Grain size effects on back stresses induced by GND: A Dislocations Dynamics study

During plastic deformation of polycrystal, plastic incompatibility develops at Grain Boundaries (GBs) due to the difference in grain orientation and slip activity. The incompatibility appears at GBs as dislocation walls and dislocation pileups. For dislocation walls, the distribution can be fully described by a singular Nye dislocation density tensor, which is known to induce back stresses inside the deforming grain. While the analytical solutions for infinite walls are known for a long time, the grain size effect on these stresses, specifically the area of the wall, did not receive enough attention in the literature. Dislocation Dynamics (DD) simulations are used to compute stresses as a function of the distance from walls of finite height formed of finite dislocation lines of different characters. It is found that, for all wall configurations, the profiles of the stress components are close to the c² – distribution functions: one is monotonously decreasing and one has a maximum close to the grain center. Besides, it is shown that the spatial evolution of the stress components scales invariably with the surface density and the dimensions of the wall. Formula accounting for the dislocation character, wall dimensions and dislocation surface density are established and tested to predict the back stresses prevailing in close grains deforming under different load and boundary conditions. The stress predicted at the grain center in seven different configurations was always found within 20% of stress computed directly in DD simulations.