A thermal stress problem of a long hollow cylinder was considered in this paper. The outer surface of the cylinder was adiabatically insulated, and the inner surface was heated axisymmetrically by a fluid with sinusoidal temperature fluctuations (hereafter called as thermal striping), whose temperature amplitude $(ΔT)$ and angular velocity $(ω)$ were constant. The heat transfer coefficient $h$ was also assumed to be constant. The stress intensity factor (SIF) due to the thermal stress for a given cylinder configuration varies not only with these three parameters $ΔT$, $ω$, and $h$, but also with time. The temperature and, as a result, SIF fluctuation amplitude soon became constant (Meshii, T., and Watanabe, K., 2004, “Stress Intensity Factor of a Circumferential Crack in a Thick-Walled Cylinder Under Thermal Striping,” ASME J. Pressure Vessel Technol., 126(2), pp. 157–162), which hereafter is called as steady state. If one is interested in fatigue crack growth (assuming Paris law) under this thermal stress, because the SIF range soon converges to a constant, it seemed important to know the maximum value of the steady state SIF range for a given cylinder configuration, for all possible combinations of $ΔT$, $ω$, and $h$. This maximum SIF evaluation is time consuming. Thus in this paper, this maximum steady state SIF range for four typical surface cracks’ deepest point, inside a hollow cylinder for all possible combinations of $ΔT$, $ω$, and $h$ were presented as a first step. Thin-to thick-walled cylinders in the range of mean radius to wall thickness parameter $rm/W=10.5–1$ were considered. Crack configurations considered were 360 deg continuous circumferential, radial, semi-elliptical in the circumferential and radial directions. Normalized crack depth for all cases was in the range of $a/W=0.1–0.5$. In case of semi-elliptical crack, the normalized crack length $a/c$ was all in the range of 0.063–1.

1.
Hoshino
,
T.
,
Aoki
,
T.
,
Ueno
,
T.
, and
Kutomi
,
Y.
, 2000, “
Leakage from CVS Pipe of Regenerative Heat Exchanger Induced by High-Cycle Thermal Fatigue at Tsuruga Nuclear Power Station Unit 2
,”
Proceeding of ICONE
, Vol.
8
, pp.
55
61
.
2.
Green
,
A. E.
, and
Sneddon
,
I. N.
, 1950, “
The Distribution of Stress in the Neighborhood of a Flat Elliptical Crack in an Elastic Solid
,”
Proc. Cambridge Philos. Soc.
0068-6735,
46
, pp.
159
163
.
3.
Newman
, Jr.,
J. C.
, and
Raju
,
I. S.
, 1981, “
An Empirical Stress Intensity Factor Equation for the Surface Crack
,”
Eng. Fract. Mech.
0013-7944,
15
(
1-2
), pp.
185
192
.
4.
Meshii
,
T.
, and
Watanabe
,
K.
, 2004, “
Stress Intensity Factor of a Circumferential Crack in a Thick-Walled Cylinder Under Thermal Striping
,”
ASME J. Pressure Vessel Technol.
0094-9930,
126
(
2
), pp.
157
162
.
5.
Meshii
,
T.
, and
Watanabe
,
K.
, 2004, “
Normalized Stress Intensity Factor Range Solutions of an Inner-Surface Circumferential Crack in Thin- to Thick-Walled Cylinder Under Thermal Striping by Semi-Analytical Numerical Method
,”
J. Therm. Stresses
0149-5739,
27
(
3
), pp.
253
267
.
6.
JSME
, 1986,
JSME Data Book: Heat Transfer
,
Japan Society of Mechanical Engineers
,
Tokyo
, pp.
35
36
(in Japanese).
7.
Shibata
,
K.
, 2006, “
Stress Intensity Factor of Various Surface Cracks Inside a Hollow Cylinder Under Steady State Thermal Striping
,” MS thesis, University of Fukui, Japan.
8.
Meshii
,
T.
, and
Watanabe
,
K.
, 2001, “
Stress Intensity Factor Evaluation of a Circumferential Crack in a Finite Length Thin-Walled Cylinder for Arbitrarily Distributed Stress on Crack Surface by Weight Function Method
,”
Nucl. Eng. Des.
0029-5493,
206
(
1
), pp.
13
20
.
9.
Meshii
,
T.
, and
Watanabe
,
K.
, 2001, “
Stress Intensity Factor for a Circumferential Crack in a Finite-Length Thin to Thick-Walled Cylinder Under an Arbitrary Biquadratic Stress Distribution on the Crack Surfaces
,”
Eng. Fract. Mech.
0013-7944,
68
(
8
), pp.
975
986
.
10.
Andrasic
,
C. P.
, and
Parker
,
A. P.
, 1984, “
Dimensionless Stress Intensity Factors for Cracked Thick Cylinders Under Polynomial Crack Face Loadings
,”
Eng. Fract. Mech.
0013-7944,
19
(
1
), pp.
187
193
.
11.
Fett
,
T.
,
Munz
,
D.
, and
Neumann
,
J.
, 1990, “
Local Stress Intensity Factors for Surface Cracks in Plates Under Power-Shapes Stress Distributions
,”
Eng. Fract. Mech.
0013-7944,
36
(
4
), pp.
647
651
.