Strain gradient plasticity analysis of the influence of grain size and distribution on the yield strength in polycrystals

Plane strain models of polycrystalline microstructures are investigated using strain gradient plasticity (SGP) and a grain boundary (GB) deformation mechanism. The microstructures are constructed using a non-linear constrained Voronoi tessellation so that they conform to a log-normal distribution in grain size. The SGP framework is used to model the grain size dependent strengthening and the GB deformation results in a cut-off of this trend below a certain critical grain size. Plastic strain field localization is discussed in relation to the non-local effects introduced by SGP and a material length scale. A modification of the Hall–Petch relation that accounts for, not only the mean grain size, but also the statistical size variation in a population of grains is proposed.