Elastic wave propagation in filamentary composite materials (original) (raw)

Elastic waves in a fiber-reinforced composite

Journal of the Mechanics and Physics of Solids, 1974

THE PROPAGATION of time-harmonic elastic waves in a fiber-reinforced composite is studied. The circular fibers are assumed to be parallel to each other and randomly distributed with a statistically uniform distribution. The direction of propagation and the associated particle motion are considered to be normal to the fibers. It is shown that the average waves in the composite separate into compressional and shear types. General formulae for the complex wave number giving the phase velocity and the damping are obtained. It is shown that these formulae lead to the Hashin-Rosen expressions for the transverse bulk modulus and the lower bound for the transverse rigidity, if the correlation in the positions of the fibers can be ignored. The correlation terms, for exponential correlation, are shown to have a significant effect on the damping property of the composite, especially at high frequencies and concentrations.

Bulk waves and dynamical behaviour in elastic solids reinforced by two families of strong fibres

Journal of Engineering Mathematics, 2014

In the study of wave propagation, bulk waves exist in infinite homogeneous bodies and propagate indefinitely without being interrupted by boundaries or interfaces. Such waves may be decomposed into finite plane waves propagating along arbitrary directions of the solid. The properties of these waves are determined by the dependence between the propagation direction and the constitutive properties of media. Three types of such waves may be distinguished in connection to the three displacement vectors which determine an acoustic polarization. These three polarization vectors are mutually orthogonal, but in most cases they are neither perpendicular nor parallel to the propagation direction. There are a number of papers and books describing wave front surfaces as a consequence of the study of the acoustic tensor, which, in fact, represents the propagation condition of such waves. The surfaces associated with wave front surfaces are slowness surfaces, with slowness defined by the inverse of the wave front speeds, and energy flow surfaces, also known as group velocity surfaces. Here slowness surfaces are studied analytically and numerically to obtain information about wave propagation in arbitrary directions. The degree of wave surface deviation depends upon degrees of anisotropy, and may give valuable information about dynamic deformations. The materials, used in the present analysis, are fibre-reinforced materials with two families of continuous elastic fibres. Since fibres are much stronger than a matrix, anisotropic properties are emphasized. Coordinate-free constitutive relations give the possibility of considering fibres embedded in such materials as extensible or inextensible. Such an approach gives the opportunity to follow behaviour directly considering both the geometry and the stiffness of the fibres. The material considered here is reinforced by two families of mechanically equivalent fibres and, therefore, behaves like orthotropic, having axes of symmetry along bisectors of the fibre directions and along the normal to the plane tangent to the fibres. Such a material has nine independent material constants. When constraints of inextensibility are imposed on the fibres, it leads to the so-called ideal fibre-reinforced material, which may be obtained from materials with extensible fibres in a limiting process. In order to follow the influence of fibre direction on the mechanical properties, constitutive relations are modelled as a function of the fibre directions in each point of the continuous media. An often-used representation of such materials is an epoxy resincarbon fibre composite whose material constants, for materials reinforced by one family of fibres, are determined using ultrasound methods. Here we consider the dynamical behaviour of the material reinforced by two families of

On the Influence of Initial Stresses on the Velocity of Elastic Waves in Composites

Computation

The paper is devoted to the problem of propagation of elastic waves in composites with initial stresses. We suppose initial stresses are well within the elastic regime. We deal with the long-wave case and use the asymptotic homogenization technique based on the two-scale asymptotic approach. The main problem lies in solving the local (cell) problem, i.e., boundary value problem on a periodically repeating fragment of a composite. In general, the local problem cannot be solved explicitly. In our work, it is obtained for any initial stresses formulas, which is convenient for solving by standard codes. An analytical solution is obtained for small initial stresses. Asymptotic expansions used a small parameter characterizing the smallness of the initial stresses. In the zero approximation, composites without initial stresses are considered; the first approximation takes into account their influence on waves propagation. Two particular cases are considered in detail: laminated media and f...

Propagation of elastic waves in one-dimensional composites

Materials Science and Engineering: A, 1989

Consideration has been given to piezoelectric composite plates formed by a series of alternating strips of piezoelectric material and epoxy. By the use of a model that takes into consideration the transmittivity and reflectivity coefficient of plate modes at the boundary between different media, dispersion velocity curves of such plates have been deduced and compared with the experimental frequen O' response. Symmetry conditions and the fact that they give rise to stop band and passband frequency edges are discussed.

Waves in approximately constrained materials and applications to fiber-reinforced composites

Wave Motion, 2002

Wave propagation in approximately constrained elastic homogeneous materials is investigated by a suitable ray method; propagation speeds and evolution equations are determined and a comparison is provided by the results of other authors. The theory is applied to isotropic and anisotropic materials and to a model for unidirectionally fiber-reinforced composites.

Wave propagation in viscoelastic composites reinforced by orthogonal fibers

Journal of Sound and Vibration, 1977

A two-dimensional lattice dynamics model for a viscoelastic composite reinforced with two setsof orthogonallyinterlockingfibers is given, and thepropagation of planeharmonic waves in such a medium is investigated. The composite considered consists of two sets of orthogonal equivalent elastic fibers and a viscoelastic matrix. The dispersion relations of waves propagating in the medium are studied and various special cases are investigated.

Elastic wave propagation in composite media

GEOPHYSICS, 1992

Numerical simulation can be a useful tool for studying composite media. It is not limited by weak or single scattering assumptions, and it requires only constituent properties and an arrangement of constituents as input. For solid/solid media with octagonal cylindrical inclusions and for typical values of constituent moduli, composite moduli are accurately predicted by twodimensional (2-D) analogs of Kuster-Toksoz formulas. For solid/solid media there is a small but discernable difference between responses of square and those of octagonal inclusions. Coherent reflections are produced by a coherent wave incident at a change in concentration of inclusions, if the contrast between material properties of the matrix and those of the inclusions is sufficient to produce significant scattering, and if the size of scatterers is sufficiently small and their concentration sufficiently large so there is constructive interference between waves originating at adjacent scatterers.

A continuum mixture theory of wave propagation in laminated and fiber reinforced composites

International Journal of Solids and Structures, 1973

A binary mixture theory is developed for wave guide-type propagation in laminated and undirectional fibrous composites. In particular, a rational construction of both mixture interaction and constitutive relations is given. The resulting theory contains microstructure. The domain of validity of the mixture theory is determined by comparison of the phase velocity spectrum with exact and/or experimental results. The utility of the model is demonstrated for both laminated and fibrous composites by correlating theoretical and experimental transient pulse data on boron-carbon phenolic and Thornelcarbon phenolic laminates, and uni-directional fibrous quartz phenolic.

Study on the Propagation of Stress Waves in Natural Fiber Composite Strips

Journal of Composites Science

The propagation of Lamb waves within the structure of natural fiber reinforced composite strips is investigated using a semi-analytical solution and a time domain spectral finite element numerical method. The need to monitor the structural health of natural fiber reinforced composites is becoming greater, as these sustainable composites are being increasingly used in various industrial applications in automotive and marine structures. Three different types of flax fiber composites were studied and the fundamental wave modes were excited on the structure. Both methods under consideration were able to capture the symmetric and antisymmetric wave modes for all the material configurations. Especially the complex nature of a hybrid flax/glass fiber composite was studied and results were very promising for future damage investigation. Further to this, an attempt was made to excite the hybrid strip at higher frequency and the study revealed the potential to capture all the existing wave mo...