On the origin of stress-strain relationships, the evaluation of softening coefficients, and mechanistic models for work hardening

Abstract

The constitutive stress-strain relationships for structural alloys under tensile loading are reconstructed by assessing the form and mechanism of work hardening relationships. The stress-strain relationships are derived that reproduce both the Hollomon and Voce expressions. The Voce expression well-reproduces the later steady-state stage of work hardening whereas the Hollomon relationship provides a better fit just beyond the proportional limit. Using the Voce relationship, sequential linear regions can be considered for the variation of work hardening with stress, wherein the slope is defined as the softening factor. It's found that the work hardening and softening factor increase as deformation initially progresses beyond yield but decrease once the steady state condition is achieved as the total plastic strain continues up to the instability. By evaluating the initial linear stage beyond yield, a formulation is developed to compute the dislocation activation volume for the onset of plastic deformation. In addition, a new constitutive nonlinear work hardening behavior is used to derive a new stress-strain relationship for the deformation of alloys that work harden to the strength instability as derived from a statistical mechanics of assessment of work hardening behavior. Utility is demonstrated for the wide range of stress-strain behavior that is observed for the additively manufactured Ti–6Al–4V alloy.