Publication: Publication Date: 1 August 2006
Kirchhoff Approximation Revisited - Some New Results for Scattering in Isotropic and Anisotropic Elastic Solids
Through a series of numerical studies that compare the Kirchhoff approximation to more exact scattering theories, it is demonstrated that the Kirchhoff approximation can accurately predict the pulse–echo peak-to-peak responses of spherical pores and circular cracks in isotropic media over a very wide range of cases that extend well beyond the limits normally associated with this approximation. The reason for this good agreement is shown to lie in the ability of the Kirchhoff approximation to model accurately the very early time response of the flaw. It is also shown that in the Kirchhoff approximation the pulse–echo response of an arbitrary traction-free scatterer in an isotropic elastic solid is identical to the same response obtained using a scalar (fluid) scattering model. This leads to simple analytical expressions for the pulse–echo far-field scattering amplitude of some canonical geometries (circular cracks, spherical voids, cylindrical holes) and to simplified numerical expressions for more general scatterers. For general anisotropic volumetric flaws in a anisotropic elastic solid, it is shown that a high-frequency asymptotic evaluation of the Kirchhoff approximation yields an explicit analytical expression for the pulse–echo leading-edge response of the flaw. Explicit expressions are also given for the pitch–catch response of an elliptical-shaped flat crack in a general anisotropic solid.
References
1. L. W. Schmerr. Fundamentals of Ultrasonic Nondestructive Evaluation—A Modeling Approach.
Plenum Press, New York (1998).
2. T. Ito, K. Kawashima, R. Omote, J. Takatsubo, and M. Imade. In Review of Progress in Quantitative
Nondestructive Evaluation, D. O. Thompson and D. E. Chimenti (eds.), 19A:97–103 (2000). American
Institute of Physics, Melville, NY.
3. A. Saez and J. Dominguez. BEM analysis of wave scattering in transversely isotropic solids. Int. J.
Numer. Meth. Engng. 44:1283–1300 (1999).
4. M. Kitahara, K. Nakahata, and T. Ichino. In Review of Progress in Quantitative Nondestructive Evaluation,
D. O. Thompson and D. E. Chimenti (eds.), 23:43–50 (2004). American Institute of Physics,
Melville, NY.
5. J. B. Cole, R. A. Krutar, S. K. Numrich, and D. B. Creamer. Finite-difference time-domain simulations
of wave propagation and scattering as a research and educational tool. Computers in Physics 9(2):148
(1995).
6. J. Opsal and W. M. Visscher. Theory of elastic wave scattering: Applications of the method of optimal
truncation. J. Appl. Phys. 58(3):1102–1115 (1985).
7. V. K. Varadan and V. V. Varadan (Eds.), Acoustic Elastic and Elastic Wave Scattering-Focus on the
T-matrix Method. Pergamon Press, New York (1980).
8. P. Fellinger, R. Marklein, K. J. Langenberg, and S. Klaholz. Numerical modeling of elastic wave propagation
and scattering with EFIT—elastodynamic finite integration technique. Wave Motion 21:47–66
(1995).
9. J. D. Achenbach, A. K. Gautesen, and H. McMaken. Ray Methods for Waves in Elastic Solids. Pitman
Publishing, Boston, MA (1982).
10. W. Kohn and J. R. Rice. Scattering of long-wavelength elastic waves from localized defects in solids.
J. Appl. Phys. 50:3346–3353 (1979).
11. J. E. Gubernatis, E. Domany, J. A. Krumhansl, and M. Huberman. Formal aspects of the scattering of
ultrasound by flaws in elastic materials. J. Appl. Phys. 48:2812–2819 (1977).
12. C. P. Chou, F. J. Margetan, and R. B. Thompson. In Review of Progress in Quantitative Nondestructive
Evaluation, D. O. Thompson and D. E. Chimenti (eds.), 15:49–55 (1996). Plenum Press, New York.
13. R. K. Chapman. A system model for the ultrasonic inspection of smooth planar cracks. J. NDE
9(2=3):197–210 (1990).
14. R. K. Chapman and J. M. Coffey. In Review of Progress in Quantitative Nondestructive Evaluation,
D. O. Thompson and D. E. Chimenti (eds.), 3A:151–156 (1984). Plenum Press, New York.
15. R. B. Thompson. In Review of Progress in Quantitative Nondestructive Evaluation, D. O. Thompson
and D. E. Chimenti (eds.), 21:1917–1924 (2002). American Institute of Physics, Melville, NY.
16. H.-J. Kim and L. W. Schmerr. In Review of Progress in Quantitative Nondestructive Evaluation,
D. O. Thompson and D. E. Chimenti (eds.), 24:851–858 (2005). American Institute of Physics,
Melville, NY.
17. L. W. Schmerr and A. Sedov. In Review of Progress in Quantitative Nondestructive Evaluation,
D. O. Thompson and D. E. Chimenti (eds.), 22:1776–1782 (2003). American Institute of Physics,
Melville, NY.
18. L. W. Schmerr, H.-J. Kim, A. L. Lopez, and A. Sedov. In Review of Progress in Quantitative Nondestructive
Evaluation, D. O. Thompson and D. E. Chimenti (eds.), 24:1880–1887 (2005). American
Institute of Physics, Melville, NY.
19. T. A. Gray, R. B. Thompson, and B. P. Newberry. In Review of Progress in Quantitative Nondestructive
Evaluation, D. O. Thompson and D. E. Chimenti (eds.), 4A:11–17 (1985). Plenum Press, NY.
20. L. W. Schmerr, T. A. Gray, A. Lopez-Sanchez, and R. Huang. In Review of Progress in Quantitative
Nondestructive Evaluation, D. O. Thompson and D. E. Chimenti (eds.), 25:1813–1819 (2006).
American Institute of Physics, Melville, NY.
21. M. Spies. Kirchhoff evaluation of scattered elastic wave fields in anisotropic media. J. Acoust. Soc.
Am. 107(5):2755–2759 (2000).
22. B. A. Auld. General electromechanical reciprocity relations applied to the calculation of elastic wave
scattering coefficients. Wave Motion 1:3–10 (1979).
23. A. Lopez-Sanchez, H.-J. Kim, L. W. Schmerr, and A. Sedov. Measurement models and scattering
models for predicting the ultrasonic pulse-echo response from side-drilled holes. J. NDE 24(3):
83–96 (2005).
24. N. F. Haines and D. B. Langston. The refraction of ultrasonic pulses from surfaces. J. Acoust. Soc. Am.
67:1443–1454 (1980).
25. A. L. Lopez-Sanchez. Ultrasonic System Models and Measurements. Ph.D. thesis, Iowa State
University (2005).
26. D. Royer and E. Dieulesaint. Elastic Waves in Solid I. Springer-Verlag, Berlin (2000).
Metrics
| Usage | Shares |
|---|---|
Total Views 62 Page Views |
Total Shares 0 Tweets |
62 0 PDF Downloads |
0 0 Facebook Shares |
| Total Usage | |
| 62 |