Handbook of Residual Stress and Steel Deformation

Handbook of Residual Stressand

Deformation of Steel

Edited by

G. TottenM. HowesT. Inoue

Materials Park, Ohio 44073-0002www.asminternational.org

2002 ASM International. All Rights Reserved.Handbook of Residual Stress and Deformation of Steel (#06700G)

www.asminternational.org

Copyright 2002by

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First printing, March 2002

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Prepared under the direction of the ASM International Technical Book Committee (20002001), Sunniva R.Collins, ChairASM International staff who worked on this project included Veronica Flint, Manager of Book Acquisitions;Bonnie Sanders, Manager of Production; Carol Terman, Production Project Manager; and Scott Henry,Assistant Director of Reference Publications.

Library of Congress Cataloging-in-Publication DataHandbook of residual stress and deformation of steel/[edited by] G. Totten, M. Howes, T. Inoue.p. cm.Includes bibliographical references and index.1. SteelFatigueHandbooks, manuals, etc. 2. Residual stressesHandbooks, manuals, etc. I. Totten,George E. II. Howes, Maurice A.H. III. Inoue, Tatsuo, 1939-

TA473 .H3215 2001620.176dc21 2001040042

ISBN: 0-87170-729-2SAN: 204-7586

ASM InternationalMaterials Park, OH 44073-0002


Printed in the United States of America

Multiple copy reprints of individual articles are available from Technical Department, ASM International.



iii

Contributors

I. AlexandruFaculty of MaterialsTechnical University of IasiRomaniaH. BhadeshiaDepartment of Materials Science and

MetallurgyUniversity of Cambridge, UKV. BulanceaFaculty of MaterialsTechnical University of IasiRomaniaV.V. DobrivecherUkraine National Academy of ScienceInstitute of Engineering ThermophysicsKiev, UkraineT. EricssonLinkopings Tekniska Hogskola IKPLinkoping, SwedenF.D. FischerVorstand des Institutes fur MechanikMontanuniversitat LoebenLoeben, GermanyA.V. FominLeading Research ScientistInstitute Russian Academy of SciencesMoscow, RussiaK. FunataniNihon Parkerizing Co. Ltd.Nagoya, JapanBo GongDepartment of Metallurgy & Materials ScienceUniversity of Toronto, CanadaJ. GrumFaculty of Mechanical EngineeringUniversity of Ljubljana, SloveniaA.Y. HassanDirector/Dean, School of Mechanical

EngineeringUniversiti Sains Malaysia, MalaysiaK. HeessKarl Heess GmbHLampertheim, GermanyF.T. HoffmannITW BremenBremen, GermanyR. HoffmannITW BremenBremen, Germany

T. InoueDepartment of Energy Conversion ScienceGraduate School of Energy ScienceKyoto University, JapanD.-Y. JuSaitama Institute of TechnologySaitama, JapanN.I. KobaskoUkraine National Academy of ScienceInstitute of Engineering ThermophysicsKiev, UkraineZ. KolozsvaryS.C. Plasmaterm S.A.Tg-Mures, RomaniaA.I. KovalevSurface Phenomena Research GroupCNIICHERMETMoscow, RussiaJ. KritzlerMetal Improvement Company, Inc.Unna, GermanyK.-H. LangInstitut fuf Werkstoffkunde 1Universitat Karlsruhe (TH), GermanyR.W. LewisDepartment of Mechanical EngineeringUniversity College of Swansea, UKD. LoheInstitut fuf Werkstoffkunde 1Universitat Karlsruhe (TH), GermanyJ. LuUniversite de Technologie de TroyesTrayes Cedex, FranceT. LubbenITW BremenBremen, GermanyM.V. MedvedevResearch ScientistInstitute Russian Academy of SciencesMoscow, RussiaV.P. MishinaSurface Phenomena Research GroupCNIICHERMETMoscow, RussiaV.S. MorganyukUkraine National Academy of ScienceInstitute of Engineering ThermophysicsKiev, Ukraine

M. NarazakiUtsunomiya UniversityTochigi, JapanJ. PanSchool of Materials Science and EngineeringShanghai Jiao Tong UniversityShanghai, P.R. ChinaP. RamakrishnanDepartment of Metallurgical Engineering and

Materials ScienceIndian Institute of TechnologyBombay, IndiaI.A. RazumovskyLeading Research ScientistInstitute Russian Academy of SciencesMoscow, RussiaT. RetiBanki Donat PolytechnicBudapest, HungaryC. RuudPennsylvania State UniversityUniversity Park, PA USAG. SchleinzerVorstand des Institutes fur MechanikMontanuniversitat LeobenLeoben, GermanyB. ScholtesInstitut fur WerkstofftechnikUniversitat Kassel, GermanyK.N. SeetharamuSchool of Mechanical EngineeringUniversiti Sains Malaysia, MalayasiaG.E. TottenG.E. Totten & Associates Inc.Stony Point, NY USAO.VohringerInstitut fuf Werkstoffkunde 1Universitat Karlsruhe (TH), GermanyD.L. WainsteinSurface Phenomena Research GroupCNIICHERMETMoscow, RussiaH.W. WaltonConsultantForest City, NC USAZ. WangDepartment of Metallurgy & Materials ScienceUniversity of Toronto, Canada



iv

G.M. WebsterUnion Carbide CorporationTarrytown, NY USAW. WubbenhorstMetal Improvement Company, Inc.Unna, Germany

V.V. ZabilskyPhysical Technical Institute, Ural Branch of

RASIjevsk, Russia

W. ZinnInstitut fur WerkstofftechnikUniversitat Kassel, Germany



vContents

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi

Effect of Materials and Processing

Material Factors .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3H.K.D.H. Bhadeshia

Prestress Engineering of Structural Material:A Global Design Approach to the Residual Stress Problem ... . . . . . . .11

J. Lu

Residual Stresses and Fatigue Behavior .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27D. Lohe, K.-H. Lang, and O. Vohringer

Stability of Residual Stresses .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54D. Lohe and O. Vohringer

Effect of Residual Stress on Hydrogen Embrittlementand Stress Corrosion Cracking.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .70

A.I. Kovalev, V.P. Mishina, D.L. Wainstein, and V.V. Zabilsky

Measurement and Prediction of Residual Stress and Distortion

Deflection Methods to Estimate Residual Stress .. . . . . . . . . . . . . . . . . . . . . . . . . .89H. Walton

Measurement of Residual Stresses .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .99C. Ruud

Stress Determination in Coatings.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118J.Albert Sue and Gary S. Schajer

Methods for Determination of Inhomogeneous ResidualStress Fields .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

I.A. Razumovsky, M.V. Medvedev, and A.V. Fomin

Residual Stress Formation in the Shaping of Materials

Residual Stress in the Forming of Materials.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141Z. Wang and B. Gong

The Effect of Final Shaping Prior to Heat Treatment .. . . . . . . . . . . . . . . . . . 150T. Ericsson

Factors Affecting Final Part Shaping .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159P. Jiansheng

Effects of Process Equipment Design.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183F.T. Hoffmann, T. Lubben, R. Hoffmann, and K. Hee

Residual Stress During Hardening Processes

Residual Stresses in Carburized, Carbonitrided,and Case-Hardened Components .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

T. Reti

Residual Stresses in Nitriding.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209Z. Kolozsvary

Induction Hardening.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220J. Grum

Hardening by Reheating and Quenching .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248M. Narazaki, G.E. Totten, and G.M. Webster

Metallo-Thermo-MechanicsApplication to Quenching.. . . . . . . . . . . . . . . 296T. Inoue

Control of Residual Stress Formation and Steel Deformationduring Rapid Heating and Cooling.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312

N.I. Kobasko, V.S. Morganyuk and V.V. Dobrivecher

Effect of Cryogenic Cooling on Residual Stresses, Structure,and Substructure .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331

Ioan Alexandru and Vasile Bulancea

Inducing Compressive Stresses through Controlled Shot Peening .. . . 345J. Kritzler and W. Wubbenhorst

Residual Stress Formation During Manufacturing Processes

Residual Stress Formation during Casting .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361R.W. Lewis, K.N. Seetharamu and A.Y. Hassan

Residual Stress Formation during Casting:Continuous and Centrifugal Casting Processes.. . . . . . . . . . . . . . . . . . . . . . . 372

D.-Y. Ju

Residual Stress Formation Processes during Welding and Joining.. . . 391W. Zinn and B. Scholtes

Residual Stresses in Powder-Metal Processing.. . . . . . . . . . . . . . . . . . . . . . . . . . 397P. Ramakrishnan

Residual Stress Formation and Distortion of Rail Steel. . . . . . . . . . . . . . . . . 424F.D. Fischer and G. Schleinzer

Residual Stresses during Gear Manufacture .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437K. Funatani

Metric Conversion Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465



vi

Preface

Control of steel deformation is one of the mostcommon concerns within the metals processingindustry. Numerous surveys have been con-ducted by various organizations in recent yearsto assess the critical needs of the industry. Innearly every survey that has been conducted, dis-tortion is either the greatest or second greatestconcern among the steel heat treating commu-nity. Steel distortion control will exhibit tremen-dous effects on the profitability of the commer-cial enterprise. Therefore, it is not surprising thatthe ability to understand the overall distortionprocess and to be able to design solutions to thisproblem typically rank very high on these samesurveys.

In view of the enormous visibility and impor-tance of steel deformation problems, the editorsdecided to put together an engineering handbookon steel deformation. To address this subjectproperly, contributing factors to overall steel de-formation problems, including material effects,machining, heating and cooling, must be exam-ined.

This handbook contains 27 articles, dividedinto five sections: Effect of Materials and Pro-cessing, Measurement and Prediction of Resid-ual Stress and Distortion, Residual Stress For-mation in the Shaping of Materials, ResidualStress During Hardening Processes, and Resid-ual Stress Formation During Manufacturing Pro-cesses.

There are five articles in the section Effect ofMaterials and Processing. Material Factorsdiscusses the effects of various material proper-ties such as thermal properties and the interac-tions of residual stresses on the transformationproducts formed and steel deformation duringfabrication. Transformation plasticity is dis-cussed in some detail along with the use of mod-eling to better understand these processes.

Prestress Engineering of Structural Materialprovides a global design approach to understand-ing the effects of residual stress generated duringsurface engineering manufacturing processessuch as PVD and CVD on the material propertiesobtained. Some of the topics discussed in thischapter include developments in the measure-ments of residual stresses, advanced mechanicalsurface treatments, and modeling of fatigue be-havior taking residual stresses into considera-tion.

The effect of residual stresses on fatigue be-havior is discussed in detail in the next article.Examples of topics discussed include stability ofresidual stresses, some aspects of fatigue in

steels, influence of residual stresses on cyclic de-formation behavior, influence of residual stresseson crack initiation and propagation, and effect ofresidual stresses on S-N curves; an overview ofmodeling of the effect of residual stresses on fa-tigue behavior is provided.

The next article provides an overview of thestability and relaxation behavior of macro andmicro residual stresses in steel due to thermaland mechanical treatments. This discussion in-cludes relaxation of residual stresses by anneal-ing, residual stress relaxation by uniaxial defor-mation, and relaxation by cyclic deformation.

Hydrogen embrittlement of metals, as well asother types of brittle fracture, result from nucle-ation and development of micro-cracks causedby internal stresses. The last article in this sec-tion provides an overview of the effect of resid-ual stress on hydrogen embrittlement and stresscorrosion cracking (SCC) of steel. This discus-sion includes the effect of hydrogen on structureand transformation of steel, types of hydrogenembrittlement, delayed fracture in steel, crackinitiation and growth, SCC of low alloy steels,crack initiation and growth mechanism of SCCprocesses, methods of estimating sensitivity toSCC, effect of alloying elements on resistanceto SCC, and the role of structure and thermalprocessing in SCC.

In the section Measurement and Prediction ofResidual Stress and Distortion, the first articledescribes a number of simple, inexpensive de-flection (dissection) methods used to estimate re-sidual stress of various types of components. Themethods include Almen strip; Navy C-Ring;plate or bar slitting and deflection; tube slittingand opening; and bending of bars, H-beams, andchannels.

The next article provides an overview of re-sidual stress measurement methods. Topics in-clude residual stresses arising from variousmanufacturing processes, measurement methodsincluding strain measuring technique, post-stressrelaxation measurement, sectioning and materialremoval methods. In addition, strain measure-ment methods such as x-ray and neutron diffrac-tion, ultrasonic, birefringent and laser, opticalgages, brittle coatings, Barkhausen noise, andchemical coatings are discussed. Semidestruc-tive methods such as blind hole drilling and ringcoring are discussed.

Measurement of residual stresses in coatingsand thin films is important because their influ-ence on mechanical and physical properties af-fect component service performance. Stress De-

termination in Coatings provides a guide formeasuring residual macrostress in coatings, Spe-cific topics include origin of residual stresses incoatings and residual stress measurement meth-ods including the deflection method, x-ray dif-fraction, and hole-drilling. A comparison ofthese methods is provided.

The last article in this section provides a de-tailed review of methods used to measure andsubsequent data analysis of inhomogeneous re-sidual stress fields. This discussion includes re-sidual stress as an inverse problem of experi-mental mechanics, indicator crack method ofmeasuring residual stress, arbitrary cut-out in-dicator method, and experimental methods andequipment including photoelastic coatingmethod, and optical interferometry. Althoughthis is a relatively rigorous numerical discussion,practical examples also are provided.

Residual Stress Formation in the Shaping ofMaterials contains four articles. The first articlecovers residual stress in the steel forming pro-cesses. The steel forming processes included arecold forming such as wire drawing, and hotforming such as extrusion, rolling, and forging.The effects of residual stresses involved in theseprocesses are reviewed, and specific topics in-clude residual stress in cold metal forming suchas bending of sheet, drawing of wire, rod, andtube, and residual stresses in deep drawn cup,sunk tubes, and radial forging products.

The effect of final shaping prior to heat treat-ment on residual stress formation is discussed inthe next article. The effects of shaping processesincluding grinding, milling, turning, shot peen-ing, and straightening on residual stress are dis-cussed. Also discussed is distortion after finalpart shaping and experimental and computa-tional studies of these processes.

The next article provides a practical overviewof the factors affecting residual stress and dis-tortion during final part shaping. Included arediscussions of influence of component shape onheat treatment distortion, the effect of cross-section size and asymmetry, effect of heat treat-ing procedure and machining process on finalcomponent shape, effect of sequence of heattreating and machining, influence of machiningallowance and stress relieving procedure, influ-ence of residual stresses caused by cutting, meth-ods of manufacturing blanks and effect of origi-nal structure, hot-rolled steels or forgings andeffect of banded segregation and carbide segre-gation, influence of heat treating methods, theeffect of heating including the rules of heating,



vii

quenching and system design, tempering, andequipment and racking.

A more focused, but practical, discussion onthe effect of process equipment design on dis-tortion follows. Subjects that are covered includedistortion generating process equipment, meth-ods that may be used to minimize equipment-related distortion, quench system design, andpress quenching.

Residual Stress During Hardening Processescontains eight articles. The first article providesa detailed discussion on the residual stresses incarburized, carbonitrided, and case-hardenedcomponents. Topics include process considera-tions for carburized and carbonitrided compo-nents, transformations and stress evolution incarburized and case-hardened components, ef-fect of heat treating operations on residual stressdistribution, relationship between residualstresses and properties of carburized parts andmodeling and prediction of residual stress field.

The article on residual stresses in steel nitrid-ing includes a discussion of nitrided layer struc-ture as a function of nitriding process, residualstresses in nitrided layers, influence of residualstresses on fatigue behavior of nitrided steelcomponents, and modeling and prediction of re-sidual stresses in nitrided steel components.

The article on residual stress formation in in-duction hardening processes include an over-view of the induction hardening process andsteels used for this process, magnetic flux con-centrators, conditions in induction heating andquenching of machine parts, residual stress sur-face profiles after induction surface hardening,stress profiles in the machine part in the loadedstate, workpiece distortion in induction surfacehardening, induction surface hardening of gearwheels, fatigue strength of materials, and resid-ual stresses after induction surface hardening andfinish grinding.

The next article provides an overview of re-sidual stresses and distortion resulting from re-heating and quenching. Topics include phasetransformation during heat treating includingsteel transformations, TTT and CCT diagrams,metallurgical crystal structure, estimation of vol-umetric change due to steel transformation uponquenching, cooling of steel with and withoutmetallurgical transformation, tempering, basicdistortion mechanism, relief of residual stresses,material movement due to thermal gradients dur-ing heating and cooling, material, componentand process effects, retained austenite, quenchseverity and uniformity and process design ef-fects on distortion, quench distortion and crack-ing, quenchant selection, measurement and eval-uation of quenching power, estimation of heattransfer coefficient, wetting behavior and non-uniform quenching, surface conditions, andquench process modeling and simulation of re-sidual stress and distortion after quenching.

A detailed approach to modeling and simula-tion of residual stress and distortion applied toquench processing follows. This discussion isbased on a metallo-thermo-mechanics approach,and topics discussed include an overview of

metallo-thermo-mechanics and numerical simu-lation methodology with practical examples.

In the article on the control of residual stressformation and steel deformation during rapidheating and cooling, a particular emphasis is onintensive quenching. This is the first detailed,article-length discussion of this old, but little-known technology in the western world. Topicsinclude mathematical model for calculation ofthermal and stress-strain state, computation ofstress-strain state, possibility of predicting hard-ening cracks, predicting the deformation of bear-ing rings during hardening, thermal stressesformed in carburized steel products due to ex-cessive cooling rates, generalization of compu-tational and experimental results for heating andcooling of parts with different geometries andthermal and physical fundamentals of processingof high-strength materials.

An often contradictory subject is the cryo-genic processing of steels, and the detailed over-view of the effect of cryogenic cooling on resid-ual stress is presented here. Specific topicsinclude role of residual stresses within marten-sitic transformation at cryogenic temperatures,evaluation of residual stresses after cryogeniccooling, influence of cryogenic cooling on resid-ual stresses and dimensional stability of steels,and influence of cryogenic cooling on the struc-ture and substructure of steels.

The practical use of controlled shot peeningto induce compressive residual stresses is de-scribed in detail next. This discussion includes ahistoric overview of shot peening, elementaryprocesses of shot peening, workpiece and ma-terial process parameters, process monitoring,process optimization, x-ray diffraction, and in-dustrial examples.

In Residual Stress Formation During Manu-facturing Processes, the first article includes anextensive discussion of residual stress and de-formation problems arising from the casting pro-cess, and modeling of residual stress formationduring casting. Discussion includes finite ele-ment analysis of heat flow during casting, for-mulation of the elasto-viscoplastic stress model,and deformation of a solidifying material.

The next article describes residual stress for-mation during the casting process, and it in-cludes continuous and centrifugal casting. Top-ics discussed include inelastic behavior andunified constitutive theory of metallic materialin solidification, analytical method of thethermal-mechanical problem for the casting pro-cess, residual stress formation during semicon-tinuous casting, residual stress formation duringcentrifugal casting, and residual stress formationduring strip casting by the twin-roll method.

The origin and assessment of residual stressesduring welding or brazing is discussed next.Welding residual stresses are discussed includ-ing residual stresses due to shrinkage, quench-ing, and phase transformations. Characteristicresidual stress distributions in brazed compo-nents is also discussed.

The article Residual Stresses in PowderMetal Processing is divided into two parts. The

first part describes manufacturing of ferrous P/M parts including powder characteristics, com-paction in rigid dies, isostatic compaction, sin-tering, heat treatment of P/M parts, hot pressing,roll compaction, powder forging, metal injectionmolding, spray forming, warm compaction, andrapid prototyping. The second part discusses re-sidual stresses in P/M processing includingpowder production, compaction of metal pow-ders, sintering of metal powders, pressure sin-tering and hot isostatic pressing, heat treatmentof P/M parts, and microstructural developmentand properties.

Residual Stress Formation and Distortion ofRail Steel covers the cooling process includingthe cooling boundary conditions and heat trans-fer, residual stress state analysis, weight and fric-tionthe rail end problem, experimental results;roller straightening including residual stresses inunused roller-straightened rails, behavior of railsteel under plastic deformation, simulation ofroller straightening; and rails in service includ-ing residual stresses due to welding and residualstress formation in rolling contact.

The last article provides a detailed descriptionof residual stress formation during hypoid gearmanufacture. It includes an overview of residualstress formation in carburized and hardenedwork, profiles and peak magnitudes of residualstresses, measurement methods including theSachs hole-drilling method, x-ray and neutrondiffraction, influence of steel properties on resid-ual stresses, influence of carburizing process pa-rameters on residual stress formation, benefits ofresidual stresses on fatigue strength, and the ef-fects of hardness, case depth, intergranular oxi-dation, influence of shot peening, change of re-sidual stresses during fatigue, and distortion ofcarburized and hardened steels.

The preparation of a text of this scope was atremendous task. The editors are deeply indebtedto many colleagues for their patience, support,and assistance; without them this text would nothave been possible. Special thanks go to theASM staff who often labor in the backgroundbut who are vital members of the team. Particu-larly, thanks go to Veronica Flint and Carol Ter-man of ASM International for their help and en-couragement.

Very special thanks go to our families for theirseemingly unending support. Without their un-derstanding and encouragement, this projectwould never have been completed.

George E. Totten, Ph.D., FASMEditor

G.E. Totten & Associates Inc.Stony Point, NY USA

Prof. Maurice A.H. Howes, Ph.D. (Retired)Editor

Worcestershire, EnglandProf. Tatsuo Inoue, Ph.D., FASM

EditorDepartment of Energy Conversion Science

Faculty of Energy ScienceKyoto University

Kyoto, Japan



Material FactorsH.K.D.H. Bhadeshia, University of Cambridge

Stress,strain

Time, temperature

Microstructure

1. Thermal stress

4. Heat of deformation6. Latent

heat 5. Stress-induced

transformation2. Temperature-

dependent phasetransformations

3. Transformationstrain

Fig. 1 The coupling of temperature, stress, and micro-structure. Source: Ref 1

Table 1 Physical properties that affect the development of residual stress in steels

Temperature, C (F)Property Phase(a) 0 (32) 300 (570) 600 (1110) 800 (1470)Elastic modulus, GPa c 200 175 150 124

P 210 193 165 120b 210 193 165 120 200 185 168 . . .

Poisson ratio c 0.291 0.309 0.327 0.345 P 0.280 0.296 0.310 0.325b 0.280 0.296 0.310 0.325 0.280 0.296 0.310 . . .

Thermal expansivity, K1 c 2.1 105 P 1.4 105b 1.4 105 1.3 105

Thermal conductivity, W/m K c 15.0 18.0 21.7 25.1 P 49.0 41.7 34.3 27.0b 49.0 41.7 34.3 27.0 43.1 36.7 30.1 . . .

Specific heat capacity, 106 J/m3 K c 4.15 4.40 4.67 4.90 P 3.78 4.46 5.09 5.74b 3.78 4.46 5.09 5.74 3.76 4.45 5.07 . . .

Yield strength, MPa c 190 110 30 20 P 360 230 140 30b 440 330 140 30 1600 1480 1260 . . .

(a) , P, b, and represent allotriomorphic ferrite, pearlite, bainite, and martensite, respectively. Source: Ref 3

RESIDUAL STRESSES are a consequence ofinteractions among time, temperature, deforma-tion, and microstructure (Fig. 1). Material ormaterial-related characteristics that influence thedevelopment of residual stress include thermalconductivity, heat capacity, thermal expansivity,elastic modulus and Poissons ratio, plasticity,thermodynamics and kinetics of transformations,mechanisms of transformations, and transfor-mation plasticity.

Many general statements can be made aboutthe role of material factors in the evolution ofresidual stress. Spatial variations in temperaturegive rise to nonuniform thermal strains, the ef-fect of which becomes exaggerated when thematerial is elastically stiff and has a high yieldstrength. A large thermal conductivity helps re-duce residual stress by reducing temperature gra-dients (Ref 2). The dissipation or absorption ofheat depends not only on the external environ-ment of the component but also on internallygenerated heatfor example, during adiabaticdeformation or due to the latent heat of transfor-mation. Similarly, the plastic strain distributionin the component depends both on the constitu-tive properties and on how the shape deforma-tions due to phase transformations compensatefor the development of stress.

The fundamental material properties are, ofcourse, temperature dependent. Table 1 illus-trates how several key properties might varywith temperature (Ref 3). Some of these prop-erties, which can to some extent be estimatedquantitatively, are discussed in detail in the sec-

tions that follow; others such as elastic modulusand thermal conductivity still have to be mea-sured for individual alloys.

Heat Capacity

The dominant contribution to specific heat ca-pacity comes from lattice vibrations (phonons),since the majority of free electrons are preventedfrom participation in heat absorption by the Pauliexclusion principle. However, for iron and itsalloys, a further important contribution comesfrom magnetic changes. The net specific heat ca-pacity can therefore be factorized into three com-ponents:

TD lLC {T} C C C T C {T} (Eq 1)P V 1 e P Twhere is the Debye specific heat func-LC {T /T}V Dtion and TD is the Debye temperature. The func-

tion C1 corrects to a specific heat atLC {T /T}V Dconstant pressure. Ce is the electronic specificheat coefficient, and is the component of thelC Pspecific heat capacity due to magnetism. Figure2 illustrates the data for ferrite and austenite inpure iron. Whereas it is well known that ferriteundergoes a paramagnetic to ferromagnetic tran-sition on cooling below 1042.15 K, the magneticproperties of austenite are seen from Fig. 2 to beof some consequence in determining the heat ca-pacity. There are two coexisting electron statesof austenite, one of which is ferromagnetic witha Curie temperature of 1800 K and the other ofwhich is antiferromagnetic with a Neel tempera-ture of 55 to 80 K (Ref 4). The balance betweenthese states changes with temperature, givingrise to corresponding changes in heat capacity.

The data in Fig. 2 are for pure iron, but thereis now sufficient understanding of the compo-nents of heat capacity to enable similar estimatesfor iron alloys, using internationally availablecomputer programs and thermodynamic data-

Handbook of Residual Stress and Deformation of Steel G. Totten, M. Howes, T. Inoue, editors, p3-10 DOI: 10.1361/hrsd2002p003

Copyright 2002 ASM International All rights reserved. www.asminternational.org

4 / Effect of Materials and Processing

V1

V

V

V0

0 300 1800

Volu

me,

cm

3 m

ol

1

Temperature, K600 900 1200 1500

6.6

7.8

8.0

7.6

7.4

7.2

7.0

6.8

Fig. 3 Molar volumes of the various forms of iron.Source: Ref 5

0 300 1800

Hea

t cap

acity

, CP,

J

mol

1K

1

Temperature, K

0

0

25

50

75

600 900 1200 1500

10

20

30

40

Austenite

Ferrite

Austenite

Ferrite

Fig. 2 Specific heat capacities of ferrite and austenite inpure iron, as a function of temperature. The thin

lines represent the combined contributions of the phononsand electrons, whereas the thicker lines also include themagnetic terms. The dashed vertical lines represent the Cu-rie, c, and c d transitions. d-ferrite is simply analternative historical name for high temperature . Source:Ref 5

Allotriomorphicferrite

Widmansttten ferriteCarbon diffusion during

paraequilibrium nucleation and growth

Bainite and acicular ferrite

Carbon diffusion duringparaequilibrium nucleation.No diffusion during growth

MartensiteDiffusionless

nucleation andgrowth

Idiomorphicferrite

Massive ferriteNo change in

bulk composition

PearliteCooperative growth

of ferrite andcementite

ReconstructiveDiffusion of all atoms during

nucleation and growth.Sluggish below about 850 K

DisplaciveInvariant-plane strain shapedeformation with large shear

component. No iron orsubstitutional solute diffusion.

Thin plate shape

Fig. 4 Transformation products of austenite. Source: Ref 12

bases (Ref 6). After all, changes in fundamentalthermodynamic quantities such as enthalpy andentropy are derived from heat capacity data. It issurprising that this capability has not yet beenexploited in any calculation of residual stress,even though the methodology is widely avail-able.

Expansion Coefficient and Density

Table 1 shows that the expansion coefficientof austenite is larger than that of ferrite; thismight be considered surprising given the lowerdensity of ferrite. However, the behavior is again

a reflection of the two coexisting electronicstates of austenite (c0 and c1), each with a ther-mal expansion coefficient that is identical to thatof ferrite. The c0 component has the lower molarvolume and is the antiferromagnetic form,whereas the denser c1 form is ferromagnetic. Therelative proportion of atoms in the c0 and c1states changes with temperature, so that the ap-parent expansion coefficient of austenite as awhole, as detected experimentally, is muchlarger than that of ferrite (Fig. 3).

The molar volumes (in cm3/mol) of c0, c1, c,and over the temperature range of 300 to 1775K are:

c 5 8 20V 6.695(1 2.043 10 T 1.52 10 T )mc 5 8 21V 7.216(1 2.043 10 T 1.52 10 T )m

c c c0 1V {T} (1 y)V {T} y V {T}m m maV {T} m

5 8 27.061(1 2.043 10 T 1.52 10 T )

where y is the fraction of atoms of austenite inthe c1 state, the details of which can be foundelsewhere (Ref 4, 5).

These data are for pure iron, but thermody-namic data can be used to assess how the expan-sion coefficients would change with alloying,since there are quite sophisticated treatments ofthe effect of solute elements on the magnetic andother components of the free energies of iron.Note that the two electronic states picture ofaustenite is a simplification of the real scenario,but first-principles calculations (Ref 7), which

deal with higher levels of complexity, are not yetapplicable to practical alloys.

Plastic Deformation

The familiar mechanisms of plastic deforma-tion are slip, mechanical twinning, and creep.Phase transformations also cause permanent de-formation (Ref 811). In steels, austenite can de-compose into a large variety of microstructuresthat are distinguished by the atomic mechanismof transformation (Fig. 4). In a displacive trans-formation, the change in crystal structure isachieved by a deformation of the parent struc-ture. A reconstructive transformation is one inwhich the change in structure is achieved by aflow of matter, which occurs in such a way thatstrains are minimized.

All the transformations cause changes inshape (Fig. 5a), which for reconstructive trans-formations simply reflects the change in density.For displacive transformations, the shape changeis an invariant-plane strain (IPS), that is, a com-bination of a shear on the invariant plane and adilatation normal to that plane. The strain energyassociated with a constrained IPS is minimizedwhen the product phase has a thin-plate shape.This is why Widmanstatten ferrite, bainite, acic-ular ferrite, and martensite in steels grow in theform of plates. The distinguishing features of avariety of deformation modes are compared inTable 2, and Table 3 describes the shape defor-mations.

The permanent strain caused by any transfor-mation is called transformation plasticity. A

Material Factors / 5

(a)

(b) (c) (d)

Singlecrystal

Reconstructive

Displacive

Fig. 5 Shape changes accompanying unconstrainedtransformations. Note that the horizontal scale

bars are all the same length. (a) The two kinds of shapechanges that occur when a single crystal of austenite trans-forms to a single crystal of ferrite, as a function of the mech-anism of transformation. (b) Polycrystalline sample of aus-tenite. (c) Polycrystalline sample of austenite that haspartially transformed by a displacive transformation mech-anism into a random set of ferrite plates. (d) Polycrystallinesample of austenite that has partially transformed by a dis-placive transformation mechanism into an organized set offerrite plates.

Table 4 Deformation systems associated with transformations

Phase Habit plane indices Displacement vector m

Martensite (0.363 0.854 0.373) [0.195 0.607 0.771] 0.185Bainite (0.325 0.778 0.537) [0.159 0.510 0.845] 0.27Widmanstatten ferrite (0.506 0.452 0.735) 0.414 0.277][0.867 0.36

Note: Typical habit plane and displacement directions for low-alloy steels. The indices all refer to the austenite phase. Note that the indices stated areapproximate, since the habit plane and displacement direction are usually irrational. The displacement vector does not quite lie in the habit planebecause the dilatational strain is directed normal to the habit plane. The magnitude of the displacement is given by m, which is the total displacementincluding the shear and the dilatational components.

Table 3 Shape change due to transformation

Transformation Shape change (a) s(b) d(b) MorphologyAllotriomorphic ferrite Volume change 0.00 0.02 IrregularIdiomorphic ferrite Volume change 0.00 0.02 Equiaxed, facetedPearlite Volume change 0.00 0.03 Spherical coloniesWidmanstatten ferrite Invariant-plane strain 0.36 0.03 Thin platesBainite Invariant-plane strain 0.22 0.03 Thin platesAcicular ferrite Invariant-plane strain 0.22 0.03 Thin platesMartensite Invariant-plane strain 0.24 0.03 Thin platesCementite plates Invariant-plane strain? 0.21? 0.16? Thin platesMechanical twins () Invariant-plane strain 1/ 2 0.00 Thin platesAnnealing twins (c) 0.00 0.00 Faceted

(a) An invariant-plane strain here implies a large shear component as well as a dilatational strain normal to the habit plane. (b) s and d refer to theshear and dilatational strains, respectively. The values stated are approximate and will vary slightly as a function of lattice parameters and the detailsof crystallography.

Table 2 Characteristics of different modes of deformation

CharacteristicSlip

deformationMechanical

twinningDisplacive

transformationReconstructivetransformation

Causes permanent change in shape Yes Yes Yes YesInvariant-plane strain shape changewith a large shear component Yes Yes Yes NoChanges crystallographic orientation No Yes Yes YesChanges lattice type No No Yes YesCan lead to a density change No No Yes Yes

phase change in a stress-free material is usuallytriggered by heat treatment, when the parentphase passes through an equilibrium transfor-mation temperature. Alternatively, the applica-tion of a stress in isothermal conditions can trig-ger transformation in circumstances where itwould not otherwise occur. Unusual effects canoccur when stress and temperature work to-gether. The transformation may occur at remark-ably low stresses or at very small deviationsfrom the equilibrium temperature. This is whyeven minute stresses can greatly influence thedevelopment of microstructure, and vice versa.It is not surprising that transformation plasticitycan be obtained at stresses that are much smallerthan the conventional yield stress of the parentphase.

Transformations, Residual Stresses,and Related Phenomena

The strains due to phase transformations canalter the state of residual stress or strain. It is wellknown that the martensitic transformation of thecarburized surface of a steel component puts thesurface under compression. It is argued that thisis because of the expansion at the surface due toformation of the lower-density martensite fromaustenite.

Phase transformation can also compensate forstress. Greenwood and Johnson (Ref 13, 14)showed that when a phase change is accompa-nied by a change in volume, the tensile strainexpected when transformation occurs under theinfluence of a tensile stress r is given by:

5 DV re (Eq 2)

6 V rY

where rY is the yield stress of the weaker phaseand DV/V is the transformation volume strain.The role of shear strains associated with trans-formation has been emphasized in later work byMagee and Paxton (Ref 15, 16), and subse-quently by Fischer (Ref 17), Leblond et al. (Ref1822), Olson (Ref 23), and Bhadeshia et al.(Ref 24). Not only does transformation affectstress, but the latter modifies the development ofmicrostructure. The microstructure tends to bemore organized when transformation occurs in astresss parent phase, because the stress favorsthe formation of certain orientations relative toothers. This is illustrated schematically in Fig.5(b) to (d). These aspects will now be discussedin more detail, because transformation plasticitycan radically alter the state of residual stress.

Deformation System

Displacive transformations can be regarded asmodes of plastic deformation. Just as a combi-nation of a plane and a direction constitutes adeformation system for slip or twinning, thehabit plane and displacement vector of theinvariant-plane strain accompanying displacivetransformation completely describe the defor-mation system responsible for transformationplasticity. The displacement vector describes thesense of the macroscopic displacements accom-panying transformation and, along with the habitplane indices, also contains information aboutthe magnitude of the shear component and dil-atational component of the displacements. Typ-ical data for the deformation systems associatedwith transformations are listed in Table 4. Notethat reconstructive transformations involve onlya volume change together with diffusional massflow, so it is not appropriate to regard them asdeformation systems in the present context.

Given the cubic crystal structure, and the factthat habit planes tend to be irrational, there willin general be 24 of these systems per austenitegrain, and they may operate simultaneously tovarying extents. Of course, unlike ordinary slip,


Table 6 Sensitivity of transformation-starttemperatures in steels to applied stress

Phase Nature of stress Sensitivity, K/MPa

Martensite Pressure 0.06Bainite Pressure 0.09Eutectoid Pressure 0.011Martensite Tensile 0.06

Source: Ref 32

Chan

ge in

bai

nite

-sta

rt te

mpe

ratu

re

Stress (below austenite yield strength)

0

+

Tensile

Compression

Hydrostaticcompression

Fig. 7 Indication of how the transformation-start tem-perature (for Widmanstatten ferrite, bainite, acic-

ular ferrite, or martensite) should vary as a function of thenature and magnitude of an applied stress whose magni-tude is less than that of the yield stress.

Table 5 Typical values of the mechanicaldriving force coefficients

Nature of stress DG/r, J/(mol MPa)Uniaxial tension 0.86Uniaxial compression 0.58Elastic crack tip (a) 1.42

(a) The stress state for the crack tip is multiaxial, but the coefficient iscalculated by expressing the stress in terms of the von Mises equivalenttensile stress. Source: Ref 32

NA (applied tensile stress)

max

d

Fig. 6 Resolution of the applied stress, rA. The normalstress, rN, and the shear stress, s, both act on the

habit plane. The vector d is the direction along which liethe shear displacements of the shape deformation. smax isthe maximum shear stress on the habit plane, but s is givenby resolving smax along d. Note that d differs slightly fromthe displacement vector of the IPS, which includes a dila-tational component in addition to the shear.

Temperature, C300 800 900

Free

ene

rgy,

J m

ol

700600500400

1000

2000

1000

0 Mechanical

Chemical

Total

Mechanical

Chemical

Total

1

Fig. 8 Typical magnitudes of the chemical and me-chanical driving forces for stress-affected trans-

formation. The mechanical driving force is estimated for anapplied stress that is equal to the yield stress of austenite.Since this yield stress becomes small at high temperatures,the contribution of the mechanical driving force also de-creases. Therefore, transformation becomes impossible asthe temperature exceeds about 700 C (1290 F).

the different deformation systems within an aus-tenite grain cannot intersect, except in specialcircumstances where intervariant transforma-tions are possible, as is the case with someshape-memory alloys. It follows that the ordi-

nary notion of work hardening does not apply.Work hardening nevertheless manifests itself viaa different mechanism, in which the stability ofthe austenite increases as it becomes ever morefinely divided.

The Taylor/von Mises criterion (Ref 25, 26)states that in any given crystal, a minimum offive independent slip systems is necessary toproduce an arbitrary shape change. A crystal ina polycrystalline aggregate has to accommodatethe arbitrary deformations of neighboring grains.Therefore, a polycrystalline material is brittleunless each grain contains at least five indepen-dent slip systems. Similar logic can be appliedto the crystallographic variants of a phase gen-erated by displacive transformation. The habitplane is predicted theoretically (Ref 27, 28) andfound experimentally (Ref 29) to have irrationalindices. This means that there exist, in principle,24 possible variants of the habit plane per grainof austenite (that is, 24 independent deformationsystems). Given this large number of transfor-mation variants available per grain, the Taylorcriterion leads to the conclusion that transfor-mation plasticity can cause, or accommodate,any externally imposed, arbitrary shapechangeassuming that a sufficient quantity ofparent phase is available. It follows that poly-crystalline samples can remain intact at grainboundaries when transformation plasticity is thesole mode of deformation.

Mechanical Driving Force

The interaction of an applied elastic stresswith a phase change can occur in two ways:1. The stress can alter the driving force for the

transformation.2. The stress can change the appearance of the

microstructure by favoring the formation ofthose variants which best comply with the ap-plied stress.

For reconstructive transformations, only thehydrostatic component of stress can interact with

the volume change. The corresponding interac-tion with displacive transformations is muchlarger because of the shear component of theIPS.

For displacive transformations, the influenceof stress on the transformation can be expressedas a mechanical driving force (DGmech), which isthe work done by the external stress in producingthe macroscopic shape deformation (Ref 30, 31):

DG r d ss (Eq 3)mech N

where rN is the normal stress on the habit planeand s is the component of the shear stress on thehabit plane that is parallel to the direction alongwhich the shear displacements of the shape de-formation occur (Fig. 6). The strains d and s arethe dilatational and shear components, respec-tively, of the shape deformation. Some typicalvalues of the mechanical driving force terms aregiven in Table 5. Given a free choice of some12 to 24 crystallographic variants of the trans-formation product in each grain of austenite, thework done by the shear stress is always expectedto be positive, whereas that due to the dilata-tional component depends on the sign of rN. Forsteels, this latter component is relatively small.Any observed consequences of stress must there-fore reflect the dominant role of the shear com-ponent unless the stress is purely hydrostatic.

Since the shear stress remains positive irre-spective of whether the sample is pulled in ten-sion or uniaxially compressed, and since theshear component of the shape change is large, auniaxial stress will always cause a temperatureincrease for displacive transformations in steels.Hydrostatic stress, on the other hand, has no de-viatoric components and consequently interactsonly with the dilatational component of theshape change. Thus, hydrostatic compression isexpected and found to lead to a decrease in thetransformation temperature (Fig. 7); some data(Ref 32) on the sensitivity of the transformationtemperature to applied stress are presented in Ta-ble 6.

Limits to Stress-AssistedTransformation

At temperatures close to that at which theequilibrium transformation occurs, an appliedstress can assist reaction when the chemical driv-ing force is insufficient to achieve the change onits own. There must exist a point, however, whenthe applied stress simply cannot provide enoughmechanical driving force to complement thechemical term to give a driving force largeenough to induce transformation. After all, themagnitude of the stress that can be applied islimited by the yield point of the parent phase.Thus, there are limits to what can be achievedby the application of stress as a stimulus to trans-formation (Fig. 8).


Fig. 10 Distortion caused by welding two plates thatwere originally flat

(a)

(b)

Temperature, C

Temperature

0 200 1400

Stre

ss, M

PaSt

ress

400 600 800

Transformationfinished

Stress due tothermal contraction

of ferrite

Transformationbegins

1000 1200

500

100

400

300

200

100

0

0

AISI 3169CrMo2CrMoAustenite YS

Plasticstrain in

austenite

Stress due tothermal

contractionof austenite

Fig. 9 (a) Plot of residual stress versus temperature fora martensitic (9CrMo), bainitic (2CrMo), and aus-

tenitic steel (AISI 316). Adapted from Ref 33, 34. (b) Inter-pretation of the Jones and Alberry experiments. The thermalexpansion coefficient of austenite is much larger than thatof ferrite.

Transformation time, s

R

L

0 100 600

Bulk

tran

sfor

mat

ion

stra

in, %

200 300 400 500

3

2

1

0

1

275 MPa compressive stress75 MPa compressive stress

Fig. 11 Development of anisotropic transformationstrain when bainite forms under the influence

of a constant, elastic applied compressive stress. Note thatthe shear strain associated with the formation of one plateis about 26%, with a volume change of about 3%. Thepotential for anisotropy is therefore much greater than il-lustrated here.

Table 7 Chemical composition, calculated transformation temperature range (DT ), andmeasured distortion (h) for two manual metal arc, multipass weld deposits

Composition, wt%C Si Mn Ni Mo Cr DT, C(F) h0.06 0.5 0.9 . . . . . . . . . 802400 (1476750) 14.50.06 0.3 1.6 1.7 0.4 0.35 422350 (792660) 8

Source: H.K.D.H. Bhadeshia and L.-E. Svensson, unpublished data, 1994

Transformation under Constraint:Residual Stress

Residual stresses are often introduced unin-tentionally during fabricationfor example,during welding or heat treatment. A few elegantexperiments illustrate how phase transforma-tions interact with the buildup of residual stress.

Using bainitic, martensitic, and stable austen-itic steels, Jones and Alberry (Ref 33, 34) de-mostrated that transformation plasticity duringthe cooling of a uniaxially constrained samplefrom the austenite phase field acts to relieve thebuildup of thermal stress as the sample cools. Bycontrast, the nontransforming austenitic steel ex-hibited a continuous increase in residual stresswith decreasing temperature, as might be ex-pected from the thermal contraction of a con-strained sample.

When the steels were transformed to bainiteor martensite, the transformation strain compen-

sated for any thermal contraction strains thatarose during cooling. Significant residualstresses were therefore found to build up onlyafter transformation was completed and the spec-imens approached ambient temperature (Fig. 9).

The experiments contain other revealing fea-tures. The thermal expansion coefficient of aus-tenite (1.8 106/K) is much larger than thatof ferrite (1.18 106/K), and yet the slope ofthe line prior to transformation is smaller whencompared with that after transformation is com-plete (Fig. 9). This is because the austenite yieldsto accommodate the thermal contraction, whichis possible because the yield strength of the aus-tenite is reduced at elevated temperatures. Ferriteis strong at low temperatures, so the slope of thestress/temperature curve (after transformation iscomplete) is steeper and consistent with the mag-nitude of thermal contraction strains.

Interpretation of experimental data of the kindillustrated in Fig. 9 is difficult in the region ofthe stress/temperature curve where transforma-tion occurs. The popular view that the volumechange due to transformation is the major com-ponent of transformation plasticity is probablyincorrect for displacive transformations such asbainite or martensite. The shape change due totransformation has a shear component that ismuch larger than the dilatational term (Table 3).Admittedly, this shear component should, on av-erage, cancel out in a fine-grained polycrystal-line sample containing plates in many orienta-tions (Fig. 5c). However, the very nature of thestress effect is to favor the formation of selectedvariants, in which case the shear component rap-idly begins to dominate the transformation plas-ticity (Fig. 5d).

The residual stress at ambient temperature islarger when the austenite finishes transformationat a high temperature. This is because thermalcontraction strains can no longer be compen-sated by transformation plasticity once the aus-tenite has decomposed. Low transformation tem-peratures help minimize residual stresses.High-strength welding alloys used for makingsubmarine hulls therefore have transformationtemperatures of less than about 250 C (480 F).

Figure 10 illustrates one kind of distortionfound in welds, measured in terms of the angleh through which the unconstrained plates rotateas they cool. Table 7 shows how the distortiondepends on the temperature at which the major-ity of the transformation is completed, for twomanual metal arc welds deposited with a 60 V-joint preparation in a multipass fabrication in-volving about 11 layers, with two beads per layerto complete the joint. The distortion is clearlylarger for the case where the transformation isexhausted at the higher temperature.

Anisotropic Strain andTransformation Plasticity

When an unstressed polycrystalline sample ofaustenite is transformed to plates of ferrite, theshear caused as each randomly oriented plateforms is canceled on a macroscopic scale; onlythe volume expansion is observed experimen-tally. However, if the plates do not form at ran-domfor example, when certain variants are fa-vored because they comply better with theexternal stressthe shear strains are no longercanceled out. Transformation will then lead tohighly anisotropic strains, as illustrated in Fig.11. Naturally, any anisotropy will be greatest fordisplacive rather than reconstructive transfor-mations, given that the former involve largeshear strains.

Modeling AnisotropicTransformation Strains

Consider a distribution of bainite variantsalong all radial directions in a circle with thecompression axis as its diameter (Ref 35, 36).The circle is divided into 18 equal segments (i 1 18), each segment representing a partic-ular orientation of bainite habit plane. Thechoice of 18 segments is convenient and arbi-trary. The compression axis of the sample istaken to be the z direction, the x and y directions


(a)

90

270240 300

210

180 0

330

60120

150 30

(b)

90

270240 300

210

180 0

330

60120

150 30

Fig. 12 Transformation behavior inherent in the model (Ref 36). The dots illustrate the area fraction of each segment,which in the calculations is scaled according to the value of Ui DGc. (a) Zero stress. All segments have

equal area fraction, and the order in which they transform is irrelevant. (b) Applied stress of 40 MPa and DG c 400 J/mol. The area fractions of the segments are no longer equal. The segments in which the distance of the dot from the originis largest transform first.

being radially orientated; the unit vectors x, y,and z define the orthonormal basis X of the sam-ple, giving a corresponding reciprocal basis X*.The shear and dilatational components of the IPSaccompanying the growth of bainite are approx-imately s 0.22 and d 0.03. Thus, the 3 3 deformation matrix describing the shape de-formation is given by:

1 fse p fdp p1 1 1 1P fse p fdp p2 1 2 1 fse p fdp p3 1 3 1

fse p fdp p1 2 1 21 fse p fdp p2 2 2 2fse p fdp p3 2 3 2

fse p fdp p1 3 1 3fse p fdp p2 3 2 3 1 fse p fdp p3 3 3 3

where p is the unit normal to the habit plane ande is the unit direction along which the shear oc-curs. This can be written more succinctly as:

e p1 1P I fs e (p p p ) fd p (p p p )2 1 2 3 2 1 2 3 e p3 3

where I is a 3 3 identity matrix. A furtherreduction of notation is achieved using theMacKenzie and Bowles notation (Ref 27):(XP X ) I f s[X;e ](p ;X*)i i i i

f d[X;p ](p ;X*) (Eq 4)i i iwhere the subscript i identifies a particular seg-ment of interest and X and X *, respectively, rep-resent the real and reciprocal bases of the coor-dinate system in which the deformation isdescribed. The notation due to MacKenzie andBowles (Ref 27) is discussed in detail in Ref 35.

The components of the shear direction and thedilatation direction are given by:

[X;e ] f [cos(h ) 0 sin(h )]i i i i[X;p ] f [sin(h ) 0 cos(h )]i i i i

where hi represents the orientation of the habitplane of variant i and fi is the volume fraction ofbainite located in segment i.

A unit vector along the z direction changes toa new vector z given by:

18

[X; z] (XP X ) [0 0 1] ii1

whereas a unit vector along x changes to

18

[X;x] (XP X ) [1 0 0] ii1

where (x 1) and (z 1) give the strainsalong the x and z directions. These are assumedto be equal to radial and longitudinal strains eRand eL, respectively.

It is expected that those segments that complybest with the applied stress transform most rap-idly, whereas the others do so at a lower rate, ornot at all. This can to some extent be incorpo-rated into the model by calculating the energychange Ui as the stress interacts with the shapedeformation of a particular variant (i). Patel andCohens method (Ref 30) gives:

rU [s sin 2h cos d(1 cos 2h )]i I i i2

where is the angle between the shear directionand the direction of the shear component of theapplied stress as resolved onto the habit plane.To facilitate a two-dimensional analysis, thevalue of i is taken to be zero. A positive valueof Ui adds to the chemical driving force (DG ac G c G a) for transformation; a negativevalue thus opposes transformation. Using thesevalues of interaction energies, the model can bemodified so that the segments transform in anorder of decreasing Ui. There is, however, a fur-ther complication. The effect of stress should belargest when the interaction energy is large com-pared with the chemical driving force. To allowfor this, the volume fraction fi of each segment

can be scaled according to the value of Ui DG ac.

Note that for the model calculations, the trans-formation occurs with the most favored variantsgrowing first (Fig. 12). The model thus exagger-ates the effect of stress, since in reality, for thesort of stress levels considered experimentally,no variant is likely to be entirely suppressed. Inaddition, the grains in a polycrystalline sampleare randomly oriented, so that perfect compli-ance with the applied stress is impossible. Nev-ertheless, the trends revealed by the model areexpected to be correct.

The experimental data that need explaining,and their interpretation in terms of the model aresummarized in Fig. 13 and may be stated as fol-lows: Without any stress, in a random polycrystal-

line sample, the transformation strains areisotropic. This is easily understood since theshear components of randomly orientedplates tend to cancel out (Fig. 13a).

The application of the small stress at a hightransformation temperature (that is, a smallchemical driving force) causes the develop-ment of anisotropic strains, the transversestrain first being negative and then positive(Fig. 13b). The same effect is observed for alarge stress and low temperature (that is, alarge driving force). The model explains thiseffect when it is assumed that the favored var-iants form first, but that the stress is not largeenough to suppress the eventual formation ofother variants. The signs of eL and eR are al-ways opposite for the favored variants, butare identical for the rest of the variants.Therefore, the transverse strain is initiallynegative but then becomes positive as trans-formation progresses. The low-stress/high-temperature situation is equivalent to thehigh-stress/low-temperature case because inboth of these circumstances, variants that arenot favored cannot be suppressed. In the for-mer case the stress is too small for suppres-sion, whereas in the latter case the chemicaldriving force is too large to permit suppres-sion.

When a large stress is applied at a high tem-perature, the favored variants dominate.Therefore, the strains are always of oppositesign (Fig. 13c).The model is thus capable of qualitatively ex-

plaining all the essential features of the forma-tion of bainite under the influence of a small ten-sile stress. A uniaxial compressive stress (asused in the experiments described below) simplycauses a reversal of the signs of the longitudinaland transverse stresses; there is also a minor ef-fect from the unfavorable interaction betweenthe compressive stress and the dilatational com-ponent of the IPS shape deformation.

The most interesting conclusion to emergefrom comparison of the model with experimentaldata is that transformation under the influence ofa mild stress occurs sequentially. Variants thatcomply with the applied stress grow first, fol-


(a)

Stra

in 0

Transformation time

LT

L

TL

L, T

T

L

T

L

T

+

Stra

in 0

Equivalent time

+

(b)

Stra

in 0

Transformation time

+

Stra

in 0

+

(c)

Stra

in 0

Transformation time

+

Stra

in 0

+

Equivalent time

Equivalent time

Fig. 13 Schematic of the reported variations (Ref 24) in longitudinal and radial strains during the isothermal formationof bainite under the influence of a tensile load, presented alongside predictions (Ref 36) from the crystallo-

graphic/thermodynamic model. The stresses are all intended to be below the austenite yield strength, and the data in thiscase refer to uniaxial tension. (a) Zero stress, any temperature. (b) Small stress, low temperature. (c) Small stress, hightemperature; or large stress, low temperature.

lowed by those that do not. This also carries theimplication that the interaction of the stress iswith the growth process (that is, the IPS shapedeformation) rather than the strain field of thenucleus, which is likely to be different. It isworth noting that there are similar results formartensite: most favored variants grow first inthe sequence of transformation under stress (Ref15, 24).

Summary

Many of the thermal properties of steelsforexample, heat capacity, thermal expansion co-efficients, and latent heats of transformationare remarkably well understood. Indeed, com-mercially available thermodynamic databasesand programs can be used to estimate thesequantities as a function of temperature andchemical composition. This capability has notbeen exploited in the analysis of residualstresses, even though phase diagram calculationsusing the same software are now routine in in-dustry and academia.

Other properties, such as elastic modulus, are

not yet calculable in the same manner. It may bethe case that they are insensitive to alloying, butthat remains to be demonstrated in the contextof residual stress analysis.

There is little doubt that transformations insteel play a major role in the development ofresidual stresses. For reconstructive transforma-tions (for example, pearlite), it is the differencein density between the parent and product phasesthat contributes to transformation plasticity. Theplasticity can be much larger for displacivetransformations (Widmanstatten ferrite, bainite,martensite) because of the large shear compo-nent of the shape deformation when these trans-formation products form. These are quite so-phisticated effects which, with few exceptions,are not incorporated in most residual stress anal-yses.

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24. H.K.D.H. Bhadeshia, S.A. David, J.M. Vi-tek, and R.W. Reed, Mater. Sci. Technol.,Vol 7, 1991, p 686698

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Stresses in Welded Constructions, WeldingInstitute, 1977, Paper 2

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Prestress Engineering of StructuralMaterial: A Global Design Approachto the Residual Stress ProblemJ. Lu, LASMIS, Universite de Technologie de Troyes, France

ALL MANUFACTURING PROCESSES in-troduce residual stress into mechanical parts,which influences its fatigue behavior, fracturestrength, and even its corrosion resistance. Fewmetalworking methods exist that do not producenew stresses. The role of residual stress is, there-fore, very important when designing mechanicalparts. Over the last few years, an increasing num-ber of studies have been carried out to under-stand the effects of residual stress on mechanicalperformance. This article attempts to present aglobal approach to including residual stress inexpected fatigue life calculations, and the pos-sibility of introducing it into mechanical engi-neering design offices. The definitions and ori-gins of residual stress according to productionmethods are first presented. Then, shown are theproblems involved in correctly adapting thesemodeling techniques for use in design officesand the industrial consequences of taking resid-ual stress into account on quality assurance con-trol procedures. This article deals mainly withresidual stress measurement techniques and theoverall necessity to combine destructive (incre-mental hole-drilling method) and nondestructive(x-ray and neutron diffraction) methods in orderto precisely evaluate the residual stress distri-bution. Some new results concerning opticalmethods are also discussed. Shown, too, are thebeneficial and harmful effects of residual stresson the resistance of structures or industrial com-ponents, depending on whether they are tensileor compressive. The different models used topredict residual stress induced by different typesof processing are then presented. The last sectionshows the effect of residual stress on fatigue be-havior. A model based on the finite elementmethod (FEM) for predicting the relaxation ofresidual stresses is presented. Finally, predictionof fatigue life, taking residual stress into account,using FEM is discussed. A new approach to con-current engineering applied to the design of me-chanical components with residual and appliedstress consideration is presented.

Residual stress is usually defined as the stressthat remains in mechanical parts that are not sub-jected to any outside stresses. Residual stress ex-ists in practically all rigid parts, whether metallicor not (wood, polymer, glass, ceramic, etc). It isthe result of the metallurgical and mechanicalhistory of each point in the part and the part asa whole during its manufacture.

In the case of structural materials, surface en-gineering can lead indirectly to the innovation ofgenuinely new materials based on conventionalmaterials. The frustrating slowness of some ofthese developments reflects not only difficultiesin scaling up laboratory techniques, but also gen-eral conservation in the engineering industriesand a reluctance to change established habits.One of the factors that contributes to slowing thepace is that the current approach to surface en-gineering directly correlates performance to pro-cessing parameters; designers are left without thetools needed to optimize and take into accountmodified or prestressed surfaces for a particularapplication, and the processors are left withoutappropriate goals for surface properties.

The recent European Network of Surface andPrestress Engineering and Design (ENSPED)project led by the University of Technology ofTroyes and funded by the European Union is oneof the contributions currently being made to thedevelopment of such tools. The aim is to developa project with a hard core of about 18 partnersrepresenting a balanced selection of Europesmajor industries, such as SNECMA; EuropeanAeronautic, Defense and Space (EADS); ABB;Siemens; Volvo; Fiat; British Aerospace; RobertBosch; Hydro Aluminum; Wartisla; and so on.It is based on building a bridge between thefields of surface modification and prestress pro-cessing in materials engineering and computer-aided design in mechanical engineering in orderto find an appropriate way of approaching thisinterdisciplinary area. The members of the pro-ject will focus on the field of prestress process-ing. The main goal of the prestress engineeringapproach is the optimization of residual stress for

an objective mechanical behavior of the materialand structure. Under this approach, the residualstress must not be considered as a parameter thatonly depends on the material processing condi-tions, but must also be considered as a parameterthat can be optimized.

There is an increasing interest in how the stateof residual stress affects the mechanical proper-ties of a material and its structure. The failure ofa structure or a mechanical component is notonly due to external loads. Residual stress is animportant parameter in this respect. All manu-facturing processes, for example, introduce anew state of residual stress. This can have a posi-tive effect, such as increasing the fatigue limit inthe case of surface compressive stress, or it canhave a negative effect, such as decreasing thestress corrosion behavior of a material in the caseof tensile residual stress.

Basic and applied research in the field of re-sidual stress has been stepped up in the last fewyears. Residual stress is taken into account inadvanced design in the aerospace, automotive,and nuclear industries. Even the microelectron-ics industry is starting to take residual stress intoaccount for the dimensional stability of elec-tronic packaging.

The introduction of advanced materials hasalso contributed to the development of knowl-edge in the field of residual stress. In fact, manynew materials are multimaterials, for example,metal-matrix composites, plasma-sprayed coat-ing, physical vapor deposition (PVD), and chem-ical vapor deposition (CVD) coatings, whichcontain residual stress as a result of the thermaland mechanical incompatibilities of the differentphases of the material or structure.

Figure 1 shows the different fields of researchin which residual stress is taken into account andits relevance for industrial applications. Threemain fields must be developed for a global ap-proach of prestress engineering: measurementtechniques for the quality control and processinganalysis, processing parameter optimization andprocessing modeling, and modern design tool for

Handbook of Residual Stress and Deformation of Steel G. Totten, M. Howes, T. Inoue, editors, p11-26 DOI: 10.1361/hrsd2002p011

Copyright 2002 ASM International All rights reserved. www.asminternational.org


Quality control Manufacturing

Measurementtechnique

Prestress processdevelopment and

modeling

Take residual stress intoaccount in integrated design

Relaxation ofresidual stress

Effect of residualstress on behaviors

Mechanicaldesign

Dimensionalstability

New design

Fig. 1 Main research fields and industrial application fields in which residual stress is taken into account

the life cycle simulation with residual stress con-sideration.

Origins of Residual Stress

In general, macroscopic residual stress can beinduced due to: Nonhomogeneous plastic flow under the ac-

tion of external treatment (shot peening, au-tofretting, roller burnishing, hammer peening,shock laser treatment)

Nonhomogeneous plastic deformation duringnonuniform heating or cooling (ordinaryquenching, molding of plastics)

Structural deformation from metalworking(heat treatment)

Heterogeneity of a chemical or crystallo-graphic order (nitriding or case hardening)

Various surface treatments (enameling,nickel plating, chrome plating, PVD andCVD coating)

Differences in expansion coefficients and me-chanical incompatibility of the different com-ponents of composites (composites with ametallic and organic matrix, ceramic coat-ings)Table 1 shows the different origins of residual

stress for metalworking operations usually car-ried out in the industry. To produce an industrialpart, one or several of the techniques listed in thetable can be used. To calculate the residual stressexisting in a part, the source of the stress mustbe identified first.

Residual Stress Measurement Techniquesin Global Approach and Quality Assurance.Over the last few decades, various quantitativeand qualitative techniques have been developed(Ref 1). These techniques are used for the pro-cessing optimization and quality control of ma-terial. In general, a distinction must be made be-tween destructive and nondestructive methods.

The first series of methods is based on de-stroying the state of equilibrium in the mechan-ical component. The residual stress is then eval-uated from its relaxation. However, it is onlypossible to measure the consequences of stressrelaxation and not the relaxation itself (displace-ment, fracture, strain). In most cases, the changein strain is selected as the parameter to be stud-ied. The following procedure is used:

1. Creation of a new stress state by machiningor layer removal

2. Detection of the local change in stress bymeasuring the strain or displacement

3. Calculation of the residual stress as a functionof the strain measured using the elastic theory(analytical approach or numerical calcula-tions such as FEM)

During the recent years, the incremental hole-drilling method is extensively used. It is sensi-tive to the first kind of residual stress, that is, themacroscopic residual stress. The principle of thistechnique is simple. It involves monitoring thechange in strain when a hole is drilled in a com-ponent with residual stress. These strain mea-surements can be related to the original residualstress distribution in the analyzed sample at thehole location. The relationship between thestrain and the residual stress can be calculatedwith the calibration coefficients Ain and Bin. Thegeneral approach used to determine the Ain andBin FEM is detailed in Ref 2. Recently, the highsensitivity moire interferometer and incrementalhole-drilling method for residual stress measure-ment has been developed. The theoretical devel-opment of a combined method is introduced inRef 3 and 4. The relationship between the three-dimensional surface displacements produced byintroducing a blind hole and the correspondingresidual stress is established by employing theexisting theoretical solution containing a set ofundetermined coefficients. The coefficients arecalibrated by the three-dimensional finite ele-

ment method. The in-plane surface displace-ments Ux and Uy and out-of-plane surface dis-placement Uz produced by the relaxation ofresidual stresses are obtained using moire inter-ferometry and Twyman-Green interferometry,respectively. Figure 2 shows three-dimensionaldisplacement as a function of the drilling depth.The main advantage of this technique is the pos-sibility of studying the residual stress with an in-plane stress gradient (Ref 5). It is also possibleto study composite materials (Ref 6). In thiscase, the through thickness residual stress distri-bution was evaluated ply by ply in a carbon fi-ber/epoxy composite. Figure 3 shows an exam-ple of residual stress determined by using thistechnique.

Recently, this method was used (Ref 7) tostudy the Plastic Ball Grid Array (PBGA) pack-age, which is a cost-effective surface-mountingpackage with a high-density interconnection,low profiles, and light weight. It is currently usedin many electronic products, including portabletelecommunication and computing products. Atypical structure in a PBGA package consists offour layers: a plastic molding compound, a sili-con chip, a chip-attach adhesive layer, and anorganic chip carrier. Due to the coefficient ofthermal expansion mismatch between the siliconchip, the plastic compound, and the organic chipcarrier, considerable residual stresses are devel-oped in the package during the assembly pro-cess. The process-induced residual stress canplay a significant role in the reliability of elec-tronic components and packages. Since a PBGApackage is small and the surface layer is madeof a plastic material, it has proved very difficultto use other existing methods of residual stressmeasurement. In this research work, a practicalmethod has been developed to determine resid-ual stress for electronic packaging. In thismethod, blind holes are drilled into the speci-mens, and relationships are established betweenthe released surface displacement and the cor-responding residual stress by introducing a setof calibration coefficients. A multilayer three-di-mensional FEM is established to determine therelevant calibration coefficients. The surface dis-placements are measured accurately in a smallregion around the hole. For a practical PBGApackage, the tensile residual stress is determinedin both the plastic molding compound and theglass/epoxy laminate chip carrier. The methodis accurate, simple, convenient, and practical.More applications in the field of electronic prod-ucts are anticipated.

The x-ray diffraction and neutron diffractionmethods are based on the measurement of latticestrains by studying variations in the lattice spac-ing of the polycrystalline material. The firstmethod measures the residual strain on the sur-face of the material, and the second measures theresidual strain within a volume of the sample.Diffraction techniques can be used to study allthree types. The peak shift method is sensitiveto the first two, whereas line broadening is sen-sitive to the second and third types. These tech-niques have been used to measure the first type

Prestress Engineering of Structural Material: A Global Design Approach to the Residual Stress Problem / 13

Fig. 2 Three-dimensional displacements measured for different hole depth by a combination of optical methods andthe incremental hole-drilling method in a shot peened sample. Champ, field

Table 1 Main origins of residual stress resulting from different manufacturing processes

Process Mechanical Thermal Structural

Casting No Temperature gradient during cooling Phase transformationShot peening, hammer peening, roller burnishing, laser

shock treatment, bending, rolling, chasing, forging,straightening, extrusion

Heterogeneous plastic deformationbetween the core and surface of thepart

No Depends on the material

Grinding, turning, milling, drilling, boring Plastic deformation due to the removalof chips

Temperature gradient due to heatingduring machining

Phase transformation during machining ifthe temperature is sufficiently high

Quenching without a phase transformation No Temperature gradient NoSurface quenching with a phase change (induction, EB,

laser, plasma, classical methods)No Temperature gradient Change of volume due to a phase change

Case hardening, nitriding No Thermal incompatibility New chemical component with volumemodification

Welding Shrinkage Temperature gradient Microstructural change (HAZ)Brazing Mechanical incompatibility Thermal incompatibility New phase at interfaceElectroplating Mechanical incompatibility Mechanical incompatibility Composition of plating depending on bath

usedThermal spraying (plasma, laser, HVOF) Mechanical incompatibility,

microcrackingThermal incompatibility, temperature

gradientChange of phase in plating

PVD, CVD Mechanical incompatibility Mechanical incompatibility Change of phaseComposite Mechanical incompatibility Mechanical incompatibility No

EB, electron beam; HVOF, high-velocity oxygen fuel; HAZ, heat-affected zone

of residual stress in different phases of advancedmaterials, such as metal-matrix composites (inmatrix and in reinforcement) (Ref 8, 9).

Residual stress can be incorporated into thedesign of mechanical components. Although thisleads to a better knowledge of the fatigue life ofparts and reduces the safety coefficient at the de-sign stage, it also poses a host of new problemson a quality assurance level. All statistical con-trols are only applied today to a few critical com-ponents in the aeronautical and nuclear indus-tries; this practice could easily become

widespread. Rapid ways of checking the residualstress must therefore be developed. The methodsused industrially (x-ray diffraction and the incre-mental hole method) will not be sufficient in thefuture. Other nondestructive testing (NDT) tech-niques (ultrasound, magnetic methods, acousticemission) are presently being developed. But asthey currently stand, these techniques use physi-cal parameters that depend not only on the resid-ual stress present in the parts, but also on mi-crostructural changes. In the near future, NDTtechniques will be applied at the same time as

the reference techniques. Figure 4 proposes a re-sidual stress inspection plan. Other new tech-niques, such as neutr

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Handbook of Residual Stress and Steel Deformation