Crack propagation from a pre-existing flaw at a notch root. I. Introduction and general form of the stress intensity factors at the initial crack tip

This paper and its companion are devoted to the study of crack kinking from some small pre-existing crack originating from a notch root (the notch root radius being zero). Both the notch boundaries and the initial crack are allowed to be curved; also, the geometry of the body and the loading are totally arbitrary. The ingredients required are knowledge of the stress intensity factors at the initial crack tip and use of a suitable mixed mode propagation criterion. This paper is devoted to the first point, and more specifically to establishing the general (that is, not yet fully explicit) form of the formulae giving these stress intensity factors. The method used is based on changes of scale (homogeneity properties of the equations of elasticity) on the one hand, and on continuity of the displacement and stresses at a given, fixed point with respect to the crack length on the other hand. The formulae derived for the stress intensity factors at the tip of the small crack are of universal value: they apply to any situation, whatever the geometry of the body, the notch and the crack and whatever the loading, the stress intensity factors depending always only upon the `stress intensity factor of the notch' (the multiplicative coefficient of the singular stress field near the notch root in the absence of the crack), the length of the crack, the aperture angle of the notch and the angle between its bisecting line and the direction of the crack.