Model for description of nonlinear unloading-reloading stress-strain response with special reference to plastic-strain dependent chord modulus

Abstract

To describe the nonlinear stress-strain response in the unloading-reloading process, a model was proposed for the variation of the elastic modulus during the process. This model is directly associated with the widely used equation for the plastic-strain dependent chord modulus, and no additional material parameters are needed for modeling. In this model, nonlinearly changing elastic modulus is explicitly determined from the current stress state, instead of using an accumulated-strain measure. Therefore, it is robust against the numerical noise (e.g., stress oscillation) in computation. Based on the same elastic modulus model, two types of calculation models were constructed, namely, a micro-plasticity model and nonlinear-elasticity model. From the numerical simulations of the non-proportional unloading-reloading processes, it was found that the stress-strain responses calculated by the two models were very similar to each other. The model was validated by comparing the calculated stress-strain results with the corresponding experimental observations on a DP980 advanced high-strength steel sheet (AHSS). The influence of the nonlinear unloading behavior on the springback prediction was discussed by performing two cases of springback simulations (a uniform bending-unbending and a hat-shaped draw-bending) on two types of AHSSs (dual-phase DP980 and precipitation strengthen 780 R), by using several types of elastic modulus models. The best choice for springback simulation is to use the nonlinear elastic model to describe the realistic stress-strain responses in the yield surface, along with an appropriate kinematic hardening model of plasticity to express smooth elastic-plastic transition behavior. In comparison with the springback calculation by the nonlinear model, a certain amount of errors were found when using the plastic-strain dependent linear models, however, they were not very large. Thus the second best option in springback simulation would be to use the chord modulus model because of its simple modeling and high computation efficiency.