The symmetric frequency-domain problem of the interaction effects in rectangular lattice system of coplanar penny-shaped cracks located in an infinite elastic solid is numerically investigated. The problem is reduced to a boundary integral equation for the crack-opening-displacement in a unit cell by means of 3D periodic elastodynamic Green's function. This function is adopted for the effective calculation by its representation in the form of exponentially convergent Fourier integrals. A collocation method is used for the solution of the boundary integral equation. Numerical results for the mode-I dynamic stress intensity factor in the crack vicinities are obtained and analyzed depending on the wave number and the lattice size.

elastodynamic interaction between a penny-shaped crack and a thin elastic interlayer joining two elastic half-spaces is investigated by an improved boundary integral equation method or boundary element method. The pennyshaped crack is embedded in one of the half-spaces, perpendicular to the interlayer and subjected to a time-harmonic tensile loading on its surfaces. Effective "spring-like" boundary conditions are applied to approximate the effects of the thin layer in the mathematical model. Integral representations for the displacement and the stress components are derived by using modified Green's functions, which satisfy the "spring-like" boundary conditions identically. Then, application of the dynamic loading condition on the crack-surfaces results in a boundary integral equation (BIE) for the crack-opening-displacement over the crack-surfaces only. A solution procedure is developed for solving the BIE numerically. Numerical results for the mode-I dynamic stress intensity factor V. Mykhas'kiv · I. Zhbadynskyi (SIF) are presented and discussed to show the variations of the mode-I dynamic SIF with the angular coordinate of the crack-front points, the dimensionless wave number, the material mismatch and the crack-layer distance.

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SUMMARYThe three-dimensional (3-D) problem of bi-materials or two ideally bonded elastic half-spaces with interacting sub-interface cracks subjected to time-harmonic loading is analyzed. The boundary value problem is reduced to a system of boundary integral equations (BIEs) in the frequency domain for the crack-opening-displacements (CODs) only. Boundary integrals over the finite crack-surfaces are obtained by introducing modified elastodynamic Green's functions, which identically satisfy the contact conditions on the infinite interface. The singularity subtraction technique under consideration of the 'square-root' behavior of the CODs at the crack-front is applied for the regularization of the BIEs. By using a collocation scheme, the BIEs are converted into a system of linear algebraic equations. Numerical calculations are performed for a bi-material with two penny-shaped cracks located on both sides of the interface subjected to time-harmonic tensile loading of constant amplitude on the crack-surfaces. Numerical results for the mode-I dynamic stress intensity factor as a function of the wave number are presented and discussed for various material combinations and distances between the interface and the cracks.

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