Forming Limit of Sheet Metal Considering Surface Roughness

Abstract

Experimental results concerning the forming limit of in-plane stretching of brass, copper and aluminum sheet alloys are presented. Theoretical curves of limit strains are calculated on the basis of the modified M-K (Marciniak and Kuc'zynski) analysis in which M-K analysis is applied to the post-diffuse necking (post-instability) condition. The imperfection is represented by the apparent initial inhomogeneity factor, f, as estimated from the ratio of the minimum to maximum thickness of the sheet at the instability condition, which is equal to unity at plane-strain condition and then decreases with an increase of strain ratio. It can be concluded that the predicted limit strains depend on the work hardening law equations applied and, when best fit work hardening law equations for the materials, namely Voce, Swift, and Hollomon law equations for brass, copper, and aluminum, respectively, are applied, the predicted limit strains are in food agreement with the experimental data plots. These results are explained in terms of the work hardening behavior.