In this paper, we consider the decrease in threshold stress intensity factor (SIF) range ▵K^th due to high maximum SIF K, which is observed for several materials in the tests with the K^max constant method when closure-free conditions are realized. We proposed an assessment criterion to predict this phenomenon from the past data for Al and Ti and showed that the criterion is valid also for steels. Finally, we proposed a simplified model to explain the phenomenon, considering the fact that marks of static fracture are observed on the fracture surface.