The influence of the Bauschinger effect (BE) on the three dimensional, Mode I, combined stress intensity factor (SIF) distributions for arrays of longitudinal coplanar, surface cracks emanating from the bore of a fully or partially autofrettaged thick-walled cylinder is investigated. The combined SIFs, $KIN$, that depend on pressure effects and the “realistic”—Bauschinger effect dependent Autofrettage (BEDA), or, that depend on pressure effects and the “ideal”—Bauschinger effect independent autofrettage (BEIA), are obtained and compared for crack depth to wall thickness, $a∕t=0.01–0.25$; crack ellipticity, $a∕c=0.5–1.5$; crack spacing ratio, $2c∕d=0.25–0.75$; and autofrettage level, $e=30%$, 60%, and 100%. The 3D analysis is performed via the finite element method and the submodeling technique, employing singular elements along the crack front. Both autofrettage residual stress fields, BEDA and BEIA, are simulated using an equivalent temperature field. The combined SIF, $KIN$, is found to vary along the crack front with the maximum determined by the crack ellipticity, crack depth, and crack spacing ratio. For a partially autofrettaged cylinder, the influence of the BE on the combined SIF, $KIN$, is substantially reduced as the level of overstrain becomes smaller. For some cases, when comparing like crack distributions, the $KIN$ values obtained from the BEDA model are found to be as much as 100% higher than the $KIN$ values that are computed using the BEIA model. A pressurized thick-walled cylinder with BEDA can be most critical when small cracks are farther apart. As crack depth increases, or when the spacing between cracks is smaller, the SIFs increase. Though the differences in the BEDA SIF, $KIA$, between $e=100%$ and 60% are small (7–15%, in most cases), the increased level of autofrettage produces a 23–30% decrease in the combined SIF values, $KIN$. In certain cases, the BEIA model implies an infinite fatigue life, whereas the BEDA model for the same parameters implies a finite life. Therefore, it is important to perform a full 3D analysis to determine the real life cycle of the pressurized cylinder for materials that exhibit the BE.

1.
Perl
,
M.
, and
Greenberg
,
Y.
, 1999, “
Three Dimensional Analysis of Thermal Shock Effect on Inner Semi-Elliptical Surface Cracks in a Cylindrical Pressure Vessel
,”
Int. J. Fract.
0376-9429,
99
(
3
), pp.
163
172
.
2.
Perl
,
M.
,
Levy
,
C.
, and
Pierola
,
J.
, 1996, “
Three Dimensional Interaction Effects in an Internally Multicracked Pressurized Thick-Walled Cylinder—Part I: Radial Crack Arrays
,”
ASME J. Pressure Vessel Technol.
0094-9930,
118
, pp.
357
363
.
3.
Perl
,
M.
, and
Nachum
,
A.
, 2000, “
3-D Stress Intensity Factors for Internal Cracks in an Over-Strained Cylindrical Pressure Vessel—Part I: The Effect of Autofrettage Level
,”
ASME J. Pressure Vessel Technol.
0094-9930,
122
(
4
), pp.
421
426
.
4.
Perl
,
M.
, and
Nachum
,
A.
, 2001, “
3-D Stress Intensity Factors for Internal Cracks in an Over Strained Cylindrical Pressure Vessel—Part II: The Combined Effect of Pressure and Autofrettage
,”
ASME J. Pressure Vessel Technol.
0094-9930,
123
(
1
), pp.
135
138
.
5.
Hill
,
R.
, 1950,
The Mathematical Theory of Plasticity
,
Clarendon
,
Oxford
.
6.
Parker
,
A. P.
, 2001, “
Bauschinger Effect Design Procedures for Compound Tubes Containing an Autofrettaged Layer
,”
ASME J. Pressure Vessel Technol.
0094-9930,
123
, pp.
203
206
.
7.
O’Donoghue
,
P. E.
,
Nishioka
,
T.
, and
Atluri
,
S. N.
, 1984, “
Multiple Surface Cracks in Pressure Vessels
,”
Eng. Fract. Mech.
0013-7944,
20
, pp.
545
560
.
8.
O’Donoghue
,
P. E.
,
Nishioka
,
T.
, and
Atluri
,
S. N.
, 1986, “
Analysis of Interaction Behavior of Surface Flaws in Pressure Vessels
,”
ASME J. Pressure Vessel Technol.
0094-9930,
108
, pp.
24
32
.
9.
Levy
,
C.
,
Perl
,
M.
, and
Kokkavessis
,
N.
, 1996, “
Three-Dimensional Interaction Effects in an Internally Multicracked Pressurized Thick-Walled Cylinder—Part II: Longitudinal Coplanar Crack Arrays
,”
ASME J. Pressure Vessel Technol.
0094-9930,
118
, pp.
364
368
.
10.
Levy
,
C.
,
Perl
,
M.
, and
Kotagiri
,
S.
, 2005, “
The Bauschinger Effect’s Influence on the SIFs of Multiple Longitudinal Coplanar Cracks in an Autofrettaged Pressurized Cylinder
,”
Eng. Fract. Mech.
0013-7944,
73
, pp.
1814
1825
.
11.
Raju
,
I. S.
, and
Newman
,
J. C.
, Jr.
, 1980, “
Stress-Intensity Factors for Internal Surface Cracks in Cylindrical Pressure Vessels
,”
ASME J. Pressure Vessel Technol.
0094-9930,
102
, pp.
342
346
.
12.
Raju
,
I. S.
, and
Newman
,
J. C.
, Jr.
, 1982, “
Stress-Intensity Factors for Internal and External Surface Cracks in Cylindrical Vessels
,”
ASME J. Pressure Vessel Technol.
0094-9930,
104
, pp.
293
298
.
13.
Perl
,
M.
, 1988, “
The Temperature Field for Simulating Partial Autofrettage in an Elasto-Plastic Thick-Walled Cylinder
,”
ASME J. Pressure Vessel Technol.
0094-9930,
110
, pp.
100
102
.
14.
ANSYS User’s Manual, 2003, Swanson Analysis System, Inc.
15.
Perl
,
M.
,
Levy
,
C.
, and
Rallabhandy
,
V.
, 2006, “
Bauschinger Effect’s Impact on the 3-D Combined SIFs for Radially Cracked Fully or Partially Autofrettaged Thick-Walled Cylinders
,”
Comput. Model. Eng. Sci.
1526-1492, Special Issue on International Workshop on the Advancement of Computational Mechanics,
11
, pp.
37
48
.