A multiscale Taylor model-based constitutive theory describing grain growth in polycrystalline cubic metals

Abstract

In this work, we have developed a thermodynamically consistent, three-dimensional, finite-deformation-based constitutive theory to describe grain growth due to stress-driven grain boundary motion in polycrystalline cubic metals. The constitutive model has been formulated in a multiscale setting using the Taylor-type homogenization scheme (Taylor, 1938), and it has also been implemented into a computational framework. In our numerical scheme, the mechanical response of a structure at the macroscale level is modeled using the finite-element method whereas at the mesoscale level, the stress-driven grain growth process within a polycrystalline aggregate is handled by phase-field-like simulations.Using our multiscale constitutive theory and computational framework, we model several boundary value problems involving grain growth in polycrystalline cubic metals. From our coupled finite-element and phase-field simulations, we obtain the following trends: (a) sufficiently stressed polycrystalline metals result in the preferential growth of elastically soft crystal orientations at the expense of elastically hard crystal orientations, and (b) grain growth stagnation effects can be responsible for preventing a polycrystalline aggregate from evolving into a single crystal under stress-driven grain growth conditions. These observations agree well with previously conducted experimental and simulation results available in the literature.