Limiting velocity of crack propagation in elastic materials with effects of small viscosity and thermal conductivity

Assuming that a crack can be described by a series of continuum linear dislocations, the elastic energy of a linear crack under arbitrary stresses applied to a crack are obtained. The associated mass and the kinetic energy of a dynamically propagating crack are calculated. The dissipative function for the material with small viscosity is also found. The expression is obtained for the rate of dissipation of the mechanical energy of a crack resulting from both inelastic internal friction and thermal conductivity. The analytical formulae for the limiting velocity of crack propagation is derived.