Modelling of Ultrasonic Bulk Wave Scattering by an Axial Crack in a Pipe
Source abstract
Abstract
Modelling of ultrasonic bulk wave scattering by an internal, infinitely long, axial crack in a thick-walled pipe is considered. The problem is formulated as a hypersingular integral equation for the crack-opening displacement (COD), the hypersingularity arises in the Green’s tensor. The COD is expanded in Chebyshev functions which have the correct square-root singularity along the crack edges, thereby regularizing the integral equation. To discretize the integral equation it is likewise projected onto the same Chebyshev functions. A model of an ultrasonic rectangular vertically polarized shear wave contact probe is developed, and the signal response is calculated using a reciprocity argument. Some numerical examples demonstrate the possible application of the method, in particular investigating the importance of the pipe curvature.
Source: openalex_inverted_index · Quality: baseline
Research context
OpenAlex topics: Ultrasonics and Acoustic Wave Propagation · Non-Destructive Testing Techniques · Geophysical Methods and Applications
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (13)
Show source-provided references
1. Achenbach, J.D.: Wave Propagation in Elastic Solids. North-Holland, New York (1973)
2. Auld, B.A.: General electromechanical reciprocity relations applied to the calculation of elastic wave scattering coefficients. Wave Motion 1(1), 3–10 (1979). doi: 10.1016/0165-2125(79)90020-910.1016/0165-2125(79)90020-9 ↗
3. Bai, H., Shah, A., Popplewell, N., Datta, S.: Scattering of guided waves by circumferential cracks in steel pipes. Appl. Mech. 68(4), 619–631 (2001)10.1115/1.1364493 ↗
4. Benmeddour, F., Treyssède, F., Laguerre, L.: Numerical modeling of guided wave interaction with non-axisymmetric cracks in elastic cylinders. Int. J. Solids Struct. 48(5), 764–774 (2011)10.1016/j.ijsolstr.2010.11.013 ↗
5. Boström, A., Wirdelius, H.: Ultrasonic probe modeling and nondestructive crack detection. J. Acoust. Soc. Am. 97(5), 2836–2848 (1995). doi: 10.1121/1.41185010.1121/1.411850 ↗
6. Boström, A., Kristensson, G., Ström, S.: Transformation properties of plane, spherical and cylindrical scalar and vector wave functions. In: Varadan, V.V., Lakhtakia, A., Varadan, V.K. (eds.) Field Representations and Introduction to Scattering, pp. 165–209. Elsevier, Amsterdam (2000)
7. Bövik, P., Boström, A.: A model of ultrasonic nondestructive testing for internal and subsurface cracks. J. Acoust. Soc. Am. 102(5), 2723–2733 (1997). doi: 10.1121/1.42032610.1121/1.420326 ↗
8. Duan, W., Kirby, R.: A numerical model for the scattering of elastic waves from a non-axisymmetric defect in a pipe. Finite Elem. Anal. Des. 100, 28–40 (2015)10.1016/j.finel.2015.02.008 ↗
9. Fletcher, S., Lowe, M.J., Ratassepp, M., Brett, C.: Detection of axial cracks in pipes using focused guided waves. J. Nondestruct. Eval. 31(1), 56–64 (2012)10.1007/s10921-011-0120-x ↗
10. Olsson, S.: Point force excitation of a thick-walled elastic infinite pipe with an embedded inhomogeneity. J. Eng. Math. 28(4), 311–325 (1994). doi: 10.1007/BF0012875010.1007/BF00128750 ↗
11. Rose, J., Ditri, J., Pilarski, A., Rajana, K., Carr, F.: A guided wave inspection technique for nuclear steam generator tubing. NDT E Int. 27(6), 307–310 (1994). doi: 10.1016/0963-8695(94)90211-910.1016/0963-8695(94)90211-9 ↗
12. Ström, S.: Introduction to integral representations and integral equations for time-harmonic acoustic, electromagnetic and elastodynamic wave fields. In: Varadan, V.V., Lakhtakia, A., Varadan, V.K. (eds.) Field Representations and Introduction to Scattering, pp. 37–143. Elsevier, Amsterdam (2000)
13. Velichko, A., Wilcox, P.D.: Excitation and scattering of guided waves: relationships between solutions for plates and pipes. J. Acoust. Soc. Am. 125(6), 3623–3631 (2009)10.1121/1.3117441 ↗