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RESEARCH PAPERS

# Unified Solutions to the Limit Load of Thick-Walled Vessels

[+] Author and Article Information
Jun-hai Zhao1

School of Civil Engineering, Chang’an University, Xi’an 710061, Chinazhaojh@chd.edu.cn

Yue Zhai, Lin Ji, Xue-ying Wei

School of Civil Engineering, Chang’an University, Xi’an 710061, China

1

Corresponding author.

J. Pressure Vessel Technol 129(4), 670-675 (Oct 20, 2006) (6 pages) doi:10.1115/1.2767356 History: Received January 31, 2006; Revised October 20, 2006

## Abstract

Unified solutions to the elastoplastic limit load of thick-walled cylindrical and spherical vessels under internal pressure are obtained in terms of the unified strength theory (UST) and the unified slip-line field theory (USLFT). The UST and the USLFT include or approximate an existing strength criterion or slip-line field theory by adopting a parameter $b$, which varies from 0 to 1. The theories can be used on pressure-sensitive materials, which have the strength difference (SD) effect. The solutions, based on the Tresca criterion, the von Mises criterion, the Mohr–Coulomb criterion, and the twin shear strength criterion, are special cases of the present unified solutions. The results based on the Mohr–Coulomb criterion $(b=0)$ give the lower bound of the plastic limit load, while those according to the twin shear strength criterion $(b=1)$ are the upper bound. The solution of the von Mises criterion is approximated by the linear function of the UST with a specific parameter $(b≈0.5)$. Plastic limit solutions with respect to different yield criteria are illustrated and compared. The influences of the yield criterion as well as the ratio of the tensile strength to the compressive strength on the plastic limit loads are discussed.

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## Figures

Figure 1

Deviatoric plane of the UST

Figure 2

Limit pressure versus the coefficient b

Figure 3

ps∕σt, versus the ratio rb∕ra

Figure 4

Sketch map of the pressured hole

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