The Rigid Die on a Half-Space with Thermal Relaxation and Convection: Influence of Sliding Speed, Die Temperature, and Geometry

Abstract

A rigid die slides without friction on the surface of a coupled thermoelastic half-space at a constant sub-critical speed. A 3D dynamic steady state is treated, i.e., contact zone and its traction are invariant in the frame of the die. The die is maintained at a temperature that differs from the uniform ambient temperature prior to sliding, and die/half-space thermal convection occurs. The half-space exhibits thermal relaxation governed by the Lord–Shulman model. Three cases are treated: The die is a sphere in Case I and a cone in Case II. Case III involves a wedgelike die, formed by joining the bases of two cones. Asymptotic expressions in analytic form are derived for contact zone traction. Expressions and calculations for contact zone geometry are also given. These show that unstable behavior occurs when die ambient temperature exceeds that of the half-space by a critical value that itself may depend on die shape and speed.