Elastic wave scattering from coated and layered cylindrical scatterers encased in an elastic matrix is reviewed. Interaction of time harmonic monochromatic longitudinal and shear ultrasonic waves with a single fiber coated by homogeneous dissipative (polymeric) materials and embedded in an unbounded elastic matrix is studied using the classical method of eigenfunction expansion. The novel features of Havriliak—Negami model is employed to include the effect of hysteresis-type of compressional and shear waves' absorption in the interphase material by introduction of proper frequency-dependent complex moduli. The pertinent integrals for the time-averaged total fiber energy induced by the elastic waves refracted along the fiber are derived and numerically evaluated. The numerical results reveal the important effects of the absorptive fiber—matrix bond as well as interphase thickness on fiber/matrix energy transfer and dynamic stress concentrations. The calculated results may be interpreted in the context of phenomena observed in acousto-ultrasonic (AU) experiments on fiber reinforced composite materials by correlating certain parameters in the frequency spectrum of the detected waveform to mechanical characteristics of the dissipative interface layer. Limiting cases are considered and good agreements with well-known solutions are established.
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): 1229-1236.
2.
Cai, L.-W. (2004). Scattering of Antiplane Shear Waves by Layered Circular Elastic Cylinder, J. Acoust. Soc. Am., 115(2): 515-522.
3.
Cai, L.-W. (2004). Multiple Scattering in Single Scatterers, J. Acoust. Soc. Am., 115(3): 986-995.
4.
Pao, Y.H. and Mow, C.C. (1973). Diffraction of Elastic Waves and Dynamic Stress Concentrations, Crane, Russack, New York.
5.
Datta, S.K. (1978). Scattering of Elastic Waves, in Mechanics Today , edited by Nemat Nasser, S.,Mechanics Today, Vol. 4, pp. 149-208, Pergamon , New York.
6.
Hackman, R.H. (1993). Acoustic Scattering from Elastic Solids, Physical Acoustics, Vol. XXII, pp. 1-193, Academic , New York.
7.
Sinclair, A.N. and Addison, Jr, R.C. (1993). Acoustic Diffraction Spectrum of a SiC Fiber in a Solid Elastic Medium, J. Acoust. Soc. Am., 94: 1126-1135.
8.
Mal, A.K. and Yang, R.-B. (1994). The Influence of the Fiber-matrix Interfacial Layer Properties on Wave Characteristics in Metal Matrix Composites, In: Thompson, D.O. and Chimenti-Plenum, D.E. (eds), Review of Progress in Quantitative Nondestructive Evaluation, Vol. 13B, pp. 1453-1460, New York.
9.
Huang, W., Brisuda, S. and Rokhlin, S.I. (1995). Ultrasonic Wave Scattering from FiberMatrix Interphases , J. Acoust. Soc. Am., 97: 807-817.
10.
Huang, W., Rokhlin, S.I. and Wang, Y.J. (1995). Effect of Fiber-Matrix Interphase of Wave Propagation along, and Scattering from, Multilayered Fibers in Composite; Transfer matrix approach, Ultrasonics, 33: 365-375.
11.
Huang, W., Wang, Y.J. and Rokhlin, S.I. (1996). Oblique Scattering of an Elastic Wave from a Multilayered Cylinder in a Solid. Transfer Matrix Approach, J. Acoust. Soc. Am. 99(5): 2742-2754.
12.
Cai, L.-W. (1998). Full-Scale Simulation of Multiple Scattering of Elastic Waves in Fiber Reinforced Composite, Sc.D. Thesis, Massachusetts Institute of Technology, Cambridge, MA.
13.
Squire, V.A. and Dixon, T.W. (2000). Scattering of Flexural Waves from a Coated Cylindrical Anomaly in a Thin Plate, J. Sound Vib., 236(2): 367-373.
14.
Qin, B. , Chen, J.J. and Cheng, J.C. (2005). Local Resonant Characteristic of a Layered Cylinder Embedded in the Elastic Medium, Chinese Physics, 14(2): 2522-2528.
15.
DeSanto, J.A. (1980). Theory of Scattering from Multilayered Bodies of Arbitrary Shape, Wave Motion, 2: 63-73.
16.
Peterson, B. and Strom, S. (1975). Matrix Formulation of Acoustic Scattering from Multilayered Scatterers, J. Acoust. Soc. Am., 57: 2-13.
17.
Pillai, T.A.K. , Varadan, V.K. and Varadan, V.V. (1983). Acoustic Wave Scattering by Elastic Cylindrical Shells in Water, J. Acoust. Soc. Am. , 74: 619-624.
18.
Olsson, P., Datta, S.K. and Bostrom, A. (1990). Elastodynamic Scattering from Inclusions Surrounded by Thin Interface Layer, ASME J. Appl. Mech., 57: 672-676.
19.
Guo, Y.P. (1995). Attenuation of Helical Wave Radiation from Cylindrical Shells by Viscoelastic Layer, J. Acoust. Soc. Am., 97(1): 298-308.
20.
Kaduchak, G. and Loeffler, C.M. (1996). Backscattering of Obliquely Incident Plane Waves by a Composite Cylindrical Shell Constructed of Isotropic and Transversely Isotropic Layers, J. Acoust. Soc. Am., 99: 2545-2574.
21.
Sastry, J.S. and Munjal, M.L. (1998). Response of a Multi-Layered Infinite Cylinder to Plane Wave Excitation by Means of Transfer Matrices, J. Sound Vib., 209: 99-121.
22.
Joo, Y.S. , Iha, J.G. and Choi, M.S. (1998). Inherent Background Coefficients for Acoustic Resonance Scattering from Submerged, Multilayered, Cylindrical Structures, J. Acoust. Soc. Am. , 103(2): 900-910.
23.
Choi, M.S. (2000). Inherent Background Coefficient of the Axisymmetric Mode in Acoustic Resonance Scattering from a System of Multilayered Shells , Journal of the Korean Physical Society, 37: 519-526.
24.
Fan, Y., Tysoe, B., Sim, J., Mirkhani, M., Sinclair, A.N., Honarvar, F., Sildva, H., Szecket, A. and Hardwick, R. (2003). Nondestructive Evaluation of Explosively Welded Clad Rods by Resonance Acoustic Spectroscopy, Ultrasonics , 41: 369-375.
25.
Hasheminejad, S.M. and Rajabi, M. (2007). Acoustic Resonance Scattering from a Submerged Functionally Graded Cylindrical shell, J. Sound Vib., 302: 208-228.
26.
Pukanszky, B. (2005). Interfaces and Interphases in Multicomponent Materials: Past, Present, Future, European Polymer Journal, 41(4): 645-662.
27.
DiBenedetto, A.T. (2001). Tailoring of Interfaces in Glass Fiber Reinforced Polymer Composites: A review, Materials Science and Engineering A, 302(1): 74-82.
28.
Yim, H. and Williams Jr, J.H. (1995). Formulation and its Energy Balance Verification for Ultrasonic Non-Destructive Characterization of a Single Fibre Composite Interphase, Ultrasonics, 33(5): 377-387.
29.
Yim, H. and Williams, Jr, J.H. (1995). Database Generation and Parametric Study for Ultrasonic Non-Destructive Characterization of a Single Fiber Composite Interphase, Ultrasonics, 33(5): 389-401.
30.
Bogen, S.D. and Hinders, M.K. (1993). Dynamics Stress Concentration in Fiber-reinforced Composites with Interface Layers , J. Compos. Mater., 27: 1272-1311.
31.
Wacker, G. (1996). Experimentell Gestuetzte Identifikation Ausgewaehlter Eigenschaften Glasfaserverstaerkter Epoxidharze unter Beruecksichtigung der Grenzschicht, PhD Thesis, Department of Mechanical Engineering, University of Kassel.
32.
Kim, J.-K. and Mai, Y.-W. (1998). Engineered Interface in Fiber Reinforced Composites, Elsevier, Oxford.
33.
Labronici, M. and Ishida, H. (1994). Toughening Composites by Fiber Coating; a Review, Composite Interfaces , 2(3): 199-234.
34.
Carman, G.P. , Averill, R.C., Reifsnider , K.L. and Reddy, J.N. (1993). Optimization of Fiber Coatings to Minimize Stress Concentrations in Composite Materials, Journal of Composite Materials, 27(6): 589-612.
35.
Hirashima, K. and Hashizume, R. (1995). Analysis of Viscoelastic Behavior of Fiber Composite Materials with Time Dependence of the Interface , Zairyo/Journal of the Society of Materials Science, Japan, 44(502): 911-915.
36.
Gosz, M., Moran, B. and Achenbach, J.D. (1991). Effect of a Viscoelastic Interface on the Transverse Behavior of Fiber-Reinforced Composites, Int. J. Solids Struct. , 27(14): 1757-1571.
37.
Chandra, R. , Singh, S.P. and Gupta, K. (2003). A Study of Damping in Fiber-Reinforced Composites, J. Sound Vib., 262: 475-496.
38.
Gu, J., Zhang, X. and Gu, M. (2005). Effect of Fiber Coating on the Longitudinal Damping Capacity of Fiber-Reinforced Metal Matrix Composites, Materials Letters, 59: 180-184.
39.
Matzenmiller, A. and Gerlach, S. (2004). Micromechanical Modeling of Viscoelastic Composites with Compliant Fiber-Matrix Bonding, Computational Materials Science, 29: 283-300.
40.
Bose, S.K. and Mal, A.K. (1974). Elastic Waves in a Fiber-Reinforced Composite , J. Mech. Phys. Solids, 22: 217-229.
41.
Achenbach, J.D. and Zhu, H. (1989). Effect of Interfacial Zone on Mechanical Behavior and Failure of Fiber-Reinforced Composites , J. Mech. Phys. Solids, 37(3): 381-393.
42.
Xu, P.C. and Datta, S.K. (1991). Characterization of Fiber-Matrix Interface by Guided Waves: Axisymmetric Case, J. Acoust. Soc. Am., 89: 2573-2583.
43.
Oshima, T., Kriz, R.D. and Nomachi, S.G. (1993). Visual Simulation of Stress Wave Propagation in Fiber Sensor with Interphase Layer in Composite Laminate, ASME, Aerospace Division (Publication) AD, Adaptive Structures and Material Systems , 35: 401-406.
44.
Matikas, T.E. and Karpur, P. (1993). Ultrasonic Reflectivity Technique for the Characterization of Fiber-Matrix Interface in Metal Matrix Composites Source, J. Appl. Phys., 74(1): 228-236.
45.
Chu, Y.C. and Rokhlin, S.I. (1992). Determination of Macro- and Micromechanical and Interfacial Elastic Properties of Composites from Ultrasonic Data, J. Acoust. Soc. Am., 92: 920-931.
46.
Chu, Y.C. and Rokhlin, S.I. (1993). Inverse Determination of Fiber-Matrix Interphase Properties in Composites from Ultrasonic Data, Ultrasonic Characterization and Mechanics of Interfaces , 117: 113-124.
47.
Chu, Y.C. and Rokhlin, S.I. (1994). Fiber-Matrix Interphase Characterization in Composites Using Ultrasonic Velocity Data, J. Appl. Phys., 76(7): 4121-4129.
48.
Chu, Y.C. and Rokhlin, S.I. (1995). Determination of Fiber-Matrix Interphase Moduli from Experimental Moduli of Composites with Multi-Layered Fibers, Mechanics of Materials, 21(3): 191-215.
49.
Balasubramaniam, K., Issa, C. and Ji , Y. (1994). Analysis of a Multi-Layered Anisotropic Model for Ultrasonic Evaluation of Adhesively Bonded Composite Structures, Review of Progress in Quantitative Nondestructive Evaluation, 13: 1555-1562.
50.
Shindo, Y., Datta, S.K. and Nozaki, H. (1995). Effect of Interface Layers on Elastic Wave Propagation in a Metal Matrix Composite Reinforced by Particles, ASME J. Appl. Mech., 62(1): 178-185.
51.
Sato, H. and Shindo, Y. (1999). Diffractions of Elastic Waves by a Circular Inclusion with a Nonhomogeneous Interface Layer and Dynamic Stress Concentrations, Theoretical and Applied Mechanics, 48: 81-94.
52.
Wang, Y., Ning, W. and Ou, X. (1995). Ultrasonic Wave Scattering in a Fiber-Reinforced Composite, Shengxue Xuebao/Acta Acustica, 20(4): 264-270.
53.
Shindo, Y. and Niwa, N. (1996). Scattering of Antiplane Shear Waves in a Fiber-reinforced Composite Medium with Interfacial Layers, Acta Mechanica, 117(1-4): 181-190.
54.
Huang, W., Rokhlin, S.I. and Wang, Y.J. (1997). Analysis of Different Boundary Condition Models for Study of Wave Scattering from Fiber-Matrix Interphases, J. Acoust. Soc. Am., 101(4): 2031-2042.
55.
Nozaki, H. and Shindo, Y. (1998). Effect of Interface Layers on Elastic Wave Propagation in a Fiber-Reinforced Metal-Matrix Composite, International Journal of Engineering Science, 36(4): 383-394.
56.
Liu, W. and Kriz, R.D. (1999). Axial Shear Waves in Fiber-Reinforced Composites with Multiple Interfacial Layers between Fiber Core and Matrix, Mechanics of Materials, 31: 117-129.
57.
Sato, H. and Shindo, Y. (2001). Multiple Scattering of Plane Elastic Waves in a Fiber-Reinforced Composite Medium with Graded Interracial Layers, International Journal of Solids and Structures, 38(15): 2549-2571.
58.
Li, F., Hu, C. and Huang, W. (2002). Scattering of Elastic waves in an Elastic Matrix Containing an Inclusion with Interfaces, Acta Mechanica Solida Sinica, 15(3): 270-276.
59.
Wei, P.J. and Huang, Z.P. (2004). Dynamic Effective Properties of the Particle-Reinforced Composites with the Viscoelastic Interphase, Int. J. Solids Struct., 41(24-25): 6993-7007.
60.
Havriliak, S. and Negami, S. (1966). A Complex Plane Analysis of α-Dispersions in Some Polymer Systems, in Transitions and Relaxations in Polymers, J. Polymer Sci. Part C, 14: 99-117.
61.
Hartman, B., Lee, G.F. and Lee, J.D. (1994). Loss Factor Height and Width Limits for Polymer Relaxations, J. Acoust. Soc. Am., 95(1): 226-233.
62.
Finegan, I.C. and Gibson, R.F. (1999). Recent Research on Enhancement of Damping in Polymer Composites, Composite Structures , 44(2-3): 89-98.
63.
Finegan, I.C. and Gibson, R.F. (2000). Analytical Modeling of Damping at Micromechanical Level in Polymer Composites Reinforced with Coated Fibers, Composites Science and Technology, 60(7): 1077-1084.
64.
Fisher, F.T. and Brinson, L.C. (2001). Viscoelastic Interphases in Polymer-matrix Composites: Theoretical Models and Finite-element Analysis , Composites Science and Technology, 61(5): 731-748.
65.
Gyekenyesi, A.L. , Morscher, G.N. and Cosgriff, L.M. (2006). In Situ Monitoring of Damage in SiC/SiC Composites Using Acousto-ultrasonics , Composites: Part B, 37: 47-53.
66.
Williams, J.H. and Nagem, R. (1989). Energy in Elastic Fiber Embedded in Elastic Matrix Containing Incident SH Wave, NASA Contractor Report, 4205.
67.
Vary, A. (1991). Acousto-Ultrasonics: Retrospective Exhortation with Bibliography, Materials Evaluation, 49: 581.
68.
Kautz, H.E. (1998). Noncontact Acousto-Ultrasonics for Material Characterization , Nasa Technical Memorandom208410.
69.
Liu, T. , Kitipornchai, S. and Veidt, M. (2001). Analysis of Acousto-Ultrasonic Characteristics for Contact-type Transducers Coupled to Composite Laminated Plates, International Journal of Mechanical Sciences, 43: 1441-1456.
70.
Hasheminejad, S.M. and Miri, A.K. (2006). Effect of Inter-fibre Distance on Energy Transfer in Unidirectional Composites Containing Ultrasonic Waves, Advanced Composite Letters, 15(5): 157-166.
71.
Srivastava, V.K. (1995). Acousto-ultrasonic Evaluation of Interface Bond Strength of Coated Glass Fibre-Reinforced Epoxy Resin Composites, Composite Structures, 30(3): 281-285.
72.
Goglio, L. and Rossetto, M. (1999). Ultrasonic Testing of Adhesive Bonds of Thin Metal Sheets, NDT&E International, 32: 323-331.
73.
Achenbach, J.D. (1976). Wave Propagation in Elastic Solids, North-Holland, New York .
74.
Christensen, R.M. (1971). Theory of Viscoelasticity: An Introduction Academic, New York.
75.
Willis, R.L. , Wu, L. and Berthelot, Y.H. (2001). Determination of the Complex Young's and Shear Dynamic Moduli of Viscoelastic Materials, J. Acoust. Soc. Am., 109(2): 1-11.
76.
Jarzynski, J. (1990). Mechanisms of Sound Attenuation in Materials, In: Cosaro, R.D. and Sperling, L.H. (eds), Sound and Vibration Damping with Polymers, pp. 167-207, American Chemical Society, Washington, DC.
77.
Vollmann, J. and Dual, J. (1997). High-Resolution Analysis of the Complex Wave Spectrum in a Cylindrical Shell Containing a Viscoelastic Medium, Part I. Theory and Numerical Results, J. Acoust. Soc. Am., 102(2): 896-908.
78.
Mitri, F.G. , Fellah, Z.E.A. and Chapelon , J.Y. (2004). Acoustic Backscattering form Function of Absorbing Cylinder Targets , J. Acoust. Soc. Am., 115: 1411-1413.
79.
Mitri, F.G. (2005). Frequency Dependence of the Acoustic Radiation Force Acting on Absorbing Cylindrical Shells, Ultrasonics, 43(4): 271-277.
80.
Mitri, F.G. (2005). Acoustic Radiation Force Acting on Elastic and Viscoelastic Spherical Shells Placed in a Plane Standing Wave Field, Ultrasonics, 43(8): 681-691.
81.
Mitri, F.G. (2005). Radiation Force Acting on an Absorbing Cylinder Placed in an Incident Plane Progressive Acoustic Field, J. Sound Vib., 284: 494-502.
82.
Hasheminejad, S.M. and Safari, N. (2005). Acoustic Scattering from Viscoelastically Coated Spheres and Cylinders in Viscous fluids, J. Sound Vib., 280(1-2): 101-125.
83.
Kim, J.F. (2003). Extinction of Elastic Wave Energy Due to Scattering in a Viscoelastic Medium, Int. J. Solids Struct., 40: 4319-4329.
84.
Abramowitz, M. and Stegun, I.A. (1964). Handbook of Mathematical Functions, National Bureau of Standards, Washington, DC.
85.
Datta, S.K., O'Leary, P.M. and Shah, A.H. (1985). Three-Dimensional Dynamic Response of Buried Pipelines to Incident Longitudinal and Shear Waves, ASME J. Appl. Mech. , 52: 919-926.
