On the effective thermal conductivity of multiphase composites

While several micromechanical models have been developed today in the literature for two-phase media, the extent of their applicability to multiphase materials need yet to be investigated. The present paper studies the effective thermal conductivity of multicomponent composites, and concentrates on two methods: (a) the Mori-Tanaka model, (b) The generalized self-consistent scheme. The Mori-Tanaka method of back-stress previously developed in the context of elasticity of composites is applied here to the conduction problem. The generalized self-consistent scheme, based on a particle-matrix embedding in the effective medium, is studied in this paper in the context of multicomponent media and two variations of this method distinctly different in their imbedding procedure are proposed.Numerical results are given for three-phase composites illustrating and comparing the proposed methods.

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Resumé Plusieurs modéles de micromécanique existent aujoud'hui dans la litérature des matériaux á deux phases. L'applicabilité de ces modéles aux matériaux á multi-phases nécessite d'autre part d'être examinée. Ce travail étudie la conductivité thermale des matériaux á multi-phases et se concentre sur deux méthodes: a) le modéle de Mori-Tanaka b) la méthode auto-consistante généralisée. La méthode de Mori-Tanaka, développée auparavant dans le cadre des propriétés mécaniques des composites est appliquée ici au probléme de conduction. La méthode autoconsistante généralisée est étudiée dans le cadre des matériaux á multi-phases et deux alternatives de cette méthode distinctement différentes dans leur formalisme sont proposées. Pour des matériaux á trois phases on donne des resultats numériques qui illustrent et comparent les méthodes proposées.

     

Effects of defects on the effective thermal conductivity of thermal barrier coatings

It is difficult to establish structure-property relationships in thermal barrier coatings (TBCs) because of their inhomogeneous-geometry microstructures caused by defects. In the current research, the effects of pores and cracks on the effective thermal conductivity of TBCs are studied. Based on the law of the conservation of energy, mathematical formulations are proposed to indicate the relationship between defects and the effective thermal conductivity. In this approach, detailed equations are illustrated to represent the shape and size of defects on the effective thermal conductivity of TBCs. Different from traditional empirical analyses, mixture law or statistical method, for the first time, our results with the aid of finite element method (FEM) and strict analytical calculation show the influence of pore radius and crack length on effective thermal conductivity can be quantified. As an example to a typical microstructure of plasma sprayed TBCs, the effects of defects on the effective thermal conductivity of TBCs are expressed by the influence parameter, which indicating that the longest transverse crack dominates the contribution of the effective thermal conductivity along the spray direction compared with any individual defect.     

A review of the mechanical properties of isolated carbon nanotubes and carbon nanotube composites

A literature review on the prediction of Young’s modulus for carbon nanotubes, from both theoretical and experimental aspects, is presented. The discrepancies between the values of Young’s modulus reported in the literature are analyzed, and different trends of the results are discussed. The available analytical and numerical simulations for predicting the mechanical properties of carbon nanotube composites are also reviewed. A gap analysis is performed to highlight the obstacles and drawbacks of the modeling techniques and fundamental assumptions employed which should be overcome in further studies. The aspects which should be studied more accurately in modeling carbon nanotube composites are identified.     

Multiwall carbon nanotube/epoxy composites produced by a masterbatch process

A masterbatch process based on a minicalander (three-roller mill) and a vacuum dissolver was developed in order to produce multiwall carbon nanotube/epoxy composites with loading fractions of 0.5, 1.0, and 2.0 wt.%. TEM and SEM analyses were performed to investigate the dispersion results. A contrast imaging in the SEM backscattering mode revealed a homogeneous distribution of carbon nanotubes in the whole volume of the material. Furthermore, an interesting correlation was found to exist between the network structure formed by the nanotubes in the epoxy matrix and the appearance of fracture surface of the nanocomposites. Furthermore, the nanocomposites exhibited an electrical conductivity in the regime of some 10⁻² S/m. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 5, pp. 567–582, September–October, 2006.     

The effective conductivity of an infinitely interchangeable mixture

We are concerned with the estimation of the effective electrical conductivity of random heterogenous materials. The purpose of this paper is to discuss a property of “statistical symmetry” verified by the symmetric cell materials of Miller. This property will be referred to as infinite interchangeability. The usual way to approach cell materials is through n-point correlation functions. The property of infinite interchangebility permits us to approach cell materials from a completely different point of view. Our main result is a simple algorithm, based on this symmetry property, for computing any coefficient of the perturbation expansion in terms of information from the dilute limit. Specifically, knowledge of the coefficients of the expansion in powers of the volume fraction up to order r allows for computation of the perturbation expansion coefficients up to order (2r + 1). This result, which was previously known for r = 2 in the isotropic case and for r = 1 in the anisotropic case, can also be obtained from the standard correlation function approach, as pointed out by Milton.     

The effective conductivity of a randomly inhomogeneous medium

Using a representation of the solution to the diffusion equation in a randomly inhomogeneous medium in the form of a Feynman path integral an explicit expression is obtained for the effective conductivity in a space of arbitrary dimension. A calculation of the path integral only turns out to be possible in the case of a large-scale limit. In particular, it is shown that in the three-dimensional case the expression for the effective conductivity does not admit of an expansion in terms of the conductivity variance. This indicates that the use of standard perturbation theory in the form of an expansion in terms of the conductivity fluctuations is incorrect.     

Analytical and numerical techniques for predicting the interfacial stresses of wavy carbon nanotube/polymer composites

By introducing a new simplified 3D representative volume element for wavy carbon nanotubes, an analytical model is developed to study the stress transfer in single-walled carbon nanotube-reinforced polymer composites. Based on the pull-out modeling technique, the effects of waviness, aspect ratio, and Poisson ratio on the axial and interfacial shear stresses are analyzed in detail. The results of the present analytical model are in a good agreement with corresponding results for straight nanotubes. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 2, pp. 299-306, March-April, 2009.     

Mathematical analysis of carbon nanotube model

In this paper, we present a recently developed mathematical model for a short double-wall carbon nanotube. The model is governed by a system of two coupled hyperbolic equations and is reduced to an evolution equation. This equation defines a dissipative semi-group. We show that the semi-group generator is an unbounded nonselfadjoint operator with compact resolvent. Moreover, this operator is a relatively compact perturbation of a certain selfadjoint operator.     

The effective conductivity equation for a highly heterogeneous periodic medium

We consider the homogenization of a conductivity equation for a medium made up of a set ${F_\varepsilon}$ ( ${\varepsilon}$ being the size of the period of the medium) of highly conductive vertical fibers surrounded by another material (the matrix) assumed to be a poor conductor. The conductivity coefficients in the fibers behave as ${\frac{1}{\varepsilon^2}}$ while whose of the matrix behave as ${\varepsilon^2}$ . We show that the homogenized problem consists of an equality of the kind u(x) = m(x) f (x) where u denotes the macroscopic temperature, f the source term and m(x) a coefficient given by solving some cell equation.     

An inverse problem in estimating simultaneously the effective thermal conductivity and volumetric heat capacity of biological tissue

An inverse problem utilizing the Levenberg–Marquardt method (LMM) is applied in this study to determine simultaneously the unknown spatial-dependent effective thermal conductivity and volumetric heat capacity for a biological tissue based on temperature measurements. The accuracy of this inverse problem is examined by using the simulated exact and inexact temperature measurements in the numerical experiments. A statistical analysis is performed to obtain the 99% confidence bounds for the estimated thermal properties. Results show that good estimation on the spatial-dependent thermal conductivity and volumetric heat capacity can be obtained using the present algorithm for the test cases considered in this study.     

Thermal conductivity of unidirectionally reinforced hybrid composites

Conclusion The thermal conductivity of organic-glass, organic-carbon, and carbon-glass plastic in dependence on the volumetric content of organic, glass, and carbon fibers was experimentally investigated. The solution for transverse thermal conductivity of unidirectional hybrid composite, obtained in [8] by generalizing the method of self-congruence to the case of a triphase model, is in satisfactory agreement with the experimental data.Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 817–822, September–October, 1990.     

Representations for the conductivity functions of multicomponent composites

The effective conductivity σ* of a multicomponent composite material is considered. Integral representations for σ* treated as a holomorphic function on a polydisk with values in a half-plane are analyzed. A representation for σ* is introduced which is symmetric in the component conductivities and for which the moments of the positive measure in the integral are directly related to the coefficients in a perturbation expansion of σ* around a homogeneous medium. This second feature, which is important for obtaining bounds on σ*, was previously available only in the two-component case. In addition, a bound valid for any holomorphic function of the above type is proven.