Mathematical modelling of thermoelastic behavior of a coating taking into account frictional heating and wear
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.