The tension-compression behavior of gradient structured materials: A deformation-mechanism-based strain gradient plasticity model

Abstract

Gradient structured (GS) metals can simultaneously achieve high strength and high ductility, which is the pursuit of structural materials. Abundant studies have pointed out that significant kinematic hardening is key to their strength-ductility combination. Unfortunately, few constitutive models were established to simulate and analyze the characteristic kinematic hardening behavior of GS metals. Thus, a systematic and deep understanding of the relationship between graded microstructure and the resulting macroscopic response needs further effort. In this work, we develop a strain gradient plasticity model that considers plasticity heterogeneities from the grain to the sample scale. A back stress model, which accounts for the dependency of dislocation pileups on grain size, is established to describe the cyclic deformation properties of GS materials. The established model unifies the concepts of geometrically necessary dislocations accommodating plasticity heterogeneities, grain size-dependent back stress, and reversible dislocation motion during reverse loading into a strain gradient plasticity framework. A finite element implementation of the model quantitatively predicts the uniaxial tensile and tensile-compressive responses of a GS copper bar as well as of homogeneously grained reference samples. The simulation indicates that the enhanced kinematic hardening of GS copper results mainly from fine grains in the GS layer and contributes to the considerable ductility of the GS material. The strain gradient cyclic plasticity model enables future investigation of the cyclic/fatigue behavior of GS materials, which is vital for the engineering application.