Third Paper: A Theoretical Estimate of the Limits of Ductility in the Free Extrusion Process

The paper presents a theoretical method of estimating the limits of ductile flow in metal forming operations. The method is applied in detail to the problems of ‘arrowhead’ and ‘fir-tree’ cracking in the free forward extrusion of a bar through conical dies.

An approximate method is introduced for integrating the equations of equilibrium along the axisymmetric slip lines in the plastic deformation zone. The results give estimates of the mean extrusion pressures and the bulge limits which compare well with experiments and thus suggest that the theoretical internal stresses will be close to the true internal stresses in free extrusion. The theoretical internal stresses are used, together with the theoretical strains to fracture from the instability theory of fracture, to predict the conditions of die and specimen geometry which lead to internal cracking. The theoretical fracture limits are found to be in close agreement with experimental results.