K-Dominance zone for a semi-infinite mode I crack in a sandwich composite

A Mode I semi-in®nite crack located at the midplane of an elastic layer sandwiched between two identical half- spaces is considered. The complete stress distribution for the eigenproblem with traction-free crack faces and loading at in®nity is obtained. The auxiliary problem for a loaded crack is ®rst solved using the Wiener±Hopf method and an eigensolution is derived by a limiting procedure. The solution is presented in closed form in terms of double quadratures. Based on an analysis of the stress ®eld the size of the K-dominance zone is determined and restrictions are established on employing the conventional K-concept.