Effects of crack surface convection for rapid crack growth in a thermoelastic solid

As a Greenʹs function for rapid steady-state crack growth with crack surface convection, semi-in®nite Mode I crack growth at subcritical speeds in an unbounded solid under the action of compressive line loads moving on the crack surfaces is considered. A standard convection law that relates heat ¯ux to change in temperature is employed, and the solid obeys the fully-coupled (dynamic) equations of thermoelasticity. The use of robust asymptotic forms reduces the problem to the solution of coupled integral equations. These exhibit both Cauchy and Abel operators, but an exact solution is possible. The solution indicates that convection can give rise to temperature changes in the crack plane that are both more prominent and extensive than those that occur for an insulated crack surface. Exact expressions for the thermoelastic Rayleigh speed, which is the critical crack speed, and for speeds that arise for a particular value of an important characteristic parameter are also presented.