On the r-value of weakly-textured sheet metals

The r-value of a sheet metal is a measure of plastic anisotropy frequently used for prediction of performance in deep-drawing. It has also gured prominently in the literature for validation of theories where the predicted angular dependence of r is compared with the measured dependence. As plastic anisotropy in sheet metals is caused mainly by the preferred orientations of grains within the polycrystalline metal, it is natural to ask how r would depend on the orientation distribution function (ODF) w which de nes the crystallographic texture of the polycrystal. In this paper a general formula relating r to w is derived for weakly-textured sheet metals whose plastic ow behavior is governed by a plastic potential f( ; w), where denotes the deviator of the Cauchy stress. Speci c forms of this formula for orthorhombic sheets of cubic and of hexagonal metals are explicitly given.