Estimation of the stress intensity factor of an interface crack by the scattered SH-far field

Abstract

The diffraction of the plane elastic SH-wave from a semi-infinite interface crack on junction of two elastic semi-infinite media is studied. The crack is modelled by the mathematical cut with no stress on its faces. The displacement and the stress fields are continuous outside of the crack. The wave diffraction problem is reduced to the solution of the mixed boundary value problem for Helmholtz equation. We search the solution which satisfies the Neumann boundary condition on the crack faces and the continuity condition for the stress and displacement fields outside of the crack. The radiation condition at the infinity and the Meixners condition at the crack tip must be also satisfied. Using the Fourier integral transform, the mixed boundary value problem is reduced to the Wiener-Hopf functional equation which is valid in the given strip of regularity in the complex plane. The method of factorization and decomposition, as well as the Liouvilles theorem, are used to solve this equation. Its kernel function is factorized and represented as a product of two split functions that are regular in the overlapping half-planes. These ones allow for the simple poles outside of the regularity regions. The solution of the Wiener-Hopf equation is presented in analytical form. The scattered displacement field is found for an arbitrary frequency and sounding angle by applying an inverse Fourier integral transform to the solution. The asympŹtotic formula for the stress intensity factor (SIF) at the crack tip is obtained. The correlation between complex amplitude of the SH-wave far scattered displacement field and the SIF caused by this field is obtained for an arbitrary radiation angle, frequency and medium parameters. This allows us to express the SIF through the amplitude of the far field if the radiation frequency, sounding angle as well as the physical characteristics of materials are known. It is shown that in the plane that is normal to the tip of the crack the ratio of SIF for the given junction and two fixed values of the sounding angle or two sounding frequencies is proportional to the ratio of the scattered fields. It is found that under above mentioned condition the proportionality rate does not depend on material properties. The obtained relations can be applied for estimation of the SIF with changing frequency and sounding angle.