Abstract
On the basis of the solution of the problem of diffraction of a field of plane SH-waves on a crack located on the interface of materials obtained by the authors earlier, we deduce asymptotic expressions for the stress intensity factors at the crack tips. The dependences of the stress intensity factors on the dimensionless crack length, the angle of incidence of the plane wave, and the mechanical and physical properties of the materials are investigated. The possibility of appearance of singularities of the stress intensity factors near the remote crack tip (relative to the source of radiation) for the tangential and critical angles of irradiation is demonstrated. It is shown that, for the critical angles of incidence, these singularities can appear only in perfect materials and that, in the presence of losses, the increase in the stress intensity factors is bounded. It is also demonstrated that the indicated effects are caused by the diffraction interaction of SH-waves with the crack tips.
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D. B. Kurylyak, Z. T. Nazarchuk, and M. V. Voitko, “Analysis of the field of plane SH-wave scattered by a finite crack on the interface of materials,” Fiz.-Khim. Mekh. Mater., 42, No. 6, 5–16 (2006).
S. C. Pal and M. L. Ghosh, “High-frequency scattering of antiplane shear waves by interface crack,” Indian J. Pure Appl. Math., 21, No. 12, 1107–1124 (1990).
R. Pramanik, S. C. Pal, and M. L. Ghosh, “High-frequency scattering due to a pair of time-harmonic antiplane forces on the faces of a finite interface crack between dissimilar anisotropic materials,” Eur. J. Mech. A, Solids, 18, 1013–1026 (1999).
S. J. Chang, “Diffraction of plane dilatational waves by a finite crack,” Q. J. Mech. Appl. Math., 24, 423–443 (1971).
P. S. Keogh, “High-frequency scattering by a Griffith crack I: A crack Green’s function,” Q. J. Mech. Appl. Math., 38, 185–204 (1985).
P. S. Keogh, “High-frequency scattering by a Griffith crack II: Incident plane and cylindrical waves,” Q. J. Mech. Appl. Math., 38, 205–232 (1985).
M. Savruk and O. Matvisiv, “Dynamic problem for a body containing a crack under the conditions of antiplane deformation,” in: Proc. of the 3d Internat. Conf. on Fracture Mechanics and Strength of Structures [in Ukrainian], Lviv (2004), pp. 255–260.
M. P. Savruk, “New method for the solution of dynamic problems of the theory of elasticity and fracture mechanics,” Fiz.-Khim. Mekh. Mater., 39, No. 4, 7–12 (2003).
K. N. Srivastava, R. M. Palaiya, and D. S. Karaulia, “Interaction of antiplane shear waves with a Griffith crack at the interface of two bonded dissimilar elastic half spaces,” Int. J. Fract., 16, No. 4, 349–358 (1980).
A. K. Mal, “Interaction of elastic waves with a Griffith crack,” Int. J. Eng., Sci., 8, 763–776 (1970).
Ch. Zhang and D. Gross, On Wave Propagation in Elastic Solids with Cracks, Computational Mechanics Publ., Southampton-Boston (1998).
V. A. Men’shikov, “A crack on the interface of elastic materials under harmonic loading,” Vestn. Kherson. Nats. Tekhn. Univ., 2, No. 25, 331–335 (2006).
A. F. Ulitko, “Semiinfinite cut along the boundary of rigidly connected half planes made of different materials,” in: Contemporary Problems of Continuum Mechanics [in Russian], Kniga, Rostov-on-Don (1995), pp. 185–193.
A. F. Ulitko and V. I. Ostrik, “Contact problem for a semiinfinite interface crack,” Mat. Met. Fiz.-Mekh. Polya, 44, No. 2, 88–95 (2001).
D. B. Kurylyak and Z. T. Nazarchuk, Numerical-Analytic Methods in the Theory of Diffraction of Waves on Conic and Wedge-Like Surfaces [in Ukrainian], Naukova Dumka, Kiev (2006).
M. Abramowitz and I. A. Stegun (editors), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Applied Mathematical Series, 55 (1964).
I. S. Gradshtein and I. M. Ryzhik, Tables of Sums, Integrals, Series, and Products [in Russian], Fizmatgiz, Moscow (1963).
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Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 43, No. 4, pp. 18–30, July–August, 2007.
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Kurylyak, D.B., Nazarchyk, Z.T. & Voitko, M.V. Stress field in a crack on the interface of materials irradiated with SH-waves. Mater Sci 43, 464–478 (2007). https://doi.org/10.1007/s11003-007-0055-7
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DOI: https://doi.org/10.1007/s11003-007-0055-7