Elastic-Viscoplastic Analyses of Simple Stretch Forming Problems

Plane strain and axisymmetric punch stretching problems incorporating Coulomb friction are considered. Based on a general rate-sensitive flow theory and the nonlinear theory of membrane shells, the formulation includes work hardening and normal anisotropy. Two numerical schemes are presented. One is an extension of a previously developed finite element method (restricted to axisymmetric or plane strain problems) while the other is a nonlinear iterative method (restricted to plane strain). Experimental data on aluminum-killed steel are used to devise an explicit form for the rate dependence, and these schemes are applied to plane strain punch stretching (by a flat bottomed punch) and to hemispherical punch stretching. It is shown that a theoretical instability associated with the elastic-plastic analysis in plane strain stretching is removed by inclusion of the strain rate effect, while a better fit to experimental data on strain distribution in hemispherical punch stretching is obtained.