Crack Healing in a Transtropic Elastic Body under Torsion

Keywords

transtropic body, disc-shaped crack healed by injection, integral equation

Abstract

A mathematic model of the healing of cracks in a torsionally deformed transtropic cylinder is developed. The problem is reduced to solving the integral equation regarding the cracked surfaces displacements. An exact analytical solution of the corresponding integral equation is obtained for the case where the crack is filled in the entire volume. The effectiveness of the cylinder reinforcement is determined as a function of the geometric parameters of the crack and the mechanical properties of the injection material after solidification.

References

1. Czarnecki L., and Emmons P.H. Naprava і ochrona konstrukcji betonowych polski cement. – Krakow, 2002. (in Polish)
2. Panasyuk V.V., Marukha V.I. and Sylovanyuk V.P. Injection technologies for the repair of damaged concrete structures. – Switzerland: Springer Int. Publ., 2013. – 230 p. https://doi.org/10.1007/978-94-007-7908-2
3. Sylovanyuk V.P., and Ivantyshyn N.A. Healing of cracks in anisotropic bodies // Mater. Sci. – 2020. – 55, №. 6. – P. 804-811. https://doi.org/10.1007/s11003-020-00373-6
4. Hu H.-Ch. On the three-dimensional problems of the theory of elasticity of a transversely isotropic body // Acta Phys. Sin. – 1953. – 9. – P. 130-148. https://doi.org/10.7498/aps.9.130
5. Chen E.P. and Sihm G.C. Torsional and anti-plane strain delamination of an orthotropic layered composite // 13th Midwestern Mechanics Conf. (August 13-15, Pittsburgh, Pennsylvania): Proc. – Pittsburgh, 1973. – P. 763-776.
6. Lekhintsi S.G. Anisotropic plates. – Moscow: Gostekhizdat, 1957. (in Russian)
7. Cherepanov G.P. Brittle fracture mechanics. – Moscow: Nauka, 1977. (in Russian)
8. Sneddon I.H. Mixed boundary value problems in potential theory. – Amsterdam: North Holland Publishing Company, 1986.