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No Access Submitted: 06 September 2020 Accepted: 23 November 2020 Published Online: 11 December 2020

  • Elastic wave velocity dispersion in polycrystals with elongated grains: Theoretical and numerical analysis

The Journal of the Acoustical Society of America 148, 3645 (2020); https://doi.org/10.1121/10.0002916
M. Huang1,a), G. Sha2, P. Huthwaite1,b), S. I. Rokhlin2, and M. J. S. Lowe1
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  • M. Huang
  • G. Sha
  • P. Huthwaite
  • S. I. Rokhlin
  • M. J. S. Lowe
ABSTRACT
The phase velocity dispersion of longitudinal waves in polycrystals with elongated grains of arbitrary crystallographic symmetry is studied in all frequency ranges by the theoretical second-order approximation (SOA) and numerical three-dimensional finite element (FE) models. The SOA and FE models are found to be in excellent agreement for three studied polycrystals: cubic Al, Inconel, and a triclinic material system. A simple Born approximation for the velocity, not containing the Cauchy integrals, and the explicit analytical quasi-static velocity limit (Rayleigh asymptote) are derived. As confirmed by the FE simulations, the velocity limit provides an accurate velocity estimate in the low-frequency regime where the phase velocity is nearly constant on frequency; however, it exhibits dependence on the propagation angle. As frequency increases, the phase velocity increases towards the stochastic regime and then, with further frequency increase, behaves differently depending on the propagation direction. It remains nearly constant for the wave propagation in the direction of the smaller ellipsoidal grain radius and decreases in the grain elongation direction. In the Rayleigh and stochastic frequency regimes, the directional velocity change shows proportionalities to the two elastic scattering factors even for the polycrystal with the triclinic grain symmetry.

ACKNOWLEDGMENTS

M.H. was supported by the Chinese Scholarship Council and the Beijing Institute of Aeronautical Materials. P.H. was funded by the UK Engineering and Physical Sciences Research Council (EPSRC) fellowship EP/M020207/1. M.J.S.L. was partially sponsored by the EPSRC. G.S. and S.I.R. were partially supported by the AFRL (USA) under the prime contract FA8650-10-D-5210.

REFERENCES

  1. 1. R. B. Thompson, “ Elastic-wave propagation in random polycrystals: Fundamentals and application to nondestructive evaluation,” in Imaging of Complex Media With Acoustic and Seismic Waves ( Springer, New York, 2002), pp. 233–257. Google ScholarCrossref
  2. 2. J. Li and S. I. Rokhlin, “ Propagation and scattering of ultrasonic waves in polycrystals with arbitrary crystallite and macroscopic texture symmetries,” Wave Motion 58, 145–164 (2015). https://doi.org/10.1016/j.wavemoti.2015.05.004, Google ScholarCrossref, ISI
  3. 3. F. E. Stanke and G. S. Kino, “ A unified theory for elastic wave propagation in polycrystalline materials,” J. Acoust. Soc. Am. 75, 665–681 (1984). https://doi.org/10.1121/1.390577, Google ScholarScitation, ISI
  4. 4. R. L. Weaver, “ Diffusivity of ultrasound in polycrystals,” J. Mech. Phys. Solids 38, 55–86 (1990). https://doi.org/10.1016/0022-5096(90)90021-U, Google ScholarCrossref, ISI
  5. 5. G. Sha, M. Huang, M. J. S. Lowe, and S. I. Rokhlin, “ Attenuation and velocity of elastic waves in polycrystals with generally anisotropic grains: Analytic and numerical modelling,” J. Acoust. Soc. Am. 147, 2442–2465 (2020). https://doi.org/10.1121/10.0001087, Google ScholarScitation, ISI
  6. 6. J. A. Turner, “ Elastic wave propagation and scattering in heterogeneous anisotropic media: Textured polycrystalline materials,” J. Acoust. Soc. Am. 106, 541–552 (1999). https://doi.org/10.1121/1.427024, Google ScholarScitation, ISI
  7. 7. A. Bhattacharjee, A. L. Pilchak, O. I. Lobkis, J. W. Foltz, S. I. Rokhlin, and J. C. Williams, “ Correlating ultrasonic attenuation and microtexture in a near-alpha titanium alloy,” Metall. Mater. Trans. A 42, 2358–2372 (2011). https://doi.org/10.1007/s11661-011-0619-x, Google ScholarCrossref
  8. 8. M. Calvet and L. Margerin, “ Velocity and attenuation of scalar and elastic waves in random media: A spectral function approach,” J. Acoust. Soc. Am. 131, 1843–1862 (2012). https://doi.org/10.1121/1.3682048, Google ScholarScitation, ISI
  9. 9. L. Yang, J. Li, O. I. Lobkis, and S. I. Rokhlin, “ Ultrasonic propagation and scattering in duplex microstructures with application to titanium alloys,” J. Nondestruct. Eval. 31, 270–283 (2012). https://doi.org/10.1007/s10921-012-0141-0, Google ScholarCrossref, ISI
  10. 10. L. Yang, J. Li, and S. I. Rokhlin, “ Ultrasonic scattering in polycrystals with orientation clusters of orthorhombic crystallites,” Wave Motion 50, 1283–1302 (2013). https://doi.org/10.1016/j.wavemoti.2013.06.003, Google ScholarCrossref, ISI
  11. 11. C. M. Kube, “ Iterative solution to bulk wave propagation in polycrystalline materials,” J. Acoust. Soc. Am. 141, 1804–1811 (2017). https://doi.org/10.1121/1.4978008, Google ScholarScitation, ISI
  12. 12. R. B. Thompson, F. J. Margetan, P. Haldipur, L. Yu, A. Li, P. D. Panetta, and H. Wasan, “ 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, Google ScholarCrossref, ISI
  13. 13. S. I. Rokhlin, J. Li, and G. Sha, “ 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, Google ScholarScitation, ISI
  14. 14. E. M. Lifshits and G. D. Parkhomovski, “ On the theory of ultrasonic wave propagation in polycrystals,” Zh. Eksp. Teor. Fiz. 20, 175–182 (1950). Google Scholar
  15. 15. A. A. Usov, A. F. Fomin, and T. D. Shermergor, “ On theory of scattering of ultrasonic waves in polycrystals,” Zh. Prikl. Mekh. Tekh. Fiz. 2, 66–73 (1972). Google Scholar
  16. 16. S. Hirsekorn, “ The scattering of ultrasonic waves by polycrystals,” J. Acoust. Soc. Am. 72, 1021–1031 (1982). https://doi.org/10.1121/1.388233, Google ScholarScitation, ISI
  17. 17. A. Maurel, F. Lund, and M. Montagnat, “ Propagation of elastic waves through textured polycrystals: Application to ice,” Proc. R. Soc. A Math. Phys. Eng. Sci. 471, 1–28 (2015). https://doi.org/10.1098/rspa.2014.0988, Google ScholarCrossref
  18. 18. A. Van Pamel, C. R. Brett, P. Huthwaite, and M. J. S. Lowe, “ Finite element modelling of elastic wave scattering within a polycrystalline material in two and three dimensions,” J. Acoust. Soc. Am. 138, 2326–2336 (2015). https://doi.org/10.1121/1.4931445, Google ScholarScitation, ISI
  19. 19. A. Van Pamel, G. Sha, S. I. Rokhlin, and M. J. S. Lowe, “ Finite-element modelling of elastic wave propagation and scattering within heterogeneous media,” Proc. R. Soc. A Math. Phys. Eng. Sci. 473, 1–21 (2017). https://doi.org/10.1098/rspa.2016.0738, Google ScholarCrossref
  20. 20. A. Van Pamel, G. Sha, M. J. S. Lowe, and S. I. Rokhlin, “ Numerical and analytic modelling of elastodynamic scattering within polycrystalline materials,” J. Acoust. Soc. Am. 143, 2394–2408 (2018). https://doi.org/10.1121/1.5031008, Google ScholarScitation, ISI
  21. 21. M. Ryzy, T. Grabec, P. Sedlák, and I. A. Veres, “ Influence of grain morphology on ultrasonic wave attenuation in polycrystalline media,” J. Acoust. Soc. Am. 143, 219–229 (2018). https://doi.org/10.1121/1.5020785, Google ScholarScitation, ISI
  22. 22. H. M. Ledbetter, “ Sound velocities and elastic-constant averaging for polycrystalline copper,” J. Phys. D: Appl. Phys. 13, 1879–1884 (1980). https://doi.org/10.1088/0022-3727/13/10/017, Google ScholarCrossref
  23. 23. S. Ahmed and R. B. Thompson, “ Attenuation of ultrasonic waves in cubic metals having elongated, oriented grains,” Nondestruct. Test. Eval. 8–9, 525–531 (1992). https://doi.org/10.1080/10589759208952729, Google ScholarCrossref
  24. 24. U. F. Kocks, C. N. Tomé, and H.-R. Wenk, Texture and Anisotropy: Preferred Orientations in Polycrystals and Their Effect on Materials Properties ( Cambridge University Press, Cambridge, UK, 1998). Google Scholar
  25. 25. L. Yang, O. I. Lobkis, and S. I. Rokhlin, “ Shape effect of elongated grains on ultrasonic attenuation in polycrystalline materials,” Ultrasonics 51, 697–708 (2011). https://doi.org/10.1016/j.ultras.2011.02.002, Google ScholarCrossref, ISI
  26. 26. M. Calvet and L. Margerin, “ Impact of grain shape on seismic attenuation and phase velocity in cubic polycrystalline materials,” Wave Motion 65, 29–43 (2016). https://doi.org/10.1016/j.wavemoti.2016.04.001, Google ScholarCrossref, ISI
  27. 27. M. Calvet and L. Margerin, “ Shape preferred orientation of iron grains compatible with Earth's uppermost inner core hemisphericity,” Earth Planet. Sci. Lett. 481, 395–403 (2018). https://doi.org/10.1016/j.epsl.2017.10.038, Google ScholarCrossref, ISI
  28. 28. C.-S. Man, R. Paroni, Y. Xiang, and E. A. Kenik, “ On the geometric autocorrelation function of polycrystalline materials,” J. Comput. Appl. Math. 190, 200–210 (2006). https://doi.org/10.1016/j.cam.2005.01.044, Google ScholarCrossref, ISI
  29. 29. A. L. Pilchak, J. Li, and S. I. Rokhlin, “ Quantitative comparison of microtexture in near-alpha titanium measured by ultrasonic scattering and electron backscatter diffraction,” Metall. Mater. Trans. A 45, 4679–4697 (2014). https://doi.org/10.1007/s11661-014-2367-1, Google ScholarCrossref
  30. 30. U. Frisch, “ Wave propagation in random media,” in Probabilistic Methods in Applied Mathematics, edited by A. Bharucha-Reid ( Academic Press, New York, 1968), pp. 75–198. Google Scholar
  31. 31. S. M. Rytov, Y. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics 4: Wave Propagation Through Random Media ( Springer, New York, 2011). Google Scholar
  32. 32. R. C. Bourret, “ Stochastically perturbed fields, with applications to wave propagation in random media,” Nuovo Cim. Ser. 26, 1–31 (1962). https://doi.org/10.1007/BF02754339, Google ScholarCrossref
  33. 33. M. Norouzian and J. A. Turner, “ Ultrasonic wave propagation predictions for polycrystalline materials using three-dimensional synthetic microstructures: Attenuation,” J. Acoust. Soc. Am. 145, 2181–2191 (2019). https://doi.org/10.1121/1.5096651, Google ScholarScitation, ISI
  34. 34. R. Quey, P. R. Dawson, and F. Barbe, “ Large-scale 3D random polycrystals for the finite element method: Generation, meshing and remeshing,” Comput. Methods Appl. Mech. Eng. 200, 1729–1745 (2011). https://doi.org/10.1016/j.cma.2011.01.002, Google ScholarCrossref, ISI
  35. 35. M. Huang, G. Sha, P. Huthwaite, S. I. Rokhlin, and M. J. S. Lowe, “ Maximizing the accuracy of finite element simulation of elastic wave propagation in polycrystals,” J. Acoust. Soc. Am. 148, 1890–1910 (2020). https://doi.org/10.1121/10.0002102, Google ScholarScitation, ISI
  36. 36. S. I. Ranganathan and M. Ostoja-Starzewski, “ Universal elastic anisotropy index,” Phys. Rev. Lett. 101, 055504 (2008). https://doi.org/10.1103/PhysRevLett.101.055504, Google ScholarCrossref
  37. 37. P. Huthwaite, “ Accelerated finite element elastodynamic simulations using the GPU,” J. Comput. Phys. 257, 687–707 (2014). https://doi.org/10.1016/j.jcp.2013.10.017, Google ScholarCrossref, ISI
  38. 38. E. P. Papadakis, “ The measurement of ultrasonic velocity,” in Physical Acoustics, edited by R. N. Thurston and A. D. Pierce ( Academic Press, San Diego, CA, 1990), Vol. XIX, pp. 81–106. Google ScholarCrossref
  39. 39. M. Arakawa, J. I. Kushibiki, and N. Aoki, “ An evaluation of effective radiuses of bulk-wave ultrasonic transducers as circular piston sources for accurate velocity measurements,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 51, 496–501 (2004). https://doi.org/10.1109/TUFFC.2004.1308685, Google ScholarCrossref
  40. 40. H. Seiner, L. Bodnárová, P. Sedlák, M. Janeček, O. Srba, R. Král, and M. Landa, “ Application of ultrasonic methods to determine elastic anisotropy of polycrystalline copper processed by equal-channel angular pressing,” Acta Mater. 58, 235–247 (2010). https://doi.org/10.1016/j.actamat.2009.08.071, Google ScholarCrossref
  41. 41. A. N. Kalashnikov and R. E. Challis, “ Errors and uncertainties in the measurement of ultrasonic wave attenuation and phase velocity,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52, 1754–1768 (2005). https://doi.org/10.1109/TUFFC.2005.1561630, Google ScholarCrossref, ISI
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