Short crack threshold estimates to predict notch sensitivity factors in fatigue

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 Delta sigma(n) is between Delta sigma(0)/K-t and Delta sigma(0)/K-f, where Delta sigma(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 Delta 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 Delta K-th and Delta sigma(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 Delta 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. (C) 2007 Elsevier Ltd. All rights reserved.