Composite materials made of fibers and a viscoelastic matrix, exhibit an orthotropic viscoelastic behavior that is described by a tensor with nine independent complex viscoelastic moduli. This tensor makes it possible to compute the velocity and attenuation of heterogeneous or homogeneous modes in any direction. In experiments, the immersion method of a plate shaped sample insonified by plane ultrasonic waves is used to measure this complex tensor. The liquid/solid interface generates heterogeneous quasilongitudinal and quasishear bulk modes that propagate through the plate with velocities and attenuations that depend on the frequency. In a viscoelastic material, velocity and attenuation are linked by the Kramers–Kronig relations. For heterogeneous modes, the attenuation that needs to be used is the projection of the damping vector on the wave vector. This paper shows that these relations limited to a “local” frequency band can be experimentally verified and permit one to link anisotropic velocity and attenuation dispersion of quasilongitudinal and quasishear modes only if their heterogeneous structure is taken into account. The extrapolation of the material properties determined by ultrasonic measurements, towards low frequencies, relies on this feature in combination with a model of the attenuation evolution versus frequency.

Topics
Ultrasound, Ultrasonics, Composite materials, Viscoelastic materials, Complex analysis, Liquid solid interfaces
1.
M. F.
Markham
, “
Measurement of the elastic constants of fiber composites by ultrasonics
,”
Composites
1
,
145
–
149
(
1970
).
Google Scholar
Crossref
Search ADS
 
2.
Y. C.
Chu
and
S. I.
Rokhlin
, “
Comparative analysis of through-transission ultrasonic bulk wave methods for phase velocity measurements in anisotropic materials
,”
J. Acoust. Soc. Am.
95
,
3204
–
3212
(
1994
).
Google Scholar
Crossref
Search ADS
 
3.
M. Ward, Mechanical Properties of Polymers (Wiley-Interscience, New York, 1971).
4.
M. J. P.
Musgrave
, “
On an elastodynamic classification of orthorhombic media
,”
Proc. R. Soc. London, Ser. A
374
,
401
–
429
(
1981
).
Google Scholar
 
5.
B. A. Auld, Acoustic Fields and Waves in Solids (Wiley-Interscience, New York, 1973), Vol. I.
6.
B.
Hosten
,
M.
Deschamps
, and
B. R.
Tittmann
, “
Inhomogenous wave generation and propagation in lossy anisotropic solids. Application to the viscoelastic characterization of composite materials
,”
J. Acoust. Soc. Am.
82
,
1763
–
1770
(
1987
).
Google Scholar
Crossref
Search ADS
 
7.
B.
Hosten
, “
Reflection and transmission of acoustic plane waves on an immersed orthotropic and viscoelastic solid layer
,”
J. Acoust. Soc. Am.
89
,
2745
–
2752
(
1991
).
Google Scholar
Crossref
Search ADS
 
8.
B.
Hosten
and
M.
Deschamps
, “
Génération d'ondes hétérogènes à l'interface liquide-solide viscoélastique. Approximation par des ondes inhomogènes
,”
Acustica
59
,
193
–
198
(
1986
).
Google Scholar
 
9.
S.
Baudouin
and
B.
Hosten
, “
Comparison between prediction and measurement of viscoelastic moduli in composite materials versus temperature using ultrasonic immersion technique with oil,’'
J. Acoust. Soc. Am.
102
,
3450
–
3457
(
1997
).
Google Scholar
Crossref
Search ADS
 
10.
M. O.
Donnell
,
E. T.
Jaynes
, and
J. G.
Miller
, “
Kramers-Kronig relationship between ultrasonic attenuation and phase velocity
,”
J. Acoust. Soc. Am.
69
,
696
–
701
(
1981
).
Google Scholar
Crossref
Search ADS
 
11.
B.
Hosten
and
M.
Castaings
, “
Transfer matrix of multilayered absorbing and anisotropic media. Measurements and simulations of ultrasonic wave propagation through composite 1 materials
,”
J. Acoust. Soc. Am.
94
,
1488
–
1495
(
1993
).
Google Scholar
Crossref
Search ADS
 
12.
B. F.
Pouet
and
N. J. P.
Rasolofosan
, “
Measurement of broadband intrinsic ultrasonic attenuation and dispersion in solids with laser techniques,'’
J. Acoust. Soc. Am.
93
,
1286
–
1292
(
1993
).
Google Scholar
Crossref
Search ADS
 
13.
H. A.
Huang
,
C. E.
Bakis
, and
H. T.
Hahn
, “
Prediction of ultrasonic wave attenuation in fiber reinforced composite laminates
,”
Rev. Prog. Quant. Nondestr. Eval.
13
,
1181
–
1188
(
1994
).
Google Scholar
 
14.
D.
Zhou
,
L.
Peirlinckx
, and
L. V.
Biesen
, “
Identification of parametric models for ultrasonic double transmission experiments on viscoelastic plates
,”
J. Acoust. Soc. Am.
99
,
1446
–
1458
(
1996
).
Google Scholar
Crossref
Search ADS
 
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© 1998 Acoustical Society of America.
1998
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