The Stress and Deformation in Mild Steel During Axisymmetric Necking

Abstract

Closed-form solutions for the stress and deformation fields near the minimum section of the neck are obtained for a mild steel rod subject to axial extension by tensile loads. The procedure involves the use of an experimental result together with the incompressibility and symmetry conditions to find the deformations independently of the stresses. The stresses are then determined with the Levy-Mises flow equations without the use of a specific work-hardening rule. The solution, because of a simplifying assumption, is not valid throughout the entire plastic flow region. Experimental evidence indicates, however, that the region of validity extends well beyond the fracture region. The results enable the tensile test to be used to provide a complete description of material behavior until fracture. To accomplish this, it is necessary to measure the axial load and the radius and radius of curvature at the minimum section. As an example, the work-hardening characteristics of mild steel are determined under the usual work or strain-hardening hypothesis. The application of the results to ductile metals, other than mild steel, is briefly discussed.