Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-28T01:07:04.933Z Has data issue: false hasContentIssue false
  • English
  • Français

Thermal Stress in a Finitely Deformed Incompressible Elastic Medium Containing a Penny-Shaped Crack

Published online by Cambridge University Press:  05 May 2011

Y. M. Tsai
Y. M. Tsai*
Affiliation:
Aerospace Engineering and Engineering Mechanics, Iowa State University, Ames, Iowa 50011–2271, U.S.A.
*
* Professor
Get access

Abstract

The thermal stress for a penny-shaped crack contained in an infinite isotropic elastic solid initially subjected to an axisymmetrical tension of any amount at infinity is investigated using the techniques of Hankel transforms and multiplying factors. The effect that the lateral normal stress has on the thermal stresses is studied on the basis of the theory of small deformations superposed on finite deformation. Symmetrical thermal loadings are applied over the crack surfaces. For the case of constant temperature over the crack surfaces, expressions for the crack shape and thermal stresses in the crack plane are obtained in closed forms. The stress intensity factor is also obtained and shown to be dependent on the lateral stress.

Keywords

Thermal stressFinitely deformed mediumPenny-shaped crack
Type
Articles
Information
Journal of Mechanics , Volume 19 , Issue 1 , March 2003 , pp. 143 - 147
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2003

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1Olesiak, Z. and Sneddon, I. N., “The Distribution of Thermal Stress in an Infinite Elastic Solid Containing a Penny-Shaped Crack,” Arch. Rat. Mech. Anal., 4, pp 238–254 (1960).Google Scholar
2Green, A. E. and Zerna, W., Theoretical Elasticity, 2nd ed., Clarendon Press, Oxford, p. 114 (1968).Google Scholar
3Eringen, A. C. and Suhubi, E., Elastodynamics, Academic Press, New York, 1, p. 246 (1974).Google Scholar
4Tsai, Y. M., “Initiation and Propagation of a Penny-Shaped Crack in a Finitely Deformed Incompressible Elastic Medium,” Engrg Fracture Mech., 14, pp. 627–636 (1981).CrossRefGoogle Scholar
5Tsai, Y. M., “Thermoelastic Behavior of a Transversely Isotropic Material Containing a Flat Toroidal Crack,” J. Thermal Stresses, 21, pp. 881–895 (1998).Google Scholar
6Sneddon, I. N., Fourier Transforms, McGraw-Hill, New York, p. 490 (1951).Google Scholar
7Suhubi, E. S., “Small Longitudinal Vibration on an Initially Stretched Circular-Cylinder,” Int. J. Engng Sci., 2, pp. 509–517 (1965).CrossRefGoogle Scholar
8Ting, T. C. T., “The Contact Stresses between a Rigid Indenter and a Viscoelastic Half-Space,” J. Appl. Mech. Trans., ASME E33, 4, pp. 845–854 (1966).Google Scholar
9Watson, G. N., Theory of Bessel Functions, 2nd ed., Cambridge University Press, London, p. 405 (1966).Google Scholar