Abstract
Ultrasonic NDE of anisotropic materials, due to its inherent complexity, demands a stringent approach to determine wave propagation path in presence of inhomogeneities. In addition to developing inspection procedures, the ray path information needs to be integrated with the tomographic reconstruction algorithm of composite materials. The present study proposes a method to identify inhomogeneity boundaries using edge detection approach and to implement the same in two-dimensional ray tracing model. In general, inhomogeneity boundaries can be detected on the basis of first-order gradient of a field value (such as Young's modulus). The boundaries can be represented in terms of location and orientation. This information is included in the algorithm for more accurate ray tracing. Examples show the usefulness of the method to take into effect poor penetration of ultrasound energy in certain regions of inhomogeneous materials.
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Reference
J. D. Achenbach, Wave Propagation in Elastic Solids, (North Holland, 1973).
E. G. Henneke, Reflection-refraction of a stress wave at a plane boundary between anisotropic media. J. Acoust. Soc. Am. 51(1), 210-217 (1972).
S. I. Rokhlin, T. K. Bolland, and L. Adler, Reflection and refraction of elastic waves on a plane interface between two generally anisotropic media. J. Acoust. Soc. Am. 79(4), 906-918, (1986).
B. Mandal, Reflection and transmission properties of elastic waves on a plane interface for general anisotropic media. J. Acoust. Soc. Am. 90(2), 1106-1118 (1991).
F. A. Chedid-Helou, and J. H. Hemann, Mathematical modeling of wave propagation in anisotropic media. Mater. Eval. June, 708-715 (1991).
J. A. Ogilvy, Computerized ultrasonic ray tracing in austenitic steel. NDT International, 18(2), 67-77 (1985).
J. A. Ogilvy, Ultrasonic beam profiles and beam propagation in an austenitic weld using a theoretical ray tracing model. Ultrasonics 24, 337-347 (1986).
A. H. Harker, J. A. Ogilvy, and J. A. G. Temple, Modelling ultrasonic inspection of austenitic welds. J. Nondestr. Eval. 9, 155-165 (1990).
A. H. Harker, and J. A. Ogilvy, Coherent wave propagation in inhomogeneous materials: a comparison of theoretical models. Ultrasonics 29, 235-244 (1991).
J. A. Ogilvy, An iterative ray tracing model for ultrasonic nondestructive testing. NDT & E International 25(1), 3-10 (1992).
V. Schmitz, F. Walte, and S. V. Chakhlov, 3-D ray tracing in austenite materials. NDT & E International 32(2/3), 201-213 (1999).
M. Spies, Elastic waves in homogeneous and layered transversely isotropic media: plane waves and gaussian wave packets: a general approach. J. Acoust. Soc. Am. 95(4), 1748-1760 (1994).
M. Spies, Transducer-modeling in general transversely isotropic media via point-source-synthesis: theory. J. Nondestr. Eval. 13(2), 85-99 (1994).
M. Spies, Modeling of transducer fields in inhomogeneous anisotropic materials using gaussian beam superposition. NDT & E International 33, 155-162 (2000).
H. Yim, and Y. Choi, Simulation of ultrasonic waves in various types of elastic media using the mass spring lattice model. Mater. Eval. pp. 889-896 (2000). Au: please supply missing information.
R. A. Kline, Y. Q. Wang, R. B. Mignogna, and P. O. Delsanto, A finite difference approach to accoustic tomography in anisotropic media. J. Nondestr. Eval. 13(2), 75-83 (1994).
Y. Q. Wang, and R. A. Kline, Ray tracing in isotropic and anisotropic materials: application to tomographic image reconstruction. J. Acoust. Soc. Am. 95(5), 2525-2532 (1994).
W. H. Press W. T. Vellerling, and P. B. Flannery, Numerical Recipe in C. (Cambridge University Press, 1992).
A. K. Jain, Fundamentals of Digital Image Processing, (Prentice Hall, 1989).
R. C. Gonzalez, and R. E. Woods, Digital Image Processing, (Addison-Wesley, 1992).
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Rathore, S.K., Kishore, N.N. & Munshi, P. An Improved Method for Ray Tracing Through Curved Inhomogeneities in Composite Materials. Journal of Nondestructive Evaluation 22, 1–9 (2003). https://doi.org/10.1023/A:1025785713768
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DOI: https://doi.org/10.1023/A:1025785713768