A non-local model for the description of twinning in polycrystalline materials in the context of infinitesimal strains: application to a magnesium alloy

TL;DR

This paper introduces a non-local polycrystalline plasticity model that incorporates deformation twinning, applied to magnesium alloys, capturing the effects of twin boundaries and predicting texture evolution consistent with experiments.

Contribution

A novel non-local model for twinning in polycrystalline materials under infinitesimal strains, including twin boundary effects and implemented in a spectral solver.

Findings

Model accurately predicts texture evolution in magnesium alloy

Twinning and slip jointly control mechanical behavior

Results align with experimental observations

Abstract

A polycrystalline plasticity model, which incorporates the contribution of deformation twinning, is proposed. For this purpose, each material point is treated as a composite material consisting of a parent constituent and multiple twin variants. In the constitutive equations, the twin volume fractions and their spatial gradients are treated as external state variables to account for the contribution of twin boundaries to free energy. The set of constitutive relations is implemented in a spectral solver, which allows solving the differential equations resulting from equilibrium and compatibility conditions. The proposed model is then used to investigate the behavior of a AZ31 magnesium alloy. For the investigated loading conditions, the mechanical behavior is controlled by the joint contribution of basal slip and tensile twinning. Also, according to the numerical results, the development of crystallographic texture, morphological texture and internal stresses is consistent with the experimental observations of the literature.