New theoretical model for predicting limit strains in the punch stretching of sheet metals

An initial non-uniformity in thickness of a sheet metal, which is commonly assumed as a basis for the theoretical prediction of limit strains in the biaxial stretching process, is considered here as a feature of the mathematical idealization of a complex process, rather than as a material imperfection existing in a real sheet metal. The present concept permits the degree of initial inhomogeneity to vary with the stress ratio, as well as with the mechanical properties of the material. When such a variation is allowed for in a suitable manner, the predicted forming limit curves exhibit a relatively small dependence on the degree of normal anisotropy of the sheet metal, and follow a trend that is in agreement with what is observed experimentally. The results demonstrate the importance of the non-quadratic yield function when dealing with sheet metals with a range of R-values of less than unity.