Short crack threshold estimates to predict notch sensitivity factors in fatigue

Abstract

The notch sensitivity factor q can be associated with the presence of non-propagating fatigue cracks at the notch root. Such cracks are present when the nominal stress range Δ σ n is between Δ σ 0/ K t and Δ σ 0/ K f, where Δ σ 0 is the fatigue limit, K t is the geometric and K f is the fatigue stress concentration factors of the notch. Therefore, in principle it is possible to obtain expressions for q if the propagation behavior of small cracks emanating from notches is known. Several expressions have been proposed to model the dependency between the threshold value Δ K th of the stress intensity range and the crack size a for very small cracks. Most of these expressions are based on length parameters, estimated from Δ K th and Δ σ 0, resulting in a modified stress intensity range able to reproduce most of the behavior shown in the Kitagawa–Takahashi plot. Peterson or Topper-like expressions are then calibrated to q based on these crack propagation estimates. However, such q calibration is found to be extremely sensitive to the choice of Δ K th( a) estimate. In this work, a generalization version of El Haddad–Topper–Smith’s equation is used to evaluate the behavior of cracks emanating from circular holes and semi-elliptical notches. For several combinations of notch dimensions, the smallest stress range necessary to both initiate and propagate a crack is calculated, resulting in expressions for K f and therefore for q. It is found that the q estimates obtained from this generalization, besides providing a sound physical basis for the notch sensitivity concept, better correlate with experimental data from the literature.