Comments on the ultrasonic estimation of the viscoelastic properties of anisotropic materials

For the numerical prediction of waves propagation in composite materials, it is necessary to estimate the mechanical properties in the relevant frequency domain. In the past [Hosten B, Deschamps M, Tittmann BR. Inhomogeneous wave generation and propagation in lossy anisotropic solids. Application to the viscoelastic characterization of composite materials. J Acoust Soc Am 1987:82(5):1763-70; Castaings M, Hosten B, Kundu T. Inversion of ultrasonic, plane-wave transmission data in composite plates to infer viscoelastic material properties. NDT&E Int 2000;33(6):377-92], ultrasonic methods were conceived to measure the viscoelastic anisotropic properties of composites made of polymeric matrix and long fibers (glass, carbon,...). The difficulty to measure many (5, 7 or 9) complex stiffness moduli for orthotropic materials leads to large uncertainties in the measurements of their imaginary parts. This paper presents a simplification of these procedures applied to polymers and reinforced polymers with long fibers. For isotropic materials, the experimental observations show that the imaginary part of any complex stiffness is almost a constant proportion of the real part whatever the modulus is. This indicates that both longitudinal or shear bulk modes have the same amount of attenuation per wavelength. In the more general case of orthotropic materials, many stiffness moduli present the same characteristic, and the benefit is significant since the same percentage may be affected to the imaginary parts of these moduli. Then the measurement procedures can be simplified. Results for isotropic homogeneous polymer and anisotropic polymer/glass fibers composites will be presented to corroborate this experimental observation and simplification. It will be shown that taking into account the attenuation measurement uncertainties, this hypothesis is fully justified. (c) 2008 Elsevier Ltd. All rights reserved.