Introducing Grain Boundary Influenced Stochastic Effects into Constitutive Models

Twinning is an important deformation mechanism in hexagonal close-packed (hcp) metals such as Mg, Zr, Ti, and Be. Twinning in hcp materials is a multiscale process that depends on microstructural and mechanical response details at the mesoscale, microscale, and atomic scales. Twinning can generally be understood as a two-step process, a nucleation step followed by propagation. The nucleation of twins is governed by both material details such as the defect configurations at potential nucleation sites within grain boundaries, as well as the highly local mechanical field near grain boundaries. These two factors, the material and mechanical, must align for a successful nucleation event. In this article, we present a stochastic constitutive law for nucleation of twins and describe its implementation into a homogenized crystal plasticity simulation. Twin nucleation relies on the dissociation of grain boundary defects under stress into the required twinning partials. This dissociation is considered to follow a Poisson process where the parameters of the Poisson distribution are related to the properties of the grain boundaries. The rate of the process is a direct function of the local stress concentration at the grain boundary. These stress concentrations are randomly sampled from a distribution calibrated to full-field crystal plasticity simulations.