Polycrystalline structural materials often contain inherent stresses that partition across the microstructure. From composites to fabricated components, stress and strain fields are often highly heterogeneous at the microstructural level, contrary to the inferences commonly made in continuum mechanics. Since these “residual” stresses are intimately linked to failure processes, one of the challenges in modeling constitutive behavior is to predict the magnitude of the stress heterogeneities in polycrystals and thus understand the implications.