THEORY OF NONISOTHERMAL CRACK-PROPAGATION IN PLASTIC AND VISCOUS-PLASTIC MATERIALS

A self-consistent model to describe the non-isothermal fracture in pla stic and viscous-plastic materials is proposed for the first time, tak ing into account the local heating near the crack tip and the temperat ure dependence of the parameters of the material (plastic yield stress , surface energy etc.). On the basis of the lagrangean approach for th e Griffith-Mott model of crack propagation, combined with the non-equi librium thermodynamical description of the dissipation effects near th e crack tip, the general system of equations is formulated to describe the joint development of the mechanical and thermal subsystems in the course of the crack propagation. Linear analysis of the system evolut ion near the equilibrium states reveals the existence of a thermomecha nical fracture instability. The instability threshold as well as the i nstability dynamics have been investigated for different heat transfer conditions on the plastic zone surface. It is found that non-isotherm al crack propagation in the extremely viscous regime acquires an explo sive behaviour, characterized by fast monotonic crack acceleration unt il total rupture, reached for a finite time interval. It is found that thermoactivative fracture may acquire a bistable character, realized in the coexistence of two stationary propagation modes with a constant velocity: (i) exponentially small and (ii) comparable with the termin al crack velocity for isothermal fracture.