Coefficient Of Thermal Expansion Of Composites Research Articles

Relationship Between the Shape of Giant Reed-Based Fillers and Thermal Properties of Polyethylene Composites: Structural Related Thermal Expansion and Diffusivity Studies

This paper describes the effect of two different fillers derived from giant reed (Arundo donax L.), namely fibers and shredded aerial parts of the plant, on the thermal properties of polyethylene-based composites, as the analysis of dimensional stability of lignocellulose-based composites, and its relationship with their thermal diffusivity, has not yet been assessed in the literature. It has been found that the introduction of such materials resulted in a significant reduction of the coefficient of thermal expansion, particularly more important in the case of fibers, due to their higher aspect ratio; in particular, this coefficient is reduced to less than half for fibrous composites (from 1.6·10− 4 K− 1 to 6.1·10− 5 K− 1 or 3.5·10− 5 K− 1 for 20 and 40% loadings). This parameter also influences the thermal diffusivity of the final parts; the diffusivity of composites increases with the ratio of lignocellulosic filler used, particularly when using fibers, due to a better orientation of these fibers than the shredded material, which does not exhibit a fibrous shape. Composites with 20% share of the filler exhibited a thermal diffusivity increased by about 15% compared to neat polyethylene, while 40% loadings resulted in a 25% and 60% increase for ground and fibrous materials, respectively. These results provide additional features to lignocellulose-composites characterization, providing properties not usually mentioned in the literature to expand the knowledge about such composite materials beyond mechanical properties, providing a broader range of properties to offer a wider application area of such composites.Statement of NoveltyArundo donax L. is of great interest to biorefineries due to its fast growth and resistance to adverse environmental conditions. Most research on this plant species focuses on obtaining energy products or valuable chemicals, while very few are related to composite production, particularly on thermoplastic materials. The work found in the literature so far does not provide insights into the relationships between the types of filler (and their aspect ratio) and their thermal properties. Therefore, this work expands the knowledge on the thermal behavior of lignocellulose-polymer composites, supplementing the research, usually focused only on mechanical properties, in their characterization by correlative analysis of thermal influenced dimensional change with structure and thermal diffusivity. Determining the coefficient of thermal expansion (CTE) is a relevant parameter to assess the possibilities of using a material at high or low temperatures and evaluate the dimensional stability of a product during its service lifetime. On the other hand, thermal diffusivity brings together the capacity of a material to store thermal energy and distribute it throughout the material; that is, it relates heat capacity and thermal conductivity, which are also essential in using materials in market applications. Therefore, the work not only provides the results of thermal diffusivity and CTE of thermoplastic-reed composites but also correlates both parameters as a way to widen the range of application of plant-based composites in areas where dimensional stability (i.e., low thermal expansion) is required.Graphical

Insight into the mechanical properties and thermal expansion behavior of epoxy nanocomposites reinforced with multi‐walled carbon nanotube solvent‐free nanofluids

AbstractEpoxy resin (EP) is a promising material that exhibits great potential in the fields of packaging and adhesion. However, reducing its brittleness and coefficient of thermal expansion (CTE) at low filler content is still a challenge. To address this problem, three types of MWCNTs nanofluids (MWCNTs NFs) with different shell structures were designed to modify epoxy resin. With the addition of 1 wt% MWCNTs‐M1, the compression, impact, and lap shear strength of the composites increased to 88.97 MPa, 81.39 kJ/m2, 12.69 MPa, respectively, which are 21.7%, 66.1%, and 58.0% higher than pure epoxy. Meanwhile, incorporating MWCNTs NFs also improved the CTE and thermal conductivity, with a 19.7% decrease in CTE and a 40% improvement in thermal conductivity at 2 wt% NFs content. Particularly, the effect of MWCNTs NFs structure on the composite properties was explored, which can be an available reference for designing specific NFs epoxy composites.Highlights Three types of MWCNTs nanofluids with different structures were designed. The MWCNTs NFs were used in packaging materials for the first time. The impact performance of composite has been improved by 66%. The CTE of composite is 19.7% lower than pure EP. The thermal conductivity of the composite increased by 40%.

Tuning high and low thermal expansion coefficients of Li2O–BaO–Al2O3–B2O3–SiO2/quartz LTCC composites by replacing quartz partly with α-Al2O3 or ZrO2

Low-temperature co-fired ceramics (LTCC) with adjustable coefficients of thermal expansion (CTE) based on Li 2 O–BaO–Al 2 O 3 –B 2 O 3 –SiO 2 /quartz LTCC composites (glass/ceramics) have been employed in electronic packaging to address the interface thermal mismatch problem caused by different thermal expansion coefficients. In the present study, sintering behavior, phase structure, and CTE of LTCC composites is controlled by replacing quartz partly with α-Al 2 O 3 or ZrO 2 . Accordingly, LTCC composites with the highest and lowest CTE values are achieved. The results show that the major phases of α-Al 2 O 3 substituted LTCC composites are hexacelsian, β-spodumene, and virgilite. Correspondingly, CTE values are in the range of 5.67–8.62 × 10 −6 /°C. Whereas, ZrO 2 substituted LTCC composites have exhibited increased CTE values to 12.27 to 13.2 × 10 −6 /°C with major phases of cristobalite, hexacelsian, and bazirite. Moreover, the negative effects of phase transformation of hexacelsian can be inhibited to a certain extent upon substitution of α-Al 2 O 3 up to 15 wt%. This work provides suitable methods for preparing LTCC composites with gradient CTE and resolving the thermal mismatch effects at different interfaces (e.g., chip/LTCC, metal electrode/LTCC) in electronic packaging structures.

High-throughput finite-element design of dielectric composites for high-frequency copper clad laminates

Dielectric substrates with low dielectric constant and good thermal stability are highly desired for high-frequency and high-speed signal transmission. It is however challenging to rationally design the demand-satisfied polymer-based composites due to the inadequate understanding of the contradictory effect of inorganic fillers on modulating dielectric-thermal-mechanical properties. In this work, taking Polytetrafluoroethylene (PTFE)-SiO2 composite as the example, we perform high-throughput finite-element calculations to systematically study the filler effects on the dielectric constant of composites εrcomposite and the coefficient of thermal expansion of composites (CTE-c). A series of influencing factors including intrinsic property, volume fraction, shape, distribution, and orientation of fillers have been considered in our models to establish the structure-property mapping of dielectric composites. It is found that CTE-c is more sensitive to the filler structure of PTFE-SiO2 composites than εrcomposite. Finally, guided by the calculation results, a skeleton structure is proposed to realize the performance targets of εrcomposite< 2.3 and CTE-c < 60 ppm/K with lower SiO2 filler content. This work provides a universal data-driven strategy for the rational design of dielectric composites with multi-objective requirements, and it is expected to spark more experimental efforts to design novel dielectric composites for high-quality signal transmission.

New numerical algorithm for the periodic boundary condition for predicting the coefficients of thermal expansion of composites

In this paper, a new algorithm for the periodic boundary condition used for numerically predicting the coefficients of thermal expansion (CTEs) of different composite systems based on the finite element homogenization method is proposed. The results demonstrate that the proposed algorithm guarantees stress and strain continuities on the opposite surfaces of the representative volume elements (RVEs) for composites with spherical particles and plain woven fabrics but not for composites with cylindrical fibers and three-dimensional four-directional braided yarns. Meanwhile, the proposed algorithm ensures the micro–macro energy balance (Hill’s lemma) and the zero macro-stress constraint of the RVEs for all composite systems. Through the comparison with experimental tests and other numerical methods, the proposed algorithm is validated to be capable of accurately predicting the CTEs of composites.

Coefficient of thermal expansion (CTE) study in metal matrix composite of CuSiC vs AlSiC

Metal matrix composites are widely used as advanced materials for thermal management applications. In view of the demands in higher temperature products application, materials with low coefficient of thermal expansion (CTE) and high thermal conductivity are required. Copper Silicon Carbide (CuSiC) is highly rated as the best materials selected for this application because it has good thermal characteristics especially in CTE, but its density is almost high for high temperature electronic device application. An aluminium silicon carbide (AlSiC) composite, on the other hand, is a new candidate for electronic device application since it has low density and good CTE characteristics. CuSiC and AlSiC composites were fabricated via powder metallurgy method through variety volume fractions such as 5%, 10%, 15% and 20%. In the present study, the comparison of CTE between CuSiC and AlSiC composites with different volume fraction of SiC particles has been carried out. The CTE of CuSiC and AlSiC composites were investigated and their responses between 25°C to 400°C were studied using horizontal dilatometer. Based on the experiment results, the density of CuSiC composites are decrease while the density of AlSiC composites is increase with increasing in SiC particles content. However, the porosity for both composites is increases with increasing in volume fraction of SiC particles. As of CTE, both composites showed decreased with increasing in SiC particles content that dispersed in their matrix. The experimental CTE values for both composites seem to be much lower than theoretical CTE value, which means that there has been excellent bonding between each particle after sintering process. The particles distribution has been observed to understand more on the aspect of SiC particles homogeneity in copper and aluminium matrix.

Thermal and Optical Performance of Glass Cloth Reinforced Organic-Inorganic Hybrid Polymer Composite Film.

Recently there has been considerable interest in flexible display as the next-generation display. The flexible plastic has been recommended as a strong candidate for substrate, but these plastic substrates have many problems to provide the comparable properties of dimensional stability, thermal stability, and solvent resistance to glass in order to apply conventional thin film transistor technology to flexible display. Then in this study, a glass cloth reinforced polymer (GCRP) composite was prepared. To improve the thermal property, glass cloth with an excellent coefficient of thermal expansion (CTE) for reinforcement and organic-inorganic hybrid nanomaterial with polyhedral oligomeric silsesquioxane (POSS) material having excellent heat resistance were introduced to ensure the excellent properties like transmittance, haze, yellow index, thermal stability and chemical resistance. The optical property of GCRP composite was measured by using a spectrophotometer and the CTE of GCRP composite was observed by thermomechanical analysis (TMA).

Micromechanics analysis for thermal expansion coefficients of three-phase particle composites

In the present investigation, a new equivalent micromechanics method is proposed, and then, an analysis model has been developed to estimate the nonlinear coefficients of thermal expansion (CTEs) of three-phase composites. As Compared with previous analytical models, the innovative point of this paper is that the influence of the debonding surface thickness is investigated. It is noted that the parameters of thickness of debonding surface have a significant effect on both the longitudinal CTEs and transverse CTEs. The CTEs of composites are also very sensitive to the different inclusion aspect ratios. The constitutive equation curves for different variable parameters can describe the influence of debonding damage on thermal expansion coefficients (CTEs) of the composites. The new model provides a direct prediction of CTEs and can account for the effects of inclusion aspect ratio, volume fractions and thickness of debonding surface.

Preparation and properties of W-SiC/Cu composites by tape casting and hot-pressing sintering

ABSTRACTIn this study, W-SiC/Cu composites were prepared by tape casting and vacuum hot-pressing sintering. The microstructures and properties of the composites were studied by means of X-ray diffraction, X-ray photoelectron spectroscopy, field emission scanning electron microscopy, Vickers hardness test, bending strength test and coefficient of thermal expansion (CTE) test. The results showed that W2C, WC and WSi2 formed in the composites. The effects of SiC particle size on the relative densities, Vickers hardness, bending strength and CTE of composites were investigated. Vickers hardness, bending strength and CTE of the composite with SiC particle size of 6 µm reached the optimal values, which were 445.2 HV, 726.1 MPa, 9.24 ppm K−1.

Effects of low contents of A2M3O12 submicronic thermomiotic‐like fillers on thermal expansion and mechanical properties of HDPE‐based composites

In this work, pristine Al2W3O12 and Y2W3O12 submicronic fillers, belonging to A2M3O12 family of thermomiotic materials, were incorporated into a high density polyethylene matrix (HDPE) in low contents (from 0.1 to 1.1 vol.%) to study the influence thereof on the coefficient of thermal expansion (CTE) and mechanical properties of the as‐prepared composites. The CTE of HDPE and HDPE/A2M3O12 composites is affected by the first heating cycle, but it remained unchanged after the second heating run. Both Y2W3O12 and Al2W3O12 fillers decrease the CTE of composites. However, Y2W3O12 acts more efficiently than Al2W3O12 to decrease this property and caused a CTE reduction in the range of 20–25% for the temperature interval between 25 and 70°C during the second heating cycle. The filler content does not have a strong influence on CTE for both types of composites, considering the standard deviations. The thermal stability of HDPE is not affected by the addition of fillers. However, the fillers significantly increase the degree of crystallinity, especially in the case of Y2W3O12. For the highest filler content (1.1 vol.%), the Young's modulus of composites increased up to 21 and 32% in the case of Al2W3O12 and Y2W3O12, respectively. POLYM. COMPOS., 39:E1821–E1833, 2018. © 2018 Society of Plastics Engineers

Properties investigation and microstructures characterization of SiCp/6061Al composites produced by PM route

In this study, 35 vol.% SiC particles with different sizes reinforced 6061 aluminium alloy matrix composites were prepared by a powder metallurgy method. The Scanning Electron Microscope (SEM) images of composites were observed, the Coefficient of Thermal Expansion (CTE) and tensile strength of composites were examined, and the influences of SiC particle size on microstructures and properties of the composites were analyzed. Furthermore, the SiCp/6061Al composites with SiC particle size of 7.5 µm were selected to investigate the SiCp/Al interface microstructure and precipitated phases by the means of SEM, TEM and HRTEM. The study indicated that, with the increase of SiC particle size, the SiC particles distributed more uniformly in the matrix, the CTE of composites increased, but the tensile strength of composites decreased. The SiCp/Al interface in this experiment is clean and smooth, and the combination mechanism of SiC and Al is the formation of a half coherent interface by closely matching of atoms. Some micron-sized coarse intermetallic particles existed in the hot-pressed composites, such as random-shaped Mg2Si, long stick shaped Al15(Mn, Fe, Cu)3Si2. When the composites were solution treated at 510 °C for 2 h and then aging treated at 190 °C for 9 h, except long stick shaped Al15(Mn, Fe, Cu)3Si2, numerous nano-sized precipitated phases (Mg2Si) with diameters of 50-200 nm dispersively distributed in the matrix. After heat treatment, the tensile strength of composite with SiC particle size of 7.5 µm enhance from 298 MPa to 341 MPa.

Potential use of CNTs for production of zero thermal expansion coefficient composite materials: An experimental evaluation of axial thermal expansion coefficient of CNTs using a combination of thermal expansion and uniaxial tensile tests

Feasibility of using multi-walled carbon nanotubes (MWCNTs) for the control of coefficients of thermal expansion (CTEs) of composite materials was evaluated, based on experimental data of CTEs and Young’s modulus newly obtained using a combined testing procedure. The axial CTE of the MWCNTs were evaluated over the temperature range −5°C to 85°C by using the MWCNT’s Young’s modulus and CTE of the aligned MWCNT reinforced epoxy composites in Turner’s model. The Young’s moduli of the MWCNTs were calculated by using Voigt model and the composite Young’s modulus measured by tensile tests. The MWCNTs were shown to possess negative CTEs, and the nanotube CTEs tended to become less negative with increasing temperature. Owing to their large Young’s modulus, aspect ratio and negative CTEs, the use of MWCNTs aligned axially was shown to be effective at controlling the CTE of polymer composites at lower volume fractions compared to conventional negative CTE materials.

Mean-field homogenization based approach to evaluate macroscopic coefficients of thermal expansion of composite materials

In this paper, a mean-field homogenization based approach implemented in the two steps sequentially is proposed to evaluate the macroscopic coefficients of thermal expansion (CTEs) of multi-phase composites. The adopted mean-field homogenization models are the quadratic interpolative M-T/D-I mean-field homogenization model in the first-step homogenization procedure and the simple interpolative Voigt/Reuss mean-field homogenization model in the second-step homogenization procedure, respectively. The proposed mean-field homogenization based approach is validated by comparing with the RVE based FE homogenization method. The simulation results indicate that with the increase of the inclusion volume fraction, the macroscopic CTEs of multi-phase composites generally decrease because that the inclusions possess the smaller CTEs than the matrices. However, in the case of multi-phase composites with the planarly distributed inclusions, the through-thickness CTEs firstly increase with the increase of the inclusion volume fraction and then decrease with the increase of the inclusion volume fraction. The effect of the inclusion aspect ratio on the macroscopic CTEs of multi-phase composites can be neglected, while the effect of the inclusion transversely isotropic material properties on the macroscopic CTEs of multi-phase composites must be considered.

Effect of (0–40) wt. % Si addition to Al on the thermal conductivity and thermal expansion of diamond/Al composites by pressure infiltration

This study pertained to the effect of (0–40) wt.% Si addition to Al on the thermal conductivities (TC) and the coefficient of thermal expansion (CTE) of diamond/Al composites by pressure infiltration. The fracture surfaces and interface microstructures by metal electro-etching were discussed with respect to Al matrix chemistry and diamond particles size. The results revealed that the diamond (single size)/Al–12.2Si (in wt.-pct) composites exhibited higher thermal conductivity of 532 W/m K due to the better interface bonding, which is over 90% of the theoretical prediction by the Hasselman–Johnson Scheme. At the interfaces, SiC was found and the undesired interface formation of Al4C3 was reduced. The CTE of diamond (single size)/Al–40Si (in wt.-pct) composites exhibited the average value of 4.5 × 10−6/K, but the TC value declined to 314 W/m K due to the inhomogeneous enrichment of Si. The bimodal mixtures of diamond particles (106–125 μm: 45–38 μm = 3:1) could improve TC and CTE of composites.

Determination of thermal expansion coefficients for unidirectional fiber-reinforced composites

In the present work, the coefficients of thermal expansion (CTEs) of unidirectional (UD) fiber-reinforced composites are studied. First, an attempt is made to propose a model to predict both longitudinal and transverse CTEs of UD composites by means of thermo-elastic mechanics analysis. The proposed model is supposed to be a concentric cylinder with a transversely isotropic fiber embedded in an isotropic matrix, and it is subjected to a uniform temperature change. Then a concise and explicit formula is offered for each CTE. Finally, some finite element (FE) models are created by a finite element program MSC. Patran according to different material systems and fiber volume fractions. In addition, the available experimental data and results of other analytical solutions of CTEs are presented. Comparisons are made among the results of the cylinder model, the finite element method (FEM), experiments, and other solutions, which show that the predicted CTEs by the new model are in good agreement with the experimental data. In particular, transverse CTEs generally offer better agreements than those predicted by most of other solutions.

Microstructure and thermal expansion behavior of diamond/SiC/(Si) composites fabricated by reactive vapor infiltration

Abstract Diamond/SiC/(Si) composites were fabricated by Si vapor vacuum reactive infiltration. The coefficient of thermal expansion (CTE) of composites have been measured from 50 to 400 °C. With the diamond content increasing, CTE of composite decreased, simultaneously, the microstructure of the composites changed from core–shell particles embedded in the Si matrix to an interpenetrating network with the matrix. The CTEs of composites versus temperature matched well with those of Si. The Kerner model was modified according to the structural features of the composites, which exhibited more accurate predictions due to considering the core–shell structure of the composites. The thermal expansion behavior of the matrix was constrained by diamond/SiC network during heating.

In-situ formation of Al-CaB6 composites with low resistivity

In this work, in-situ CaB6 reinforced aluminum matrix composites were fabricated, and the microstructure, resistivity, microhardness and coefficient of thermal expansion (CTE) of Al-CaB6 composites were studied. It is found that CaB6 compounds can be formed by reducing reaction occurred in the Al melt: AlB2 + Ca → CaB6 + [Al]. CaB6 exhibits a hexahedron morphology and distributes uniformly in the Al alloy matrix. The resistivity of Al-CaB6 composites is 3.02×10−8 Ω·m, which is close to that of pure Al and lower than that of 6063Al/Ga composites. The average microhardness of Al-CaB6 composites can reach 1270 MPa, 259.8% higher than that of pure Al. Compared to pure Al, the CTE of Al-CaB6 composites is much lower.

The effect of phase transformation on the thermal expansion property in Al/ZrW2O8 composites

This article studied the effect of phase transformation on the thermal expansion property in Al/ZrW2O8 composites. The Al/ZrW2O8 composites of low-thermal expansion were fabricated by a squeeze casting method. The coefficient of thermal expansion (CTE) of as-made composites was discovered sharply increased at around 130 °C. The X-ray diffraction (XRD) spectra showed the existence of high-pressure γ-phase in the as-made composites. This high-pressure γ-phase was considered to be induced by the compressive residual stress originated from the thermal mismatch between Al matrix and ZrW2O8 particles. The in situ high-temperature XRD and the differential scanning calorimetry technique were used to study this thermally expanded abruption phenomenon. It was found that the phase transformation from high-pressure γ-phase to the low-pressure phases (α/β phase) in the composites should be responsible for fluctuation in the CTE of composites. Furthermore, using a proper heat treatment to eliminate the high-pressure phase in the composite, the Al/ZrW2O8 composites of low and uniform CTE (from 20 to 200 °C) could be achieved. And when temperature increased again, the thermal mismatch stresses between the metal matrix and ceramic particles in the composite were not large enough to re-induce the α-γ transformation.

Fabrication and infiltration kinetics analysis of Ti-coated diamond/copper composites with near-net-shape by pressureless infiltration

Abstract The Ti-coated diamond/copper composites with near-net-shape are manufactured by pressurelessly infiltrating liquid copper into porous Ti-coated diamond preforms. The contact angle between diamond and copper, relative density, thermal conductivity (TC), coefficient of thermal expansion (CTE), leak rate and microstructure are evaluated and characterized. In addition, the numerical analysis of the pressureless infiltration kinetics is also discussed. The results indicate that the relative density, TC and CTE of composites are 99.3%, 385 Wm−1 k−1 and 3–8 × 10−6 K−1, respectively. It can meet heat-sink package requirement of high-power electronic devices as LED, insulated gate bipolar transistor (IGBT), etc. The liquid copper exhibits a turbulent flow with the Reynolds number in the range of 27.83–49.7. The porosity ϕ and the pressure drop Δp are the main influence factors controlling the velocity of liquid copper. Moreover, under vacuum condition of 8.7 × 10−3 Pa, the maximum theoretical infiltration length Lmax of Ti-coated diamond/copper composites is found to be 552 mm.

판상형 충전제의 함량과 배향에 따른 PP복합체의 열팽창계수 영향 연구

두 가지의 종횡비(<TEX>${\rho}_{\alpha}=a_1/a_3$</TEX> and <TEX>${\rho}_{\beta}=a_1/a_2$</TEX>)에 의해 특징지어진 3차원 타원체(<TEX>$a_1$</TEX> > <TEX>$a_2$</TEX> > <TEX>$a_3$</TEX>)를 사용하여 polypropylene 복합체의 판상형 충전제 함량과 방향이 열팽창률에 미치는 영향에 대해 실험적인 연구를 수행하였다. 측정된 실험적인 값은 Lee와 그의 연구자들이 제안한 이론적인 모델에 의한 계산 값과 비교분석되었다. 판상형 충전제로는 운모와 탈크가 사용되었다. 실험 결과로 운모의 경우 종횡비는 <TEX>${\rho}_{\alpha}=13.5$</TEX>, <TEX>${\rho}_{\beta}=1.8$</TEX>이 사용되어, 20 wt% 함량일 때 <TEX>${\alpha}_{11}/{\alpha}_m$</TEX>는 약 0.56으로 감소하였으나, <TEX>${\alpha}_{33}/{\alpha}_m$</TEX>는 오히려 1.018로 증가함을 보였다. 탈크의 경우의 종횡비는 <TEX>${\rho}_{\alpha}=3.7$</TEX>, <TEX>${\rho}_{\beta}=1.4$</TEX>이었고 <TEX>${\alpha}_{11}/{\alpha}_m$</TEX>는 0.63으로 감소하였다. 결국 운모와 탈크 모두 그 함량증가에 따라 종단방향과 횡단방향에서 열팽창률은 감소하였으나 수직방향에서는 초기 낮은 충전제 함량에서는 오히려 증가하는 경향을 보였다. Experimental study was performed regarding the effects of disc-like filler orientation and contents on the coefficient of thermal expansion (CTE) of polypropylene composites using the three dimensional ellipsoids (<TEX>$a_1$</TEX> > <TEX>$a_2$</TEX> > <TEX>$a_3$</TEX>) analyzed by two aspect ratios(<TEX>${\rho}_{\alpha}=a_1/a_3$</TEX>and <TEX>${\rho}_{\beta}=a_1/a_2$</TEX>). Measured data were compared with the theoretical approaches proposed by Lee et al. Mica and talc were useed as disk-like fillers in the composites. As experimental results, <TEX>${\alpha}_{11}/{\alpha}_m$</TEX> decreased down to ca. 0.56 with mica content of 20 wt% and the aspect ratios, <TEX>${\rho}_{\alpha}=13.5$</TEX>, <TEX>${\rho}_{\beta}=1.8$</TEX>. However, <TEX>${\alpha}_{33}/{\alpha}_m$</TEX> increased to more than 1. In the case of talc, <TEX>${\alpha}_{11}/{\alpha}_m$</TEX> decreased to ca. 0.63 with 20 wt% and <TEX>${\rho}_{\alpha}=3.7$</TEX>, <TEX>${\rho}_{\beta}=1.4$</TEX>. Finally, the longitudinal CTEs (<TEX>${\alpha}_{11}$</TEX>) of polypropylene composites decreased as filler contents increased, but normal CTE (<TEX>${\alpha}_{33}$</TEX>) increased in the low filler contents like the theory.