A Method for Determining the Workability Diagram by Varying Friction Conditions in the Upsetting of a Cylinder between Flat Dies

Abstract

This paper aims to develop a method for determining the workability diagram by varying frictional conditions in the cylinder upsetting test. The method is based on a known theoretical relationship between the average stress triaxiality ratio and in-surface strains if the initiation of fracture occurs at a traction-free surface. This relationship is valid for any rigid/plastic strain hardening material obeying the Mises-type yield criterion and its associated flow rule, which shows the wide applicability of the method. The experimental input to the method is the strain path at the site of fracture initiation. Neither experimental nor numerical determination of stress components is required at this site, though the general ductile fracture criterion involves the linear and quadratic invariants of the stress tensor. The friction law’s formulation is neither required, though the friction stress is the agent for varying the state of stress and strain at the site of ductile fracture initiation. The upsetting tests are carried out on normalized medium-carbon steel C45E, for which the workability diagram is available from the literature. Comparison of the latter and the diagram found using the new method shows that the new method is reliable for determining a certain portion of the workability diagram.

Keywords

• ductile fracture
• workability diagram
• upsetting
• friction