A constitutive law based on the self-consistent homogenization theory for improved springback simulation of a dual-phase steel

It has been widely observed that below the flow stress of a plastically deformed material the stress-strain response of the material does not obey the linear relation assumed in classical elasto-plastic models. As a matter of fact, a closer observation indicates that the stress-strain response of the material is nonlinear upon unloading. This results in a larger strain recovery than predicted by the linear elastic law which consequently results in an error in springback prediction. Furthermore, when the material undergoes compression after tension, it exhibits Bauschinger effect, transient behavior and permanent softening. The accuracy of the springback prediction is dependent on the capability of the model in capturing the above mentioned phenomena. In this work a constitutive law based on the self-consistent homogenization method is developed. In this model the stress inhomogeneity in the material is realized through considering a distribution in yielding of individual material fractions. The model was calibrated using stress-strain curves obtained from tension-compression experiments. The model has shown to be capable of predicting the nonlinear unloading behavior and the Bauschinger effect while maintaining computational efficiency for FEM simulations.