The development of temperature gradients and thermal stresses during the heating of large ingots has been investigated with special reference to the selection of heating schedules for brittle intermetallic materials such as titanium aluminides. A 1-D analytical (series) solution for radial temperature transients was used in conjunction with an elasticity analysis to determine the maximum thermal stresses that would be generated during ingot heating. The temperature gradients and stresses were seen to be strongly dependent on Fourier and Biot Numbers. In addition, finite element method simulations incorporating end effects and variations of thermal and elastic properties with temperature were performed and compared to the analytical results. Comparison of the predicated thermal stresses and actual ingot heating observations suggest that cracking is controlled by a maximum normal stress criterion.

1.
Sun
R. C.
,
1970
, “
Determination of the Forging-Heating Schedule for a Large Hastelloy Alloy X Ingot
,”
Metall. Trans.
, Vol.
1
, pp.
1881
1887
.
2.
Finlayson
P. C.
, and
Schofield
J. S.
,
1959
, “
Heating for Forging in a Batch Type Furnace
,”
J. Iron and Steel Institute
, Vol.
193
, pp.
238
252
.
3.
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
.
4.
Jaeger
J. C.
,
1945
, “
On Thermal Stresses in Circular Cylinders
,”
Phil. Mag.
, Vol.
36
, pp.
414
428
.
5.
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, OH.
6.
Carslaw, H. S., and Jaeger, J. C., 1959, Conduction of Heat in Solids, Oxford University Press, London, pp. 225–228.
7.
Matsumura
T.
,
1923
, “
A Contribution to the Theory of Thermal Stress in a Long Hollow Cylinder
,”
Memoirs of the Faculty of Engineering, Kyoto University
, Vol.
3
, No.
3
, June, pp.
61
80
.
8.
Boley, B. A., and Weiner, J. H., 1985, Theory of Thermal Stresses, Krieger Publishing Co., Malabar, FL.
9.
Oh
S. I.
,
1982
, “
Finite Element Analysis of Metal Forming Processes with Arbitrarily Shaped Dies
,”
Inter. J. Mech. Sci.
, Vol.
24
, pp.
479
493
.
10.
Oh
S. I.
,
Wu
W. T.
,
Tang
J. P.
, and
Vedhanayagam
A.
,
1991
, “
Capabilities and Applications of FEM Code DEFORM: The Perspective of the Developer
,”
J. Mat. Proc. Techn.
, Vol.
27
, pp.
25
42
.
11.
Hallquist, J. O., 1986, NIKE 2D User’s Manual, Lawrence Livermore Laboratory, December.
12.
Lipsitt, H. A., 1985, “Titanium Aluminides-An Overview,” High Temperature Ordered Intermetallic Alloys, C. C. Koch, C. T. Liu, and N. S. Stoloff, eds., Materials Research Society, Pittsburgh, pp. 351–364.
13.
Burte, P. R., and Semiatin, S. L., 1988, Unpublished Research, The Ohio State University, Columbus, OH.
14.
Wagner, D. A., and Johansen, E. W., 1990, Unpublished Research, G. E. Aircraft Engines, Cincinnati, OH.
15.
DeLuca, D. P., Cowles, B. A., Haake, F. K., and Holland, K. P., 1990, “Fatigue and Fracture of Titanium Aluminides,” Technical Report WRDC-TR-89-4136, Pratt and Whitney Engineering Division, United Technologies Corporation, West Palm Beach, FL.
16.
Chu
W. H.
, and
Dodge
F. T.
,
1968
, “
End Thermal Stresses in a Long Circular Rod
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
90
, June, pp.
267
273
.
17.
Lipsitt
H. A.
,
Shectman
D.
, and
Schafrik
R. E.
,
1975
, “
The Deformation and Fracture of TiAl at Elevated Temperatures
,”
Met. Trans. A
, Vol.
6A
, pp.
1991
1996
.
18.
Lipsitt
H. A.
,
Shectman
D.
, and
Schafrik
R. E.
,
1980
, “
The Deformation and Fracture of Ti3Al at Elevated Temperatures
,”
Met. Trans. A
, Vol.
11A
, pp.
1369
1375
.
19.
Ali, Z., and Alam, M. K., 1994, “Thermal Stresses in a Circular Cylinder with Temperature Dependent Properties,” Thermal Processing of Materials, Proceedings of HTD, ASME Winter Annual Meeting, Chicago, November.
20.
Noda, N., 1986, Thermal Stresses, Richard B. Hetnarski, ed., North Holland, Vol. 1, pp. 391–476.
This content is only available via PDF.
You do not currently have access to this content.