Mixed mode crack in a periodically-layered composite

The problem on a crack in a bimaterial periodically-layered composite is co nsidered. The single finite length crack parallel to the interfaces is load ed 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 prese nted as distributed dislocations with unknown density and the problem is re duced to a system of singular integral equations of the first kind. The coe fficients of the system are derived from the application of the Green funct ion for a single dislocation which is obtained in a closed form with the he lp of the representative cell approach. The dependence of the stress intens ity 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 t he 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 d issimilar behavior of the stress intensity factors was revealed. In particu lar, we discovered that K-II may vanish not only for the symmetric crack po sition in the midplane of the layer but also in several additional ones. Fo r some limiting cases the solution is seen to coincide with known results.