Abstract
An ultrasonic method is proposed for the determination of the elastic constants of orthotropic solids with a laser source of ultrasound and wide-band registration of acoustic pulses. The propagation of acoustic transients in unidirectional fiber-reinforced graphite-epoxy composites is investigated. The experimental data show that the model of orthotropic solids is valid for the description of the mechanical properties of these materials. The absence of frequenc dispersion of the phase velocity in the spectral range of 1–15 MHz for every direction of propagation of ultrasound waves in the composite was confirmed. A complete set of elastic constants of unidirectional fiber-reinforced graphite-epoxy composites is calculated.
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Abbreviations
- xi :
-
principal axes of a 1D graphite-epoxy (GE) composite,i=1, 2, 3,
- x1 :
-
axis of symmetry
- L :
-
thickness of a specimen, m
- k:
-
wave vector of the acoustic wave
- v1, v2, v3 :
-
direction cosines of the wave vector
- n:
-
normal vector to the surface of a specimen
- n1 :
-
normal vector to the incidence plane (nk)
- θ:
-
incidence angle of the acoustic wave to the specimen, rad
- β:
-
refraction angle of the acoustic wave at the interface of immersion medium and compsite, rad
- α:
-
angle between the normal n1 to the incidence plane (nk) and the direction of fibers in composite x1, rad
- f :
-
frequency of the acoustic wave, Hz
- V :
-
phase velocity of the acoustic wave in the tested specimen, m/s
- V 0 :
-
phase velocity of the longitudinal acoustic wave in the immersion medium, m/s
- QL, QT, L, andT :
-
quasi-longitudinal, quasi-shear, longitudinal, and shear waves, respectively
- δϕ :
-
phase difference between the frequency harmonicsf of reference and tested signals, rad
- ρ:
-
density of a 1D GE composite, kg/m3
- C ijkl ,C αβ :
-
full and abbreviated notation of the stiffness matrix, Pa, and Γ il tensor
References
Z. Hashin, “The elastic moduli of heterogeneous materials,” J. Appl. Mech.,29, 143–151 (1962).
Z. Hashin and B. W. Rosen, “The elastic moduli of fiber-reinforced materials,” J. Appl. Mech.,31, 223–232 (1964).
Z. Hashin, “Viscoelastic fiber reinforced materials,” AIAA J.,4, 1411–1420 (1966).
W. B. Rassel, “On the effective moduli of composite materials effect of fiber length and geometry at dilute concentrations,” Z. Angew. Math. Phys.,24, 581–588 (1973).
A. H. Nayfeh and R. L. Crane, “Reflection of acoustic waves from water/composite interfaces,” J. Appl. Phys.,55, No. 3, 685–689 (1984).
E. Dielessant and D. Royet, Elastic Waves in Solid Bodies [Russian translation], Nauka, Moscow (1982).
G. I. Petrashen', Wave Propagation in Anisotropic Elastic Media [in Russian], Nauka, Leningrad (1980).
R. M. Christensen, Mechanics of Composite Materials, John Wiley & Sons, New York (1979).
B. Hosten and M. Deschamps, “Inhomogeneous wave generation and propagation in lossy anistropic solids. Application to the characterisation of viscoelastic composite materials,” J. Acoust. Soc. Amer.,82, No. 5, 1763–1770 (1987).
B. Hosten, “Reflection and transmission of acoustic plane waves on an immersed orthotropic and viscoelastic solid layer,” J. Acoust. Soc. Amer.,89, No. 6, 2745–2752 (1991).
R. D. Kriz and W. W. Stinchomb, “Elastic moduli of transversely isotropic graphite fibers and their composites,” Exp. Mech.,19, No. 1, 41–49 (1979).
S. I. Rokhlin and W. Wang, “Critical angle measurement of elastic constants in composite material,” J. Acoust. Soc. Amer.,86, No. 5, 1876–1882 (1989).
Y. C. Chu, A. D. Degtyar, and S. I. Rokhlin, “On determination of orthotropic material moduli from ultrasonic velocity data in nonsymmetry planes,” J. Acoust. Soc. Amer.,95, No. 6, 3191–3203 (1993).
Y. C. Chu and S. I. Rokhlin, “Comparative analysis of through-transmission ultrasonic bulk wave methods for phase velocity measurements in anisotropic materials,” J. Acoust. Soc. Amer.,95, No. 6, 3204–3212 (1994).
A. D. Degtyar and S. I. Rokhlin, “Absolute stress determination in orthotropic materials from angular dependences of ultrasonic velocities,” J. Appl. Phys.,78, No. 3, 1547–1556 (1995).
A. J. Every and W. Sachse, “Determination of the elastic constant anisotropic solids from acoustic-wave group-velocity measurements,” Phys. Rev. B.,42, 8196–8205 (1992).
V. E. Gusev and A. A. Karabutov, Laser Optical Acoustics [in Russian], Nauka, Moscow (1991).
A. A. Karabutov, M. P. Matrosov, N. B. Podymova, and V. A. Pyzh, “Impulse acoustic spectroscopy with a laser source of sound,” Akust. Zh.,37, No. 2, 311–323 (1991).
A. A. Karabutov, M. P. Matrosov, and N. B. Podymova, “Thermooptical generator of wide-band impulses of shear waves,” Akust. Zh.,39, No. 2, 373–375 (1993).
A. A. Karabutov, K. V. Kokonets, and N. B. Podymova, “Wide-band acoustic spectroscopy of shear waves on the basis of thermooptical source of ultrasound,” Akust. Zh.,41, No. 1, 95–100 (1995).
Additional information
International Laser Center, Lomonosov Moscow State University, Moscow, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 6, pp. 811–822, November–December, 1998.
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Karabutov, A.A., Kershtein, I.M., Pelivanov, I.M. et al. Laser ultrasonic investigation of the elastic properties of unidirectional graphite-epoxy composites. Mech Compos Mater 34, 575–582 (1998). https://doi.org/10.1007/BF02254668
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DOI: https://doi.org/10.1007/BF02254668