Thermal conductivity model of filled polymer composites

Theoretical and empirical models for predicting the thermal conductivity of polymer composites were summarized since the 1920s.The effects of particle shape,filler amount,dispersion state of fillers,and interfacial thermal barrier on the thermal conductivity of filled polymer composites were investigated,and the agreement of experimental data with theoretical models in literatures was discussed.Silica with high thermal conductivity was chosen to mix with polyvinyl-acetate （EVA） copolymer to prepare SiO2/EVA co-films.Experimental data of the co-films＇ thermal conductivity were compared with some classical theoretical and empirical models.The results show that Agari＇s model,the mixed model,and the percolation model can predict well the thermal conductivity of SiO2/EVA co-films.

Multi-scale Modeling and Finite Element Analyses of Thermal Conductivity of 3D C/SiC Composites Fabricating by Flexible-Oriented Woven Process

Thermal conductivity is one of the most significant criterion of three-dimensional carbon fiber-reinforced SiC matrix composites(3D C/SiC).Represent volume element(RVE)models of microscale,void/matrix and mesoscale proposed in this work are used to simulate the thermal conductivity behaviors of the 3D C/SiC composites.An entirely new process is introduced to weave the preform with three-dimensional orthogonal architecture.The 3D steady-state analysis step is created for assessing the thermal conductivity behaviors of the composites by applying periodic temperature boundary conditions.Three RVE models of cuboid,hexagonal and fiber random distribution are respectively developed to comparatively study the influence of fiber package pattern on the thermal conductivities at the microscale.Besides,the effect of void morphology on the thermal conductivity of the matrix is analyzed by the void/matrix models.The prediction results at the mesoscale correspond closely to the experimental values.The effect of the porosities and fiber volume fractions on the thermal conductivities is also taken into consideration.The multi-scale models mentioned in this paper can be used to predict the thermal conductivity behaviors of other composites with complex structures.

A composite sphere assemblage model for porous oolitic rocks:Application to thermal conductivity

The present work is devoted to the determination of linear effective thermal conductivity of porous rocks characterized by an assemblage of grains(oolites) coated by a matrix. Two distinct classes of pores, i.e.micropores or intra oolitic pores(oolite porosity) and mesopores or inter oolitic pores(inter oolite porosity), are taken into account. The overall porosity is supposed to be connected and decomposed into oolite porosity and matrix porosity. Within the framework of Hashin composite sphere assemblage(CSA)models, a two-step homogenization method is developed. At the first homogenization step, pores are assembled into two layers by using self-consistent scheme(SCS). At the second step, the two porous layers constituting the oolites and the matrix are assembled by using generalized self-consistent scheme(GSCS) and referred to as three-phase model. Numerical results are presented for data representative of a porous oolitic limestone. It is shown that the influence of porosity on the overall thermal conductivity of such materials may be significant.

Simultaneously enhanced thermal conductivity and mechanical performance of carbon nanotube reinforced ZK61 matrix composite

Alloying seriously deteriorates the thermal conductivity of magnesium(Mg)alloys,thus,restricts their applications in the fields of computer,communication,and consumer products.In order to improve the thermal conductivity of Mg alloys,adding carbon nanotube(CNT)combined with aging treatment is proposed in this work,i.e.fabricating the D-CNT(a kind of dispersed CNT)reinforced ZK61 matrix composite via powder metallurgy,and conducting aging treatment to the composite.Results indicate the as-aged ZK61/0.6 wt.%D-CNT composite achieved an excellent thermal conductivity of 166 W/(mK),exhibiting 52.3%enhancement in comparison with matrix,as well as tensile yield strength of 321 MPa,ultimate tensile strength of 354 of MPa,and elongation of 14%.The simultaneously enhanced thermal conductivity and mechanical performance are mainly attributed to:(1)the embedded interface of the D-CNT with matrix and(2)the coherent interface of precipitates with matrix.It is expected the current work can provide a clue for devising Mg matrix composites with integrated structural and functional performances,and enlarge the current restricted applications of Mg alloys.

Breaking Through Bottlenecks for Thermally Conductive Polymer Composites:A Perspective for Intrinsic Thermal Conductivity,Interfacial Thermal Resistance and Theoretics

Rapid development of energy,electrical and electronic technologies has put forward higher requirements for the thermal conductivities of polymers and their composites.However,the thermal conductivity coefficient(λ)values of prepared thermally conductive polymer composites are still difficult to achieve expectations,which has become the bottleneck in the fields of thermally conductive polymer composites.Aimed at that,based on the accumulation of the previous research works by related researchers and our research group,this paper proposes three possible directions for breaking through the bottlenecks:(1)preparing and synthesizing intrinsically thermally conductive polymers,(2)reducing the interfacial thermal resistance in thermally conductive polymer composites,and(3)establishing suitable thermal conduction models and studying inner thermal conduction mechanism to guide experimental optimization.Also,the future development trends of the three above-mentioned directions are foreseen,hoping to provide certain basis and guidance for the preparation,researches and development of thermally conductive polymers and their composites.

Temperature-dependent thermal conductivity and fuel performance of UN-UO_(2) and UN-X-UO_(2)(X=Mo,W)composite nuclear fuels by finite element modeling

The temperature-dependent effective thermal conductivity of UN-X-UO_(2)(X=Mo,W)nuclear fuel composite was estimated.Following the experimental design,the thermal conductivity was calculated using Finite Element Modeling(FEM),and compared with analytical models for 10%,30%,50%,and 70%(in mass)uncoated/coated UN microspheres in a UO_(2) matrix.The FEM results show an increase in the fuel thermal conductivity as the mass fraction of the UN microspheres increases from 1.2 to 4.6 times the UO_(2) reference at 2,000 K.The results from analytical models agree with the thermal conductivity estimated by FEM.The results also show that Mo and W coatings have similar thermal behaviors,and the coating thickness influences the thermal conductivity of the composite.At higher weight fractions,the thermal conductivity of the fuel composite at room temperature is substantially influenced by the high thermal conductivity coatings approaching that of UN.Thereafter,the thermal conductivity from FEM was used in the fuel thermal performance evaluation during LWR normal operation to calculate the maximum centerline temperature.The results show a significant decrease in the fuel maximum centerline temperature ranging from−94 K for 10% UN to−414 K for 70%(in mass)UN compared to UO_(2) under the same operating conditions.

Adaptive Neuro-Fuzzy Inference System for Prediction of Effective Thermal Conductivity of Polymer-Matrix Composites

In the present study, the adaptive neuro-fuzzy inference system (ANFIS) is developed for the prediction of effective thermal conductivity (ETC) of different fillers filled in polymer matrixes. The ANFIS uses a hybrid learning algorithm. The ANFIS is a class of adaptive networks that is functionally equivalent to fuzzy inference systems (FIS). The ANFIS is based on neuro-fuzzy model, trained with data collected from various sources of literature. ETC is predicted using ANFIS with volume fraction and thermal conductivities of fillers and matrixes as input parameters, respectively. The predicted results by ANFIS are in good agreements with experimental values. The predicted results also show the supremacy of ANFIS in comparison with other earlier developed models.

Fabrication and thermal conductivity of copper matrix composites reinforced by tungsten-coated carbon nanotubes

Carbon nanotubes （CNTs） were coated by tungsten using metal organic chemical vapor deposition. Magnetic stirring was employed to disperse the W-coated CNTs （W-CNTs） in a Cu matrix, and then, the mixed powders were consolidated by spark plasma sintering. The W-CNTs obtained a uniform dispersion within the Cu matrix when the W-CNT content was less than 5.0vo1%, but high content of W-CNTs （10vol%） resulted in the presence of clusters. The W-CNT/Cu composites containing low content of W-CNTs （〈5.0vol%） exhibited a higher thermal conductivity than the sintered pure Cu, while the CNT/Cu composites exhibited no increase in thermal conductivity after the incorporation of uncoated CNTs. The W-CNT content was found to play a crucial role in determining the thermal conductivity of the W-CNT/Cu composites. The thermal conductivity of the W-CNT/Cu composites increased first and then decreased with the W-CNT content increasing. When the W-CNT content was 2.5vo1%, the W-CNT/Cu composite obtained the maximum value of thermal conductivity. The thermal resistance of the （W-CNT）-Cu interface was predicted in terms of Maxwell-Gamett effective medium approximation, and its calculated value was about 3.0× 10-9 m2.K.W-l.

An Application of the Modified Shear Lag Model to Study the Influence of Thermal Residual Stresses on the Stiffness and Yield Strength of Short Fiber Reinforced Metal Matrix Composites

The modified shear lag model proposed recently was applied to calculate thermal residual stresses and subsequent stress distributions under tensile and compressive loadings. The expressions for the elastic moduli and the yield strengths under tensile and compressive loadings were derived which take account of thermal residual stresses. The asymmetries in the elastic modulus and the yield strength were interpreted using the derived expressions and the obtained results of the stress calculations. The model predictions have exhibited good agreements with the experimental results and also with the other theoretical predictions

Prediction of Viscoelastic Behavior of Unidirectional Polymer Matrix Composites

To develop a novel method predicting the viscoelastic behavior of polymer matrix composites according to the viscoelasticity of the matrix, we used the viscoelastic model of the matrix to build new models for unidirectional composites in both 0° and 90° directions. Viscoelastic parameters for both new models were derived, and the obtained equations shared the same form as the viscoelastic constitutive equation of matrix material. The viscoelastic behaviors of matrix material and unidirectional composites were also tested. Results showed that fitting parameters of creep compliance equation were close to the theoretical values of viscoelastic constitutive parameters of the unidirectional composites, proving the validity of the models. A new method was obtained to predict the viscoelastic property of the unidirectional composites based on the viscoelastic property of composite matrix and elastic property of the unidirectional composites. This method provides a theoretical basis for future studies on the viscoelasticity of composite laminates.

A new model for thermal conductivity of“continuous matrix/dispersed and separated 3D-particles”type composite materials and its application to WC-M(M=Co,Ag)systems

In the present work a new thermal conductivity model is developed for two-phase composite materials,which are consisted of a continuous matrix and dispersed 3 D-particles separated from each other by the matrix as a function of grain size and volume ratio of the dispersed particles at different temperatures.The model is applied to reproduce experimental thermal conductivity values of cemented carbide systems WC-Co and WC-Ag.Good agreement was found between measured thermal conductivity data originating from both this work and recent literature and the calculated ones only using semi-empirical parameters for the interfacial thermal resistance(ITR)values at WC/Co,WC/Ag and WC/WC interfaces as a function of temperature.Additionally,the temperature and grain size dependence of the thermal conductivity for WC is established for the first time.The model works well for the case when the matrix(Ag)has a higher thermal conductivity compared to that of the WC particles and also for the case when the matrix(Co)has a lower thermal conductivity compared to that of the WC particles.The new model forms a physically sound basis for further development/materials design of cemented carbides and particlereinforced composite materials.

INTERACTION MODELS FOR EFFECTIVE THERMAL AND ELECTRIC CONDUCTIVITIES OF CARBON NANOTUBE COMPOSITES

The present article provides supplementary information of previous works of analytic models for predicting conductivity enhancements of carbon nanotube composites. The models, though fairly simple, are able to take account of the effects of conductivity anisotropy, nonstraightness, and aspect ratio of the CNT additives on the conductivity enhancement of the composite and to give predictions agreeing well with existing experimental data. The omitted detailed derivation of this model is demonstrated in the present article with a more systematical analysis, which may help with further development in this direction. Furthermore, the effects of various orientation distributions of CNTs are reported here for the first time. The information may be useful in design or fabrication technology of CNT composites for better or specified conductivities.

Nonlinear Micromechanical Modelling of Transverse Tensile Damage Behavior in Fiber-Reinforced Polymer Composites

The investigation focusing on the mechanical behaviors at the microstructural level in composite materials can provide valuable insight into the failure mechanisms at larger scales.A micromechanics damage model which comprises the coupling of the matrix constitutive model and the cohesive zone(CZM)model at fiber-matrix interfaces is presented to evaluate the transverse tensile damage behaviors of unidirectional(UD)fiber-reinforced polymer(FRP)composites.For the polymeric matrix that exhibits highly non-linear mechanical responses,special focus is paid on the formulation of the constitutive model,which characterizes a mixture of elasticity,plasticity as well as damage.The proposed constitutive model includes the numerical implementation of a fracture plane based ellipse-parabola criterion that is an extension of the classic Mohr-Coulomb criterion,corresponding post-yield flow rule and post-failure degradation rule in the fully implicit integration scheme.The numerical results are in good agreement with experimental measurements.It is found that directly using the matrix properties measured at the ply level to characterize the mechanical responses at the constituent level may bring large discrepancies in homogenized stress-strain responses and dominant failure mechanisms.The distribution of fracture plane angles in matrix is predicted,where it is shown to provide novel insight into the microscopic damage initiation and accumulation under transverse tension.

Prediction of the Enhanced Out-of-Plane Thermal Conductivity of Carbon Fiber Composites Produced by VARTM

The thermal conductivity of epoxy resin can be increased by a factor of eight to ten by loading with highly conductive particles. However, higher loadings increase the viscosity of the resin and hamper its use for liquid composite molding processes. Thus, the enhancement of the out-of-plane thermal conductivity of carbon composites manufactured by VARTM and accomplished by matrix filling is limited to about 250%. In order to derive higher increases in out-of-plane thermal conductivity, additional measures have to be taken. These consist of introducing thermally conductive fibers in out-of-plane direction of the preform using a 3D-weaving process. Measured out-of-plane thermal conductivities of 3D-woven fabric composites are significantly increased compared to a typical laminated composite. It has been shown that if introducing highly conductive z-fibers, the use of a particle filled resin is not necessary and furthermore should be avoided due to the manufacturing problems mentioned above. An existing analytical model was altered to predict the effective thermal conductivity as a function of the composite material properties such as the thermal conductivities and volume contents of fibers in in-plane and out-of-plane directions, the thermal conductivity of the loaded resin, the grid-density of the out- of-plane fibers, and material properties of the contacting material. The predicted results are compared with measured data of manufactured samples.

Predicted interfacial thermal conductance and thermal conductivity of diamond/Al composites with various interfacial coatings

The interfacial thermal conductance （ITC） and thermal conductivity （TC） of diamond/Al composites with various coatings were theoretically studied and discussed. A series of predictions and numerical analyses were performed to investigate the effect of thickness, sound velocity, and other parameters of coating layers on the ITC and TC. It is found that both the ITC and TC decline with increasing coating thickness, especially for the coatings with relatively low thermal conductivity. Nevertheless, if the coating thickness is close to zero, or quite a small value, the ITC and TC are mainly determined by the constants of the coating material. Under this condition, coatings such as Ni, TiC, Mo 2 C, SiC, and Si can significantly improve the ITC and TC of diamond/Al composites. By contrast, coatings like Ag will exert the negative effect. Taking the optimization of interfacial bonding into account, conductive carbides such as TiC or Mo 2 C with low thickness can be the most suitable coatings for diamond/Al composites.

Selective interfacial bonding and thermal conductivity of diamond/Cu-alloy composites prepared by HPHT technique

Cu-based and Cu-alloy-based diamond composites were made by high-pressure-high-temperature （HPHT） sintering with the aim of maximizing the thermal conductivity of the composites. Improvements in interfacial bonding strength and thermo-physical properties of the composites were achieved using an atomized copper alloy with minor additions of Co, Cr, 13, and Ti. The thermal conductivity （TC） oh- mined exhibited as high as 688 W.m-1.K-1, but also as low as 325 W.m-1.K-l. A large variation in TC can be rationalized by the discrepancy of diamond-matrix interfacial bonding. It was found from fractography that preferential bonding between diamond and the Cu-alloy matrix occurred only on the diamond {100} faces. EDS analysis and Raman spectra suggested that selective interfacial bonding may be attributed to amorphous carbon increasing the wettability between diamond and the Cu-alloy matrix. Amorphous carbon was found to significantly affect the TC of the composite by interface modification.

Effect of sintering parameters on the microstructure and thermal conductivity of diamond/Cu composites prepared by high pressure and high temperature infiltration

Pure Cu composites reinforced with diamond particles were fabricated by a high pressure and high temperature （HPHT） infiltration technique. Their microstructural evolution and thermal conductivity were presented as a function of sintering parameters （temperature, pressure, and time）. The improvement in interfacial bonding strength and the maximum thermM conductivity of 750 W/（m.K） were achieved at the optimal sintering parameters of 1200℃, 6 GPa and 10 min. It is found that the thermal conductivity of the composites depends strongly on sintering pressure. When the sintering pressure is above 6 GPa, the diamond skeleton is detected, which greatly contributes to the excellent thermal conductivity.

Effect of processing parameters on the microstructure and thermal conductivity of diamond/Ag composites fabricated by spark plasma sintering

Diamond/metal composites with 50 vol.% diamond have been produced by spark plasma sintering（SPS） using pure Ag as a matrix and diamond particles as reinforcement.Three kinds of powder mixing processes were used to prepare the mixture of diamond/Ag powders：dry mixing without milling medium,wet mixing and magnetic blending.Subsequently,they were all consolidated by SPS at various processing parameters to produce bulk diamond/Ag composites.Then samples were heat treated in order to obtain a higher thermal conductivity.The effect of processing parameters on the morphologies of the mixed powders,the microstructure and the thermal conductivity of the composites were investigated by comparing the experimental data.It reveals that particles were easy to agglomerate and the distribution of mixed powders was inhomogeneous by dry mixing method,and wet mixing method is too complex.The most favorable mixing process is magnetic blending by which the powders can be homogenously mixed and the composites prepared by optimized SPS processing parameters can obtain the highest relative density and the best thermal conductivity among the composites prepared by different processes.The magnetic blending diamond/Ag composites even have a 23% increase in thermal conductivity compared with pure silver sintered by SPS.

Thermal conductivity behavior of SPS consolidated AlN/Al composites for thermal management applications

A1N/A1 composites are a potentially new kind of thermal management material for electronic packaging and heat sink applications. The spark plasma sintering （SPS） technique was used for the first time to prepare the A1N/A1 composites, and attention was focused on the effects of sintefing parameters on the relative density, microstructure and, in particular, thermal conductivity behavior of the composites. The results showed that the relative density and thermal conductivity of the composites increased with increasing sintering temperature and pressure. The composites sintered at 1550℃ for 5 min under 70 MPa showed the maximum relative density and thermal conductivity, corresponding to 99% and 97.5 W.m-1.K-1, respectively. However, the thermal conductivity of present A1N/A1 composites is still far below the theoretical value. Possible reasons for this deviation were discussed.

Thermal conductivity of carbon nanotube-silver composite

The molecular level mixing method was extended to fabricate carbon nanotube reinforced silver composite. The influence of type of carbon nanotubes（single/multiwall） reinforcement and their mode of functionalization（covalent/non-covalent） on thermal conductivity of silver composite was investigated. X-ray diffraction and electron diffraction spectroscopy（EDS） confirm the presence of silver and carbon in the composite powder. High resolution scanning electron microscopy and transmission electron microscopy ascertain embedded, anchored and homogeneously implanted carbon nanotubes in silver matrix. Effect of covalent functionalization on multiwall carbon nanotubes was monitored by Raman and Fourier transform infrared spectroscopy. These investigations confirm the addition of functional groups and structural integrity of carbon nanotubes even after covalent functionalization. Thermal conductivity of composites was measured by a laser flash technique and theoretically analyzed using an effective medium approach. The experimental results reveal that thermal conductivity decreases after incorporation of covalently functionalized multiwall nanotubes and single wall carbon nanotubes. However, non-covalently functionalized multiwall nanotube reinforcement leads to the increase in effective thermal conductivity of the composite and is in agreement with theoretical predictions derived from effective medium theory, in absence of interfacial thermal resistance.