Long-range internal stress from non-uniform geometrically necessary dislocations: A prediction method refined by dislocation dynamics simulations

Abstract

The accumulation of geometrically necessary dislocations (GND) at grain boundaries is a primary source of long-range internal stress (LRIS) in polycrystals. The distribution of GNDs is typically inhomogeneous, and certain dislocation substructures with concentrated GNDs introduce a strong non-local effect. While many studies have explored the relationship between LRIS and the density of GNDs in polycrystals, few have discussed the influences of GND distribution patterns on LRIS calculations. This study employs dislocation dynamics (DD) simulations to investigate the LRIS of non-uniform GNDs confined within a grain boundary facet. First, the stress fields of three elementary types of GND bands with twist, tilt, and epitaxial dislocations are systematically analyzed using DD simulations. Considering the finite-size effect, scaling coefficients for recovering the LRIS around these GND bands are identified. Subsequently, non-uniform dislocation patterns are built to examine the distribution of LRIS at varying distances from grain boundary facets. In line with determining LRIS derived from an averaged surface GND density, an improved calculation method that accounts for the non-homogeneity of GNDs is developed. Finally, this method is applied to predict the LRIS of a set of GND facets with more complex dislocation patterns extracted from face-centered cubic grains. The predictions show good agreement with stress results computed by DD simulations, suggesting potential for further improvement of the dislocation density-based constitutive approach.