Abstract
A method for the reconstruction of the configuration of cracks is suggested based on finding heat sources that model the interaction between cracks’ edges (such as friction and collapse) in solids exposed to external ultrasound. The input information for reconstruction is a stationary temperature field on a solid boundary. The functional of “nonreciprocity” was constructed; the study of this functional made it possible to convert the problem of determining a crack’s parameters into a few transcendental equations; explicit formulas were obtained for small cracks. The results of computational experiments on reconstruction of the parameters of a straight crack are considered.
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REFERENCES
Nerazrushayushchii kontrol’ i diagnostika (Nondestructive Testing and Diagnostics), Klyuev, V.V., Ed., Moscow: Mashinostroenie, 1995.
Ermolov, I.N., Lange, Yu.V., and Shcherbinskii, V.G., Progress in Ultrasonic Testing (Based on the Proceedings of the 15th International Conference). 1. New Methods and Equipment, Kontrol’. Diagnostika, 2002, no. 3.
Kazakov, V.V. and Sutin, A.M. Using the Effect of Ultrasound Modulation by Vibrations for Pulse Localization of Cracks, Akust. Zh. 2001, vol. 47, no. 3, pp. 364–369.
Parton, V.Z. and Boriskovskii, V.G., Dinamika khrupkogo razrusheniya (Dynamics of Brittle Fracture), Moscow: Mashinostroenie, 1988.
Zozulya, V.V. and Men’shikov, A.V., About One 3D Contact Problem of Fracture Mechanics in a Case of Normal Action of Tension-Compression Wave, Int. Appl. Mech. 2002, vol. 38, no. 7, pp. 74–78.
Zozulya, V.V. and Men’shikov, A.V., Contact of Planar Elliptically-Shaped Crack Edges in the Case of Normal Action of Tension-Compression Wave, Teor. Prikl. Mekh. 2003, no. 37, pp. 168–172.
Kovalev, A.V., Survey Facilities Based on Introscopy Methods. Acoustic Searching Systems, Spets. Tekh. 2000, no. 2, http://st.ess.ru/publications/articles/kovalev4/kovalev.htm.
Bannour, T., Abda, A.B., and Jaoua, M., A Semi-Explicit Algorithm for the Reconstruction of 3D Planar Cracks, Inverse Probl. 1997, no. 13, pp. 899–917.
Andrieux, S., Abda, A.B., and Jaoua, M., On the Inverse Emergent Plane Crack Problem, Math. Methods Appl. Sci. 1998, vol. 21, no. 10, pp. 895–906.
Vatul’yan, A.O., Baranov, I.V., and Guseva, I.A., Identification of a Crack-Like Flaw in an Orthotropic Layer, Defektoskopiya, 2001, no. 10, pp. 48–52 [Rus. J. of Nondestructive Testing (Engl. Transl.), vol. 37, no. 10, p. 718].
Vatul’yan, A.O. and Solov’ev, A.N., Determination of the Size of a Defect in a Compound Elastic Body, Defektoskopiya, 2004, no. 5, pp. 15–24 [Rus. J. of Nondestructive Testing (Engl. Transl.), 2004, vol. 40, no. 5, p. 298].
Novatskii, V., Dynamiczne zagadnienia termosprezystosci, Warsaw, 1966. Translated under the title Dinamicheskie zadachi termouprugosti, Moscow: Mir, 1970.
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Translated from Defektoskopiya, Vol. 40, No. 10, 2004, pp. 62–69.
Original Russian Text Copyright © 2004 by Vatul’yan, Solov’ev.
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Vatul’yan, A.O., Solov’ev, A.N. On reconstruction of cracks with interacting edges. Russ J Nondestruct Test 40, 689–695 (2004). https://doi.org/10.1007/s11181-005-0075-z
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DOI: https://doi.org/10.1007/s11181-005-0075-z