Modeling of stable cyclic stress‐strain responses under non‐proportional loading

This paper proposes a simple two‐surface plasticity model for strain controlled conditions which includes only five material constants to describe the stable stress‐strain relationship under extensive non‐proportional loadings. In this model, the Mróz kinematic hardening rule is adopted to describe the instantaneous translation of the yield surface, and a larger radius of the limit surface is selected to avoid overlapping of the one with the limit surface. A non‐proportionality measure of strain path on the basis of the minimum normal strain range is proposed. Procedures to determine the minimum normal strain range are also presented for general multiaxial loadings. The proposed two‐surface model is relatively convenient to be used since it is not overly sensitive to the modeling parameters. Four kinds of material (type 304 stainless steel, S460N steel, 30CrNiMo8HH steel, and 1%CrMoV steel) tested under strain controlled conditions are used to validate the reliability of the proposed model. Comparisons between test results and model predictions under 19 types of nonproportional strain paths show that the proposed model predicts relatively accurate stress responses under non‐proportional loading paths by introducing non‐proportional cyclic hardening coefficient and non‐proportionality factor into the developed evolution equations.