Herein, a substitute series solution, which is unavailable in literature, pertaining to the antiplane diffraction problem by a vertical edge crack, is derived via the region-matching technique combining with the method of images. The dynamic stress intensity factor can be straightforwardly extracted from the expression of the radial stress field, fulfilling the crack-tip singularity inherently. Computed results of the extremely near-, near-, and far-field solutions agree well with those of exact analytical solution and available data. The proposed approach can be applied to cope with the diffraction problems by multiple cracks or branched cracks under SH-wave incidence.
Issue Section:
Technical Briefs
1.
Datta
, S. K.
, 1979, “Diffraction of SH Waves by an Edge Crack
,” ASME Trans. J. Appl. Mech.
JAMCAV 0021-8936, 46
, pp. 101–106.2.
Stone
, S. F.
, Ghosh
, M. L.
, and Mal
, A. K.
, 1980, “Diffraction of Antiplane Shear Waves by an Edge Crack
,” ASME Trans. J. Appl. Mech.
JAMCAV 0021-8936, 47
, pp. 359–362.3.
Huang
, J. Y.
, 1995, “Interaction of SH-Waves With a Finite Crack in a Half-Space
,” Eng. Fract. Mech.
EFMEAH 0013-7944, 51
, pp. 217–224.4.
Ciarletta
, M.
, Passarella
, F.
, and Sumbatyan
, M. A.
, 1996, “Scattering of a Horizontally Polarized Oblique Wave by a Pair of Surface-Breaking Cracks
,” J. Acoust. Soc. Am.
JASMAN 0001-4966, 100
, pp. 2937–2941.5.
Datta
, S. K.
, Shah
, A. H.
, and Fortunko
, C. M.
, 1982, “Diffraction of Medium and Long Wavelength Horizontally Polarized Shear Waves by Edge Cracks
,” J. Appl. Phys.
JAPIAU 0021-8979, 53
, pp. 2895–2903.6.
Abduljabbar
, Z.
, Datta
, S. K.
, and Shah
, A. H.
, 1983, “Diffraction of Horizontally Polarized Shear Waves by Normal Edge Cracks in a Plate
,” J. Appl. Phys.
JAPIAU 0021-8979, 54
, pp. 461–472.7.
Liu
, S. W.
, Sung
, J. C.
, and Chang
, C. S.
, 1997, “Transient Scattering of SH Waves by Surface-Breaking and Sub-Surface Cracks
,” Int. J. Solids Struct.
IJSOAD 0020-7683, 34
, pp. 4019–4035.8.
Sabina
, F. J.
, and Babich
, V. M.
, 2001, “Low-Frequency Scattering of Acoustic Waves by a Bounded Rough Surface in a Half-Plane
,” J. Acoust. Soc. Am.
JASMAN 0001-4966, 109
, pp. 878–885.9.
Tsaur
, D. H.
, 2010, “Exact Scattering and Diffraction of Antiplane Shear Waves by a Vertical Edge Crack
,” Geophys. J. Int.
GJINEA 0956-540X, 181
, pp. 1655–1664.10.
Datta
, S. K.
, and Shah
, A. H.
, 1982, “Scattering of SH Waves by Embedded Cavities
,” Wave Motion
WAMOD9 0165-2125, 4
, pp. 265–283.11.
Lu
, J. F.
, and Hanyga
, A.
, 2004, “Scattering of Antiplane Shear Wave by a Kinked Crack
,” Eng. Fract. Mech.
EFMEAH 0013-7944, 71
, pp. 1289–1305.12.
Særmark
, K.
, 1959, “A Note on Addition Theorems for Mathieu Functions
,” Z. Angew. Math. Phys.
ZAMPA8 0044-2275, 10
, pp. 426–428.13.
Watson
, G. N.
, 1944, A Treatise on the Theory of Bessel Functions
, 2nd ed., Cambridge University Press
, Cambridge
.14.
Daux
, C.
, Moës
, N.
, Dolbow
, J.
, Sukumar
, N.
, and Belytschko
, T.
, 2000, “Arbitrary Branched and Intersecting Cracks With the Extended Finite Element Method
,” Int. J. Numer. Methods Eng.
IJNMBH 0029-5981, 48
, pp. 1741–1760.15.
Abramowitz
, M.
, and Stegun
, I. A.
, 1972, Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables
, Dover
, New York
.16.
Loeber
, J. F.
, and Sih
, G. C.
, 1968, “Diffraction of Antiplane Shear Waves by a Finite Crack
,” J. Acoust. Soc. Am.
JASMAN 0001-4966, 44
, pp. 90–98.Copyright © 2011
by American Society of Mechanical Engineers
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