The thermal stresses in a long circular cylinder are analyzed by two approximate methods. An interpolation formula is then used to develop a semi-empirical solution for thermal stresses which is then validated by a test case of a nondimensional temperature profile with temperature dependent modulus of elasticity, coefficient of thermal expansion and Poisson’s ratio. The interpolation formula is compared with the numerical solution by a finite element code (ABAQUS). It is shown that the interpolated approximation compares well with the finite element solution for a range of parameters that are typical for processing of billets.

1.
Alam
M. K.
,
Goetz
R. L.
, and
Semiatin
S. L.
,
1996
, “
Modeling of Thermal Stresses and Thermal Cracking During Heating of Large Ingots
,”
ASME JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING
, Vol.
118
, pp.
235
243
.
2.
Arpaci, V., 1966, Conduction Heat Transfer, Addison Wesley Publishing Co., Mass., pp. 284–285.
3.
Boley, B. A., and Weiner, H. J., 1960, Theory of Thermal Stresses, John Wiley & Sons Inc.
4.
Chandrasekharan, S., and Shivpuri, R., 1992, “Optimization of Preheating Schedules for Nickel Base Superalloy Ingots Using Finite Element Method,” Report No. ERC/NSM-B-92-09, Engineering Research Center for Net Shape Manufacturing, The Ohio State University, Columbus, Ohio.
5.
Dahl
O. G. C.
,
1924
, “
Temperature and Stress Distributions in Hollow Cylinders
,”
Transactions of the ASME
, Vol.
46
, pp.
161
208
.
6.
Hertzberg, R. W., 1996, Deformation and Fracture Mechanics of Engineering Materials, Jon Wiley, New York, pp. 8–9.
7.
Jaeger
J. C.
,
1945
, “
On Thermal Stresses in Circular Cylinders
,”
Phil. Mag.
, Vol.
36
, pp.
414
428
.
8.
Kent
C. H.
,
1932
, “
Thermal Stresses in Spheres and Cylinders Produced by Temperatures Varying With Time
,”
Transactions of the ASME
, Vol.
54
, pp.
185
196
.
9.
Matsumura, T., 1923, “A Contribution to the Theory of Thermal Stress in a Long Hollow Cylinder,” Kyoto Imperial University, College of Engineering Memoirs, Vol. 3, No. 3, pp. 61–80.
10.
Noda, N., 1986, Thermal Stresses, Richard B. Hetnarski, ed., North Holland, Vol. 1, pp. 391–476.
11.
Suhara, T., 1918, “Elasticity of Steel Strained by Unequal Heating,” J. Japan Soc. Mech. Engrs., pp. 25–63.
12.
Sun
C. R.
,
1970
, “
Determination of the Forging-Heading Schedule for a Large HASTELLOY Alloy X Ingot
,”
Metallurgical Transactions
, Vol.
1
, pp.
1881
1886
.
13.
Takeuti
Y.
, and
Noda
N.
,
1978
, “
A Three-Dimensional Treatment of Transient Thermal Stresses in a Circular Cylinder Due to an Arbitrary Heat Supply
,”
ASME Journal of Applied Mechanics
, Vol.
45
, pp.
817
821
.
14.
Tsumura, T., 1979, “An Approximate Calculation of the Thermal Stress in a Cylinder of Axial Symmetry, when E and α are Functions of Temperature,” Rep. Faculty of Technology Kanagawa Univ., Vol. 17, pp. 16–21.
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