\ PERGAMON Journal of the Mechanics and Physics of Solids 36 "0888# 186Ð213 S9911Ð4985:88:, ! see front matter Þ 0888 Elsevier Science Ltd[ All rights reserved PII]S9911Ð4985"87#99970Ð6 Strain gradient crystal plasticity] size!dependent deformation of bicrystals John Y[ Shu a\ \ Norman A[ Fleck b a En`ineerin` Department\ Lawrence Livermore National Laboratory\ Livermore\ CA 83449\ U[S[A[ b En`ineerin` Department\ University of Cambrid`e\ Trumpin`ton Street\ Cambrid`e CB1 0PZ\ U[K[ Received 15 January 0887^ in revised form 08 June 0887 Abstract The role of the grain boundary in in~uencing the deformation of a bicrystal is explored using a rate!dependent crystal formulation of the FleckÐHutchinson strain gradient plasticity theory[ The physical basis of the theory is the elevated strengthening of a slip system due to geo! metrically necessary dislocations\ associated with spatial gradients of slip[ The theory is implemented within the _nite element framework and is used to study the deformation of a bicrystal under in!plane shear loading[ Contrary to classical scale!independent crystal plasticity theories\ the strain gradient theory predicts that the deformation state depends strongly upon grain size[ Strain gradient e}ects are pronounced within a narrow layer at the grain boundary of a bicrystal\ and a signi_cant grain!size dependence of the yield strength is predicted[ Þ 0888 Elsevier Science Ltd[ All rights reserved[ Keywords] Grain boundaries^ Strengthening mechanisms^ Constitutive behaviour^ Crystal plasticity^ Non! local plasticity 0[ Introduction Conventional continuum mechanics theories assume that the stress at a material point depends upon variables such as strain at the same point only[ This local assumption has long been shown to be adequate when the wavelength of the defor! mation _eld is much larger than the dominant length scale of the microstructure[ Material behaviour predicted by such a local theory exhibits scale!independence ] no length scale is present within the constitutive law[ However\ accumulating exper! imental evidence suggests that a strong size!dependence of mechanical behaviour Corresponding author[ Tel[] 990 814 311 5222^ fax] 990 814 312 9344^ e!mail] jyshuÝllnl[gov
Strain gradient crystal plasticity] size!dependent deformation of bicrystals
Jun 23, 2023
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