The fourth mode of fracture in fractal fracture mechanics

This paper offers a systematic approach for obtaining the order of stress s ingularity for different self-similar and self-affine fractal cracks. Mode II and Mode III fractal cracks are studied and are shown to introduce the s ame order of stress singularity as Mode I fractal cracks do. In addition to these three classical modes, a Mode IV is discovered, which is a consequen ce of the fractal fracture. It is shown that, for this mode, stress has a w eaker singularity than it does in the classical modes of fracture when self -affine fractal cracks are considered, and stress has the same order of sin gularity when self-similar cracks are considered. Considering this new mode of fracture, some single-mode problems of classical fracture mechanics cou ld be mixed-mode problems in fractal fracture mechanics. By imposing a cont inuous transition from fractal to classical stress and displacement fields, the complete forms of the stress and displacement fields around the tip of a fractal crack are found. Then a universal relationship between fractal a nd classical stress intensity factors is derived. It is demonstrated that f or a Mode IV fractal crack, only one of the stress components is singular, the other stress components are identically zero. Finally, stress singulari ty for three-dimensional bodies with self-affine fractal cracks is studied. As in the two-dimensional case, the fourth mode of fracture introduces a w eaker stress singularity for self-affine fractal cracks than classical mode s of fracture do.