A mode I crack parallel to the interfaces in a periodically layered medium

The plane problem of a single crack in a periodically layered bimaterial co mposite is considered. For the case of a long crack loaded by opening norma l tractions, the universal relation obtained between the Mode I and Mode II stress intensity factors show that the most dangerous crack location lies in the midplane of the layer. This crack location of the Mode I finite leng th crack is examined in detail. A closed form expression of the Green's fun ction for a single dislocation is derived and the problem is reduced to a s ingular integral equation of the first kind. The study of the dependence of the normalized stress intensity factor upon the crack length reveals a wav y nonmonotonic behavior. A simple analytic formula for the limiting case of a semi-infinite crack is derived. It is found to be valid for a broad rang e of parameters.