FREE-SURFACE DUCTILITY IN UPSETTING

Cold upsetting of a circular cylinder is often used to evaluate the co ld forgeability of forming materials. The index of the forgeability is the critical strain at which a crack occurs on the expanding free sur face of the upsetting cylinder. The forming limit due to the cracking is analyzed by a method based on the sufficient condition for the coll apse of the unique solution. The modes of cracking are determined by c omparing the stabilities of deformation from the forming limit to the two modes able to permit strain rate discontinuity on the plane of loc alized necking. Numerous experiments published in the literature have shown a linear relationship with a slope of -0.5 in circumferential st rain vs axial strain at the forming limit. The forming limit and the m ode predicted are in very good agreement with the experimental results .