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By incorporating the constitutive equations based on classical plasticity and the mechanism-based strain gradient plasticity with finite element software, the stress–strain relationships and uniform elongations of Al polycrystals with different grain sizes were studied numerically. The calculation results indicate that grain refinement cannot substantially improve the uniform elongation but can increase the yield strength of Al polycrystals when the grain size is of the order of the micron and submicron scale. The Hall–Petch relationship for yield strength holds and the uniform elongation decreases with decreasing grain size. The calculation results in general agree well with the experiment data.

A numerical study of grain size effects on the strength and elongation of Al polycrystals using strain gradient plasticity theory