Fatigue crack growth from small to large cracks on very high cycle fatigue with fish-eye failures

In previous works [Paris Paul C, Marines-Garcia Israel, Hertzberg Richard W, Donald J Keith. The relationship of effective stress intensity, elastic modulus and Burgers-vector on fatigue crack growth as associated with “fish eye” gigacycle fatigue phenomena. In: Proceedings of the international conference on very high cycle fatigue III, Kyoto, Japan, September 2004; Marines-Garcia Israel. Doctoral Dissertation at ITMA, CNAM, Paris, October 2004 (Claude Bathias director)], the general relationship between ΔKeff and crack growth rate, dadN, was used to demonstrate that, with gigacycle “fish-eye” fatigue failures, the crack growth was not a significant portion of total life. These works assumed that for “small cracks” the crack would be opened during its positive load cycle so that ΔKeff = ΔK (load ratio, R > 0) and that cracks after becoming “long cracks” would propagate so rapidly that crack closure would not affect that conclusion. Therefore, in this discussion the effects of crack closure at various load ratios, R, will be considered as it might impact this conclusion. It will be shown that such considerations do not discredit the previous results. Furthermore, the presence of closure will be explored for a range of transition sizes from small to long crack as well as various load ratios.