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The Quarterly Journal of Mechanics and Applied Mathematics 1985 38(2):205-232; doi:10.1093/qjmam/38.2.205
© 1985 by Oxford University Press
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HIGH-FREQUENCY SCATTERING BY A GRIFFITH CRACK II: INCIDENT PLANE AND CYLINDRICAL WAVES

P. S. KEOGH

( 25 Cramer Street, Stafford ST17 4BX )

The general problem of scattering of elastic waves by a Griffith crack can be solved using a crack Green's function which is the displacement field due to oscillatory line-force loading of the crack faces. In Part I an exact high-frequency representation for the Fourier transform of the crack opening displacement was derived. In this paper we consider applications to cases of incident plane-compressional, plane-shear, and cylindrical waves. For incident plane waves, rigorous high-frequency asymptotic approximations of the far field are derived, uniform for all angles of incidence and scattering, but non-uniform for small values of Poisson's ratio. These confirm the existing results from elastodynamic ray theory and prove the significant contribution due to the multiple reflection of Rayleigh surface waves between the crack edges. However, to obtain completely uniform results, particularly for scattered shear waves, the interactions of body waves between the crack edges must also be included.


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