Implications of a {open_quotes}cross-rolled{close_quotes} yield surface approximation on deep drawing

Abstract

During deep-drawing, two issues manifest themselves that are due to normal and planar anisotropy in the sheet. These are a dependence of the Limiting Draw Ratio (LDR) on the average thinning ratio (R-value), and a dependence of ear formation and thinning around the circumference on the variation of R-value in the plane of the sheet. The quadratic (1948 Hill) yield surface has been applied to these issues and it has been demonstrated that there are numerous higher exponent yield criteria that may more closely duplicate experimental trends. These predict varying degrees of R-value dependencies of uniaxial yields and strength ratios in multiaxial loading paths. The result of this is that there are sometimes subtle and sometimes substantial differences in the predictions of the various yield surfaces on deep drawing regarding LDR and earing. Additional differences arise due to the way the shear term (45-degree yield) and the 0-degree vs. 90-degree strengths are treated in each criterion. These dependencies (in-plane strengths generated by the yield surfaces) are shown to affect the results of both LDR and earing during cupping. In particular, the 1979 Hosford and 1989 Barlat (Tricomponent) criteria, although identical for the normal anisotropy (planar isotropy) case, are strikingly different for cases where there are differences at 45 degrees and 90 degrees from the rolling direction