Summary
The interaction of plane time-harmonic SH-waves with micro-cracks in transversely isotropic materials is investigated. Elastic wave scattering by a single micro-crack is first analyzed. The scattered displacement is expressed as a Fourier integral containing the crack opening displacement. By using this representation formula and by invoking the traction-free boundary condition on the faces of the crack, a boundary integral equation for the unknown crack opening displacement is obtained. Expanding the crack opening displacement into a series of Chebyshev polynomials and adopting a Galerkin method, the boundary integral equation is converted into an infinite system of inear algebraic equations for the expansion coefficients which is solved numerically. Numerical results are presented for the elastodynamic stress intensity factors, the scattered far-field and the scattering cross section of a single crack. Then, propagation of plane time-harmonic SH-waves in a transversely isotropicmaterial permeated by a random and dilute distribution of micro-cracks is investigated. The effects of the micro-crack density on the attenuation coefficient and the phase velocity are analyzed by appealing to a simple energy consideration and by using Kramers-Kronig relations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Achenbach, J. D.: Wave propagation in elastic solids. Amsterdam: North-Holland 1973.
Ang, W. T.: Transient response of a crack in an anisotropic strip. Acta Mech.70, 97–109 (1987).
Ang, W. T.: A crack in an anisotropic layered material under the action of impact loading. J. Appl. Mech.55, 120–125 (1988).
Angel, Y. C., Achenbach, J. D.: Attenuation and speed of antiplane waves in a cracked solid using the Kramers-Kronig relations. J. Acoust. Soc. Am.90, 2757–2762 (1991).
Beltzer, A. I.: Acoustics of solids. Berlin Heidelberg New York-Tokyo: Springer 1988.
Danyluk, H. T., Singh, B. M.: Closed form solutions for a finite length crack moving in an orthotropic layer of finite thickness. Lett. Appl. Eng. Sci.22, 637–644 (1984).
Dhawan, G. K.: Interaction of elastic waves by a Griffith crack in an infinite transversely-isotropic medium. Int. J. Fract.19, 29–37 (1982).
Dhawan, G. K.: Interaction of SV-waves by a Griffith crack in an infinite transversely-isotropic medium. Int. J. Fract.20, 103–110 (1983).
Kassir, M. K., Bandyopadhyay, K. K.: Impact response of a cracked orthotropic medium. J. Appl. Mech.50, 630–636 (1983).
Kassir, M. K., Tse, S.: Moving Griffith crack in an orthotropic material. Int. J. Eng. Sci.21, 315–325 (1983).
Kundu, T.: Scattering of torsional waves by a circular crack in a transversely isotropic solid. J. Acoust. Soc. Am.88, 1975–1980 (1990).
Kundu, T., Boström, A.: Scattering of a plane longitudinal wave by a circular crack in a transversely isotropic solid. J. Appl. Mech.58, 695–702 (1991).
Kuo, A.-Y.: Transient stress intensity factors of an interfacial crack between two dissimilar anisotropic half-spaces. Part 1. Orthotropic materials. J. Appl. Mech.51, 71–76 (1984).
Kuo, A.-Y.: Transient stress intensity factors of an interfacial crack between two dissimilar anisotropic half-spaces. Part 2. Fully anisotropic materials. J. Appl. Mech.51, 780–786 (1984).
Lobanov, E. V., Novichkov, Y. N.: Diffraction of SH-waves by an oblique crack in an orthotropic half-space. Soviet Appl. Mech.17, 610–615 (1981).
Norris, A. N., Achenbach, J. D.: Elastic wave diffraction by a semi-infinite crack in a transversely isotropic material. Q. J. Mech. Appl. Math.37, 565–580 (1984).
Ohyoshi, T.: Effect of orthotropy on singular stresses produced near a crack tip by incident SH-waves. ZAMM53, 409–411 (1973).
Ohyoshi, T.: Effect of orthotropy on singular stresses for a finite crack. J. Appl. Mech.40, 491–497 (1973).
Piva, A.: Elastodynamic crack problems in an anisotropic medium through a complex variable approach. Quart. Appl. Math.44, 441–445 (1986).
Piva, A.: An alternative approach to elastodynamic crack problems in an orthotropic medium. Quart. Appl. Math.45, 97–104 (1986).
Shindo, Y., Nozaki, H., Higaki, H.: Impact response of a finite crack in an orthotropic strip. Acta Mech.62, 87–104 (1986).
Tsai, Y. M.: Penny-shaped crack in a transversely isotropic plate of finite thickness. Int. J. Fract.20, 81–89 (1982).
Tsai, Y. M.: Dynamic penny-shaped crack in a transversely isotropic material. Eng. Fract. Mech.31, 977–984 (1988).
Tsai, Y. M.: Torsional vibration of a penny-shaped crack in a transversely isotropic material. In: Adv. in Fract. Res. ICF7 (Salama, K. et al., eds.), vol. 3, pp. 2363–2368. Oxford: Pergamon Press 1989.
Zhang, Ch., Gross, D.: Wave attenuation and dispersion in randomly cracked solids I: slit cracks. Int. J. Eng. Sci. (in press).
Zhang, Ch., Gross, D.: Wave attenuation and dispersion in randomly cracked solids II: penny-shaped cracks. Int. Sci. J. Eng. Sci. (in press).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Zhang, C., Gross, D. Interaction of antiplane cracks with elastic waves in transversely isotropic materials. Acta Mechanica 101, 231–247 (1993). https://doi.org/10.1007/BF01175608
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01175608