Fracture prediction in steady ideal plastic flows

Abstract

The theory of ideal plastic flows is a powerful tool for the preliminary design of metal forming operations. The present paper develops an approach to include a fracture criterion in this design procedure. The fracture criterion is based on the workability diagram and an average value of the triaxiality factor. In the case of three dimensional flows, this fracture criterion is modified which leads to mathematical advantages. It is shown that in many cases the modified criterion coincides with the original criterion. Using the proposed approach fracture initiation in drawing and extrusion processes is predicted. In particular, it is demonstrated that fracture predictions may be carried out without having the solution for stress and strain in the plastic zone (it is only necessary to know that it exists). The maximum possible area reduction with no fracture is given by the solution to a quadratic equation (in general, it might be a transcendental equation).