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

摘要

Based on Hill's theory of plasticity and the Swiftdiffuse instability criterion, new theoretical models are proposedfor predicting the drawing fracture load and limit drawing ratio(LDR) of an axisymmtric cup drawing. These models take intoaccount the influence of triaxial stress state, anisotropy, strainhardening, bending, and tool geometry. By introducing bothconventional and modified Hollomon's equations, the influencesof these variables on the constitutive relation of sheet steels arealso analyzed. It is shown that the theoretical predictions of thedrawing fracture load are in good agreement with experimentalresults for a wide range of sheet steels currently used in theautomotive industry. Specific tool geometries are found todecrease the drawing fracture load and the LDR, because ofincreased triaxial stress states and bending effects at the criticalsection of the workpiece. The optimum punch-profile radius isfound to be between 5.0 and 7.0 times the thickness of the sheet.Additionally, the role of both the anisotropy and strain-hardeningproperties of the sheet steels in determining the drawing fractureload and the LDR are, subsequently, discussed.