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1、Chapter8CrystalPlasticityandEvolutionofPolycrystallineMicrostructureChristianMieheandJanSchotteUniversityofStuttgart,Pfaffenwaldring,Stuttgart,Germanycrystallographicsystemswheretheshearstressesreachcrit-1Introduction267icalvalues.Mathematicalcontinuumdescriptionsofelas-2The
2、ContinuumSlipTheoryofCrystalticplasticdeformationsincrystalshavebeendevelopedbyPlasticity269Hill(1966)inthesmall-strainformatandbyRice(1971),3StressUpdateAlgorithmsinSingleCrystalHillandRice(1972),Mandel(1972),Teodosiu(1970),Plasticity274KronerandTeodosiu(1972),andAsaro(1983
3、a)inthecon-¨4VariationalFormulationofElasticPlastictextoffinitestrains;seealsothereviewsLin(1971),AsaroCrystals280(1983b),Havner(1992),andBassani(1993).Thegeomet-ricbasisofwhatisoftencalledthemacroscopiccontinuum5RepresentativeNumericalExamples283sliptheoryoffinitecrystalelast
4、oplasticityisamultiplica-6Conclusion287tivedecompositionofthelocaldeformationgradientintoaReferences287plasticpartsolelyduetomultislipongivencrystallographicplanesandaremainingpartthatdescribeselasticdistortionsandrigidrotationsofthelattice.Theconstitutiveequations1INTRODUCT
5、IONthatgoverntheslipresistanceandtheslipevolutioncanbemotivatedbymicromechanicalinvestigationsofdefectsThecontinuumsliptheoryofcrystalsprovidesacanonicalincrystalsasreviewedinCottrell(1953),Seeger(1958),frameworkoffiniteplasticitywithphysicallywell-definedNabarro(1967),Hirthan
6、dLothe(1968),Mura(1987),Hullrootsinthedislocationmechanicsofmetals.Reliablealgo-andBacon(1984),andPhillips(2001).Theformulationofrithmicsettingsofcrystalplasticityarenotonlyneededmicromechanicallymotivatedhardeninglawsformultislipforstructuralanalysesofsinglecrystalsbutalsop
7、ro-isacornerstoneofthecontinuumsliptheoryandstillanvideacornerstoneformultiscalecomputationsofevolvingareaofintensiveresearch.WerefertothereviewsKocksanisotropicmicrostructuresinpolycrystals.Thephysically(1966,1977),Kocks,ArgonandAshby(1975),Asarobasedphenomenologicaldescrip
8、tionofmacroscopicplastic(1983b),Perzyna(1988),Havner(1992),Bassani(1993),st
