Mixed mode crack in a periodically-layered composite

The problem on a crack in a bimaterial periodically-layered composite is considered. The single finite length crack parallel to the interfaces is loaded by normal opening tractions but the fracture mode is the mixed one as a result of non–symmetric crack location within the layer. The crack is presented as distributed dislocations with unknown density and the problem is reduced to a system of singular integral equations of the first kind. The coefficients of the system are derived from the application of the Green function for a single dislocation which is obtained in a closed form with the help of the representative cell approach. The dependence of the stress intensity factors K_I and K_II upon the geometric and elastic mismatch parameters is examined. The numerical study allowed to point out the cases in which the simplified sandwich model can be employed for the analysis. On the other hand, for the case of very thin and stiff non–cracked layers essentially dissimilar behavior of the stress intensity factors was revealed. In particular, we discovered that K_II may vanish not only for the symmetric crack position in the midplane of the layer but also in several additional ones. For some limiting cases the solution is seen to coincide with known results.