Analysis of Forming Limits Using the Hill 1993 Yield Criterion

Forming limits of thin sheets are investigated using a yield criterion recently proposed by Hill (1993). This criterion utilizes five independent material parameters, which can be determined from uniaxial and balanced biaxial experiments, to describe a wide range of material properties of sheet metals, including the anomalous behavior of aluminum. In the present work, a bifurcation analysis is pursued to predict the onset of localized necking in strain rate insensitive sheet materials. A detailed parametric study is then conducted to evaluate the effect of various material parameters on the positive minor strain side of the forming limit diagram. It is observed that limit strains are strongly dependent on the shape of the yield locus. Forming limits predicted using Hill’s 1993 yield criterion are compared with those predicted using Hill’s 1948 and 1979 criteria. Results from the bifurcation analysis are also compared with experimental observations, as well as the limit strain predicitons based on the M-K analysis.