Plane strain finite element simulation of shear band formation during metal forming

Abstract

AbstractA plane strain finite element formulation and solution procedure for shear band failure during the plane strain metal forming process are developed and presented. The large strain elastic‐plastic formulation includes a 5‐node 10‐degree‐of‐freedom (d.o.f.) ‘crossed‐triangle’ element, a 4‐node 8‐d.o.f. element with selective reduced integration, an 8‐node 16‐d.o.f. element and a 4‐node 8‐d.o.f. element with an embedded shear band. The formulation includes an elastic‐plastic material model with a modified Gurson yield function and combined isotropic‐kinematic hardening. The solution procedure is based on a Newton–Raphson incremental‐iterative method with an orthogonal projection of zero or negative eigen‐modes when required. Two different examples of plane strain tension test are studied with results compared with available numerical solutions to evaluate the present formulation and solution procedure of the four different elements. The results demonstrate that both types of the 4‐node quadrilaterals are comparable to the 5‐node crossed‐triangle element as well as the 8‐jiode element. To further validate and to demonstrate the predictive capability and practical applicability of the present development, two plane strain metal forming examples are investigated. The first application is a numerical simulation of a sheet‐stretching test with results compared with experimental data for a commercially pure aluminium–magnesium 5182‐O sheet. The load vs. extension history and the through‐thickness strain are compared. The good agreement suggests that it is possible to numerically determine the parameters needed for the modified Gurson yield function. The second application is a numerical simulation of the formation of dead metal zones in the extrusion process. A plane strain extrusion of a short aluminium billet through straight‐sided dies is presented and characteristic features of the formation of dead metal zone are observed.