Abstract
The effect of a shock load on the interaction of circular cracks in an elastic half-space is studied. In the space of Fourier time transforms, the problem is reduced to a system of two-dimensional boundary integral equations in the form of the Helmholtz potential with unknown densities characterizing the discontinuities in the displacements of the opposite crack faces. Discrete analogs of those equations are constructed. As an example, two cracks are considered whose faces are under the action of shock tensile loads varying in time as the Heaviside function. The time dependences of the dynamic stress intensity factors are obtained. Their dependence on the relative position of the cracks in the half-space is analyzed.
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REFERENCES
A. N. Guz and V. V. Zozulya, Brittle Fracture of Materials under Dynamic Loads, Vol. 4, Book 2 of the four-volume five-book series A. N. Guz(general editor), Nonclassical Problems of Fracture Mechanics [in Russian], Naukova Dumka, Kiev (1993).
V. V. Mikhas'kiv, V. Z. Stankevich, and M. V. Khai, “Boundary integral equations in the three-dimensional steady-state vibrations of a half-space with plane cracks,” Izv. RAN, Mekh. Tverd. Tela, 6, 44–53 (1993).
V. Z. Stankevich and M. V. Khai, “Interaction of a crack with a half-space boundary under a shock load,” Fiz.-Khim. Mekh. Mater., No. 6, 46–50 (1995).
M. V. Khai, Two-Dimensional Integral Equations in the Form of the Newtonian Potential and Their Application [in Russian], Naukova Dumka, Kiev (1993).
J. Balas, J. Sladek, and V. Sladek, Stress Analysis by Boundary Elements Methods, Elsevier, New York(1989).
S. Itou, “Transient response of a finite crack in a half-plane under impact load,” Trans. ASME, J. Appl. Mech., 48, 534–538 (1981).
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, 191–207 (1996).
L. M. Keer, W. Lin, and J. D. Achenbach, “Resonance effects for a crack near a free surface,” Trans. ASME, J. Appl. Mech., 51, 65–70 (1984).
V. V. Mikhas'kiv, “Opening-function simulation of the three-dimensional nonstationary interaction of cracks in an elastic body,” Int. Appl. Mech., 37, No. 1, 75–84 (2001).
Ch. Zhang and D. Cross, On Wave Propagation in Elastic Solids with Crack, Computational Mechanics Publications, Southampton (1998).
V. V. Zozulya and V. A. Menshykov, “Solution of three-dimensional problems of the dynamic theory of elasticity for bodies with cracks using hypersingular integrals,” Int. Appl. Mech., 36, No. 1, 74–81 (2000).
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Stankevich, V.Z., Khai, M.V. Study into the Interaction of Cracks in an Elastic Half-Space under a Shock Load by Means of Boundary Integral Equations. International Applied Mechanics 38, 440–446 (2002). https://doi.org/10.1023/A:1016220628759
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DOI: https://doi.org/10.1023/A:1016220628759