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

• Method for constructing grain structures with desired statistical properties.
• Modeled with SGP and a GB model that acts as a barrier to plastic flow.
• Results regarding the level of plastic homogeneity vs. grain size are discussed.
• Predicts a yield stress dependent on grain size variation and relative length of GB.

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.