The plastic strain and the rolling direction dependence of the traditional and the biaxial r-values

Abstract

The Lankford number (i.e. r-value) has long been used as a key parameter in the science of sheet metal forming, for the mathematical description of plasticity. The traditional way of thinking is that this value is a constant in a given direction, and the definition is recommended at Ag-1 % plastic strain. In this study we focused on the evolution tendency of r-value in the function of the plastic strain, in different loading directions. Two automotive thin sheets, DC04 and DP1000 were examined by uniaxial tensile tests and compression tests to investigate both the traditional and the biaxial r-values. The axial and the transverse deformations during the tensile tests were applied under continuous process monitoring with a touchless video extensometer. The compression tests were carried out intermittently, i.e. the tests were stopped after given forces, and the thickness as well as the diameters were measured parallel and perpendicular to the rolling direction. Our results show that the evolution of the traditional r-value is clearly shown for both materials, and its value is given here by linear and polynomial functions. Besides, the changing characteristic of the r-value as a function of deformation does not show a trend with respect to the rolling direction. The biaxial r-value can be well-defined by compression tests despite the small thickness, and the results are less dependent on friction.