Abstract
The problem of stationary thermal conductivity and thermoelasticity is solved by the method of boundary integral equations for a semiinfinite body containing a circular crack perpendicular to its edge provided that temperature (or a heat flow is specified) on the crack surfaces. The boundary of the body is unloaded and either is thermally insulated or its temperature is equal to zero. We study the influence of the depth of location of the circular crack on the stress intensity factor for a constant temperature (or heat flow) specified on the crack surfaces. Under thermal loading (unlike the case of constant force loading), the stress intensity factors attain their maximum values on the side of the half space opposite to its boundary.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
N. M. Borodachev, “Thermoelastic problem for a finite body containing an axisymmetric crack,” Prikl. Mekh., 2, No.2, 93–99 (1966).
Z. Olesiak and J. N. Sneddon, “Thermal stresses in an infinite elastic solid containing a penny-shaped crack,” Arch. Ration. Mech. Anal., 4, No.3, 238–254 (1960).
E. Deutch, “The distribution of axisymmetric thermal stress in an infinite elastic medium containing a penny-shaped crack,” Int. J. Eng. Sci., 3, No.5, 485–490 (1965).
R. Shail, “Some thermoelastic stress distributions in an infinite solid and a thick plate containing a penny-shaped crack,” Mathematica, 11, No.2, 102–118 (1964).
K. N. Srivastava and R. M. Palaiya, “The distribution of thermal stress in a semiinfinite elastic solid containing a penny-shaped crack,” Int. J. Eng. Sci., 7, No.7, 647–666 (1969).
B. R. Das, “Thermal stresses in a long circular cylinder containing a penny-shaped crack,” Int. J. Eng. Sci., 6, No.9, 497–516 (1968).
B. R. Das, “A note on thermal stresses in a long circular cylinder containing a penny-shaped crack,” Int. J. Eng. Sci., 7, No.7, 667–676 (1969).
K. N. Srivastava and J. P. Dwivedi, “Thermal stresses in an elastic sphere containing a penny-shaped crack,” Z. Ang. Math. Phys., 21, No.6, 864–886 (1970).
K. N. Srivastava, R. M. Palaiya, and A. Choudhary, “Thermal stresses in an elastic layer containing a penny-shaped crack and bonded to dissimilar half space,” Int. J. Frac., 13, No.1, 27–38 (1977).
M. K. Kassir and A. Bregman, “Thermal stresses in a solid containing parallel circular cracks,” Appl. Sci. Res., 25, No.3–4 (1971).
G. S. Kit and M. V. Khai, “An axisymmetric problem of thermoelasticity for an infinite body weakened by two parallel circular slots,” Tepl. Napryazh. Elem. Konstr., Issue 12, 101–108 (1972).
G. S. Kit and M. V. Khai, “Integral equations of axisymmetric problems of thermoelasticity for bodies with cracks,” Mat. Met. Fiz.-Mekh. Polya, Issue 6, 3–7 (1977).
G. S. Kit and M. V. Khai, Method of Potentials in Three-Dimensional Problems of Thermoelasticity for Bodies with Cracks [in Russian], Naukova Dumka, Kiev (1989).
G. S. Kit and M. V. Khai, “Integral equations of three-dimensional problems of heat conduction for bodies with cracks,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 8, 704–707 (1975).
G. S. Kit and M. V. Khai, “Integral equations of three-dimensional problems of thermoelasticity for bodies with cracks,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 12, 1108–1112 (1975).
V. Novatskii, Problems of Thermoelasticity [Russian translation], Izd. Akad. Nauk SSSR, Moscow (1962).
M. V. Khai, Two-Dimensional Integral Equations of Newton-Potential Type and Their Applications [in Russian], Naukova Dumka, Kiev (1993).
O. P. Sushko and M. V. Khai, “Solution of the problems of elasticity theory for a half space containing plane edge cracks,” Mat. Met. Fiz.-Mekh. Polya, Issue 37, 58–63 (1994).
H. S. Kit, M. V. Khaj, and O. P. Sushko, “Investigation of the interaction of flat surface cracks in a half space by BIEM,” Int. J. Eng. Sci., 38, 1593–1616 (2000).
M. V. Khai and I. V. Kalynyak, “An approach to the numerical solution of problems of the mathematical theory of cracks,” Mat. Met. Fiz.-Mekh. Polya, Issue 20, 38–42 (1984).
V. V. Panasyuk (ed.), Fracture Mechanics and Strength of Materials. A Handbook [in Russian],Vol. 2: M. V. Savruk, Stress Intensity Factors in Cracked Bodies, Naukova Dumka, Kiev (1988).
H. S. Kit, B. E. Monastyrs'kyi, and O. P. Sushko, “Thermoelastic state of a semiinfinite body with place surface crack under the action of a heat source,” Fiz.-Khim. Mekh. Mater., 37, No.4, 71–73 (2001).
Author information
Authors and Affiliations
Additional information
__________
Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 41, No. 2, pp. 16–22, March–April, 2005.
Rights and permissions
About this article
Cite this article
Kit, H.S., Sushko, O.P. Thermoelastic State of a Half Space Containing a Thermally Active Circular Crack Perpendicular to Its Edge. Mater Sci 41, 150–157 (2005). https://doi.org/10.1007/s11003-005-0145-3
Received:
Issue Date:
DOI: https://doi.org/10.1007/s11003-005-0145-3