Strain gradient plasticity with nonlinear evolutionary energetic higher order stresses

Abstract

This paper explores the effect of evolutionary-type nonlinear energetic higher order stress inside the strain gradient plasticity framework that allows nonlinearity in dissipation. Based on the fundamental principles of thermodynamics, a multi-term Chaboche-type model has been formulated to describe the evolution of energetic moment stresses that depend on strain gradient and effective plastic strain. The derived evolutionary relation shows a coupling between energetic and dissipative length scales. The energetic part of the higher order stress, related to the GND formation, saturates as effective plastic strain increases during plastic flow. Higher order stress update equation and material tangent are derived using implicit time discretization. The proposed nonlinear energetic moment stress model confirms its applicability compared to experimentally observed responses. Our study demonstrates the importance of incorporating a nonlinear kinematic hardening rule to accurately represent the Bauschinger effect in samples with a thickness of less than 1μm. The cyclic bending experiment with a single slip sample shows that the nonlinear kinematic hardening rule can effectively capture nonlinearity in the experimental observation. Compressed shear layer simulation reveals that consideration of thickness-dependent relaxation coefficient accurately models the experimental observations. Thus, it makes further relevant consideration of a more advanced kinematic hardening rule through the proposed approach.