Rapid sliding indentation with friction of a pre-stressed thermoelastic material (Q1976112)

A rigid indentor travels with a constant speed over the surface of an isotropic thermoelastic half-space. Friction exists between the indentor and half-space, and the latter is initially in equilibrium at a uniform temperature under a uniform normal pre-stress. This pre-stress, below but near yield, is assumed to produce deformations that dominate the additional deformations due to indentation. Thus, the process is treated as small deformations superposed upon (relatively) large ones. The governing equations for the superposed deformation are those of anisotropic coupled thermoelasticity. A steady-state two-dimensional study uses robust asymptotic analytical solutions to reduce the associated mixed boundary value problem to a classical singular integral equation which can be solved analytically. The solutions show that the pre-stress-induced de facto anisotropy alters the values of rotational and dilatational wave and Rayleigh speeds in the half-space and, in the case of a compressive pre-stress, generates a second, lower, critical speed. In addition, pre-stress generates noncritical sliding speeds at which the friction-dependent integral equation eigenvalue changes sign. For purposes of illustration, for a parabolic indentor the author derives expressions for half-space surface temperature change and for its average over the contact zone, the equations necessary to determine contact zone size and location, the resultant moment on the indentor, and the maximum compressive stress in the contact zone.