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.

1.
Hill
,
R.
, 1950,
The Mathematical Theory of Plasticity
,
Clarendon
,
Oxford
.
2.
Prager
,
W.
, and
Hodge
,
P. G.
, Jr.
, 1951,
Theory of Perfectly Plastic Solids
,
Wiley
,
New York
.
3.
Johnson
,
W.
, and
Mellor
,
P. B.
, 1962,
Plasticity for Mechanical Engineers
,
Van Nostrand
,
Princeton
.
4.
Kalnins
,
A.
, and
Updike
,
D. P.
, 2001, “
Limit Pressures of Cylindrical and Spherical Shells
,”
ASME J. Pressure Vessel Technol.
0094-9930,
123
(
3
), pp.
288
292
.
5.
Yu
,
M. H.
, 1983, “
Twin Shear Stress Yield Criterion
,”
Int. J. Mech. Sci.
0020-7403,
25
(
1
), pp.
71
74
.
6.
Huang
,
W. B.
, and
Zeng
,
G. P.
, 1989, “
Solving Some Plastic Problems by Using the Twin Shear Stress Criterion
,”
Acta Mech. Sin.
0459-1879,
21
(
2
), pp.
249
256
.
7.
Yu
,
M. H.
, and
He
,
L. N.
, 1991, “
A New Model and Theory on Yield and Failure of Materials Under Complex Stress State
,”
Mechanical Behavior of Materials-6
,
Pergamon
,
London
, Vol.
3
, pp.
841
846
.
8.
Yu
,
M. H.
, 2002, “
Advances in Strength Theories for Materials Under Complex Stress State in the 20th Century
,”
Appl. Mech. Rev.
0003-6900,
55
(
3
), pp.
169
218
.
9.
Ma
,
G. W.
,
Iwasaki
,
S.
,
Miyamoto
,
Y.
, and
Deto
,
H.
, 1998, “
Plastic Limit Analysis of Circular Plates With Respect to the Unified Yield Criterion
,”
Int. J. Mech. Sci.
0020-7403,
40
(
10
), pp.
963
976
.
10.
Ma
,
G. W.
,
Hao
,
H.
, and
Iwasaki
,
S.
, 1999, “
Plastic Limit Analysis of a Clamped Circular Plate With Unified Yield Criterion
,”
Struct. Eng. Mech.
1225-4568,
7
(
5
), pp.
513
525
.
11.
Ma
,
G. W.
,
Hao
,
H.
, and
Iwasaki
,
S.
, 1999, “
Unified Plastic Limit Analysis of Circular Plates Under Arbitrary Load
,”
ASME J. Appl. Mech.
0021-8936,
66
(
2
), pp.
568
570
.
12.
Yu
,
M. H.
, 2004,
Unified Strength Theory and its Applications
,
Springer
,
Berlin
.
13.
Lee
,
Y. K.
, and
Ghosh
,
J.
, 1996, “
The Significance of J3 to the Prediction of Shear Bands
,”
Int. J. Plast.
0749-6419,
12
(
9
), pp.
1179
1197
.
14.
Yan
,
Z. D.
, and
Bu
,
X. M.
, 1996, “
An Effective Characteristic Method for Plastic Plane Stress Problems
,”
J. Eng. Mech.
0733-9399,
122
(
6
), pp.
502
506
.
15.
Yu
,
M. H.
,
Li
,
J. C.
, and
Zhang
,
Y. Q.
, 2001, “
Unified Characteristics Line Theory of Spatial Axisymmetric Plastic Problem
,”
Sci. China, Ser. E: Technol. Sci.
1006-9321,
44
(
2
), pp.
207
215
.