Prediction of forming limit curves for nonlinear loading paths using quadratic and non-quadratic yield criteria and variable imperfection factor

Industrial sheet metal forming processes often involve complex deformation modes and it is necessary to consider nonlinear loading path effects when predicting forming limit curves. Moreover, the yield criterion plays a critical role in the accuracy of predicted forming limits.In this work the MK analysis was modified to relate the initial imperfection factor to a physical property such as the surface roughness, and the orientation of the imperfection was also allowed to vary. This model was used to predict the strain-based and stress-based forming limit curves (FLC and SFLC) of sheet materials that are subject to either linear or non-linear strain paths.Two different yield criteria were employed in this study, Hill's 1948 quadratic yield criterion and Hosford's 1979 non-quadratic yield criterion. The theoretical model was validated by comparing predicted FLC and experimental FLC curves obtained from the literature. FLCs and SFLCs predicted with these two yield criteria were compared for both linear and nonlinear loading paths.Results showed that both the quadratic and non-quadratic yield criteria predict the FLC with acceptable accuracy however on the whole the non-quadratic yield criterion generally provides a slightly better correlation with experimental data, especially on the right side of the FLC. Keywords: Forming limit curve, Formability, Yield criterion, MK analysis, Sheet metal, Loading path