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Numerical and Experimental Evaluation of the Critically Refracted Longitudinal Waves (LCR) Beam Profile Generated by a Transducer

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Abstract

Due to its advantageous properties, the critically refracted longitudinal waves (LCR) are used in various fields of nondestructive evaluation, especially for residual stress measurements. However, although many researches use these waves, the characteristics of the LCR beams are not completely understood to date. This paper contributes to clarify in a complete way and gives numerical and experimental analysis of the ultrasonic beam of the LCR waves generated by a transducer. It also answers questions about the parameters that influence its beam profile and therefore allow performance optimization when used for NDE and NDT applications. First, beam particle displacement components are numerically calculated in both tangential (surface) and normal (depth) directions; the reflectivity diagrams are then deduced. The experimental study is also used to confirm the numerical results. Numerical and experimental studies have shown that the displacement of the LCR waves at the surface follows a constant law, which does not depend on the frequencies of the sensor. On the other hand, it is shown that the incidents angles, the aperture diameter and the center frequency are the most important factors in controlling the directivity and subsequently the position of the main lobe of the LCR waves.

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REFERENCES

  1. Liu, B., Li, J., Dong, S., and Shu, F., Correction for microstructure effect on residual stress measurement of  SR-FSW joint with LCR wave, Russ. J. Nondestr. Test., 2020, vol. 56, p. 131. https://doi.org/10.1134/S1061830920020023

    Article  CAS  Google Scholar 

  2. Liu, Y., Long, Z., Gong, Y., Ju, J., Wang, Y., Li, Z., and Liu, M., Norm and interpolation based absolute stress evaluation in steel members using the LCR wave, NDT & E Int., 2023, vol. 137, p. 102783. https://doi.org/10.1016/j.ndteint.2022.102783

    Article  Google Scholar 

  3. Geľatko, M., Hatala, M., Vandžura, R., and Botko, F., Longitudinal critically refracted (LCR) ultrasonic wave for residual stress measurement, IOP Conf. Ser.: Mater. Sci. Eng., 2021, vol. 1199, p. 012060. https://doi.org/10.1088/1757-899X/1199/1/012060

  4. Djerir, W., Ourak, M., and Boutkedjirt, T., Characterization of the critically refracted longitudinal (LCR) waves and their use in defect detection, Res. Nondestr. Eval., 2014, vol. 25, p. 203. https://doi.org/10.1080/09349847.2014.890262

    Article  Google Scholar 

  5. Djerir, W., Ourak, M., and Boutkedjirt, T., Experimental Investigation of the parameters Influencing the surface defect detection by using the critically refracted longitudinal waves, Russ. J. Nondestr. Test., 2021, vol. 57, p. 55. https://doi.org/10.1134/S106183092130001X

    Article  Google Scholar 

  6. Li, Y., Liu, H., Liu, Y., Zhang, X., and Wang, Y., In-plane elastic anisotropic constants (IEACs) measurement of rolling aluminum plate at different depth using ultrasonic LCR wave, Appl. Acoust., 2019, vol. 149, p. 59. https://doi.org/10.1016/j.apacoust.2019.01.018

    Article  Google Scholar 

  7. Basatskaya, L.V. and Ermolov, I.N., Theoretical study of ultrasonic longitudinal subsurface waves in solid media, Defektoskopiya, 1980, vol. 16, p. 524.

    Google Scholar 

  8. Chaki, S., Ke, W., and Demouveau, H., Numerical and experimental analysis of the critically refracted longitudinal beam, Ultrasonics, 2013, vol. 5, p. 65. https://doi.org/10.1016/j.ultras.2012.03.014

    Article  Google Scholar 

  9. Pei, N., Zhao, B., Zhao, X., Liu, Z., and Bond, L.J., Analysis of the directivity of longitudinal critically refracted (LCR) waves, Ultrasonics, 2021, vol. 113, p. 106359. https://doi.org/10.1016/j.ultras.2021.106359

    Article  Google Scholar 

  10. Danilov, V.N., Calculations of parameters of longitudinal surface waves on a free planar boundary of a material, Russ. J. Nondestr. Test., 2001, vol. 37, p. 700. https://doi.org/10.1023/A:1015563802910

    Article  Google Scholar 

  11. Schmid. R., Ultrasonic testing of austenitic and dissimilar metal welds, in: Ultraschallprüfung von austenitischen Plattierungen, Mischnähten und austenitischen Schweißnähten, Neumann, E., Ed., NDTnet, 1997. http://www.ndt.net/article/pow1297/schmid/schmid.htm

  12. Cauchman, J.C. and Bell, J.R., Prediction, detection and characterization of a fast surface wave produced near the first critical angle, Ultrasonics, 1978, vol. 16, p. 272. https://doi.org/10.1016/0041-624X(78)90054-9

    Article  Google Scholar 

  13. Uberall, H., Physical Acoustics, Mason, P., Thurston, R.N., Eds., Amsterdam: Elsevier, 1973. https://doi.org/10.1016/B978-0-12-477910-5.50006-4

  14. Murav’ev, V.V., Gushchina, L.V., and Kazantsev, S.V., Evaluating damage accumulated in car wheelset axle journals by the ultrasonic method using Rayleigh and head waves, Russ. J. Nondestr. Test., 2019, vol. 55, p. 713. https://doi.org/10.1134/S1061830919100085

    Article  Google Scholar 

  15. Yuozonene, L.V., Measurement of sound wave velocity propagation on the surface layer, 2nd Sov. Union Conf. Meth. Techn. Ultrason. Spectrosc., Kaunas, 1973, p. 87.

  16. Langenberg, K.J., Fellinger, P., and Marklein, R., On the nature of the so-called subsurface longitudinal wave and/or the surface longitudinal “creeping” wave, Res. Nondestr. Eval., 1990, vol. 2, p. 59. https://doi.org/10.1080/09349849009409488

    Article  Google Scholar 

  17. Belgroune, D., De Belleval, J.F., and Djelouah, H., A theoretical study of ultrasonic wave transmission through a fluid-solid interface, Ultrasonics, 2008, vol. 48, p. 220. https://doi.org/10.1016/j.ultras.2008.01.003

    Article  Google Scholar 

  18. Djerir, W., Boutkedjirt, T., Si-Chaib, M.O., and Djelouah, H., Spatio-temporal deconvolution of pulsed ultrasonic fields received by a transducer of linear aperture, Proc. IEEE Ultrason. Symp. (Rotterdam, 2005), p. 1781. https://doi.org/10.1109/ULTSYM.2005.1603212

  19. Badidi Bouda, A., Aljohani, M.S., Mebtouche, A., Halimi, R., and Djerir, W., Characterization of grains size by ultrasounds, Key Eng. Mater., 2011, vol. 482, p. 49. https://doi.org/10.4028/www.scientific.net/KEM.482.49

    Article  CAS  Google Scholar 

  20. Janssen, M., Reproducible time-of-flight measurements with a piezoelectric transducer for acoustoelastic stress evaluation, Exp. Mech., 1995, vol. 35, p. 266. https://doi.org/10.1007/BF02319667

    Article  Google Scholar 

  21. Djerir, W. and Boutkedjirt, T., Simulation study of super-resolution in hydrophone measurements of pulsed ultrasonic fields, Can. Acoust., 2018, vol. 46, p. 19. https://jcaa.caa-aca.ca/index.php/jcaa/article/view/3205

    Google Scholar 

  22. Djerir, W., Boutkedjirt, T., and Badidi Bouda, A., Application of inverse methods for spatial deconvolution of pulsed ultrasound fields radiated in solids, Mater. Sci. Forum, 2010, vol. 636, p. 1541. https://doi.org/10.4028/www.scientific.net/MSF.636-637

    Article  Google Scholar 

  23. Qozam, H., Chaki, S., Bourse, G., Robin, C., Walaszek, H., and Bouteille, P., Microstructure effect on the LCR elastic wave for welding residual stress measurement, Exp. Mech., 2010, vol. 50, p. 179. https://doi.org/10.1007/s11340-009-9283-0

    Article  Google Scholar 

  24. Royer, D. and Dieulesaint, E., Ondes élastiques dans les solides, Paris: Edition Masson, 2000.

    Google Scholar 

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Funding

This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

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Authors and Affiliations

  1. Research Center in Industrial Technologies (CRTI), P.O. Box 64, DZ-16014, Cheraga, Algiers, Algeria

    W. Djerir, R. Halimi, A. Rezzoug, F. M. L. Rekbi & A. Allag

  2. Laboratory of Materials Physics, Faculty of Physics, University of Sciences and Technology Houari Boumédiène, USTHB, BP 32, DZ-16111, El-Alia, Algeria

    T. Boutkedjirt

  3. University Polytechnique Hauts-de-France, CNRS, University Lille, YNCREA, Centrale Lille, UMR 8520, IEMN, DOAE, F-59313, Valenciennes, France

    M. Ourak

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  1. W. Djerir
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  2. T. Boutkedjirt
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  3. M. Ourak
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  4. R. Halimi
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Correspondence to W. Djerir or T. Boutkedjirt.

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Djerir, W., Boutkedjirt, T., Ourak, M. et al. Numerical and Experimental Evaluation of the Critically Refracted Longitudinal Waves (LCR) Beam Profile Generated by a Transducer. Russ J Nondestruct Test 59, 654–664 (2023). https://doi.org/10.1134/S1061830923600272

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  • DOI: https://doi.org/10.1134/S1061830923600272

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