Distribution-based model for the grain boundaries in polycrystalline plasticity
The paper identifies suitable transmission conditions for geometrically necessary dislocations (GNDs) across a grain boundary (GB) using the physically motivated gradient-enhanced crystal plasticity. Based on a variational formulation of governing field equations, the authors elaborate the driving force for GB dislocations and formulate transmission criteria for GNDs. A methodological novelty is that the various fields involved in the analysis of GB behavior are split into regular and singular components. The driving force for GNDs at the GB is evidenced as the projection of lattice microtraction in the direction of glide velocity in the adjacent grain, built from quantities involving the jumps of the lattice first Piola-Kirchhoff stress tensor defined in the lattice configuration. The introduced dislocation tensors characterize the kinematic incompatibilities associated with the accumulation and production of GNDs. A more physical approach allows to estimate the GND driving force from the singular stress solution for a single dislocation, integrated via a dislocation density experiencing a jump across the GB. Here, the singular internal stresses due to edge and screw dislocations are considered in complete duality to singular elastic strain gradients. The obtained singular terms constitute a basis for a GB model in terms of the constitutive relationship between the singular resolved effective stress and the jumps of GND densities on various slip systems. Then, the lattice microtracton is calculated as the projection onto the GB normal of the singular stress field due to edge and screw dislocations. Based on the obtained driving forces, two possible transmission criteria for the GND motion through the GB are proposed in strong and weak formulations. As an illustrative example of the polycrystalline model developed, the authors consider a bicrystal under strict plane strain and obtain an analytical solution. The ability of incoming dislocations to cross the GB is evaluated by using the transmission criterion and the above physically oriented constitutive equation in the cases of screw and edge dislocations.
scientific article; zbMATH DE number 5355945
scientific article