Analytical Description of Neck Profile during Tensile Testing of Cylindrical Specimens

Abstract

One of the problems of studying the rheological properties and plasticity of metals and alloys from the results of tensile tests of cylindrical specimens is the need to determine the stress triaxiality value, which depends on the shape and size of the neck formed. An analytical description of the neck profile makes it possible to increase the accuracy of experimental measurements of its dimensions, in particular, the radius of curvature in the smallest cross-section of specimen. This paper is devoted to searching a universal neck profile equation that allows calculating the radius of neck curvature regardless of the nature of the material hardening curve and the stage of strain localization. The exact surface equation is established and its accuracy is estimated for hardening and softening material.