Steady-state mode III delamination crack in a periodically layered medium

A non-homogeneous layered space with a semi-infinite interface crack is considered. Isotropic elastic layers having dissimilar thicknesses and shear moduli are arranged periodically and the antiplane stress state is produced by a shear loading applied to the crack faces. Application of the representative cell method based on the discrete Fourier transform allows to reduce the initial problem to the problem for a single bi-layered cell in the transform space and to formulate theWiener-Hopf equation. The final result is presented in the form of triple quadratures. A parametric study of the stress intensity factor revealed some qualitative differences in its behavior for the cases of equal and non-equal layers thicknesses. The obtained analytical result is employed to derive of the closed form eigensolution corresponding to the traction free crack faces and vanishing remote loading. In addition to the local near tip square root asymptote this solution has also the remote one on a macroscale. The influence of the problem parameters on the ratio of the near to the far stress intensity factor is investigated and expressed by a simple algebraic formula which is confirmed by energy considerations. It is found that when the thin layers are more compliant this ratio is always less than unity, while in the opposite case the local stress singularity may exceed the remote one.