Crack propagation from a pre-existing flaw at a notch root – II: Detailed form of the stress intensity factors at the initial crack tip and conclusion.

Abstract

This paper pursues the study of crack kinking from a pre-existing crack emanating from some notch root. It was shown in Part I that the stress intensity factors at the tip of the small initial crack are given by universal (that is, applicable in all situations, whatever the geometry of the body and the loading) formulae; they depend only on the `stress intensity factor of the notch' (the multiplicative coefficient of the singular stress field near the apex of the notch 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. Here we identify the universal functions of the two angles just mentioned which appear in these formulae, by considering the model problem of an infinite body endowed with a notch with straight boundaries and a straight crack of unit length. The treatment uses Muskhelishvili's complex potentials formalism combined with some conformal mapping. The solution is expressed in the form of an infinite series involving an integral operator, which is evaluated numerically. Application of Goldstein and Salganik's principle of local symmetry then leads to prediction of the kink angle of the crack extension. It is found that although the direction of the crack is closer to that of the bisecting line of the notch after kinking than before it, the kink angle is not large enough for the crack tip to get closer to this line after kinking, except perhaps in some special situations.