Stress fields of finite-size dislocation walls and prediction of back stress induced by geometrically necessary dislocations at grain boundaries.

At low strain, geometrically necessary dislocations (GND) confined in the close vicinity of grain boundaries can be approximated as a dislocation wall structure called a GND facet. Analytical solutions derived from Field Dislocations Mechanics (FDM) theory allow calculating the stress components associated with the GND facets but are unable to account for the stress field variation induced by finite size effect. Dislocation dynamics simulation is used to investigate the true stress field of GND facets. The geometry, dimension and dislocation density of three generic types of GND facets (twist, tilt and epitaxial facets) are systematically studied. In all cases, the stress field generated by GND facets is proportional to the surface GND density and its spatial distribution can be recovered using FDM solution combined with two scaling parameters identified from DD simulation results. This calculation procedure can be generalized to any crystal structure by relating the components of the surface Nye's tensor to the solutions of simple cubic slip systems. Finally, static and dynamic tests are made to validate the calculation of back stress within regular grains bounded by GND facets. [ABSTRACT FROM AUTHOR]