Geometrically necessary dislocations and related kinematic hardening in gradient grained materials: A nonlocal crystal plasticity study

Gradient grained metals whose microstructure is characterized by a spatially graded grain size distribution show a better strength-ductility combination than their homogeneous counterparts. Kinematic hardening associated with geometrically necessary dislocations (GNDs) is considered to be a dominant strengthening mechanism in gradient grained metals. However, the precise kinematics of GND accumulation and the nature of the back stress fields remain unclear, restricting the understanding of their deformation mechanisms. In this work, a nonlocal crystal plasticity model which explicitly accounts for the interaction between dislocations and grain boundaries is developed. The nonlocal feature is achieved by introducing a flux term to account for the spatial redistribution of dislocations due to their motion. In addition, back stress produced by the spatial variation of GND density introduces an explicit internal length scale into the model. The nonlocal nature of the model on the slip system level enables the direct investigation of strain gradient effects caused by internal deformation heterogeneities. Furthermore, the interaction between dislocations and grain boundaries leads to the formation of pileups near grain boundaries, which is key to studying the grain size effects in polycrystals. Finite element implementation of the model for polycrystals with different grain sizes quantitatively captures the grain size effect. Simulation results of gradient grained materials and their homogeneous counterparts demonstrate that smaller grains lead to higher GND density and enhanced back stress. Small grains significantly contribute to the GND-induced isotropic hardening and GND-induced kinematic hardening in gradient grained metals. This investigation helps to understand the underlying strengthening mechanisms of gradient grained metals, and the model can be readily applied to other kinds of heterogeneous materials.