13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- was drastically reduced due to the short crack growth, which may lead to the non-propagating crack phenomena. In the present paper, based on their analytical methodology, a modified method has been provided to quantify the short crack behavior. And the variation of the stress gradient and the resulting ΔK along with the short cracks growth has been presented. 2. Stress gradient at the sharp notch root along with the short cracks growth It is well known that the stress concentration is usually caused by geometrical discontinuity or heterogeneity of microstructure which involves an appearance of the maximum stress compared to the calculated median values based on the smooth section. In mechanical design, one attaches rather importance to the high stress fields which arise in the majority of the industrial components (shoulder, holes, fillets etc.). The stress concentrations can be regarded as the origin of the fatigue cracks or the unstable ruptures. In this paper, the authors are devoted to the investigation of the stress concentrations due to the geometry imposed by the industrial design. The notch effect is modeled by an increase of the local stress in a restricted volume, compared to the distribution of nominal stress. However, the concept of stress gradient can be generalized with any cross-section of a specimen or with any volume element of a mechanical component. Therefore, for a plate containing cracks at the bottom of an elliptic notch as illustrated in Fig. 1, the stress σy, which acts in the remaining ligament of an infinite plate with an elliptic hole, is given by Eq. (1) at points (x ≥ b, 0) (see [5]). ( )( )( ) ( ) ( ) ( ) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 y n b bcx xbc xbc bcbcx b c x b c x b c σ σ − − − + − + + − − = − − + − + (1) Fig. 1. Centre elliptic notch with a fatigue cracks formed at the notch roots The σy/σn can be defined as the stress concentration factor in the presence of short crack Ktf. Thus, the gradient of σy at the bottom of notch (at the edge of the elliptic hole) is given by the following equation: ( ) ( ) 2 / 2 1 / 3 4 / / y t n n x b d dx K b c b c σ σ ρ σ = = − + = − + (2) The stress gradient increases with the increase of Kt and/or the reduction of ρ, whereK t 1 2 b/ ρ = + according to [6]. In this paper, five different configurations with the same dimension of elliptic notch b = 27.5 mm (see Table 1) have been analyzed, and five radii values of which have been
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