A mathematical model of longitudinal shear crack healing in an anisotropic body was constructed. The problem was reduced to the solution of the singular integro-differential equation with respect to the displacement function of the crack surfaces. An exact analytical solution of the integral equation in the case of filling the crack with injection material in the whole volume was obtained. The strength of a body with a healed crack was calculated on the basis of the force criterion of fracture mechanics. It was established that the geometric parameters of the crack (the defects with small opening of the banks heal better) and the ratio of elastic constants of the main material to the injected one are the main factors which influenced the effectiveness of the strength restoration of the body damaged by the crack. It was shown that a possible complete recovery of the body strength by the injection material, which stiffness was less by an order of magnitude than that of the matrix. In practice, this can be observed in the example of crack healing in concrete by polymer injection materials.
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References
L. Czarnecki and P. H. Emmons, Naprava i Ochrona Konstrukcji Betonowych, Polski Cement, Krakow (2002).
V. V. Panasyuk, V. I. Marukha, and V. P. Sylovanyuk, Injection Technologies for the Repair of Damaged Concrete Structures, Springer, Dordrecht (2014).
V. P. Sylovanyuk, V. I. Marukha, and N. V. Onyshchak, “Strength of a body containing a crack partially filled with injection material,” Mater. Sci., 45, No. 5, 696–701 (2009).
V. P. Sylovanyuk, V. I. Marukha, and N. V. Onyshchak, “Residual strength of cylindrical elements with cracks healed by using the injection technology,” Mater. Sci., 43, No. 1, 109–116 (2007).
V. I. Marukha, V. V. Panasyuk, and V. P. Sylovanyuk, Injection Technologies for Restoration of Serviceability of Damaged Structures of Long-Term Operation [in Ukrainian], Spolom, Lviv (2009).
V. P. Sylovanyuk and N. A. Ivantyshyn, “Long healing of cracks in anisotropic bodies,” Mater. Sci., 55, No. 6, 26–31 (2019).
G. T. Sulim, Fundamentals of Mathematical Theory of Thermoelastic Equilibrium of Deformed Solids with Thin Inclusions [in Ukrainian], Scientific and Research Center of NTSh, Lviv (2007).
V. A. Kryven and V. B. Valyashek, “Initial stage of plastic exfoliation of a rectangular inclusion under conditions of one-sided contact with a medium,” J. Math. Sci., 181, No. 4, 425–437 (2012).
G. C. Sih, P. C. Paris, and G. R. Irwin, “On cracks in rectilinearly anisotropic bodies,” Int. J. Fract. Mech., 1, No. 3, 189–203 (1965).
S. V. Serensen and G. P. Zaitsev, Bearing Capacity of Thin-Walled Structures Made of Reinforced Plastics with Defects [in Russian], Naukova Dumka, Kiev (1982).
V. V. Panasyuk, M. M. Stadnik, and V. P. Silovanyuk, Stress Concentration in Three-Dimensional Bodies with Thin Inclusions [in Russian], Naukova Dumka, Kiev (1986).
G. P. Cherepanov, Fracture Mechanics of Composite Materials [in Russian], Nauka, Moscow (1983).
R. I. Asaro and D. M. Barnett, “The non-uniform transformation problem for an anisotropic ellipsoidal inclusion,” J. Mech. Phys. Solids, 23, No. 1, 77–83 (1975).
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Translated from Problemy Mitsnosti, No. 2, pp. 52 – 58, March – April, 2022.
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Sylovanyuk, V.P., Ivantyshyn, N.A. Crack Healing under Antiplane Deformation of Anisotropic Bodies. Strength Mater 54, 210–215 (2022). https://doi.org/10.1007/s11223-022-00401-7
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DOI: https://doi.org/10.1007/s11223-022-00401-7