Analysis of Local Fields of Elastic Stress Generated by Rotational-Shear Mesodefects Near the Junctions of Grains

Abstract

The work is devoted to the study of the structure of the elastic stress field in the area of junctions of grain boundaries containing strain-induced rotational-shear mesodefects. The jumps in plastic distortion of grains when passing through grain boundaries create additional misorientations on them, the mismatch of which at the junctions of grains leads to the appearance of linear mesodefects of the rotational type – junction disclinations. Planar mesodefects of the shear type appear on the flat sections of the boundaries, which are plastic shears uniformly distributed along the boundaries. These mesodefects create spatially inhomogeneous elastic stress fields near the junctions and ledges of the grains. They increase during plastic deformation and, at sufficiently large value of strain, initiate the formation of a fragmented material structure. Rotational-shear mesodefects are also the cause of the nucleation and accumulation of microcracks at the stage of viscous fracture of polycrystalline solids. In this work, asymptotic formulas are obtained that make it possible to analyze the distribution and anisotropy of the internal stress field in the vicinity of the grain junction from rotational-shear mesodefects. It was found that the components of the stress field weakly depend (logarithmically) on the length of the grain boundaries formatting junction of the grains. It is shown that the screening disclination of the dipole leads to the appearance of an angular dependence of the diagonal components of the elastic stress tensor in the vicinity of the junctions and its contribution to the elastic field of the disclinations dipole is about 10–15%. The obtained asymptotic expressions can be used to study the kinetics of a dislocation ensemble and to analyze the conditions for the nucleation of microcracks in the vicinity of joints and ledges of grains.