Compatibility stresses in fatigued bicrystals: Dependence on misorientation and small plastic deformations

Compatibility stresses are calculated for twist boundaries about [149] and a "random" high angle boundary between a [149] grain and a [100] grain, assuming piecewise homogeneous elastic fields and copper as model material. The "in-plane" compatibility stresses produced by uniaxial tension perpendicular to the boundary are a strong function of the crystallography of the grains and their misorientation. The effects of small plastic strains via crystallographic slip are also studied for three particular misorientations ([149] 90° and 180° twist boundaries and the "random" misorientation) and the type and amount of slip close to the boundary predicted by minimizing the elastic energy and using experimental measurements of the axial component of the plastic strain. The predictions agree quite well with experimental observations of slip traces close to the boundaries of copper bicrystals with those misorientations tested under high cycle fatigue conditions.