Modeling intrinsic size effects using dislocation density-based strain gradient plasticity

This work proposes a dislocation density-based strain gradient J2 plasticity framework that models the strength contribution due to Geometrically Necessary Dislocations (GNDs) using a lower order, Taylor hardening backstress model. An anisotropy factor is introduced to phenomenologically represent the differential hardening between grains in this J2 plasticity framework. An implicit numerical algorithm is implemented for the time integration of the finite deformation plasticity model. The framework is used to predict the intrinsic, grain size-dependent strengthening of polygrain ensembles. Deformation contours show the pile up of GNDs and backstress in the vicinity of grain interfaces. Model predictions of simulations with different grain sizes are shown to agree with the Hall–Petch effect and also with Ashby’s model of hardening due to GNDs in polygrain ensembles.