Finite strain crystal plasticity-phase field modeling of twin, dislocation, and grain boundary interaction in hexagonal materials

Abstract

Twin, dislocation, and grain boundary interaction in hexagonal materials, such as Mg, Ti, and Zr, has critical influence on the materials’ mechanical properties. The development of a microstructure-sensitive constitutive model for these deformation mechanisms is the key to the design of high-strength and ductile alloys. In this work, we have developed a mechanical formulation within the finite strain framework for modeling dislocation slip- and deformation twinning-induced plasticity. A dislocation density-based crystal plasticity model was employed to describe the dislocation activities, and the stress and strain distributions. The model was coupled with a multi-phase-field model to predict twin formation and twin-twin interactions. The coupled model was then employed to study twin, dislocation, and grain boundary interactions in Mg single- and polycrystals during monotonic and cyclic deformation. The results show that twin-twin interactions can enhance the strength by impeding twin propagation and growth. The role of dislocation accommodation on twin-twin interactions was twofold. Dislocation slip diminished twin-twin hardening by relieving the development of back-stresses, while it effectively relaxed the stress concentration near twin-twin intersections and thus may alleviate crack nucleation. The plastic anisotropy in each grain and the constraints imposed by the local boundary conditions resulted in stress variations among grains. This stress heterogeneity was responsible for the observed anomalous twinning behaviour. That is, low Schmid factor twins were activated to relax local stresses and accommodate the strain incompatibility, whereas the absence of high Schmid factor twins was associated with slip band-induced stress relaxation.