Fracture limit curve in upset forging of cylinders

The fracture limit curve in upsetting cylindrical billets is predicted. The analysis uses a semi-empirical solution for the stresses and strains together with a formulation based on plasticity theory for voided solids. Two fracture criteria are suggested. The first monitors the growth of the initial void volume fraction to the point where the load-carrying capacity of the material vanishes. The equatorial axial and hoop strains attained at this incident represent fracture strains. Being in disagreement with experiments, a second modified fracture criterion is proposed in which the equatorial free surface axial and hoop strains being related through a void growth law are calculated to the point at which deformation becomes localized. The predictions of this second criterion is in favorable agreement with experiments on several conventional and powder compact materials for a variety of upsetting conditions.