Normalized resolved shear stress calculations for single crystals subjected to multiaxial loading

Abstract The propensity for activation of uniaxially loaded slip systems within uniquely oriented crystals can be calculated via Schmid's law. A similar procedure for multiaxial loads is desired. We present a method for bounding tensor-based resolved shear stress calculations by [0, 0.5] using normalized multiaxial stress tensors, allowing interpretation analogous to Schmid factors. We also present a method to visualize orientation dependence of slip system activity resulting from these calculations using pole figures. Variance in this visualization method changes with crystal and slip system symmetries. Demonstrations are shown for hexagonal close-packed, face-centered cubic, and body-centered cubic slip systems under plane stress tension-tension loadings.