Continuum Modelling of Shear-Coupled Grain Boundary Migration

The deformation accommodation mechanisms associated to grain boundaries (GBs) significantly affect the mechanical behavior of nano-polycrystals. Among these mechanisms, stress-induced GB migration is now seen to compete or interplay with other intra-granular and GB mechanisms in a wide range of temperatures. A complete micromechanics-based model is here proposed using the concepts of continuum thermodynamics and kinematics to derive a new constitutive model able to describe stress-induced GB migration. Like non diffusive phase-transformations, stress-induced GB migration can be considered on the thermodynamics point of view of conservative nature (diffusionless but thermally activated) until high temperature with respect to melting point. Here, in the framework of continuum micro-mechanics which should be easily implemented in a polycrystalline model, we will first describe the micromechanical framework: the kinematics and the thermodynamics associated with additive mechanisms including plastic deformation in the bulk crystals, GB migration and GB sliding. For the sake of illustration of the present general theory, we will focus on planar bi-crystals and only perfect shear-coupling GB migration situations of [001] symmetric tilt GBs in Cu. Numerical examples and responses of the micromechanical model are given for these bi-crystals considering both isotropic and anisotropic elasticity. These ones are fed by computer-aided MD simulations for which deformation mechanisms are identified.