Influence of Hardening and Softening on Limit Pressure of Cylindrical Cavity Expansion

Abstract

This paper presents a large strain solution for the problem of cylindrical cavity expansion embedded in hardening–softening, non-associative Mohr-Coulomb material. The solution is obtained by transforming the problem from the original radial domain to the effective stress space in the hardening regime and to the effective plastic strain in the softening regime. The robustness of the solution is demonstrated by tracing the entire loading history of a pressurized cavity embedded in weak sandstones in large expansions and the calculation of the limit pressure beyond which the hole expands without further pressurization. The calculated radial stress profiles are completely smooth at the elastoplastic (EP) and the hardening–softening boundaries. The calculated limit pressure increases with increasing degree of pressure sensitivity, as expected for a stronger material. The limit pressure decreases dramatically as the rate of material softening increases. The elastic perfectly plastic limit-pressure solution, which ignores hardening, is quite close to the value determined from the full EP hardening with the same peak strength. The combination of non-associativity and material softening causes the breakdown of the solution before reaching the limit pressure due to emergence of bifurcation in the form of shear banding and surface instabilities.