Multiscale stress and strain statistics in the deformation of polycrystalline alloys

Abstract

Multiscale stresses and strains in polycrystalline metals are always inhomogeneous. In this study, a rate-independent crystal plasticity formulation was implemented for a cubic representative volume element (RVE) of an fcc polycrystal generated by 3D Delaunay tessellation. Multiple realizations were generated with crystallographic orientation permutations and different grain morphologies in order to investigate the statistical distribution of stress, elastic lattice strain and total strain at the macro-, meso- and micro-scale. Macroscopically, at 1.55% total strain (elasto-plastic deformation), the overall stress statistics among different RVEs were observed to follow a normal distribution, whose profile shape is affected by the parameters that describes the lognormal grain size distribution. On the mesoscale, the orientation-specific elastic strains were accurately reproduced via the use of diffraction post-processing and validated by neutron diffraction data for a polycrystalline alloy. Microscopically, the local elastic strains (and hence stresses) universally follow a normal distribution, while plastic strains follow a lognormal probability distribution. Reliable knowledge of the statistical distributions of stresses and strains give new guidance for the determination of the minimum RVE size. The above finding reveals the nature of stress and strain inhomogeneity at multiple scales and emphasizes the fact that the dispersion of local stress and strain is much larger than that of the macroscopic average. The statistical analysis of stress and strain distribution at multiple scales provide further rich insights into the connection between microstructure and mechanical properties under monotonic and cyclic loading.