Dislocation-Evolution Based Comprehensive Phenomenological Model for Continuum-Scale Description of Stress–Strain and Work-Hardening Behavior

Abstract

Bridging continuum-scale description of uniaxial tensile plastic stress–strain behavior with adjacent mesoscale deformation models is important and, hence, requires identification of appropriate physical processes and the associated parameters. In this work, a comprehensive phenomenological model (CPM) for true stress–true strain behavior of a polycrystalline material in the plastic regime was developed based on the postulation of physical processes, viz. dislocation nucleation, multiplication, and annihilation, satisfying the statistical perception of dislocation evolution during deformation. Incorporation of these processes through intricate formulations using physical parameters, such as dislocation density, dynamic mean-free-path (MFP), fixed MFP etc. demonstrated a precise fit of a uniform tensile plastic flow curve and of its spin-off work-hardening (WH) behavior, simultaneously. Variation in the calculated parameters for different stress–strain responses of different alloy systems and the sensitivity analyses helped in appreciating the discrete modular nature of the model. Precise fits in both plastic stress–strain and WH responses using the same set of coefficients ensured the CPM to be reliable in simulating realistic uniaxial stress–strain plots from the physical parameters for various alloys. The model advances the understanding of phenomenological modeling especially in terms of incorporation of the dislocation nucleation mechanism in the evolution process, ensuing explicit expression for dislocation evolution with strain and grain size dependence. The present approach is deemed appropriate for linking the length scales in the multiscale description of deformation.