Elastodynamic analysis of multiple crack problem in 3‐D bi‐materials by a BEM

Abstract

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.

The investigation of semi‐strip's stress state with a longitudinal crack

“…Accordingly to the approach, [36] the Fourier's transformation was applied to the system of Lame's equations (2) and to the boundary conditions (3)-(5) by the scheme…”

“…The mixed elasticity problems were solved in [1]. Elastodynamic analysis of multiple crack problem in 3-D bi-materials was made in [2]. A new type of cracks adding to Griffith-Irwin cracks was investigated in [3].…”

“…Its solving is important both for the development of theoretical methods and for the practical demand of engineering problems.The problems of elastic strips and semi-strips weakened by cracks have been solved by many methods: with the help of harmonic functions, simple and double layer potentials, integral transformations, asymptotic methods and others.The mixed elasticity problems were solved in [1]. Elastodynamic analysis of multiple crack problem in 3-D bi-materials was made in [2]. A new type of cracks adding to Griffith-Irwin cracks was investigated in [3].…”

Dynamic Stresses Due to Time-Harmonic Elastic Wave Incidence on Doubly Periodic Array of Penny-Shaped Cracks

“…In many cases, periodic systems of cracks can act as wave scatterers in periodic structures with generation of specific wave patterns due to their sharp edges. The previous known works that take into account the presence of multiple cracks in 3D elastic wave fields are related to the situations with a few defects [2,5,6]. The reason is connected with the computational difficulties of the corresponding large-scale problems.…”

Elastodynamic problem for a layered composite with penny‐shaped crack under harmonic torsion

“…The propagation of time‐harmonic elastic waves through an array of periodically distributed interfacial penny‐shaped and elliptic cracks was investigated by Golub and Doroshenko . Frequency‐domain analysis of the mode‐I dynamic stress intensity factor (DSIF) for the sub‐interfacial single and multiple penny‐shaped cracks, located perpendicularly to the interface of a bimaterial solid, was realized also with the extension of results on the situation with penny‐shaped crack near thin interlayer joined two elastic half‐spaces, where the effective boundary conditions are used for modeling the interlayer as the structural element. Non‐stationary elastodynamic problems for the interfacial penny‐shaped crack under impact loading were solved by the conjunction of integral equation method with the Laplace transform technique …”