13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- tested on a purely comparative basis (ρ = 0.5, 1, 2.5, 3 and 27.5mm), which correspond to the critical value of the elliptic notch. ρ (mm) b (mm) c (mm) 0,5 27,5 0,5 1 27,5 1 2,5 27,5 2,5 3 27,5 3 27,5 27,5 27,5 Table 1. Notches dimensions The high value Ktf = σy/σn in the presence of a short crack is always localized close to the edges of the hole according to the curves of Fig. 2. In fact, in the case of an elliptic notch (b > c), the ratio of the stress σy(x) along the remaining ligament and the nominal stress σn, i.e. Ktf, is roughly equal to 3 for the distance x = 1.1b. This ratio falls to a value of 2 independently of the radius ρ when x reaches approximately 1.2b. The Eq. (3) enables us to quantify the influence of the stress gradient on the variation of the Ktf according to x/b. Fig. 2. Evolution of the stress concentration in the presence of a short crack Fig. 3 illustrates explicitly the relationship between the stress concentration Kt (without crack) and the stress concentration (Ktf = σy/σn) (in the presence of a crack) with respect to the distance away from the edge of the notch. The reduction of Ktf /Kt is practically linear and not very sensitive to the value of Kt. The ratio decreases steeply from 1 for a point located at the end of the notch to 0.9 for a point which is very close to the crack length a = b/20. This rather high stress gradient can cause an initiation of the fatigue short crack, even in the case of a nominal stress lower than the yield stress.
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