for this multilayered scale. For mild steel 1 at 783 °C, the oxide/metal interface was the weakest one. However, for Si–Mn steel oxide scale, the scale layer closest to the metal surface usually consisted of small equiaxed grains and the outer scale layer consisted of large grains, while the interface is a potential location for the separation within the scale. Such separation within the scale layers, called delamination, was also observed within mild steel 1 oxide at 1150 °C, when relative sliding of the layers took place under elongation of the specimen [3]. In that case, the innermost

8.3 Oxide Scale Behavior and Composition Effects

thin layer had no observable porosity and adhered tightly to the metal surface even after 10% strain. Two different modes leading to oxide spallation during tensile testing were observed for both steel grades. The modes corresponded to the modes that had been observed earlier for the low-carbon mild steel and discussed earlier in this book [3]. According to the ﬁrst mode observed at lower temperatures, throughthickness cracks are formed during tension followed by the initiation of a crack along the oxide–metal interface that might result in spallation at higher strains (Figures 8.11(1a), (2a), and (2b)). This type of oxide scale behavior can be explained by assuming that the interface between metal and oxide scale is stronger than the oxide scale itself. It is well known that through-thickness cracks most likely initiate

1

2

3

4

Figure 8.11 Oxide scale on the specimen after tensile testing. (a) Steel 1; (b) steel 2 (for steel compositions see Table 8.1) (after [5]). 1 T = 830 °C, ε = 2.0%, ε = 0.2 s −1 , tox = 800 s, δox = 60 μm; 2 T = 975 °C, ε = 5.0%, ε = 2.0 s −1 , tox = 800 s, δox = 178 μm; 3 T = 1150 °C, ε = 5.0%, ε = 4.0 s −1 , tox = 100 s, δox = 172 μm; 4 T = 975 °C, ε = 5.0%, ε = 2.0 s −1 , tox = 100 s, δox = 62 μm.

219

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8 Understanding and Predicting Microevents

at pre-existing ﬂaws and grow into the scale when its energy release rate exceeds the critical energy release rate of the material [17]. The variations in crack spacing might be due to the apparently random distribution of voids and pre-existing cracks within the scale. The second mode of oxide spallation was observed at higher temperatures (Figure 8.11 (3a,b)). In this mode, the oxide scale was slipping along the interface throughout elongation under the uniaxial tensile load after spallation at one end of the specimen gage length. It is evident that the interface becomes weaker than the oxide scale at higher temperatures. Sometimes spallation of the whole oxide raft took place after cooling, mainly because of the changes in the diameter of the specimen during elongation. Despite both modes of oxide failure in tension being observed for both steel grades, signiﬁcant differences in scale state after tension for the same test parameters were recorded. Through-scale cracks and near-full spallation of the fractured oxide scale occurred for steel 1 after tension at 830 °C, while no visible throughthickness cracks were observed for steel 2 after tension under the same conditions (Figure 8.11 (1a,b)). Scale thickness inﬂuences behavior, as can be seen in Figure 8.11 (2 and 4), comparing a relatively thin scale (about 40–65 μm) with a 150–180-μm-thick scale following 5% strain at 975 °C. Both steels had throughthickness cracks in the thicker scale, whereas the thinner scale showed no tensile cracks for either steel. However, for the thicker scale, slipping of the nonfractured scale raft for steel 1 and through-thickness cracks for steel 2 were observed when the strain rate was decreased from 2.0 to 0.2 s−1 at the same temperature. This suggests that the viscous component of oxide scale sliding at a high temperature could be signiﬁcant. One of the signiﬁcant features of this failure is the transfer from the throughscale crack mechanism of oxide failure to slipping of the nonfractured oxide raft along the oxide/metal interface with increasing temperature. In terms of the oxide scale model, it implies that the separation stress within the scale fragments is less than that at the oxide/metal interface at low temperature. At the high-temperature range, the separation stress at the oxide/metal interface is less than that within the scale fragments. The available experimental data provide a basis for modeling the two modes of oxide scale failure in tension. Slipping along the scale/metal interface at high temperatures is possible when either the stress from the tensile deformation exceeds that necessary for viscous ﬂow without fracture at the scale/ metal interface, or the energy release rate exceeds its critical level, resulting in fracture along the interface. For the ﬁrst case, tangential viscous sliding of the oxide scale on the metal surface is allowed due to the shear stress transmitted from the specimen to the scale. For the second case, fracture along the interface can result in the separation of the whole scale raft from the metal surface. It is probable that this type of sliding of the detached oxide scale dominates in the tensile tests. By assuming the transition temperature range, it is possible to model the transfer from one oxide scale failure mechanism to another (Figure 7.10, Section 7.2). However, there is a necessity to broaden the assumption when the model is adjusted to mimic the effect of changing the chemical composition of the steel.

8.3 Oxide Scale Behavior and Composition Effects

Figure 8.12 Effect of temperature on the separation stresses of scale/metal system for two steel grades – model assumption [5].

To reconcile the differences between the states of the oxide scale after tension, two changes were made to the model (Figure 8.12). First, it was assumed that the transition temperature range for steel 2 is at the higher temperature level, observed to be above 950 °C. Second, it was assumed that the separation stresses for steel 2 both within the oxide scale and for the oxide/metal interface exceed the corresponding stresses for steel 1. Both assumptions were made mainly to satisfy the differences observed in the slow tests (0.2 s−1 strain rate) for oxidation at 830–975 °C for 800 s when a relatively thick scale (100–160 μm) was formed. Assuming a stronger scale for steel 2 allows simulation of the differences in oxide state that were observed at 830 °C. However, this assumption alone is insufﬁcient to predict the different behavior of the oxide scale observed at 975 °C when the scale grown on steel 1 showed slipping during tension while the scale corresponding to steel 2 failed by through-thickness fracture. Modeling the differences observed at 975 °C is only possible by assuming the displacement of the transition temperature at the higher temperature range for steel 2. Such an assumption in turn implies a relative increase in the separation stress for the oxide/metal interface for steel 2. Thus, these two assumptions for the model were sufﬁcient to match the differences in states of the oxide scale observed after hot tensile testing. At the same time, these assumptions were necessary because excluding either of them results in inadequate prediction of scale behavior either in the low-temperature range or in the temperature range where transfer from one mode of scale failure to another takes place. The model assumptions shown in Figure 8.12 have been used to produce the simulation results for two modes of oxide failure shown in Figure 8.13. These computed results match very well the experimental observations for both steel grades at the same test parameters. It has been shown above that the small differences in chemical content, mainly of Si and Mn, for the mild steel containing 0.02–0.07 Ni and 0.08–0.14 Cu, can be

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8 Understanding and Predicting Microevents

Figure 8.13 Distribution of εx strain component predicted for (a) steel 1 and (b) steel 2 at different times during tension for T = 975 °C, ε = 5.0%, ε = 0.2 s −1 , and δox = 170 μm (after [5]).

the reason for different modes of scale failure. It is known that the small additions of elements with a high afﬁnity for oxygen, such as Y, Ce, Hf, and Si, can be very effective in promoting the formation of an adherent oxide layer more resistant to applied stresses. The active element can have an inﬂuence on the elemental form or as an oxide dispersoid. There are various theories that have been proposed to account for an effect of active elements, which include enhanced scale plasticity, modiﬁcation to the oxide growth process, stronger chemical bonding at the interface, and oxide protrusions into the metal base that can improve adhesion [18, 19]. It has been proposed that segregation of sulfur to the scale/metal interface reduces the adhesion of the scale, and that the effect of the active element is to scavenge the sulfur present in the alloy, thereby improving the intrinsically strong adherence [20]. Other authors propose that the active element blocks active sites, such as interfacial dislocations, that support diffusion growth at the scale/metal interface, thereby altering both the growth mechanism and the adhesion of the scale [21]. No one theory can yet satisfactorily explain all the reported experimental observations. The elemental mappings for Fe, Mn, Cu, and Si over the area of the inner porous FeO layer made for Cu-containing low-carbon steels [22] indicate that Mn is not enriched in the scale or in the substrate, while Si is enriched in the porous FeO layer. The enrichment of Cu became less signiﬁcant as the Cu content decreased

8.3 Oxide Scale Behavior and Composition Effects

and it was not recognizable with less than 0.5 wt% Cu steels. The explanation of different properties of the scale and the scale/interface observed in the hot tensile tests for the two low-carbon steels requires more research work. Nevertheless, different properties can be related to different Si and Cu contents at the interface, so it was assumed that the steel more enriched in Si has the stronger scale/metal interface and has a higher level of separation load, leading to failure within the scale. The temperature dependence of the stress necessary for causing the scale failure at the interface for the two steels can be understood by taking into account the possibility of formation of FeO/Fe2SiO4 eutectic compound (fayalite) instead of the porous FeO layer [23]. It is well known that fayalite reduces the removability of primary scale [24]; therefore, the strength of the interface is greater for the steel richer in Si. However, since it was reported [25] that FeO is plastic above about 827 °C, a part of the stress might be relieved by the plastic deformation of FeO and metal, so the separation stress to cause the failure seems to be slightly reduced. The oxidation at 1150 °C resulted in the formation of Fe2SiO4 grains in an inner FeO layer. The particles of Fe2SiO4 are harder than the FeO matrix and disturb its plastic deformation. Additionally, they decrease the contact area between the two FeO layers. Both of these can weaken the adhesion between the two FeO layers, which might result in delamination within the scale, as has been reported for this temperature range [3]. Liquid Cu enrichment in the scale/metal interface at high temperatures may contribute additional lowering of adhesion for steel 1 (0.14 wt% Cu steel) in comparison with steel 2. The mode of failure for Mn–Mo and Si–Mn steel oxide scales (Table 8.1) was conﬁrmed only to through-thickness cracks within the temperature range from 783 to 1200 °C, the thickness of the oxide scale maintained within 5–250 μm, strain 1–5%, and strain rate 0.2–4.0 s−1. This favors the assumption that the presence of alloying elements such as manganese, molybdenum, and silicon results in strengthening of the oxide–metal interface at high temperatures compared with mild steel. The stainless steel had also shown only the through-thickness mode of failure. For this steel, the thickness of the oxide scale formed at 1074 °C for 800 s was less than 10 μm and the through-thickness cracks presented within the scale after the test were only visible under SEM observations (Figure 8.10c). There is a high probability that sliding of the oxide scale during tension would be observed for any of the steel grades at higher temperatures, outside the tested range. An assumption has been implemented in the oxide scale model for mimicking these experimental observations, namely that the ratio of the separation loads within the oxide scale and the scale/metal interface is less than 1 within the range 783– 1200 °C for the tested Mn–Mo, Si–Mn, and stainless steels (Figure 8.14). This is in good agreement with the results obtained for two low-carbon steels, where it was shown that signiﬁcantly lower alloy content lowered the transition temperature range by over 100 °C. It is clear that the observed differences in the deformation behavior are much larger than would be expected from the differences in oxidation. The chemical content of the underlying steel inﬂuences the fracture energy of the oxide scale and its adherence to the metal surface, both reﬂected in

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8 Understanding and Predicting Microevents

Ratio of the separation loads within the scale and the scale/metal interface

224

Mild steel 1 Mild steel 2 Mn-Mo, Si-Mn, Stainless steel

1

700

800

900

1000

1100

Temperature (°C)

Figure 8.14 Schematic representation of the temperature effect on the ratio of the separation loads within the oxide scale and the scale/metal interface for different steel grades (after [4]).

the observed differences in their failure. This raises important issues requiring further research work. The direct measurement of the scale/metal separation loads coupled with physically based modeling is one of the issues. The next, and probably biggest, challenge is to link the macrolevel models, developed in terms of mechanics, to the thermodynamic and the increasingly sophisticated atomistic models, with the goal of predicting macroscopic properties from basics. If the interactions within the oxide could be described and, with more difﬁculty, the interactions across the scale/metal interface to understand how any given oxide bonds to any given metal, it would be possible to inﬂuence the oxide scale state during the metal-forming operations by scientiﬁc alloy design and process control. However, the main physicochemical processes responsible for scale/metal adhesion at high temperatures are still under discussion [26, 27]. One of the issues is whether adhesion theory for solid oxide/liquid metal systems can be extended to solid oxide/solid metal systems. Making relevant measurements for such systems at high temperatures is extremely difﬁcult. The high-temperature tensile test seems to be helpful for estimating the scale adhesion for temperature conditions similar to those of hot rolling. As discussed above for low-carbon steels, the transition temperature from one mode of scale failure in tension to another is highly sensitive to the chemical composition of the steel. Similar behavior of the cracking–sliding transition in tension has also been observed for different model iron alloys (Figure 8.15). Pure iron, Fe-4at.% Mo and Fe-4at.% Ti alloys were used to study the inﬂuence of the chemical composition on oxide scale adhesion (Table 8.2). Decrease of the number of alloying elements to two gives the possibility of understanding the role of a particular additive. The type and amount of the alloying elements were chosen to be similar to previously studied solid oxide/liquid metal systems. The experimental results showed displacement of the transition temperature toward higher temperatures for the alloys in the sequence Fe → Fe/Mo → Fe/Ti. Since both Mo and Ti do not decrease the strength of the corresponding oxides [29], simulation

8.3 Oxide Scale Behavior and Composition Effects

Fe

225

Fe-M o

Figure 8.15 Two modes of oxide scale failure in tension: “cracking” and “sliding” observed for pure Fe and Fe–4 atomic % Mo alloy (after [28]).

Table 8.2

Chemical composition of metals used for the preparation of modeled alloys (wt%).

Composition

C

S

Si

Fe rod samples (ppm)

<200

<150

Fe lamp meltings (wt%)

0.004

<0.001

<0.01

Mo powder (wt%)

0.04

0.006

Ti granules (wt%)

0.04

0.008

Mn

Cr

Ni

Mo

V

Al

Ti

Co

Cu

<0.01

<0.01

<0.01

<0.01

<0.01

<0.01

<0.01

<0.01

<0.01

0.15

<0.01

<0.01

<0.01

<0.01

0.05

<0.01

0.06

0.03

<0.01

<0.01

<0.01

<0.01

0.05

<0.01

<0.01

<800

<0.01

of such displacement has been obtained by implementing it into the oxide scale ﬁnite element model as a relative increase in the separation loads for the oxide/ metal interface, which means an increase in relative adhesion of the oxide scale to the underlying metal. Similar to the relevant scale/liquid metal systems, the assumption has been made that the adhesion depends on the probability of chemical interaction at the interface, which is expressed through the Gibbs energy of possible chemical reactions. The more negative is the value of the Gibbs energy, the higher is the adhesion. This model was initially proposed by McDonald and Eberhart for aluminum oxide in contact with liquid metals [30]. Later it was expanded to a number of oxide/liquid metal systems [27], and then to nitride/ liquid metal systems [31]. Assuming that the following reactions take place at the interface [29, 32], the scale adhesion of the chosen oxide/metal systems in solid state can also be associated with a decrease in Gibbs energy of oxidation of the alloying element:

8 Understanding and Predicting Microevents

1400 Fe-Ti Transition temperature, oC

226

1300

Fe-Mo

1200 1100 Fe 1000 900 800 0

200

400

600

800

1000

0

- ΔG298 (MenOm), kJ/mole Figure 8.16 Correlation between the transition temperature from “cracking” to “sliding” mode and Gibbs energy of reactions at the metal/scale interface (after [28]).

2Fe s + O2 g = 2FeO Mo s + O2 g = MoO2 Ti s + O2 g = TiO2

ΔG298o = −492 kJ/mol ΔG298o = −502 kJ/mol ΔG298o = −889 kJ/mol

(8.3)

The observed correlation (Figure 8.16) supports the key role of chemical composition for the scale/metal adhesion and shows the sensitivity of the experimental technique to registering the relevant differences at high temperatures. It also indicates that the main assumption of the adhesion model developed for solid oxide/liquid metal system is applicable to solid scale/solid metal oxide systems.

8.4 Surface Finish in the Hot Rolling of Low-Carbon Steel

Product surface ﬁnish is becoming one of the most important concerns in the hot rolling of ﬂat steel products. In many applications, a brilliant and highly reﬂective surface is desired and the product from the ﬁnishing stands is expected to be rolled as smooth as possible. The oxide scale related defects on the product ﬁnish has been classiﬁed and discussed in Section 2.4. One of the factors that deteriorates the product surface ﬁnish from hot rolling is metal extrusion through the cracks in the oxide scale during a rolling pass, forming an asperity pattern on the metal surface [33, 34]. Such asperities cannot be completely eliminated and can be noticed in successive processing. Another scale-related defect is the so-called tiger stripes, irregularly striped scale defects, which are often formed on hot rolled steel strips, resulting in an inhomogeneous or dirty appearance [35]. These scale defects have been observed in hot rolled low-carbon steel with more than 0.5 wt.% Si, and

8.4 Surface Finish in the Hot Rolling of Low-Carbon Steel

were also mentioned as appearing in lower Si steels (0.005% Si) [36]. The defects are formed when the scale thickness before the rolling pass is higher than 20 μm, rolled below 900 °C and followed by a water spray. To prevent these defects, several approaches have been proposed, such as control of slab temperature and strengthening of water jet descaling [35, 37, 38]. However, the reason why complete removal of the scale is not always possible is unclear. It has been shown that the main parameters of hydraulic descaling are the time for through-thickness cooling of the scale and the heat transfer coefﬁcient between scale and stock [39]. This last parameter depends on the level of adhesion between the two surfaces. In other work, the mechanism of scale removal and the scale properties at high temperatures were analyzed while varying different operational factors in a plate rolling mill [8]. It was found that the subsequent descalability of the steel products was inﬂuenced by the state of scale cracks during air cooling. The crack patterns formed in scale during hot rolling to a great extent depend on the technological parameters such as temperature, scale thickness, and reduction [2]. As discussed earlier in this book, oxide scales on low-carbon steels during deformation either in tension or under rolling cannot be assumed both to be perfectly adhering at high temperatures, in the sense of sliding along the interface, and to be fully brittle. Sliding and subsequent delamination was also observed within nonhomogeneous, multilayered scale grown at high temperatures, around 1100 °C. The outer scale layers were porous and much thicker that the inner one. This nonseparated oxide layer was usually 3–8 μm thick. These thin scales adhere tightly to the metal surface even after relatively large strains. At low temperatures, initial through-thickness cracking occurs, followed by the initiation and propagation of a crack along the oxide–metal interface between adjacent through-thickness cracks. This is in agreement with the observations of other authors for tensile failure at low temperatures [40, 41]. The secondary oxide scale is inevitably formed on a hot surface of steel during hot rolling. Two possible ways seem to be beneﬁcial in terms of surface improvement of the hot rolling product. The ﬁrst is maintaining the oxide scale on the metal surface during the process as a continuous, uncracked layer. The second is the complete removal of the scale from the surface of the stock during descaling operations. For the second, increasing the descaling effectiveness is becoming a priority issue. Although attaining these two extreme cases is difﬁcult in practice, the numerical analysis showed that maintaining the optimum temperature of the surface of the stock while entering the roll gap is essential for both the cases. It has already been discussed that if the scale reaches the roll gap at high temperature, which is speciﬁc for the underlying steel composition, or if the thickness of the scale is beneath the lower limit when the stress for through-thickness crack propagation exceeds the yield stress assumed for the oxide scale, then the oxide scale will be able to deform in a ductile manner and not fail by through-thickness cracking. The temperature of the oxide–metal interface at the roll gap can be controlled by the initial temperature of the stock just before the rolling pass, by the thickness of the oxide scale, and also by the heat transfer coefﬁcient of the roll coating. In many cases, the oxide scale on the surface of the roll can act as a

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8 Understanding and Predicting Microevents

Figure 8.17 Fragmentized, partly spalled oxide scale predicted after the rolling pass and schematic illustration of forces contributing toward hydraulic descaling.

thermal barrier, reducing heat transfer within the roll gap, thereby maintaining the scale–metal interface at higher temperature. If the oxide scale comes to the roll gap at the low-temperature range, in other words, when the scale–metal interface is strong enough to transmit the shear stress to the oxide scale while entering the roll gap, the probability of scale failure during the rolling pass is high. In this case, optimal choice of parameters controlling the scale spallation during subsequent descaling is beneﬁcial. Experiments have demonstrated that descaling sprays cannot penetrate or pulverize the oxide scale [42]. There was no sign of descaling spray penetration on the surface of the oxide scale and also no dust was found due to the scale being pulverized. Hence, oxide scale can be removed by a combination of shear force Fs and vertical force Fv created by the water rebounding off the strip underneath the edge of the scale fragment. A third force is the angular force Fa tumbling the oxide scale off the metal surface (Figure 8.17). The design of any efﬁcient descaling system including sprays depends primarily on the magnitude of the descaling force necessary to remove the oxide scale. As can be seen in Figure 8.17, the forces to a large extent depend on the state of the oxide scale to be removed in the consecutive descaling operation. The oxide scale fragments that were partly spalled during hot rolling will inevitably be easier to remove, hence reducing the required descaling force. Prediction of the average descaling force, necessary for the removal of the scale after the rolling pass, lies outside the overall scope of this work. However, assuming that the experimental technique based on the modiﬁed tensile test (Sections 5.3 and 6.1) enables the measurement of separation loads within the oxide scale and at the scale/metal interface at high temperatures, evaluation of the required average descaling force for material deformed under speciﬁc hot rolling conditions seems to be possible and is a topic for future work. The mechanism of development of the interface crack leading to the spallation of a scale fragment is illustrated in Figure 8.18 [43]. Cracking starts at the scale– metal interface at the exit from the roll gap when the scale is fragmented during

8.4 Surface Finish in the Hot Rolling of Low-Carbon Steel

Figure 8.18 Formation of the scale separation from the strip surface predicted at the exit from the roll gap for two consecutive time steps.

Figure 8.19 Different consecutive stages of scale failure predicted at the exit from the roll gap. Note the transfer of the shorter scale fragment to the roll surface, while the longer ones still remain adhered to the stock surface.

the rolling pass. Both the longitudinal tension, extensively developed at the surface layer of the stock at the exit zone due to friction, and the roll pickup contribute toward the separation. The scale fragments at the roll gap are of different length. As can be seen in Figure 8.19, where consecutive stages of the scale spallation are shown, the shorter scale fragment has been transferred to the roll surface while the longer one remains adherent to the surface of the stock. This favors the conclusion that shorter scale fragments can be more easily removed from the stock surface than the longer ones, and that fragmentation of the secondary scale during a rolling pass should make a consecutive descaling operation more efﬁcient. This is in agreement with the earlier results on mechanical descaling, where it was shown that relatively thicker and shorter scale fragments can be more easily removed from the metal surface [44]. Hence, additional fragmentation of the scale is beneﬁcial for descaling. However, the through-thickness gaps formed within the oxide scale should be small enough to prevent extrusion of the hot metal and the subsequent formation of bumps on the rolled metal surface. Figure 8.20 illustrates the effect of water jet impact on the oxidized stock surface. The water jet impinging on a hot stock surface with continuous, uncracked oxide scale was only thermal and was modeled by applying transient boundary conditions for heat transfer on the basis of available experimental results [45]. The heat transfer coefﬁcient was assumed to have a Gaussian distribution over the surface with a

229

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8 Understanding and Predicting Microevents

Figure 8.20 Progressive temperature distributions at the surface layer of the stock entering the roll gap. Note the scale crack opening after application of the water jet cooling and crack closure after removal of the water cooling.

maximum of 30 kW/m2 K. It can be seen in Figure 8.20 that about 3.4 ms after the application of the water cooling, the oxide scale exhibited through-thickness cracking as a result of stresses caused by different thermal contraction of the scale and the underlying steel. Some cooling of the underlying steel surface layer is also visible at the oxide-free places. However, assuming that in practice the scale layer entering the roll gap is initially continuous, the effect can be decreased to minimum. As follows from previous sections, the crack width should not exceed some critical level before entering the roll gap to prevent metal extrusion into the gap under the roll pressure. Figure 8.20 shows that the crack width is subject to water cooling impact. The crack width decreases and tends to be closed after removing the water cooling at 0.031 s. It can be concluded that there is an optimal water cooling impact for the rolling pass when cracking of the secondary oxide scale while entering the roll gap increases the subsequent scale descalability while the gaps formed in the cracked oxide scale under the roll compression are small enough to prevent metal extrusion, hence improving the surface ﬁnish of the rolled product.

8.5 Analysis of Mechanical Descaling: Low-Carbon and Stainless Steel

Coiled low-carbon steel rod produced by hot rolling for subsequent wire drawing inevitably possesses an oxidized surface. The oxide scale must be removed before

8.5 Analysis of Mechanical Descaling: Low-Carbon and Stainless Steel

the drawing operation. The amount of scale formed is dependent on the rolling conditions, particularly the billet reheating temperature, which determines the rolling temperature, the laying temperature, and the cooling rate. Study of the inﬂuence of rolling conditions on descalability of high-carbon steel wire rod showed that the billet reheating temperature does not seem to affect the amount of residual scale signiﬁcantly at the end of rolling, although a small increase is recognizable with increased reheating temperature [46]. This phenomenon has been explained by the repeated scale formation and peeling during multipass rolling. The billet passes through many stands, and scale is repeatedly formed and peeled. Scale remaining on the wire rod at the laying stage is generally a few microns in thickness. Therefore, the laying temperature and cooling after laying have the largest inﬂuence on the formation of the ﬁnal scale on the rod. It has been shown that the higher is the laying temperature or the lower is the cooling rate, the thicker is the scale formed and easier it is to remove [47]. Understanding the scale removal mechanism is important for the optimization of industrial descaling conditions. There are three main sources of stresses in the oxide metal system that arise from external mechanical (thermal) load, from the oxidation process itself, and from geometrically induced stresses. Thermal stresses arise because of the differences in thermal expansion coefﬁcients of metal and oxide during cooling, heating, or thermal cycling [48]. During cooling, compressive stresses usually develop in the oxide layer, since the expansion coefﬁcient of the oxide is less than that of the metal substrate. Temperature transients above the notional oxidation temperature will, thus, usually generate in-plane tensile stresses within the oxide layer that can be calculated [49]. Growth stresses arise mainly from the volume change during the formation of the oxide. The growth stresses are mainly compressive because most materials exhibit a volume expansion during oxidation [50]. Quantitative modeling of this process has been presented in a series of papers [51–53]. The third source of stresses develops during the oxidation of a curved surface. These stresses will be high when the oxide thickness is large relative to the radius of the curvature of the substrate, and can then have a pronounced effect on oxide integrity. However, for cases where the oxide layer is relatively thin, geometrically induced stresses are small compared with those developed as a result of temperature changes [48, 54]. For different cases, different stress sources play a key role. For the oxide on the surface of the steel grade rod used for cold drawing, external mechanical load is the main source of stress in the oxide scale. When these stresses exceed critical values, various types of scale damage may occur, such as microcrack formation, through scale cracking, formation of cracks at the interfaces between different oxide layers, stable development of the delamination at the scale/metal interface, and/or sudden spalling of parts or of the entire scale [40]. As has been shown by many authors, oxide scale displays brittle characteristics at the intermediate and room temperatures [25, 51, 55–57]. The substrate–oxide system can accommodate strain by elastic deformation. If the elastic limit is exceeded, stress relaxation can take place by the mechanical failure of the oxide. Failure can start within the oxide or the substrate, or at the interface by

231

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8 Understanding and Predicting Microevents

delamination [58]. At a high temperature, oxide scale often shows signs of plastic or ductile behavior. Although possible mechanisms of plastic behavior of oxide scale at high temperatures are still under discussion [57, 59–62], it has been shown that stress relaxation can also happen by induced oxide growth processes [63] and diffusional related processes [64, 65]. Mathematical modeling coupled with experimental testing is sufﬁciently developed for the analysis of the complicated mechanisms of oxide scale failure on a microstructural level. The details of the modeling approach have been discussed earlier in Chapter 7. This numerical approach has been developed for the analysis of scale failure in hot rolling. It has enabled the estimation of deformation, viscous sliding along the oxide/metal interface, cracking, and spallation of the oxide scale from the metal surface. Oxide scale failure has been predicted by considering the temperature dependence of the main physical phenomena, namely thermal expansion, stress-directed diffusion, fracture, and adhesion. The thermomechanical model has been extended to the analysis of descalability of the deformed, cracked, and partly spalled secondary oxide scale on the strip surface during a subsequent hydraulic descaling operation [9]. This numerical approach, coupled with experimental observations, is also applicable to the analysis of oxide failure during mechanical descaling when bending, tension, and compression at room temperature are operational factors inﬂuencing scale spallation [44]. There is a possibility to change the amount of longitudinal tension in the steel rod in commercial mechanical descaling practice. Such a change will inevitably inﬂuence the spacing between neighboring through-thickness cracks formed at the earlier stages of bending. Another process parameter, which varies in practice, is oxide scale thickness. It was, therefore, important to investigate the inﬂuence of both these variables on the descalability of oxide fragments. To do this, behavior of the single scale fragments of different length and thickness attached to the tensile surface of the metal rod was analyzed after bending. The results, obtained for 50-μm-thick scales, revealed that the longer (5 mm) fragment adheres to the metal surface after signiﬁcant bending, while the 0.8-mm-long fragment shows the ability to descale. At the same time, a thinner scale fragment, having the same 0.8 mm length but 25 μm thickness, does not lose adherence to the metal surface at a much higher degree of deformation [44]. These results indicate that, to improve the descalability on the convex part of a steel rod during mechanical descaling, both decreasing the length and increasing the thickness of the scale fragments are beneﬁcial. This thickness effect agrees with experimental observations, except that crack spacing also tends to increase, making separation of the variables in practice rather difﬁcult. Taking into account that the properties of both the oxide scale and the scale/metal interface are dependent on the chemical composition of the steel and the scale growth conditions, implementation of the ﬁnite element model with the data obtained for a particular steel grade and scale growth conditions becomes critical. The mechanism of oxide scale spallation for the opposite, concave, side of the steel rod, where longitudinal compression stresses are developed, is different. For an ideally smooth scale adhered to a smooth metal surface, the interfacial stresses,

8.5 Analysis of Mechanical Descaling: Low-Carbon and Stainless Steel

which can inﬂuence the spallation, will be close to zero, provided that there are no discontinuities in the scale. Actual scales, having more or less wavy interfaces with defects, contain sites where, owing to inhomogeneous deformation, the formation of new defects or growth of the existing defects is facilitated when the scale is under compression acting parallel to the interface. It has been shown that the initiation of local decohesion and through-thickness cracks may occur because of grain boundary sliding of the underlying metal, which in turn could occur as a result of deformation during hot coiling [40]. As can be seen in Figure 8.21a, through-thickness cracks could form a wedge between the oxide scale fragments and the metal surface. Other sources of the initiation of decohesion under compression are locally convex parts of the oxide scale (Figures 8.21b and c). At these sites, the oxide scale was lifted from the metal and scale separation was initiated. An approach to the understanding of the spall initiation was suggested by Evans, who described two mechanisms for scale spallation during cooling when the oxide scale is under compression, depending on the relative fracture strengths of the oxide scale and the oxide/metal interface [66]. For a strong interface and relatively weak oxide, compressive shear through-thickness cracks are formed

Figure 8.21 SEM images illustrating sources of initiation of decohesion on compression side of steel rod during bending (after [44]).

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8 Understanding and Predicting Microevents

before failure of the scale/metal interface, and as a result of subsequent cooling and contraction the oxide scale fragment can slide upward along the crack faces owing to wedging of the adherent scale. The alternative mechanism occurs when local decohesion of the scale leads to progressive buckling as a way of reducing scale stress. The scale does not fracture until the local convex parts coalesce by the propagation of tensile cracks along the interface. The local buckle can itself fracture, releasing a spalled fragment. Mathematical modeling was applied to trace the development of spallation of the oxide scale during the bending test. As can be seen in Figure 8.22, spallation in a “wedge” mode at the concave side of the rod can occur during bending. To repeat the continuous oxide scale layer in the model, the left and right edges of the scale fragments were ﬁxed to the metal surface in terms of zero freedom in the longitudinal direction. The wedge formation can be followed by the delamination within the adherent oxide scale block, leaving only the innermost oxide sublayer adhered to the metal surface, according to the stress distribution and relative strength of different interfaces within the scale–metal system. Development of spallation by local buckling of a pre-existing ridge or blister is shown in Figure 8.23. When the blister in the scale is below a critical size, the compressive stresses in the scale do not lead to tensile stresses perpendicular to the interface, and spalling does not occur (Figure 8.23a). The energy balance during bending, in addition to the oxide strain and surface energy terms, should also take into account the strain energy associated with the buckling. An initial separation leading to the formation of oxide ridges of critical size is necessary for spalling under compressive longi-

Figure 8.22 Distribution of longitudinal component of total strain predicted on the concave side of steel rod for multilayer oxide scale during bending. Note the spallation of scale owing to “wedge” mechanism (after [44]).

8.5 Analysis of Mechanical Descaling: Low-Carbon and Stainless Steel

Figure 8.23 Distribution of longitudinal component of total strain predicted on the concave side of steel rod for one-layer scale for given time increments during bending. Note the adhesion of scale to metal surface and spallation when an oxide ridge of critical size has formed (after [44]).

tudinal stresses developed at the concave side of the steel rod (Figure 8.23b). Figure 8.24 illustrates the inﬂuence of both the scale thickness and the length of the scale fragment (i.e., the crack spacing) on the descalability of single oxide fragments. Similar to the convex side, it can be concluded for the concave side of the steel rod that both decreasing the length and increasing the thickness of the scale fragment lead to the improvement of the descalability. The surface quality and ﬁnish of stainless steels is one of their most important marketable factors. The most effective method of scale removal seems to be using both chemical and mechanical descaling. The combination of these descaling techniques facilitates to have a good surface quality and, at the same time, reduces both the process costs and the environmental impact of acid pickling. Preceding the chemical stage with mechanical fracture of the oxide provides paths to the chromium depletion layer of the steel where the acid works to undermine the scale [67, 68]. For stainless steels, substantial work has been done on the growth and behavior of oxide scales with the emphasis ﬁrmly on the austenitic grades [69–72]. A similar bias toward the austenitic grades is evident in the evaluation of descaling, despite analysis of the ferritic stainless steel response to mechanical and chemical processing illustrating signiﬁcant differences in behavior to their austenitic counterparts. The majority of research into the ferritic stainless steels has, however, concentrated either on the ﬁnal surface defects themselves or on the growth of oxides in carefully controlled process conditions that are unlikely to be practicable in an industrial setting [73–75]. However, the problem of complete oxide scale

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8 Understanding and Predicting Microevents

Figure 8.24 Prediction of spallation of one-layer scale fragment on the concave side of steel rod during bending for given scale lengths and thicknesses: note the better descalability of shorter and thicker scale fragment developing from blister (after [44]).

removal after high-temperature processing is even more essential for ferritic stainless steels. The steels are soft enough to retain the surface damage caused by shot blasting, causing this mechanical method to be rejected because of the postprocessing defects, such as spangling. For such steels, roll breaking is the preferred mechanical method for oxide scale fracturing. The levels of spalling observed for different steel grades suggest signiﬁcant behavioral differences showing the necessity for understanding and quantiﬁcation of the microevents behind the descaling method. The laboratory research has been carried out recently to measure the effects of strip tension and bend radius as the main variables during roll scale breaking [76]. The work has examined AISI430 grade strip exclusively; the chemical composition of the two samples are given in Table 8.3. Industrially scale-broken sections were used as a datum, with postanneal hot band sections providing the ideal test material as the oxide would be received at the descaling line. All test samples took the form of 25-mm wide strips machined from the as-received material in such a manner so as to have the rolling direction along the long axis, varying in length from 150 to 250 mm. Testing was carried out at ambient temperature and humidity. Observations of the oxide layer are used to tailor the mathematical model to precisely reﬂect the real morphological features and the composition of the scale layers, the inner wavy chromium-rich oxide, and the outer iron-chromium oxide layer (Figure 8.25). The model was considered for each key stress situations imposed in the laboratory tests; three-point bending, uniaxial tension, and a combination of bending and tension (Figure 8.26).

8.5 Analysis of Mechanical Descaling: Low-Carbon and Stainless Steel Table 8.3

Chemical composition of AISI430 strip samples tested for scale breaking (wt%).

Coil

Fe

Cr

C

Mn

Si

Ni

A B

>80 >80

16.56 16.55

0.046 0.049

0.46 0.45

0.265 0.282

0.31 0.19

a

Iron Chromium oxide Chromium oxide Scale/metal interface

10 μm

b Iron chromium oxide

Big void

2–5 μm 40–50 μm

Chromium oxide Metal

Mathematical model c

Metal Oxide scale Wavy scale/metal interface

Left part of the oxide scale

Chromium oxide

Right part of the oxide scale

Big void

Iron Chromium oxide

Figure 8.25 (a) Scanning electron micrograph of the cross-section of as-received postanneal hot band strip; (b) schematic representation of the characteristic features, and (c) the ﬁnite element model setup of the oxide scale cross-section placed on the metal surface.

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8 Understanding and Predicting Microevents

a

b

c Figure 8.26 Schematic diagrams of the macro model setup for (a) cantilever bend, (b) uniaxial tension, and (c) simultaneous cantilever bend and tension testing.

a

b Figure 8.27 Schematic representation of the strip path with direction marked as red arrows (a) and photograph of VAI UK pilot plant roll-breaker (b) (after [77]).

Simultaneous bend and tension tests were also conducted using a pilot plant roll-breaker (courtesy of VAI UK) and narrow coils of AISI430 steel. During testing, the steel passes through two roll pairs, shown in Figure 8.27, with tension supplied by a coiling unit at either end. The strip was subjected to two reverse bends while under sufﬁcient tension to maintain roll–strip contact. Figure 8.28 illustrates how a shallow bend with strain levels of less than 1% will suffer from subsurface defects. The discontinuous strain pattern across the multilayer scale on the right-hand side shows that the outer layer has been delaminated at points outside the void. It shows minimal strain in the outer iron chromium oxide layer, where it has been relieved by detachment from the chromium-rich

8.5 Analysis of Mechanical Descaling: Low-Carbon and Stainless Steel ε 9.00e–003

Macro part: specimen after bending

7.900e–003 6.800e–003 5.700e–003 4.600e–003

Macro part: scale/metal interface after bending

3.500e–003 2.400e–003 1.300e–003 2.000e–003 –9.000e–003 –2.000e–003

No delamination within the scale layer

Delamination within the scale layer

Figure 8.28 Longitudinal component of the total strain predicted at the initial stage of scale failure during a bending test.

subsurface scale layer. The low level of strain indicated in the outer oxide by blue coloring shows that the iron chromium layer is no longer attached to the sample and the oxide would most likely have been lost from the surface. The red-orange color of the inner chromium-rich oxide layer is part of the strain-distribution pattern of the substrate, showing that this layer is still stuck to the metal surface and hence subject to the same strains. Extending the bend to the limit achieved in the experimental tests produces the macro part shown in Figure 8.29. Figure 8.29b illustrates the right-hand side of the scale raft and the large subsurface crack that has formed. It also shows the ﬁrst crack that extends through the thickness of the outer oxide layer. Simultaneous application of tension to the bending resulted in an increase in the corresponding cracking events. The number of cracks in the subsurface layer increases and the crack through the outer oxide extends to the steel surface, and also becomes wider. The effect of uniaxial tension was considered for the oxide scale with both types of scale–metal interface, planar and wavy. The oxide scale model consisted of the scale having the wavy interface on the left of the multilayer scale raft placed in the middle of the macrobend model, and the planar interface on the right. The planar section of the interface shows little difference between the damage caused by tension, and by tests including a bend proﬁle (Figure 8.30). In both the cases, the interface has experienced delamination at the inter oxide boundary, with subsequent cracking of the inner oxide layer. The subsurface cracks have widened in comparison to the cracks produced by bending. The wavy proﬁle section of the scale raft shows damage imposed by a uniaxial tensile force compared to the planar section. The failure on the wavy proﬁle side of the scale/ metal interface is exclusively due to outer oxide cracking, where the cracks propagate through both oxide layers to the oxide/metal interface. Closer examination of

239

240

8 Understanding and Predicting Microevents ε Macro part: specimen after bending

5.000e–002 4.480e–002 3.960e–002 3.440e–002

a

2.920e–002 2.400e–002

Macro part: scale/metal interface after bending

1.880e–002 1.360e–002

crack

crack

8.400e–003 3.200e–003 –2.000e–003

ε

Macro part: specimen after bending

5.000e–002 4.480e–002 3.960e–002 3.440e–002

b

2.920e–002 2.400e–002 1.880e–002

crack

Macro part: scale/metal interface after bending crack

crack

crack

1.360e–002 8.400e–003 3.200e–003 –2.000e–003

Figure 8.29 Longitudinal component of the total strain predicted at left (a) and right (b) hand side of the scale raft during bending test. Note the crack development in the subsurface oxide and the ﬁrst crack through the outer oxide layer.

the through-thickness cracks reveals progression of the crack opening, also seen in the laboratory tests allowing paths for delivering a pickling agent. The mean crack width measurements support the damage progression mechanism discussed above. Figure 8.31 illustrates the similar behavior of the crackwidth and the crack-spacing values over the same range of strains. At 1% strain, the crack spacing can be measured due to the small separation between the faces making the cracks visible. As the strain is increased, the crack spacing values also increase as the steel is extending and the faces of the brittle oxide material move further apart due to sliding failure at the underlying interface. The crack-spacing values drop drastically in the range of 4–10% strain, as new cracking events occur in the outer oxide layer. Over a similar range (2–5%), the crack width values experience a small drop, although this is due to the relaxation of the interface strain with

8.5 Analysis of Mechanical Descaling: Low-Carbon and Stainless Steel

Figure 8.30 State of the oxide scale predicted after application of tension simultaneously to the bending. Note the through-thickness crack development allowing paths for delivering a pickling agent.

Figure 8.31 Comparison of the measured mean crack spacing and the mean crack width values as a function of the applied strain during tension tests (after [77]).

the new cracking events and the total open space between islands of oxide being redistributed. Between 5% and 15% strain, the crack width increases as the strain causes extension in the steel substrate and the oxide islands become more isolated. The proposed cyclic nature of the damage progression would suggest that at strains exceeding 15%, the oxide would achieve stress relief by fracturing, causing the crack spacing values to drop and the free space exposed to be redistributed, thus reducing the mean crack width even though the total exposed space may not change. When considering the exposed space on the surface, especially at strains above 5%, it is important to differentiate between crack width and where an oxide island

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8 Understanding and Predicting Microevents

Figure 8.32

Material spallation as a function of the applied strain (after [77]).

may have spalled. The spalling of oxide as a result of the surface strain alone, without using brushes or hydraulic jets during upstream process stages or more usually for the descaling of other steel grades 18, opens routes to the chromium depletion layer by removing the outer layer of the scale and exposing the cracks in the subsurface layer, and should dramatically decrease the time required to pickle the steel. Figure 8.32 illustrates how increasing tensile strain increases the amount of material lost from the outer layer of the oxide. As in the crack spacing calculations, the mean values for the as-received material are plotted as asymptotes with no reference to the value of strain imposed. The red line indicates the increasing level of material spalled when the tensile strain, imposed in the original rolling direction, is increased. At 4% strain and below, the surface has lost less than 5% of the outer oxide layer. Once the surface strain exceeds 5%, the amount of material spalled increases dramatically, and continues to increase as the strain is raised to the upper limit for these trials. The brown line, representing skew test results, shows that although the misalignment of the load axis with respect to the rolling direction reduces the crack spacing, the amount of material spalled is reduced. Clearly, the threshold strain for the spalling mechanism of a sample under uniaxial tension is 5%. Considering the mean crack spacing achieved during all laboratory tests indicates that the threshold strain for producing a minimum value, regardless of load state, is approximately 3%. Any further increase in strain would not reduce the mean value sufﬁciently to merit the additional force were crack spacing the only mechanism for increasing the number of paths to the chromium depletion layer at the steel surface. The threshold strain for both a minimum crack spacing and signiﬁcant levels of spallation should be set at 5% (Figure 8.33). Given the heavy bias toward austenitic grades, limited published work exists on the acid pickling of ferritic stainless steel. Iron oxide layers of varying phase compositions have been pickled using hydrochloric acid [78], which acts to remove the material from the outer surface creating chemical cracks that accelerate the undermining of the resulting scale fragments. However, the detrimental effects of residual chloride ions make other acid solutions more desirable. The other work

8.5 Analysis of Mechanical Descaling: Low-Carbon and Stainless Steel

Figure 8.33 Comparison of the mean crack spacing and mean percentage of the spalled material, with respect to the applied strain (after [77]).

Figure 8.34

The effect of strain on pickling times and mean crack spacing (after [77]).

on 430 type stainless steel provides conﬁrmation that the introduction of scalelayer damage is the most effective route to pickling optimization [79]. Chemical scale conditioning, leaching soluble salts from the scale layer, produces voids, which provides fast routes to the chromium depletion layer for the hydroﬂuoric and nitric acid mixture. Scales that had undergone conditioning treatments were exclusively free of scale after pickling, but untreated samples showed more than 80% of the oxide material remained after straight pickling, strongly indicating that reduction of the scale layer integrity was the route to optimizing the ﬁnal descaling process. The introduction of mechanical damage during the current work has been shown to be an effective method of reducing the pickling time; results obtained for tension test samples and the as-received material are shown in Figure 8.34, where the industrial range is deﬁned for these tests by the times recorded for the postanneal hot-band and scale-broken materials. The time taken to remove the scale from the 1% tension test samples is less than the postanneal hot-band time, as expected, and it continues to drop as the strain is increased to 4%, although the removal of the oxide still takes longer than the industrially scale-broken material.

243

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8 Understanding and Predicting Microevents

The pickling time drops below the value for the industrially scale-broken material for the ﬁrst time when the imposed strain reaches 5% and the reduction in time required is over 40%, with the removal of scale completed in 4 min. The application of 5% strain has also proved to be signiﬁcant when considering the amount of material spalled from a surface and the ﬁnal reduction of mean crack spacing values. As roll-breaking is an end-stage process in terms of thermomechanical work, consideration must be given to the effect of deformation on the microstructure, and hence properties, of the strip. The microstructure of the underlying steel is considered elsewhere [80], but an acknowledgment of its effects leads to the conclusion that an extreme deformation could adversely alter the careful manipulations of the upstream process stages and should be avoided if possible. To this end, a combination of bend and tension provides a practical method of introducing the required strain range while reducing the size of the individual loads.

8.6 Evaluation of Interfacial Heat Transfer During Hot Steel Rolling Assuming Scale Failure Effects

Quantitative characterization of heat transfer at the workpiece/tool interface during hot metal-forming operations is still inconsistent and in most cases creates a major hindrance to produce accurate and reliable models for hot metal working processes. The reason for this is partly because of the complicated physical phenomena taking place at the contact. Along with surface roughness and lubrication effects, the importance of oxide scale behavior, mainly secondary, on interfacial heat transfer coefﬁcient (IHTC) in hot rolling of steel has been widely recognized [81]. The strain imposed on the steel surface when stock enters the roll gap, because of drawing in by frictional contact with the roll, produces longitudinal tensile stresses ahead of the arc of contact, which may result in oxide failure. The fractured scale, which has a thermal conductivity about 10–15 times less than the steel, can enable direct contact of hot metal with the cold roll due to extrusion through fractured scale up to the cool roll surface [82]. Such spaces, distributed along the arc of contact, will increase the IHTC through the oxide thermal barrier. At higher temperatures, the oxide–metal interface is weaker than the oxide and shear stresses cannot be fully transmitted to the oxide raft due to sliding, which complicates the crack pattern formation [3]. The location of the plane of sliding is determined by the cohesive strength at different interfaces within the steel-inhomogeneous oxide scale and by the stress distribution when delamination within the scale takes place. A major problem is the high sensitivity of properties and morphology of both the scale itself and the interfaces to the chemical content of steel and the conditions of their growth. Numerical characterization of these phenomena can be achieved using the physically based ﬁnite element model described in Chapter 7. This model, upgraded with experimental data related to the oxide scale, has been applied for the evaluation of the IHTC [83].

8.6 Evaluation of Interfacial Heat Transfer During Hot Steel Rolling Assuming Scale Failure Effects

Extruded metal Zone 3 Figure 8.35

Oxide scale Zone 1

Gap Zone 2

Different zones predicted at the oxidized stock/roll interface during hot rolling.

gap (Zone 2)

Oxide scale (Zone 1)

roll

Direct contact (Zone 3) Steel stock

Boundary gap

Scale on the roll

Figure 8.36 Schematic representation of the heat transfer zones at the roll/stock interface during hot rolling.

The apparent contact surface in the roll gap consists of three types of zones: the roll and stock oxide scale zone, and two nonscaled zones forming gaps between stock scale fragments (Figure 8.35). Some gaps can have direct contact between the roll surface and extruded hot metal. This behavior of the oxide scale and fresh steel allows for the assumption that there are three parallel channels (zones) for the heat from the high-temperature stock to be transferred to the low-temperature rolls. In the ﬁrst zone, the heat is transported through the scale layer, the boundary gap due to partial contact between roll and scale and, possibly, the roll scale. In the second zone, the heat is transported through the boundary gap developed between the oxidized roll and the steel surface. The third zone is formed when the extruded metal has a direct contact with the relatively cold surface of the roll. In such cases, the heat is transferred through the gap and the direct contact. The boundary gap due to partial contact between roll and the fresh metal is also assumed for the third zone. These assumptions are schematically illustrated in Figure 8.36. It is also assumed that the surface geometry of the roll is not changed signiﬁcantly during the rolling pass. The roll surface roughness is measured and included in the numerical analysis, while the scale surface is assumed to be ﬂat. The total thermal resistance over the apparent contact area can, therefore, be determined as Aa A1 A2 A3 = + + Re Re 1 Re 2 Re 3

(8.4)

where Aa is apparent contact area and A1, A2, and A3 are apparent areas occupied by the scale, gaps, and the extruded metal. A1 = ∑ A1i , i is the number of the scale i

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8 Understanding and Predicting Microevents

fragments; A2 = ∑ A2 j , j is the number of gaps; and A3 = ∑ A3k, k is the number j

k

of the direct contact zones. The effective IHTC at the arc of contact is, therefore, determined as a sum of the heat transfer coefﬁcients Cei determined within the corresponding zones Ce = Ce1α 1 + Ce 2α 2 + Ce 3α 3

(8.5)

where αi = Ai/Aa is the area fraction of the corresponding zones: the scale, the gap, and the extruded metal zone such that α1 + α2 + α2 = 1. Assuming no scale on the roll surface, the heat transfer coefﬁcient through the scale (zone 1), Ce1, is determined as Ce1 =

C oxCb1 C ox + Cb1

(8.6)

where Cox is the heat transfer coefﬁcient through the oxide scale layer and Cb1 is the heat transfer coefﬁcient due to partial contact at the boundary gap (Figure 8.36). This is usually called contact conductance. The heat transfer coefﬁcient through the scale layer is determined as C ox =

kox (T ) δ ox ( pa )

(8.7)

where kox is the thermal conductivity of the scale depending on the temperature, T, and δox is the scale thickness, which depends on the pressure pa. In the case when the roll scale cannot be neglected in terms of the heat transfer, Equation 8.6 can be rewritten as Ce1 =

C oxCb1CRox CRoxC ox + CRoxCb1 + C oxCb1

(8.8)

where CRox is the heat transfer coefﬁcient through the roll scale layer determined as CRox =

kRox (T ) δ Rox ( pa )

(8.9)

where the parameters kRox and δRox have the same meaning as in (8.7) but related to the roll scale. The contact conductance parameter, Cb1, has proved to be difﬁcult to determine. No systematic measurements or analyses have been found for the quantitative variations with the surface, interface, and deformation conditions during metalforming processes. It has been shown that the contact conductance, in addition to the effects of the surface roughness and the thermal conductivity of two contacting materials, is related to the apparent contact pressure pa and the hardness, HV, of the softer material in the contact [84, 85]. In view of the exponential variation in the real degree of contact and of the dependence of interfacial heat ﬂux on the real degree of contact, the following exponential relationships have been estab-

8.6 Evaluation of Interfacial Heat Transfer During Hot Steel Rolling Assuming Scale Failure Effects

lished by Li and Sellars between the contact conductance and the contact pressure during hot rolling [86]: Cbi = Ai

khi ⎡ p 1 − exp ⎛⎜ −0.3 a ⎞⎟ ⎤⎥ Rar ⎢⎣ HVi ⎠ ⎦ ⎝

Cbi = Ai

khi Rar

Bi

(8.10)

Bi

⎛ 0.3 pa ⎞ ⎟ ⎜ ⎝ HVi ⎠

for low pressure only

(8.11)

where i indicates the corresponding zone of the contact. The parameters Ai, Bi, khi, and HVi have different values depending on the type of the contacting materials. For zone 1, for instance, kh1 is the harmonic mean of the thermal conductivity of the oxide, kox, and the roll steel, kr, and is determined as 1 (1 kr + 1 kox ) = 2 kh 1

(8.12)

The Vickers hardness, HV1, of the oxide scale is considered varying with the surface temperature of the oxide scale. It is determined from the following approximate expression obtained using the experimental data [87]: HV1 = 7075 − 538 Toxs

for 273 K ≤ Toxs ≤ 1273 K

(8.13)

The parameters A1 and B1 for zone 1 are 0.4 × 10−3 and 0.392, respectively. For zone 2, when there is no direct contact between solids, the heat transfer coefﬁcient Ce2 depends on the roll oxide thickness, lubricant thermal conductivity, and other parameters. It was assumed to be negligibly small in this analysis. For zone 3, the heat transfer coefﬁcient Ce3 is determined as C e 3 = C b 3 β s + C e 2 (1 − β s )

(8.14)

where βs is the degree of the fresh steel contact. The contact conductance Cb3 between extruded fresh steel and the roll surface is determined from Equations (8.10) and (8.11), assuming A3 = 0.405 and B3 = 1.5. The harmonic mean of the thermal conductivity of the roll and specimen steel, kh3, is determined as shown in Equation (8.12). The Vickers hardness of the fresh plain-carbon steel, HV3, can be calculated approximately by using the ﬂow stress σs at 8% strain, neglecting work hardening [88]: HV3 = 3σ s

(8.15)

The degree of the fresh steel contact βs is determined as the ratio between the length of the fresh steel contact and the length of the gap in the oxide scale formed at the arc of contact during the rolling pass (Figure 8.37). It has to be noted that the parameter βs is changed during the rolling pass depending on various technological parameters such as temperature, scale thickness, chemical composition of the steel, gap width at the entry into the roll gap, rolling reduction, etc. The area fraction αi of the corresponding zones with the scale (i = 1), gap (i = 2), and the extruded metal zone (i = 3) is changed during the rolling pass and depends,

247

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8 Understanding and Predicting Microevents

Figure 8.37 Temperature distribution at the cross-section of the roll/stock interface predicted during the rolling pass. Note the determination of the degree of the fresh steel contact βs.

1.2

1.2 Reduction 20%

Reduction 40% 1

0.8

Zone 1 – scale

0.6 0.4

Zone 3 – big gaps

Zone 2 – small gaps

0.2

Area fraction

Area fraction

1

0.8 Zone 1 – scale 0.6 0.4

Zone 3 – big gaps Zone 2 – small gaps

0.2

0 700 750 800 850 900 950 1000 1050 1100 Temperature (°C)

0 700 750 800 850 900 950 1000 1050 1100 Temperature (°C)

Figure 8.38 Effect of the initial stock temperature on the area fraction of the scale failure zones predicted for different rolling reductions and scale thickness of 0.1 mm.

among others, on the initial stock temperature and the oxide scale thickness, as can be seen in Figures 8.38 and 8.39. The gaps within the oxide scale are formed presumably at the relatively low temperatures and are more pronounced at higher reductions. It can be explained by the fact that the scale/metal interface of the low-carbon steel becomes weaker at higher temperatures and the scale tends to slide along the interface rather than cracking in the through-thickness mode. The scale with approximately 100 μm thickness exhibits more tendency toward developing a crack during the rolling pass rather than thinner scale layers. The heat transfer coefﬁcient through the scale layer, Cox, is also changed during the rolling pass, mainly because of the changes in the thermal conductivity of the scale, kox, and the scale thickness, δox, depending on the temperature, type of the oxide scale, and the rolling reduction (Figures 8.40 and 8.41). As can be seen in Figure 8.41, the thickness of the oxide scale is changed during the rolling pass according to the reduction. The changes are more pronounced when the scale consists of a few sublayers and big voids, which are closed at the initial deformations during the rolling pass. These changes will effect the heat transfer coefﬁcient through the oxide scale layer according to (8.7).

8.6 Evaluation of Interfacial Heat Transfer During Hot Steel Rolling Assuming Scale Failure Effects 1.2

1.2 Reduction 20%

0.8 Zone 1 - scale

0.6 0.4

Zone 3 - big gaps

Reduction 20%

Zone 1 - scale

1

Zone 2 - small gaps

Area fraction

Area fraction

1

0.2

0.8 0.6 Zone 3 - big gaps

0.4

Zone 2 - small gaps

0.2 0

0 0

0.05

0.1

0.15

0.2

0.25

0.3

0

Scale thickness, mm

0.05

0.1

0.15

0.2

0.25

Scale thickness, mm

Figure 8.39 Effect of the oxide scale thickness on the area fraction of the scale failure zones predicted for different rolling reductions and a temperature of 800 °C. Thermal Conductivity, W/m K

249

2.5 2 1.5

kox (T ) = 1 + 7 .833 × 10−4T

1

for T ∈ 600 − 1200 o C

0.5 0 600

700

800

900

1000

1100

1200

Temperature (°C)

Figure 8.40 (after [89]).

Temperature dependence of the thermal conductivity of the oxide scale

The degree of fresh steel contact, βs, due to steel extrusion within the gap between the scale fragments is changed during the rolling pass and, among other rolling parameters such as the scale thickness and temperature, depends to a large extent on the initial gap width at the entry into the roll gap and the rolling reduction (Figure 8.42). It follows from Section 8.2 that the small gaps, formed presumably due to bending at the roll bite, tend to close during further compressive deformation within the arc of contact during a rolling pass, and there is no contact between the roll surface and fresh stock steel observed (Figure 8.42a). As the initial gap becomes wider, the gap narrows until about 10% reduction. Then, at higher reductions, the gap widens, allowing fresh steel to be extruded into the gap under the roll pressure. The ﬁrst direct contact between the fresh steel and the roll surface occurs at approximately 20–30% reduction, depending on the initial gap width and the degree of fresh steel contact increase up to about 0.5–0.8 at 40% reduction. These changes in the degree of fresh steel contact lead to some signiﬁcant changes in IHTC calculated for different reductions, as shown in Figure 8.43. To a large extent, the success of any mathematical model depends on the appropriate formulation of the boundary conditions, which, as seen from the evaluation

0.3

8 Understanding and Predicting Microevents

Scale thickness, micrometre

120 100 80 60 40

a

20 0 0

10

20

30

40

Reduction, % 120 Scale thickness, micrometre

250

100 80 60 40 20

b

0 0

5

10

15

20

25

30

35

40

Reduction, % Figure 8.41 The oxide scale thickness predicted for different reductions during the rolling pass. (a) One-layer oxide scale, no big voids; (b) three-layer oxide scale, big voids.

of IHTC, could be as sophisticated as the model itself. The method described, based on ﬁnite element modeling, allows for the calculation of the IHTC at the stock/roll interface assuming the effects of failure of secondary oxide scale. However, including all the mentioned complexities into a single mathematical model describing the dependence of IHTC is not always necessary. Instead, relatively simple formulae for heat transfer can be developed for general applications based on the understanding and prediction of the microevents at the roll/stock interface affecting the IHTC. Of course, reasonable choices are necessary to achieve desirable precision; they should consider the most important dependencies that affect the tribological system.

8.7 Scale Surface Roughness in Hot Rolling

Surface roughness plays a major role in the downstream metal forming and signiﬁcantly affects the surface quality of the ﬁnal product, particularly during sheet metal forming and strip coating. The oxide scale, inevitably formed on the steel surface during high-temperature processing even when the oxidation time is less

8.7 Scale Surface Roughness in Hot Rolling

L, micrometre

200 a

150 L

100 Ls

50 0 0

10

20

30

40

L

Ls b 0

10

20 30 Reduction, %

L, micrometre

500

40

L

400 300

Ls

200 d

100 0

700 600 500 400 300 200 100 0

10

20 30 Reduction, %

40

10

20 30 Reduction, %

40

0.8 0.6 0.4 e

0.2 0 0

0.4 0.2

f 20 30 Reduction, %

0

10

20

30

40

1 0.8 0.6

Ls

10

c

Reduction, %

L

0

0.6 0.5 0.4 0.3 0.2 0.1 0

Degree of fresh steel contact

L, micrometre

0

Degree of fresh steel contact

300 250 200 150 100 50 0

Degree of fresh steel contact

L, micrometre

Reduction, %

40

g

0 0

10

20

30

40

Reduction, %

Figure 8.42 Effect of the rolling reduction on the gap width L (a, b, d, f) and degree of fresh steel contact βs (c, e, g) predicted for the different gap width at the entry into the rolling pass and the initial temperature T = 1000 °C.

than 0.6 s [90], plays its own role by changing tribological conditions at the roll bite and affecting the surface quality. That is why the mechanical and tribological characteristics of the oxide scale have been the subject of intensive research in recent years, estimating the resistance of the carbon steel oxide scale to the deformation in hot rolling [91–93], evaluating its inﬂuence on interfacial friction [94] or even the grain-scale surface roughing in face-centered cubic (FCC) metals due

251

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8 Understanding and Predicting Microevents

Figure 8.43 Effect of the rolling reduction on the interface heat transfer coefﬁcient predicted for different oxide scale thicknesses and the initial temperature T = 800 °C.

to plastic deformation using a ﬁnite element crystal-plasticity model [95]. The mixed circumstances in the roll bite, for instance, due to the oxide scale and lubrication, have signiﬁcant impact on the changes of the required rolling forces and power consumption. It will also affect the overall roll wear and the surface quality [96]. The tribological behavior of the hot rolling rolls assuming oxidation was analyzed recently [97, 98]. Changes of the surface roughness of the oxide scale due to the deformation at the strip/roll interface, the effects of lubrication at the roll bite, are discussed in this section based on the recent modeling results obtained by Tang et al. [99]. The authors used commercial MSC-MARC ﬁnite element software to model the oxide surface roughness changes with and without oil lubrication, by comparing the results with some experimental results. In the simulation, the surface roughness proﬁle of the hot rolled strip oxidized at 900 °C was measured using atomic force microscope, and then matched by generating numerically the surface proﬁle similar to the measured one. It was assumed that the shape of surface roughness asperity can be described by a normal function: z = Ae

− ⎡⎣( x − μ )2 σ x2 + ( y −ν )2 σ y2 ⎤⎦ 2

(8.16)

where A is the height of the surface roughness asperity, μ and ν the summit coordinates of the surface roughness asperity, respectively, and σx, σy are the parameters that reﬂect the sharpness of the surface roughness asperity. The proﬁle of the surface roughness asperity is then determined by these parameters. In order to ensure that the outlines of the surface roughness asperities can be joined continuously to form a rough surface, the parameters reﬂecting the sharpness of the surface roughness asperity are assumed to be determined as

σ x = ( x2 − x1 ) 6 = λx 6

(8.17)

σ y = ( y2 − y1 ) 6 = λy 6

(8.18)

8.7 Scale Surface Roughness in Hot Rolling

Figure 8.44 Schematic representation of the ﬁnite element model setup for the analysis of changes in the oxide scale surface roughness during hot rolling [99].

where λx, λy are the wavelength of the surface roughness asperity in the x- and y-directions, respectively. The height of every surface roughness asperity in the boundary of the rectangular area was assumed to be close to zero. The summit of a surface roughness asperity proﬁle in the small rectangle is assumed to be in the center of the rectangle so that μ and ν can be determined. For a rough surface, the height A and the wavelengths λx, λy are random numbers. Normally, the secondary oxide scale that is grown on the fresh strip surface is very thin, supporting the assumption that the proﬁle of the steel surface asperities is similar to the proﬁle of the oxidized surface when the thickness of the scale layer is uniform. Although the assumption is not always correct, it can be acceptable for the purpose of the analysis. The ﬁnite element model setup has been schematically illustrated in Figure 8.44. It consists of the work roll modeled as a rigid body with ﬂat surface and the steel stock having the uniform oxide layer covering the metal surface with a generated proﬁle. The steel layer model consists of triangular ﬁnite elements signiﬁcantly reﬁned toward the roll/stock interface. Figure 8.45 illustrates the scanned real strip surface and the one generated using the model (8.16). The parameters used to generate the rough surface are Am = 1.3 μm, λxm = 2.2 μm, λym = 2.1 μm, σxm = 0.9, and σym = 0.8. The distribution of peaks and the proﬁles of the two surface asperities are reasonably close. The produced shape or proﬁle of the surface roughness asperity has a random pattern and is similar to the real one. The effect of the oxide scale thickness on oxide scale and steel ﬁnal roughness during rolling with 60% reduction is presented in Figure 8.46. It can be seen that the ﬁnal surface roughness of both the oxide scale and steel increases with an increase in the oxide scale thickness, assuming that the initial roughness was roughly the same. The ﬁnal surface roughness of steel is greater than that of the oxide scale, and it may be larger than the initial surface roughness if the oxide scale thickness is over about 43 μm. The difference between the ﬁnal surface roughness of steel and the oxide scale increases with an increase in the oxide scale thickness.

253

254

8 Understanding and Predicting Microevents Digital instrument Scan size Scan rate Number of samples Image Date Data scale

4

Nanoscope 120.0 0.5003 256 Height 2.000 μm

2

20 40 60 80 100

20.000 μm/div 2.000 μm/div

x z

μM

a

5 0 –5 50 40 50

30 20 20

10

30

40

10

0 0

b Figure 8.45 Three-dimensional surface image of oxide scale scanned by atomic force microscope (a) and generated random surface roughness (b) (after [99]).

The effect of the reduction on the surface roughness of the oxide scale with and without lubrication is shown in Figure 8.47. There were two cases modeled during the hot strip rolling, with and without lubrication. The rolling parameters are the following: the rolling temperature 1025 °C, the rolling speed 0.12 m/s, the oxide scale thickness 25.5 μm, and the work roll surface roughness 0.45 μm. Surface roughness of the oxide scale and strip was measured by a surface proﬁlometer. As can be seen in Figure 8.47, the predicted roughness of the oxide scale is less for higher values of the rolling reduction. The predicted surface and measured roughness of oxide scale are reasonably close [100]. No signiﬁcant effect of lubrication on oxide scale surface roughness was observed in the study. The oxide scale surface roughness is also inﬂuenced by the rolling temperature (Figure 8.48) decreasing with the rolling temperature. The inﬂuence of the reduction on surface roughness was similar for both rolling temperatures, 900 °C and 1025 °C. However, the surface roughness is different for different temperatures.

8.8 Formation of Stock Surface and Subsurface Layers in Breakdown Rolling of Aluminum Alloys

Figure 8.46 Effect of oxide scale thickness on surface roughness predicted during hot rolling of steel [99].

Figure 8.47 Effect of reduction and lubrication on surface roughness of oxide scale predicted during hot rolling of steel [99].

It was smaller for oxide scale rolled at 900 °C comparing with the scale surface roughness obtained when rolling at 1025 °C. The calculated values of the scale surface roughness were reasonably close to the measured ones [100].

8.8 Formation of Stock Surface and Subsurface Layers in Breakdown Rolling of Aluminum Alloys

The mechanisms and processes involved in the formation of the surface and subsurface layers in hot rolled aluminum ﬂat products are of considerable

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8 Understanding and Predicting Microevents

Figure 8.48 Effect of rolling temperature on surface roughness of oxide scale predicted during hot rolling of steel [99].

interest to the aluminum industry [101–103]. For example, hot rolling enhances the ﬁliform corrosion (FFC), which is known to be strongly related to the process history. It is interesting that similar layers induced by cold rolling do not enhance FFC rates to the same extent as by hot rolling. It is thought that the formation of the surface and near-surface layers depends on a range of factors, and particularly on the tribological conditions at the stock/roll interface. It has been shown that the high shear processing during hot rolling is involved in producing a highly deformed near-surface layer [102]. This is due to asperities that affect the contact conditions between the stock and the work rolls. The surface region of a hot rolled aluminum alloy is characterized by a surface layer of continuous oxide 25–160 nm thick, and a subsurface layer of about 1.5– 8 μm thickness (Figure 8.49) [103]. The subsurface layer is much dispersed and consists mainly of small grained metal with a grain boundaries pinned by small (approximately 3–30 nm) crystalline and amorphous oxides. The type and properties of the oxides depend on the stage of the process. MgO, γ-Al2O3, MgAl2O4, and amorphous Al2O3 are observed at the start of the process, while only MgO oxides were found at the end. This is associated with the decrease in the processing temperature. Grain growth in this subsurface layer was retarded by Zener pinning by small oxide particles. For aluminum AA3XXX alloys, the most signiﬁcant microstructural feature inﬂuencing FFC susceptibility appeared to be the redistribution of intermetallic particles in the signiﬁcantly deformed subsurface layer, which results in ﬁner intermetallic particles in this region compared to the initial material [102]. Simulation of the reheating and breakdown laboratory rolling of the Al–Mg–Mn aluminum alloy AA3104 was carried out recently [104]. Examination of the specimens using glow discharge optical emission spectrometry (GDOES) revealed that the reheating induced signiﬁcant magnesium enrichment in the surface and near-

8.8 Formation of Stock Surface and Subsurface Layers in Breakdown Rolling of Aluminum Alloys Metal grains (0.04 - 0.2 μm in size) Continuous oxide layer

Oxide particles (2.5 - 50 nm in size)

A

B

Boundary between the subsurface layer and the bulk Voids

Bulk metal grains Inclusions

Figure 8.49 Schematic representation of the surface layer containing microcrystalline oxides mixed with small grained metal and covered with a continuous layer of surface oxide [103].

40

Reheated only 30 Mg (Wt%)

Reheated and laboratory rolled 20

10 0

1

2

3

Depth (µm)

Figure 8.50

Distribution of Mg in the surface layer of aluminum alloy AA3104 [105].

surface regions and that Mg diffusion and oxidation continued throughout the reheating. The rate of oxidation decreased with time during the reheating process. As shown in Figure 8.50, the level of Mg in the near-surface regions of the rolled specimen was an order of magnitude less than that observed in the reheated specimens (it peaked at about 40 wt%, ignoring the presence of oxygen). It has been shown that the subsurface layers obtained from the industrially hot rolled transfer bar and the laboratory rolled materials were similar in terms of both

257

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8 Understanding and Predicting Microevents

Subsurface layer Pt

2 μm

Figure 8.51 Cross-section of the surface layer of the industrially rolled aluminum alloy AA3104 [105].

thickness and microstructure. The particles seen in both subsurface layers are sufﬁciently small to provide Zener pinning to stabilize the ﬁne structure of the layers. The scale of the subgrains in the laboratory specimens (about 50–350 nm) was similar to the transfer bar. Inspection of the work roll surfaces after the test indicated that, under the rolling conditions used, the fall in Mg content arose mainly due to the removal of some of the thin oxide layer by abrasion and adhesion to the work roll surface. In addition, a small amount of Mg (as oxides) was intermixed into the subsurface layer by the deformation during rolling. A focused ion beam (FIB) image illustrating the subsurface layer obtained in the industrially hot rolled aluminum alloy is presented in Figure 8.51. It is thought that the mechanisms leading to the deformation and mixing of the oxide particles into the subsurface layer arose from slip at the roll/stock interface and the action of roll surface asperities on the stock surface. In both the industrially and laboratory rolled samples, the depth of raised magnesium content correlated well with the observed thickness of the subsurface particle layer. One of the assumptions of the modeling approach, applied for understanding and prediction of the microevents responsible for the formation of the subsurface layer, is that the frictional force and wear result from the interaction of asperities on the contacting surfaces. The most widely used of all asperity deformation models is the adhesion model of Bowden and Tabor [106]. In this model, the frictional force is derived from the force needed to shear the welded junctions formed by adhesion at the tips of contacting surfaces. However, it seems unlikely that the model can be applicable to the rolling conditions of aluminum alloys since the involvement of fracture in the process appears far more severe; in fact, according to the model, welds are formed even for the sliding of smooth lubricated surfaces over each other. The model does not depend on the information about the asperities. This will not be the case where one surface is signiﬁcantly harder than the other, a condition which is expected to apply in hot rolling of aluminum alloys. In this case, the energy produced by sliding is dissipated mainly by plastic deformation of the surface layer, by shearing and failure that take place near the

8.8 Formation of Stock Surface and Subsurface Layers in Breakdown Rolling of Aluminum Alloys

Hard asperities

Stock surface Stock surface

Wave

Wave removal

Stock

Material flow

Figure 8.52

Roll

Chip formation

Circumferential Circumferential roughness roughness

Schematic representation of the roll/stock interface model (after [107]).

surface. Other forms of energy dissipation such as those resulting from overcoming atomic and molecular forces acting between surfaces are relatively small for the metal surfaces and can be neglected. An approach to explain the mechanics of metallic sliding friction was developed by Kopalinsky and Oxley [107]. A schematic representation of the mechanical model developed on the basis of the approach is presented in Figure 8.52. The roll surface is signiﬁcantly harder than the hot aluminum surface being deformed during a rolling pass. The hard roll asperities can form a wave of the underlying soft metal at the contact area, which can be removed in subsequent sliding or even by the chip formation during further shearing. Following this schematic representation, the following assumptions have been made for the ﬁnite element model of the stock/roll interface in hot aluminum rolling: the elastic (or elastic-plastic and hard) roll with asperities or grinding defects on the roll surface; elastic-plastic (soft) stock; friction taken into consideration as the Coulomb friction model; no welded junctions assumed at the tips of contacted surfaces; and the thin continuous oxide scale assumed only as a thermal barrier at the stock/roll interface. The assumed friction model is used for most applications with the exception of signiﬁcant bulk deformations; for such an application, the shear friction model is more appropriate. Figures 8.53a, and b illustrate asperities and grinding defects being introduced on the roll surface. They originate from the observation of the roll surface used for hot rolling of aluminum [108], which is illustrated in Figure 8.53c. The sizes, shape, and distribution of the surface defects along the roll surface can be different depending on the preparation of the roll surface. When the roll surface comes into the contact with the stock, it forms waves in the relatively soft surface layer of aluminum due to the indentation of the roll surface imperfections. The roll surface moves faster than the surface of the stock at the entry into the roll gap. As shown in Figure 8.54, the waves of the deformed material are pushed in the rolling direction due to the relative movement. After the neutral zone along the arc of contact, the relative movement of the roll and stock surface is reversed, causing the highly deformed near-surface layers of the stock to be pushed in the direction opposite to the rolling direction. This kind of backward and forward slip at the roll/stock interface can result in churning out of the soft aluminum surface layer that leads to the mechanical mixing near the interface.

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8 Understanding and Predicting Microevents

Figure 8.53 Asperities and grinding defects on the roll surface: (a, b) FE model setup; (c) scanning electron micrograph (after [108]).

Figure 8.54 Deformation near the roll/stock interface predicted before (a, b) and after (c, d) the neutral zone. Backward/forward sliding is shown by arrows [105].

There are many factors that can have an inﬂuence on the mechanical mixing. One is the aspect ratio of the rolling pass AR deﬁned as a ratio between the projected length of contact and the mean thickness of the material in the pass: AR =

( ho − h f ) R 0.5 ( ho + h f )

(8.19)

where R is the roll radius; ho and hf are the initial and ﬁnal thickness of the material, respectively. A typical AR range for industrial aluminum breakdown rolling is 0.15–3.75, and it was simulated in the laboratory conditions by changing the stock thickness. The relative velocity between the chosen point on the stock surface and the surface of the roll during the rolling pass for different aspect ratios is shown in Figure 8.55. It can be seen that the relative velocity is higher at the entry into the roll gap and reduces toward the exit. The maximum forward slip at the exit from the roll gap was about −2.58 mm/s during the rolling pass with AR = 1.4,

8.8 Formation of Stock Surface and Subsurface Layers in Breakdown Rolling of Aluminum Alloys

Relative velocity, mm/s

90

90

80

AR = 3.7

80

70

70

60

60

50 40 30 20

AR = 1.4

50

Last contact

First contact

Last contact

40 30 20

10 0 -100.04

261

First contact

10 0

0.05

0.06

0.07

0.08

0.09 -100.05

Time, s

0.07

0.09

0.11

0.13

0.15

0.17

Time, s

Figure 8.55 Relative velocity between the stock and the roll surface predicted for the different AR and the following rolling parameters: roll radius 69.7 mm; strain 0.4 [105].

a Rolling direction

b

c

Figure 8.56 Proﬁle of the stock surface layer during aluminum hot rolling formed due to relative slip at the roll/stock interface. Prediction (a) and SEM images (b, c) [109].

while it was only −1.64 mm/s for AR = 3.7 under the same rolling conditions. Thus, for other than very low aspect ratios (AR < 1.0), it is thought that a decrease in AR will increase the churning effect at the surface layer. As mentioned earlier, the proﬁle and distribution of the surface defects along the roll surface can be different depending on the preparation of the roll surface or the history of the roll use. It is thought, therefore, that the microproﬁle of the roll surface will also affect the formation of the stock surface. The mechanical properties of this very thin surface layer of the stock can be signiﬁcantly different from the bulk properties of the material. It has been shown by modeling, for example, that changes in the yield stress can signiﬁcantly affect the deformation and failure at the surface layer. The lower the assumed yield stress of the surface layer, the less is the probability of churning, which has been predicted for higher values of the yield stress. The prediction of the surface proﬁle was validated during the experimental work, showing reasonable agreement (Figure 8.56) [109]. Again, the arrows (Figure 8.56a) indicate the relative slip between the “hard” roll and the “soft” stock surface near the exit from the roll gap. The highlighted lines (Figures 8.56b and c) exhibit the observed proﬁle of the workpiece surface, which is similar to the predicted one.

0.19

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8 Understanding and Predicting Microevents

Figure 8.57 Displacement of the discrete element particles/blocks in Y (vertical) (a, b) and in X (longitudinal) (c) directions predicted in the subsurface layer during aluminum hot rolling [109].

In addition to this, application of the developed combined discrete/ﬁnite element model allows for the prediction of the mechanical mixing in the thin subsurface layer on a mesoscale level due to the speciﬁc tribological conditions in the roll gap (Figure 8.57). The predicted displacements both in vertical (Y) and horizontal (X) directions allow for the assumption that the particles can be displaced by a distance at least comparable with the size of the roll asperities and intermixed in the layer. As seen in Figure 8.58, the numerical approach allows diffusion between the discrete element blocks that are discretized into ﬁnite elements. The concentrations of 13–14 particles chosen randomly at the same depth within the surface layer are plotted against corresponding depths for the different time during the rolling pass. Figure 8.58 illustrates a typical trend in the Mg redistributions predicted in the surface layer of the aluminum stock. The progressive increase in the scatter illustrates the role of the mechanical mixing in the combined mass transfer. The effect of the mixing becomes more pronounced toward the end of the rolling pass that ﬁnds its reﬂection in the concentration proﬁles. Further work is needed to validate the model predictions with the measured Mg distributions during different stages of the rolling process. The approach presented here for the analysis of the physical phenomena responsible for the formation of the thin stock surface layer during hot rolling of aluminum alloys presents the possibility of linking technological parameters with the ﬁne mechanisms taking place within the surface layer at the mesolevel, such as diffusion, churning, and mechanical mixing coupled with the heat transfer. It has been shown that these mechanisms have a signiﬁcant impact on structure, thick-

References

Figure 8.58 Displacement of the discrete element blocks (a) and Mg redistribution in the surface layer illustrated as Mg content plotted versus depth for different time moments (b–f) predicted during hot rolling of aluminum [109].

ness of the subsurface layers, and the subsequent effect on FFC, and they arise from slip at the roll/stock interface and the action of roll surface imperfections on the stock surface. The numerical approach developed allows for a systematic investigation of these relationships that would lead to a new level of material understanding and design.

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ability in Si-added hot-rolled steel sheets. Tetsu-to-Hagan′e, 82 (1), 63–70. Hancock, P., and Nicholls, J.R. (1988) Application of fracture mechanics to failure of surface oxide scales. Materials Science and Technology, 4, 398–406. Eustathopoulos, N., Nicholas, M.G., and Drevet, B. (1999) Wetability at High Temperatures, Pergamon, Amsterdam, New York. Naidich, Y.V. (1972) Contact Phenomena in Metal Melts. Naukova Dumka, Kiev, Russia. Beynon, J.H., Krzyzanowski, M., and Taranets, N. (2005) Surface scale evolution in the hot rolling of steel, Invited plenary lecture at Joint International Conference of HSLA Steels 2005 and ISUGS 2005, Sanya, China, 8–10 November 2005. Proceedings of 5th International Conference on HSLA Steels “HSLA Steels 2005’, Iron and Steel Supplement, vol. 40, pp. 83–90. Samsonov, G.V. (ed.) (1982) The Oxide Handbook, 2nd edn, IFI/Plenum, New York. McDonald, J.E., and Eberhart, J.G. (1965) Adhesion in aluminum oxide–metal systems. Transactions of the Metallurgical Society of AIME, 233, 512–517. Taranets, N.Y., and Naidich, Y.V. (2002) Forecasting capillary characteristics for aluminum nitride ceramic– liquid metal systems. Powder Metallurgy and Metal Ceramics, 41 (3–4), 177–182. Benard, J. (1964) Oxidation of Metals. Vol. II, Monographies, Gauthier-Villars Editeur, Paris. Blazevic, D.T. (1996) Tertiary rolled in scale – the hot strip mill surface problem of the 1990s. Proceedings of the 37th Mech. Work Steel Process Conference MWSP, ISS, 33, 33–38. Li, Y.H., and Sellars, C.M. (1996) Evaluation of interfacial heat transfer and friction conditions and their effects on hot forming processes. Proceedings of the 37th Mech. Work Steel Process Conference MWSP, ISS, 33, 385–393. Krzyzanowski, M., and Beynon, J.H. (2006) Modelling the behaviour of oxide scale in hot rolling. ISIJ International, 46 (11), 1533–1547.

36 Okada, H., Fukagawa, T., Ishihara, H., Okamoto, A., Azuma, M., and Matsuda, Y. (1995) Prevention of red scale formation during hot rolling of steels. ISIJ International, 35 (7), 886–891. 37 Chattopadhyay, A., and Chanda, T. (2008) Role of silicon on oxide morphology and pickling behaviour of automotive steels. Scripta Materialia, 58 (10), 882–885. 38 Blazevic, D.T. (1987) Rolled in scale – the consistent problem. Proceedings of 4th Int. Steel Roll Conf., Danville, France, vol. 1, pp. 381–402. 39 Krzyzanowski, M., and Beynon, J.H. (2001) Modelling descaling events in metal forming – a surface quality issue, in Proceedings of the Modelling of Metal Rolling Processes; Symposium 10: Surface Quality, 19 April 2001, London, IOM Communications Ltd., London, UK, p. 7. 40 Moon, C.O., and Lee, S.B. (1993) Analysis on failures of protective-oxide layers and cyclic oxidation. Oxidation of Metals, 39 (1/2), 1–13. 41 Nagl, M.M., Evans, W.E., Saunders, S.R.J., and Hall, D.J. (1992) Investigation of failure of brittle layers under compressive stresses using acousticemission. Materials Science and Technology, 8 (11), 1043–1049. 42 Blazevic, D.T. (2000) Newton and descaling. Part II. Descaling spray forces and the eleventh question, in Proceedings of the 3rd Int. Conf. on Hydraulic Descaling, IOM Communications, London, pp. 3–13. 43 Krzyzanowski, M. and Beynon, J.H. (2004) Improvement of surface ﬁnish in steel hot rolling by optimal cooling ahead of entry into the roll gap: numerical analysis. Proceedings of International Conference on Materials Science & Technology, MS&T ’04, September 26–29, 2004, New Orleans, Louisiana, USA, pp. 77–87. 44 Krzyzanowski, M., Yang, W., Sellars, C.M., and Beynon, J.H. (2003) Analysis of mechanical descaling: experimental and modelling approach. Materials Science and Technology, 19, 109–116.

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55 Coutsouradis, D., Bachelet, E., Brnetaud, R., Esslinger, P., Ewald, J., Kvernes, I., Lindblom, Y., Meadowcroft, D.B., Regis, V., Scarlin, R.B., Schneider, K., Singer, R. (eds) (1994) Materials for Advanced Power Engineering, Part II, Kluwer Academic Publishers, Dordrecht, The Netherlands. 56 Hou, P.Y., and Saunders, S.R.J. (2005) A survey of test methods for scale adhesion measurement. Materials at High Temperatures, 22 (1–2), 121–129. 57 Schütze, M. (1990) Plasticity of protective oxide scales. Materials Science and Technology, 6, 32–38. 58 Eisenblätter, J. (1980) The origin of acoustic emission – Mechanisms and models. Proceedings of the Meeting on ‘Acoustic emission’, Oberursel, Deutsche Gesellschaft für Metallkunde e, vol. V, pp. 189–204. 59 Zhang, Y., Gerberich, W.W., and Shores, A. (1997) Plastic deformation of oxide scales at elevated temperatures. Journal of Materials Research, 12, 697–705. 60 Douglass, D.L., Kofstad, P., Rahmel, A., Wood, G.C. (eds) (1996) International workshop on high-temperature corrosion. Oxidation of Metals, 45 (5/6), 529–620. 61 Frost, H.J., and Ashby, M.F. (1982) Deformation-Mechanism Maps, Pergamon Press, Oxford, UK. 62 Barnes, J.J., Goedjen, J.G., and Shores, D.A. (1989) A model for stress generation and relief in oxide–metal systems during a temperature change. Oxidation of Metals, 32 (5/6), 449–469. 63 Schütze, M. (1985) Deformation and cracking behaviour of protective oxide scales on heat-resistant steels under tensile strain. Oxidation of Metals, 24 (3/4), 199–232. 64 Guttmann, V., and Merz, M. (eds) (1981) Corrosion and Mechanical Stress at High Temperatures, Applied Science Publishers, London, UK. 65 Evans, H.E., Nicholls, J.R., and Saunders, S.R.J. (1995) The inﬂuence of diffusion-related mechanisms in limiting oxide-scale failure. Solid State Phenomena, 41, 137–156.

References 66 Evans, H.E. (1988) Central electricity generating board. Oxide/metal interface and adherence. Materials Science and Technology, 4 (5), 415–420. 67 Reichardt, M. (2001) Surface oxide formation and acid-descaling for stainless steel – Part I. Wire Industry (UK), 68, 503. 68 Reichardt, M. (2002) Surface oxide formation and acid-descaling for stainless steel. II. Wire Industry (UK), 69, 334–338. 69 Osgerby, S. (2000) Oxide scale damage and spallation in P92 martensitic steel. Materials at High Temperatures, 17 (2), 307–310. 70 Lille, C., and Jargelius-Pettersson, R.F.A. (2000) Factors affecting the oxidation mode of stainless steels. Materials at High Temperatures, 17 (2), 287–292. 71 Fujikawa, H., Morimoto, T., and Nishiyama, Y. (2000) Direct observation and analysis of the oxide scale formed on Y-treated austenitic stainless steels at high temperature. Materials at High Temperatures, 17 (2), 293–298. 72 Evans, H.E., Donaldson, A.T., and Gilmour, T.C. (1999) Mechanisms of breakaway oxidation and application to a chromia-forming steel. Oxidation of Metals, 52 (5/6), 379–402. 73 Nagumo, M., Hong, T., and Ogushi, T. (1996) The effect of chromium enrichment in the ﬁlm formed by surface treatments on the corrosion resistance of Type 430 stainless steel. Corrosion Science (USA), 38, 881–888. 74 Nomura, K., Hosoya, Y., Nishimura, H., and Terai, T. (2001) Characterisation of oxide layers and interface layers of ferrite stainless steel (SUS 430) by 57Fe CEMS. Czechoslovak Journal of Physics, 51, 773–780. 75 Saeki, I., Saito, T., Furuichi, R., Konno, H., Nakamura, T., Mabuchi, K., and Itoh, M. (1998) Growth process of protective oxides formed on type 304 and 430 stainless steels at 1273K. Corrosion Science (USA), 40 (8), 1295–1302. 76 Clowe, S.J., Krzyzanowski, M., and Beynon, J.H. (2005) Mechanical scale-breaking of AISI430 stainless

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on contact conductance. Journal of Heat Transfer –-Transactions of the ASME, 114, 802–810. Li, Y.H., and Sellars, C.M. (1996) Modelling deformation behaviour of oxide scales and their effects on interfacial heat transfer and friction during hot steel rolling, in Proceedings of the 2nd Int. Conf. On Modelling of Metal Rolling Processes (eds J.H. Beynon, P. Ingham, H. Teichert, and K. Waterson), The Institute of Materials, London, UK, pp. 192–206. Samsonov, G.V. (1973) The Oxide Handbook, IFI/Plenium, New York. Tabor, D. (1951) The Hardness of Metals, Clarendon Press, Oxford. Ranta, H., Larkiola, J., Korhonen, A.S., and Nikula, A. (1993) A study of scale-effects during accelerated cooling, in Proc. 1st Int. Conf. on ‘Modelling of Metal Rolling Processes’, September 1993, London, UK, The Institute of Materials, UK, pp. 638–649. Sun, W.H., Tieu, A.K., Jiang, Z.Y., Zhu, H.T., and Lu, C. (2004) Oxide scales growth of low carbon steel at high temperatures. Journal of Materials Processing Technology, 155/156, 1300–1306. Yu, Y., and Lenard, J.G. (2002) Estimating the resistance to deformation of the layer of scale during hot rolling of carbon steel strips. Journal of Materials Processing Technology, 121, 60–68. Sun, W.H., Tieu, A.K., and Jiang, Z.Y. (2004) Effect of rolling condition on mill load and oxide scale deformation in hot rolling of low carbon steel. Steel GRIPS – Journal of Steel and Related Materials, 2, 579–583. Sun, W.H., Tieu, A.K., and Jiang, Z.Y. (2003) Experimental simulation of oxide scales surface characteristics during hot strip rolling. Journal of Materials Processing Technology, 140, 77–84. Munther, P.A., and Lenard, J.G. (1999) The effect of scaling on interfacial friction in hot rolling of steels. Journal of Materials Processing Technology, 88, 105–113.

95 Zhao, Z., Radovitzky, R., and Cuitino, A. (2004) A study of surface roughening in fcc metals using direct numerical simulation. Acta Materialia, 52, 5791–5804. 96 Jiang, Z.Y., Tieu, A.K., and Zhang, X.M. (2004) Finite element modelling of mixed ﬁlm lubrication in cold strip rolling. Journal of Materials Processing Technology, 151, 242–247. 97 Vergne, C., Boher, C., Levaillant, C., and Gras, R. (2001) Analysis of the friction and wear behavior of hot work tool scale: application to the hot rolling process. Wear, 250 (1–12), 322–333. 98 Pellizzari, M., Molinari, A., and Straffelini, G. (2005) Tribological behaviour of hot rolling rolls. Wear, 259, 1281–1289. 99 Tang, J., Tieu, A.K., and Jiang, Z.Y. (2006) Modelling of oxide scale surface roughness in hot metal forming. Journal of Materials Processing Technology, 177, 126–129. 100 Sun, W.H. (2005) A study on the characteristics of oxide scale in hot rolling of steel, Ph.D. thesis, University of Wollongong, Australia. 101 Afseth, A., Nordlien, J.H., Scamans, G.M., and Nisancioglu, K. (2002) Effect of thermo-mechanical processing on ﬁliform corrosion of aluminum alloy AA3005. Corrosion Science, 44, 2491–2506. 102 Scamans, G.M., Afseth, A., Thompson, G.E., and Zhou, X. (2002) Ultra-ﬁne grain sized mechanically alloyed surface layers on aluminium alloys. Materials Science Forum, 396, 1461–1466. 103 Fishkis, M., and Lin, J.C. (1997) Formation and evolution of a subsurface layer in a metal working process. Wear, 206, 156–170. 104 Frolish, M.F., Walker, J.C., Jiao, C., Rainforth, W.M., and Beynon, J.H. (2005) Formation and structure of a subsurface layer in hot rolled aluminium alloy AA3104 transfer bar. Tribology International, 38, 1050–1058. 105 Krzyzanowski, M., Frolish, M.F., Rainforth, W.M., and Beynon, J.H. (2007) Modelling of formation of stock surface and subsurface layers in

References breakdown rolling of aluminum alloy. Computer Methods in Material Science, 7 (1), 1–11. 106 Bowden, F.P., and Tabor, D. (1964) The Friction and Lubrication in Solids, Part II, Clarendon Press, Oxford. 107 Kopalinsky, E.M. and Oxley, P.L.B. (1995) Explaining the mechanics of metallic sliding friction and wear in terms of slipline ﬁeld models of asperity deformation. Wear, 190, 145–154.

108 Smith, A.M., Barlow, E., Amor, M.P., and Davies, N.C. (1978) The mechanism of roll-coating buildup during hot rolling of aluminum. Tribology Transactions, 21 (3), 226–230. 109 Krzyzanowski, M., and Rainforth, W.M. (2009) Application of combined discrete/ﬁnite element multiscale method for modelling of Mg redistribution during hot rolling of aluminium. Computer Methods in Materials Science, 9 (2), 271–276.

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From an industrial perspective, high-temperature tribology during rolling is a means of ensuring effective engagement, stable roll bite process conditions, and control, as well as good surface ﬁnish of the deforming and ﬁnished product. The increasing demand for better surface quality products not only requires optimum rolling but also high-pressure water (HPW) descaling capable of controlled operation under a wide range of mill pacing, product sizes, and steel grade compositions. Since oxidation rates are most rapid at high temperature, previous studies have focused on the highest temperature part of the process, especially furnace operation, which is one of the most important topics for the steel industry since it inﬂuences scale, scale losses, decarburization, and energy/emission. Furnace control has been improved by new models, sequential on/off heating techniques, and the development of supervisory and optimization systems. Changing the furnace conditions affects the scale adherence as seen, for instance, when direct hot charging is applied and descalability is markedly changed [1]. Improvement of product quality, focused on surface quality, temperature uniformity, and minimization of scale generation, has been studied in previous work [2–11]. However, scale formation and the inﬂuence of its behavior during hot rolling remains a major issue, especially for highly alloyed steels where adherent subsurface interfacial scale can be formed, representing a major source of surface defects during rolling. This aspect is being addressed incrementally by a growing number of studies focusing on the deformability of oxide scale (for C–Mn and low-alloy steels) prior to and within the roll bite, with the aim to derive a better understanding of interfacial friction as a tribosystem of the work roll, feedstock, and oxidized layers [12–15]. The challenge, however, remains for steels with elements that are easier to oxidize than Fe, that is, containing high levels of Mn, Cr, and Si, which will react with iron oxide to form solid solutions (Mn) or mixed oxides (fayalite Fe2SiO4) at the metal–oxide interface [16]. The formation of a fayalite liquid phase in the furnace increases the adherence of the scale to the substrate and will require greater impact pressure (IP) and surface water impingement (SWI) with minimum Oxide Scale Behaviour in High Temperature Metal Processing. Michal Krzyzanowski, John H. Beynon, and Didier C.J. Farrugia Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-32518-4

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cooling and heat losses during descaling to minimize surface defect and frictional issues during subsequent hot rolling. Some aspects of industrial HPW descaling will be described in Section 9.3.2 in order to highlight the importance of HPW descaling, or indeed alternative techniques, to condition the oxide scale prior to the roll bite and the challenges that remain in mapping the postdescaling surface state to roll bite friction models. Rolling is a metal-forming process where friction is positively required for ensuring effective feedstock engagement and process stability. A careful balance needs to be achieved to minimize pick-up, seizing, pass overﬁlling and, in the case of ﬂat products (plate, strip, and sheet), dimensional, sweep, and ﬂatness control issues. During ﬂat product rolling of steels, with the exception of newly developed direct sheet plant (DSP) [17], the deformation and shape change process begins with hot rolling (T > 1200 °C) of various cast slab thicknesses (50–210 mm) depending on mill and caster conﬁguration. Asymmetric conditions during roughing can lead to excessive turn-up or turn-down (ski-end effect) depending on roll velocity mismatch, surface temperature differential, roll gap reduction, pass line height, and differential frictional conditions, which can in turn result in downstream engagement issues, such as a cobble. Therefore, optimization of friction (via roll surface ﬁnish, oxide scale, lubrication) can lead to better control of curvature, particularly for thicker gauges. The rolling of bimetallics or brazing sheets will, on the other hand, require asymmetrical rolling conditions but again, in this case, friction will need to be optimized to avoid excessive ski-end and potential decohesion or delamination of the bimaterial layers [18]. The transfer bar between roughing and ﬁnishing is generally rolled in a four-high tandem continuous mill where the ﬁnal microstructure and properties are determined, and the likely issues of roll gap, ﬂatness, and shape control require optimum and stable conditions for today’s range of advanced steel grades. This regime relies on accurate predictions of the roll-separating force (RSF), roll torque, strip speed, and forward slip, which are based on accurate prediction or derivation of the roll gap friction and the input factors inﬂuencing the tribological conditions [19]. Long products (i.e., all nonﬂat products) are today rolled in continuous or semicontinuous mill trains usually made up of a breakdown or roughing/cogging mill followed by intermediate and/or ﬁnishing mills tailored to the size and shape of the ﬁnished rolled product. Contrary to strip rolling (with the exception of deformation during roughing and edge deformation during ﬁnishing), long product rolling is a purely 3D process relying on accurate spread and elongation predictions, which are particularly difﬁcult for open pass regimes. The deformation process varies widely from localized cross-sectional deformation during heavy kniﬁng of beam blanks to horizontal/vertical (H/V) no-twist mill conﬁgurations for rod and bar rolling. Mills are typically two-high (duo), four-high quarto (plate mill), four-roll ﬂat/grooved universal, and three-roll Kocks block conﬁguration, operating with or without the application of tension (see Figure 9.1). Slip and neutral zones are complex and vary across the feedstock contact perimeter depending on drafting, pitch and pass line height, roll/product contact area, lubrication

9.1 Background

(a)

(b)

(c)

Figure 9.1 Typical long product rolling passes and mill conﬁgurations: (a) bar rolling; (b) universal mill roll for structural sections; (c) three-roll precision sizing block (PSB) (Kocks® type).

conditions (lubricant, oxide scale, etc.), and process stability. Typical long and ﬂat product installations and layouts are shown in Figure 9.2. Deformation is heterogeneous in view of the low roll gap shape factor L/hm (L, mean projected length of arc of contact (in mm), hm, mean thickness in mm) and the combined interaction of friction and redundant deformation (see Section 9.2). This, in the case of plate rolling, can lead to turn-up/turn-down if all the parameters described above during slab roughing are not controlled. Both direct and indirect drafting coexist, creating regimes of high-pressure low-slip with lowpressure high-slip. Strain path effects are also complex with in-plane reversal as well as 90° inversion, but their effects are only relevant for thermomechanically controlled rolling (TMCR), low-temperature rolling, and high-speed rolling [20]. Thus friction will vary in both longitudinal and transverse directions, and its inﬂuence depends heavily not only on the cross-sectional roll gap shape factor but also, to some extent, on the engagement conditions due to the front-end proﬁle and operator manipulation, as well as mill acceleration regime. Therefore, for both industrial ﬂat and long product rolling, a detailed knowledge of the inﬂuence of friction is required to ensure dimensional and ﬂatness control as well as process stability with respect to the engagement and roll degradation. The very nature of the rolling process, its stability and robustness as a function of process and product conditions (see Table 9.1), makes direct examination of the roll bite contact and deformation conditions difﬁcult, particularly when considering today’s high-speed rolling (in excess of 100 m/s), fully enclosed and compact blocks, varying rolling contact length, roll cooling, surface chilling, and lubrication (see Table 9.1, Section 9.2). Therefore for a steel producer, two main avenues can be pursued for understanding and quantifying the evolution and role of friction in the roll gap. One is through the measurement and acquisition of common but often indirect plant information such as motor currents, RSF, roll torque, temperature, work roll, and feedstock speed. These quantities are dependent primary on the roll gap conditions such as geometry, product/roll material constitutive behavior, mill stand elasticity and, of course, interfacial conditions, without the need for direct measurements. These quantities are also dependent on prior

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(a) Measuring devices

Reheat Furnaces

Descaler

Service Center

Furnace Charging Equipment Slab Discharger Edger & Rougher Mills

Transfer Bar from Rougher

Reversing Mill Finishing Mill

Crop Sherar

Measure Room

Descaling Box

Run-out Table Cooling

Downcoilers and Coil Handling

(b) Figure 9.2 (a) Typical Long product rolling mill installation (rail Medium Section Mill – Corus Scunthorpe); (b) typical hot strip mill layout.

surface and bulk state of the product (temperature, oxide scale thickness/composition, etc.) emphasizing the need for through-process understanding and if possible characterization. Today’s modern mills are fully instrumented, providing a range of signals and data from standard SCADA/SQL (supervisory control and data acquisition/structured query language) database and PLC (programmable logic controller) systems [21]. Gauge and ﬂatness measurements are commonly used in on-line process control feedback loops. New instrumentation, sensors, and surface quality optical detection equipment are also being installed in strip mill

9.1 Background

ﬁnishing stands to accurately measure new on-line properties such as slip via a laser velocimeter, roll surface degradation (e.g., with Centre de Recherche Metallurgique (CRM) rollscope optical technology [22]), product surface quality (PARSYTEC [23], JLI [24], etc.), shape (e.g., TopPlanReﬂect [25]) and solid-state phase transformation. In the near future, scale thickness and cracking detection (on-line Laser Induced Breakup System (LIBS) [8.26]), as well as more reliable roll gap heat transfer coefﬁcient (HTC) measurements will be available. In reality, a plethora of signals and data are available to the mill personnel and engineers and one of the greatest challenges and activity of steel producers is to more intelligently derive and apply the hidden knowledge that is available to output key mill performance indicators (KPIs) and encapsulate the product-rolling mill signature. On one hand, this has opened the way for better tuning of off-line setup models (gap settings, etc.) and developing improved on-line control systems. It has also led to improved feedback and validation of physical models, which can then be integrated into hybrid or grey box models where both data and models coexist [27] for enhanced property predictions, such as those for instance developed by the IMMPETUS group [28]. The ever increasing use of advanced statistical data analysis and artiﬁcial intelligence models (ANN – artiﬁcial neural networks [29–32], SOM – self-organizing maps [33], etc.) can today map the most signiﬁcant parameters and their interactions leading to enhanced steady-state operation and control as well as process–product correlation (e.g., shape defects). This approach is ideal for deriving a friction coefﬁcient, where the available online data (RSF, etc.) can be combined with simple linear friction models such as those of Coulomb [34–36] or Tresca [37] giving the possibility to back-derive a global coefﬁcient of friction (COF) through time as a way to verify process stability, occurrence of roll wear, etc. Most conventional roll gap models rely on imposing prescribed boundary conditions (friction, HTC) to estimate the measurable indirect quantities such as roll force and torque. By “inversing” the roll gap model from measured data, primary roll gap conditions such as friction can be estimated. This approach, well described in the paper of Martin [19], may be sufﬁcient to quantify the frictional effect and may not require a more in-depth understanding, assuming that the steel manufacturer product portfolio is small and well understood, and plant issues are minimized. Statistical process control (SPC) combined with recent on-line roll and product surface detection and characterization (see for instance [22]) could be used to provide at a base industrial level the required process stability or steady state. This approach could be classiﬁed as Level I friction in view of the direct analogy to Level I control systems. However, industrial reality and pace of change and innovation in the competitive steel industry pave the way for a more in-depth analysis of the tribological conditions developed in the roll bite. This development is driven by the need for new steel grades (steels with higher alloying additions of Si-Mn-Cr) and products with ever increasing surface and geometrical tolerances. It is also driven by new technical innovations, for instance in roll cooling (high turbulence roll cooling (HTRC) [38], etc.), hot lubrication, and coating application systems [39], which require optimum scheduling, pacing, pass designs, and understanding of the complex

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interactions created before, during, and after the roll bite. Optimization of roll dressing campaigns, maintenance schedules, mill caliber, and the effect of planned or unplanned mill event (delays, cobbles, etc.) are also requiring a more detailed understanding of roll bite conditions. Finally, climate change directives and the need to minimize or rebalance overall energy consumption in mills, as well as looking at new ways of rolling more sustainable products, will in the near future be the major factors for mastering the roll bite conditions and frictional energy [40]. This, therefore, requires an understanding of the through-process and product sensitivities through time and space, the detailed inﬂuence of temperature, oxide scale and roll behavior, as well as the detailed deformability of the stock. This knowledge could lead, depending on the approach, to a local optimization of a speciﬁc rolling pass where, for instance, partial lubrication is required or where optimization of the roll cooling and/or chilling properties of the product’s skin is needed to enhance oxide scale thickness and behavior for improved ﬁnal properties. The Level I friction approach described previously must be reﬁned or augmented in this case by using laboratory mechanical testing (e.g., ring uniaxial compression testing) and pilot rolling mills, where controlled experiments could lead to the development of regime maps or calibration curves of friction as a function of input conditions, such as temperature, strain rate, and internal and surface states of the product. The end-value (depending on the pilot line speciﬁcation) may not directly come from the mapping of the entire domain of processing conditions but depend on the direct control of key input properties and access to more physical knowledge. When combined with detailed off-line surface characterization techniques such as scanning electron microscopy (SEM), glow discharge optical emission spectroscopy (GDOES), and microindentation, this approach will provide a means of enhancing and controlling industrial practices by predicting the sensitivities to any change in input conditions and be used as a basis to enhance existing friction formulation. Physically understanding the complex synergies between friction, heat transfer coupled with surface, subsurface, and bulk steel behavior during multipass hot rolling of both ﬂat and long products will lead to better control and optimization of the processing conditions and is a precursor to the establishment of process maps of improved surface ﬁnish, where friction and wear mechanisms could be optimized as a function of grade rolled and setups. This approach is similar to the one provided by a typical Level II control system and should run in parallel with the application and development of friction models. Today’s friction models range from linear to more sophisticated multiscale models within the mathematical framework of the rolling process, obtained via classical rolling theory or more recent ﬁnite element modeling (FEM). Models based on ﬁrst principles and potentially at an ab initio level would provide the basis for predicting and isolating friction as a ﬁrst order parameter, that is, a parameter or function derived purely from the physical and chemical state in the roll bite. However, in practice, most of the friction models applied in industry rely on the classical friction formulations of Coulomb–Amonton (CA), Tresca, and NortonHoff [41, 42], which operate within the range of macro- to mesoscopic scale (i.e.,

9.1 Background

used in a discrete manner as described later) where the interfacial friction stress is related to the shear stress, normal pressure, or slip speed via linear relationships. More physical friction models have been developed over the years, such as those by Wilson et al. [43–47], Sutcliffe [48–50], and Marceau [51, 52], although these have targeted cold rolling of thin strip for studying the surface ﬁnish (pit evolution) and lubrication, cooling, and chatter conditions. These models rely on both the adhesion and asperity contact theory, where the geometry of the workpiece and roll is required to calculate the fractional contact area. As mentioned, this approach is being applied to cold rolling with full coupling of the elasto-plasto hydrodynamic conditions (including at microlevel, i.e., pit geometry, see [47]) and to some extent at high temperature (with the application of the Wilson model [19]). These models have also been used to back-derive friction coefﬁcient based on plant data. Recent developments by Fletcher [12, 13], Talamentes-Silva [53, 54], and Farrugia and Onisa [55–57] have also further reﬁned the classical friction theories by developing variable roll bite friction models, combining information obtained from microscopic models of the contact deformation in the roll bite and information at the same length scale from oxide scale fragments, fresh parent steel extrusion conditions, etc. The coupling from macro- to microlevel has been developed recently by Krzyzanowski [58–60] (see also other chapters) and Picque et al. [15] by mapping the boundary conditions experienced at the macro–mesoscale within the roll bite (displacement, HTC, etc.) using ﬁnite element (FE) models or submodels. However, there exist few approaches which fully demonstrate, in a true multiscale sense, how the knowledge obtained at this scale could be used as part of a bottomup approach in the steel industry. The approach by Li and Sellars [61] is to be commended as perhaps one of the ﬁrst approaches to demonstrate how microinformation of oxide scale and HTC behavior can be utilized to derive an enhanced friction formulation. The industrial interest in friction modeling is twofold: ﬁrst, to derive better friction sensitivities and regime maps as a function of process and product conditions; and second, to enhance existing roll gap setup or control models. The former should be achieved through the development and application of a relatively simple friction formulation, which can be easily integrated into off-line analytical or FE codes for better predicting process constraints (roll force, torque, etc.) as a function of steel grades and processing conditions. Therefore, the need for a bottom-up length scale approach, coupled with laboratory trials and characterization as described earlier, is important and should lead to an enhanced friction formulation where the friction coefﬁcient is not ﬁxed but derived from the properties and tribological conditions in the roll bite. The integration of these regime maps into existing roll gap setup models will then provide a means of reﬁning forward predictions and reduce the dependency on feedback control. Although microscale models still rely on a deﬁnition of the contact interface, which is itself based on macroscopic friction models (except Jupp [62, 63]), the inﬂuence of roll roughness, oxide scale fracture, delamination, and deformation at the asperity contact, together with the effect of steel extrusion through the oxide scale fragments, provide a means to compute the real contact area together with

277

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9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input

the mechanisms or rules for changing the local conditions based on the thermophysical properties of the scale, steel substrate, etc. This gives the potential, depending on how tight the coupling from micro to meso is, to develop evolution equations to account for the microscale information such as the effect of roll roughness or oxide scale behavior, which represent an attempt to integrate a more multiscale approach to the problem of friction. This chapter will focus on a phenomenological approach to enhance or combine existing friction models with the knowledge of the tribology at the microscale for both long and ﬂat products. In practice, the experimental and mathematical/physical avenues brieﬂy described above are complementary and required in order to validate, calibrate, and develop new friction algorithms. Models and data are needed to perform inverse analysis for the identiﬁcation of a friction coefﬁcient [64] or to control the roll gap by implementing a friction model in on-line roll gap Level II control models [21]. Experimental data cannot be dissociated from the theoretical development of the understanding of friction and, although work presented in this book addresses how new knowledge relating friction, heat transfer, and oxide scale behavior is required across the physical length scale, it is still difﬁcult to reliably represent frictional conditions; much more work is required across the physical length scale to develop a more representative theory of contact [65]. Therefore, from an industrial point of view, a combined experimental and mathematical approach to friction is required and this forms the basis of this chapter.

9.2 Brief Summary of the Main Friction Laws Used in Industry

During rolling, the product is engaged in the roll bite by the rotation of the rolls and momentum of the metal propelled by the entry roller table and manipulator. Hence, the reduction Δh in product thickness is imposed only if the shear frictional stress is greater than a minimum value. The product front end is submitted to normal (σn) and tangential (τ) stresses. Considering a rectangular coordinate system (x,y,z), where z is the direction of rolling, the bite angle α along the transverse direction x is deﬁned as follows:

α (x ) =

Δh ( x ) Reff ( x )

(9.1)

where Reff(x) is the minimum roll radius at contact with stock. The product engagement can only be achieved if, along the transverse direction x, the frictional shear stress τ(x) is greater than or equal to the horizontal component of the normal stress. From Figure 9.3 (with respect to the stress component), it transpires that s nx ( x ) = s n ( x ) sin a ( x )

(9.2)

t x ( x ) = t ( x ) cos a ( x )

(9.3)

9.2 Brief Summary of the Main Friction Laws Used in Industry

Direction of roll rotation A

α

θ Direction of frictional forces

τ(X) σn(X)

N

B

Neutral plane Figure 9.3 Roll bite geometry and stresses acting along the arc of contact without consideration of front and back tension (ﬂat rolling) (see W.L. Roberts [66]), where σn(x) and τ(x) are the normal and shear stress, N indicates the location of the neutral point, α is the roll bite angle and θ the same for N, and A and B indicate the start and end of contact with the roll, respectively.

Using a simple Coulomb relationship (τ(x) = μ. σn(x)) as detailed below, engagement will be guaranteed if tan α(x) is less than μ. For small angle approximation, this translates to μ >α(x). As expected, as reduction or drafting increases or roll diameter decreases, the value of engagement friction increases. This simple analysis will be reviewed in the next section to account for variable cross-width conditions. The determination of the friction law is based on the establishment of the frictional shear stress as a function of the key parameters accounting for the rheology of the contact (elastic and plastic conditions), surface properties, roll and product roughness, process parameters (slip, temperature, etc.), and interfacial conditions (roll composition, oxide scale, lubrication, etc.). Both isotropic and anisotropic friction laws have been developed and most deal with macroscopic behavior, except those based on Tabor [67] or Wilson’s formulation [44, 47]. The isotropy of the friction law means that the frictional shear stress vector is colinear with the slip velocity vector but takes an opposite sign. The most utilized friction formulation from the point of view of industrial use will be brieﬂy reviewed here, laying the foundation for more advanced models as described in Section 9.4. A good description of friction is given in Jupp’s Ph.D. thesis [63] and in [68]. Macroscopic laws of friction

•

The CA law relates the frictional shear stress to the normal stress along the direction rolling (z) as follows:

τ ( z ) = − μσ n ( z )

Δv ( z ) Δv ( z )

If Δv ( z ) = 0 ( no slip ) then t ( z ) < m s n ( z )

(9.4) (9.5)

A linear relationship, therefore, exists between the normal pressure or force and the interfacial shear stress whose slope is deﬁned by COF μ. The frictional force

279

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9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input

is independent of the size of the apparent contact area. Therefore, the frictional shear stress must increase as normal pressure increases, which is valid in the case of (dynamic) sliding friction. The plasticity criterion (from Orowan, [36]) limits the tangential shear stress (maximum shear stress) with t ( z ) = t max =

s0 3

( von Mises criterion )

(9.6)

t ( z ) = t max =

s0 2

( Tresca criterion )

(9.7)

or

Therefore, CA law can be rewritten as follows:

τ ( z ) < Min ( μσ n ( z ), τ max )) when Δv ( z ) = 0 (static friction ) τ ( z ) < Min ( μσ n ( z ) , τ max ))

Δv ( z ) when slip occurs Δv ( z )

(9.8) (9.9)

When τ(z) reaches τmax, less energy is required for the material to shear internally (soft material) rather than to slide against the roll. This is referred as sticking friction although no actual sticking to the roll has to occur. This condition is met when τ(z) > τmax. The maximum theoretical friction coefﬁcient can be estimated when full surface conformity is reached at yielding, that is, σn = σ0. As σ0 is related to τmax by Equation (9.6), it transpires that μmax = 0.577. In reality, full surface conformance is reached at a pressure multiple of σ0 (two to four times). Therefore, the calculated friction μ drops. In all cases, the shear yield stress τmax remains constant, which puts into question the term COF when no relative sliding occurs at the interface. In this relationship, μ is taken to be constant along the roll bite. We will see in the latest development of friction models how this assumption can be modiﬁed with the knowledge of the microscopic effects of oxide scale and tribological conditions within the roll bite.

•

The Tresca or interfacial shear stress model where

τ ( z ) = −mτ max

Δv ( z ) Δv ( z )

(9.10)

where m is the interface shear (or friction) factor and varies from 0 to 1. When m = 1, sticking friction is imposed and shear occurs at the interface of the softer product with a shear stress of τmax. The Tresca formulation treats the contact as independent of normal pressure and instead relates the interfacial friction stress directly to the yield strength in shear of the softer material. The assumption of constant interfacial friction precludes the coexistence of slipping and sticking conditions, unlike the CA law above.

9.2 Brief Summary of the Main Friction Laws Used in Industry

•

Norton’s law

This law is derived from the rheological Norton–Hoff law (viscoplastic behavior) [41] and is dependent on slip velocity as follows:

τ ( z ) = −β Δv ( z )

p

Δv ( z ) Δv ( z )

(9.11)

with τ(z) < τmax for a rigid plastic body, p is a constant between 0 and 1, β is here COF, and, contrary to the two previous laws, it is dimensional (in SI units: Pa (s/m)p). From this relation, when p reduces to zero, this law is equivalent to the Tresca law. For p = 1, there is a linear relationship between τ and the slip velocity. Combining Norton and Coulomb approaches has been considered in the past (Ayache [69], Farrugia [55]) and is further described in Section 9.4. This approach is interesting as it can take account of the presence and role of an oxide or lubricant layer via a Norton approach combined with the inﬂuence of normal pressure via the CA law. A typical value of the coulomb coefﬁcient for hot steel during rolling is 0.3. Microscopic law of friction and adhesion The conventional adhesion theory, due to Bowden and Tabor [67], was the ﬁrst modern explanation of the existence of friction. At the contact area of an asperity junction, the combined effect of normal pressure and shear stress is considered to act on a simple element in plane strain conditions. Bowden and Tabor assumed that in order for the bodies to slide relative to each other: a)

The asperities are plastically deformed; that is, the mean pressure corresponds to about three times the yield pressure, σ0, of the material, that is, pm,crit ≈ 2.8σ0, and

b) The interfacial stress component corresponds to the shear strength of the soft material τmax. In general, these laws consider the interaction between the roll (tool) and the workpiece by considering the real apparent contact area from the point of view of asperity contact and junction growth theory. Plastic deformation of the softer body (workpiece) is then assumed using various hypotheses regarding the roughnesses of tool and workpiece. Consequently, the friction coefﬁcient can be expressed as the ratio between the shear strength of the softer material and about three times the yield pressure;

μk =

F σ crit Ar σ crit σ crit = = ≈ P pm ,crit Ar pm ,crit 2.8σ 0

(9.12)

thereby providing via the inelastic adhesive theory a constant kinetic friction of about 1/(3.(3)0.5) ≈ 0.19. Further advancements on the Tabor and Bowden theory have over the years accounted for asperity interaction and dynamic changes to the real area of contact.

281

282

9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input

A typical index of plasticity for the microcontact can be estimated by the following relationship: Φ = 0.5

E * Rz ⋅ H v rca

(9.13)

with Rz being the peak or asperity height (microns), rca the radius of curvature of the asperity, and E* the combined Young’s modulus of both roll and feedstock. For plasticity to occur at the microcontact or asperities, the index of plasticity Φ should be greater than 1. At the contact area of an asperity junction, the combined effect of normal pressure and shear stress can be considered assuming plane strain and a material obeying a von-Mises yield criterion: s n2 + 3t 2 = 3t max = 3k 2

(9.14)

where σn is normal pressure, k is shear strength of workpiece, and τ is the friction stress which can be described as

τ = ma k

(9.15)

with ma representing the interface shear factor of the real area of contact. The COF μ according to junction growth can be expressed as follows:

μ (z ) =

Ff (z ) t ( z )⋅ Ar ma ⎛ τ max ⎞ = = ma ⎜ = ⎟ 0.5 ⎠ ⎝ N ( z ) σ n ( z )⋅ Ar σ n (z ) (a (1 − ma2 ))

(9.16)

with a = (H/τmax)2 and H is the hardness of asperities. The average value of a is about 20 for mild steel. For clean surfaces, the real junction area is at its maximum, so ma = 1 which raises μ to inﬁnity [68]. To avoid the Tabor assumption at full contact, Johnson [70] has proposed a modiﬁed version where both junction growth and internal shear in the junction are acting:

μ (z ) =

ma

(a1 − a2ma2 )

0.5

(9.17)

where a1 and a2 are constants, which could result in a friction coefﬁcient greater than unity. These approaches have opened the ﬁeld of mathematical treatments of interfacial friction at a microscopic level under dry or lubricated conditions. Idealized roll and feedstock asperities (triangular) are typically assumed. Since Bowden and Tabor, a number of authors were inspired to develop more advanced analyses concerning the plastic deformation of asperities at low to moderate normal pressures. Models from Wanheim and Bay [71, 72] for cases of relatively high contact pressure (P/σ0 > 1.5) with interaction of asperities is worth highlighting. The model of Tabor is further reﬁned to take account of the ratio of real contact area (Ar) over the apparent contact area (Aa). The coefﬁcient of friction μ becomes

μ (z ) =

maατ max σ n (z )

with α = Ar/Aa

(9.18)

9.2 Brief Summary of the Main Friction Laws Used in Industry

These models work well up to moderate contact pressure (1.5σ0). It shows that up to σn/2k or P/2k < 1.3, the real contact area ratio increases as normal pressure increases, thereby also increasing the interfacial frictional stress, and making μ fairly constant throughout (Figure 9.4). At higher pressure, extensive interaction of deformed asperities, and plastic constraints need to be taken into account and μ then becomes dependent on normal pressure. Depending on models, a typical relationship between micro- and macrofriction can be derived (Figure 9.5).

A 1 0.8 0.6 0.4 0.2

0

1

2

3

4

P/2k

Figure 9.4 Evolution of real contact area as a function of contact pressure (P/2k) (according to Wanheim & Bay [72]).

3

1.5

2.5

1.5

P/2k

2

1

p m

a

1

0.5 θ

0.5 0

0 0

0.2

0.4

0.6

0.8

1

m relation micro to macro friction - moderate asperity slope relation micro to macro friction - elevated asperity slope Pressure (P/2k) - moderate asperity slope Pressure (P/2k) - elevated asperity slope – ) and macrofriction (μ) coefﬁcient for two types Figure 9.5 Typical relation between micro (m of asperity slopes θ (moderate and elevated [up to 90 °]) and associated evolution of contact pressures P/2k [73].

283

284

9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input

More complex macroscopic–microscopic interaction of both asperities and bulk metal have been developed based on Greenwood and Rowe [73, 74], Wilson and Sheu [47], and Sutcliffe and Marceau [50, 52] models. These models have targeted plane strain compression/indentation and have been applied to the cold rolling of stainless steel and aluminum [49]. A good description is given by Leu [68]. The later models couple the deformation of roughness (ﬂattening of asperities) with bulk metal deformation using a ﬂattening rate approach accounting for the contact ratio and pressure difference between asperity top and bottom (pit). Dry and lubricated conditions involving micro-plasto-hydrodynamic (MPHL) conditions have also been coupled [50]. Under such conditions, an evolution equation for the real apparent contact area has to be formulated and integrated. The model of Wilson et al. [47], for instance, combines the adhesion between the workpiece and tool surfaces as well as the asperity interactions using a similar formulation to the one of Tresca and Tabor, as follows:

τ ( z ) = (ma + mi )τ max ≡ (cα + Pθ t )τ max

(9.19)

where ma is the friction factor due to contact adhesion, mi is the friction factor due to asperity interaction, θt is the tooling asperity angle as shown in Figure 9.6 and deﬁned as arctan(8Ra/λ), where Ra is the center-line average (CLA) roughness, and λ is the peak-to-peak wavelength. The real apparent contact area in these types of models needs to be computed by means of an evolution equation, which is a function of feedstock strain, normalized pressure, etc. [19]: dα σ n ⋅ f 1 (α ) = dε 2α − σ n ⋅ f 2 (α )

(9.20)

Finally, the adhesion model from Jupp [63] is an interesting further development of the simpliﬁed approach from Straffelini [75] and Rabinowicz [76] that links friction with material properties, including oxide scale, based on adhesion and growth of real contact area. The average shear strength of asperity junctions and friction are expressed via simple analytical equations based on the thermodynamic work of adhesion and irreversible local phenomena. From the Lenard–Jones interaction potential and contact mechanics, the adhesion force for fcc metals can be calculated based on an average equilibrium roughness angle (asperity slope) of 0.9 ° [63]:. 2 ℓt tooling

workpiece Figure 9.6

θt Po

2Aℓt

Microscopic friction asperity model [19].

9.2 Brief Summary of the Main Friction Laws Used in Industry

μ

(1 + 12μ 2 )

0.5

= 0.127Wab

285

(9.21)

where Wab (Jm−2) is the thermodynamic work based on the surface energy of materials a and b and interface energy for ab. Application of this theory according to Jupp (see Figure 9.7) shows that the friction coefﬁcient would continuously vary from 0.25 (entry) to 0.35 (exit) when roll gap conductance thermal effects are considered, which will affect surface energies of steel and oxide scale (0.94 J m−2 surface energy for wüstite vs 1.5 J m−2 for magnetite). In summary, the use of a speciﬁc friction law depends on the rheology of the contacting bodies but also on the way these laws can be integrated or used in roll gap models. Where elastic contact prevails, CA law should be used. Where plastic 0.6

1.6 1.4

Friction coefficient

1+12·m2

= 0.127·Wab

1.2 Cu/Cu

1.0 0.8 Cu-8Sn/Cu-8Sn

0.6

Al/Al

0.4 Al/Cu

(a)

0.2 0.0 –0.2 –0.4

0.2 0.0 0.6

μ = 0.5 μ = 0.3 μ = f(Wab)

0.4

Traction coefficient

m

–0.6 0.8

1.0

1.2

1.4

1.6

2.0

2.2

Thermodynamic work of adhesion (J

m–2)

2.0

1.8

Period II III

1.8

0

2.4

5

10

(b)

IV

V

VI

Ni

Surface Energy (J m–2)

1.6 Fe

15

20

Path (mm)

Pt

Co

1.4 1.2

Au

Cu 1.0

Be Al

Si

Ag

0.8

Zn

0.6

Cd

Mg

Pb

0.4

Sb

Ge

Bi

0.2 0.0 0

10

20

30

40

50

Atomic Number

60

70

80

90

(c)

Figure 9.7 (a) Simpliﬁed adhesion theory according to Equation (9.21) compared with experimental data for face-centered cubic alloys; (b) friction shear stress during rolling compared with two simulations based on ﬁxed Coulomb coefﬁcient of friction; (c) variation of surface energy with atomic number (dashed lines generated by analytical equation Y = 10−0.111 47(Atomic Number)+C according to [76]) [63].

25

30

35

286

9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input

deformation occurs with little sensitivity to velocity, the Tresca law should be adopted. However, comparing the shear yield stress (0.577 times the von Mises equivalent stress) to the shear stress at the steel surface while assuming a COF of 0.5 shows that the Coulomb friction model is always valid in the roll bite [63]. Also, from adhesion theory and application of sticking friction (m = 1), the smoothest surface (roughness angle or asperity slope) before the adhesion takes place can be deﬁned by the following equation: tan θ =

2⋅ 3 β × Gc C1

(9.22)

with β = 0.5, GC effective work of adhesion (J m−2). Where strong interaction with slip rate exists, Norton’s law should be implemented. The next section will show that new approaches have looked at combining normal force and slip rate, that is, adopting a Coulomb–Norton approach, to account for critical tribological effects affecting, for instance, the rolling of long products. The introduction of anisotropy has also been investigated and correlated with experimental trials of drilled billets. Back-deriving a COF will inevitably depend on the choice of the friction laws; this is further detailed in Section 9.6. Implementation of the friction law into FEM models generally relies on the underlying FEM formulation (static implicit or explicit dynamics) and, therefore, will vary from code to code. This is brieﬂy covered in Section 9.4.6.

9.3 Industrial Conditions Including Descaling 9.3.1 Rolling 9.3.1.1 Inﬂuence of Roll Gap Shape Factor It is well known that the roll gap shape factor, expressed as the ratio between the projected length of arc of contact over the mean stock thickness (L/hm), is a key factor inﬂuencing the regime of frictional conditions and has often been used by steel producers to characterize rolling regimes during direct drafting. L is usually expressed as follows (for plane strain, ﬂat rolling):

(hentry − hexit ) ⎞ ⎛ L = ⎜ Reff (hentry − hexit ) − ⎟⎠ ⎝ 4 2

0.5

≈ (Reff (hentry − hexit ))0.5

(9.23)

with the mean thickness in our case deﬁned as hm =

(hentry + hexit ) 2

(9.24)

From the classical theory of indentation of Hill [77] supplemented by a frictional component obtained by slab analysis [78], thick and thin stock regimes can be

9.3 Industrial Conditions Including Descaling

1+π/2

2.0 μ = 0.5 (P + Pf) / 2k

μ=0

1.0

0

0

Figure 9.8

1

2

3

1

0.5

0.3

4

0.25

5

0.2

6

0.17

7

8

0.14

0.1

9

0.11

10

hm/L

0.1 L /hm

Rolling regimes based on roll gap shape factor [78].

analyzed to show that the greatest sensitivity of friction to loading (P/2k) occurs as L/hm increases above 1 (Figure 9.8). Thus an initial distinction between long and ﬂat products is required in order to assess the inﬂuence of frictional conditions and surface state. Three subregimes can be observed as follows (see dashed lines in Figure 9.8):

• • •

one where L/hm > 1 (case of strip products) where friction is the main contributor to roll pressure; an intermediate regime where L/hm is greater than 0.5 and less than 1; where L/hm < 0.5, where pressure is much less sensitive to friction.

The case where L/hm > 1 shows a very steep increase in normalized mean pressure ((P + Pf)/2k) – equivalent to rolling load – and is a regime where friction and lubrication need to be optimized so as to minimize excessive contact between asperities and, as a consequence, frictional heating. This is typical of entry ﬁnishing pass strip rolling where reduction is high and both engagement and steady-state rolling rely on optimum roll bite conditions. Oxide scale composition, thickness, and behavior before, during, and at the exit of the roll bite will play a key role in determining the tribological conditions. This is a regime of open pass direct drafting under quasiplane strain conditions, where the main frictional component is unidirectional and undergoes reversal at the neutral point or zone. Both center and edge proﬁles will inﬂuence the discrete deformability of the strip and, therefore, the localized frictional and contact conditions, which in turn inﬂuence the

287

9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input 3 1+π/2 2.5 2 P/2k

288

1.5 1 0.5 0 0.00

0.20

0.40

0.60

0.80

1.00

1.20

L/hm Figure 9.9 P/2k evolution function of roll gap shape factor L/hm for L/hm less than 1 (typical case of long product rolling).

pressure distribution. Ingoing or induced asymmetry due to geometrical proﬁle or shape effects, coupled with variable temperature and surface state, may require compensation via roll bite actuators (automatic gage control, roll shifting and bending, etc.) to avoid ﬂatness and shape defects, thereby creating cross-width frictional conditions. The two regimes where L/hm is less than unity are typical of long product rolling where a mixed regime of sticking and slipping exists, together with direct and indirect drafting. The mean contact pressure increases as L/hm decreases, up to the Hill’s ratio of 1 + π/2 (Figure 9.9). This chapter will focus on these two regimes. From the analogy of Hill and Kim’s shear line ﬁeld indentation theory [79], the rolling load per unit width (RSF), without any frictional and curvature effect, can be obtained using the following equation (9.25): RSF = 2k

P L 2k

(9.25)

– where P /2k is the normalized mean deformation pressure accounting for redundant deformation. – It can be observed that P /2k varies as a function of the roll gap shape factor as shown in Figure 9.9, increasing as the roll gap shape factor decreases as a greater proportion of redundant shear deformation is created in the deforming feedstock. Deformation is gradually more concentrated toward the surface. This behavior has been expressed by the author by a ﬁtted fourth-order polynomial equation as follows: P = 9.3259x 4 − 25.692x 3 + 26.862x 2 − 13.242x + 3.7507 2k where x = L/hm.

(9.26)

9.3 Industrial Conditions Including Descaling

289

The effect of redundant deformation (Figure 9.10) is further highlighted in this series of 2D plane strain FE simulations of ﬂat rolling carried out by the author, where the L/hm ratio has been varied from 0.3 to 0.56. Assuming a ﬁxed Coulomb friction coefﬁcient of 0.3, shearing is further promoted to subsurface as L/hm reduces (Figures 9.10a and b). A redundant deformation factor (ϕ) [80] has been used as follows:

ϕ=

εm ε

(9.27)

where εm is the average effective strain in the cross-section of the material and the nominal strain imposed in the rolling process under plane strain conditions. It can be observed that the factor ϕ depends on the roll gap shape factor increasing as L/hm reduces. In fact a reduction from 0.56 to 0.3 in L/hm will increase the redundant deformation by about 30% (see Figure 9.10d). Slip line ﬁeld theory assumes that a rigid contact between the tool and feedstock exists and, therefore, no shear stress is required at the interface and that the solution is valid for any tool roughness/contacting conditions. Interfacial conditions

(b)

0.20 RDF

Strain

0.25

0.15 0.10 0.05

20.

40. 60. True distance along path

80.

100.

1.7

35

1.6

30

1.5

25

1.4

20

1.3

15

1.2

10

1.1

5

1 0

0.2

0.4

% NTDF

(a)

0 0.6

L/hm Redundant deformation ratio (RDF) Normalized % redundant deformation factor (%NRDF)

(c)

(d)

Figure 9.10 Inﬂuence of roll gap shape factor L/hm on shear deformation pattern (a) L/hm = 0.56, (b) L/hm = 0.3, (c) through-thickness effective strain L/hm = 0.56, 0.52, 0.3 (top line for smallest L/hm value showing the most redundant deformation), (d) calculated redundant deformation factor and percentage of normalized redundant factor according to [80].

290

9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input σy

sticking mixed, sticking-slipping slipping

2k

x 0

x1

l/2

Figure 9.11 Inﬂuence of different friction roll gap regimes on mean pressure according to indentation theory [78].

in rolling can, however, be taken into account by combining the deformation heterogeneity provided by the slip line ﬁeld analysis with the frictional component obtained from slab analysis of indentation. An expression of the mean pressure Pf due to frictional conditions can be developed based on slipping, sticking, or mixed regimes (Figure 9.11). The mixed regime consists of slip at entry and exit (or near edges in the case of indentation) and sticking within a proportion of the roll bite around the neutral point (or near the die center). Relations for Pf representing the inﬂuence of friction on the mean pressure are given in Equations (9.28) and (9.29) for the cases of slipping friction, where τ = μσy, and sticking, respectively. These equations represent the envelope of the friction hill shown in Figure 9.11. For a more complete description of the theory see [78]: L Pf 1 hm ⎛ μ hm ⎞ = − 1⎟ − 1 ⎜⎝ e ⎠ 2k μ L

Pf 1 L = 2k 4 hm

(9.28) (9.29)

The mixed regime condition can be calculated from the knowledge of the location of the transition from sticking to slipping xstsl. xstsl varies from 0 to L/2 and when xstsl = 0, slipping friction is created over the whole interface: x stsl =

L ⎡ hm ⎛ 1 ⎞ ⎤ ln ⎜ ⎟ 1− 2 ⎢⎣ μL ⎝ 2μ ⎠ ⎥⎦

(9.30)

Therefore, assuming a ﬁxed COF and using the above theory, slipping friction will prevail at the roll/stock interface for most cases where L/hm > 1, as shown in Figure 9.12. This ﬁgure plots the normalized distance up to half the length of contact (right-hand side of the friction hill) where sticking and slipping friction are acting.

9.3 Industrial Conditions Including Descaling

0.5 0.45 0.40 0.35 0.3 xstsl/L 0.25 0.2 0.15 0.1 0.05 0.0 1.0

0.1 0.2

0.7

0.5

0.4

L/hm

0.5 0.4 0.3 0.2 m 0.1

0.3 0.4 0.5

0.3

Figure 9.12 Fraction of contact that is sticking, xstsl/L, as a function of friction coefﬁcient μ and roll gap shape factor L/hm (μ = 0.5 shows sticking for all values of L/hm, μ = 0.3 shows slipping throughout, and a mixed regime occurs in between).

0.25

0.1 0.2

0.2

0.3

0.15 Pf/2k

0.4

0.1

0.5

0.05 0 1.0

0.7 L/hm

Figure 9.13

0.5

0.4

0.5 0.4 0.3 m 0.2 0.1 0.3

Response surface of Pf/2k as a function of friction and roll gap shape factor.

The mixed regime is only predicted to occur when the Coulomb friction coefﬁcient is greater than or equal to 0.4. The sticking zone normalized to the length of contact reduces sharply as L/hm reduces from 1 to 0.57 (hm/L of 1.75). Sticking friction will be acting over the whole interface when μ is equal to 0.5 irrespective of L/hm values. Therefore, for long product rolling, according to this theory, deformation will become more localized toward the surface as L/hm reduces. Sticking or mixed regimes will prevail as L/hm reduces, that is, as the entry feedstock becomes thicker. For low L/hm values, spread will be of the hour-glassing type, further increasing the contribution of friction in semi-enclosed passes. Figure 9.13 shows the computed inﬂuence of friction on the mean contact pressure. A maximum of 25% increase in pressure (equivalent to rolling load) due to

291

9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input

friction is predicted at L/hm = 1 assuming a friction coefﬁcient of 0.5. Contrary to ﬂat product rolling, this inﬂuence reduces quickly, as slipping conditions start to dominate as L/hm reduces. For the intermediate values of the roll gap shape factor L/hm (i.e., between 1 and 0.3), which represent the most likely regime for long product rolling, the mean contact pressure reduces sharply for L/hm > 0.7. This is interpreted as a reduction of the contribution of friction to the total pressure by at least 70% when the roll gap shape factor decreases from 1 to 0.3, which is typical of initial bloom rolling in open pass conditions. Therefore, the inﬂuence of friction on rolling load reduces as L/hm reduces. However, maintaining an adequate level of friction is still required for the engagement as well as optimizing the product surface quality, according to the prevailing slipping or mixed conditions. The preceding discussion assumes a ﬁxed roll gap shape factor L/hm which in practice is not representative of the cross-width deformation conditions imposed by the roll pocket and/or ingoing cross-sectional geometry in long product rolling. Such rolling is characterized by a variable cross-width roll gap shape factor, so the effect presented in Figure 9.13 will need to be integrated to account for the variable distribution of contact cross the section. This will create a nonuniform contact area with a complex neutral zone. Variability in cross-width drafting due to the shape of the ingoing stock and roll proﬁle will create variable engagement friction conditions. These can be computed analytically for simple bar-type passes, as shown in Figure 9.14. These engagement proﬁles are calculated by discretizing the effective radius and localized reduction along the transverse direction based on mathematical representations of round or oval pass geometries and ingoing stock proﬁles. Finite element simulations of typical rolling passes can provide details of the nonuniform nature of the contact area within the roll bite for both simple and complex long product sections. This is shown in Figure 9.15 as plots of variable

m engagement

292

0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0

RO R=90 mm RO R=200 mm SO R=90 mm SO R=200 mm

0

5

10

15

transverse position (mm) Figure 9.14 Engagement friction analytically calculated for simple bar pass geometry; RO = round oval, SO = square oval of similar reduction; ingoing round diameter = 25 mm, ingoing square side length = 23 mm, exit oval height = 18 mm [81].

9.3 Industrial Conditions Including Descaling

Fn (a)

Slip rate

(b)

Figure 9.15 (a) Contact forces and variable contact time in the contact area (square-oval pass); (b) variable normal force Fn and slip rate magnitude in square diamond pass roll bite contact area (outputs created using Abaqus commercial FE code).

pressure or normal force, contact shear stress, slip rate or velocity, and contact time. The contact time Δt can be expressed as follows: ⎛ draft ⎞ arcsin ⎜ ⎝ R ⎟⎠ Δt = ω

(9.31)

where R is the local roll radius and ω is the local rotational speed of the roll. Both the frictional shear stresses and the slip rates are computed as a ﬁeld output in the given local directions and can be used to assess the amount of forward and backward slip, as shown in Figures 9.15b and 9.16a–d. Figure 9.17 shows the sensitivity of reduction and roll gap shape factor as well as mill conﬁguration setup for a four-roll universal rolling pass. Typical initial web and ﬂange reduction (∼20%) was varied for assessing sensitivity on slip rate and shear stress, RSF, and contact pressure according to position (Figure 9.18). A map of slip velocity can also be computed to reveal the nonuniformity of the tribological conditions within the inner web/ﬂange roll bite of a structural section (Figure 9.19). Finally, the contact area for the same ingoing feedstock will vary as a function of the roll gap shape factor, that is, reduction, as shown in Figure 9.20. 9.3.1.2 Inﬂuence of Pass Geometry and Side Restraints The frictional forces acting in the lateral direction resist the spread of the deforming feedstock, as shown in Figure 9.21a [66]. Backward and forward slips are developed over the contact area. At point b of Figure 9.21a, all components of friction are equal to zero. A special case needs, however, to be drawn up for fully or partially enclosed passes where side wall friction will have a greater inﬂuence on the roll force and torque for a given roll gap shape factor, as shown in Figure 9.21b. Due to the presence of the side wall with different conditions of peripheral velocity and hence slip, point e of Figure 9.21a will not be aligned to b in the neutral

293

294

9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input

μ=0.1 α n=0˚

Backward slip

μ=0.3 α n=2˚

(a)

(b) μ=0.5 α n =7˚

(c)

αn

αn

T =1100 ˚C μ=0.3

(d) Figure 9.16 (a–c) Predicted contact shear stress in the longitudinal direction as a function of friction coefﬁcient, R = 300 mm, 33% reduction, (d) slip rate (longitudinal direction) for the inner ﬂange/web of a structural section (outputs created using Abaqus commercial FE code).

zone and different frictional forces will be developed compared with pure open pass ﬂat rolling. FEM is ideal for studying the increased lateral restraint and friction forces acting on the side faces of the rolled stock. It can be observed that as the pass width is reduced, greater contact restraint increases RSF and torque. The effect of side pocket restraint is further visualized in Figure 9.22 with respect to contact shear forces (Figures 9.22a and b) where the shear reversal in the contact area becomes more complex as side restraint is imposed. Figure 9.22c shows the results of a sensitivity analysis of decreasing width on key roll bite parameters where side restraints increase slip, among other mechanical parameters. 9.3.1.3 Inﬂuence of Friction and Tension on Neutral Zone During steady-state rolling, the frictional forces acting in the entry zone assist rolling, whereas those acting after the neutral zone hinder rolling by pulling back on the stock as it attempts to leave the roll bite. By considering the equilibrium of forces, the position of the neutral point or zone can be derived from a knowledge

9.3 Industrial Conditions Including Descaling Vertical load separaton force

5000

295

Contact pressure 2500

4600

4500 4000

2168

2000

3500 3000 (kN) 2500 2000

1500 1160 1470

(MPa)

664

760

1500 1000 590 500 0

1500

1000

990

500

990

Initial Pass T=900 ˚C No Off Side Roll Web : red=50%, hm/L=0.17

390

0.1 COF

391 383

Initial Pass T=900 ˚C No Off Side Roll Web : red=50%, hm/L=0.17

352 326

COF

Flange : red=33%, hm/L=0.2

0.3

Forward slip rate - on web

1400

352

563

0.1

0.3

4600

242

0

Flange : red=33%, hm/L=0.2

1600

405

424

Forward slip rate - on flange 1000

993

1200 800

1000 806

(mm/s) 800

395 267 115

600

755 600

755

(mm/s)

196 400

400

3

197

659

200 0 0

Initial Pass T=900 ˚C No Off Side Roll

0

0.1

0

450

0

200 0

0.1

Initial Pass T=900 ˚C No Off Side Roll Web : red=50%, hm/L=0.17

0

0 0

Web : red=50%, hm/L=0.17

COF

Flange : red=33%, hm/L=0.2

COF

381 326

163

Flange : red=33%, hm/L=0.2

0.3

0.3

Forward contact shear stress

Backward contact shear stress

350

400

319

300 319

300

250 200

(MPa) 200

99.6

(MPa) 40 24

127

83

39

32

50 82

0

83

Initial Pass

0.1

23

131

35 Initial Pass T=900 ˚C No Off Side Roll Web : red=50%, hm/L=0.17

85

0

No Off Side Roll

0.1

COF COF

Wedge : red=33%, hm/L=0.2

Wedge : red=33%, hm/L=0.2

0.3

0.3

Figure 9.17 Inﬂuence analysis of reduction, temperature, Coulomb friction coefﬁcient (0.1, 0.3) for a universal rolled structural section; initial conditions temperature = 1100 °C, for a typical ﬂange and web reduction of ∼20% (typical L/hm ∼2.0).

Figure 9.18

Web and ﬂange beam position.

84

39

100

38

100

100

150

9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input

Figure 9.19 Slip velocity map at inner ﬂange/web within roll bite of structural section using a ﬁxed Coulomb coefﬁcient of friction; 3 indicates the longitudinal rolling direction and 1 the vertical (outputs created using Abaqus commercial FE code).

16%, hm/L = 2.6 31%, hm/L = 1.35 46%, hm/L = 1.05

(×103) 10.00

8.00

mu = 0.3

Contact area (mm2)

296

6.00

4.00

2.00

0.00 0.00

0.50

1.00 Time

Figure 9.20 Contact area as a function of the inverse of the roll gap shape factor (expressed as hm/L) and reduction (16–46%) for box pass rolling.

9.3 Industrial Conditions Including Descaling

(a)

(b)

(c)

(d)

(e)

(f) 1200 T [kN.m]

RSF [kN]

1000 800 600 400

80 70 60 50 40 30 20 10 0 0

200 0

0.5

1

1.5

2

2.5

3

3.5

std open pass

std box 0 mm

1

1.5

2

2.5

3

3.5

reduced width - 2 mm box pass

reduced width - 4 mm box pass

reduced width 2 box pass std width box pass reduced width -10 mm box pass 2 per, Mov. Avg. (reduced width - 10 mm box pass)

reduced width - 10 mm box pass

(g)

0.5

std open pass reduced width 1 box pass

0

(h)

Figure 9.21 Inﬂuence of pass width and lateral restraint: (a) schematic of frictional forces over the contact area according to [66]; (b) case of box pass with reducing width; (c) derived coefﬁcient of friction (COF) in contact area no contact; (d) COF for standard contact; (e) COF for 2 mm reduced width (width1); (f) COF for 4 mm reduced width (width 2); (g) RSF; (h) roll torque, all for a typical box pass with 15.5% reduction in height, 16 ° bite angle and 0.28 friction engagement (outputs created using Abaqus commercial FE code).

297

298

9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input

(a) Spread

48.3 %

(b) Vertical def.

51.7 %

50.6 %

Backward CSHEAR

49.4 %

Von Mises stresses

49.6 %

Forward CSHEAR

39.5 %

41.3 % 58.7 %

50.4 %

Eq. plastic strain

45.3 %

Forward slip rate

45.4 % 60.5 %

54.6 %

Contact pressure

38.6 % 54.7 %

61.4 %

Backward slip rate

43.7 % 56.3 %

(c)

(d)

(e) Figure 9.22 (a) Box pass rolling contact frictional stress (longitudinal); (b) vector plot of frictional stress; (c) inﬂuence of lateral constraint on key roll bite parameters where green relates to an unconstrained box pass as shown in (d) and red a constrained box pass as highlighted in (e) (outputs created using Abaqus commercial FE code).

of the bite angle α and friction coefﬁcient μ using an expression such as that of Ekelund [66]:

ϕ=

α⎛ α⎞ ⎜⎝ 1 − ⎟⎠ 2 2μ

(9.32)

9.3 Industrial Conditions Including Descaling

Figure 9.23

Forces acting along arc of contact with large entry tension [66].

where φ is roll angle between the exit plane and the neutral point. Thus increasing friction shifts the neutral point or zone toward entry plane (Figure 9.23). When tension is applied, the neutral zone can be changed according to a formulation proposed by Ford et al. [66]. This will affect forward/backward slip and surface ﬁnish. A knowledge of the neutral zone is crucial for optimizing surface ﬁnish in the case of bright anneal stainless steel strip where forward slip is required to increase surface bufﬁng and brightness, mostly in the presence of optimum lowviscosity lubricant and smooth roll roughness:

ϕ=

α ⎛ σ (hentry − hexit ) + hentry s back − hexit s front ⎞ ⎜ ⎟⎠ 2⎝ 4σR ′μ

(9.33)

where σfront and σback are the entry and exit tensile stresses due to back and front tension, respectively, and σ is the mean yield stress. The forward slip is given by Sf =

v1 − v r vr

(9.34)

where Sf is the forward slip, v1 and vr are the stock exit speed and the roll speed, respectively. This is shown schematically in Figure 9.23. Tension control in a no-twist ﬁnishing rod mill is critical in view of the short interstand distance between H/V stands (around 500 mm), speed, and size (about 5 mm rod diameter) to avoid unstable rolling conditions where back tensions are creating a stress close to the yield stress at entry to next pass, mostly in cases where metadynamic recrystallization occurs. A good review is given by Bayoumi and Lee [82] on the effect of interstand tension on load, torque, and deformation during rod rolling. Threshold limits on velocity increase based on interstand distance are given to avoid a stress discontinuity at entry to next pass. This will also be affected by frictional behavior. 9.3.2 Inﬂuence of High-Pressure Water Descaling

High-pressure water (HPW) descaling systems are now an integrated part of the rolling train, positioned at key locations prior to cogging/roughing and ﬁnishing

299

120 100 80 60 40 20 0

1.20 1.00 0.80 0.60 0.40 0.20 0.00

O Fe O/Fe

1

2

3

4

5 6 Zone

7

8

At %O / At %Fe

9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input

At % (Fe,O)

300

9

Figure 9.24 Typical oxide scale proﬁle obtained by wave dispersion spectrometer (WDS) electron microprobe on an undeformed C–Mn steel grade [15].

stands, and operating within a wide range of ﬂow and IP to cater for both primary and secondary scale removal for a wide range of steel compositions [83–85]. Oxidation of steels at temperatures above 570 °C generally results in a three-layer scale consisting of wüstite (FeO), magnetite Fe3O4, and hematite (Fe2O3). FeO is stable above 570 °C [86] and constitutes approximately 95% of the scale, although different scale mechanisms can exist as a function of temperature, time, atmosphere, and steel grade (Figure 9.24). Following secondary descaling in a hot rolling mill, hematite and magnetite tend to be absent as the solid-state diffusion of Fe ions will be limited by the short-time exposure (which means linear growth of the oxide). So the scale will be primarily wüstite and mostly type W1, which is the most plastic and adjacent to the metal. However, prior to the roll bite, cracks or gaps can be initiated which will increase the tendency for the formation of magnetite and hematite since they obstruct the supply of Fe ions and facilitate inward migration of oxygen. A good description of inﬂuence of descaling and ﬁnishing processes on scale formation and composition is given in [87, 88]. The principal mechanisms for scale removal rely upon differential contraction of the oxide scale by means of the cooling by the descaling sprays together with mechanical effect of water impingement (impact force). Both effects are dependent on key process and product parameters, which need to be maintained in a narrow band in order to minimize chilling of the product surface while maximizing descalability [89]. The cooling effect depends on the speciﬁc water impingement (SWI in l/m2) and the IP (in MPa) and is a function of ﬂow rate, stand-off distance, spray angle (itself a function of nozzle type), and feed pressure. These are deﬁned as follows: SWI =

G bv

(9.35)

where G = ﬂow rate (l/min), b = descaling width (mm), and v = product speed (mm/s).

9.3 Industrial Conditions Including Descaling

301

Typically, IP increases as the square root of pressure, thus IP = A

G P tan2 (α 2) d b

(9.36)

where α = spray angle (degree) and d = stand-off distance (mm). Typical X–Y plots of SWI as a function of IP have over the years been developed (see schematic, Figure 9.25a) using experimental trials on laboratory rigs (Figure 9.25b). Data points of SWI/IP located above the respective limits can be used as “safe”, but may be nonoptimum setups for descaling. More work is required to fully characterize the complex interactions between oxide scale and substrate as a function of nozzle geometry, SWI, mechanical and thermal effects, mostly for the case of complex alloy steels. For simple oxide states, typical pareto curves and response surface plots have been developed [89] that account for the inﬂuence of process parameters. For instance, descalability can be signiﬁcantly improved by moving the descaling unit closer to the furnace in order to maintain a high temperature and also by decreasing the product speed through descaler (Figure 9.26a). Other factors such as product cross-sectional area, oxide scale thickness, nozzle type, stand-off distance, and IP have, in this case, had a second-order effect for a typical Ni–steel. In practice, the location of the secondary descaler needs to be optimized to promote an optimum scale growth proﬁle and state. Descaling will also inﬂuence the surface chilling effect, as shown in Figure 9.27. Figure 9.27 shows typical surface chilling effect (especially at the corner) due to HPW descaling. Figure 9.28 shows two typical surface states ahead of the roll bite in the case of efﬁcient (case a) and poor descaling (case b). This surface state will be inﬂuenced by the reheating cycle (time at temperature), reheating furnace atmosphere (mainly the O2 content), and alloying elements (Si, Cr, Ni) where adherent scale can be formed at the metal–oxide interface. Solid solutions (Mn) or mixed oxide can be formed with elements that are easier to oxidize than Fe. The amount of fayalite present after primary descaling will be a good indication of the amount of remained Variation of impact pressure & SWI required for primary descaling steels using different reheating conditions 45 40

SWI (l/sq m)

35 30

Si/Ni low Si plain C

25 20 15 10 5 0 0

0.5

1 1.5 Impact pressure (MPa)

2

(a)

Figure 9.25 (a) Typical primary scale SWI/IP setups for a range of steel compositions; (b) Swinden Technology Centre pilot laboratory descaling rig [89].

(b)

302

9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input Pareto Chartoft-Values for Coefficients; df=25 Varialble: Rs Sigma-restricted parameterization

T

>1 < 0.925 < 0.825 < 0.725 < 0.625

1.1

3.752659

1.0 v

2.233218 0.9

hsc

.8942716

Desirability

A

.2922847

spray T

.2342783

IP

.1922065

0.8 0.7 0.6 0.5 1200 1000

p=.05 t-Value (for Coefficient Absolute Value)

(a)

(b)

800 600 V 400 200 0 0.0

0.2

0.4

0.6

1.0 0.8 IP

1.4 1.2

1.6

Figure 9.26 (a) Pareto chart of statistically signiﬁcant main effects obtained from multiple regression model such as product temperature (T), speed (V), cross-sectional area (A), etc. (b) Example of a regime map showing the descalability of Ni–steel expressed as a desirability index function of speed and IP (note that a desirability index of 0 means full oxide scale removal) [89].

Scale on 1150.00 1100.00 1050.00

NT11:

1000.00 950.00

Scale off

900.00 850.00 800.00 750.00 700.00 650.00 0.00

40.00 Time

80.00

Figure 9.27 Typical billet temperature (NT11) – time simulation proﬁle prior roughing. Graph shows the effect of scale insulation on surface heat loss if HPW descaling is not applied compared to fully descaled surface [89].

residual primary scale on the deforming feedstock. Water pressure up to 2–3 MPa may be required to fully remove the primary scale and subsurface fayalite layer. A good description of an effective descaling system with determination of impingement pressure and ways to predict oxide scale adhesive strength using the maximum shear strength theory is given by Yu [90].

9.3 Industrial Conditions Including Descaling

(a)

(b) (c)

10μm

(d)

20μm

(c) Figure 9.28 (a) Typical macros of nondescaled and (b) fully descaled surfaces (Si-grade steel). (c,d) Typical SEM for a strip steel following HPW descaling with secondary scale spalled off (c) and presence of fayalite particles within secondary oxide scale (d). Red arrows indicate fayalite (H. Bolt, see also [88])).

The range of surface states illustrated by the extremes shown in Figures 9.28a and b will inﬂuence frictional conditions and the surface ﬁnish of the ﬁnal product as a mixed regime of secondary scale, and remnant of primary scale will be present in the roll bite. This is further supported by detailed SEM characterization of oxide scale proﬁles, as shown in Figure 9.28c. The presence of fayalite may cause surface defects such as tiger stripes in ﬂat products. In addition, other through-process effects such as presence of mold ﬂux from casting, which reacts with Fe, can cause interlocking at the surface and increase adherence. In summary, a through-process understanding of the surface state is required to account for the effect of primary and secondary oxide scale, temperature, and microstructural state prior to rolling, but also prior cooling, which will inﬂuence the formation of tertiary scale. Among the key oxide scale properties are

• •

scale thickness and uniformity; scale composition (i.e., ratio of wüstite (FeO), magnetite (Fe3O4), and hematite (Fe2O3));

303

304

9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input

• • • • • •

scale mechanical properties (plasticity/strength/hardness, behavior in shear, etc.); scale thermal properties (expansion coefﬁcient); scale structure (how layered, voided, or porous the scale is, see Figure 9.28d); scale adherence and cohesion; steel–oxide scale interface morphology (see Figure 9.28d); and enrichment and inﬂuence of alloying elements (Cr, Ni, Si, etc.).

These properties will be dependent on

• • • • • •

steel grade; rolling temperature, including ﬁnishing temperature for tertiary scale; coiling temperature for strip or rod (e.g., Stelmor process); reduction and pacing sequence; interstand cooling, including water box cooling prior to laying in the case of rod; and product dimensions.

The HPW descaling operation will have an inﬂuence on surface temperature, depending on timing and thermal capacity of the stock. It will also condition, at a microscale, the nature of the oxide scale prior to rolling (e.g., extent of remnant scale, cracking). Chilling effects also have to be considered since they further affect secondary scale growth and may take the scale into its ductile-brittle transition regime as well as affecting its surface ductility. Depending on pacing (time) following descaling, a rough or smooth oxide scale interface will be promoted, this being linked to the mechanism of oxide scale growth, which will be linear or, for longer times, parabolic. It is also known that high-temperature oxidation leads to growth stresses according to the Pilling-Bedworth ratio (PBR), which is related to the volume ratio of oxide and metal, as well as a much rougher steel/scale interface [91–93]. The plasticity of scale is more pronounced when wüstite is formed. The inﬂuence of stress induced by thermal expansion mismatch is also key for the mode of cracking. Scale adhesion is a function of scale thickness, surface energy, and any changes brought about by alloying elements such as Mn, Al, and Ti, mostly above 1100 °C. At lower temperatures, the presence of Cu and Ni will create a rough metal–scale interface. Worse effects during rolling are predicted when primary or indeed secondary descaling processing conditions are below threshold in terms of SWI and IP to remove completely the oxide scale, leaving mixed oxide layers on the entry to the roll bite. An optimum through-process route accounting for descalability and rollability is, therefore, required in order to optimize surface quality of ﬁnished products. The state of the secondary scale will condition the scale during cooling, that is, the tertiary scale, via possible changes in scale composition due to oxide phase change. This is especially important for hot strip mills where the conditioning of the tertiary scale will directly inﬂuence pickling, powdering during stamping, and oxide dust formation during cutting by lasers. A wellcompacted, adherent secondary or tertiary scale is required and achieving this is receiving increasing attention in Europe and worldwide [94, 95].

9.3 Industrial Conditions Including Descaling

9.3.3 Inﬂuence of Oxide Scale During Rolling

Studies by Lenard [96] have demonstrated that the scale thickness, its strength, and adhesion/cohesion to the steel substrate are the most signiﬁcant factors inﬂuencing events at entry and within the roll bite. Oxide scale reduces heat transfer increasingly as thickness increases. Oxide scale can act as a lubricant (i.e., wüstite at high temperature) or as an abrasive (particularly hematite at lower temperatures) with major consequences on roll wear, depending on temperature and scale composition. The oxide scale thickness reduces as a function of bulk rolling reduction with its structure being changed by the rolling process with respect to porosity, cracking (normal to the surface or delamination parallel to the steel/oxide interface), oxide scale fragmentation or powdering, roughening, etc. Depending on the roll gap shape factor L/hm (see Section 9.3.1.1), the oxide scale will either plastically deform or fracture at entry and during rolling. Several models to account for the through-thickness cracking and also delamination have been proposed [15, 58–61, 97, 98]. Both compressive and tensile behavior of the oxide scale are important. It is known that brittle fracture occurs at lower temperatures (below the so-called transition temperature) through the oxide scale layer followed by fracture parallel to the interface (see [58–61]). At high temperature, the viscoplastic behavior of the scale and the potentially weak interface with the metal (assuming the primary scale has been removed) can lead to slipping of unfractured oxide rafts during rolling. Friction will be reduced as oxide scale thickness increases if it behaves in a ductile manner and if there is no pulverization of the brittle wüstite, which would then promote further oxidation to magnetite and hematite. Average scale thickness ranges from primary (200–2000 μm) to secondary–tertiary (5–40 μm) depending on pacing and descaling practice [10, 99, 100]. Decarburization, which can be prevalent at medium to high temperatures depending on the partial pressure of carbon monoxide and on the adherence and state of oxide scale, as well as carbon activity, will also need to be considered since it will affect the mechanical properties of the steel surface, particularly if a ferrite rim is formed [101, 102]. Controlling the stock temperature after secondary descaling (say below 950 °C) is crucial for ensuring a thin but adherent oxide scale layer with a minimum presence of magnetite as wüstite can be converted to magnetite in areas where the scale is separated from the steel substrate [86]. Pacing and reduction are, therefore, the two critical process parameters that inﬂuence the oxide scale behavior during rolling. The mechanical properties of the oxide scale and the triaxial stresses developed at the steel/oxide scale interface will determine the mode of failure. Many mechanisms exist, such as stresses induced by oxide growth and relaxed by deformation or fracture, mechanical and thermal stresses, and stresses generated by gas entrapment. Thermal stresses are well understood from the point of view of heating/ cooling and differential thermal expansion characteristics. In general, with the exception of magnetite, compressive stresses will be generated during cooling

305

9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input

above transformation due to lower thermal expansion coefﬁcients (for wüstite and hematite they are around 12 × 10−6 K−1). With regard to high-temperature hardness, little data are available for magnetite and hematite. Vagnard and Marenc [103] have measured the degree of softening of wüstite as a function of temperature and reported a typical hardness of about 10 HV. Similarly, Tylecote [104] measured tensile strength at high temperature with values for wüstite dependent on strain rate in the temperature range of 500–700 °C but independent of strain rate at 1000 °C, and found a typical value of around 3 MPa compared with 0.4 MPa at room temperature. By comparison, tensile strength for magnetite and hematite at room temperature are of the order of 40 and 10 MPa, respectively. The relatively low values of oxide tensile strength at room temperature are due to extreme brittleness. An interesting graph of creep rate as a function of oxide scale thickness (Figure 9.29) has been obtained by Manning [105]. The limiting creep rate before fracture or spalling increases as temperature rises and scale thickness decreases (assuming secondary scale). For primary scale, created during high oxidation temperature, signiﬁcant plastic ﬂow can occur without cracking, leading to the relaxation of the growth stress and retention of contact despite the increased thickness. This is somewhat contrary to the behavior of secondary scale where scale adhesion or 3

Compression

Spalling

Total elastic strain × 103

2

1 Region of scale integrity 0 100 Scale thickness, μm

200

–1 Tension

306

Through-scale cracking –2

Multilaminations Spalling

–3 Figure 9.29

Oxide failure map from [105].

9.3 Industrial Conditions Including Descaling

resistance to failure decreases with increasing scale thickness. Krzyzanowski and Beynon have investigated different models of oxide spalling in the temperature range of 800–1150 °C and scale thickness of 10–300 μm [106]. The aim was to study the tensile behavior of the oxide scale at roll gap entry as the stock is pulled into the roll gap. Therefore, both tensile and compressive behavior of the scale is important and should be accounted for during rolling. 9.3.4 Comparison of Processing Conditions Between Flat and Long Products

In this section, a brief comparison is made regarding the process and product parameters for ﬂat and long products in order to better position the long product envelope of processing conditions and to highlight the key inﬂuencing variables to account for when modeling roll gap interfacial behavior. Table 9.1 presents the list of the key processing parameters. Although no attempt has been made to integrate a wide range of processes and products, some of these parameters will be intrinsically linked to the local through-process conditions and to a given mill and deformation mode. Table 9.1

Typical envelope of processing conditions.

Typical envelope

Long product

Flat product

Discharge temperature (°C)

1150–1300

1150–1260

Roll diameter (mm)

150–1200

650–1600

Roll gap shape factor L/hm

<1, typically 0.3–0.9

−1

>1

Speed (m s )

0.1–120

0.5–20

Forward slip rate (%)

0.5–8

1–10

Tension (kN)

1–8

5–15

Pass temperature (°C)

>Ac3 (excluding the surface)

Roll separating force (tonf)

20–1200

700–1500

Oxide scale thickness (μm) (* primary scale not removed)

10–1500*

10–200

Interpass time (s)

0.005–15

5–40

Lubrication

Yes/no

Yes/no

Average rolling time (s)

170+

130+

Finished rolling temperature (°C)

>Ac3

Maximum bite angle (°)

24–25

30

Maximum reduction in height per pass (%)

30

50

>< Ac3

850–940

307

308

9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input

9.3.5 Summary

In summary, this section has laid out the foundations for the conditions where the tribological conditions of the roll bite will be most relevant to long product rolling. On one hand, it shows that the major contributor to rolling load is provided by redundant shear with deformation gradually being more localized to the surface as the roll gap shape factor decreases. However, the condition of slip and shear at the surface will still be important for rolling load and surface ﬁnish, thereby exposing the important role of oxide scale and its behavior in compression, tension, and shear. Therefore, assuming that the correct regime of rolling is established and characterized, a detailed understanding of the effect of friction will lead to increased accuracy in load predictions, process control, and surface quality.

9.4 Recent Developments in Friction Models 9.4.1 Mesoscopic Variable Friction Models Based on Microscopic Effects

From the description in Section 9.2, which layouts the various friction regimes and a review of previous studies [107–113], process parameters such as normal force, roll and sliding velocities, reduction, temperature, as well as product parameters such as roll surface roughness, roll material grade, and deforming high-temperature material ﬂow stress will affect the coefﬁcient of friction. This in turns will affect the rolling load, torque, and ﬁnal surface quality depending on the roll gap shape factor regime, as discussed above. Previous studies indicated that reduction (mostly for high roll gap shape factor L/hm), stock temperature, roll surface roughness, and oxide scale thickness have a signiﬁcant effect on COF. The adhesion friction theory hypothesis of Bowden and Tabor [63] indicates that the relative velocity between the contacting surfaces should also inﬂuence COF. The processing conditions, with respect to uniformity of contact area, trajectory, conformance (real contact area), roll contact time, and roll surface topography will also inﬂuence the surface state. The surface state is further complicated by the presence of primary or, usually, secondary oxide scale [114], which increases the complexity of the interaction at the stock–roll interface and has often been overlooked. Contact time inside the roll gap varies for sections, which in turn will affect the inﬂuence of oxide scale on the friction coefﬁcient by changing its thermomechanical properties [115]. Recent studies have shown the importance of taking into account the behavior of the ductile and/or brittle regime of the oxide scale, depending upon the temperature and steel composition [106]. Physical understanding of length scale effects and microscopic behavior of the oxide scale during and after rolling are needed to explain mesoscopic and macroscopic behavior of friction and wear mechanisms as well as providing a mean of

9.4 Recent Developments in Friction Models

developing and implementing technical solutions for minimizing their effects within the constraints of the rolling mill (torque, power, roll sizes, and types) for engagement/threading as well as indirect drafting and slip. This needs to be combined with any advancement in roll cooling such as HTRC [38], hot lubrication [116], but also thermomechanical controlled rolling (TMCR) which will dictate the strain-temperature regime to be applied to control recrystallisation of the deforming feedstock. Therefore, practical and theoretical investigations have been initiated to study the oxide scale, resulting in the development of computer-based models [117]. The modeling approach to friction has often assumed a ﬁxed, isotropic Coulomb coefﬁcient of friction along the contact length, typically with an average friction value of 0.3 over the temperature range 1000–1200 °C. This section describes the development of a high-temperature macroscopic friction/shear stress model to replace the ﬁxed Coulomb friction coefﬁcient with a formula that takes into account not only the state variables such as normal force and relative velocity, but also various parameters characterizing the state of the steel and oxide scale. Different formulae describing the evolution of COF at a macroscale were proposed over the past 50 years (see Section 9.2) mostly as a function of stock temperature. Recently, Fletcher has developed a more complex function of COF based on 2D micromodels for hot rolling of strip products [53]. This was further developed by Talamentes-Silva (see Section 9.4.5, [54, 111]). A 2D mathematical model [55–57] describing the evolution of the frictional tangential force at the roll/stock interface is presented in this section. This model was developed from both laboratory rolling trials (see Section 9.6) and literature, and coded into a Fortran subroutine within the Abaqus/Explicit FE software. It relies on the combined macroscopic formulation of a Coulomb–Norton friction approach from the point of view of normal forces and slip velocity acting in the roll bite, and a mesoscopic representation and effect of the thermomechanical behavior of the oxide scale from the point of view of ductile and brittle transition temperature, likeliness for cracking and steel extrusion through the cracks, and oxide scale thickness. It was developed for a range of plain carbon steels and, therefore, does not cover high alloy steel grades where a combination of Si–Mn–Cr will signiﬁcantly affect the oxide scale behavior. This is still a ﬁeld where research is needed. However, this model is capable of studying the inﬂuence of a range of rolling conditions such as roll velocity, roll surface roughness, thickness of secondary oxide scale, stock temperature, interstand and contact time, ﬂow stress, and slip rate on the coefﬁcient of friction, pinpointing, eventually, those circumstances where extreme friction conditions may occur. The results derived from drawing up regime maps can be used to study conditions and regions in the roll bite where surface shear stress could be reduced to improve product surface quality, where selective lubrication could be applied, to minimize roll wear, and lower rolling power/load. The model described below calculates incrementally the instantaneous COF, taking into account various contact conditions inside the roll bite (Figure 9.30). This approach is a step forward from the standard CA friction model where a mean constant COF has up to now been imposed, irrespective of material grade and

309

310

9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input

COF 0.32 0.27 0.22 0.16

Square oval pass, 1180 ˚C, tscale=5s. Ra=1.5μm. v roll=7.7 rad/s

0.11 0.054 10 0 5

10 5 0 0

Rolling dir. Figure 9.30 Instantaneous coefﬁcient of friction (COF) as calculated for a typical square oval pass [55] (outputs created using Abaqus commercial ﬁnite element code).

deformation. The inﬂuence of conditions of high slip rate–low contact pressure or low slip rate–high contact pressure can be studied, together with the sensitivity of processing conditions on friction (see Section 9.4.4). This model can be used analytically “off-line” for sensitivity analysis or fully integrated within an FE framework, such as in the case below within the dynamic explicit formulation of the commercial code Abaqus. The implementation within the VFRIC user friction subroutine is brieﬂy described in Section 9.4.6. The application to secondary oxide scale rolling is also shown below. The analytical equation for the friction coefﬁcient is calculated as a function of contact force at a node (fnormal), sliding velocity (vrel), stock temperature (T), roll surface roughness (Ra), and secondary oxide scale thickness factor, which is thermomechanically affected by the contact inside the roll bite (Hsc): − log

μ = k1 Hsc

( ) 1200 T

T k3 ⎛ ⎞ log (1 + f normal ) a tan ⎜ Ra1200 ⎟ ⎝ ⎠ log (k2 + v rel )

(9.37)

9.4 Recent Developments in Friction Models

where k1, k2, and k3 are constants established experimentally to enforce equation dimensionality and smooth FE response. The Hsc factor is a function of thickness of secondary oxide scale (hsc), its thermal diffusivity (ac), and contact time (Δt) [118]: H sc = hsc (6ac Δt )−0.5

(9.38)

Three oxide scale regimes can be established according to the a-dimensional value of Hsc:

•

If Hsc > 2, oxide scale is thick and ductile; therefore, friction is low and shear is predominantly within the oxide scale layer.

•

As Hsc falls below 0.02, the oxide scale layer becomes more brittle, heavily cooled within the roll bite, and typically friction is proportional to the normal contact force (the Coulomb assumption).

•

In the intermediate regime (the most likely to be encountered during rolling), friction is dependent on contact time and normal pressure due to a mixed oxide scale regime.

In both Equations (9.37) and (9.38),

• •

• • • • •

hsc = thickness of secondary oxide scale (in μm) ac = thermal diffusivity of secondary oxide scale (in m2/s) (i.e., k/ρCp, where k = thermal conductivity of oxide scale (W m−1 °C−1), ρ = density (kg m−3), and Cp = speciﬁc heat (J kg−1 °C−1)) Δt = contact time inside the roll bite (s) T = instantaneous temperature of stock for a speciﬁc point (°C) Ra = roll surface roughness (μm) fnormal = normal contact force (N) vrel = stock–roll relative velocity (slip rate) (mm/s).

Figure 9.31 shows the variation of Hsc as a function of contact time for typical wüstite oxide scale. The behavior of the oxide scale suggested by Li [115] has been described mathematically here by Equation (9.39). Coefﬁcient of friction originates from two kinds of interactions: one between the roll surface and fragments of oxide scale and another between the roll surface and fresh steel extruded through the opening cracks during deformation:

μ = α ox ⋅ μox + α st ⋅ μst ⋅ β extr β ext =

log(1 + f normal )

(9.39)

a

( )

log hsc*

(9.40)

311

312

9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input 0.4

0.3 Hsc(1000, 5, deltat) Hsc(1000, 10, deltat)

0.2

Hsc(1000, 50, deltat) 0.1

0

0

0.2

0.4

0.6

0.8

1

deltat Figure 9.31 Evolution of secondary oxide scale thickness factor thermomechanically affected by the contact time inside the roll bite (Hsc) at 1000 °C, function of time (s), and three oxide scale thicknesses (5, 10, and 50 μm) for a wüstite oxide scale layer (ρ = 5700 kg × m−3, Cp = 675 + 0.297T – 4.367 × 10−5T, k = 1 + 7.833 × 10−4T).

where αox and αst are the fractional contact area of oxide scale and potentially extruded steel with the roll surface, respectively, and βextr is the probability of the extruded steel making contact with the roll and is mainly a function of deforming oxide scale thickness ( hsc* ) and reduction (normal force) as shown in Figure 9.37a. Evolution of fraction of oxide and steel follows a proﬁle shown in Figure 9.37c. A typical evolution of friction is shown in Figure 9.32. The physical assumptions of the model are illustrated below and rely on:

•

Oxide scale growth and thickness calculated prior to the roll bite according to a linear-parabolic oxidation law (Figure 9.33) and oxide scale layer deformed according to bulk feedstock deformation as shown in Figure 9.34.

•

Brittle/ductile transition temperature, which is dependent on steel grade and oxide scale, Krzyzanowski et al. [106]. This deﬁnes the likeliness for scale cracking when the brittle regime is reached (Figure 9.35). The use of this criterion will rely on fully thermocoupled simulation where temperature losses in the roll bite via roll gap conductance can shift the oxide scale regime from ductile to brittle. The temperature will also have an effect on the thickness of scale thermomechanically affected according to Equation (9.38) (Figure 9.35b). This temperature gradient will lower the plasticity of the outer scale layer while the inner layer will remain ductile [10].

•

Roll roughness, because of the mechanical interaction between roll surface and stock (with or without scale), takes place through roll surface asperities. The main parameter that counts here is the slope of these asperities, λa. In order to

9.4 Recent Developments in Friction Models μ full steel extursion

0.6

0.4 no steel extursion 0.2

0 length of arc of contact

Thickness of oxide scale (microm)

Thickness of oxide scale (microm)

Figure 9.32 Typical evolution of coefﬁcient of friction in the roll bite depending on whether or not the oxide scale has fractured during rolling [55].

1500

1000

Mix law

500

0

Parabolic law 500 Time (s)

1000

(a)

60

40

20

0

5

Tdisch=1100 ˚C

10 Time (s)

15

20

(b)

Figure 9.33 Oxide scale growth, T = 1100 °C, according to Li [115] (linear – parabolic) (a) full period (s) and (b) ﬁrst 20 s of Figure 9.32a.

express this parameter in a practical manner, the link between λa and Ra (CLA) was investigated. A direct correspondence between these two parameters was observed (Figure 9.36), and consequently Ra, which is easier to measure, was chosen to reﬂect the effect of roll roughness in the current friction model.

•

The amount of the fresh steel extruded (βextr) is a function of load and thickness of the secondary oxide scale. In the brittle oxide scale regime, COF originates from two kinds of interactions: one between the roll surface and fragments of oxide scale and another between the roll surface and fresh steel extruded through the opening cracks during deformation. More investigation is required as to take account of the width of the oxide fragment gap as well as changes in localized pressure based on microscopic asperity contact, as deﬁned by models such as Wanheim and Bay or Wilson (see Section 9.2). βextr is capped between 0 and 1. Therefore, the contact between the roll surface and the fresh steel extruded needs to be amended by the βextr coefﬁcient, as per relation (9.40).

313

314

9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input Exit from roll gap

After rolling

Before roll gap

Rolling direction

h_sc = 0.027 mm

h_sc = 0.019 mm

h_scale (microm)

τ2 τ1

h_sc = 0.040 mm

Oxide scale

40.39 37.91 33.43 32.95 30.47 27.99 25.51

Contact arc

Stock

Figure 9.34 reduction).

Variation of secondary oxide scale thickness during rolling (Tscale = 1050 °C, 33%

τ2

τ

0.34 0.3

τ1

0.27

Hsc

0.23

0.05 < Hsc < 2 As Hsc decrease, m increases

0.2

Brittle

Tc r

T Ductile

0.16 0.13

Length of arc of contact (mm) (a)

(b)

Figure 9.35 (a) Ductile–brittle transition temperature, where τ1 and τ2 are the failure shear stresses for ductile and brittle deformation, respectively [106]. (b) Typical evolution along the arc of contact of the a-dimensional factor Hsc (thickness of scale affected by thermal effect) [55].

Once brittle conditions are reached, the fraction of oxide and steel obeys a relation shown in Figure 9.37c. Although the current model does not take account of oxide scale fragment width, work by Krzyzanowski et al. [119], Figure 9.38, shows increased width as scale thickness decreases. This gives rise to an increase in the friction as both components of oxide scale and steel extrusion coexist (Figure 9.32). A simpliﬁed ﬂow diagram of the structure of the subroutine is shown in Figure 9.39. The friction force, which is determined incrementally in the subroutine, is the minimum value between the Coulomb friction force for the sliding conditions

9.4 Recent Developments in Friction Models

Delq (deg)

μ

315

Slope asperity (Delq) vs Ra 18 16 14 12 10 8 6 4 2 0

Measured Predicted

0.5

0

1

1.5

2

2.5

3

Ra (μm) Figure 9.36

Correlation between roll slope asperity angle λa and CLA roughness Ra [55].

b

Fn Scale

Fresh steel

Scale

b = f(Fn/hsc, W*)

0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 0.E+00 2.E+03 4.E+03 6.E+03 8.E+03 1.E+04 Contact force [N] thin scale

50%

αs

100%

αox

–50%

thick scale

Contact arc (b)

(a)

(c)

Figure 9.37 (a) Microscopic geometry effect of oxide scale fragment, note w* is the width of oxide scale fragment but is not taken into account in the current model; (b) typical βextr evolution as a function of normal force (hsc = 30 μm); (c) fraction of steel and oxide on the surface during deformation in the roll bite.

180 Initial scale thickness 50 μm

Gap width (μm)

160 140 Initial scale thickness 100 μm

120 100 80 60 40 20 0

Figure 9.38 [119].

5

10

15 20 25 percent reduction

30

35

40

Oxide scale gap width evolution as a function of reduction and scale thickness

316

9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input

Figure 9.39

Simpliﬁed ﬂowchart of friction model [55].

and the force for the sticking friction conditions, which is calculated automatically by the Abaqus software, based on slip rate and mass associated with the contact node. The coefﬁcient of friction μ for the sliding friction conditions is a mathematical function of contact force, slip rate, surface roll roughness, temperature of the contact point, and the thickness of secondary oxide scale thermally affected by the contact time. In Equation (9.37), an upper bound value of μ has been imposed based on Coulomb’s theory (i.e., 0.577). Similarly, a lower bound value of 0.2 has also been imposed based on frictional behavior of an ideal plastic material in plane strain [67]. The contact force at a node (fnormal) is a function of the RSF and the mesh density of the discretized stock in the FEM model. For example, in the case of ﬂat rolling of a 52-mm2 low-carbon steel square bar (34% reduction, 1100 °C), the RSF is about 30 tonf. This corresponds to an average of 1000 N contact force at a node in the case of an FE model comprising an average of 280 nodes in contact with the roll (i.e., around 300 000/280). The output of the current isotropic friction model is the friction force, ftan, which is passed on from the subroutine in the current increment. Table 9.2 summarizes the assumptions and bounds of the friction model of Equation (9.37). The model has been applied to a wide range of long products such as sections, rails, and bars (Figure 9.40a). A friction map of the contact area can be computed as illustrated by an example in Figures 9.40b–c. Complex neutral zones can be observed with inverted slip rates between web (direct drafting) and ﬂange (indirect drafting). High friction values are predicted in the web/ﬂange area. The results show ﬁrstly a differentiation of the parameters into two classes:

9.4 Recent Developments in Friction Models

317

Table 9.2 Process and product parameters considered in the mathematical friction model.

Aimed factors

Roll

Surface topography Thermo-insulating effect

Product parameters

Process parameters

Oxide scale

Physical parameters

Input

Mathematical model

Dimension Roughness

R Ra

R Ra

Thickness

hSC

Composition Hardness

– – Tcrit

Tcrit

Behavior

Behavior Brittle or Ductile

Stock

Material’s resistance to deformation

Flow stress Shear limit stress

Roll speed

Peripheral velocity

Sliding velocity

Adhesion bonds

Vrel (upper limit: 3788 mm/s)

Reduction

Contact force

fnormal (upper limit: 111 100 N)

Draft

Contact angle

h0–h1

Engagement friction

Minimum coefﬁcient of friction

COF >sin [sqrt(draft/R)]

Stick – slip

Neutral zone

ftangential = min(COF*fnormal, fstick)

Temperature

Flow stress and scale behavior

T

Interstand time

Scale growth

Contact time

Thermal effect on scale

fnormal COF < 0.577

RPM

t

RPM

T Δt = (RPM, contact angle)

•

Parameters that have an increasing effect on the COF, such as contact force (Fn), roll surface roughness (Ra), and draft. Increasing any of these parameters will lead to an increase in friction, which is the mathematical description of the effect of increasing reduction, roll surface slope asperity, and contact time inside the roll bite.

•

Parameters that have a decreasing effect on COF, such as slip rate (vrel), roll angular velocity (ωr), and thickness of the secondary oxide scale (hsc), roll radius (Rr). Increasing any of these will lead to a decrease in COF. This is the mathematical reﬂection of the adhesion theory, according to which the strength of the adhesive bonds is inversely proportional to slip rate and/or roll velocity,

318

9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input

Figure 9.40 Example of application of friction model to beam rolling; steel grade plain C–Mn steel (S275), hsc = 18 μm, T = 989 °C, 23% reduction at the web and 16% at the ﬂange (outputs created using Abaqus commercial FE code).

but also dependent on the lubricating effect of secondary scale in the ductile regime and of the contact time inside the roll bite. Figure 9.41 illustrates an application of this model to rolling at low temperature. It can be observed that COF decreases as the stock temperature increases. The stock–oxide scale interface becomes weaker, prone to be sheared and, at the same time, the material resistance to deformation decreases. For temperatures around 1000 °C, the sticking region could be seen on the plotted surface of instantaneous COF. Again the contact points, where the contact force is high, are characterized by a high value of COF, even though the slip rate is high. In the case of shaped passes, such as square-diamond, diamond-square, etc., the rolling contact length and time varies as the roll radius changes (see Equation (9.31)). Therefore, the oxide scale layer is deformed under different contact time conditions. Two effects are combined, the strain or deformation path coupled with the cooling effect due to the different contact time with the roll surface, leading to a different magnitude of the interface strength. For speciﬁc contact conditions, the friction model predicts an increase in COF as the amount of draft increases (Figure 9.42).

9.4 Recent Developments in Friction Models

Square diamond pass, 1000 ˚C, tscale=5s, Ra=1.5 μm, vroll=7.7 rad/s

Square diamond pass, 1000 ˚C, tscale=5s, Ra=1.5 μm, vroll=7.7 rad/s

Medium reduction (16%)

High reduction (30%)

COF

COF

0.3

0.3

0.2

0.2

0.1

0.1

0

0

g llin

dir.

Ro

Figure 9.41 Typical square–oval pass showing effect of temperature (1000 and 1180 °C) on normal force (Fn) and slip rate (top) as well as COF map (bottom) (outputs created using Abaqus commercial ﬁnite element code).

Figure 9.42 Effect of temperature on reduction of COF (outputs created using Abaqus commercial FE code).

9.4.2 Anisotropic Friction

The current friction model in Equation (9.37) is isotropic, that is, only the friction force along the rolling direction is considered, which tends to overpredict the amount of lateral spread in a typical open pass. In order to assess the magnitude

319

320

9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input

Figure 9.43

Typical drilled hole bar rolling for assessing friction anisotropy.

of the transverse component of friction, a bar with three equidistant holes (Figure 9.43) was rolled. By comparing the ratio of the deformed orthogonal axes of the elliptic holes with the FE model (Figure 9.44), the magnitude of transverse component of friction force has been established. The magnitude imposed depends on the type of contact (kinematic, penalty) and formulation, but in the case of Abaqus Explicit, a ratio of 0.2*μ*Fn for the tangential friction force gave improved spread characteristics. 9.4.3 Application to Wear

The friction model [55] can also be used to study the effect of worn work roll groove proﬁles. The COF map is shown in Figure 9.45 for the case of a round oval pass. It can be observed that the neutral zone is much clearer, stretching perpendicular to the rolling direction and almost along the entire cross-section of the bar. Along the rolling direction, COF increases slightly due to the thermomechanical effect of the secondary oxide scale, which becomes thinner and cooler, as described by Equation (9.38). The COF map is similar to that of ﬂat rolling. Although exact mathematical relationships between wear and friction are still to be developed, the current friction model offers a possible explanation of wear patterns developed during rolling. As can be observed in Figure 9.46, for a piling section, the maximum COF inside the roll bite appears at the inner side of the roll lock area, where the real wear pattern presents a peak. A similar correlation between high COF and the actual wear proﬁle was found for the case of an ovalround pass (Figure 9.47); the actual wear roll pattern follows the distribution of high instantaneous COF inside the roll bite. Even though in some cases, due to the low value of the L/hm ratio, friction is not the main factor inﬂuencing rolling loads, local frictional conditions have an effect on the localized roll wear. The rolling regime here is associated with high contact pressure and very little slip rate. This raises the possibility of applying localized lubrication to reduce localized wear and optimizing the roll design.

9.4 Recent Developments in Friction Models

(a)

(b)

(c)

(d) Spread (%) 20 [% spread]

19 18 17 16 15

isotropic 17.6 18.2 17.2 anisotropic 15.6

19.2 19 18.25 16.8 16.2

14.8

14 (e)

COF=0.5 One Ftang COF=0.3 Two FTang Experim

916 1155 Stick temperature (°C)

Figure 9.44 (a–d) FE modelling of bar with drilled holes to assess tangential component of friction stress, (e) spread prediction validation and sensitivity as a function of anisotropy of friction law.

9.4.4 Sensitivity and Regime Maps

As described in Section 9.2, the COF is highly dependent on the geometrical aspects of the process (i.e., the roll gap shape factor), the processing conditions (temperature, etc.), and product properties of both oxide scale and parent steel. Previous studies [107–113] have shown that COF decreases with increasing roll velocity and temperature, and increases with increasing reduction. On the other

321

322

9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input

COF

TD RD Figure 9.45 Instantaneous COF, normal force, and slip rate map inside the roll bite for oval-round bar with a worn proﬁle (FE mesh on left).

hand, considering the complexity of the tribological phenomena taking place at the stock–roll interface, the slip rate and the thickness of oxide scale together with its strength, which is highly temperature dependent, and also the strength of adhesive bonds formed during the contact are all expected to inﬂuence the COF as well. An extensive study of these parameters has been carried out by Lenard et al. [107–110, 120]. In [108], results from a series of laboratory trials are presented together with several graphs showing the variation of COF with temperature, roll velocity (Figure 9.48a), reduction (Figure 9.48b), oxide scale thickness (Figure 9.49), roll roughness, etc. A commercial FE code was involved for predicting the ﬁxed COF for which the predicted load-separating force, roll torque, and forward slip approximated best the experimental results. Despite the poor correlation coefﬁcient, the trend of COF variation is clearly presented. In [120], Lenard proposed a COF relation for the hot rolling of carbon steel strips as a function of strain rate, roll velocity, temperature, contact pressure, the metal’s resistance to deformation, inferred by inverse 1D modeling. The drawback of this model was that it neglected the effect of oxide scale, roughness, slip velocity/rate, and contact forces. The friction model of Equation (9.37) has been submitted by Onisa and Farrugia [55] to a sensitivity analysis, within the MathCad™ commercial software, to predict the inﬂuence of key process and product parameters on the magnitude of friction. It is worth pointing out that this sensitivity has been carried out “off-line” using the current analytical equation of the friction model and not through the implementation of the friction model as a VFRIC subroutine within the FE rolling models. For comparing the extent to which key process and product parameters inﬂuence the COF, a 100% increase in value of each parameter was considered. Therefore, this study does not predict the incremental evolution of friction in the roll bite, nor the sensitivity of changing key process and product parameters which will inﬂuence the key rolling parameters such as spread, rolling load and torque, etc. Its primary aim is to identify the sensitivities of key process and product parameters affecting friction and, therefore, it acts as a precursor to the establish-

9.4 Recent Developments in Friction Models (a)

323

(b)

Fn

Slip rate

Rolling direction Max COF

Max COF

(c)

(d)

Figure 9.46 Maps of normal force (Fn in (N)), slip rate (mm/s), and COF for a typical piling section (d) showing lock area where instantaneous COF achieves the highest value (outputs created using Abaqus commercial ﬁnite element code).

ment of regime maps where frictional conditions could be optimized. The model equation is dependent on roll roughness, slip rate, temperature, normal force, and oxide scale (temperature and thickness). The effect of roll roughness and roll diameter (changing L/hm conditions as well as contact time) are not taken into account. This sensitivity is based on the current form of the friction model, which

324

9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input

3.0 2.5 2.0 1.5 1.0 0.5 0.0

Cross section Coefficient of friction (from FEA)

Cross section

[mm]

Actual wear

0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00

(a)

(c)

(b)

Figure 9.47 Comparison between instantaneous coefﬁcient of friction (b) and actual wear (a) in the transversal rolling direction for a typical oval-to-round pass; (c) 3D plot of discretized computed COF, Tin = 1000 °C, hm/L > 1, about 21% reduction, low-carbon S275 steel (outputs created using Abaqus commercial FE code).

0.6

0.6

AISI 1018 Velocity =150 mm/s 0.5 Scale thickness = 0.29 mm Coefficient of Friction

Coefficient of Friction

Red. = 21.6% AISI 1018 0.5 Scale thickness = 0.29 mm

0.4 0.3 0.2 0.1

0.3 0.2 0.1

0 0

200 400 600 Roll Velocity (mm/s)

1050˚C (a)

0.4

975˚C

900˚C

0 10

800

825˚C

15 1050˚C

20 25 Reduction (%) 975˚C

900˚C

30

35

825˚C

(b)

Figure 9.48 Evolution of COF function of roll velocity and reduction for carbon steel AISI 1018, scale thickness 290 μm [108].

9.4 Recent Developments in Friction Models

Coefficient of Friction

0.4

AISI 1018 Red. = 25% Roll Velocity = 170 mm/s

0.3

0.2

0.1 0

0.5 1 1.5 Scale Thickness (mm) 825˚C

975˚C

1050˚C

Inﬂuence of oxide scale thickness on COF [108].

0.5

0.5

0.4

0.4

0.3

0.2 0

Figure 9.50

COF (Fn)

COF (Fn)

Figure 9.49

900˚C

2

draught=2 mm (short contact time) 5000 1·104 Contact force, Fn (N)

1.5·104

T=930 °C (hsc = 11 μm) T=1200 °C (hsc = 71 μm)

0.3

0.2

draught=20 mm (long contact time) 0

1·104 5000 Contact force, Fn (N)

1.5·104

The effect of draft on the COF; Rr = 152.5 mm, ω = 8 rad/s, Ra = 1.5 μm [55].

has been developed and calibrated within a range of processing conditions (see Table 9.2). 9.4.4.1 The Effect of Draft on the Coefﬁcient of Friction The amount of draft (dr) inside the roll bite reﬂects the length of the contact time, as well as the amount of mechanical work. The bigger the draft, the longer the contact time, and hence a cooler and thinner secondary oxide scale will be developed. This also means that the bonds developed at the roll-stock/scale require more friction force to be sheared off when the stock temperature is relatively low (i.e., around 900 °C). At higher temperatures, these bonds are weaker, requiring less force to break. As can be seen in Figure 9.50, a larger draft (i.e., longer contact time) will increase the COF for lower temperature rolling; the

325

9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input

0.4

0.3

0.5

T=930 °C (hsc = 11 μm) T=1200 °C (hsc = 71 μm)

COF (Fn)

0.5

COF (Fn)

326

0.4

0.3

ω=7 rad/s 0.2 0

1·104 5000 Contact force, Fn (N)

ω=20 rad/s 1.5·104

0.2

0

1·104 5000 Contact force, Fn (N)

1.5·104

Figure 9.51 The effect of roll velocity ω (7 and 20 rad/s) on the coefﬁcient of friction (Rr = 152.5 mm, draft = 8 mm, tsc = 13 s, Ra = 1.5 μm) [55].

effect at higher temperature remains small. A 100% increase in draft (i.e., longer contact time) leads to an increase in COF of about 3% at 900 °C and around just 1% at 1200 °C. 9.4.4.2 The Effect of Roll Velocity on the Coefﬁcient of Friction The roll velocity reﬂects the adhesion effect of the friction force. There is less time for bonds to form when the roll velocity is high, and, thus, less friction/shear force is required (Figure 9.51). This statement should, however, be moderated by the potential hardening effect due to strain rate dependency of the rolled stock. Once bonds are formed, these will be experiencing cooling due to heat transfer to the roll, their strength tending to increase as roll velocity decreases. At lower temperatures, the COF is more sensitive to variation in roll velocity, while at higher temperature, due to the weakness of the bonds, these effects tend to be minimized. This results in a reduction of the COF, especially at lower temperature when the roll velocity is increased. A 100% increase leads to a decrease of about 4% at 900 °C and only around 0.5% at 1200 °C. It should be noted that no hardening effect due to increasing strain rate has been taken into account. 9.4.4.3 The Effect of Roll Velocity on the Coefﬁcient of Friction Including the Effect of the Thickness of Secondary Scale, hsc The thickness of secondary oxide scale alters the effect of the roll velocity on the COF due to its capacity to lubricate the interface in the oxide’s ductile regime (Figure 9.52). Thus, in the case of rolling with a thin oxide scale (around 10 μm), increasing the roll velocity should lead to a decrease in the COF, with a more pronounced effect at lower temperatures (while still above the ductile transition). For thicker scale (e.g., 80 μm), this effect tends to be minimized. Although the aim is to reduce the secondary scale thickness, for rolling applications where load and torque are constraints (assuming L/hm approaching 1 or above), a decrease in friction could be achieved by allowing the secondary oxide scale to grow to compensate for the negative effect due to rolling with a lower roll velocity (Figures 9.52a and

(a)

0.5

0.5

0.4

0.4

(b)

0.2

0.3 0.2 0

5000 1·10 4 Contact force, F n (N)

10

COF (Fn)

0.5

(c)

1.5·10 4

T=1200 °C 0.3

(d)

0.2

7

1.5·10 4

0.5

0.4

1·10 4 5000 Contact force, F n (N)

1·10 4

5000

Contact force, F n (N)

T=930 °C

0

327

0.3

0

COF (Fn)

80

COF (Fn)

hsc (μm)

COF (Fn)

9.4 Recent Developments in Friction Models

1.5·10 4

0.4 0.3 0.2 0

1·10 4

5000

1.5·10 4

Contact force, F n (N) 20

Figure 9.52 The effect of roll velocity on the coefﬁcient of friction (imposing the thickness of scale, hsc, Rr = 152.5 mm, draft = 8 mm, Ra = 1.5 μm [55]. (a) ω = 7 rad/s, hsc = 80 μm; (b) ω = 20 rad/s, hsc = 80 μm; (c) ω = 7 rad/s, hsc = 10 μm; (d) ω = 20 rad/s, hsc = 10 μm.

b). Of these two operational parameters, the lowest COF can be obtained with a thick oxide scale and a high roll velocity (ignoring the hardening effect due to strain rate). In the case of a thicker secondary ductile oxide scale (wüstite, built-up due to a higher stock temperature or a longer interstand time) and because of its lubrication properties in the ductile regime, the effect of increasing roll velocity is overcome. Hence, if a lower COF is targeted, there is little beneﬁt in increasing the roll velocity when a thicker oxide scale is expected. Again, increasing roll velocity at high stock temperature leads to almost no variation in COF for the reasons explained above. 9.4.4.4 The Effect of Interpass Time on the Coefﬁcient of Friction for a Range of Secondary Oxide Scale Thickness The secondary oxide scale grows when the interpass time and/or temperature increase [56]. A longer interpass time (limited in real conditions by an excessive cooling of the stock) leads to a thicker secondary oxide scale that offers some degree of lubricity, especially at lower temperatures (Figure 9.53). By comparison, a doubling of scale thickness at 1200 °C has a smaller effect than a 50% increase in scale thickness at 930 °C. Again, this effect is stronger at higher reduction or normal contact force. A 100% increase in the secondary oxide scale thickness

(rad/s)

9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input

0.5

T=930 °C (hsc = 10 μm)

0.4

COF (Fn)

COF (Fn)

0.5

T=1200 °C (hsc = 51 μm) 0.3 0.2 0

1·104 5000 Contact force (N)

0.3 0.2 0

1.5·104

T=930 °C (hsc = 17 μm)

0.4

tsc = 6 s

T=1200 °C (hsc = 105 μm) tsc = 55 s

5000 1·104 Contact force (N)

1.5·104

Figure 9.53 The effect of interstand time on the coefﬁcient of friction through the inﬂuence of secondary oxide scale growth; Rr = 152.5 mm, draft = 8 mm, ω = 9 rad/s, Ra = 1.5 μm [55].

0.55

0.55 Thin scale (10 μm)

Thin scale (10 μm)

0.43

Thick scale (80 μm)

0.32

COF (Fn)

COF (Fn)

328

0.43

T=930 °C 0.2 700

4025

Thick scale (80 μm)

0.32 T=1200 °C

7350

1.07·104 1.4·104

Contact force (N)

0.2 700

4025 7350 1.07·104 1.4·104 Contact force (N)

Figure 9.54 The effect of thickness of oxide secondary scale on the coefﬁcient of friction; Rr = 152.5 mm, draft = 8 mm, ω = 9 rad/s, Ra = 1.5 μm [55].

(achievable either through a longer interstand time or a higher initial temperature) leads to a decrease in COF from about 8% at 900 °C down to around 2% at 1200 °C (this temperature range corresponds to the ductile regime for secondary oxide scale). 9.4.4.5 The Effect of Thickness of Secondary Oxide Scale on the Coefﬁcient of Friction As described above, a thicker secondary oxide scale leads to a lower COF. This becomes more effective once the stock temperature is low, as shown in Figure 9.54, although in an industrial context, the lower the temperature, the less the growth of secondary oxide scale will be. At higher temperature, the positive effect of the thicker scale in reducing the friction coefﬁcient is reduced due to the lower stock resistance to deformation. Consequently, rolling with a thicker secondary oxide scale (provided it remains in the ductile regime) leads to a decrease in COF.

9.4 Recent Developments in Friction Models

0.5

T=930 °C (hsc = 10 μm)

0.4 T=1200 °C (hsc = 51 μm)

0.3

COF (Fn)

COF (Fn)

0.5

0.4

5000 1·104 Contact force (N)

T=1200 °C (hsc = 51 μm)

0.3

Rr=152.5 mm 0.2 0

T=930 °C (hsc = 10 μm)

Rr=452.5 mm 1.5·104

0.2 0

5000 1·104 Contact force (N)

1.5·104

Figure 9.55 The effect of roll radius (Rr) on the coefﬁcient of friction, draft = 8 mm, ω = 9 rad/s, Ra = 1.5 μm) [55].

9.4.4.6 The Effect of Roll Radius Rr (Effectively Contact Time) on the Coefﬁcient of Friction Alongside draft, the roll radius is directly related to the contact time. The larger the roll diameter, the shorter will be the contact time, assuming similar draft (Figure 9.55). If there is an opportunity to replace a smaller roll with a larger diameter one yet aiming to achieve the same ﬁnal shape, a bigger roll is more desirable for lowering the COF (providing the friction force still plays a role in the deformation process). A 100% increase in roll radius (i.e., shorter contact time, assuming the same reduction and same angular velocity) leads to a decrease in COF of about 3% at 900 °C and around just 1% at 1200 °C. The effect of increasing roll radius is directly linked to the contact time, thus

⎡ Rr + ΔRr 1 ⎤ tRr + ΔRr = tRr ⎢ ⎣ Rr + ΔRr Δh ⎥⎦

(9.41)

9.4.4.7 The Effect of Roll Surface Roughness on the Coefﬁcient of Friction with Consideration of the Interpass Time The current friction model takes into account both adhesion and plowing components of the friction force. The adhesion component is mainly inﬂuenced by the contact time during which adhesive bonds develop inside the roll bite. This contact time is mathematically expressed by means of the draft, roll velocity, and roll radius (see Equation (9.31)). The plowing component of the friction force is dependent on the slope of the asperities on the roll surface, as the hot rolling process is more compliant to surface interaction and conformance than cold rolling. As this parameter is by nature microscopic and not easily quantiﬁable by portable surface analysis equipment, the slope asperity was linearly correlated with the arithmetic mean roll surface roughness (Ra) following a series of roll roughness measurements taken from multiple grooves of a worn roll (see Figure 9.36). It should be noted that this correlation is weak as roll proﬁles with similar Ra may not necessarily possess similarly sloped asperities, with potential consequences on COF from effect of varied bearing lengths (adhesion) and slope angle (plowing).

329

9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input

0.5

0.4

0.3

0.2 0

0.5

Ra = 0.8 μm T=930 °C (hsc = 11 μm)

COF (Fn)

COF (Fn)

330

T=1200 °C (hsc = 71 μm) 5000 1·104 Contact force (N)

T=930 °C (hsc = 11 μm)

0.4 T=1200 °C (hsc = 71 μm)

0.3 Ra = 1.5 μm

1.5·104

0.2 0

5000 1·104 Contact force (N)

1.5·104

Figure 9.56 The effect of roll surface roughness (Ra) on the COF for two different scale thicknesses (11 and 71 mm), temperatures (930 and 1200 °C), and contact forces (draft = 8 mm, ω = 9 rad/s) [55].

Characterization of the roll surface topography for parameters as input to the friction model is further complicated by the potential nonuniformity (transverse and evolving through time and duty) of the surface proﬁle of rolls during the rolling campaign. The current form of the friction model predicts an increase in the COF as roll roughness increases (the plowing component of friction force prevails) (Figure 9.56). The effect is strong at both lower and higher stock temperature and increases with reduction. A 100% increase in Ra leads to an increase in COF of about 34% at 900 °C and around 47% at 1200 °C. 9.4.4.8 The Inﬂuence of Roll Surface Roughness and Secondary Oxide Scale on the Coefﬁcient of Friction Considering separately the effect of secondary oxide scale thickness and roll roughness, it appears that the negative effect (i.e., increasing friction) of increasing Ra or the slope asperity is counterbalanced by the lubricity of a thick secondary oxide scale in the ductile regime. As shown in Figure 9.57, for a thin oxide scale, doubling the roll roughness seems to result in a drastic increase in COF. Once the scale becomes thicker, this effect is very much reduced. Two extreme cases can therefore be distinguished:

• •

Thin scale and rough roll, causing COF to increase, Figure 9.57d; and Thick scale and smooth roll, causing COF to decrease, Figure 9.57a.

The model can also be used to investigate the sensitivity of further key input factors, such as: Contact force, Fn (900–14 000 N): for a given pass proﬁle, the contact force (related to the reduction) has an immediate effect – a doubling of Fn leads to an increase in COF of about 10%. The effect of temperature is taken into account here through the ﬂow stress value. Slip rate, vrel: the slip rate is temperature independent in the model. Depending on its upper and lower limit, doubling the slip rate leads to a decrease in COF

9.4 Recent Developments in Friction Models

COF (Fn)

80

0.5 COF (Fn)

0.5

hsc (μm)

0.4 0.3 0.2 0

1·104 5000 Contact force (N)

5000 1·104 Contact force (N)

1.5·104

5000 1·104 Contact force (N)

1.5·104

0.5 T=930 °C

0.4 0.3 0.2 0

T=1200 °C 5000 1·104 Contact force (N)

0.8

1.5·104

COF (Fn)

COF (Fn)

0.3

(b) 0.5

(c)

0.4

0.2 0

1.5·104

(a)

10

0.4 0.3 0.2 0

(d)

1.5

Figure 9.57 The effect of roll surface roughness on the COF (thickness of secondary oxide scale imposed) function of contact force (draft = 8 mm, ω = 9 rad/s, Rr = 152.5 mm) [55]. (a) hsc = 80 μm, Ra = 0.8 μm; (b) hsc = 80 μm, Ra = 1.5 μm. (c) hsc = 10 μm, Ra = 0.8 μm; hsc = 10 μm, Ra = 1.5 μm.

from about 8% at high slip rate to just 0.5% at low slip rate. It should be noted that this parameter is a “passed-in” variable taken by the commercial FEM Abaqus software from the previous increment. The magnitude of friction will affect slip rate in the next increment. It represents the mathematical interpretation of the adhesion theory. Figure 9.58 shows the sensitivity of friction as a function of temperature when a 100% change in input parameters is imposed. The strongest positive variations in the friction model are given by the contact force and roll surface roughness. The other variables, particularly the slip rate, have a greater inﬂuence at lower temperature, that is, around 900 °C. In summary, the COF increases when the following parameters increase:

• • •

331

contact force; roll roughness (plowing component prevails); contact time, which is the effect of either draft increase or roll radius decrease.

Ra (μm)

9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input Variation of COF for 100% increase of the variable magnitude 10 decrease COF (%) increase

332

5

Fn

Ra**

Slip rate (10–20)

Slip rate (100–200)

Slip rate (1000–2000)

Rr

ω

hsc

Draught

0

–5

–10 880

930

980

1030

1080

Discharge temp (°C)

1130

1180

**COF variation to be multiply by 10

Figure 9.58 Sensitivity analysis of COF as a function of key input factors such as normal force (Fn (N)), slip rate, roll radius Rr, scale thickness (hsc), etc. (using analytical friction model of Equation (9.37)).

Alternatively, COF decreases when the following parameters increase:

•

slip rate (reducing the adhesive bonds);

• • •

thickness of secondary oxide scale (ductile behavior assumed); stock temperature; and roll velocity (attention should be paid to an increase in strain rate, which results in contact force rising, hence COF may increase, depending on the rolling temperature).

Of these potential cases, the worst scenario in terms of friction occurs when:

• • • • • •

roll surface roughness is high; secondary oxide scale is thin; stock temperature is low; slip rate is low; contact time is long; and reduction is severe.

9.4.5 Macro- and Micromodels of Friction

The work by Fletcher [12, 13] in developing multilevel FE models of friction and heat transfer based on the experimental work of Li [14] is worth highlighting, although initially in 2D plane strain conditions, as one of the ﬁrst attempt to establish a link of the tribological conditions developed in the roll bite at both

9.4 Recent Developments in Friction Models

micro- and mesoscale level. Speciﬁc functions accounting for asperity modeling (roughness) and local conditions of friction and heat transfer were established by mapping and discretizing the boundary conditions calculated from FEM mesoscale models of the rolling process. The approach involved developing a mesoscale FEM rolling model for given roll bite conditions (reduction, thermal coupling, etc.), assuming a ﬁxed friction coefﬁcient to give predictions of normal pressure, shear, relative slip, and temperature throughout the entire roll bite. A scheme was then implemented to discretize the modeled roll gap into a set of partitions or zones (function of length of arc of contact), which are sufﬁciently reﬁned to capture the changes in boundary conditions from the mesoscale model in terms of relative slip, local temperature, and loading history. Using this information and submodel mapping scheme, a new friction drag per partition and contact area ratio was calculated, which integrated through the contact area, allowed to establish an updated friction function φ(ζ). This function (following a regression ﬁt from the FEM micromodel see Equation (9.42)) was then substituted back into the mesoscale global FEM rolling model for a second analysis, and the process of partitioning and mapping between the mesoscale and submodels was continued until the surface loads variation between each micro- and macroiteration was predicted to be below a given tolerance. A typical polynomial curve ﬁt, as expressed by Equation (9.42), is shown in Figure 9.59: Φ (z ) = 0.49 − 1.24z + 1.27z 2

(9.42)

with ζ = z/L (normalized position within roll gap), z representing the longitudinal position, and L the length of arc of contact.

Shear/Pressure Ratio

0.5

0.4

0.3

0.2

0.1 0

2

4 6 8 10 Distance Along Arc of Contact [mm]

12

Figure 9.59 Typical friction function derived from micro–macro modeling of the rolling process (2D plane strain strip rolling) [14].

333

9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input 0.5 Variable friction

334

Entry

0.4 0.3 0.2

Neutral zone

0.1

Exit

0 0

20 40 60 Contact distance along the top of the stock

80

Figure 9.60 Typical friction function derived from micro–macro modeling of the rolling process (3D box pass bar rolling) [54].

This work was subsequently expanded to three dimensions by Talamentes-Silva [54] for the case of the long product bar rolling process (box pass). Boundary conditions applied to the microscale models accounted for the plastic constraint and the material surrounding and expansion due to lateral spread. A Coulomb-type variable function is shown in Figure 9.60 showing a small rise in friction from entry to some distance prior to the establishment of the neutral zone, with ﬁnally the friction increasing again toward exit. The author [54] highlighted the relative low value of friction at roll bite entry (for a 3D box pass) together with the reduced slip rate diminishing friction in the neutral zone. It can be observed that derived functions accounting for variation of local slip, asperity contact, and heat transfer can be signiﬁcantly different as shown in both Figures 9.59 and 9.60, thereby representing a step forward from the assumption of a ﬁxed Coulomb friction coefﬁcient. It can also be observed that variation of friction from Figure 9.59 is not too dissimilar to a variable function developed by Farrugia and Onisa [55] as shown in Figure 9.61. However roll bite conditions are extremely complex and variable due to the presence of oxide scale and other tribological factors; therefore, more work is required to further develop this type of micro–mesoscale approach. Depending on the roll gap shape factor regime (see Section 9.3.1.1), applying this type of formulation will bring more sensitivity to the rolling load and torque (especially passes where torque split occur) but a huge challenge remains to properly validate these modeling approaches (see Section 9.6) as well as automatizing the procedure and speed of execution. Sensitivity analyses as described in Section 9.4.4 are a way of generating knowledge of the roll bite using this type of length scale modeling technique. 9.4.6 Implementation in Finite Element Models

Of the two contact formulations available in Abaqus Explicit, the kinematic contact algorithm proved to lead to reasonable results. Although oxide scale property data

9.4 Recent Developments in Friction Models (a) 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 length of arc of contact

fTang (N), 0.1*slip rate (mm/s)

(b) 1500

angle of contact (rad)

Slip rate *100 (mm/s)

normal force *100 (N)

COF

fTan(COF=0.25) fTan(COF=funct.) V_rel(COF=0.25) V_rel(COF=funct.)

fTan(COF=0.4) fTan3(COF=funct.) V_rel(COF=0.4)

1000 500 0 –500

Contact arc

Nzfunct NZ0.4

NZ0.25

(c)

Figure 9.61 (a) The tribology of the roll bite (ﬂat pass) showing slip rate, normal force and back derived COF (output from commercial Abaqus FEM software); (b) neutral zone for different COF and user friction subroutine model [55]; (c) implementation of user friction subroutine model [55] into Corus FE Roll Pass Design Software® [121, 122].

335

336

9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input

exist for the brittle-ductile temperature transition at least for the simple steel grade composition, the model yields a good prediction of friction for the ductile regime, where experimental data obtained through a series of laboratory pilot mill trials (see Section 9.6) were used for calibration. Based on the information provided by the current mathematical friction model, a useful insight into the roll bite tribology during hot rolling can be obtained. This is highlighted in Figure 9.61a for a ﬂat rolling case with a roll gap shape factor L/ hm greater than 2. It can be observed that friction varies with an initial slight rise in friction from entry to some distance before the neutral zone. The two “humps” of the normal force observed are typical of a rolling process with large L/hm. There is a marked reduction in friction predicted in the neutral zone due to the enforcement of the sticking conditions (see the following section) as both roll and stock are moving at a similar speed, before friction increases again as slip rate increases steeply and oxide scale is thinning. This behavior has been observed by Talamentes-Silva [54]. Figure 9.61b shows the evolution along a single-point deformation path of the tangential force magnitude ( ftan) from the friction model and two ﬁxed values of COF, together with the longitudinal rolling component of ftan ( ftan3) (friction model only) for a typical bar rolling. In the sticking zone area, the tangential force in the neutral zone μfnormal is replaced by the sticking force. This is the force required to maintain the node’s position on the opposite surface in the predicted conﬁguration, and is calculated using the mass associated with the node, the distance the node has slipped, the shear traction-elastic slip slope (if softened contact is speciﬁed in the tangential direction), and the time increment. The current model uses the kinematic contact formulation. This ﬁgure also shows the different neutral zone predicted by the variable friction model together with the ﬁxed Coulomb friction coefﬁcient. Figure 9.61c shows a screenshot of the Simulation Options form regarding friction and the implementation of the user subroutine within the Roll Pass Design Software® from Corus UK [121, 122].

9.5 Application of Hot Lubrication

In this section, the effect of hot lubrication [57] is presented not only as a function of the nondimensional roll gap shape factor L/hm but also temperature, application technique, and others. Regime maps, where lubrication can be effectively applied, have also been reviewed. The model previously validated by experimental rolling trials under dry conditions (see Equation (9.37) and Section 9.6) and pilot plant rolling mill facilities has been further validated under a range of hot lubrication conditions. It has proved to be a useful tool in assessing the applicability and efﬁciency of lubrication during hot long product rolling, as well as predicting friction evolution for a wide range of hot rolling conditions. The lubricant used was Houghton-Roll KL4 [123], produced by Houghton plc and was applied from a pressurized tank as an oil mist through atomizing

9.5 Application of Hot Lubrication

nozzles on to both rolls. The application rate was controlled between 1 to 20 g/min, respectively. Two types of passes were used – ﬂat rolling and shaped bar type rolling. The aim was to describe the effect of lubrication on the instantaneous COF inside the roll bite, taking into account various contact conditions and the contribution of lubrication through its main controllable parameters, such as lubricant type, ﬂow rate, and application technique. Interaction between secondary oxide scale and hot lubrication is brieﬂy presented; however, more work is required to account for all possible regimes and state of contact area and roll materials. The friction model described in Equation (9.37), assuming a continuous or broken layer of oxide scale attached to the steel substrate, has been further adapted to account for hot lubrication via the multiplicative effect of ﬂow rate, temperature dependency, and type of lubricant, as shown in Equation (9.43). The model is still a function of contact force ( fnormal), sliding velocity (vrel), stock temperature (T), roll surface roughness (Ra), and secondary oxide scale thermomechanically affected by the contact inside the roll bite (Hsc), see Equation (9.38): − log

μ = k1 × α flow × α lub × α typeH sc

( ) × a tan ⎛ R 1200 T

⎜⎝

T * k3 1200 a

og(1 + f normal ) ⎞ lo ⎟⎠ × log (k2 + vrel )

(9.43)

where k1, k2, k3 are constants established experimentally to enforce equation dimensionality and smooth FE response, and αﬂow, αlub, αtype describe the lubrication process through its ﬂow rate, temperature dependency, and type of lubricant. The lubrication model was validated only for a mineral-based oil air sprayed on to the roll surface. During hot rolling, competition exists between burn-off and effective lubricant entrapment due to inlet pressurization. It is known that the lubricant viscosity is a function of temperature and it will decrease rapidly with increasing temperature, according to the Barus equation [124]. Also, tribology theory [126, 127] suggests that less boundary layer or a thinner ﬁlm will be built up when the viscosity is low, that is, at high temperature. When the temperature is high enough, the oil can burn and a thinner boundary layer will be formed with little lubrication beneﬁt; this is the case for temperatures above 1100 °C. This balance will depend on the pacing of the process and the competition effect between entrapment/ entrainment of oil and burn-off. At high temperature, the secondary oxide scale growth will be rapid, potentially masking the effect of lubrication, but this will depend on scale thickness and rolling regime. With the decreasing temperature, a thicker residual oil layer will be formed and a greater beneﬁt from lubrication is expected at lower temperature. To put this into context of rolling, a heat ﬂux (φ) will be transferred from the hot deforming feedstock, reducing signiﬁcantly the dynamic viscosity according to the Barus equation [125] modiﬁed to account for temperature sensitivity [124]: h = h0 exp (g p − d T )

(9.44)

where η is the viscosity (Pa s−1), γ (Pa−1), and δ (°C−1) are the pressure and thermodependent coefﬁcients, respectively.

337

9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input

Therefore, although some authors have considered the application of hydrodynamic lubrication for estimating the roll bite ﬁlm thickness, in practice the lubricant or lubricant residue thickness (tar, etc.) is severely reduced due to the temperature effect and its effect is inﬂuenced by the presence of the oxide scale (type, thickness, state, etc.). This also assumes that the roll cooling is optimized and does not interfere with the lubrication system, which for long products is often difﬁcult to achieve due to the lack of roll wipers. Burn-off will induce a lubricant ﬂow reduction (Q): dQ ϕ =− dx ρL

(9.45)

where ρ is lubricant density (g/cm3) and L the latent heat of vaporization (J/g). A critical speed, therefore, exists under which the effect of lubricant (depending on its physical–chemical nature) will be drastically reduced [128]: Vc =

ϕ cot gα ρL

(9.46)

Assuming a bite angle between 5° and 25° (maximum reduction), density of 8 g/cm3, a range of heat ﬂux from 0.2 to 4 W/mm2, and latent heat of vaporization of 250 J/g, a surface plot of critical speed is shown in Figure 9.62. It shows that a minimum speed, as a function of reduction, is required during rolling with a value that is much greater than found during plane strain rolling (Figure 9.63).

250 200 150 3.8

100

V critical vaporization (mm/s)

2.6 50

1.4

0–50

50–100

100–150

5

0

0.2

15

Thermal flux (W/mm2)

25

338

bite angle (deg)

150–200

200–250

Figure 9.62 Typical critical speed for minimizing the lubricant vaporization effect according to Equation (9.46).

9.5 Application of Hot Lubrication

2

2 1 3

1 3

Figure 9.63 Effect of hot lubrication (right) compared with dry contact (left) predicted by the friction model of Equation (9.42) where Rr = 457.5 mm, ω = 13 rad/s, Ra = 1.5 μm, hsc = 35 μm, T = 900 °C, and lubrication rate = 20 g/min [57].

An example of the model’s application to an FE hot rolling model is presented in Figure 9.61, for the case of dry rolling and lubricated conditions, with a ﬂow rate of 20 g/min. A similar off-line analysis to the one presented in Section 9.4.4 has been carried out to assess the inﬂuence lubrication has on friction for a range of key process and product parameters. The above model was run in isolation, varying each input parameter separately. The results of this study are presented below. 9.5.1 The Effect of Stock Surface Temperature on COF for Different Lubricant Flow Rates

In the absence of lubrication, the COF decreases when the stock surface temperature increases. When applied, the lubrication efﬁciency is dependent on the thickness of secondary scale. For a thin secondary oxide scale, corresponding to a short interstand time (e.g., 6 s) (Figure 9.64a), lubrication is more effective at lower temperatures around 800 °C, providing that the presence of primary scale is minimized (i.e., descaling is used). As the stock temperature increases, the oxide scale becomes more ductile, the shearing plane shifts from interfacial (brittle scale at low temperature) to intrascale in the ductile material. Accordingly, the presence of lubricant in its residual state, following burning-out at the roll/stock interface, no longer separates the roll and feedstock surface; hence its efﬁciency in reducing COF decreases. When the secondary oxide scale is thicker (Figure 9.64b) corresponding to a longer interstand time (of the order of a minute), lubrication efﬁciency also decreases, since the COF is already lowered by the presence and

339

340

9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input Coefficient of friction

Coefficient of friction 0.58

0.58

0.51

0.51

0.45

0.45

0.45

0.45

0.32

0.32

0.26

0.26

0.19 800

900

1000 T lubr 10 g/min lubr 1 g/min dry (a)

1100

0.19 800

900

1000 T lubr 10 g/min lubr 1 g/min dry (b)

1100

Figure 9.64 The effect of stock surface temperature on COF for different lubricant ﬂow rates in case of (a) a short and (b) a longer interstand time; Rroll = 152 mm, Ra = 1.5 μm, ωroll = 7.9 rad/s, draft = 7 mm [57].

thickness of the oxide scale (depending on composition). It should be noted that for large feedstock with a high enough heat capacitance to promote the growth of secondary scale at low temperature, the effect of lubrication at low temperature can still remain positive, even if thick scale is present. 9.5.2 The Effect of Lubricant Flow Rate on COF

In the range of the experimental ﬂow rates tested, 1 to 20 g/min, the dissociated effect of increasing this parameter in the model shows a parabolic decrease of COF. The temperature effect is predominant in the case of thin oxide scale and a minimum in the case of thick oxide scale due to the reasons outlined above (Figure 9.65). 9.5.3 The Effect of Interstand Time, for the Purpose of Secondary Scale Growth, on COF Under Lubrication

A shorter interstand time, due to its effect on limiting the growth of secondary scale, increases the beneﬁt of lubrication. This effect is prevalent at low temperature, where scale grows slower than at high temperature. This observation underlines again the beneﬁt of adding lubrication toward the ﬁnishing passes of hot rolling, when the surface is proportionately so much larger (Figure 9.66).

9.5 Application of Hot Lubrication Coefficient of friction

Coefficient of friction 0.58

0.58

0.51

0.51 Thin scale

Thick scale

0.45

0.45

0.45

0.45

0.32

0.32

0.26

0.26

0.19

5

10 15 flow 800 °C (0.001 mm) 1200 °C (0.006 mm)

20

0.19

5

10 15 flow 800 °C (0.020 mm) 1200 °C (0.110 mm)

(a)

20

(b)

Figure 9.65 The effect of lubricant ﬂow rate on COF for (a) thin scale and (b) thick scale; Rroll = 152 mm, Ra = 1.5 μm, ωroll = 7.9 rad/s, draft = 7 mm [57].

Coefficient of friction

Coefficient of friction 0.58

0.58

0.51

0.51

0.45

0.45

0.45

0.45

0.32

0.32

0.26

0.26

0.19

20

40

60

0.19

t lubr (5 g/min, 800 °C) dry (800 °C) (a)

20

40 t lubr (5 g/min, 1200 °C) dry (1200 °C)

60

(b)

Figure 9.66 The effect of interstand time on COF at (a) low and (b) high stock surface temperature; Rroll = 152 mm, Ra = 1.5 μm, ωroll = 7.9 rad/s, draft = 7 mm [57].

9.5.4 The Effect of Reduction on COF Under Lubrication

Rolling reduction affects the COF through the contact time between roll and stock. For a small reduction, corresponding to a short contact time, lubrication has a lower effect than at high reduction, when there is more cooling and thinning of

341

342

9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input Coefficient of friction

Coefficient of friction 0.58

0.58

0.51

0.51

0.45

0.45

0.45

0.45

0.32

0.32

0.26

0.26 0.19

0.19 t lubr (5 g/min, 800 °C) dry (800 °C)

40 t lubr (5 g/min, 800 °C) dry (800 °C)

(a)

(b)

20

40

60

20

60

Figure 9.67 The effect of draft on COF under lubrication for (a) small draft and (b) heavy draft; Rroll = 152 mm, Ra = 1.5 μm, ωroll = 7.9 rad/s, 5 g/min lubricant ﬂow rate [57].

the oxide scale, allowing the lubricant to have a greater effect in reducing COF (Figure 9.67). 9.5.5 The Effect of Roll Speed on COF Under Lubrication

As in the case of reduction, the rolling speed affects the COF through the contact time (neglecting the hardening effect due to increasing strain rate). The main effect for lubrication is predicted to occur at low rolling speed, with the highest decrease in COF. It should be noted that the current friction model does not consider the possible temperature-dependent degradation/transformation of the lubricant’s physicochemical composition, which might reduce the effect at low roll speed. The third factor to affect contact time is the roll radius, the effect of which is similar to that of reduction and roll speed (Figure 9.68). 9.5.6 Summary of Effect of Hot Lubrication

In view of the regime maps plotted above, applying hot lubrication for the purpose of reducing the COF seems to be most effective when:

• • •

The feedstock surface temperature is low. The secondary oxide scale is thin (assuming no primary scale inﬂuence). The contact time in the roll bite is large, which can be generated by either: – Heavy draft at constant roll radius and constant roll speed, or – Low roll speed at constant roll radius and constant draft.

9.6 Laboratory and Industrial Measurements and Validation Coefficient of friction

Coefficient of friction 0.58

0.58

0.51

0.51

0.45

0.45

ωroll=20 rad/s ωroll=0.5 rad/s

0.45

0.45

0.32

0.32

0.26

0.26 0.19

0.19 20

40

20

60

40

t

t

lubr (5 g/min, 800 °C) dry (800 °C)

lubr (5 g/min, 800 °C) dry (800 °C)

60

Figure 9.68 The effect of roll speed (0.5 and 20 rad/s) on COF under lubrication; Rroll = 152 mm, Ra = 1. 5 μm, draft = 3 mm [57].

This simpliﬁed and somewhat semiempirical approach could be further extended to analyze the combined effect of two or more factors, using for instance quadratic optimization and studying the various surface response generated. As a direct utilization of these results, new thermomechanical processing conditions can be drawn up, with a more efﬁcient use of lubrication, leading to reduced cost and power consumption.

9.6 Laboratory and Industrial Measurements and Validation 9.6.1 Typical Laboratory Experimental Procedure

In order to support the development of the friction model of Equation (9.43), a series of laboratory trials using typical bar rolling pass sequences (square/diamond/ square, square/oval/round, etc.) and also ﬂat passes were carried out on a two-high mill stand (Figure 9.69). Although this section is speciﬁc in supporting the formulation of the Coulomb–Norton model, the approach is universal and common across many research groups for developing a more physical understanding of the effect of processing conditions on friction. It sets out a typical Level II approach or methodology (see Section 9.1) for deriving friction insight. A minimum level of instrumentation is required in order to study the inﬂuence of processing conditions on roll bite tribology as well as back-deriving a friction coefﬁcient. The mill stand in Figure 9.69 was equipped with transducers and data recording equipment to measure and record the following parameters:

343

344

9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input

Figure 9.69

A typical two-high mill stand for long product rolling [55].

•

top and bottom spindle torque, using an FM radio telemetry system connected to a strain gage in Wheatstone bridge conﬁguration;

• •

drive side and open side load, using two 100 tonne capacity load cells; roll speed, using an incremental shaft encoder mechanically ﬁxed to the roll end.

•

stock velocity, using a laser surface velocimeter and/or HMD detectors positioned at the exit bite. The laser-emitting head has to be positioned such that the laser is focused on a point just at the exit side of the roll pass in question. This measurement is important in assessing the amount of forward slip. Care should be taken when rolling with the presence of lubricant, which can cause ﬂames with the laser beam during the burning process, with the consequence of loss of signals. This drawback can be overcome by moving the focusing spot a little distance away from the roll gap or by hot metal detection (HMD). In the HMD method, two hot metal detectors are used, one situated as close as possible to the exit of the roll gap, another one at an offset distance of up to 300 mm. Using the time delay of these two signals and geometrical arrangement, the exit speed of the stock can be measured and the forward slip rate evaluated. Experience suggests that HMD method accuracy is about 6%, compared with less than 1% for the laser velocimeter; and

•

roll displacement at center and both edges of the roll using three noncontacting displacement transducers (working range 0–6 mm) whose output voltage is proportional to the distance from the roll.

A typical speed measurement is shown in Figure 9.70.

9.6 Laboratory and Industrial Measurements and Validation

speed (m/min)

7.50E+01 7.00E+01 Bar 31

6.50E+01 6.00E+01 5.50E+01 5.00E+01 0.35

0.4

0.45

0.5

0.55

0.6

0.65

Rolling time (s)

Forward slip

Figure 9.70

Typical exit speed time history plot for bar rolling in the mill of Figure 9.69.

0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0

unlubricated lubricated

0

Figure 9.71

1

2

3 4 Case number

5

6

7

Typical forward slip obtained in a series of trials for the hot ﬂat rolling of steel.

Two parts can be identiﬁed on this curve. The ﬁrst part is almost a plateau, where the speed is constant, corresponding to the steady-state rolling conditions. In the second part, the bar accelerates as it leaves the roll bite. The steady-state exit stock speed can be used to calculate the forward slip rate. Using Equation (9.33) and exit speed history plots, typical forward slip data between 4% and 8% can be obtained, as shown in Figure 9.71. A range of ultralow carbon (ULC), low carbon (LC), low carbon, free-machining steel (LCFCS), and high-carbon (HC) steel bars, typically 52 mm square × 350 mm length, were reheated/soaked to 1000 °C and 1200 °C in a laboratory gas furnace. Cast compositions are shown in Table 9.3. Hot rolling was performed with a combination of lubricated and nonlubricated passes. Hot lubrication using a Houghton-Roll KL4 lubricant [123] was applied, via a pressurized tank unit, as an oil mist through atomizing nozzles on to both top and bottom work rolls. From furnace discharge, the primary oxide scale layer was removed manually in the absence of a HPW descaling procedure. It was observed that in the case of rolling with primary scale, the lubrication lost most

345

346

9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input Table 9.3 Typical cast composition.

(Wt%)

C

Si

Mn

HC LC ULC LFCS

0.7 0.16 0.004 0.07

<0.3 0.2

0.60 0.77 0.04 1.1

P

S

0.298

Cr

Mo

Ni

Al

N

0.13

0.06

0.2 0.18

0.034

0.01

<0.1

Pb

0.3

20% 15%

B6-1200 deg C-NL

B8-1200 deg C-L

B2-1000 deg C-NL

B3-1000 deg C-L

10% 5% 0% –5% Rolling time (s) Figure 9.72

Measured forward slip for a ﬂat pass, 23% reduction, L/hm = 1.4.

of its beneﬁcial effect. During rolling, side guides were used to guide the bar into the pass groove. Various bar type and ﬂat rolling schedules were imposed, with reductions ranging from 11% to 33%, in order to achieve an envelope of L/hm ratios. Typical reductions aimed at high L/hm were 36% for ﬂat pass, 30% for a square-diamond pass, 37% for diamond-square, 33% for square-oval, and 30% for oval-round. The time between primary descaling and rolling was recorded in order to control the thickness of the secondary oxide scale growth. Using the laser velocimeter and/or HMD, forward slip was measured for each bar, as shown in Figure 9.72. It was found that greater forward slip was measured under unlubricated conditions with neutral point/zones typically at 6° to 7° from the exit plane. The friction coefﬁcient could be derived by simple application of the equation for skidding: μ=

T P ×R

(9.47)

However when forward slip becomes signiﬁcant, Roberts’ technique for inferring the COF [66] should be used, although there is uncertainty regarding its accuracy. The COF can be back-calculated according to the following equation: μ=

T F × Rr × ⎛ 1 − ⎝

2 × S f × h1 ⎞ h0 − h1 ⎠

(9.48)

9.6 Laboratory and Industrial Measurements and Validation

where μ is the COF, T torque, F RSF, Rr roll radius, Sf is the forward slip as deﬁned by Equation (9.34), h0 initial stock thickness, and h1 ﬁnal stock thickness. A summary of a series of laboratory experiments is presented here covering inﬂuence of reduction (L/hm), oxide scale thickness, and lubrication on RSF and torque. Back-derivation of COF according to either Equation (9.47) or (9.48) is also reported. No correlation with wear was made in view of the low tonnage rolling and the rolling mill used. For studying friction- and wear-related effects, a pilot mill equipped with coiler/downcoiler for either ﬂat or rod should be used. Such facilities exist at Corus IJmuiden [129], CRM [130], and Freiberg University [131] to mention a few. 9.6.1.1 The Effect of Contact Force and L/hm Ratio on COF In order to assess the effect of the contact force on COF, for each of the grade shown in Table 9.3, three different reductions were investigated. Figure 9.73 shows back-calculated COF for the LC grade rolled at 1000 °C with a secondary oxide scale about 40 μm thick. The conclusion that COF was directly dependent on the contact force was used in developing the mathematical friction model. 9.6.1.2 The Effect of Scale Thickness on Friction According to [108], the effect of scale thickness seems to overcome that of the scale bulk composition at least for a given thickness threshold. Our trial results showed that a thicker oxide scale lowers the COF, acting as a lubricant at least in the ductile regime of the scale behavior that was investigated (Figure 9.74). This is in agreement with work from Luong and Heijkoop [114]. When lubrication was used, the positive effect of decreasing the COF was more obvious for thin scale rather than thick one (see also Section 9.5, Figure 9.54). 9.6.1.3 The Effect of Lubrication on Friction The experiments presented below did not study the interaction between roll cooling and hot lubrication, as will be expected in normal industrial rolling

0.4 32% (0.7-B134_15_1) 13% (1.2-B136_17_1) 8.8% (1.5-B138_19_1)

0.35

COF*

0.3 0.25 0.2 0.15 0.1

Rolling time (s)

Figure 9.73 The effect of reduction in the normalized COF for a low-carbon steel, ﬂat pass, with L/hm in the range 0.66–1.4. Rolling temperature of 1050 °C.

347

9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input

0.38

27microns (B81) 45microns (B82)

COF*

0.33

75microns (B106)

0.28 0.23 0.18 Rolling time (s)

Figure 9.74 The effect of scale thickness on the normalized COF for LFCS steel in a hot ﬂat rolling pass, 33% reduction, reheating temperature of 1150 °C.

0.35 0.30 0.25 COF*

348

0.20 0.15 0.10

r=37% L/hm=1.66 NL (B113_1)

0.05

r=37% L/hm=1.66 L (B112_1) r=11% L/hm=0.77 NL (B110_1) r=11% L/hm=0.77 L (B111_1)

0.00

Rolling time (s)

Figure 9.75 The effect of lubrication on the normalized COF for different hm/L ratios. Low-carbon steel, 1150 °C.

conditions. Hot lubrication using a Houghton-Roll KL4 lubricant [121] was applied via a pressurized tank unit as an oil mist through atomizing nozzles onto the top and bottom work rolls.

•

Combined inﬂuence of lubrication and L/hm ratio.

The effect of lubrication on friction for different L/hm ratios is presented in Figure 9.75 for a typical ﬂat pass using LC steel (Table 9.3). The conclusion was that lubrication leads to a decrease in COF for high values of L/hm ratios. This means that lubrication is more efﬁcient for larger reductions. A typical threshold observed was above 25% reduction, with beneﬁts decreasing as temperature increased. According to Briscoe et al. [126, 127], the shear strength of the boundary layer will increase with increasing contact pressure. As larger reduction is characterized

9.6 Laboratory and Industrial Measurements and Validation

by larger pressure, a stronger lubricant boundary layer will be formed and better lubrication will result. So the larger the reduction, the more signiﬁcant is the role of lubrication, especially at lower temperatures where the oxide scale may become brittle. The lubricant can play a positive role in reducing friction at the interface between the roll and the top layer of the oxide scale, in contrast to ductile oxide scale, where a decrease in frictional force is attributed to intrascale shearing instead. This effect is again emphasized in Figures 9.76 and 9.77 for a reduction of 33%.

2.50E+01 2 per. Mov. Avg. (Lubricated, reduction 33%, bar 4.) Roll separation force (tonne)

2.00E+01

2 per. Mov. Avg. (No lubrication, reduction 33%, bar 3.)

1.50E+01

1.00E+01

5.00E+00

0.00E+00 0

0.2

0.4

0.6

0.8

1

1.2

-5.00E+00 Rolling time (s)

Figure 9.76 The temperature normalized RSF for rolling with and without lubrication (ﬂat rolling pass, low-carbon steel, rolling temperature of 1000 °C).

6000

no lubrication, reduction 33%,bar 3. no lubrication, reduction 25%,bar 19. lubricated, reduction 25%,bar 21. lubricated,reduction 33%, bar 4.

5000

Torque (Nm)

4000

3000

2000

1000

0 0.15

0.25

0.35

0.45

0.55

0.65

Rolling time (s)

Figure 9.77 The temperature normalized torque for different reductions with and without lubrication (ﬂat rolling pass, low-carbon steel, rolling temperature of 1000 °C).

349

9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input

Further veriﬁcation of this effect is shown next by prerolling bars through a series of square-diamond-square passes to allow for descaling of primary oxide scale (in view of the absence of HPW descaling in our tests). Lubrication (on-off) was then applied in a subsequent pass where bars were rolled with an L/hm value of 1.12. The results of load and torque are plotted in Figures 9.78 and 9.79, respectively. The hot lubrication reduces RSF and torque by about 20%. Therefore, following efﬁcient primary descaling and a regime where secondary scale thickness

Roll separating force (tonne)

4500 no lubrication, 850 degree lubricated, 850 degree.

4000 3500 3000 2500 2000 1500 1000 500 0 0.15

0.25

0.35

0.45

0.55

0.65

0.75

0.85

0.95

Time (s)

Figure 9.78 Roll separation force (RSF) results for bar rolling with low-carbon steel and a lubricant ﬂow rate of 1 g/min.

4500

no lubrication, 850 degree

4000

lubricated, 850 degree.

3500 Torque (Nm)

350

3000 2500 2000 1500 1000 500 0 0.15

0.35

0.55

0.75

0.95

Time (s)

Figure 9.79 1 g/min.

Torque results for bar rolling with low-carbon steel and a lubricant ﬂow rate of

9.6 Laboratory and Industrial Measurements and Validation The effect of lubrication and scale thickness on COF (HC, T_reh = 1250 °C, 33% red) 0.60 0.070 mm, NL (B134_15) 0.096 mm, NL (B135_16)

0.55

0.068 mm, L (B136_17) 0.071 mm, L (B137_18)

COF*

0.50 0.45 0.40 0.35 0.30 Rolling time (s)

Figure 9.80 The effect of lubrication on the normalized COF for different scale thicknesses for high-carbon steel, ﬂat pass, 1050 °C rolling temperature, 33% reduction.

is controlled to stay below 40 μm, hot lubrication at L/hm greater than 1 will have a positive effect in reducing loading, torque, and power. In terms of engagement, at a high reduction of 33%, lubrication will inﬂuence engagement of the bar or require a lower bite angle. This suggests that the classical relation of predicting the COF for engagement as a function only of draft and roll radius must be enhanced with lubrication and temperature components.

•

Combined inﬂuence of lubrication and secondary oxide scale thickness.

Complementary to Figure 9.74, a thick secondary oxide scale seems to mask the inﬂuence of lubrication, as shown in Figure 9.80. Our trial results showed that a thicker oxide scale lowers the COF, acting as a lubricant, at least in the ductile regime of the scale behavior that was investigated. It also shows that the COF is sensitive to the steel grade with the HC steel showing a greater COF than the LFCS steel. This will inﬂuence the spread during rolling.

•

Effect of lubricant ﬂow rate.

In this section, results are presented regarding the effect of lubrication ﬂow rate on the hot rolling process using the lubrication and application system described above (atomized system with Houghton-Roll KL4 neat oil-based lubricant). Three ﬂow rates, 1, 10, and 20 g/min, were chosen to study the effect of ﬂow rate on RSF and torque. The load and torque results are presented in Figures 9.81 and 9.82. The main objective behind this series of tests was to assess interaction between heat transfer and roll bite bearing and lubricity efﬁciency, as well as economics of operation. The effect of lubricant formulation via kinematic viscosity, saponiﬁcation index, or acid number was not studied. It was found that the highest ﬂow rate of 20 g/min produced the lowest RSF. A ﬂow rate of 10 g/min produced the highest

351

Roll separation force (tonne)

9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input

2.50E+01 20 g/min, bar 50.

2.00E+01

10 g/min, bar 49. 2 per. Mov. Avg. (1 g/min, bar 4.)

1.50E+01 1.00E+01 5.00E+00 0.00E+00 0

0.2

0.4

0.6

0.8

1

1.2

-5.00E+00

Rolling time (s) Figure 9.81 The temperature-normalized RSF for different ﬂow rates for ﬂat rolling of low-carbon steel with 33% reduction.

7000 6000

20 g/min, bar 50. 1 g/min, bar 4.

5000

Torque (Nm)

352

10 g/min, bar 49.

4000 3000 2000 1000 0 -1000

0

0.2

0.4

0.6

0.8

1

1.2

Rolling time (s) Figure 9.82 The temperature-normalized torque for different ﬂow rates for ﬂat rolling of low-carbon steel with 33% reduction.

load with the minimum ﬂow rate of 1 g/min in between, highlighting a nonlinear inﬂuence of ﬂow rate. In Figure 9.82, a ﬂow rate of 1 g/min produced the lowest torque, followed in ascending order by ﬂow rates of 20 and 10 g/min. Taking into account economics of operation, these relatively simple trials show that a ﬂow rate of 1 g/min may be optimum with regard to friction under the conditions studied. In order to relate the oil ﬂow rate with the amount of oil ﬁlm adhering to the roll surface for various application times, a set of measurements was carried out

9.6 Laboratory and Industrial Measurements and Validation Histogram of Oil Coverage for Various Flow Rates 250

g/mm^2

200 150 100 50 0

30 Secs

60 Secs

90 Secs

Time Flow rate 0.7 g/min Flow rate 45 g/min Poly. (Flow rate 2.8 g/min)

Figure 9.83

Flow rate 2.8 g/min Poly. (Flow rate 45 g/min) Poly. (Flow rate 0.7 g/min)

Flow rate 11 g/min Poly. (Flow rate 11 g/min)

The effects of ﬂow rate and time on the oil stuck on the roller surface.

by spraying oil on a speciﬁc roll surface area (100 × 200 mm). The results of these tests are shown in Figure 9.83. A saturation phenomenon starts to take place for 45 g/min after 90 s of continuous spraying. During the present rolling trial, due to the application time and ﬂow rate used, as well as cleaning of the roll surface after each experiment, it is believed that this phenomenon was not achieved. Consequently, the lowest RSF for 20 g/min is thought to be due to the decrease in the interfacial HTC in the roll bite for the thicker lubricant residue ﬁlm. These trials showed that ﬂow rates of 10 and 20 g/min are not beneﬁcial to frictional forces, but give rise to higher torque values. Of 10 and 20 g/min, the lower torque obtained with 20 g/min is thought to be due to the higher stock temperature preserved by a thicker insulation layer. There exists, therefore, a competing effect between the cooling/insulation of the stock and the lubricant ﬁlm residue shearing in the roll bite for high rates of application. In summary, relatively low lubricant ﬂow rate could lead to lower torque, especially for bigger stock sizes, where heat recovery is high and the localized surface cooling in roll bite could be counterbalanced. The trial results and the model predictions for COF show the followings: a)

The COF increases when reduction increases (due to an increase in contact force).

b) The COF decreases when temperature increases (in the range 950–1200 °C). c)

The COF decreases when lubrication is applied (low hm/L). The roll separation force is less affected by the lubrication (approximately 10%) than the torque (about 30%), being highly dependent on temperature and material ﬂow stress.

d) The COF decreases for thick secondary oxide scale (about 80 μm). e)

Lubrication is more effective at low temperatures, that is, 1000 °C, rather than at temperatures around 1200 °C where oxide scale plays a dominant role.

353

9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input

f)

Spread increases for higher temperatures from around 14% (950 °C, 30% reduction) to about 16% (1150 °C, 30% reduction). When lubrication is applied for ﬂat rolling in an open pass, spread is slightly reduced. This reinforces the fact that anisotropic conditions of slip/friction exist during rolling due to a competing process between spread and elongation, and this anisotropy will be dependent on hm/L, temperature, ﬂow stress, pass type (open, closed), etc.

g)

Exit velocity decreases when the COF decreases (the neutral point moving toward the exit plane) but the laser beam is very sensitive to ﬂame and smoke, and measurements are therefore prone to scatter. Skidding inside the roll bite occurs frequently, particularly at high temperature and large reductions.

h) When the ratio hm/L < 1, friction and hence lubrication play a signiﬁcant role, as tested during ﬂat rolling. i)

Lubrication proves efﬁcient when: – hm/L < 1; – The contact length is large and stock temperature low (<1100 °C); and – The reduction is high.

9.7 Industrial Validation and Measurements 9.7.1 Beam Rolling Example

Inverse calculation of the evolution of COF through the length of a bar can be carried out for a given rolling schedule, assuming that drafting is known, measurements or estimation by a thermal model of surface temperature are available, and roll force measurements have been obtained. Applying Equation (9.37) of the Coulomb–Norton friction model, the friction coefﬁcient at key positions can be derived for a typical structural beam section at key positions of interest, for instance ﬂange top edge (E), exterior ﬂange (F), and web (W) as shown in Figure 9.84a.

0.55

B A

0.50 Global COF

354

0.45 W front F front E front W end F end E end

0.40 0.35 0.30 0.25 0.20 Stand

Figure 9.84 (a) Structural beam geometry, (b) derived COF for beam rolling at ﬂange top edge (E), exterior ﬂange (F), and web (W) for both front and back end of bar.

9.7 Industrial Validation and Measurements

Due to the thermal gradient alongside the bar’s length, different friction behavior at the front and back ends of the bar is observed. The COF (Figure 9.84b) is a global “mean” friction, with the forces, temperatures, and drafts provided by the rolling schedule. In this case, the highest COF predicted is on the web area (W), due to the highest direct drafting reduction, but also due to the lower temperature developed induced by heat losses through roll gap conductance. The lowest COF is predicted to be on the top of the ﬂange (E), where the contact force is lower, as is the contact time. With the secondary scale buildup toward the end of the bar (hsc ≈ 25 μm, for temperature averaging 1000 °C at a growth time ≈ 20 s), COF is slightly decreased for all the contact surfaces, despite the lower temperature. This example shows interesting avenues for exploiting industrial mill data acquisition as a vehicle for inverse calculation of friction coefﬁcient and, therefore, calibration of the model. In order to improve prediction, additional measurements may be required, such as ﬂange length detection and detailed temperature measurement. 9.7.2 Strip Rolling

From the measurement of forward slip and RSF, the friction coefﬁcient can be estimated according to the friction model selected (see Section 9.1). A good description is given by Martin et al. [19] where the CA, Tresca, and microscopic friction models of Wilson are presented and used to back-derive the friction coefﬁcient and the normal and frictional stress evolution in the roll bite. By analyzing more than 1000 rolled microalloyed as well as plain C–Mn strips, a mean forward slip and RSF from stand to stand during threading was obtained. The method was similar to that of Oda et al. [132]. In addition to these primary data, secondary data such as temperature and strip tension were obtained. Figure 9.85 shows typical normal and friction stresses computed using CA, Tresca, and Wilson models. The position of the neutral zone or point is clearly visible and the general form of each friction hill is similar. The friction shear stress shows more differences between the three friction models with both the CA and Wilson models being dependent on normalized pressure, unlike the Tresca model. The application of the Wilson model gives intermediate results between those of Tresca and CA. A small sticking zone is predicted close to the neutral point with the application of the CA model. Therefore sliding friction dominates the solution. Typical friction coefﬁcients vary between 0.2 to 0.26 with a standard deviation of 0.06 for the ﬁrst rolling stand, which are similar values to the Oda results using high-chromium steel rolls. Application of this type of analysis relies on a good knowledge of the rolling process and on minimizing inaccuracies from the process variability, that is, selecting the best location in the mill where, for instance, forward slip can be measured reliably. This becomes difﬁcult when rolling is performed in an enclosed stand or when the interstand distance is very small and subject to intense cooling. In general, the lower the speed, the better is the accuracy. The analysis also relies on the possibility of separating inﬂuencing variables such as reduction and speed, which may not

355

356

9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input

600

Stress (MPa)

Sample Friction Hill

500 400 300 200 100 0 –100

Angular Coorindate (radians)

–200 0

0.01 0.02 0.03 0.04 AC law normal Tresea Law normal Wilson model normal

0.05

0.06 0.07 0.08 Ac law tangential Tresea Law tangential Wilson model tangential

0.09

Figure 9.85 Normal and tangential stress evolution based on three friction models (AC, Tresca, and Wilson) (according to Martin et al. [19]).

be always the case, mostly when downstream stands are selected. In this case, the work rolls were high-speed steel grades, but no on-line roll surface characterization was available to visualize the work roll degradation; the CLA Ra and mean peakto-peak wavelength for the high-speed steel rolls were just measured before the rolling campaign. This information is required for the initialization of the Wilson model part of the asperity interaction assumptions (Eqs. 9.19 and (9.20)). The method by Martin et al. [19] included the use of a residual function deﬁned as the root mean squared sum of the proportional RSF and forward slip errors between measured and predicted data, which has been used to rank the applicability of the various friction models selected. Outcome of this work show good applicability of both Wilson and AC models. A trend of evolution of friction coefﬁcient during several rolling campaigns is shown in Figure 9.86. As expected, friction coefﬁcient reduces as roll tonnage increases due to the buildup of a roll oxide layer. Figure 9.87 shows a typical correlation plot between friction and rolling speed for the ﬁrst two stands of a ﬁnishing strip mill. It can be seen that more variability occurs for the second stand due to tension and variable speeds to account for reduction changes. 9.7.3 Inverse Analysis Applied to the Evaluation of Friction

Identiﬁcation of friction and rheological parameters during rolling and metal forming in general has shown many advances over recent years. The modern

9.7 Industrial Validation and Measurements

357

Tresca m

0.55 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35

Rolling sequence number

0.35 0.35 0

20

40

60

80

100

120

Figure 9.86 Evolution of Tresca friction factor through a rolling campaign for the ﬁrst rolling stand of a ﬁnishing hot strip mill (according to Martin et al. [19]).

0.30

AC mu

0.28 0.26 0.24 0.22 0.20 0.18 0.16 Rolling speed (m/s)

0.14 0.12 1.2

2.0 1.6 First Stand Second Stand

2.4

2.8

3.2

3.6

Figure 9.87 Apparent correlation between Coulomb–Amonton COF and rolling speed for the ﬁrst two stands of a hot ﬁnishing strip mill, according to Martins et al. [19].

4.0

358

9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input

approach relies on a combination of the application of a model, either analytical or numerical, experimental data/measurements, and objective algorithms with cost or goal functions usually deﬁned as an average square root error between predictions and measurements. A mathematical model of an arbitrary process or physical phenomenon can be described by a set of equations: d = F ( a, p ) ,

F : Rk → Rr

(9.49)

where: d = {d1, … , dr} is a vector of output variables for the process. In the case of roll force and torque, a = {a1, … , al} is a vector of coefﬁcients of the model, p = {p1, … , pk} is a vector of the known process parameters such as roll radius, etc. When both vectors p and a are known, the solution of the problem (9.48) is called a direct solution. The inverse solution of the problem is deﬁned as the determination of the components of the vector a for known vectors d and p. In a problem such as friction, the vector of output parameters d includes RSF and/or torque, as deﬁned by the Roberts equation, for instance, which are measured in a laboratory or production mill. The problem could also be based on laboratory ring compression testing. Vector a includes the unknowns, that is, friction coefﬁcient and additional parameters depending on model, and vector p is composed of process parameters such as roll radius and deformation. The objective of the inverse analysis is to determine the optimum components of vector a, that is, COF. It is achieved by searching for the minimum, with respect to the vector a, of the objective function deﬁned as a square root error between measured and calculated components of the vector d: n

Φ ( x, p ) = ∑ βi [d ic ( x, pi ) − d mi ]

2

(9.50)

i =1

where d mi is a vector containing measured values of output parameters, d ci is a vector containing calculated values of output parameters, βi is the weights of the points (i = 1, … , n), where n is the number of measurements. Measurements d mi are obtained from rolling mill trials or compression tests. Components d ci are calculated using one of the models of the direct problem. A good description of the theory, as well as a range of applications of inverse analysis, can be obtained from [64]. These techniques have been applied as described in Section 9.7.2.

9.8 Conclusions and Way Forward

An important consideration for the manufacturers of rolled steel products is the frictional conditions acting in the roll bite between the deforming feedstock and work rolls, and to what extent existing friction models should be enhanced to consider aspects of oxide scale behavior at high temperature. Another important issue comes from the through-process characterization and inﬂuence of the surface state, which is conditioned by HPW descaling and rolling. As such, this

9.8 Conclusions and Way Forward

chapter can be considered as complementary to the previous chapters describing in detail the behavior of the oxide scale. From an industrial perspective, high-temperature tribology during rolling is a means of ensuring control and stability of the process (e.g., effective engagement, stable roll bite process conditions) as well as meeting ever-increasing demands for dimensional tolerances and surface ﬁnish. An innovative two-step approach has been presented here, drawing parallels to the existing control level strategies. For the regimes where friction plays a signiﬁcant role, that is, where the roll gap shape factor, L/hm > 0.5, the modeling approach is reviewed with recent concepts that take into account microscale knowledge of oxide scale behavior, while implementation and use remains at industrial and research laboratory levels. A friction/shear stress mathematical model has been presented, based on experimental rolling trials and current literature. This model is coded in a usersubroutine of an FE program and can be used to investigate a wide range of processing and tribological conditions, including the effect of hot lubrication, suppressing the need for a ﬁxed Coulomb friction coefﬁcient. The level of friction is derived from the evolution of state variables such as normal force and relative velocity. Good correlation with torque/load and experimental friction coefﬁcient has been obtained. However, further work is required to further assess the value of the βextr coefﬁcient, which is a function of reduction and the widening of the oxide scale cracks. For the steel manufacturer, this model can be utilized to develop regime maps where friction and surface quality need to be optimized. It also pinpoints conditions where hot lubrication can be most effective in multipass hot rolling. By using the current friction model, a series of process as well as product parameters can be studied simultaneously in an FEM. This analytical sensitivity analysis was performed by extracting each variable and assessing its effect upon the COF. In practice, these operational parameters will act in a coupled manner. The present study was aimed at shedding light on the isolated effect of each parameter, helping to highlight the worst circumstance, in which the COF may achieve its highest value, thus showing where remedies such as hot lubrication are needed. The following circumstances give rise to high roll surface roughness:

• • • • •

thin oxide secondary scale; low stock temperature; low slip rate; long contact time; and severe reduction.

The hot rolling operational parameters responsible for the magnitude of friction can be classiﬁed into two groups:

•

Parameters leading to an increase in COF when they themselves increase: – contact force – roll surface roughness – contact time, through 䊊 draft increases, or 䊊 roll radius decreases.

359

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9 Oxide Scale and Through-Process Characterization of Frictional Conditions: Industrial Input

•

Parameters leading to a decrease in COF when they increase: – slip rate – thickness of secondary oxide scale – stock temperature – roll velocity.

By understanding the inﬂuence these parameters exert on COF, new and useful rolling thermomechanical processing conditions can be devised, leading to better control of product surface quality, and a minimization of rolling constraints, such as decreasing power consumption. However, oxide scale behavior and the inﬂuence of its behavior during hot rolling remains a major issue, especially for high alloyed steels where adherent subsurface interfacial scale can be formed, representing a major source of surface defects during rolling. This should be a major thrust of research activity.

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Index a ABAQUS/Explicit ﬁnite element code – anisotropic friction 320 – implementation 334, 335 – mesoscopic variable friction models 308, 309, 314 – pass geometry and side restraints 292–294, 297 – roll gap shape factor 292, 293 – secondary oxide scales 12 – sensitivity and regime maps 323, 324, 331 abrasive oxide scales 10 acid pickling 235, 240, 242, 243 acoustic emission (AE) 137–140 adherence 1 adhesion model – microevents 224–226, 232 – through-process characterization 276, 280–286, 303, 304, 307, 329 AE, see acoustic emission AFM, see atomic force microscopy aluminum – ﬁnite element model 203 – laboratory testing 131, 132 – microevents 225, 255–263 – scale growth 31, 33, 57–62 – secondary oxide scales 8, 14, 15 – subsurface layers 57–62 anisotropic friction laws 279, 319, 320 artiﬁcial intelligence models 275, 276 aspect ratios 72–74, 260 asperities – microevents 226, 252, 253, 256, 259, 260 – numerical interpretation of test results 158 – scale growth 31, 57, 62 – secondary oxide scales 11, 16

– through-process characterization 276, 277, 281–284, 303, 304, 329, 330 atomic force microscopy (AFM) 254

b backscattered electron imaging (BEI) 189, 209 backward slip 62 banding 21, 22 beam rolling validation 354, 355 BEI, see backscattered electron imaging bend testing 130 – four-point-bend testing 46, 47, 135–140, 158–164 – numerical interpretation of test results 171–175 – room temperature 143–146, 171–175 – through-process characterization 233–235, 238–243 bilinear interpolation functions 69, 70 billet reheating temperature 231 biquadratic interpolation functions 69, 70 blistering 23, 24 – ﬁnite element model 189 – laboratory testing 109 – microevents 234–236, 248 – numerical interpretation of test results 151, 171 – scale growth 40 boundary conditions – ﬁnite element model 180, 182, 189, 197 – microevents 229, 230 – numerical interpretation of test results 152 – quantitative characterization 82, 83 – secondary oxide scales 8, 13 box pass rolling 296–299, 334 breakdown rolling 255–263 brittle oxide scales 10, 46, 47

Oxide Scale Behaviour in High Temperature Metal Processing. Michal Krzyzanowski, John H. Beynon, and Didier C.J. Farrugia Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-32518-4

368

Index – – – –

ﬁnite element model 186, 187 laboratory testing 109–111, 113 microevents 208, 227, 231, 232, 240 numerical interpretation of test results 149, 152 – quantitative characterization 92 – through-process characterization 303, 308, 311–314, 339 buckling 23, 233–235 burgers vectors 55, 56, 126 burn-off 337, 338

c CA, see Coulomb–Amonton cantilever bending test 143–146, 171 carbon steels, see high-carbon steels; low-carbon steels center-line average (CLA) roughness 284, 313, 356 chromium alloys – microevents 215, 216, 235–239, 242 – scale growth 33, 59 – through-process characterization 271, 276 churning 261 CLA, see center-line average cobbling 272, 276 cold bend testing 143–146, 171–175 cold rolling 31, 37–40 cold stalling rolling tests 110–112 combined discrete/ﬁnite element models 195–203 comet tails 21, 22 compression testing – ﬁnite element model 193, 194 – hot plane strain testing 127–135, 156–158 – hot tension–compression testing 140–143, 164–171, 193, 194, 212 – microevents 211–215, 233 – scale growth 45 computer-based modeling 1–5 – see also ﬁnite element model; quantitative characterization constrained bend testing 144, 145, 171 contact conductance 16, 17 contact electrical resistance 131–135 continuous cooling 29, 41–44 copper alloys 33, 34, 215, 216, 222, 223 Coulomb–Amonton (CA) friction model – quantitative characterization 69 – secondary oxide scales 9–11 – through-process characterization 276, 279, 280, 284, 285, 290, 295, 308, 314, 315, 334, 355–357

Coulomb–Norton friction model 11, 281, 286, 309, 343, 354 crack closure 209, 230 cracking, see scale failure; through-thickness cracking cross-width deformation 292, 293

d decarburization 30, 271, 305, 306 deformation – ﬁnite element model 195–197, 199–201 – laboratory testing 107, 112–117, 126, 127, 130, 135–146 – microevents 211, 213, 214, 218, 223, 233, 258–261 – numerical interpretation of test results 158, 166, 169 – quantitative characterization 74, 75, 96 – through-process characterization 272, 273, 276, 281, 288–292, 310 delamination – ﬁnite element model 186, 189–191, 199 – laboratory testing 117, 130, 131, 146 – microevents 208, 210, 216–218, 227, 231, 232, 239 – numerical interpretation of test results 151, 174 – quantitative characterization 76–80, 94 – secondary oxide scales 8 – through-process characterization 276 descaling 2, 3, 5 – chilling effects 301–305 – ﬁnite element model 196 – high-pressure water 227–230, 271, 272, 299–304 – laboratory testing 144–146 – long product rolling 288, 291, 292 – mechanical 230–244 – microevents 210, 211, 216, 217, 227–244 – neutral zone forces 299–301, 316 – numerical interpretation of test results 171–175 – pass geometry and side restraints 294–299 – roll gap shape factor 286–293, 296, 305 – scale growth 29, 36, 37, 54 – scale thickness 305, 306 – secondary oxide scales 17–19, 22 – through-process characterization 271, 272, 286–307, 350 diffusion creep 55, 127 discrete/ﬁnite element models 195–203 dislocation climb 55–57, 91, 127 dislocation glide 55

Index dispersoids 31 displacement curves 47–49, 136–140, 153–155, 157, 160–163 drafting 287, 288, 292, 325, 326 ductile oxide scales – ﬁnite element model 187, 188 – laboratory testing 113 – microevents 232 – numerical interpretation of test results 149, 154, 167 – quantitative characterization 80 – scale growth 46, 47 – secondary oxide scales 10, 12, 13 – through-process characterization 303, 308, 311–313, 336, 339

e EBSD, see electron backscattered diffraction elastic shear modulus 49, 50 elastic–plastic with hardening model 71–73 elastic–plastic model – ﬁnite element model 187 – numerical interpretation of test results 158–160, 162, 167 – quantitative characterization 69, 71–73, 82 electrical resistance 131–135 electron backscattered diffraction (EBSD) 34, 102, 189, 209 ELFEN software 198, 199, 202 elongation 115–117 embedded defects 22–24 engagement friction 292 enrichment 30 entry into roll gap – ﬁnite element model 196 – laboratory testing 91–93, 107, 111 – microevents 207, 208, 211, 215, 228, 230, 249, 259–261 – quantitative characterization 89–99 – through-process characterization 289, 297, 299, 305 eutectoid reaction products 30, 41–44 exit from roll gap 207, 208, 211, 290, 312 extrusion – laboratory testing 114, 115, 131, 133, 134 – microevents 208, 209, 211, 214, 215, 226, 230, 245–249 – numerical interpretation of test results 170, 171 – through-process characterization 277, 308, 310, 313, 314

f fayalite layers 35, 41, 223, 302–304 FEM, see ﬁnite element model FIB, see focused ion beam ﬁliform corrosion (FFC) 58–60, 256, 263 ﬁnite element model (FEM) 4, 5, 179–205 – brittle oxide scales 186, 187 – combined discrete approach 195–203 – delamination 186, 189–191 – ductile oxide scales 187, 188 – hot rolling conditions 179–203 – hot tension–compression testing 193, 194 – implementation 334–336 – laboratory testing 146 – microevents 207, 215, 220–222, 232–237, 249–254, 259–263 – multilayered oxide scales 180, 189–191 – multilevel analysis 179–182 – multipass rolling 192–195 – numerical interpretation of test results 149, 156, 161–164, 166, 170–175 – physically based 179–205 – quantitative characterization 67, 68, 73, 80, 84, 91–99, 101–103 – reﬁnements to the mesh 179, 180 – scale failure 182–189 – secondary oxide scales 12 – tensile strain 187, 188, 193 – through-process characterization 276, 277, 286, 288, 292–298, 308, 309, 314, 315, 320–324, 331–336, 339, 359 – viscous sliding 185, 186, 189, 199, 200 ﬂaky scale 21 ﬂow stresses 49–51 focused ion beam (FIB) imaging 60, 258 force–deﬂection curves 136–140, 153–155, 162, 163 forge2005 software 156 forward slip 10, 62 four-point-bend testing 46, 47, 135–140, 158–164 fracture, see scale failure friction 1–3, 5, 6 – anisotropic friction laws 279, 319, 320 – beam rolling 354, 355 – descaling 299–305, 350 – drafting 287, 288, 292, 325, 326 – ﬁnite element model 200 – future developments 358–360 – implementation in FEM 334, 335 – industrial validation and measurements 354–358 – interpass time 327–330 – inverse analysis 356–358

369

370

Index – – – – – –

laboratory testing 131 laws used in industry 278, 279–285 long product rolling 272–274, 288, 308 lubrication 272, 273, 276, 336–343 macroscopic laws 279 mesoscopic variable friction models 308–319 – micro–macro models 332–334 – microevents 207, 208, 213, 229, 251, 252, 259 – microscopic laws 281–287 – neutral zone 298–300, 316, 336 – numerical interpretation of test results 156, 157 – pass geometry and side restraints 294–299 – quantitative characterization 67–69, 71, 72, 92, 96 – roll gap shape factor 287–294, 296, 305, 318, 319, 359 – roll radius/contact time 329 – roll velocity 326, 327 – scale thickness 305, 306, 312–315, 324–328, 347, 348, 350, 351 – secondary oxide scales 7–12, 22 – sensitivity and regime maps 321–332 – strip rolling 355, 356 – surface roughness 283–286, 308–311, 323, 329–332, 356, 359 – through-process characterization 271–366 – tool degradation 320, 321

– microevents 208, 227, 229, 230, 244–250, 252 – quantitative characterization 67, 68, 81–83, 92 – secondary oxide scales 7, 12–17, 19 – through-process characterization 275, 276, 278 hematite layers – microevents 216 – scale growth 29, 30, 32–36, 41, 52 – through-process characterization 300, 301, 304, 306 high turbulence roll cooling (HTRC) 276 high-carbon steels 33, 345, 351 high-pressure water (HPW) descaling 227–230, 271, 272, 300–305 history plots 345 HMD, see hot metal detection hot compression testing 211–215, 233 hot four-point-bend testing 135–140, 158–164 hot lubrication 5, 6, 336–343 hot metal detection (HMD) 344, 346 hot mill pick-up 22 hot plane strain compression testing 127–135, 156–158 hot stalling rolling tests 101, 107–116, 200 hot tension–compression testing 140–143, 164–171, 193, 194, 212 HPW, see high-pressure water HTRC, see high turbulence roll cooling

g i

GDOES, see glow discharge optical emission spectroscopy geometrically induced stresses 231, 315 gibbs energy 225, 226 glow discharge optical emission spectroscopy (GDOES) 59, 61, 256, 257, 276 grain boundaries – ﬁnite element model 185 – laboratory testing 127 – microevents 213 – quantitative characterization 83, 92 – scale growth 30, 32, 33, 55, 58–60 grain size 31, 58–61 grinding defects 259, 260 growth stresses 24, 231

IHTC, see interfacial heat transfer coefﬁcient image quality (IQ) maps 34–36 impact pressure (IP) 301, 302, 305 indentation theory 133, 135, 288, 290 interfacial heat transfer coefﬁcient (IHTC) 244–250, 252 interfacial shear stress model 277, 280 intermediate rate law 33 intermetallics 31, 256 interpass time 327–330 inverse analysis method 161–164, 356–358 inverse pole ﬁgures (IPFs) 35 IP, see impact pressure IQ, see image quality isotropic friction laws 279, 316

h

k

hardness ratios 164 heat transfer 1–3 – ﬁnite element model

key performance indicators (KPIs) 275 kikuchi diffraction patterns 35, 36

189, 200

Index kocks block conﬁguration 272, 273 KPIs, see key performance indicators

l laboratory testing 1–4, 105–148 – cold bend testing 143–146, 171–175 – cold stalling rolling tests 110–112 – contact electrical resistance 131–135 – entry into roll gap 107, 111 – equipment 107, 108, 115–118, 122–124, 127–129, 132–138, 140–145 – ﬁnite element model 179 – hot four-point-bend testing 135–140, 158–164 – hot plane strain compression testing 127–135, 156–158 – hot rolling conditions 105–127, 149–155 – hot stalling rolling tests 107–116 – hot tension–compression testing 140–143, 164–171 – microevents 236–238, 255–263 – multipass rolling tests 112–116 – numerical interpretation of test results 149–177 – quantitative characterization 67, 68, 95, 99–103 – sandwich rolling 105–107 – stress–strain curves 124, 126, 127 – tensile strain 115–127, 140–146, 149–155, 164–171 – through-process characterization 343–354 lacquer simulations 110–112 laser surface velocimeters 344, 346 laser-induced breakup systems (LIBS) 275 LEFM, see linear elastic fracture mechanics Lenard–Jones interaction potential 285 LIBS, see laser-induced breakup systems linear elastic fracture mechanics (LEFM) 84, 92, 184, 185 linear rate law 33, 38, 39, 41 load–displacement curves 47–49, 136–140, 153–155, 157, 160–163 local buckling 233–235 long product rolling 272–274, 288, 308 low-carbon steels – ﬁnite element model 186, 190–192, 197–200 – laboratory testing 105–148 – microevents 214–244 – numerical interpretation of test results 149–177 – scale growth 32, 33, 36, 43, 45, 52 – surface quality/defects 226–230

– through-process characterization 324, 345, 347–352 lubrication 5, 6 – burn-off 337 – ﬁnite element model 196 – ﬂow rates 339, 340, 351–354 – interstand time 340, 341 – microevents 254, 255 – model predictions 353, 354 – numerical interpretation of test results 164 – roll velocity 342, 343 – rolling reduction 341, 342 – scale growth 31 – secondary oxide scales 11, 12, 14, 15 – surface temperature 339, 340 – through-process characterization 272, 273, 276, 336–343 – viscosity 337

m macro ﬁnite element model 179–182, 196, 197, 200, 201, 224, 239, 240 macroscopic laws of friction 279 magnesium alloys 31, 59, 61, 62, 256–258, 262, 263 magnetite layers – microevents 216 – scale growth 29, 30, 32–37, 40–44, 52 – through-process characterization 300, 302, 304, 306 manganese alloys – microevents 215–218, 222–224, 256, 257 – scale growth 31, 34, 59 – through-process characterization 271, 276 MARC ﬁnite element code, see MSC/MARC ﬁnite element code mathematical modeling 1–5 – see also ﬁnite element model; quantitative characterization mechanical descaling 230–244 meso ﬁnite element model 180–182, 196–198, 201, 203 mesoscopic variable friction models 308–319 meteor-like scale 21 microevents – crack development 211–215 – descaling 210, 211, 216, 217, 227–244 – heat transfer 208, 227, 229, 230, 244–250, 252 – hot compression testing 211–215, 233 – hot rolling conditions 207–211, 226–230, 244–263

371

372

Index – scale behavior and composition effects 215–226 – subsurface layers 255–263 – surface quality/defects 226–230 – surface roughness 245, 250–256 – surface scale evolution 207–211 micro–macro models of friction 332–334 micro-plasto-hydrodynamic (MPHL) conditions 284 microscopic laws of friction 279–287 microstructure 4, 5 – ﬁnite element model 179, 195 – laboratory testing 107, 131 – microevents 244 – scale growth 31, 34, 35, 39, 40, 58, 59 model reduction 67 molybdenum alloys 215–218, 223–226 MPHL, see micro-plasto-hydrodynamic MSC/MARC ﬁnite element code 188, 189, 198, 202 – microevents 252–254 – numerical interpretation of test results 152, 164, 166 – quantitative characterization 80, 84, 91–99 multilayered oxide scales – ﬁnite element model 180, 189–191, 196 – microevents 210, 218, 234 – numerical interpretation of test results 151, 152, 171, 174 multilevel analysis 179–182 multipass rolling 192–195

orientation imaging maps (OIM) oxidation rate constants 40, 41 oxidation resistance 34 oxide scale, see scale oxide spallation, see spallation

34, 36

p

neutral zone forces 298–300, 316, 336 nickel alloys 33, 34, 215, 216, 302 nonoxidizing conditions 47 Norton–Hoff law 276, 281 nucleation, preferential 31 numerical interpretation of test results 149–177 – cold bend testing 171–175 – ﬁnite element model 179 – hot four-point-bend testing 158–164 – hot plane strain compression testing 156–158 – hot rolling conditions 149–155 – hot tension–compression testing 164–171 – tensile strain 149–155, 164–171

parabolic rate law 33, 38–41 pareto curves 301 pass geometry 292, 293 PBR, see Pilling–Bedworth ratio perfectly plastic model 71–73 physically based ﬁnite element model, see ﬁnite element model pick-up 22, 142, 143, 191–193, 211 pickling 235, 240, 242, 243 Pilling–Bedworth ratio (PBR) 125, 126, 304 pinning 58, 61, 256, 258 pitting 21, 22, 31 plane strain compression testing 127–135, 156–158 plastic deformation 2 – laboratory testing 130 – microevents 223, 252, 258, 259 – scale growth 45–57 – secondary oxide scales 7, 8, 19, 20 – through-process characterization 282 PLC, see programmable logic controller poisson’s ratio 85, 152, 173, 191 porosity – ﬁnite element model 190 – laboratory testing 125, 126, 130 – microevents 216, 217 – quantitative characterization 78, 79 precipitation, preferential 31 precision sizing blocks (PSB) 272, 273 preferential nucleation 31 preferential precipitation 31 primary oxide scales 7, 18, 19 – growth mechanisms 52–54 – laboratory testing 113 – microevents 223 – through-process characterization 300–306, 308, 339, 345, 346, 350 proeutectoid reaction products 30, 42–44 programmable logic controller (PLC) systems 274 PSB, see precision sizing blocks

o

q

OIM, see orientation imaging maps one-layer zones 15–17 optical microscopy 78, 125, 133

quantitative characterization 1, 3, 4, 67–104 – assumptions of model 91

n

Index – combined computing/laboratory approach 67, 68, 95, 99–103 – entry into roll gap 89–102 – evaluation of technological parameters 69–73 – hot rolling conditions 73–80, 99–103 – scale failure 67–103 – secondary oxide scales 8–13, 15, 16, 18–20 – tensile strain 70–89, 95–99, 101 – thermal and mechanical properties 85 – veriﬁcation of model 99–103

r rankine formulation 197–199 RDF, see redundant deformation factors red scale 21 redundant deformation factors (RDF) 290 regime maps 321–332, 336 roll banding 130 roll bite – laboratory testing 107, 109, 112 – quantitative characterization 70, 71 – secondary oxide scales 8, 11, 14 – through-process characterization 276–279, 281, 286, 290, 300, 311, 312, 317, 320, 334, 337 roll-breaking 244 roll cooling 276 roll gap entry – ﬁnite element model 196 – laboratory testing 100–102, 107, 111 – microevents 207, 208, 211, 215, 228, 230, 249, 259–261 – quantitative characterization 89–99 – through-process characterization 290, 298, 300, 309 roll gap exit 207, 208, 211, 290, 314 roll gap shape factor 286–293, 296, 305, 318, 319, 359 roll grip 182, 210 roll pick-up effect 142, 143, 191–193, 211 roll radius/contact time 329 roll-separating force (RSF) 272–275, 288, 294, 298, 316, 349–358 roll velocity 326, 327, 342, 343 rolled-in-scale defects 22–24 rolling reduction 341, 342 Rotating Crack formulation 197–199 rough-scale areas 39, 40, 42 roughing rolling – scale growth 29, 54 – secondary oxide scales 19, 20, 24

– see also surface roughness RSF, see roll-separating force

s sand-like scale 21 sandwich rolling 105–107 SCADA/SQL systems 274 scale cracking model 20 scale failure 2 – assumptions of model 91, 92 – cold bend testing 143–146, 171–175 – entry into roll gap 89–102 – evaluation of technological parameters 69–73 – ﬁnite element model 182–189, 193–200 – hot four-point-bend testing 139, 140 – hot plane strain compression testing 130–135, 156–158 – hot rolling conditions 73–80, 99–103, 105–107, 110–116, 118–127 – hot tension–compression testing 141–143, 164–171 – laboratory testing 105–107, 110–116, 118–127, 130–135, 139–146 – microevents 207–212, 216–220, 223–229, 231–250 – numerical interpretation of test results 149–158, 164–175 – quantitative characterization 67–103 – scale growth 30, 33 – secondary oxide scales 7, 8, 10–12, 14, 15, 20, 23 – tensile strain 70–89, 95–101, 118–127, 140–146, 150–155, 164–171 – thermal and mechanical properties 85 – through-process characterization 305, 306, 309, 311–315 – veriﬁcation of model 99–103 scale growth 29–57 – aluminum alloys 31, 33, 57–62 – continuous cooling 29, 41–44 – high-temperature oxidation of steel 29, 30, 32–36 – laboratory testing 142 – microevents 231 – oxidation rate constants 40, 41 – plastic deformations 45–57 – short-time oxidation of steel 36–41 – subsurface layers 57–62 – three-layered structure 29, 30, 52 – through-process characterization 337 scale thickness – continuous cooling 29, 41–44 – ﬁnite element model 192, 193

373

374

Index – high-temperature oxidation of steel 29, 33, 34 – laboratory testing 105, 106, 109, 113, 117, 118, 128, 137–139 – microevents 208, 209, 214–218, 220, 231, 235, 236, 248–252 – numerical interpretation of test results 153–155, 166 – plastic deformations 45, 49, 50, 52–54 – quantitative characterization 75, 92–94, 96–99 – secondary oxide scales 10, 11, 14–17, 19–20 – short-time oxidation of steel 36, 37 – through-process characterization 305, 306, 312–315, 324–328, 330–332, 347, 348, 350, 351 scanning electron microscopy (SEM) – ﬁnite element model 183, 184, 187–189, 196 – laboratory testing 143, 145, 146 – microevents 209, 216–218, 233, 237, 261 – numerical interpretation of test results 151, 152, 170, 171, 174, 175 – quantitative characterization 75, 77, 79–81, 101, 102 – scale growth 32, 42 – through-process characterization 276, 303 secondary oxide scales 3, 7–27 – friction 7–12, 22 – growth mechanisms 29–57 – heat transfer 7, 12–17, 19 – microevents 227, 228 – quantitative characterization 68–103 – surface quality/defects 20–24 – thermal evolution in hot rolling 17–20 – through-process characterization 301–305, 309–317, 326–328, 330–332, 337, 351 – tool degradation 21–24 selective oxidation 34 SEM, see scanning electron microscopy sensitivity maps 321–332, 334 separation loads – laboratory testing 119–122 – microevents 223, 224, 228 – numerical interpretation of test results 149, 152, 154, 155 separation stresses 85, 86 shear line ﬁeld indentation theory 288, 289, 291 side restraints 293–299

silicon alloys – microevents 215–218, 222, 223 – scale growth 33–36 – through-process characterization 271, 275 single lens reﬂex (SLR) cameras 145 sliding – ﬁnite element model 185, 186, 189, 199, 200 – laboratory testing 121 – microevents 209, 211–214, 225–227, 240, 244, 259 – numerical interpretation of test results 149, 150, 154, 156, 157, 166, 169, 174 – quantitative characterization 75, 76, 83–85, 88, 92, 95, 102 – secondary oxide scales 8 – through-process characterization 280, 281, 288–298, 309, 310, 316, 317, 322, 323, 331, 332, 336, 345–347 slip line ﬁeld theory 289–296, 298 SLR, see single lens reﬂex smooth-scale areas 42 spallation – ﬁnite element model 184, 195 – laboratory testing 117, 136, 139, 145, 146 – microevents 208, 219, 220, 228, 229, 231–236, 241–244 – numerical interpretation of test results 171, 173, 174 – quantitative characterization 75–79, 84, 88, 89, 93–95 – through-process characterization 303, 306, 307 SPC, see statistical process control speciﬁc water impingement (SWI) 271, 272, 300, 304 spindle-shaped scale 21 stainless steel 215–218, 230–244 stalled rolling tests, see cold stalling rolling tests; hot stalling rolling tests statistical process control (SPC) 275 steady-state deformation 126, 127 steel – ﬁnite element model 186, 189–192, 197–200 – laboratory testing 105–148 – microevents 207–250 – numerical interpretation of test results 149–177 – quantitative characterization 68–103 – scale failure 68–103 – scale growth 29, 30, 32–57 – secondary oxide scales 8, 14–20

Index – surface quality/defects 226–230 – through-process characterization 271–366 stick–slip friction – ﬁnite element model 185 – laboratory testing 156, 157 – microevents 213 – quantitative characterization 83 – scale growth 62 – secondary oxide scales 24 – through-process characterization 280, 281, 286–288, 290–292, 315–318, 321, 336, 355 streak coating 22 stress–displacement curves 47–49, 157 stress intensity factors 85, 87, 166, 172 stress–strain curves 124, 126, 127, 160–162 strip rolling validation 355, 356 subsurface layers 3–5 – ﬁnite element model 196 – microevents 255–263 – scale growth 57–62 – secondary oxide scales 8 – through-process characterization 303 supersaturation 31, 42, 43 surface fracture energy 87, 88, 91, 93, 172, 173 surface quality/defects 1–3 – classiﬁcation 21 – microevents 226–230 – secondary oxide scales 20–24 – through-process characterization 271, 272, 276 surface roughness – microevents 245, 250–256 – through-process characterization 283–286, 313–316, 323, 329–332, 356, 359 SWI, see speciﬁc water impingement

t tabor and Bowden theory 281, 285 tangential viscous sliding, see viscous sliding tensile strain – ﬁnite element model 187, 188, 193 – laboratory testing 45, 115–127, 140–146 – microevents 207, 208, 219–223, 238–245 – numerical interpretation of test results 149–155 – quantitative characterization 70–89, 95–99, 101 – through-process characterization 298–300 tension–compression testing 140–143, 164–171, 193, 194, 212

tertiary oxide scale 36, 37, 155, 303, 304 thermal conductivity 16, 17 thermal evolution in hot rolling 17–20 thermal fatigue 2 thermal history plots 100, 101, 124, 192 thermal stresses 231 three-roll precision sizing blocks 272, 273 through-process characterization 5, 6, 271–366 – anisotropic friction laws 279, 319, 320 – beam rolling 354, 355 – chilling effects 300–303, 319 – descaling 271, 272, 286–308, 350 – drafting 286, 288, 292, 325, 326 – friction laws used in industry 276, 278–286 – future developments 358–360 – hot rolling conditions 271–360 – implementation in FEM 334, 335 – industrial validation and measurements 354–358 – instrumentation and process control 274, 275 – interpass time 327–330 – inverse analysis 356–358 – laboratory testing 343–354 – long product rolling 272–274, 288, 307, 308 – lubrication 272, 273, 276, 336–343 – mesoscopic variable friction models 308–319 – micro–macro models of friction 332–334 – multiscale models 277, 278 – neutral zone forces 294–299, 316, 336 – pass geometry and side restraints 293–299 – processing conditions 273–307 – recent developments in friction modeling 308–336 – roll gap shape factor 286–293, 296, 305, 319, 321, 359 – roll radius/contact time 329 – roll velocity 326, 327 – scale thickness 305, 306, 312, 314, 315, 324–328, 347, 348, 350, 351 – sensitivity and regime maps 321–332 – strip rolling 355, 356 – surface roughness 282–286, 312–317, 323, 329–332, 356, 359 – tool degradation 320, 321 through-thickness cracking – ﬁnite element model 184–188 – laboratory testing 120, 121, 130, 141, 145

375

376

Index – microevents 208–210, 214, 219–223, 227, 232–234, 239–241, 248 – numerical interpretation of test results 149, 150, 152, 157, 158, 165–169, 171–175 – quantitative characterization 80, 83–88, 93–97, 99, 100, 103 – secondary oxide scales 14, 15, 20 – through-process characterization 307 tiger stripes 226, 227 titanium alloys 225, 226 tool degradation – mechanisms 1, 2 – secondary oxide scales 21–24 – through-process characterization 320, 321 transfer bars 29 transmission electron microscopy (TEM) 55, 126 tresca friction model 9, 10, 276, 280, 355–357 trilateral plane strain elements 69, 70 two-layer zones 15–17

– quantitative characterization 83, 85, 88, 92, 96, 103 voids – ﬁnite element model 180, 189 – microevents 234–236, 248 – numerical interpretation of test results 151, 171, 173 – scale growth 32

w wave dispersion spectrometry (WDS) 300 wear, see tool degradation web and ﬂange reduction 293, 295, 316, 355 wedge mechanism 234 wilson model 277, 284, 285, 355, 356 work hardening 54, 55 wüstite layers – scale growth 29, 30, 32–37, 40–44, 52 – through-process characterization 300, 301, 304, 306, 312

x u ultraﬁne graining 31 ultralow carbon (ULC) steels

X-ray diffraction (XRD) 345

v VFRIC subroutine 12, 310, 322 vickers hardness 17, 164, 246, 247 viscoplasticity 281 viscous sliding – ﬁnite element model 185, 186, 189, 199, 200 – microevents 213 – numerical interpretation of test results 149, 150, 174

52, 123, 125

y yield drops 20 Young’s modulus – ﬁnite element model 185, 190 – laboratory testing 140 – numerical interpretation of test results 151, 152, 161, 162, 172, 173 – quantitative characterization 85, 91, 93 – through-process characterization 282

z Zener pinning

58, 61, 256, 258