Investigation of Critical Stress Concentration Factor in Analytical Stress Based Forming Limit Criterion

Tearing concerns in sheet metal forming have traditionally been predicted by comparing the strain state imposed on a material to its associated strain based Forming Limit Diagram. A shortcoming of this strain based failure criterion is that the Forming Limit Curves exhibit strain path dependence. Alternatively, a stress based failure criterion was introduced and shown analytically and numerically to exhibit less strain path dependence. In our past research, an analytical model was created to predict the stress based Forming Limit Curve. Inputs into the model include a material constitutive relationship, anisotropic yield criterion and a critical stress concentration factor, defined as the ratio of the effective stress in the base material to the effective stress in the necking region. This stress concentration factor is thought to be a material parameter, which characterizes a material’s ability to work harden and prevent the concentration of stress which produces the necking condition. In this paper, the critical stress concentration factors for steel and aluminum alloys were determined by comparing analytical model predictions and experimental data and found to be significantly different. A setup is then proposed to experimentally measure the critical stress concentration factors and initial results are presented.