Increased strength-to-weight ratio and extended fatigue life are the main objectives in the optimal design of modern pressure vessels. These two goals can mutually be achieved by creating a proper residual stress field in the vessel’s wall by a process known as autofrettage. Although there are many studies that have investigated the autofrettage problem for cylindrical vessels, only a few of such studies exist for spherical ones. Because of the spherosymmetry of the problem, autofrettage in a spherical pressure vessel is treated as a one-dimensional problem and solved solely in terms of the radial displacement. The mathematical model is based on the idea of solving the elastoplastic autofrettage problem using the form of the elastic solution. Substituting Hooke’s equations into the equilibrium equation and using the strain-displacement relations yield a differential equation, which is a function of the plastic strains. The plastic strains are determined using the Prandtl–Reuss flow rule and the differential equation is solved by the explicit finite difference method. The existing 2D computer program, for the evaluation of hydrostatic autofrettage in a thick-walled cylinder, is adapted to handle the problem of spherical autofrettage. The presently obtained residual stress field is then validated against three existing solutions emphasizing the major role the material law plays in determining the autofrettage residual stress field. The new code is applied to a series of spherical pressure vessels yielding two major conclusions. First, the process of autofrettage increases considerably the maximum safe pressure that can be applied to the vessel. This beneficial effect can also be used to reduce the vessel’s weight rather than to increase the allowable internal pressure. Second, the specific maximum safe pressure increases as the vessel becomes thinner. The present results clearly indicate that autofrettaging of spherical pressure vessels can be very advantageous in various applications.

1.
Parker
,
A. P.
,
Underwood
,
J. H.
, and
Kendall
,
D. P.
, 1999, “
Bauschinger Effect Design Procedures for Autofrettaged Tubes Including Material Removal and Sachs Method
,”
ASME J. Pressure Vessel Technol.
0094-9930,
121
, pp.
430
437
.
2.
Parker
,
A. P.
, 2001, “
Autofrettage of Open-End Tubes-Pressures, Stresses, Strains, and Code Comparisons
,”
ASME J. Pressure Vessel Technol.
0094-9930,
123
, pp.
271
281
.
3.
Perry
,
J.
, and
Aboudi
,
J.
, 2003, “
Elasto-plastic Stresses in Thick Walled Cylinders
,”
ASME J. Pressure Vessel Technol.
0094-9930,
125
, pp.
248
252
.
4.
Gibson
,
M. C.
,
Hameed
,
A.
,
Parker
,
A. P.
, and
Hetherington
,
J. G.
, 2006, “
A Comparison of Methods for Predicting Residual Stresses in Strain-Hardening, Autofrettaged Thick Cylinders, Including the Bauschinger Effect
,”
ASME J. Pressure Vessel Technol.
0094-9930,
128
, pp.
217
222
.
5.
Hill
,
R.
, 1950,
The Mathematical Theory of Plasticity
,
Oxford University Press
,
New York
.
6.
,
R.
, and
Livieri
,
P.
, 2007, “
Analytical Approach in Autofrettaged Spherical Pressure Vessels Considering Bauschinger Effect
,”
ASME J. Pressure Vessel Technol.
0094-9930,
129
(
3
), pp.
411
419
.
7.
Parker
,
A. P.
, and
Huang
,
X.
, 2007, “
Autofrettage of a Spherical Pressure Vessel
,”
ASME J. Pressure Vessel Technol.
0094-9930,
129
, pp.
83
88
.
8.
Perl
,
M.
, and
Perry
,
J.
, 2006, “
An Experimental-Numerical Determination of the Three Dimensional Autofrettage Residual Stress Field Incorporating Bauschinger Effect
,”
ASME J. Pressure Vessel Technol.
0094-9930,
128
, pp.
173
178
.
9.
Chakrabarty
,
J.
, 1987,
Theory of Plasticity
,
McGraw-Hill
,
Singapore
.
10.
Perry
,
J.
,
Perl
,
M.
,
Shneck
,
R.
, and
Haroush
,
S.
, 2006, “
The Influence of the Bauschinger Effect on the Yield Stress, Young’s Modulus, and Poisson’s Ratio of a Gun Barrel Steel
,”
ASME J. Pressure Vessel Technol.
0094-9930,
128
, pp.
179
184
.
11.
Jahed
,
H.
, and
Dubey
,
R. N.
, 1997, “
An Axisymmetric Method of Elasto-plastic Analysis Capable of Predicting Residual Stress Field
,”
ASME J. Pressure Vessel Technol.
0094-9930,
119
, pp.
264
273
.