On Predicting Forming Limits Using Hill\u27s Yield Criteria

The analysis of localized necking is strongly dependent on the yield function. To predict forming limits, therefore, numerous yield criteria have been postulated to characterize the plastic deformation of sheet materials. Among them Hill\u27s 1948 and the fourth form of 1979 yield criteria are the most commonly used. A new yield criterion was proposed by Hill in 1993. It uses five independent and easily obtainable material parameters, which makes it flexible in representing the shape of the yield locus for different materials. The present investigation compares these three yield criteria in forming limit predictions based on both the Marciniak and Kuczynski (M-K) approach and the bifurcation analysis. It is observed that the M-K analysis based on Hill\u27s 1993 yield criterion provides forming limit predictions in agreement with experimental data. The bifurcation analysis based on Hill\u27s 1948 yield criterion also provides an acceptable prediction of forming limits for aluminum, although they are slightly higher. All three yield criteria are found to provide acceptable predictions for aluminum-killed (AK) steel based on the M-K method. For brass, only the prediction based on the M-K method and Hill\u27s 1993 yield criterion is close to the trend of experimental data