Formability evaluation based on a constitutive model with stress rate direction dependency considering bifurcation modes

Abstract

Accurately predicting the fractures that occur in materials during forming not only improves quality, but also reduces the amount of material that is discarded. Therefore, as a key technology for digital transformation to achieve carbon neutrality, it is necessary to improve the accuracy of forming analysis and establish an efficient method for predicting forming limits. Formability assessment is typically performed using ductile fracture criteria or experimental forming limit diagrams (FLDs), which require prior fracture testing. The authors have established a forming evaluation method based on three-dimensional local bifurcation theory as a versatile method that does not require destructive testing. This method can follow abrupt changes in the stress field, such as localized necking, by using a flow rule that takes into account the directionality of the stress rate. In this study, the proposed method is applied to the tensile testing and the forming analysis of a square cup drawing to analytically verify the location and onset time of local bifurcation modes that may lead to fracture.