The ring delamination between bodies under the action of heat sinks distributed along a circle

Fìz.-mat. model. ìnf. tehnol. 2016, 26:55-62

Abstract

The frictionless contact an elastic half-space and a rigid thermo-insulated base with a local delamination between them on a ring domain under the action of heat sinks distributed uniformly along a circle and located in the half-space some distance away from its surface, is considered. The corresponding contact thermos-elasticity problem is reduced to a singular integral equation for a height of a ring gap. The solution of the singular integral equation and the internal and external radius of the ring are numerically determined using the method of collocation and the method of successive approximations. The dependence of the form of gap and normal contact stresses on the distance between the heat sinks and the surface of the half-space and the intensity of the heat sink are analyzed.

References

1. Monastyrskyy, B. Ye., Mykytyn, M. M. (2011). Axially symmetric problem of local separation of an elastic half-space from a rigid base due to a point source of cooling. Journal of Mathematical Sciences, 178(5), 467-480.
   DOI https://doi.org/10.1007/s10958-011-0563-8
2. Comninou, M., Dundurs, J. (1980). On lack of uniqueness in heat conduction through a solid to solid contact. Trans. ASME: J. Heat Transfer, 102(2), 156-162.
   DOI https://doi.org/10.1115/1.3244281
3. Krishtafovich, A. A., Martynyak, R. M. (1998). Thermoelastic contact of anisotropic half-spaces with thermal resistance. International Applied Mechanics, 34(7), 629-634.
   DOI https://doi.org/10.1007/bf02702067
4. Krishtafovich, A. A., Martynyak, R. M. (1999). Lamination of anisotropic half-spaces in the presence of contact thermal resistance. International Applied Mechanics, 35(2), 159-164.
   DOI https://doi.org/10.1007/bf02682149
5. Martynyak, R. M., Chumak, K. A. (2009). Thermoelastic delamination of bodies in the presence of a heatconducting filler of the intercontact gap. Materials Science, 45(4), 513–522.
   DOI https://doi.org/10.1007/s11003-010-9209-0
6. Martynyak, R. M., Serednickaya, H. I. (2012). Termouprugost' kusochno-odnorodnogo tela s mezhfaznoj teplopronicaemoj treshchinoj. Teoret. i prikl. mekhanika, 50(5), 91–98.
7. Goldstein, R. V., Kit, H. S., Martynyak, R.M., Serednytska, Kh. I. (2014). Effect of partial closure of an interface crack with heat-conducting filler and surface films in the case of thermal loading of a bimaterial. Journal of Mathematical Sciences, 198(1), 75-86..
   DOI https://doi.org/10.1007/s10958-014-1774-6
8. Martyniak, R. M., Serednytska, Kh. I. (2017). Kontaktni zadachi termopruzhnosti dlia mizhfaznykh trishchyn v bimaterialnykh tilakh. Lviv: Rastr-7.
9. Martynyak, R. M. (1999). Thermal opening of an initially closed interface crack under conditions of imperfect thermal contact between its lips. Mater. Sci., 35(5), 612–622.
   DOI https://doi.org/10.1007/bf02359347
10. Martyniak, R. M. (1998). Porushennia kontaktu pivprostoriv pry termomekhanichnii dii pidpoverkhnevoho vkliuchennia. Dop. NAN Ukrainy, 12, 71-77.
11. Malanchuk, N. I., Slobodyan, B. S., Martynyak, R. M. (2017). Friction sliding of elastic bodies in the presence of subsurface inclusion. Materials Science, 52(6), 819–826.
    DOI https://doi.org/10.1007/s11003-017-0026-6
12. Kit, H. S., Monastyrskyy, B. Ye. (1999). Thermoelastic interaction of two semi-infinite bodies under condition of local contact absence,Therm. Stresses’99: Proc. 3rd Int. Congr. on Thermal Stresses. Cracow (Poland).
13. Monastyrskij, B. Ye., Mykytyn, M. M. (2009). Kontakt uprugogo poluprostranstva i zhestkogo osnovaniya pod dejstviem sosredotochennogo istochnika ohlazhdeniya. Teor. i prikladnaya mekhanika, 46, 36-41.
14. Mkhitaryan, S. M., Shekyan, L. A., Verlinski, S. V., Aidun, D., Marzocca, P. (2012). Stationary theory of heatconductivity for anaxi-symmetrical piece homogeneous space with circular inclusion. J/Thermal Stresses, 35(5), 424-447.
    DOI https://doi.org/10.1080/01495739.2012.663691
15. Andriichuk, R. M., Kit, H. S. (2015). Osesymetrychne statsionarne temperaturne pole u bimaterialnomu tili za teplovydilennia na kruhovii oblasti. Prykl. problemy mekhaniky i matematyky, 13, 58-62.
16. Kit, H. S., Andriychuk, R. M. (2017). Thermoelastic State of a Half Space with Fixed Boundary Under the Conditions of Heat Generation in a Circular Domain Parallel to the Boundary. Materials Science, 53(3), 398–406.
    DOI https://doi.org/10.1007/s11003-017-0088-5
17. Kit, H. S. (2008). Zadachi statsionarnoi teploprovidnosti ta termopruzhnosti dlia tila z teplovydilenniam na kruhovii oblasti (trishchyni). Mat. metody ta fiz.-mekh. polia, 51(4), 120–128.
18. Kit, H. S., Sushko, O. P. (2011). Statsionarne temperaturne pole u pivbezmezhnomu tili z teploaktyvnym abo teploizolovanym dyskovym vkliuchenniam. Fiz.-mat. modeliuvannia ta inform. tekhnolohii, 13, 67-80.
19. Kit, H. S., Sushko, O. P. (2011). Axially symmetric problems of stationary heat conduction and thermoelasticity for a body with thermally active or thermally insulated disk inclusion (crack). Journal of Mathematical Sciences, 176(4), 561-577.
    DOI https://doi.org/10.1007/s10958-011-0422-7
20. Martyniak, R. M. (2000). Metod funktsii mizhkontaktnykh zazoriv u zadachakh lokalnoho porushennia kontaktu pruzhnykh pivprostoriv. Mat. metody ta fiz.-mekh. polia, 43(1), 102-108.
21. Martyniak, R. M. (2000). Mekhanotermodyfuziina vzaiemodiia til z kontaktno-poverkhnevymy neodnoridnostiamy i defektamy.(Dys. ... d-ra fiz.-mat. nauk: 01.02.04). Lviv.
22. Monastyrs'kyi, B. E., Martynyak, R. M. (2003). Contact of Two Half Spaces One of Which Contains a Ring-Shaped Pit. Part 1. Singular Integral Equation. Materials Science, 39(2), 206–213.
    DOI https://doi.org/10.1023/b:masc.0000010270.46373.a6
23. Monastyrs'kyi, B. E. (2003). Problem of Contact of Two Half Spaces with a Ring-Shaped Groove in One of Them. Part 2. Numerical Method and Results. Materials Science, 39(4), 505–510.
    DOI https://doi.org/10.1023/b:masc.0000010927.00263.bf