A comparison between different numerical methods for the modeling of polycrystalline materials with an elastic-viscoplastic behavior

Abstract

The macroscopic behavior of polycrystalline materials is largely influenced by the shape, the arrangement and the orientation of crystallites. Different methods have thus been developed to determine the effective behavior of such materials as a function of their microstructural features. In this work, which focuses on polycrystalline materials with an elastic-viscoplastic behavior, the self-consistent, finite element and spectral methods are compared. These common methods are used to determine the effective behavior of \textit{different 316L polycrystalline aggregates} subjected to various loading conditions. Though no major difference is observed at the macroscopic scale, the hardening rate is found to be slightly overestimated with the finite element method. Indeed, spatial convergence cannot be guaranteed for finite element calculations, even when fine mesh resolutions, for which the computational cost is important, are used. Also, as the self-consistent method does not explicitly account for neighborhood effects, important discrepancies between the self-consistent method and the other methods exist regarding the mechanical response of a specific grain. The self-consistent method nevertheless provides a reasonable description of the average response obtained for a group of grains with identical features (e.g. shape, orientation).