Material Model based on Stress-rate Dependency Related with Non-associated Flow Rule for Fracture Prediction in Metal Forming

Fracture prediction in metal forming has captured attention because of its practical importance. Recently, demand for fracture prediction has grown to conduct an effective forming process design using numerical simulation; however, the increasing use of high-strength steels and anisotropic materials prevents accurate simulation in large strains in which fracture tend to occur. In this study, a fracture prediction framework based on the bifurcation theory is constructed. The core is a material model based on stress-rate dependency related with non-associate flow rule. This model is based on non-associated flow rule with arbitrary higher order yield function and plastic potential function for any anisotropic materials. And this formulation is combined with the stress-rate-dependency plastic constitutive equation, which is known as the Ito-Goya plastic constitutive equation, to construct a generalized plastic constitutive model in which non-normality and non-associativity are reasonably included. Then, by adopting the three-dimensional bifurcation theory, more accurate prediction of the initiation of shear band is realized, leading to general and reliable construction of forming limit diagram.