A micro-mechanics model for composites reinforced by regularly distributed particles with an inhomogeneous interphase

Based on the Mori–Tanaka method, a micro-mechanics model is developed to study the effective elastic properties of composites reinforced by regularly distributed particles. The spatial distribution of particles is supposed to be cube symmetric in the three-dimensional space, and the corresponding finite element method (FEM) computation has been performed through a unit cell model. Additionally, particle interaction and distribution are simultaneously taken into account by using the strain Green’s function, and the specified strain Green’s function is determined by utilizing the necessary conditions of geometric symmetry. In order to analyze particle size effect on the effective properties of composites, the Double-inclusion configuration and related theory are introduced to describe the role of the interphase between the matrix and particles. Finally, the overall elastic properties of the composite with regularly distributed particles are described by three independent elastic constants expressed in the explicit form, and the accuracy of the developed model is verified by comparing with FEM results.     

A self-consistent approach to dynamic effective properties of a composite reinforced by distributed spherical particles

Summary A self-consistent approach to dynamic effective properties of a composite reinforced by randomly distributed spherical inclusions is studied. The coherent plane waves propagating through the particle-reinforced composite are of attenuation nature. It implies that there is an analogy between the particle-reinforced composite and the effective medium with complex-valued elastic constants from the viewpoints of wave propagation. A composite sphere consisting of the inclusion, the matrix and the interphase between them is assumed embedded in the effective medium. The effective wavenumbers of the coherent plane waves propagating through the particle-reinforced composite are obtained by the dynamic self-consistent conditions which require that the forward scattering amplitudes of such a composite sphere embedded in the effective medium are equal to zero. The dynamic effective properties (effective phase velocity, effective attenuation and effective elastic constants) obtained by the present dynamic self-consistent approach for SiC-Al composites are compared numerically with that obtained by the effective field approach at various volume concentrations. It is found that there is a good agreement between the two approaches at a relatively low frequency and low volume concentration but the numerical results deviate from each other at a relatively high frequency and high volume concentration.     

Thermal conductivity of a reinforced plate

Multiscale expansion is used in asymptotic integration of a steady-state heat-conduction problem for a thin plate of periodic structure; results are presented for the boundary layer near the end.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 35, No. 3, pp. 497–504, September, 1978.     

Bulk permittivity of a composite with coated spheroidal filler particles

The bulk complex permittivity of a composite material is calculated analytically. The filler particles are spheroidal and may be coated with a surface layer whose intrinsic material properties differ from those of the core. Making the assumption that the filler particles are arranged on a simple-cubic lattice, interactions between the particles are accounted for by treating each particle mathematically as a multipole source. The coefficients of the multipole expansion, suitably-truncated, are determined by solving a matrix equation obtained by matching with the general solution of Laplace's equation in the interstitial domain, expressed in terms of an expansion in spheroidal harmonics. Matching is carried out at the surface of a representative particle according to electromagnetic continuity conditions. Example calculations demonstrate the effect of varying filler volume fraction, intrinsic material properties, layer thickness, particle shape and frequency. Results are shown to agree with independent work, where available.     

Creep property of composite solders reinforced by nano-sized particles

In the present work the creep properties of Sn37Pb and Sn0.7Cu based composite solders with nano-sized metallic Cu, Ag and nano-sized oxide Al₂O₃, TiO₂ reinforcement particles have been studied. First, a series of volume percentages of reinforcements were selected for optimizing the content of particles. Then, the composite solder with optimum volume fraction of the reinforcement particles, corresponding to maximum creep rupture life, is selected for investigating the effect of applied stress level and test temperature on creep rupture life of the composite solder joints. In the creep rupture life test, small single-lap tensile-shear joints were adopted. The results indicate that all the composite solders have improved creep resistance, comparing to the eutectic Sn37Pb solder and the Sn0.7Cu lead-free solder. The creep rupture life of the composite solder joints is first increased with the increase in the volume fraction of reinforcement in the composite solders. Then, the creep rupture life is decreased, as the reinforcement content exceeds a certain value. The creep rupture life of the solder joints is decreased with the increase of applied stress and testing temperature. Moreover, the reinforced efficiency of nano-sized Ag particles is the best in all the tested nano-sized reinforcements for the Sn37Pb based and Sn0.7Cu based composite solders, when the particles contents are in their own optimum content.     

Thermoelastic properties and conductivity of composites reinforced by spherically anisotropic particles

The present paper is concerned with the overall thermoelastic properties and conductivity of composites reinforced by spherically anisotropic particles. Based on the concept of the replacement particle an equivalent bulk modulus, thermal expansion coefficient and thermal conductivity are derived for the spherically anisotropic particle. Such equivalent properties can be employed in the micromechanical models to predict the overall behavior of the composite. In addition to these, the shear loading is considered. The effective shear modulus is evaluated on the basis of Mori and Tanaka's approximations and the dilute phase concentration factors are derived from exact solutions of an auxiliary boundary value problem.     

Thermal conductivity of boron nitride reinforced polyethylene composites

The thermal conductivity of boron nitride (BN) particulates reinforced high density polyethylene (HDPE) composites was investigated under a special dispersion state of BN particles in HDPE, i.e., BN particles surrounding HDPE particles. The effects of BN content, particle size of HDPE and temperature on the thermal conductivity of the composites were discussed. The results indicate that the special dispersion of BN in matrix provides the composites with high thermal conductivity; moreover, the thermal conductivity of composites is higher for the larger size HDPE than for the smaller size one. The thermal conductivity increases with increasing filler content, and significantly deviates the predictions from the theoretic models. It is found also that the combined use of BN particles and alumina short fiber obtains higher thermal conductivity of composites compared to the BN particles used alone.     

Thermal conductivity of a material containing cracks of arbitrary shape

The problem of thermal conductivity of a material containing microcracks of arbitrary shape (including non-flat ones) is considered. The resistivity contribution tensor of a crack – the quantity that determines the decrease in the overall conductive properties of a solid due to introduction of such cracks – is derived on the basis of the solution for the strength of a singularity of the heat flux near a crack tip (heat flux intensity factor). The approach is illustrated with several examples. It is also shown how the resistivity contribution tensor can be used to calculate effective conductive properties in the framework of various self-consistent schemes – effective media, effective field and differential scheme.     

Heat conduction of orthogonally reinforced composite material

The problem of the heat flux in a medium with orthogonally positioned rows of periodically applied fibers is solved.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 51, No. 2, pp. 260–267, August, 1986.     

Thermal conductivity of a fiberglass material with a complex spatial structure

A method is given for calculating the thermal conductivity of a fiberglass material having a complicated spatial structure. This method can be applied up to the onset of pyrolysis.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 35, No. 1, pp. 25–28, July, 1978.     

Thermal conductivity of multiphase particulate composite materials

Hollow particle filled composites, called syntactic foams, are used in weight sensitive structural applications in this paper. In this paper, homogenization techniques are used to derive estimates for thermal conductivity of hollow particle filled composites. The microstructure is modeled as a three-phase system consisting of an air void, a shell surrounding the air void, and a matrix material. The model is applicable to composites containing coated solid particles in a matrix material and can be further expanded to include additional coating layers. The model is successful in predicting thermal conductivity of composites containing up to 52% particles by volume. Theoretical results for thermal conductivity are validated with the results obtained from finite element analysis and are found to be in close agreement with them. A simplified approximation of the theoretical model applicable to thin shells is also validated and found to be in good agreement with the corresponding finite element results. The model is applicable to a wide variety of particulate composite materials and will help in tailoring the properties of particulate composites as per the requirements of the application.     

Thermal conductivity measurement of the epoxies and composite material for low temperature superconducting magnet design

The thermal conductivities of solid materials were measured by a G-M cryo-cooler based apparatus in the temperature range of 2.6–21.0 K. The performance of this apparatus was verified by measuring the thermal conductivity of 304-stainless steel, and good reproducibility as well as accuracy was shown when compared with the certified values. The thermal conductivities of EC1017 and Stycast2850FT and a composite material were measured. Similar behavior to amorphous materials was shown for EC1017 and Stycast2850FT in that there was an apparent plateau, which could be ascribed to a very lower crystallinity of epoxy. An equivalent model was proposed to predict the thermal conductivity of the composite material.     

填料型高导热复合材料的研究现状与发展趋势

填料型导热复合材料是LED等半导体在封装及使用过程中一种常见的散热材料,它利用高导热填料填充具有密度小、可加工性能好、成本低廉等优点的高分子聚合物制备而成,对降低半导体器件的结温、增强其综合特性大有裨益。简要概述了近年来填料型导热复合材料的研究现状,并对其发展趋势进行了预测,以期为LED的实际散热需要提供技术参考,进而推动LED产业的发展。     

Development of Cu particles and Cu core-shell particles reinforced Al composite

Copper particles were incorporated and retained in elemental state in an aluminium matrix by friction stir processing thereby producing a non-equilibrium particulate composite. The processed Al–Cu_p composite exhibited improved strength with significantly high ductility. The composite was stable up to a temperature of more than 300°C. Thermal exposure at 350°C for more than 10 min led to diffusion of Cu atoms into the Al matrix forming a core-shell type structure in the Cu particles and thus producing an Al–Cu core-shell composite. The shell consists of multiple layers, the thickness of which was controllable.     

The effective thermal conductivity of a composite material with spherical inclusions

A new method is presented for calculating the effective thermal conductivity of a composite material containing spherical inclusions. The surface of a large body is assumed kept at a uniform temperature. This body is in contact with a composite material of infinite extent having a lower temperature far from the heated body. Green's theorem is then used to calculate the rate of heat transfer from the heated body to the composite material, yielding $$k_e /k = 1 + \frac{{3(\alpha - 1)}}{{[\alpha + 2 - (\alpha - 1)\phi ]}}\{ \phi + f(\alpha )\phi ^2 + 0(\phi ^3 )\} $$ where k _e is the effective thermal conductivity, k is the thermal conductivity of the continuous phase, α is the ratio of the thermal conductivity of the spherical inclusions to k, and φ is the volume fraction occupied by the dispersed phase. The function f(α) is presented in this work. Although a similar result has been found previously by renormalization techniques, the method presented in this paper has merit in that a decaying temperature field is used. As a result, only convergent integrals are encountered, and a renormalization factor is not needed. This method is more straightforward than its predecessors and sheds additional light on the basic properties of two-phase materials.     

Effective conductivity of a composite of poly-dispered spherical particles in a linear continuum

Rayleigh's method is used to find the electric potentials of a composite of poly-dispered spherical particles in a linear continuum in an external electric field. Based on the solutions of potentials, analytical formula for the effective electric conductivity is derived. Based on the formula, several factors, such as the number of spherical inclusions, the spatial distribution of the spheres, the contrast ratio _i / _h (where, _i and _h are the conductivities of the spherical inclusion and the host medium, respectively) and volume fraction of the inclusions, are discussed. Our results show that at high volume fraction, the effective conductivity is also affected by the spatial distribution of the inclusions.     

颗粒增强铝基功能梯度复合管研究

对强化颗粒进行了预处理,通过控制搅拌条件及感应炉供电功率等参数,使颗粒直接加入到基体铝合金中,并在浆体中呈现不同的分布,再通过调整其它的工艺参数,利用水平式离心铸造机制了三种具有不同强化部位和不同颗粒分布的功能梯度复合管,外层强化,内层强化以及内外层同时强化,结果表明：功能梯度复合管的显微硬度与颗粒分布具有良好的对应关系,而且显微组织也呈呈现梯度变化,强化部位的多样化可为功能梯度厚壁复合管的应用开辟新的领域。