An Analytic Solution for an Expanding/Contracting Strain-Hardening Viscoplastic Hollow Cylinder at Large Strains and Its Application to Tube Hydroforming Design

Abstract

This paper presents a semi-analytic rigid/plastic solution for the expansion/contraction of a hollow cylinder at large strains. The constitutive equations comprise the yield criterion and its associated flow rule. The yield criterion is pressure-independent. The yield stress depends on the equivalent strain rate and the equivalent strain. No restriction is imposed on this dependence. The solution is facilitated using the equivalent strain rate as an independent variable instead of the polar radius. As a result, it reduces to ordinary integrals. In the course of deriving the solution above, the transformation between Eulerian and Lagrangian coordinates is used. A numerical example illustrates the solution for a material model available in the literature. A practical aspect of the solution is that it readily applies to the preliminary design of tube hydroforming processes.

Numerical and asymptotic solutions of the unsteady mixed convection boundary-layer flow over an expanding/contracting vertical cylinder

“…The application of an expanding cylinder can be found in the engineering context as well such as tube hydroforming process. During the process of tube hydroforming, not only the internal pressure that controlled the speed of expansion (Lang et al , 2021) plays an important role, but the heat transfer process that involved in this process is also a matter of concern.…”