Simulation of shear band phenomenon in metal forming and cutting

A plane strain finite element formulation and solution procedure for shear band formation during the plane strain metal forming and cutting process are developed and presented. The large-strain 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 eigenmodes when required. A five-node ten degree-of-freedom (d.o.f) \u27crossed-triangle\u27 element, a four-node eight d.o.f. element with selective reduced integration, an eight-node sixteen d.o.f. element, and a four-node eight d.o.f. element with an embedded shear band are formulated. 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 four node quadrilaterals are comparable to the five node crossed-triangle element as well as the eight node element. To further validate and to demonstrate the predictive capability and practical applicability of the present development, two plane strain metal forming examples and an orthogonal metal cutting example are investigated. The first application is a numerical simulation of a sheet-stretching test with results compared with experimental data for a commercially pure aluminum-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 aluminum billet through straight-sided dies is presented and characteristic features of the formation of dead metal zone are observed. The final application is a numerical simulation of the formation of a discontinuous chip in the orthogonal metal cutting. Features of discontinuous chip formation are observed during the simulation and are compared with experimental results