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Identification of parameters of a plane elliptic crack in an isotropic linearly elastic body from the results of a single uniaxial tension test

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Abstract

The method earlier developed by one of the authors for identifying ellipsoidal defects is numerically tested for the applicability to the problem of identification of a degenerate ellipsoidal defect, i.e., an elliptic crack. The method is based on the reciprocity functional and the assumption that the displacements are measured in a uniaxial tension test of an isotropic linearly elastic body. Calculations show that the earlier developed method is also efficient for identification of an elliptic crack and its parameters (the center coordinates, the normal to the crack plane, and the directions and lengths of the semiaxes) can be determined with high accuracy. Some examples where the crack has a non-elliptic shape are also considered. It is discovered that, in many cases, the ellipsoids that were constructed by formulas reconstructing the ellipsoidal crack from the data on the external boundary of the body that correspond to a nonelliptic crack, approximate the actual defect with sufficient accuracy. The method stability was investigated with respect to noise in the initial data.

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Authors and Affiliations

  1. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526, Russia

    A. V. Kaptsov, E. I. Shifrin & P. S. Shushpannikov

Authors
  1. A. V. Kaptsov
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  2. E. I. Shifrin
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  3. P. S. Shushpannikov
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Correspondence to A. V. Kaptsov.

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Original Russian Text © A.V. Kaptsov, E.I. Shifrin, P.S. Shushpannikov, 2012, published in Izvestiya Akademii Nauk. Mekhanika Tverdogo Tela, 2012, No. 4, pp. 71–87.

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Kaptsov, A.V., Shifrin, E.I. & Shushpannikov, P.S. Identification of parameters of a plane elliptic crack in an isotropic linearly elastic body from the results of a single uniaxial tension test. Mech. Solids 47, 433–447 (2012). https://doi.org/10.3103/S0025654412040085

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  • DOI: https://doi.org/10.3103/S0025654412040085

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