Scattering of elastic waves in unidirectional fiber-reinforced porous–matrix composites is studied using novel features of Biot classic model for dynamic poroelasticity. The method of separation of variables along with the appropriate wave field expansions, the pertinent boundary conditions, and the translational addition theorems for cylindrical wave functions are employed to develop a closed-form solution in form of infinite series. The analytical results are illustrated with numerical examples in which a pair of rigid or elastic fibers are insonified by a plane fast compressional or shear wave at end-on/broadside incidence. The effects of incident wave frequency, proximity of the two fibers, fiber material properties and angle of incidence on the far-field backscattered radial and shearing stress amplitudes are examined. Particular attention has been focused on multiple scattering interactions in addition to the slow wave coupling effects which is known to be the primary distinction of the scattering phenomenon in poroelasticity from the classical elastic case. Limiting cases are considered and fair agreements with well-known solutions are established.
Zok, F. W. and Levi, C. G. (2001). Mechanical Properties of Porous-Matrix Ceramic Composites, Advanced Engineering Materials, 3(1–2): 15–23.
2.
Marshall, D. B. and Davis, J. B. (2001). Ceramics for Future Power Generation Technology: Fiber Reinforced Oxide Composites, Current Opinion in Solid State and Material Science, 5: 283–289.
3.
Cinibulk, M. K., Keller, K. A. and Mah, T. I. (2004). Effect of Yttrium Aluminum Garnet Additions on Alumina-Fiber-Reinforced Porous-Alumina-Matrix Composites, Journal of the American Ceramic Society, 87(5): 881–887.
4.
Kanka, B. and Schneider, H. (2000). Aluminosilicate Fiber/Mullite Matrix Composites with Favorable High-Temperature Properties, Journal of the European Ceramic Society, 20: 619–623.
5.
Haslam, J. J., Berroth, K. E. and Lange, F. F. (2000). Processing and Properties of an All-Oxide Composite with a Porous Matrix, Journal of the European Ceramic Society, 20: 607–618.
6.
Kanka, B. J., Goring, J., Schmucker, M. and Schneider, H. (2001). Processing, Microstructure and Properties of Nextel [Trademark] 610, 650 and 720 Fiber/Porous Mullite Matrix Composites. In: Ceramic Engineering and Science Proceedings, 25th Annual Conference on Composites, Advanced Ceramics, Materials and Structures, 22(3), pp. 703–710, Cocoa Beach, FL, USA.
7.
Schmucker, M., Kanka, B. and Schneider, H. (2000). Temperature-Induced Fiber/Matrix Interaction in Porous Alumino Silicate Ceramic Matrix Composites, Journal of the European Ceramic Society, 20: 2491–2497.
8.
Tsukrov, I., Piat, R., Novak, J. and Schnack, E. (2003). Influence of Pores on Effective Elastic Properties of Unidirectional Carbon/Carbon Composites, Key Engineering Materials, 251–252: 339–344.
9.
Naplocha, K., Janus, A., Kaczmar, J.W. and Samsonowicz, Z. (2000). Technology and Mechanical Properties of Ceramic Preforms for Composites Material, Journal of Materials Processing Technology, 106: 119–122.
10.
Roerden, A. M. and Herakovich, C. T. (2000). The Inelastic Response of Porous, Hybrid-Fiber Composites, Composites Science and Technology, 60: 2443–2454.
11.
Neithalath, N., Weiss, J. and Olek, J. (2004). Acoustic Performance and Damping Behavior of Cellulose-Cement Composites, Cement and Concrete Composites, 26(4): 359–370.
12.
Olek, J., Weiss, W. J. and Neithalath, N. (2004). Concrete Mixtures that Incorporate Inclusions to Reduce the Sound Generated in Portland Cement Concrete Pavements, Center for Advanced Cement-Based Materials, 26(4): 359–370.
13.
Ulm, F. J., Constantinides, G. and Heukamp, F. H. (2004). Is Concrete a Poromechanics Material? – A Multiscale Investigation of Poroelastic Properties, Materials and Structures/Materiaux et Constructions, 37(265): 43–58.
14.
Ishimaru, A. (1999). Wave Propagation and Scattering in Random Media (Ieee/Oup Series on Electromagnetic Wave Theory), Wiley–IEEE Press.
15.
Fan, Y., Sinclair, A. N. and Honarvar, F. (1999). Scattering of a Plane Acoustic Wave from a Transversely Isotropic Cylinder Encased in a Solid Elastic Medium, J. Acoust. Soc. Am., 106(3) Pt.1: 1229–1236.
16.
Bose, S. K. and Mal, A. K. (1973). Longitudinal Shear Waves in a Fiber-Reinforced Composite, Int. J. Solids Struct., 9: 1075–1085.
17.
Bose, S. K. and Mal, A. K. (1974). Elastic Waves in a Fiber-Reinforced Composite, Int. J. Solids Struct., 22: 217–229.
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, J. Acoust. Soc. Am., 63(5): 1310–1319.
19.
Hinders, M., Fang, T., Bronson, S., Bogan, S., Nagem, R. and Sandri, G. (1992). Dynamic Stress Concentrations in Particle- and Fiber-Reinforced Composite Materials, ASME, Aerospace Div., Topics in Composite Materials and Structures, 26: 1–11.
20.
Yang, R. B. and Mal A. K. (1994). Multiple Scattering of Elastic Waves in a Fiber-Reinforced Composite, J. Mech. Phys. Solids, 42(12): 1945–1968.
21.
Liu, W. (1997). Multiple Wave Scattering and Calculated Effective Stiffness and Wave Properties in Unidirectional Fiber-Reinforced Composites, Doctor of Philosophy, Virginia Polytechnic Institute.
22.
Shindo, Y., Niwa, N. and Togawa, R. (1998). Multiple Scattering of Antiplane Shear Waves in a Fiber-Reinforced Composite Medium with Interfacial Layers, Int. J. Solids Struct., 35(7–8): 733–745.
23.
Lavrov, N. A. and Pavlovskaia, E. E. (2001). Elastic Wave Scattering on a System of Rod-Like Inclusions, J. Sound Vib., 248(2): 329–350.
24.
Lu, Y. (1994). Three-Dimensional Reflection and Transmission of Elastic Waves by an Array of Cylinders, J. Sound Vib., 175(1): 1–15.
25.
Wang, X. D. and Gan, S. (2002). Effective Antiplane Dynamic Properties of Fiber-Reinforced Composites, ASME J. Appl. Mech., 69(5): 696–699.
26.
Biwa, S., Watanabe, Y. and Ohno, N. (2003). Analysis of Wave Attenuation in Unidirectional Viscoelastic Composites by a Differential Scheme, Composites Science and Technology, 63(2): 237–247.
27.
Kanaun, S. K. and Levin, V. M. (2003). Effective Medium Method in the Problem of Axial Elastic Shear Wave Propagation through Fiber Composites, Int. J. Solids Struct., 40(18): 4859–4878.
28.
Kim, J. Y. (2003). Antiplane Shear Wave Propagation in Fiber-Reinforced Composites, J. Acoust. Soc. Am., 113(5): 2442–2445.
29.
Hu, C., Li, F. M. and Huang, W. H. (2003). Elastic Wave Scattering and Dynamic Stress in Composite with Fiber, Applied Math. Mech. (English Edition), 24(7): 808–816.
30.
Biwa, S., Yamamoto, S., Kobayashi, F. and Ohno, N. (2004). Computational Multiple Scattering Analysis for Shear Wave Propagation in Unidirectional Composites, Int. J. Solids Struct., 41(2): 435–457.
31.
Reynolds, W. N. and Wilkinson, S. J. (1978). Analysis of Fiber-Reinforced Porous Composite Materials by the Measurement of Ultrasonic Wave Velocities, Ultrasonics, 16(4): 159–163.
32.
Blodgett, E. D., Thomas, L. J. III. and Miller, J. G. (1986). Effects of Porosity on Polar Backscatter from Fiber Reinforced Composites, Review of Progress in Quantitative Nondestructive Evaluation, 5B: 1267–1274.
33.
Widrig, J. E., McCabe, D. D. and Conner, R. L. (1988). Nondestructive Evaluation of Fiber FP Reinforced Metal Matrix Composites, ASTM Special Technical Publication, STP(964): 227–247.
34.
Qu, J., Achenback, J. D. and Roberts, R. A. (1988). Backscatter from Porosity in Fiber-Reinforced Composites, AMD (Symposia Series) (ASME Appl. Mech. Div.), 92: 69–77.
35.
Kunerth, D. C., Lott, L. A. and Walter, J. B. (1990). Nondestructive Evaluation of Ceramic Matrix Composites. In: Ceramic Engineering and Science Proceedings, 14th Annual Conference on Composites and Advanced Ceramic Materials, 11(9–10), pp. 1685–1688, Cocoa Beach, FL, USA.
36.
Generazlo, E. R. (1990). Theory and Experimental Technique for Nondestructive Evaluation of Ceramic Composites, NASA Technical Memorandum, 102561-102561.
37.
Jeong, H. and Hsu, D. K. (1995). Experimental Analysis of Porosity-Induced Ultrasonic Attenuation and Velocity Change in Carbon Composites, Ultrasonics, 33(3): 195–203.
38.
Zhou, X., You, H. and Cheng, Y. (1997). Ultrasonic attenuation model of void contained carbon-fiber reinforced plastics, Fuhe Cailiao Xuebao/Acta Materiae Compositae Sinica, 14(3): 99–106.
39.
Ono, T., Miyakoshi, S. and Watanabe, U. (2002). Acoustic Characteristics of Unidirectionally Fiber-Reinforced Polyurethane Foam Composites for Musical Instrument Sound boards, Acoustical Science and Technology, 23(3): 135–142.
40.
Abdul-Aziz, A., Ghosn, L. J., Baaklini, G. and Bhatt, R. (2003). A Combined NDT/Finite Element Technique to Study the Effects of Matrix Porosity on the Behavior of Ceramic Matrix Composites, Materials Evaluation, 61(11): 1217–1221.
41.
Tournat, V., Pagneux, V., Lafarge, D. and Jaouen, L. (2004). Multiple Scattering of Acoustic Waves and Porous Absorbing Media, Physical Review E, 70(026609): 1–10.
42.
Achenbach, J. D. (1973). Wave Propagation in Elastic Solids, North-Holland, New York.
43.
Abramowitz, M. and Stegun, I. A. (1964). Handbook of Mathematical Functions, National Bureau of Standards, Washington D.C.
44.
Allard, J. F. (1993). Propagation of Sound in Porous Media: Modeling Sound Absorbing Materials, Elsevier Applied Science, London.
45.
Johnson, D. L., Koplik, J. and Dashen, R. (1987). Theory of Dynamic Permeability and Tortuosity in Fluid-Saturated Porous Media, J. Fluid Mech., 76: 379–402.
46.
Luppe, F., Conoir, J. M. and Franklin, H. (2002). Scattering by a Fluid Cylinder in a Porous Medium: Application to Trabecular Bone, J. Acoust. Soc. Am., 111(6): 2573–2582.
47.
Ivanov, Y. A. (1970). Diffraction of Electromagnetic Waves on Two Bodies, National Aeronautics and Space Administration, Washington D.C.
48.
Allard, J. F., Henry, M., Glorieux, C., Lauriks, W. and Petillon, S. (2004). Laser Induced Surface Modes at Water-Elastic and Poroelastic Solid Interfaces, J. Applied Physics, 95(2): 528–535.
49.
Sato, H. and Shindo, Y. (1999). Diffractions of Elastic Waves by a Circular Inclusion with a Nonhomogeneous Interface Layer and Dynamic Stress Concentrations. In: Proceedings of the 48th Japan National Congress on Theoretical and Applied Mechanics, pp. 81–94.
50.
Bourbie, T., Coussy, O. and Zinszner, B. E. (1987). Acoustics of Porous Media, Gulf Publishing, Houston.
51.
Gaunaurd, G. C., Huang, H. and Strifors, H. C. (1995). Acoustic Scattering by a Pair of Spheres, J. Acoust. Soc. Am., 98(1): 495–507.
52.
Young, J. W. and Berrand, J. C. (1975). Multiple Scattering by Two Cylinders, J. Acoust. Soc. Am., 58(6): 1190–1193.
53.
Sancar, S. and Sachse, W. (1981). Spectral Analysis of Elastic Pulses Backscattered From Two Cylindrical Cavities in a Solid, Part II, J. Acoust. Soc. Am., 69: 1597–1609.
