Skip to main content
Log in

Modeling and simulation of ultrasonic beam skewing in polycrystalline materials

  • Published:
International Journal of Advances in Engineering Sciences and Applied Mathematics Aims and scope Submit manuscript

Abstract

Ultrasonic wave propagation through polycrystalline media results in scattering caused by the anisotropy of single grains and randomness in the orientation of the individual grains making up the polycrystal. Scattering leads to variation in phase velocity and beam skewing of elastic waves leading to a loss in energy of the forward propagating wave, significantly affecting the ability to perform material characterization, defect detection and sizing in structural components. The present work addresses the problem of beam skewing of ultrasonic longitudinal waves using FEM-based wave propagation studies in a simulated polycrystal. A well-established Voronoi tessellation algorithm is used to represent an equiaxed polycrystalline morphology. Numerical simulations are performed on beam skewing in both weak (Aluminum) and strong (Copper) anisotropic media as a function of beam launch angles. The effect of a small number of large grains and a large number of small grains on the beam quality is described. The effective refraction in polycrystals is quantified with respect to the corresponding reference isotropic media and the implications for various applications are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Nicoletti, D., Bilgutay, N., Banu, O.: Power-law relationships between the dependence of ultrasonic attenuation on wavelength and the grain size distribution. J. Acoust. Soc. Am. 91, 3278–3284 (1992). https://doi.org/10.1121/1.402862

    Article  Google Scholar 

  2. Yalda, I., Margetan, F.J., Thompson, R.B.: Predicting ultrasonic grain noise in polycrystals: a Monte Carlo model. J. Acoust. Soc. Am. 99, 3445–3455 (1996). https://doi.org/10.1121/1.414991

    Article  Google Scholar 

  3. Papadakis, E.P.: 5. Scattering in polycrystalline media. In: Edmonds, P.D. (ed.) Methods in Experimental Physics. Ultrasonics, vol. 19, pp. 237–298. Academic Press, Cambridge (1981). https://doi.org/10.1016/S0076-695X(08)60336-1

    Google Scholar 

  4. Thompson, R.B., Margetan, F.J., Haldipur, P., Yu, L., Li, A., Panetta, P., et al.: Scattering of elastic waves in simple and complex polycrystals. Wave Motion 45, 655–674 (2008). https://doi.org/10.1016/j.wavemoti.2007.09.008

    Article  MATH  Google Scholar 

  5. Lifshits, I.M., Parkhomovskii, G.D.: Theory of propagation of ultrasonic waves in polycrystals. Zh. Eksp. Teor. Fiz. 20, 175–182 (1950)

    Google Scholar 

  6. Bhatia, A.B.: Scattering of high frequency sound waves in polycrystalline materials. II. J. Acoust. Soc. Am. 31, 1140 (1959). https://doi.org/10.1121/1.1907843

    Article  Google Scholar 

  7. Papadakis, E.P.: Ultrasonic attenuation caused by scattering in polycrystalline metals. J. Acoust. Soc. Am. 37, 711 (1965). https://doi.org/10.1121/1.1909401

    Article  Google Scholar 

  8. Hirsekorn, S.: The scattering of ultrasonic waves by polycrystals. J. Acoust. Soc. Am. 72, 1021–1031 (1982). https://doi.org/10.1121/1.388233

    Article  MATH  Google Scholar 

  9. Stanke, F.E.: A unified theory for elastic wave propagation in polycrystalline materials. J. Acoust. Soc. Am. 75, 665 (1984). https://doi.org/10.1121/1.390577

    Article  MATH  Google Scholar 

  10. Weaver, R.L.: Diffusivity of ultrasound in polycrystals. J. Mech. Phys. Solids 38, 55–86 (1990). https://doi.org/10.1016/0022-5096(90)90021-U

    Article  MathSciNet  MATH  Google Scholar 

  11. Thompson, B.R.: Elastic-Wave Propagation in Random Polycrystals: Fundamentals and Application to Nondestructive Evaluation. Imaging Complex Media with Acoustic Seismic Waves, pp. 233–257. Springer, Berlin (2002)

    Google Scholar 

  12. Calvet, M., Margerin, L.: Velocity and attenuation of scalar and elastic waves in random media: a spectral function approach. J. Acoust. Soc. Am. 131, 1843 (2012). https://doi.org/10.1121/1.3682048

    Article  Google Scholar 

  13. Rokhlin, S.I., Li, J., Sha, G.: Far-field scattering model for wave propagation in random media. J. Acoust. Soc. Am. 137, 2655–2669 (2015). https://doi.org/10.1121/1.4919333

    Article  Google Scholar 

  14. Kube, C.M., Turner, J.A.: Ultrasonic attenuation in polycrystals using a self-consistent approach. Wave Motion 57, 182–193 (2014). https://doi.org/10.1016/j.wavemoti.2015.04.002

    Article  MathSciNet  Google Scholar 

  15. Silk, M.G.: A computer model for ultrasonic propagation in complex orthotropic structures. Ultrasonics 19, 208–212 (1981). https://doi.org/10.1016/0041-624X(81)90004-4

    Article  Google Scholar 

  16. Ogilvy, J.A.: Ultrasonic beam profiles and beam propagation in an austenitic weld using a theoretical ray tracing model. Ultrasonics 24, 337–347 (1986). https://doi.org/10.1016/0041-624X(86)90005-3

    Article  Google Scholar 

  17. Kolkoori, S., Rahman, M.U., Prager, J.: Effect of columnar grain orientation on ultrasonic plane wave energy reflection and transmission behaviour in anisotropic austenitic weld materials. J. Nondestruct. Eval. 31, 253–269 (2012). https://doi.org/10.1007/s10921-012-0140-1

    Article  Google Scholar 

  18. Ghoshal, G., Turner, J.A.: Numerical model of longitudinal wave scattering in polycrystals. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 56, 1419–1428 (2009). https://doi.org/10.1109/TUFFC.2009.1197

    Article  Google Scholar 

  19. Shahjahan, S., Rupin, F., Aubry, A., Chassignole, B., Fouquet, T., Derode, A.: Comparison between experimental and 2-D numerical studies of multiple scattering in Inconel600® by means of array probes. Ultrasonics 54, 358–367 (2014). https://doi.org/10.1016/j.ultras.2013.06.012

    Article  Google Scholar 

  20. Van Pamel, A., Brett, C.R., Huthwaite, P., Lowe, M.J.: Finite element modelling of elastic wave scattering within a polycrystalline material in two and three dimensions. J. Acoust. Soc. Am. 138, 2326 (2015). https://doi.org/10.1121/1.4931445

    Article  Google Scholar 

  21. Shivaprasad, S., Balasubramaniam, K., Krishnamurthy, C.V.: Voronoi based microstructure modelling for elastic wave propagation. AIP Conf. Proc. 1706, 70013 (2016). https://doi.org/10.1063/1.4940531

    Article  Google Scholar 

  22. Volker, A., Soares, M.D.E., Melo, S.E., Wirdelius, H., Lundin, P., Krix, D., et al.: Ultrasonic assessment of metal microstructures, modelling and validation. In: Proceedings on 19th WCNDT 2016, pp. 1–8 (2016)

  23. Pandala, A., Shivaprasad, S., Krishnamurthy, C.V., Balasubramaniam, K.: Modelling of elastic wave scattering in polycrystalline materials. In: 8th International Symposium on NDT Aerospace (2016)

  24. Adithya, R., Shivaprasad, S.B., Balasubramaniam, K., Krishnamurthy, C.V.: Finite element modelling of elastic wave propagation in polycrystalline media. Indian National Seminar & Exhibition. Non-Destructive Evaluation. NDE 2016 (2016)

  25. Voronoi, G.: Nouvelles applications des parametres continus à la theorie des formes quadratiques. Deuxième Mémorie: Recherches sur les paralléloèdres primitifs. J. Für Die Reine Und Angew Math. 134, 198–287 (1908)

    MathSciNet  MATH  Google Scholar 

  26. Kumar, S., Singh, R.: Thermal conductivity of polycrystalline materials. J. Am. Ceram. Soc. 78, 728–736 (1995)

    Article  Google Scholar 

  27. Espinosa, H.D., Zavattieri, P.D.: A grain level model for the study of failure initiation and evolution in polycrystalline brittle materials. Part II: numerical examples. Mech. Mater. 35, 365–394 (2003). https://doi.org/10.1016/S0167-6636(02)00287-9

    Article  Google Scholar 

  28. Zhang, P., Balint, D., Lin, J.: An integrated scheme for crystal plasticity analysis: virtual grain structure generation. Comput. Mater. Sci. 50, 2854–2864 (2011). https://doi.org/10.1016/j.commatsci.2011.04.041

    Article  Google Scholar 

  29. Zhu, H.X., Thorpe, S.M., Windle, A.H.: The geometrical properties of irregular two-dimensional Voronoi tessellations. Philos. Mag. A 81, 2765–2783 (2001). https://doi.org/10.1080/01418610010032364

    Article  Google Scholar 

  30. Suzudo, T., Kaburaki, H.: An evolutional approach to the numerical construction of polycrystalline structures using the Voronoi tessellation. Phys. Lett. Sect. A Gen. At. Solid State Phys. 373, 4484–4488 (2009). https://doi.org/10.1016/j.physleta.2009.09.072

    Google Scholar 

  31. Auld, B.A.: Acoustic Fields and Waves in Solids, vol. I. RE Krieger, London (1975). https://doi.org/10.1016/0003-682x(75)90008-0

    Google Scholar 

  32. COMSOL: LiveLink for MATLAB User’s Guide: Version 5.2 (2015)

  33. Ledbetter, H.M., Naimon, E.R.: Elastic properties of metals and alloys. II. Copper. J. Phys. Chem. Ref. Data 3, 897–935 (1974). https://doi.org/10.1063/1.3253150

    Article  Google Scholar 

Download references

Funding

Funding was provided by Board of Research in Nuclear Sciences (Grant No. MEE/11-12/282/BRNS/KRIS).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to C. V. Krishnamurthy.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shivaprasad, S., Krishnamurthy, C.V. & Balasubramaniam, K. Modeling and simulation of ultrasonic beam skewing in polycrystalline materials. Int J Adv Eng Sci Appl Math 10, 70–78 (2018). https://doi.org/10.1007/s12572-018-0209-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12572-018-0209-x

Keywords

Navigation