Dynamic effective elastic modulus of polymer matrix composites with dense piezoelectric nano-fibers considering surface/interface effect

Based on effective field method,the dynamic effective elastic modulus of polymer matrix composites embedded with dense piezoelectric nano-fibers is obtained,and the interacting effect of piezoelectric surfaces/interfaces around the nano-fibers is considered.The multiple scattering effects of harmonic anti-plane shear waves between the piezoelectric nano-fibers with surface/interface are averaged by effective field method.To analyze the interacting results among the random nano-fibers,the problem of two typical piezoelectric nano-fibers is introduced by employing the addition theorem of Bessel functions.Through numerical calculations,the influence of the distance between the randomly distributed piezoelectric nano-fibers under different surface/interface parameters is analyzed.The effect of piezoelectric property of surface/interface on the effective shear modulus under different volume fractions is also examined.Comparison with the simplified cases is given to validate this dynamic electro-elastic model.     

Kink instability of a highly deformable elastic cylinder

When a soft elastic cylinder is bent beyond a critical radius of curvature, a sharp fold in the form of a kink appears catastrophically at its compressed side while the tensile side remains smooth. The critical radius increases linearly with the diameter of the cylinder but remains independent of its material properties such as modulus; the maximum deflection at the location of the kink depends on both the material and geometric properties of the cylinder. The catastrophic dynamics of evolution of the kink depicts propagation of a shear wave from the location of the kink towards the edges signifying that kinking is an elastic response of the material which results in extreme localization of curvature. We have rationalized this phenomenon in the light of the classical Euler's buckling instability in slender elastic rods.     

Investigation of Lamb elastic waves in anisotropic multilayered composites applying the Green’s matrix

This article presents a numerical study of dispersion characteristics of some symmetric and antisymmetric composites modelled as multilayered packets of layers with arbitrary anisotropy of each layer. The authors introduce a subsidiary boundary problem of three-dimensional elasticity theory for the system of partial differential equations describing the harmonic oscillations of the composite caused by a surface load. The problem reduces to a boundary problem for ordinary differential equations by employing the Fourier transform. An algorithm of constructing the Fourier transform of the Green’s matrix of the given boundary problem is presented. The wave numbers of Lamb waves propagating in composites, their phase velocity surfaces and group wave surfaces are presented through the poles of the transform of the Green’s matrix. The authors obtain the dispersion curves for different directions and frequencies and investigate the dispersion curves and surfaces of wave numbers, phase velocities and group wave surfaces for various composites. The numerical results are then compared with the results obtained by applying other methods.     

Highly filled composites with thermoplastic elastomers matrix

The mechanical and Theological properties of blends based on commercial types of thermoplastic elastomers (TPEs) Finaprene with polystyrene and ethylene-vinylacetate copolymer, used as suitable materials to produce highly filled composites with magnetically hard fillers, have been investigated. The influence of a 90% to 93% filler content and the morphology of the fillers on mechanical, Theological, and magnetic properties of composites is discussed. The influence of changes of other technological parameters, such as type of treatment of the fillers and type of mixer, on properties of composites has been studied.     

Anomalous elastic behaviour of Bi-Pb-Ag composites

Bi-Pb and Bi-Pb-Ag superconducting composites have been prepared by the solid state reaction method. After the usual characterization, ultrasonic longitudinal velocity and attenuation studies have been undertaken over a temperature range 80–300 K by the pulse transmission technique. In contrast to normal solids, the ultrasonic velocities of both the samples in the temperature range 200-100 K are found to decrease with decreasing temperature (softening), followed by a velocity maximum. The samples are also found to exhibit longitudinal attenuation peaks at TEMPERATURES = 260, 160 and 120 K. An attempt has also been made to verify whether the Wachtman's equations can theoretically explain the low-temperature behaviour of the Young's modulus of these materials. A qualitative explanation for both the phenomena of softening of velocity as well as the occurrence of attenuation peaks is given.     

Effective elastic properties of two-phase composites

Expressions for the effective elastic constants of two-phase composites in the form of series obtained with Fourier transforms have been analyzed. In certain cases, such series are shown to be fully summed up; as a result, one can directly obtain exact expressions for the effective bulk modulus of a composite. It is found that the symmetry of the coefficients in series for the shear modulus and Young’s modulus and the corresponding reciprocal quantities can be used to relate these series to each other. Thus, all well-known exact relations for the effective elastic constants can be derived. A set of equations is proposed to compute the effective constants of a two-dimensional isotropic symmetrical composite with arbitrary properties of its phases.     

Determination of transmission and insertion loss for multi-inlet mufflers using impedance matrix and superposition approaches with comparisons

This paper details how transmission and insertion loss can be defined for the multi-inlet case. Two different procedures are used for calculations and are compared against one another. The first is an impedance matrix method that has been proposed in the past and is especially suitable for deterministic approaches like the boundary element method. The other is a superposition method that does not require assembling or inverting a matrix. Though each method can be extended to the n-inlet situation, the superposition approach is mathematically simpler but requires the source impedance to be known a priori. Transmission and insertion loss can be determined using either method, and results using both are shown to be equivalent. The methods are demonstrated and compared for a two-inlet one-outlet expansion chamber. After which, the superposition method is used to determine the insertion loss for a two-inlet one-outlet generator set muffler experimentally.     

Effective elastic properties of piezoelectric composites with radially polarized cylinders

Effective elastic properties of piezoelectric composites containing an infinitely long, radially polarized cylinder embedded in an isotropic non-piezoelectric matrix are theoretically investigated under an external strain field. Analytical solutions of elastic displacement and electric potentials are exactly derived, and the effective elastic responses are formulated in the dilute limit. Meanwhile, a vanishing piezoelectric response mechanism is revealed in the piezoelectric composite containing radially polarized cylinders. Furthermore, it is shown that the effective elastic properties can be enhanced (or reduced) due to the increase of the piezoelectric (or dielectric) constants of the cylinders.     

Adiabatic and isothermal elastic constants for highly anharmonic crystals

The mass operator of the phonon Green function for a highly anharmonic crystal in the ladder approximation is derived. In order to calculate the mass operator in the collision-dominated regime it is necessary to solve the Boltzmann-like equations. These solutions allow us to find the thermal conductivity coefficient and to prove that the thermodynamic relation between adiabatic and isothermal elastic constants is satisfied.     

An energy criterion for the initiation of interface failure ahead of a matrix crack in brittle matrix composites

The mechanism of interfacial failure occurring as a consequence of the stress concentration induced by a matrix crack located in the vicinity of the interface is analysed. For this purpose, an asymptotic analysis is carried out to assess the competition between the propagation of the matrix crack towards the interface and the nucleation of an interfacial debond. An energetic approach provides a necessary condition comparing the ratio of the interfacial toughness over the matrix toughness to a critical value depending on the elastic mismatch between the fibre and the matrix and the ratio of the interfacial nucleation length over the width of the matrix ligament. Presented results show that the interfacial debonding is enhanced if the matrix is softer than the fibre. Further, a modified condition which does not involve the crack increment ratio is established if the matrix crack lies in the stiffest material.     

Mechanical behaviour of ceramic matrix composites

Thermomechanical ceramics have interesting properties: mainly high hardness, high wear resistance, good chemical resistance, good mechanical strength at high temperatures and generally low thermal conductivity. But, the engineering use of ceramics as structural parts is at the moment limited by their inherent brittleness. The toughness values of ceramics are between about to 5 MPa √m whereas the toughness values of metals are much higher (from 20 to 200 MPa √m). To avoid this brittleness, composite ceramics have to be used. Two types of composite materials can be developed: particle-reinforced composites and fiber-reinforced composites. In this paper, some examples of reinforcement of ceramics are presented. Two cases will be developed: second-phase reinforcement with zirconia particles or other particles, and the composites reinforced by fibers or whiskers.     

Mechanical properties of metal matrix composites

The concept of reinforcing a material by the use of a fiber is not a new one. The Egyptian brick layer employed the same principle more than three thousand years ago when straw was incorporated into the bricks. More recent examples of fiber reinforced composites are steel-reinforced concrete, nylon and rayon cord reinforced tires, and fiberglass reinforced plastics. In the last several years considerable progress has been made on new composite structures particularly utilizing boron (on tungsten substrate) fibers in various matrices. Many of these advances have been reviewed recently by P. M. Sinclair¹ and by Alexander, Shaver, and Withers.² An excellent earlier survey is available by Rauch Sutton, and McCreight.³ Boron-reinforced epoxy composites are being fabricated and tested as jet engine components, fuselage components, and even as a complete aircraft wing because of the tremendous gain in experimentally demonstrated properties such as modulus, strength, and fatigue resistance, particularly on a weight normalized (e.g., strength/density) basis. Other than glass/epoxy and boron/ epoxy composites and perhaps boron/aluminum, the systems now under study are in the early stages of research and development. These include other boron/metal composites, graphite/polymer, graphite/metal, graphite/graphite, alumina/metal, and aligned eutectic (directionally, solidified) combinations. As Sinclair points out, designers are wary about filamentary composites because “there is little background information and scant experience.”     

Bending wave propagation of carbon nanotubes in a bi-parameter elastic matrix

This article studies transverse waves propagating in carbon nanotubes (CNTs) embedded in a surrounding medium. The CNTs are modeled as a nonlocal elastic beam, whereas the surrounding medium is modeled as a bi-parameter elastic medium. When taking into account the effect of rotary inertia of cross-section, a governing equation is acquired. A comparison of wave speeds using the Rayleigh and Euler-Bernoulli theories of beams with the results of molecular dynamics simulation indicates that the nonlocal Rayleigh beam model is more adequate to describe flexural waves in CNTs than the nonlocal Euler-Bernoulli model. The influences of the surrounding medium and rotary inertia on the phase speed for single-walled and double-walled CNTs are analyzed. Obtained results turn out that the surrounding medium plays a dominant role for lower wave numbers, while rotary inertia strongly affects the phase speed for higher wave numbers.     

Viscoelasticity of a polymer matrix and fracture of heat-resistant fiber composites

This paper reports on the results of investigations into the general regularities of deformation and fracture of fiber composite materials based on new heat-resistant polymer binders. Fiber composites based on these binders can find wide application in various fields of engineering. It is established that an increase in the loss modulus of the polymer matrix decreases the probability of formation of a brittle crack in the matrix at the fiber break and increases the time interval between breakages of adjacent fibers. This leads to retardation of the correlated breakage of the fibers in fiber composite materials under loading, i.e., to an increase in their strength and fracture toughness. The inference is made that the matrix of high-strength heat-resistant fiber composites with a high fracture toughness should possess not only a high elasticity (this has long been known) but also good dissipative properties over the entire temperature range of operation.     

Hologram multiplexing in a highly photosensitive photopolymerizable material in a sol-gel matrix

In this paper, we present a photopolymerizable material in a sol-gel matrix suitable for recording a large number of multiplexed diffraction gratings with low total exposure energy. The matrix of this material is an inorganic porous silica glass, a material that does not shrink when radical photopolymerization is initiated. The photosensitive component is based on acrylamide, N,N′-methylenebisacrylamide, triethanolamine and yellow eosine as a photoinitiator. In the reported study, 50 holograms were angularly multiplexed with diffraction efficiencies between 0.1 and 1.9% resulting in a dynamic range of M/# = 3.9. The total exposure was 4.5 mJ/cm² and the energy used in recording each hologram was 95 μJ/cm². This indicates a very high sensitivity for this material in the range of 3.3 to 15.5 cm/mJ. Due to this good holographic performance, the material is suitable for holographic data storage applications.