The micro-heterogeneity which resulted from dislocation sub-structure evolution was introduced into polycrystalline elastoviscoplasticity by means of a second-rank tensorial internal state variable. This evolving tensorial variable operated at the scale of the grain size and captured the effects of the sub-grain scale of dislocation sub-structure. The above micro-heterogeneity was seen by each single crystal slip system as a kinematic hardening, and also affected the larger-scale intergranular constraints in a self-consistent manner. The anisotropy arising from the micro-heterogeneity internal state variable improved the degree of correlation between calculated polycrystalline macro-scale responses (stress-strain curve, texture, axial stresses during fixed-end torsion) and experimental results. The elastic moduli under finite strains were measured experimentally in order to confirm the numerical predictions. Calculations which were performed using the micro-heterogeneity internal state variable agreed better, with elastic moduli measurements, than did the Taylor model.

Modeling Effects of Dislocation Substructure in Polycrystal Elastoviscoplasticity. M.F.Horstemeyer, D.L.McDowell: Mechanics of Materials, 1998, 27, 145-63