Analytical prediction and homogenization analysis of grain fining effects using a strain gradient plasticity theory

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The increase of yield stress due to grain fining is experimentally well-known as the Hall-Petch relation. It has been, however, reported that the grain size dependence of yield stress in the submicron to several-micron range of grain sizes is stronger than that in the Hall-Petch relation. In this study, by implementing the self-energy of dislocations in a strain gradient plasticity theory, the grain size dependence of yield stress is analytically estimated, and the resulting prediction is examined using experimental data. Then, an implicit method of homogenization analysis is developed by taking account of the self energy of dislocations.