Mathematical modelling of thermoelastic behavior of a coating taking into account frictional heating and wear
Vladimir Borisovich Zelentsov,
Boris Igorevich Mitrin,
Igor Anatolyevich Lubyagin,
Sergey Mikhailovich Aizikovich 
Abstract
This work describes application of the integral transform method to solution of a quasi-static contact problem of the coating wear-out. Frictional heating and wear of the coating occurs during the sliding of a rigid body over its surface. The problem is considered in the framework of the coupled thermoelasticity theory. The solution of the problem is constructed in the form of contour quadratures of the inverse Laplace transformation. After the calculation of the quadratures the solution of the problem is constructed in the form of series over the poles of the integrands. Investigation of the poles of integrands is performed in dependence on four dimensionless parameters of the problem. The solutions obtained are studied in detail with respect to the dimensionless and dimensional parameters of the problem. Numerical examples of the obtained solutions for contact stresses, displacements, temperature and wear of the coating are presented.
Keywords
Supporting agencies: The work was carried out within the framework of the Governmental Assignment of the Ministry of Education and Science of the Russian Federation no. 9.1481.2017/4.6 and RFBR grants nos. 16-07-00929-а, 17-07-01376-а.
About the Authors
Vladimir Borisovich Zelentsov
Don State Technical University (1 Gagarin sq., Rostov-on-Don, Russian Federation)
Russian Federation
Russian Federation
Zelentsov Vladimir Borisovich, Head of Center, Scientific Equipment Joint Use Center, Research and Education Center "Materials", Don State Technical University (1 Gagarin sq., Rostov-on-Don, Russian Federation), Candidate of Science in Physics and Maths, Senior researcher
Boris Igorevich Mitrin
Don State Technical University
(1 Gagarin sq., Rostov-on-Don, Russian Federation)
Russian Federation
Russian Federation
Mitrin Boris Igorevich, Junior researcher, Functionally graded and composite materials laboratory, Research and Education Center "Materials", Don State Technical University (1 Gagarin sq., Rostov-on-Don, Russian Federation), Candidate of Science in Physics and Maths
Igor Anatolyevich Lubyagin
Don State Technical University
(1 Gagarin sq., Rostov-on-Don, Russian Federation)
Russian Federation
Russian Federation
Lubyagin Igor Anatolyevich, Junior researcher, Functionally graded and composite materials laboratory, Research and Education Center "Materials", Don State Technical University (1 Gagarin sq., Rostov-on-Don, Russian Federation)
Sergey Mikhailovich Aizikovich
Don State Technical University
(1 Gagarin sq., Rostov-on-Don, Russian Federation)
Russian Federation
Russian Federation
Aizikovich Sergey Mikhailovich, Head of Laboratory, Functionally graded and composite materials laboratory, Research and Education Center "Materials", Don State Technical University (1 Gagarin sq., Rostov-on-Don, Russian Federation), Doctor of Science in Physics and Maths, Senior researcher.
References
1. Biot, M.A. Thermoelasticity and irreversible thermodynamics. Journal of Applied Physics, 1956, vol. 27, no. 3, pp. 240-253.
2. Deresiewicz, H. Solution of the equations of thermoelasticity. Proc. 3rd U.S. Nat. Congr. Appl. Mech. ASME. Providence, Brown University, 1958, pp. 287-291.
3. Chadwick, P. Thermoelasticity. The dynamical theory. Progress in Solid Mechanics. eds. I.N. Sneddon, R. Hill. Amsterdam, North-Holland Publishing Company, 1960, pp. 263-328.
4. Boley, B.A., Weiner, J.H. Theory of thermal stresses. New York, London, John Wiley and Sons, Inc. 1960.
5. Nowacki, V. Dynamic problems of thermoelasticity. Moscow, Mir, 1970, transl. from Polish, 256 p.
6. Nickell, R.E., Sackman J.L. Approximate Solutions in linear, coupled thermoelasticity. Journal of Applied Mechanics, 1968, vol. 35, no. 2, pp. 255-266.
7. Oden, J.T. Finite element analysis of nonlinear problems in the dynamical theory of coupled thermoelasticity. Nuclear Engineering and Design, 1969, vol. 10, no 4, pp. 465-475.
8. Prevost, J.H., Tao, D. Finite element analysis of dynamic coupled thermoelasticity problems with relaxation times. Journal of Applied Mechanics, 1983, vol. 50, no. 4a, pp. 817-822.
9. Carter, J.P., Booker, J.R. Finite element analysis of coupled thermoelasticity. Computers & Structures, 1989, vol. 31, no. 1, pp. 73-80.
10. Hacquin, A., Montmitonnet, P., Guillerault, J.P. A steady state thermo-elastoviscoplastic finite element model of rolling with coupled thermo-elastic roll deformation. Journal of Materials Processing Technology, 1996, vol. 60, no. 1, pp. 109-116.
11. Repka, M., Lion, A. Simulation of the coupled thermo-elastic behavior of constrained films in differential scanning calorimetry using the finite element method. Thermochimica Acta, 2014, vol. 581, pp. 62-69.
12. Gribanov, V.F., Panichkin, N.G. Coupled and dynamic thermoelasticity problems. Moscow, Mashinostroeniye, 1984, 151 p. (in Russian)
13. Alexandrov, V.M., Annakulova, G.K. A contact problem of thermo-elasticity with wear and heat release caused by friction. Trenie i Iznos, 1990, vol. 11, no. 1, pp. 24-28. (in Russian)
14. Alexandrov, V.M., Annakulova, G.K. Interaction between coatings of a body with deformation, wear, and heat release due to friction. Trenie i Iznos, 1992, vol. 13, no. 1, pp. 154-160. (in Russian)
15. Evtushenko, A.A., Pyryev, Y.A. Influence of wear on the development of thermoelastic instability of a frictional contact. Proceedings of the Russian Academy of Sciences. Mechanics of solids, 1997, no. 1, pp. 114-121. (in Russian)
16. Pyryev, Y.A., Grilitsky, D.V. The non-stationary problem of the frictional contact for a cylinder taking into account heat release and wear. Applied Mathematics and Technical Physics, 1996, p. 37, no. 6, pp. 99-104.
17. Pyryev, Y.A. Frictional contact of a cylinder with a clip, taking into account inertia, heat release and wear. Physico-chemical mechanics of materials, 2000, vol. 36, no. 3, pp. 53-58.
18. Awrejcewicz, J., Pyryev, Y. Thermoelastic contact of a rotating shaft with a rigid bush in conditions of bush wear and stick-slip movements. International Journal of Engineering Science, 2002, vol. 40, no. 10, pp. 1113-1130.
19. Zelentsov, V.B., Mitrin, B.I., Lubyagin, I.A. Influence of wear on frictional heating and appearance of thermoelastic instability of a sliding contact. Computational Mechanics of Continuous Media, 2016, vol. 9, no. 4, pp. 430-442.
20. Strömberg, N., Johansson, L., Klarbring, A. Derivation and analysis of a generalized standard model for contact, friction and wear. International Journal of Solids and Structures, 1996, vol. 33, no. 13, pp. 1817-1836.
21. Andrews, K.T., Shillor, M., Wright, S., Klarbring, A. A dynamic thermoviscoelastic contact problem with friction and wear. International Journal of Engineering Science, 1997, vol. 35, no. 14, pp. 1291-1309.
22. Strömberg, N. Finite element treatment of two-dimensional thermoelastic wear problem. Computer Methods in Applied Mechanics and Engineering, 1999, vol. 177, no. 3-4, pp. 441-455.
23. Kovalenko, A.D. Introduction to thermoelasticity. Kiev, Naukova Dumka, 1965, 204 p.
24. Archard, J.E. The temperature of rubbing surfaces, Wear, 1959, vol. 2, no. 6, pp. 438-455.
25. Ditkin, V.A., Prudnikov, A.P. Operational calculus. Moscow, Vishaya Shkola, 1975, 407 p.
26. Brychkov, Y.A., Prudnikov, A.P. Integral transformations of generalized functions. Moscow, Nauka, 1977, 287 p.
27. Gurvits, A., Courant, P. Theory of functions. Moscow, Nauka, 1968, 648 p.
28. Zabreiko, P.P. Integral equations. Moscow, Fizmatlit, 1968, 448 p.
Review
For citations:
Zelentsov V.B., Mitrin B.I., Lubyagin I.A., Aizikovich S.M. Mathematical modelling of thermoelastic behavior of a coating taking into account frictional heating and wear. Computational Mathematics and Information Technologies. 2017;1(1).
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