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Journal of Nondestructive Evaluation

, Volume 5, Issue 1, pp 37–43 | Cite as

Ultrasonic crack characterization via a constrained inversion algorithm

  • Lester W. SchmerrJr.
  • Alexander Sedov
Article

Abstract

The Kirchhoff approximation is used to show that the time domain impulse response of an isolated flat crack can be given a simple geometrical interpretation in terms of the derivative of a projected length function. For an elliptical crack, this derivative can be obtained explicitly to yield the two edge-diffracted waves which originate from the “flashpoints” of the crack. An explicit coordinate invariant expression is obtained from this elliptical crack solution which relates the time difference, Δt, between the arrival of these edge-diffracted waves and the crack size and orientation. Previously, we have proposed that this expression, together with Δt measurements in different scattering directions, could be used in a regression analysis as the basis for performing a constrained inversion of crack scattering data (i.e., where we attempt to obtain the “best” equivalent flat elliptical crack that fits the scattering measurements). Here we will demonstrate some results of applying the proposed algorithm using “noisy” synthetic data. The sensitivity of the results to both, number of measurements and transducer orientation, will be discussed.

Key words

Kirchhoff approximation crack scattering ultrasonics NDE inverse scattering 

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References

  1. 1.
    D. K. Hsu, J. H. Rose, and D. O. Thompson, Reconstruction of inclusions in solids using ultrasonic Born inversion,J. Appl. Phys.,55: 162–168 (1984).Google Scholar
  2. 2.
    A. Sedov and L. W. Schmerr, The time domain elastodynamic Kirchhoff approximation for cracks: The inverse problem, submitted toWave Motion.Google Scholar
  3. 3.
    J. H. Rose and J. M. Richardson, Time domain Born approximation,J. Nondestr. Eval. 3: 45–53 (1982).Google Scholar
  4. 4.
    F. Cohen-Tenoudji and G. Quentin, Characterization of surfaces by deconvolution of ultrasonic echos using extended bandwidth,J. Appl. Phys. 53: 4057–4063 (1982).Google Scholar
  5. 5.
    J. D. Achenbach, A. K. Gautesen and H. McMaken, Application of ray theory to diffraction of elastic waves by cracks, Acoustic, Electromagnetic and Elastic Wave Scattering, V. K. Varadan and V. V. Varadan, eds. (Pergamon Press, New York, 1980), pp. 355–371.Google Scholar
  6. 6.
    J. D. Achenbach, A. K. Gautesen and H. McMaken, Application of elastodynamic ray theory to diffraction by cracks,Modern Problems in Elastic Wave Propagation, J. Miklowitz and J. D. Achenbach, eds. (John Wiley & Sons, New York, 1978), pp. 219–238.Google Scholar
  7. 7.
    J. D. Achenbach A. Norris and K. Viswanathan, Inversion of crack scattering data in the high frequency domain,Acoustic, Electromagnetic and Elastic Wave Scattering, V. K. Varadan and V. V. Varadan, eds. (Pergamon Press, New York, 1980), pp. 591–604.Google Scholar

Copyright information

© Plenum Publishing Corporation 1985

Authors and Affiliations

  • Lester W. SchmerrJr.
    • 1
  • Alexander Sedov
    • 2
  1. 1.Department of Engineering Science and Mechanics and the Engineering Research InstituteIowa State UniversityAmes
  2. 2.School of EngineeringLakehead UniversityThunder BayCanada

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