CRACK EXTENSION UNDER MIXED‐MODE LOADING IN AN ANISOTROPIC MODE–ASYMMETRIC MATERIAL IN RESPECT OF RESISTANCE TO FRACTURE

Abstract

Abstract— Recently, a crack path fracture criterion was proposed by Kfouri and Brown, based on maximum energy release rates at the tip of short kinks emanating from an existing crack when the main crack is subjected to mixed‐mode loading. Assuming a ‘mode asymmetry’ in respect of the fracture resistances of the material, KIr, and KIIr, for pure mode I and pure mode II, respectively, i.e., KIIr, differing from KIr, generally, the modified criterion proposed that the resistance to fracture is a function of the ratio q (=k2/k1) of the mode II to the mode I stress intensity factors at the tip of the kink.The aim of the present paper is to extend the modified criterion by presenting it in a form that takes into account material fracture resistance anisotropy in addition to the fracture resistance mode asymmetry previously described. Note however that the material's elastic properties are still assumed to be isotropic. A short FORTRAN computer program has been written to predict the kink angle under mixed‐mode loading for cracks in materials with mode asymmetry and material anisotropy with respect to their fracture resistance properties, and the inclination angle, θ, defining the direction of the main crack in the material. The values of four parameters, r0, r90, s and θ, described in the text, characterising the material fracture resistance asymmetrical and anisotropic properties and the orientation of the main crack, are prompted by the program, which provides, almost instantaneously, the kink angles under various loading modes and much additional relevant information. The effects of the variation of these parameters, treated singly or in combination, and the discontinuous “catastrophic” character of many of the responses at certain “transition” values of the parameters, are illustrated further. In the discussion it is recognised that the translation of the results of the analysis of a highly idealised situation to actual practical problems on real materials encountered in practice, is not straightforward but, notwithstanding, since material fracture resistance anisotropy and fracture resistance mode asymmetry may well be present in the real world, the possible influence of these factors perhaps needs to be taken into account in studies on crack paths.