Analytical Approach for Predicting the Thickness Distribution and Plastic Strain of an Axisymmetric Deep Drawn Part

Abstract

This contribution established an axisymmetric mathematical modeling for a prediction of induced plastic strain from sheet metal thinning of the achieved final part geometric shape in deep drawing process and the fundamentals of deformation mechanics in plane strain bending around a straight line, bending around a curve and stretch/draw forming condition. The mechanics and the closed-form solutions facilitate for the prediction of the final achieved plastic strains, stresses, and loads in the deep drawing operations without using FEM. A closed-form solution from a 2D final part geometric cross-section input was developed to calculate a deep draw effect to the achieved residual plastic strain due to variation of die profile radius, punch nose radius, sheet thickness and steel material types. Close agreement with FE results was achieved for the plastic strain values at the concave and convex interface regions with the proposed bend-unbend additional thinning method when compared to membrane calculation method.