In some recent works for 1Cr-Mo-V steel and 304L stainless steel, it has been reported that the fatigue lives were significantly reduced under the tensile hold low cycle fatigue conditions though the cavitation damages were not observed and the cracks were transgranularly propagated. So these phenomena have some important sense that the reason of fatigue lives reduction have another new factor except cavitation damage under the creep-fatigue interaction condition.
Recently, Oh and Nam suggested a new crack advance and life prediction model based on the fatigue process zone in front of the cracktip, where the actual degradation of the material occurred with crack advance.
Using the life prediction model, the predicted fatigue life is in good agreement with the experimentally observed one for 1Cr-Mo-V steel. According to Oh, $\alpha_f$ which is newly introduced in the life prediction model is constant regardless temperature and strain range. But the experimental results for 1Cr-Mo-V steel showed that $\alpha_f$ is a function of temperature, the value of $\alpha_f$ decreases with increasing temperature.
So the smaller $\alpha_f$ in high temperature contributes to the decrease of process zone($D_p$) size and cyclic plastic zone($r_f$) size. Therefore, $\alpha_f$ is considered as a stress concentration factor on the crack-tip region. And also in tensile hold life prediction model, the value of C is increased with increasing the hold time.
Considering the relationship between $\alpha_f$ and C, a modified life prediction model is suggested and it may give the more precise predicted fatigue life.