Yield Strength Asymmetry Predictions From Polycrystal Elastoplasticity

Since the 1960s, it has been known that elastoplastic polycrystal models predict asymmetries in the yield strength for polycrystals that have been prestrained. After prestraining in tension, a model polycrystal exhibits Bauschinger-like behavior in that it yields in compression at a lower stress magnitude than in tension. Furthermore, the knee of the reloading stress-strain curve is more gradual for compression than for tension. The origins of these behaviors reside in the assumption that links the macroscopic deformation to the deformations in individual crystals. More precisely, the reloading response is biased by the residual stress field which is induced with plastic straining by the anisotropy of the single crystal yield surface. While the earlier work pointed to the polycrystalline origins of the asymmetry, it did not resolve the degree to which the particular linking assumption affects the amount of asymmetry. However, due to the strong influence of the linking assumption on the crystal stresses, the sensitivity of the asymmetry to the linking assumption is expected to be appreciable. In this paper we examine the influence of the linking assumption on the magnitude of the computed yield strength asymmetry of prestrained polycrystals. Elastoplastic polycrystal simulations based on upper bound (Taylor) and lower bound (equilibrium-based) linking assumptions are compared to finite element computations in which elements constitute individual crystals. The finite element model maintains compatibility while satisfying equilibrium in a weak sense and treats the influence of neighboring crystals explicitly. The strength of the predicted Bauschinger effect does depend on the linking assumption, with ‘compatibility first’ models developing stronger yield strength asymmetries.