A new strain gradient viscoplastic self-consistent crystal plasticity model for predicting geometrically necessary dislocations and length-scale dependent mechanical response

This paper describes a formulation of the first strain gradient (SG) viscoplastic self-consistent (VPSC) crystal plasticity model. The SG-VPSC model is based on the intragranular orientation spreads estimated from the fluctuations in the lattice rotation rates stemming from the second moments of the stress fields in the grains of a polycrystalline aggregate. The orientation spreads are spatially arranged to attain a functional form of the rotation tensor fields per grain for the calculations of spatial derivatives. The spatial derivatives pertaining to the “curl” operation are then taken to obtain the Nye dislocation tensor from the rotation tensor fields per grain. The Nye tensor is lastly used to calculate the density of geometrically necessary dislocations (GNDs) per grain. A dislocation density-based hardening law and an advanced composite grain model for twinning available in VPSC are extended to include the effects of GNDs. The potential and utility of the developed SG-VPSC model to simulate the mechanical response and concomitant evolution of microstructure including GNDs in polycrystalline metals are demonstrated using a few simulation case studies including compression of α-Ti specimens with different initial grain sizes along two specimen directions and a set of strain-path change deformation conditions applied to AA6016-T4.