Fundamentals of Creep in Metals and Alloys, Third Edition PDF
Preview Fundamentals of Creep in Metals and Alloys, Third Edition
Fundamentals of CREEP IN METALS AND ALLOYS THIRD EDITION M.E. KASSNER Departments of Aerospace and Mechanical Engineering, Chemical Engineering, and Materials Science University of Southern California Los Angeles, CA USA AMSTERDAM(cid:129)BOSTON(cid:129)HEIDELBERG(cid:129)LONDON NEWYORK(cid:129)OXFORD(cid:129)PARIS(cid:129)SANDIEGO SANFRANCISCO(cid:129)SINGAPORE(cid:129)SYDNEY(cid:129)TOKYO Butterworth-HeinemannisanimprintofElsevier Butterworth HeinemannisanimprintofElsevier 225Wyman Street,Waltham,MA02451,USA TheBoulevard,LangfordLane, Kidlington,Oxford, OX51GB,UK Copyright©2015, 2009,2004ElsevierLtd.Allrightsreserved. Nopartofthis publication maybereproduced ortransmitted inanyform orbyany means,electronic ormechanical,including photocopying,recording,oranyinformation storage andretrieval system,withoutpermission inwritingfrom thepublisher. 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Tothefullestextent ofthelaw,neitherthePublisher northeauthors, contributors, or editors,assume anyliabilityfor anyinjuryand/or damagetopersons orproperty asa matterof productsliability,negligence orotherwise, orfromany useoroperation ofany methods,products, instructions,orideascontainedinthematerial herein. ISBN:978-0-08-099427-7 BritishLibraryCataloguing inPublication Data Acataloguerecordforthisbookisavailable fromtheBritishLibrary LibraryofCongressCataloging-in-Publication Data Acatalogrecordforthis bookisavailablefrom theLibraryofCongress ForinformationonallButterworthHeinemannpublications visitourwebsiteathttp://store.elsevier.com PREFACE Thisbookonthefundamentalsofcreepplasticityisareviewandanalysisof investigations in a variety of areas relevant to creep plasticity. These areas includefive-power-lawcreep,whichissometimesreferredtoasdislocation climb-controlled creep (in metals, alloys, and ceramics), viscous glide or three-power-law creep (in alloys), diffusional creep, Harper–Dorn creep, superplasticity, second-phase strengthening, and creep cavitation and fracture. Many quality reviews and books precede this attempt to write an extensive review of creep fundamentals and the improvement was a chal- lenge. One advantage with this attempt is the ability to describe the sub- stantialworkpublishedsubsequenttotheseearlierreviews.Anattemptwas made to cover the basic work discussed in these earlier reviews but especially to emphasize more recent developments. This is the second edition of this book and one aspect of this recent editioniscorrectingerrorsinthefirstedition,also,manyadvancesoccurred over the five years since the first edition and theses are also incorporated. Dr Maria-Teresa Perez-Prado was a co-author of the first edition. While she did not participate in the formulation of the second and third editions, Chapters 5, 6, and 9 remain largely a contribution by Dr Perez-Prado, and her co-authorship is indicated on these chapters. xi LIST OF SYMBOLS AND ABBREVIATIONS a Cavityradius a Lattice parameter o A0 L9A0000 Constants AAF >>>>>>>>= ACeJ Solute dislocationinteraction parameters AAASNPB>>>>>>>>; A CR A Grainboundary area gb A HarpereDornequationconstant HD A Constants PL A Projected areaofvoid v A eA Constant 0 12 APB Antiphaseboundary b Burgers vector B Constant BMG Bulkmetallic glass c Concentration ofvacancies c* Crack growthrate c Concentration ofjogs j c Concentration ofvacancies inthevicinityofajog p c(cid:2) Steady-state vacancy concentrationnearajog p c Equilibrium vacancyconcentration v cD Vacancyconcentration nearanodeordislocation v c Initial cracklength 0 c1e2 Constants C Concentration ofsolute atoms C* Integral forfracturemechanicsoftime-dependentplasticmaterials C1e2 Constant C LarsoneMillerconstant LM CBED Convergent beamelectron diffraction CGBS Cooperativegrainboundary sliding CS Crystallographic slip CSF Complexstacking fault CSL Coincident sitelattice C(cid:2) Constant 0 C eC Constants 0 5 d Averagespacingofdislocations thatcompriseasubgrainboundary D Generaldiffusioncoefficientorconstant D0 Constant xiii xiv ListofSymbolsandAbbreviations D Diffusioncoefficientforclimb c D Effectivediffusioncoefficient eff D Diffusioncoefficientforglide g D Diffusioncoefficientalonggrainboundaries gb D Interfacialdiffusion i D Surfacediffusioncoefficient s D Latticeself-diffusion coefficient sd D Diffusioncoefficientforvacancies v D Diffusionconstant 0 DRX Discontinuous dynamicrecrystallization D~ Diffusioncoefficientforthesolute atoms e Soluteesolventsizedifferenceormisfitparameter E Young’smodulus orconstant E Formation energyforajog j EBSP Electron backscatterpatterns f Fraction f Fractionofmobiledislocations m f Chemicaldragging forceon ajog p f Fractionofmaterialoccupiedby subgrains sub F Totalforceper unitlengthonadislocation FEM Finiteelementmethod g Averagegrainsize(diameter) g0 Constant G Shearmodulus GBS Grainboundarysliding GDX Geometricdynamicrecrystallization GNB Geometrically necessaryboundaries h Hardeningrate r h Average separation between slip planes within a subgrain with gliding m dislocations h Dipoleheightorstrain-hardeningcoefficient HAB Highangleboundary HVEM Highvoltagetransmission electronmicroscopy j Jogspacing J Integralforfracture mechanicsofplasticmaterial J Vacancyfluxalongagrainboundary gb k Boltzmann constant k0ek000 Constants k HallePetch constant y k MonkmaneGrant constant MG k Relaxationfactor R k ek Constants 1 10 K Strengthparameterorconstant K Stressintensityfactor I K eK Constants 0 7 [ LinklengthofaFrank dislocationnetwork [ Criticallinklengthtounstablybowapinneddislocation c ListofSymbolsandAbbreviations xv [ Maximumlinklength m l Migration distanceforadislocation inHarpereDorncreep L Particle separationdistance LAB Low angleboundary LM LarsoneMillerparameter LRIS Long-rangeinternalstress m Strain-rate sensitivity exponent(¼1/N) m0 Transientcreeptime exponent m00 Strain-rate exponentintheMonkmaneGrantequation m Constant c M AverageTaylor factorforapolycrystal Mr Dislocation multiplicationconstant n Steady-state creepexponentorstrain-hardening exponent n* Equilibrium concentrationofcritical sizednuclei n Steady-state stressexponentofthematrix inamulti-phase material m N Constant structure stress exponent and dislocation link length per unit volume _ N Nucleationrateandrate ofreleaseofdislocationloops p Steady-state dislocation densitystress exponent p0 Inverse grainsizestressexponentforsuperplasticity PLB Power lawbreakdown POM Polarizedlightopticalmicroscopy PSB Persistent slipband q Dislocation spacing,d,stressexponent Q Activation energyforcreep(withEorGcompensation) c Q0 Apparentactivationenergyforcreep(noEorGcompensation) c Q Activation energyfordislocation pipediffusion p Q Activation energyforlattice self-diffusion sd Q Formation energyforavacancy v Q* Effectiveactivationenergiesincompositeswhereloadtransferoccurs r Recoveryrate r R Diffusiondistance o R Radius ofsolventatoms s s Structure SAED Selectedareaelectron diffraction SESF Superlattice extrinsicstackingfault SISF Superlattice intrinsicstackingfault STZ Sheartransformation zone t Time t Timeforcavitycoalescenceon agrainboundary facet c t Timetofracture (rupture) f t Timetotheonsetofsteady-state s T Temperature T Dislocation linetension d T Glass transitiontemperature g T Melting temperature m T Temperatureofthepeakyieldstrength p xvi ListofSymbolsandAbbreviations T Onsetcrystallization temperature x TEM Transmission electronmicroscopy TeTeT Timeetemperatureetransformation diagram v Dislocation glidevelocity v Dislocation climbvelocity c v Criticaldislocation velocityatbreakaway cr v Debyefrequency D v Jogclimbvelocity p v Averagedislocation velocity v[ Climbvelocityofdislocation linksofaFranknetwork V Activation volume w Widthofagrainboundary x Averagedislocation climbdistance c x Averagedislocation sliplengthduetoglide g XRD X-raydiffraction a Taylor equationconstant a Constant o a0 Climbresistance parameter a1e3 Constants b,b1e3 Constants g Shearstrain g Characteristic strainofanSTZ o g Anelasticunbowingstrain A g Interfacialenergyofagrainboundary gb g Surfaceenergyofametal m g_ Shearcreeprate g_ Steady-state shearcreeprate ss d Grainboundarythickness orlatticemisfit Da Activation area DG Gibbsfreeenergy DV Activation volumeforcreep C DV Activation volumeforlattice self-diffusion L e Uniaxialstrain e Instantaneous strain o e_ Strainrate e_min Minimumcreeprate e_ Steady-state uniaxialstrainrate ss e EffectiveuniaxialorvonMisesstrain q Misorientationangleacross high-anglegrainboundaries ql Misorientationangleacross (low-angle)subgrainboundaries qlave Averagemisorientationangleacross (low-angle)subgrainboundaries l Averagesubgrainsize(usuallymeasured asanaverageintercept) l Cavityspacing s l Averagesteadystatesubgrainsize ss n Poisson’sratio n Attempt frequency(oftenDebyefrequency) o r Densityofdislocations notassociated withsubgrainboundaries ListofSymbolsandAbbreviations xvii r Mobile dislocationdensity m r Mobile screwdislocationdensity ms r Steady-state dislocation densitynot associatedwithsubgrainwalls ss s Applieduniaxialstress s Internal stress i s Singlecrystal yieldstrength o s0 Annealedpolycrystal yieldstrength o s00 Sintering stressforacavity o s Peierls stress p s Uniaxial steady-state stress ss s transition stressbetweenfive-powerlawandHarpereDorncreep T ssTyH(cid:2)(cid:2)sT;e_ TYhierledshoorlfldoswtresstsrefsosrastuaperrepfelarsetniccedetefomrmpeartaiotunre andstrain rate s0:002 0.2%offsetyieldstress y s Effectiveuniaxial,orvonMises,stress s Shearstress s Breakawaystressofthedislocationsfromsoluteatmospheres b s Critical stressforclimboverasecondphaseparticle c s Detachment stressfromasecond phaseparticle d s Stresstomovescrewdislocationswithjogs j s Orowanbowingstress or s Shearstressnecessary toejectdislocation fromasubgrainboundary B s Maximumstressfromasimpletiltboundary BD s Stress to move a dislocation through a boundary resulting from jog L creation s ShearstrengthofaFrankNetwork N (s/G) Normalized transitionstress t f(P) Frank networkfrequency distributionfunction c Stacking faultenergy c0 Primary creepconstant j Anglebetweencavitysurfaceandprojected grainboundary surface u Maximum interaction energy between a solute atom and an edge m dislocation U Atomic volume u Fractionofgrainboundary areacavitated CHAPTER 1 Fundamentals of Creep in Materials Contents 1. Introduction 1 1.1 Description ofCreep 1 1.2 Objectives 6 1. INTRODUCTION 1.1 Description of Creep Creep of materials is classically associated with time-dependent plasticity under a fixed stress at an elevated temperature, often greater than roughly 0.5T ,whereT istheabsolutemeltingtemperature.Theplasticityunder m m these conditions is described in Figure 1 for constant stress (a) and constant strain rate (b) conditions. Several aspects of the curve in Figure 1 require explanation. First, three regions are delineated: Stage I, or primary creep, which denotes that portion where (in (a)) the creep rate (plastic strain rate), ε_ ¼ dε=dt is changing with increasing plastic strain or time. In Figure 1(a), the primary creep rate decreases with increasing strain, but with some types of creep, such as solute drag with “3-power creep,” an “inverted” primary occurswherethestrainrateincreaseswithstrain.Analogously,in(b),under constant strain rate conditions, the metal hardens, resulting in increasing flow stresses. Often, in pure metals, the strain rate decreases or the stress increasestoavaluethatisconstantoverarangeofstrain.Thephenomenon is termed Stage II, secondary, or steady-state (SS) creep. Eventually, cavi- tationand/orcrackingincreasestheapparentstrainrateordecreasestheflow stress.ThisregimeistermedStageIII,ortertiary,creepandleadstofracture. Sometimes,StageIleadsdirectlytoStageIIIandan“inflection”isobserved. Thus, care must sometimes be exercised in concluding a mechanical SS. The term “creep” as applied to plasticity of materials likely arose from the observation that at modest and constant stress, at or even below the macroscopicyieldstressofthemetal(ata“conventional”strainrate),plastic deformationoccursovertimeasdescribedinFigure1(a).Thisisincontrast FundamentalsofCreepinMetalsandAlloys ISBN978-0-08-099427-7 ©2015ElsevierLtd. http://dx.doi.org/10.1016/B978-0-08-099427-7.00001-3 Allrightsreserved. 1 2 FundamentalsofCreepinMetalsandAlloys Figure 1 Constant true stress and constant strain rate creep behavior in pure and ClassM(orClassI)metals. with the general observation, such as at ambient temperature, where a material deformed at, for example, 0.1–0.3T , shows very little plasticity m underconstantstressatorbelowtheyieldstress,again,at“conventional”or typical tensile testing strain rates (e.g., 10(cid:2)4–10(cid:2)3s(cid:2)1). (The latter obser- vation is not always true as it has been observed that some primary creep is observed (e.g., a few percent strain, or so) over relatively short periods of time at stresses less than the yield stress (e.g., [1,2])). We observe in Figure 2 that at the “typical” testing strain rate of about 10(cid:2)4s(cid:2)1, the yield stress is s . However, if we decrease the testing strain y1 rateto,forexample, 10(cid:2)7s(cid:2)1,theyieldstress decreasessignificantly, aswill beshowniscommonformetalsandalloysathightemperatures.Toa“first approximation,” we might consider the microstructure (created by dislo- cationmicrostructureevolutionwithplasticity)atjust0.002plasticstrainto be independent of ε_. In this case, we might describe the change in yield
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