Stabilized cyclic stress‐strain calculation for metals under multiaxial loading

Abstract

A simple plasticity model for modeling the stabilized cyclic stress-strain responses is developed to consider the effect of non-proportional additional hardening. In the proposed model, the plastic modulus for uniaxial loading is extended to multiaxial loading by introducing the non-proportionality factor and the additional hardening coefficient. The two introduced factors take into account the effects of non-proportional additional hardening, not only on the shape of the loading path, but also on the material and its microstructure. And then, the basic Armstrong-Frederick nonlinear hardening rule is modified to model the evolution of the back stress. The consistency condition is enforced to obtain the relationship between the back stress and plastic modulus. The proposed model requires only six material constants for estimating the stabilized responses. Comparisons between the test results (30CrNiMo8HH steel, SA 333 Gr.6 steel, and 1 %CrMoV steel) and model predictions show that the proposed model predicts relatively accurate stress responses under both proportional and non-proportional loading paths. Keywords: Stabilized response / multiaxial fatigue / plastic constitutive model / nonproportionality factor / additional hardening coefficient Schlüsselwörter: Stabilisierende Resonanz / mehraxiale Belastung / plastisch konstitutives Model / Nichtproportionalitätsfaktor / zusätzlicher Härtungskoeffizient