Journal of the Korean Society for Nondestructive Testing (비파괴검사학회지)

The Korean Society for Nondestructive Testing (한국비파괴검사학회)
권호 표지

Numerical Evaluation of Phase Velocity and Attenuation of Ultrasonic Waves in Fiber-Reinforced Composites Using the Mass-Spring-Dashpot Lattice Model

  • Baek, Eun-Sol (Hongik University, Department of Mechanical Engineering) ;
  • Yim, Hyun-June (Hongik University, Department of Mechanical Engineering)
  • Published : 2008.12.30
Download PDF
⟨ Previous Next ⟩

Abstract

The paper presents a numerical study to evaluate the phase velocities and attenuations of the average longitudinal and shear ultrasonic waves resulting from multiple scattering in fiber-reinforced composites. A computational procedure developed in this work is first used to produce a random, yet largely even distribution of fibers. Both the viscoelastic epoxy matrix and lossless randomly distributed graphite fibers are modeled using the mass-spring-dashpot lattice model, with no damping for the latter. By numerically simulating ultrasonic through-transmission tests using this direct model of composites, phase velocities and attenuations of the longitudinal and shear waves through the composite are found as functions of frequency or fiber concentration. The numerical results are observed to generally agree with the corresponding results in the literature. Discrepancies found in some detail aspects, particularly in the attenuation results, are also addressed.

Keywords

References

  1. Baek, E. and Yim, H. (2004) Development of an Ultrasonic Testing Simulator Using the Mass- Spring Lattice Model, Review of Quantitative Nondestructive Evaluation, Vol. 23, pp. 67-73
  2. Baek, E. (2007) Numerical Modeling of Ultrasonic Testing for Anisotropic Elastic Welds and Biological Tissues, Ph. D. Thesis, Hongik University
  3. Biwa, S., Yamamoto, S., Kobayashi, F. and Ohno, N. (2004) Computational Multiple Scattering Analysis for Shear Wave Propagation in Unidirectional Composites, International Journal of Solids and Structures, Vol. 41, pp. 435-457 https://doi.org/10.1016/j.ijsolstr.2003.09.015
  4. Bose, S. K. and Mal, A. K. (1973) Longitudinal Shear Waves in a Fiber-reinforced Composite, International Journal of Solids and Structures, Vol. 9, pp. 1075-1085 https://doi.org/10.1016/0020-7683(73)90016-4
  5. Bose, S. K. and Mal, A. K. (1974) Elastic Waves in a Fiber-reinforced Composite, Journal of the Mechanics and Physics of Solids, Vol. 22, pp. 217-229 https://doi.org/10.1016/0022-5096(74)90026-X
  6. Christensen, R. M. and Lo, K. H. (1979) Solutions for Effective Shear Properties in Three Phase Sphere and Cylinder Models, Journal of the Mechanics and Physics of Solids, Vol. 27, pp. 315-330 https://doi.org/10.1016/0022-5096(79)90032-2
  7. Datta, S. K., Ledbetter, H. M., Shindo, Y. and Shah, A. H. (1988) Phase Velocity and Attenuation of Plane Elastic Waves in a Particle-Reinforced Composite Medium, Wave Motion, Vol. 10, pp. 171-182 https://doi.org/10.1016/0165-2125(88)90042-X
  8. Dorighi, J., Krishnaswamy, S. and Achenbach, J. (1997) A Fiber Optic Ultrasonic System to Monitor the Cure of Epoxy, Research in Nondestructive Evaluation, Vol. 9, pp. 13-24 https://doi.org/10.1080/09349849708968118
  9. Foldy, L. L. (1945) The Multiple Scattering of Waves I. General Theory of Isotropic Scattering by Randomly Distributed Scatterers, Physical Review, Vol. 67, No. 3&4, pp. 107-119 https://doi.org/10.1103/PhysRev.67.107
  10. Kinsler, L. E., Frey, A. R., Coppens, A. B. and Sanders, J. V., (1999) Fundamentals of Acoustics, 4th ed., John Wiley & Sons
  11. Kolsky, H. (1963) Stress Waves in Solids, Dover, New York
  12. Pao, Y. H. and Mow, C. C (1963) Scattering of Plane Compressional Waves by a Spherical Obstacle, Journal of Applied Physics, Vol. 34, No. 3, pp. 493-499 https://doi.org/10.1063/1.1729301
  13. Sayers, C. M. (1980) On the Propagation of Ultrasound in Highly Concentrated Mixtures and Suspensions, Journal of Physics D: Applied Physics, Vol. 13, pp. 179-184 https://doi.org/10.1088/0022-3727/13/2/014
  14. Sayers, C. M. and Smith, R. L. (1983) Ultrasonic Velocity and Attenuation in an Epoxy Matrix Containing Lead Inclusions, Journal of Physics D: Applied Physics, Vol. 16, pp. 1189-1194 https://doi.org/10.1088/0022-3727/16/7/009
  15. Thomas, A. F. (2006) Lattice Modeling of Ultrasonic Nondestructive Evaluation of Attenuating Materials, Ph. D. Thesis, M.I.T
  16. Twersky, V. (1962a) On the Scattering of Waves by Random Distributions I. Free-space Scatterer Formalism, Journal of Mathematical Physics, Vol. 3, No. 4, pp. 700-715 https://doi.org/10.1063/1.1724272
  17. Twersky, V. (1962b) On Scattering of Waves by Random Distributions II. Two-Space Scatterer Formalism, Journal of Mathematical Physics, Vol. 3, No. 4, pp.724-734 https://doi.org/10.1063/1.1724274
  18. Varadan, V. K., Varadan,V. V. and Pao, Y. H. (1978) Multiple Scattering of Elastic Waves by Cylinders of Arbitrary Cross Section. I. SH Waves, Journal of Acoustical Society of America, Vol. 63, No. 5, pp. 1310-1319 https://doi.org/10.1121/1.381883
  19. Varadan, V. K., Ma, Y. and Varadan,V. V. (1986) Multiple Scattering of Compressional and Shear Waves by Fiber-Reinforced Composite Materials, Journal of Acoustical Society of America, Vol. 80, No. 1, pp. 333-339 https://doi.org/10.1121/1.394151
  20. Waterman, P. C. and Truell, R. (1961) Multiple Scattering of Waves, Journal of Mathematical Physics, Vol. 2, No. 4, pp. 512-537 https://doi.org/10.1063/1.1703737
  21. Willis, J. R. (1980a) A Polarization Approach to the Scattering of Elastic Waves-I. Scattering by a Single Inclusion, Journal of the Mechanics and Physics of Solids, Vol. 28, pp. 287-305 https://doi.org/10.1016/0022-5096(80)90021-6
  22. Willis, J. R. (1980b) A Polarization Approach to the Scattering of Elastic Waves-II. Multiple Scattering from Inclusions, Journal of the Mechanics and Physics of Solids, Vol. 28, pp. 307-327 https://doi.org/10.1016/0022-5096(80)90022-8
  23. Yang, R. B. and Mal, A. K. (1994) Multiple Scattering of Elastic Waves in a Fiber-Reinforced Composite, Journal of the Mechanics and Physics of Solids, Vol. 42, No. 12, pp. 1945-1968 https://doi.org/10.1016/0022-5096(94)90020-5
  24. Yang, R. B. (2003) A Dynamic Generalized Self-Consistent Model for Wave Propagation in Particulate Composites, Journal of Applied Mechanics, Vol. 70, pp. 575-582 https://doi.org/10.1115/1.1576806
  25. Yim, H. and Sohn, Y. (2000) Numerical Simulation and Visualization of Elastic Waves Using Mass-Spring Lattice Model, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, Vol. 47, No. 3, pp. 549-558 https://doi.org/10.1109/58.842041
  26. Yim, H. and Choi, Y. (2000) Simulation of Ultrasonic Waves in Various Types of Elastic Media Using the Mass Spring Lattice Model, Materials Evaluation, Vol. 58, pp. 889-896
  27. Yim, H. and Lee, C. (2002) Quantitative Accuracy of the Mass-spring Lattice Model in Simulating Ultrasonic Waves, Review of Quantitative Nondestructive Evaluation, Vol. 21, pp. 152-156
  28. Yim, H. and Baek, E. (2002) Two-Dimensional Numerical Modeling and Simulation of Ultrasonic Testing, Journal of the Korean Society for Nondestructive Testing, Vol. 22, No. 6, pp. 649-658
  29. Yim, H. and Baek, E. (2004) Modeling of Transmitting and Receiving Ultrasonic Probes for Use with the Mass-Spring Lattice Model, Key Engineering Materials, Vol. 270-273, pp. 384-389 https://doi.org/10.4028/www.scientific.net/KEM.270-273.384