A general approach for predicting the drawing fracture load and limit drawing ratio of an axisymmetric drawing process

Abstract

Based on Hill’s theory of plasticity and the Swift diffuse instability criterion, new theoretical models are proposed for predicting the drawing fracture load and limit drawing ratio (LDR) of an axisymmetric cup drawing. These models take into account the influence of triaxial stress state, anisotropy, strain hardening, bending, and tool geometry. By introducing both conventional and modified Hollomon’s equations, the influences of these variables on the constitutive relation of sheet steels are also analyzed. It is shown that the theoretical predictions of the drawing fracture load are in good agreement with experimental results for a wide range of sheet steels currently used in the automotive industry. Specific tool geometries are found to decrease the drawing fracture load and the LDR, because of increased triaxial stress states and bending effects at the critical section of the workpiece. The optimum punch-profile radius is found to be between 5.0 and 7.0 times the thickness of the sheet. Additionally, the role of both the anisotropy and strain-hardening properties of the sheet steels in determining the drawing fracture load and the LDR are, subsequently, discussed.