Effect of wear on frictional heating and thermoelastic instability of sliding contact

In this work, we consider a relationship between the wear of an elastic coating and the frictional heating on a sliding contact, as well as their joint effect on initiation and development of thermoelastic instability of sliding thermoelastic frictional contact. The initial boundary-value quasi-static problem of uncoupled thermoelasticity involving the sliding of a rigid body represented by a half-plane over the surface of an elastic coating is formulated with regard to Coulomb friction and frictional heat generation. The half-plane slides with a constant velocity; the coating is bonded to a rigid substrate. The work of frictional forces at the contact is spent on heating the coating and on its abrasive wear. To solve this problem, the Laplace integral transform is used. Solutions of the problem, namely temperature, stresses and displacements both on contact and in the depth of the coating, are represented in the form of the Laplace convolution. Integrand functions in stresses and displacements integrals are non-decaying at infinity (they remain constant), so the integrals containing them are understood in a generalized meaning. After regularization of integrands of displacements and stresses integrals, a solution to the problem is written as the sum of the regular constituent of a generalized part and the Laplace convolution. It is shown that the integrals depend on three dimensionless parameters of the problem. The placement of the poles of integrands in the complex plane of an integration variable is studied in detail. This gives the domains of stable and unstable solutions in the space of dimensionless parameters of the problem. After calculation of convolutions, the problem solution is represented by functional series over the poles of integrands, which is convenient for evaluation and analysis. The properties of stable and unstable exact solutions for temperature, wear and stresses on a sliding thermoelastic frictional contact are investigated in relation to the values of dimensional and dimensionless parameters of the problem.