Analyzing the orientation dependence of stresses in polycrystals using vertices of the single crystal yield surface and crystallographic fibers of orientation space

The influence of the polygonal geometry of the restricted slip-associated yield surface on the distribution of stresses over a polycrystalline aggregate is examined. The vertices of the yield surface (stress states corresponding to polyslip) are grouped according to symmetries imposed by crystal structure. A measure of coaxiality between crystal stresses and yield surface vertex stresses is used to quantify the proximity of the stress in each crystal to a yield surface vertex. It is shown that for prescribed stress states, crystal stresses align more closely with certain families of vertices than with others and this relation between crystal and vertex stresses is found to depend on crystallographic fibers. Using this information, the stress distributions from finite element simulations of face centered cubic polycrystals are analyzed for different stress states ranging from uniaxial to balanced biaxial. Over the fundamental region of orientations, the propensity for the stress to align with a vertex is demonstrated. Further, the stresses in elements contributing to certain crystallographic fibers are shown to favor the vertex families aligned with those fibers. The implications of these results on mechanical behaviors, especially with respect to those observed in diffraction experiments, are discussed.