Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-15T13:22:20.620Z Has data issue: false hasContentIssue false
  • English
  • Français

Effect of Interface Anisotropy on Elastic Wave Propagation in Particulate Composites

Published online by Cambridge University Press:  05 May 2011

S. M. Hasheminejad  and
M. Maleki
S. M. Hasheminejad*
Affiliation:
Acoustics Research Laboratory, Department of Mechanical Engineering, Iran University of Science and Technology, Narmak, Tehran 16844, Iran
M. Maleki*
Affiliation:
Acoustics Research Laboratory, Department of Mechanical Engineering, Iran University of Science and Technology, Narmak, Tehran 16844, Iran
*
*Professor
**Graduate student
Get access

Abstract

The scattering of time harmonic plane longitudinal and transverse elastic waves in a composite consisting of randomly distributed identical isotropic spherical inclusions embedded in an isotropic matrix with anisotropic interface layers is examined. The interface region is modeled as a spherically isotropic shell of finite thickness with five independent elastic constants. The Frobenius power series solution method is utilized to deal with the interface anisotropy and the effect of random distribution of particulates in the composite medium is taken into account via a recently developed generalized self-consistent multiple scattering model. Numerical values of phase velocities and attenuations of coherent plane waves as well as the effective elastic constants are obtained for a moderately wide range of frequencies, particle concentrations, and interface anisotropies. The numerical results reveal the significant dependence of phase velocities and effective elastic constants on the interface properties. They show that interface anisotropy can moderately depress the effective phase velocities and the elastic moduli, but leave effective attenuation nearly unaffected, especially at low and intermediate frequencies. Limiting cases are considered and good agreements with recent solutions have been obtained.

Keywords

Multiple scatteringSpherically isotropic interfaceEffective elastic constants
Type
Articles
Information
Journal of Mechanics , Volume 24 , Issue 1 , March 2008 , pp. 79 - 93
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Pao, Y. H. and Mow, C. C., Diffraction of Elastic Waves and Dynamic Stress Concentration, Russak & Company Inc., New York (1973).CrossRefGoogle Scholar
2.Gaunaurd, G. C., “Elastic and Acoustic Resonance Wave Scattering,” Appl. Mech. Rev., 42, pp. 143–192 (1989).CrossRefGoogle Scholar
3.Ying, C. and Truell, R., “Scattering of a Plane Longitudinal Wave by a Spherical Obstacle in an Isotropically Elastic Solid,” J. Appl. Phys., 27, pp. 1086–1097 (1956).CrossRefGoogle Scholar
4.Einspruch, N., Witterholt, E. and Truell, R., “Scattering of a Plane Transverse Wave by a Spherical Obstacle in an Elastic Medium,” J. Appl. Phys., 31, pp. 806–818 (1960).CrossRefGoogle Scholar
5.Clebsch, A., “Ueber die reflection an einer kugelf” Crelle ' Journal, 61, pp. 195–262 (1863).Google Scholar
6.Jain, D. L. and Kanwal, R. P., “Scattering of Elastic Waves by an Elastic Sphere,” Int. J. Eng. Sci., 18, pp. 1117–1127(1980).CrossRefGoogle Scholar
7.Hinders, M. K., “Elastic Wave Scattering from an Elastic Sphere,” Il Nuovo Cimento, 106B, pp. 799–818 (1991).CrossRefGoogle Scholar
8.Sessarego, J.-P., Sageloli, J., Guillermin, R. and Uberall, H., “Scattering by an Elastic Sphere Embedded in an Elastic Isotropic Medium,” J. Acoust. Soc. Am., 104, pp. 2836–2844 (1998).CrossRefGoogle Scholar
9.Wei, P. J. and Huang, Z. P., “Dynamic Effective Properties of the Particle-Reinforced Composites with the Viscoelastic Interphase,” Int. J. Solids Struct., 41, pp. 6993–7007 (2004).CrossRefGoogle Scholar
10.Hashin, Z. and Rosen, B. W., “The Elastic Moduli of Fiber-Reinforced Materials,” J. Appl. Mech., 31, pp. 223–228 (1964).CrossRefGoogle Scholar
11.Eshelby, J. D., “The Determination of the Elastic Field of an Ellipsoidal Inclusion, and Related Problems,” Proc. R. Soc. London, A241, pp. 376–396 (1957).Google Scholar
12.Torralba, J. M., Velasco, F., Costa, C. E., Vergara, I. and Caceres, D., “Mechanical Behavior of the Interphase Between Matrix and Reinforcement of Al 2014 Matrix Composite Reinforced with (Ni3Al)p,” Composites, Part A, 33, pp. 427–434 (2002).CrossRefGoogle Scholar
13.Mittleman, J., Roberts, R. and Thompson, R. B., “Scattering of Longitudinal Elastic Waves from an Anisotropic Spherical Shell,” J. Appl. Mech., 62, pp. 150–158 (1995).Google Scholar
14.Ozmusul, M. S. and Picu, R. C., “Elastic Moduli of Particulate Composites with Graded Filler-Matrix Interfaces,” Polymer Composites, 23, pp. 110–119 (2002).CrossRefGoogle Scholar
15.Musgrave, M. J. P., “The Propagation of Elastic Waves in Crystals and Other Anisotropic Media,” Report on Progress in Physics, 22, pp. 74–96 (1959).CrossRefGoogle Scholar
16.Mal, A. K. and Bose, S. K., “Dynamic Moduli of a Suspension of Imperfectly Bonded Spheres,” Proc. Cambridge Philos. Soc., 76, pp. 578–600 (1974).CrossRefGoogle Scholar
17.Datta, S. K., Ledbetter, H. M., Shindo, Y. and Shah, A. H., “Phase Velocity and Attenuation of Plane Elastic Waves in a Particulate-Reinforced Composite Medium,” Wave Motion, 10, pp. 171–182 (1988).CrossRefGoogle Scholar
18.Olsson, P., Datta, S. K. and Bostrom, A., “Elastodymaic Scattering form Inclusions Surrounded by Thin Interface Layer,” J. Appl. Mech., 57, pp. 672–676 (1990).CrossRefGoogle Scholar
19.Shindo, Y., Nozaki, H. and Kusumi, R., “Phase Velocity and Attenuation of Plane Elastic Waves in a Particle- Reinforced Metal Matrix Composite with Interfacial Layers,” Nippon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A, 57, pp. 1561–1568 (1991).Google Scholar
20.Shindo, Y., Nozaki, H. and Datta, S. K., “Effect of Interface Layers on Elastic Wave Propagation in a Metal Matrix Composite Reinforced by Particles,” J. Appl. Mech., 62, pp. 178–185 (1995).CrossRefGoogle Scholar
21.Kiriaki, K., Polyzos, D. and Valavanides, M., “Low-Frequency Scattering of Coated Spherical Obstacles,” J. Eng. Math., 31, pp. 379–395 (1997).CrossRefGoogle Scholar
22.Baird, A. M., Kerr, F. H. and Townend, D. J., “Wave Propagation in a Viscoelastic Medium Containing Fluid-Filled Microspheres,” J. Acoust. Soc. Am., 105, pp. 1527–1538 (1999).CrossRefGoogle Scholar
23.Haberman, M. R., Berthelot, Y. H., Cherkaoui, M. and Jarzynski, J., “Micromechanical Modeling of Viscoelastic Voided Composites in the Low-Frequency Approximation,” J. Acoust. Soc. Am., 112, pp. 1937–1943 (2002).Google Scholar
24.Chen, T., “Thermoelastic Properties and Conductivity of Composites Reinforced by Spherically Anisotropic Particles,”Mech. Mat., 14, pp. 257–268 (1993).CrossRefGoogle Scholar
25.He, L.-H. and Cheng, Z.-Q., “Correspondence Relations Between the Effective Thermoelastic Properties of Composites Reinforced by Spherically Anisotropic Particles,” Int. J. Eng. Sci., 34, pp. 1–8 (1996).CrossRefGoogle Scholar
26.Kushch, V. I. and Sevostianov, I., “Effective Elastic Properties of the Particulate Composite with Transversely Isotropic Phases,” Int. J. Solids Struct., 41, pp. 885–906 (2004).CrossRefGoogle Scholar
27.He, L. and Liu, R., “Bounds of the Expansion Coefficients of Composites Reinforced by Spherically Isotropic Particles,” Appl. Math. Mech., 18, pp. 341–348 (1997).Google Scholar
28.Huang, H. L. and He, Q.-C., “Micromechanical Estimation of the Shear Modulus of a Composite Consisting of Anisotropic Phases,” J. Mat. Sci. Tech., 20, pp. 6–10 (2004).Google Scholar
29.Hata, T., “Thermal Stress-Focusing Effect in a Transversely Isotropic Spherical Inclusion Embedded in an Isotropic Infinite Elastic Medium,” J. Thermal Stresses, 25, pp. 691–702 (2002).CrossRefGoogle Scholar
30.Liu, H. T., Sun, L. and Ju, J. W., “Micromechanics-Based Elastoplastic and Damage Modeling of Particle Reinforced Composites,” American Society of Mechanical Engineers, Materials Division (Publication) MD, Proceedings of the ASME Materials Division, 99, pp. 63–70 (2004).Google Scholar
31.Yang, R.-B. and Mal, A. K., “Elastic Waves in a Composite Containing Inhomogeneous Fibers,” Int. J. Eng. Sci., 34, pp. 67–79 (1996).CrossRefGoogle Scholar
32.Achenbach, J. D., Wave Propagation in Elastic Solids, North-Holland, New York (1976).Google Scholar
33.Stratton, J. A., Electromagnetic Theory, McGraw-Hill (1941).Google Scholar
34.Lekhnitskii, S. G., Theory of Elasticity of an Anisotropic Body, Mir Publishers, Moscow (1981).Google Scholar
35.Ding, H. J., Liang, J., Zou, D. Q. and Chen, W. Q., Transversely Isotropic Elasticity, Zhejiang University Press, Hangzhou (1997).Google Scholar
36.Ding, H. J. and Chen, W. Q., “Nonaxisymmetric Free Vibrations of a Spherically Isotropic Spherical Shell Embedded in an Elastic Medium,” Int. J. Solids Struct., 33, pp. 2575–2590(1996).Google Scholar
37.Hildebrand, F. B., Advanced Calculus for Engineers, Prentice-Hall, Inc., Englewood Cliffs, NJ (1962).Google Scholar
38.Rayleigh, J. W., “On The Influence of Obstacle Arranged in Rectangular Order Upon the Properties of the Medium,” Philosophical Magazine, 34, pp. 481–497 (1892).Google Scholar
39.Foldy, L. L., “The Multiple Scattering of Waves,” Phys. Rev., 67, pp. 107–119(1945).Google Scholar
40.Lax, M. “Multiple Scattering of Waves,” Review of Modern Physics, 23, pp. 287–310 (1951).CrossRefGoogle Scholar
41.Waterman, P. C. and Truell, R., “Multiple Scattering of Waves,” Journal of Mathematical Physics, 2, pp. 512–537(1961).CrossRefGoogle Scholar
42.Berryman, J. G., “Long-Wavelength Propagation in Composite Elastic Media I. Spherical Inclusions,” J. Acoust. Soc. Am., 68, pp. 1809–1819 (1980).Google Scholar
43.Sabina, F. J. and Willis, J. R., “A Simple Self-Consistent Analysis of Wave Propagation in Particulate Composites,” Wave Motion, 10, pp. 127–142 (1988).Google Scholar
44.Yang, R. B. and Mal, A. K., “Multiple Scattering of Elastic Waves in a Fiber-Reinforced Composite,” J. Mech. Phys. Solids, 42, pp. 1945–1968 (1994).CrossRefGoogle Scholar
45.Kanaun, S. K., “Self-Consistent Methods in the Propagation through Heterogeneous Media,” Markov, K. Z., Preziosi, L., Eds., Heterogeneous Media-Micromechanics Modeling Methods and Simulations, Birkhauser, Boston (2000).Google Scholar
46.Yang, R.-B., “A Dynamic Generalized Self-Consistent Model for Wave Propagation in Particulate Composites,” J. Appl. Mech., 70, pp. 575–582 (2003).CrossRefGoogle Scholar
47.Kim, J.-Y., “On the Generalized Self-Consistent Model for Elastic Wave Propagation in Composite Materials,” International Journal of Solids and Structures, 41, pp. 4349–4360 (2004).CrossRefGoogle Scholar
48.Aggelis, D. G., Tsinopoulos, S. V. and Polyzos, D., “An Iterative Effective Medium Approximation (IEMA) for Wave Dispersion and Attenuation Predictions in Particulate Composites, Suspensions and Emulsions,” Journal of the Acoustical Society of America, 116, pp. 3443–3452 (2004).CrossRefGoogle ScholarPubMed
49.Sato, H. and Shindo, Y., “Multiple Scattering of Plane Elastic Waves in a Particle-Reinforced-Composite Medium with Graded Interfacial Layers,” Mech. Mat., 35, pp. 83–106 (2003).CrossRefGoogle Scholar
50.Christensen, R. M., Mechanics of Composite Materials, John Wiley and Sons, New York (1979).Google Scholar
51.Hasheminejad, S. M., “Acoustic Scattering by a Fluid-Encapsulating Spherical Viscoelastic Membrane Including Thermoviscous Effects,” Journal of Mechanics, 21, pp. 205–215(2005).Google Scholar
52.Hill, R., “A Self-Consistent Mechanics of Composite Materials,” Journal of the Mechanics and Physics of Solids, 13, pp. 213–222 (1965).CrossRefGoogle Scholar
53.Hashin, Z., “The Elastic Moduli of the Heterogeneous Matrials,” ASME Journal of Applied Mechanics, 29, pp. 143–150(1962).Google Scholar
54.Christensen, R. M. and Lo, K. H., “Solutions for Effective Shear Properties in Three Phase Sphere and Cylinder Models,” Journal of the Mechanics and Physics of Solids, 27, pp. 315–330 (1979).CrossRefGoogle Scholar