Abatraet-Yokobori
and colleagues have treated timedependent fracture, such as fatigue and creep fracture, as a stochastic process and a thermally activated process, extended the studies, and proposed the crack growth rate equations for fracture of various kinds. Among those for high temperature creep, fatigue and creep-fatigue multiplications, the following equation has been proposed for crack growth rate based on stochastic and thermally activated processes: da _ =AeQ' C-It where -.
It has been found that, using the Q* parameter, the high temperature creep crack growth rate is very well characterized. In smooth specimens, final fracture of two types may be realistic. One is where one crack which started from the small original defect extends and the final fracture is caused by the stress intensity factor for the critical length of the crack attained due to this one-crack extension. The other may be the case where multi-site cracks, say a number of cracks initiated from a number of small defects, grow and join together. In the latter case it was shown previously that the fracture time is determined by the time when each growing crack attains the critical length depending on the distance between each tip of the originally initiated small cracks. Thus, for the final fracture of both types mentioned above, creep fracture time r,can be obtained by integrating da/dt expressed in terms of Q* mentioned above. Using creep strain rate (for steady creep or minimum creep) expressed for a thermally activated process, and calculating t/i, then the equation t,i is found to be given as the equation of activation type. This equation thus obtained for smooth specimen includes, as a special case, the formula experimentally obtained by Monkman and Grant, and nearly coincides with the formula modified experimentally by Wiederhom et al. for alumina ceramics. For notched or cracked specimens, it has not been found whether the Larson-Miller formula is valid or not. By integrating the equation expressed in terms of Q*, it was found that the master curve for creep fracture time t, was obtained in terms of applied stress and temperature. In conclusion, it may be possible to predict or characterize the creep crack growth rate and the creep life throughout, from high temperature ductile materials such as Cr-Mo-V steel and SUS 304 stainless steel to high temperature brittle materials such as alumina ceramics, using the unified formula based on the Q* parameter cowed. The effect of creep ductility on creep life can be discriminated by the matehal constants. _