Abstract
The paper addresses the three-dimensional problem on steady-state vibrations of an elastic body consisting of two perfectly joined dissimilar half-spaces with an elliptic mode I crack located in one of the half-spaces normally to the interface. The problem is reduced to a boundary integral equation for the crack opening function. The integration domain of the equation is bounded by the crack domain, and the interaction between the crack and the interface is described by a regular kernel. The equation is solved using the map** method. Numerical results are obtained for the case where the surfaces of the elliptic crack are subjected to harmonic loading with constant amplitude. The dependences of the stress intensity factors on the wave number are presented for various relationships among the mechanical constants that ensure the absence of near-surface waves
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REFERENCES
V. T. Grinchenko and V. V. Meleshko, Harmonic Vibrations and Waves in Elastic Bodies [in Russian], Naukova Dumka, Kiev (1981).
A. N. Guz and V. V. Zozulya, Brittle Fracture of Materials under Dynamic Loads [in Russian], Naukova Dumka, Kiev (1993).
V. V. Mikhas'kiv and M. V. Hai, “Applying the image method to solve problems on steady-state vibrations of an infinite body with a flat cut,” Izv. AN SSSR, Mekh. Tverd. Tela, No. 1, 122–126 (1989).
J. J. Rushchitsky and S. I. Tsurpal, Waves in Microstructural Materials [in Ukrainian], Inst. Mekh. Im. S. P. Timoshenka NAN Ukrainy, Kiev (1997).
V. Samukha and V. Loboda, “A plate with an interfacial crack under harmonic loading,” in: Mathematical Problems of the Mechanics of Inhomogeneous Structures [in Ukrainian], Vol. 2, Inst. Prikl. Probl. Mekh. Mat. Im. Ya. S. Podstrigacha NAN Ukrainy, Lvov (2000), pp. 23–26.
M. V. Hai and A. I. Stepanyuk, “Interaction of cracks in a piecewise-homogeneous body,” Prikl. Mekh., 28, No. 12, 46–56 (1992).
J. Balas, J. Sladek, and V. Sladek, Stress Analysis by Boundary Element Methods, Elsevier, Amsterdam (1989).
M. C. Chen, N. A. Noda, and R. J. Tang, “Application of finite-part integrals to planar interfacial fracture problems in three-dimensional bimaterials,” Trans. ASME,J. Appl. Mech., 66, 885–890 (1999).
M. V. Dudik, L. A. Kipnis, and A. V. Pavlenko, “Analysis of plastic slip lines at the tip of a crack terminating at the interface of different media,” Int. Appl. Mech., 38, No. 2, 197–202 (2002).
A. N. Guz, “Critical phenomena in cracking of the interface between two prestressed materials. 1. Problem formulation and basic relations,” Int. Appl. Mech., 38, No. 4, 423–431 (2002).
A. N. Guz, “Critical phenomena in cracking of the interface between two prestressed materials. 2. Exact solution. The case of unequal roots,” Int. Appl. Mech., 38, No. 5, 548–555 (2002).
H. S. Kit, M. V. Khaj, and V. V. Mykhas'kiv, “Analysis of dynamic stress concentration in an infinite body with parallel penny-shaped cracks by BIEM,” Eng. Fract. Mech., 55, No. 2, 191–207 (1996).
V. V. Mykhas'kiv and O. I. Stepanyuk, “Boundary integral analysis of the symmetric dynamic problem for an infinite bimaterial solid with an embedded crack,” Mechanica, 36, No. 4, 479–495 (2001).
G. C. Sih and E. P. Chen, “Axisymmetric elastodynamic response from normal and radial impact of layered composites with embedded penny-shaped crack,” Int. J. Solids Struct., 16, 1093–1107 (1980).
Ch. Zhang and D. Gross, On Wave Propagation in Elastic Solids with Cracks, Comput. Mech. Publ., Southampton (1998).
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Mikhas'kiv, V.V., Sladek, J., Sladek, V. et al. Stress Concentration Near an Elliptic Crack in the Interface Between Elastic Bodies under Steady-State Vibrations. International Applied Mechanics 40, 664–671 (2004). https://doi.org/10.1023/B:INAM.0000041394.83873.2f
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DOI: https://doi.org/10.1023/B:INAM.0000041394.83873.2f