Localization models for the plastic response of polycrystalline materials using the material knowledge systems framework

Abstract

Crystal plasticity finite element simulations provide physics-based predictions of the plastic response in polycrystalline metals subjected to large plastic strains. Despite their demonstrated high fidelity in a number of applications, these approaches have not yet been adopted broadly by the metal working industry because of their extremely high computational cost. This work develops and applies a novel strategy for reduced-order partitioning of the macroscopically applied plastic stretching tensor on a polycrystalline aggregate to regions within individual grains (i.e. localization of the plastic stretching tensor). This new strategy is seen to provide reasonable predictions for the localized plastic stretching tensors at dramatically reduced computational cost. The strategy presented here extends the prior successes of the materials knowledge system (MKS) framework for the localization of the plastic stretching tensor in composites of two isotropic phases to polycrystalline volumes through the use of the generalized spherical harmonics as a Fourier basis for capturing the functional dependence of the localization kernels on the crystal lattice orientation. It is demonstrated that this extension of the MKS framework is capable of providing good predictions for all components of the second-rank local plastic stretching tensor for any given macroscale imposed plastic stretching tensor with about three to four orders of magnitude savings in the computational cost. This work has the potential to open new research avenues for computationally low-cost, fully coupled, multiscale simulations of plastic deformations in polycrystalline metals.