We consider a dynamic problem of interaction of a plane penny-shaped crack with thin elastic interlayer connecting two identical elastic half spaces. The crack is located in one of the half spaces perpendicularly to the interlayer and the crack faces are subjected to the action of impulsive tensile forces. The thin interlayer is modeled by the conditions of imperfect contact of the half spaces. By using the Fourier transformation with respect to time, we reduce the problem to a Helmholtz-potential-type boundary integral equation for the function of dynamic crack opening displacements. As a result of the numerical solution of this equation and transition to the originals, we get the time dependences of mode-I stress intensity factors in the vicinity of the crack for various types of dynamic loads, ratios of the elastic parameters of the half spaces and the interlayer, and the distance between the crack and the interlayer.
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References
G. C. Sih and E. P. Chen, “Normal and shear impact of layered composite with a crack: dynamic stress intensification,” Trans. ASME, J. Appl. Mech., 47, 351–358 (1980).
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).
J. Lei, Y. S. Wang, and D. Gross, “Dynamic interaction between a subinterface crack and the interface in a bimaterial time-domain BEM analysis,” Arch. Appl. Mech., 73, 225–240 (2003).
C. H. Kuo and L. M. Keer, “Three-dimensional analysis of cracking in a multilayered composite,” J. Appl. Mech., 62, 273–281 (1995).
N. A. Noda, T. Kouyama, and Y. Kinoshita, “Stress intensity factors of an inclined elliptical crack near a bimaterial interface,” Eng. Fract. Mech., 73, 1292–1320 (2006).
H. T. Xiao, Z. Q. Yue, L. G. Tham, and Y. R. Chen, “Stress intensity factors for penny-shaped cracks perpendicular to graded interfacial zone of bonded bimaterials,” Eng. Fract. Mech., 72, 121–143 (2005).
C. Xu, T. Qin, L. Yuan, and N. A. Noda, “Variation of the stress intensity factors for a planar crack parallel to a bimaterial interface,” Struct. Eng. Mech., 30, 317–330 (2008).
V. V. Mykhas’kiv and I. Ya. Zhbadyns’kyi, “Solution of nonstationary problems for composite bodies with cracks by the method of integral equations,” Fiz.-Khim. Mekh. Mater., 43, No. 1, 33–42 (2007); English translation: Mater. Sci., 43, No. 1, 27–37 (2007).
V. Z. Stankevych, “Stress intensity near a crack in the composition of a half space and a layer under harmonic loading,” Fiz.-Khim. Mekh. Mater., 44, No. 2, 27–32 (2008); English translation: Mater. Sci., 44, No. 2, 175–182 (2008).
V. V. Mykhas’kiv, V. Z. Stankevych, E. V. Hlushkov, and N. V. Hlushkova, “Dynamic stresses in a compound body with penny-shaped crack in the case of sliding contact of its components,” Mat. Metody Fiz.-Mekh. Polya, 53, No. 1, 80–87 (2010).
J. Pujol, Elastic Wave Propagation and Generation in Seismology, Cambridge Univ. Press, New York (2003).
V. Mykhas’kiv, V. Stankevych, I. Zhbadynskyi, and C. Zhang, “3-D dynamic interaction between a penny-shaped crack and a thin interlayer joining two elastic half spaces,” Int. J. Fracture, 159, No. 2, 137–149 (2009).
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Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 48, No. 1, pp. 47–53, January–February, 2012.
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Zhbadyns’kyi, I.Y., Stankevych, V.Z. Nonstationary problem for a bimaterial containing a crack and an interlayer. Mater Sci 48, 46–53 (2012). https://doi.org/10.1007/s11003-012-9471-4
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DOI: https://doi.org/10.1007/s11003-012-9471-4