An extended formulation of rate equation is proposed so as to treat the rate process in a heterogeneous system, such as crack propagation velocity in brittle fracture. The proposal can be applied for a process in which the excess energy stored in the system is directly relaxed by the reaction. The generalized expression is given as follows,
υ=ƒ·exp (-ΔGa/RT) ·ψ· {1-exp (-ΔG0/RT)}
where, ν; velocity of the reaction, ƒ; frequency factor, ΔGa; activation energy, ψ; measure unit of the reaction rate remarked (i. e. lattice parameter, in case of crack propagation), ΔG0; excess energy stored in the system which is finally relaxed through the reaction.
The term expressed in the parenthesis, corresponds to an effective probability of transformation and it becomes zero under equilibrium state. By the expression, the equilibrium and the rate process can be treated continuously.
Assuming linear elasticity and Griffith type crack in SiC single crystal, the relationships between stress-crack length-rate of crack propagation and stress-crack length-time to failure are numerically calculated, and the results are discussed. An example of actual application of the present proposal is shown.
