On the analysis of stress state in elliptical tensile neck

The tensile necking in cylindrical and plate specimens is described based on a modification of the Bridgman theory for an isotropic case. A method of determination of principal stress trajectories in an elliptical tensile neck is put forward, which involves transformation of the initial coordinate grid by means of conformal mappings. Expressions are derived for the principal stresses and the radius of curvature of stress trajectories. Based on assumptions that depart from the Bridgman theory, an approximate analytical solution is obtained for the stress distribution in specimens with an elliptical cross-section. The new solution belongs to the one-parameter family of solutions which includes the Bridgman’s and Davidenkov–Spiridonova’s solutions.