Mutual influence of the faces contact area and the pre-fracture zone near the tip of the interfacial crack

BACKGROUND: Under plane strain conditions, a crack model was developed on a plane interface between two different materials, which assumes the existence near its tip of the faces contact area and a narrow lateral pre-fracture zone in a less crack-resistant material of the composite compound. The pre-fracture zone is modeled by the line of normal displacement rupture, on which the normal stress is equal to the tensile strength of the material. Assuming that the dimensions of the pre-fracture zone and the contact zone have the same order of magnitude and are significantly smaller than the crack length, the problem is reduced to the vector Wiener–Hopf equation. METHODS: An approximate method for solving the vector Wiener–Hopf equation was developed, which was used to obtain the equations for determining the sizes of the pre-fracture zone and the contact faces area. The pre-fracture zone orientation was determined from the condition of the potential energy maximum accumulated in the zone. Numerical calculations of the indicated parameters and analysis of their dependences on the configuration and module of external load are executed. RESULTS: A significant mutual influence of the pre-fracture zone and crack faces contact on their sizes and orientation of the zone was revealed.

Diffraction of sound waves by a lined cylindrical cavity

In this paper, diffraction of sound waves through a lined cavity is analyzed rigorously. The inner–outer surfaces of the cavity and the base of the cavity are coated with three different absorbing linings. By using the Fourier transform technique in conjunction with the Mode-Matching method, the related boundary value problem is formulated as a Wiener–Hopf equation. In the solution, two infinite sets of unknown coefficients are involved that satisfy two infinite systems of linear algebraic equations. Numerical solution of this system is obtained for various values of the parameters of the problem. The graphical results are also presented which show that how efficiently the sound diffraction can be reduced by selection of problem parameters.