An exact rigid/plastic solution for a thick-walled tube subject to internal pressure and axial load considering a general isotropic hardening law and its application

Abstract

The paper presents a new exact rigid/plastic solution that describes the combined elongation (or shortening) and expansion of a tube. The von Mises yield criterion and its associated flow rule are adopted. No restriction is imposed on the isotropic hardening behavior of the material. The solution is facilitated using a Lagrangian coordinate. A numerical technique is only required for evaluating ordinary integrals. The solution applies to the preliminary design of tube hydroforming. In particular, the variation of the inner pressure with the current tube’s length that ensures a prescribed change in the tube’s radii is determined. Moreover, the modified Cockroft-Latham fracture criterion applies to predict ductile fracture initiation.