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

Based on Hill's theory of plasticity and the Swift diffuse instability crit erion, new theoretical models are proposed for predicting the drawing fract ure load and limit drawing ratio (LDR) of an axisymmetric cup drawing. Thes e models take into account the influence of triaxial stress state, anisotro py, strain hardening, bending, and tool geometry. By introducing both conve ntional and modified Hollomon's equations, the influences of these variable s on the constitutive relation of sheet steels are also analyzed. It is sho wn that the theoretical predictions of the drawing fracture load are in goo d agreement with experimental results for a wide range of sheet steels curr ently used in the automotive industry. Specific tool geometries are found t o decrease the drawing fracture load and the LDR, because of increased tria xial stress states and bending effects at the critical section of the workp iece. The optimum punch-profile radius is found to be between 5.0 and 7.0 t imes the thickness of the sheet. Additionally, the role of both the anisotr opy and strain-hardening properties of the sheet steels in determining the drawing fracture load and the LDR are, subsequently, discussed.