Generalised continuum modelling of grain size effects in polycrystals

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• 作者：Nicolas M. Cordero ; Samuel Forest ; ^{samuel.forest@mines-paristech.fr} ; Esteban P. Busso
• 关键词：Crystal plasticity ; Strain gradient plasticity ; Micromorphic theory ; Kinematic hardening ; Dislocation density tensor ; Grain boundary ; Polycrystalline aggregate ; Hall&ndash ; Petch effect
• 刊名：Comptes Rendus Mecanique
• 出版年：2012
• 期刊代码：116_16310721
• 类别：ms
• 出版时间：April-May, 2012
• 卷：340
• 期：4-5
• 页码：261-274
• 文件大小：1680 K

摘要

The effect of the dislocation density tensor is introduced into the classical crystal plasticity framework by means of the micromorphic theory of single crystals. A computational homogenisation strategy is presented in order to describe the global and local responses of two-dimensional polycrystalline aggregates for grain sizes ranging from 1 to 200 microns. The model is shown to naturally predict a size-dependent kinematic hardening behaviour which is responsible for the observed strong size effects. The yield stress at a given averaged plastic strain is shown to follow a power law scaling relation for grain sizes larger than a critical one. The field of plastic deformation is also strongly affected by grain size, whereby micron-size grains lead to the formation of intense slip bands crossing several grains.