A tensor function for the R-value of sheet metal

Abstract

Tensile testing of sheet metals shows that both the orientation of the testpiece in the plane of the sheet and the degree of rolling reduction can influence the R-value. To explain this a quadratic and a cubic yield function are adapted to published results for a number of sheet metals. The cubic function can reproduce every dependence of R upon orientation as found from off-axis tensile tests. Present work shows that a simpler quadratic function lies within the material deviations. The theory of tensor functions enables this function to be expressed in terms of prior plastic strain, and so they provide a description of the dependence of the R-value on the processing history of a sheet metal. It is demonstrated how this junction can be applied to account for the in-plane R-variations observed when rolling a copper sheet under plane strain laboratory conditions. Of particular interest are the predictions that lead to improved drawability, i.e., the rolling reduction and sheet orientation that optimize R. A further examination is made of the stability of the R-variation pertaining to a given rolling reduction. It is shown that R remains stable under subsequent uniaxial plastic straining for any direction in the plane of the sheet. Moreover R is not altered appreciably by relatively small amounts of tensile plastic prestrain aligned with the rolling direction. That R is sensibly constant is the usual assumption made in plasticity theory.