Dislocation saturation in slip rate driven processes and initial microstructure effects for large plastic deformation of crystals

Abstract

Dislocation-density-based crystal plasticity (CP) models are introduced to account for the microstructural changes throughout the deformation process, enabling more quantitative predictions of the deformation process compared to slip-system resistance-based plasticity models. In this work, we present a stability analysis of slip-rate-driven processes for some established dislocation density-based models, including the Kocks and Mecking (KM) model and its variants. Our analysis can be generalized to any type of dislocation density model, providing a broader framework for understanding the stability of such systems. We point out the existence of saturation dislocation densities and the essential role of initial dislocation density in distinguishing between hardening and softening responses. Since the initial microstructure, modeled through the dislocation density, could be related to the size or the sample preparation process, implicit size-dependent effects can also be inferred. To further explore these phenomena, we conduct numerical simulations of pillar compression using an Eulerian crystal plasticity framework. Our results show that dislocation-density-based CP models effectively capture microstructural evolution in small-scale materials, offering critical insights for the design of miniaturized mechanical devices and advanced materials in nanotechnology.