# Stress-wave displacement polarizations and aftenuation in unidirectional composites: Theory and experiment

## Abstract

The wave propagation mechanism of changes in displacement polarizations was studied in unidirectional graphite/epoxy composite materials. Change in Displacements can be large enough to cause a transition in the mode or displacement polarizations from longitudinal to transverse. These unusual mode transitions are a result of the peculiar elastic anisotropy observed in only a few crystals and unidirectional graphite/epoxy composities at high-fiber volume fractions Theoretical calculation of these mode transitions were compared with experimental measurements Mode transitions occur when the wave vector orientation is varied from 51.9° to 74.4° in unidirectional samples of T300/5208 graphite/epoxy composite with a 0.6°-fiber volume fraction. Energy flux deviation and particle displacement directions and amplitudes also were compared with theory. To show this mode transition, an attenuation study was performed. The attenuation coefficient, measured in units of reciprocal time, does not appear to depend on the wave vector orientation and the wave type (quasi-transverse and quasi-longitudinal waves) at 5-MHZ frequency. But the attenuation coefficient, expressed in units of reciprocal length, does depend on the wave type and the wave vector orientation because the wave velocity is included in the calculation of this coefficient. Previous studies have focused on how anisotropy and attenuation influence the stress wave speed (eigenvalues), but in this study we focused more on how the same parameters influence the displacement polarizations (eigenvectors) of the same propagating waves. Because eigenvalues and their corresponding eigenvectors are both solutions of the same eigenvalue problem, more attention should be given to measurement of the eigenvectors.

## Keywords

Mode Transition Particle Displacement Unidirectional Composite Displacement Polarization Displacement Deviation## List of Symbols

*E*_{i}Young’s moduli

*G*_{ij}shear moduli

*v*_{ij}Poisson’s ratios

*C*_{ij}elastic-stiffness coefficients

*C*_{ijkl}fourth-rank elastic-stiffness tensor

*n*_{j}normalized wave vector (vector perpendicular to the plane wave)

*p*mass density

- δ
_{ij} Kronecker delta function

*v*phase velocity

*w*_{i}normalized particle displacement direction

*J*_{i}energy flux vector

- σ
_{ij} stress tensor

*U*_{j}particle displacement velocity

*U*_{I}incident wave of particle displacement amplitude

*U*_{QL}quasi-longitudinal wave of particle displacement amplitude

*U*_{QT}quasi-transverse wave of particle displacement amplitude

*U*_{T}pure transverse of particle displacement amplitude

- α
_{t} attenuation coefficients in

*s*^{−1}- α
_{l} attenuation coefficients in l

^{−1}*A*_{0}maximum amplitude

*Q*_{LL}(θ)longitudinal component of quais-longitudinal wave at θ

*Q*_{LT}(θ)transverse component of quasi-longitudinal wave at θ

*Q*_{TL}(θ)longitudinal component of quasi-transverse wave at θ

*Q*_{TT}(θ)transverse component of quasi-transverse wave at θ

- θ
_{mt} wave vector orientation corresponding to mode transition

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