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

Elena Lyamina

doi:10.15625/2525-2518/18665

Author affiliations

Authors

Elena Lyamina Laboratory of Mechanics of Technological Processes, Ishlinsky Institute for Problems in Mechanics RAS, pr. Vernadskogo 101-1, 119526 Moscow, Russia https://orcid.org/0000-0002-7319-8703

DOI:

https://doi.org/10.15625/2525-2518/18665

Keywords:

combined elongation (or shortening) and expansion, rigid plastic material, general hardening law, tube hydroforming, analytical solution

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.

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