“…To calculate the number of cycles to initiate a fatigue crack from an inclusion, several models are used more or less successfully. In the Gigacycle fatigue range, the integration of Paris' law (Xue et al, 2006a(Xue et al, ,b, 2005Puskar, 1977;Luong, 1998Luong, , 1995Bayraktar et al, 2006Bayraktar et al, , 2004Xue, 2005;Garcia et al, 2006;Audenino et al, 2003;Wang, 1998;Meyendorf et al, 2002) allows to predict the number of cycles in the fish eye and obtain the crack initiation number of cycles. The crack initiation stage in the very high cycle fatigue can generally be described in terms of a local micro structurally irreversible portion of the cumulative plastic strain.…”