Geodesic
The task of thermal conductivity for a bimaterial with a system of partially heat permeable cracks and a heat source
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 4 (2009), pp. 154-170 Cet article a éte moissonné depuis la source Math-Net.Ru

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The work is devoted to the stationary task of thermal conductivity about crack interaction in a bimaterial subjected to a heat source. It was assumed that the cracks are heat permeable though the heat permeability is different for internal cracks and for an interface crack. The methods of complex potentials and the method of superposition are used for the construction of equations to the problem. In case when the length of the interface crack is much lager than the characteristic length of the internal crack the singular integral equations are solved by small parameter method. The asymptotic analytical formulas for coefficient intensity of thermal flow at the crack tips are derived. The influence of the crack locations and their orientations on the coefficients of thermal intensity at the interface crack tips are investigated for different thermal conductivity coefficients of the crack surfaces and for different location of the heat source.
Keywords: heat source, interfacial area, crack, the coefficient of the termal flow intensity, thermal conductivity coefficient, complex potential, singular integral equation, small parameter. 
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M. G. Ordyan; V. E. Petrova. The task of thermal conductivity for a bimaterial with a system of partially heat permeable cracks and a heat source. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 4 (2009), pp. 154-170. http://geodesic.mathdoc.fr/item/VSGU_2009_4_a10/

[1] Petrova V., Herrmann K., “Thermal crack problems for a bimaterial with an interface crack and internal defects”, International Journal of Fracture, 128 (2004), 49–63 | DOI | Zbl

[2] Panasyuk V. V., Savruk M. P., Datsyshin A. P., Raspredelenie napryazhenii okolo treschin v plastinakh i obolochkakh, Nauk. dumka, Kiev, 1976, 445 pp. | MR

[3] Tamuzh V. P., Petrova V. E., “O vzaimodeistvii makrotreschiny s mikrodefektami”, Prikladnaya mekhanika, 2002, no. 10, 3–34

[4] Tamuzs V., Romalis N., Petrova V., Fracture of Solids with Microdefects, NOVA Science Publishers Inc., New York, 2000, 247 pp.

[5] Lee K. Y., Park S. J., “Thermal stress intensity factors for partially insulated interface crack under uniform heat flow”, Eng. Fract. Mech., 50:4 (1995), 475–482 | DOI

[6] Kit G. S., Poberezhnyi O. V., Nestatsionarnye protsessy v telakh s defektami tipa treschin, Nauk. dumka, Kiev, 1992, 216 pp.

[7] Muskhelishvili N. I., Nekotorye osnovnye zadachi matematicheskoi teorii uprugosti, Nauka, M., 1966, 707 pp.

[8] Gakhov F. D., Kraevye zadachi, Nauka, M., 1970, 640 pp. | MR

[9] Prusov I. A., Nekotorye zadachi termouprugosti, Izd-vo BGU, Minsk, 1972, 200 pp.

[10] Suo Z., “Singularities interacting with interfaces and cracks”, International Journal Solids Structures, 25 (1989), 1133–1142 | DOI