Longitudinal Coefficient Of Thermal Expansion Research Articles

Research on the Mechanical and Thermal Properties of Carbon-Fiber-Reinforced Rubber Based on a Finite Element Simulation.

The comprehensive performance of rubber products could be significantly improved by the addition of functional fillers. To improve research efficiency and decrease the experimental cost, the mechanical and thermal properties of carbon-fiber-reinforced rubber were investigated using finite element simulations and theoretical modeling. The simplified micromechanical model was constructed through the repeatable unit cell with periodic boundary conditions, and the corresponding theoretical models were built based on the rule of mixture (ROM), which can be treated as the mutual verification. The simulation results suggest that, in addition to the fiber volume fraction Vfc increasing from 10% to 70%, the longitudinal Young's modulus, transversal Young's modulus, in-plane shear modulus, longitudinal thermal expansion coefficient, and transversal thermal expansion coefficient changed from 2.31 × 1010 Pa to 16.09 × 1010 Pa, from 0.54 × 107 Pa to 2.59 × 107 Pa, from 1.66 × 106 Pa to 10.11 × 106 Pa, from -4.98 × 10-7 K-1 to -5.89 × 10-7 K-1, and from 5.72 × 10-4 K-1 to 1.66 × 10-4 K-1, respectively. The mechanism by which Vfc influences the properties of carbon-fiber-reinforced rubber was revealed through the distribution of Von Mises stress. This research will contribute to improving the performance of carbon-fiber-reinforced rubber and promote its application.

Thermo-mechanical behavior of 3D multi-directional braided composites based on a two-scale method

Two-scale modeling is adopted to investigate the thermo-mechanical behavior of 3D four-directional (3D4D), 3D five-directional (3D5D), and 3D full five-directional (3DF5D) braided composites. Based on the stress-strain relationship considering thermal expansion and the periodic boundary conditions, the elastic constants and the coefficients of thermal expansion (CTE) of the three types of braided composites are predicted by a two-scale homogenization method. The micro stress under free expansion and thermo-mechanical coupling is also simulated. The calculated results are in good agreement with experimental results from relevant references. The numerical results show that the longitudinal elastic and thermal expansion properties are gradually improved with the increase of axial yarn content from 3D4D to 3D5D and then to 3DF5D braided composites. The braiding angle corresponding to the zero longitudinal CTE of each braided structure is basically about 40°. Furthermore, with the increase of temperature, the longitudinal micro-stress in yarns increases gradually, but that in matrix drops. These conclusions will provide a reliable basis for the structural optimization design and safety evaluation of 3D multi-directional braided composites in a thermal environment.

Computational examination of the effect of voids on the mechanical response of composites with emphasize on the cure hardening behavior

This study investigates the effect of voids on the mechanical response of a carbon fiber reinforced polymer composite with simple finite elements micromechanical analysis. Cure hardening behavior of resin is implemented into the model to calculate the cure shrinkage, coefficients of thermal expansion (CTEs) and residual stresses. It is seen that voids cause more detrimental decrease on longitudinal CTE than transverse direction. Tensile loading to void containing residual stress-induced models show that the increasing void content diminishes the initial failure stress in longitudinal direction. Also, the reduction in transverse tensile strength with increasing voids is consistent with experimental results.

Process optimization, microstructure characterization and thermal properties of mesophase pitch-based carbon fiber reinforced aluminum matrix composites fabricated by vacuum hot pressing

Continuous mesophase pitch-based carbon fiber (MPCF) reinforced aluminum (Al) matrix composites were fabricated by vacuum hot pressing to meet the requirements of good thermal conductivity (TC), low coefficient of thermal expansion (CTE) and resistance to deformation for thermal management materials. The effect of process parameters on the microstructures and TC of 40 vol % MPCF/Al composites and the influence of MPCF volume fraction on the thermal-mechanical properties of MPCF/Al composites were studied. The results reveal that the composites with 20–50 vol % MPCF fabricated at 650 °C/45 MPa/60 min have longitudinal TC of 230.3–288.3 W/(m⋅K), over 90% of the predictions by rule of mixture, longitudinal CTE of 2.28−-0.22 ppm/K and elastic modulus of 147.5–324 GPa. The interface is mainly composed of an amorphous interface layer of 2–5 nm and a very small amount of carbide crystals. Furthermore, these composites have moderate TC, lower CTE and higher specific modulus compared with other Al matrix composites and Al alloys, which indicates they are expected to become unidirectional thermal management materials with integrated structure and function.

The effect of graphene on the deflections of multiscale composites under thermo-mechanical loading

The present investigation aims to shed light on an important aspect of graphene reinforced multiscale composites that may appear in the form of reduced dimensional stability of the structure when exposed to thermal gradients. The study consists of two main parts: an extensive review of the related literature and a thermo-mechanical analysis of a laminated composite beam made of three-phases: arbitrary oriented Graphene Nanoplatelets (GNPs) embedded in an epoxy resin (ER) polymer matrix, reinforced with E-Glass fibers.The review of related literature reveals that the problem of finding the equivalent coefficient of thermal expansion (CTE) for multiscale composites is not as easy as the conventional composites, the trend is different, and more complicating parameters are involved. The analysis includes the predictions of the effective thermo-elastic properties of the multiscale composite laminate, based on Halpin-Tsai theory and hierarchy modeling, and the formulation of the beam deflection governing equation, based on Timoshenko nonlinear (large deflection) beam theory. Different GNPs weight fractions, different E-glass fiber volume fractions, and three lamination layups are investigated. It is found that the addition of GNPs increases the beam deflections when exposed to temperature gradients and that the laminate longitudinal CTE is the main factor responsible for this effect.

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.

Microscopic damage behavior in carbon fiber reinforced plastic laminates for a high accuracy antenna in a satellite under cyclic thermal loading

For a high accuracy antenna in next radio astronomy satellite, a candidate material is carbon fiber reinforced plastics (CFRP), because negative longitudinal coefficient of thermal expansion (CTE) for unidirectional CFRP enables a laminate with 0 CTE through appropriate laminate design. This enables high structural accuracy under large temperature fluctuation like space. On the other hand, when the laminate is subjected to thermal cycles, cyclic thermal stress occurs and causes microscopic damages. In this study, we characterized damage progress in CFRP laminates and resultant variation in mechanical properties under cyclic thermal loading. Three types of matrices, such as polycyanate ester, polyimide and epoxy resin were used to prepare CFRP laminates. Specimens were subjected to thermal cycles from −197°C to 120°C. The test was periodically stopped for surface observation and flexural loading. Transverse cracks in 90° plies accumulated with thermal cycles, whereas flexural modulus remained constant. We also numerically evaluated temperature gradient and resultant thermal stress distribution during cooling by finite element analysis. The result indicates higher transverse stress appeared in the surface of the specimen and saturated to constant value which corresponded with the value calculated based on classical lamination theory.

Thermal expanding behavior of carbon nanotube-reinforced metal matrix nanocomposites-A micromechanical modeling

Thermoelastic responses of carbon nanotube (CNT)-reinforced aluminum (Al) metal matrix nanocomposites (MMNCs) are studied comprehensively using an analytical micromechanical model. The effects of various parameters, including CNT volume fraction, cross-section shape, aspect ratio, directional behavior, non-straight shape, dispersion type, arrangement type, agglomerated state and generating the aluminum carbide (Al4C3) interphase between the CNT and Al matrix on the Al MMNCs coefficient of thermal expansion (CTE) are investigated. To verify the presented model for both aligned CNT-reinforced Al MMNC and randomly oriented CNT-reinforced Al MMNC systems, the predictions are well compared with the available experimental data in the literature. It is found that both cross-section shape and arrangement type of aligned CNTs do not affect the Al MMNC thermal expansion response. With increasing the CNT volume fraction, the transverse CTE of the aligned CNT-reinforced Al MMNCs increases up to the peculiar value and then decreases. However, the longitudinal CTE and the CTE of Al MMNCs containing randomly oriented CNTs continuously decrease by increasing the volume fraction. It is observed that the Al MMNC CTE is very sensitive to the CNT directional behavior, non-straight shape and the aspect ratio. The results indicate the CNT agglomerated state can degrade the Al MMNCs CTE.

Microstructure evolution of innovative thermal bridge composite (i-TBC) for power electronics during elaboration

To improve the reliability of the power electronic modules for the high temperature applications, an innovative Thermal Bridge Composite (i-TBC) was designed. It has the architectured structure consisting of perforated FeNi36 sheet inserted between two Cu sheets. Due to simultaneous use of Cu and FeNi36, i-TBC possesses both a good thermal transverse conductivity and a limited longitudinal coefficient of thermal expansion. Different characterisations of i-TBC are required to understand the formation of its microstructure leading to the final properties. Therefore, the aim of this study was to analyse the integrity of Cu-Cu and Cu-FeNi36 interfaces as well as copper microstructure evolution throughout all elaboration steps: (i) first cold rolling, (ii) heat treatment and (iii) second cold rolling. First cold rolling did not lead to a bonding of Cu-Cu interfaces in the thermal bridge. Moreover, heterogeneity of Cu grain microstructure was observed with formation of ultra-fine grained structure close to junctions of Cu and FeNi36. The heat treatment led to a degradation of different interfaces adherence and to a complete copper recrystallization. Finally, the second cold rolling ensured an efficient solid welding of Cu-Cu interfaces and led to a heterogeneity of strain hardening of copper.

Micromechanical modeling of thermal expansion coefficients for unidirectional glass fiber-reinforced polyimide composites containing silica nanoparticles

The coefficients of thermal expansion (CTEs) of unidirectional glass fiber-reinforced polyimide composites containing silica nanoparticles are investigated. To this end, a three-dimensional unit cell-based micromechanical model together with an individual representative volume element (RVE) with c×r×h sub-cells is proposed. The interphase region between silica nanoparticle and polyimide matrix is considered as an equivalent solid continuum. Comparisons are made between the results of present model with those of available cylinder model and experiment. The results reveal that with adding silica nanoparticles to glass fiber-reinforced polyimide composites, the transverse CTE of composite decreases, while its longitudinal CTE increases. The effects of fiber volume fraction and aspect ratio, interphase thickness and material properties, silica nanoparticle volume fraction and diameter on the thermal expansion behavior of silica nanoparticle-glass fiber-reinforced polyimide composites are studied. The obtained results could be useful to guide the design of composites with optimal CTEs.

Fabrication, interface characterization and modeling of oriented graphite flakes/Si/Al composites for thermal management applications

Highly thermally conductive graphite flakes (Gf)/Si/Al composites have been fabricated using Gf, Si powder and an AlSi7Mg0.3 alloy by an optimized pressure infiltration process for thermal management applications. In the composites, the layers of Gf were spaced apart by Si particles and oriented perpendicular to the pressing direction, which offered the opportunity to tailor the thermal conductivity (TC) and coefficient of thermal expansion (CTE) of the composites. Microstructural characterization revealed that the formation of a clean and tightly-adhered interface at the nanoscale between the side surface of the Gf and Al matrix, devoid of a detrimental Al4C3 phase and a reacted amorphous Al–Si–O–C layer, contributed to excellent thermal performance along the alignment direction. With increasing volume fraction of Gf from 13.7 to 71.1vol.%, the longitudinal (i.e. parallel to the graphite layers) TC of the composites increased from 179 to 526W/mK, while the longitudinal CTE decreased from 12.1 to 7.3ppm/K (matching the values of electronic components). Furthermore, the modified layers-in-parallel model better fitted the longitudinal TC data than the layers-in-parallel model and confirmed that the clean and tightly-adhered interface is favorable for the enhanced longitudinal TC.

Effect of 3D-Braided Structure on Thermal Expansion of PIP–Cf/SiC Composites

3D3d, 3D4d, 3D5d-braided Cf/SiC composites were fabricated by precursor infiltration and pyrolysis (PIP) with polycarbosilane as the matrix precursor. The coefficient of thermal expansion (CTE) of Cf/SiC composites was measured in longitudinal and transversal directions in the temperature range from –150°C to 25°C. The longitudinal CTE varies in the range (0.09–0.68) × 10–6/°C, and the transversal CTE varies in the range (0.21–1.95) × 10–6/°C. Various CTEs of 3D-braided Cf/SiC composites were mainly determined by different braided structures of carbon fibers. The longitudinal CTE is lower than transversal CTE for the negative axial expansion of carbon fibers at cryogenic temperature. Microcracks were examined to understand the effect of structure on the thermal expansion of composites.

Thermal expansion behaviors of unidirectional carbon/carbon composites from 800 to 2500 °C

Unidirectional carbon/carbon (C/C) composites were prepared by the isothermal chemical vapor infiltration (ICVI) process. Thermal expansion behaviors of the composites from 800 to 2500°C were investigated along the longitudinal and vertical directions. Meanwhile, the thermal expansion curves of carbon fibers (CF) and pyrolytic carbon (PyC) from 800 to 2500°C were investigated individually. It was shown that coefficients of thermal expansion (CTEs) of untreated unidirectional C/C composites measured in the longitudinal and vertical directions gently increased with the increase of temperature from 800 to 1200°C. But in the temperature range of 1200–1600°C, longitudinal CTE of the untreated composites decreased sharply till reaching the lowest point at around 1600°C, and increased linearly as the temperature increased. While vertical CTE of the untreated ones increased rapidly over 1200°C until arriving the peak value at around 1600°C and fell rapidly in the temperature range of 1600–2500°C. On the other hand, for treated (2500°C, 2h) unidirectional C/C composites, CTEs in both directions increased slowly as the temperature increased from 800 to 2500°C, which varied from 1.68 to 3.07×10−6K−1 in the longitudinal direction and from 6.78 to 8.04×10−6K−1 in the vertical direction.

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.

Communication: Identical temperature dependence of the time scales of several linear-response functions of two glass-forming liquids

The frequency-dependent dielectric constant, shear and adiabatic bulk moduli, longitudinal thermal expansion coefficient, and longitudinal specific heat have been measured for two van der Waals glass-forming liquids, tetramethyl-tetraphenyl-trisiloxane (DC704) and 5-polyphenyl-4-ether. Within the experimental uncertainties the loss-peak frequencies of the measured response functions have identical temperature dependence over a range of temperatures, for which the Maxwell relaxation time varies more than nine orders of magnitude. The time scales are ordered from fastest to slowest as follows: Shear modulus, adiabatic bulk modulus, dielectric constant, longitudinal thermal expansion coefficient, and longitudinal specific heat. The ordering is discussed in light of the recent conjecture that van der Waals liquids are strongly correlating, i.e., approximate single-parameter liquids.

The hierarchical structure and properties of multifunctional carbon nanotube fibre composites

The axial mechanical, electrical and thermal properties of carbon nanotubes (CNTs) can be exploited macroscopically by assembling them parallel to each other into a fibre during their synthesis by chemical vapour deposition. Multifunctional composites with high volume fraction of CNT fibres are then made by direct polymer infiltration of an array of aligned fibres. The fibres have a very high surface area, causing the polymer to infiltrate them and resulting in a hierarchical composite structure. The electrical and thermal conductivities of CNT/epoxy composites are shown to be superior to those of equivalent specimens with T300 carbon fibre (CF) which is widely used in industry. From measurements of longitudinal coefficient of thermal expansion (CTE) of the composites we show that the CTE of CNT fibres is approximately −1.6 × 10 −6 K −1, similar to in-plane graphite. The combination of electrical, thermal and mechanical properties of CNT fibre composites demonstrates their potential for multifunctionality.

Nonlinear Thermal Expansion Model for SiC/Al

The thermal expansion behaviour of silicon carbide (SCS-2) fibre reinforced 6061 aluminium matrix composite subjected to the influenced thermal mechanical cycling (TMC) process were investigated. The thermal stress has important effect on the longitudinal thermal expansion coefficient of the composites. The present paper used experimental data of the thermal expansion behaviour of a SiC/Al composite for temperatures up to 370°C, in which their data was used for carrying out modelling of theoretical predictions.

충전제 함량 및 형태에 따른 PP복합체의 열팽창계수 변화에 대한 실증적 연구

The effects of the filler shapes and contents on the coefficient of thermal expansion (CTE) for polypropylene (PP) composites which included three dimensional ellipsoids (a1>a2>a3), as determined by two aspect ratios (ρα=a1/a3 and ρβ=a1/a2) were analyzed by the theoretical approach proposed by Lee and Paul and compared with the experimental results. The shapes of fillers in the composites were various, such as spherical, fiber, disc, and ellipsoid, using barium sulfate, glass fiber, and mica. The longitudinal CTE of barium sulfate whose shape was sphere (ρα=ρβ=1) decreased. For the glass fiber, primary aspect ratio decreased with the filler content, and longitudinal CTE decreased as filler contents increased. Normal CTE initially increased in the lower filler content. For the mica, longitudinal and transverse CTE decreased but normal CTE increased in the lower filler content like predicted values.

Nonlinear temperature characteristic of thermal expansion of Grf/Mg composites

Graphite fiber reinforced magnesium matrix(Grf/Mg) composites were fabricated by squeeze casting technology. M40 graphite fibers were reinforced to AZ91D and ZM6, their thermal expansion behaviors of M40/AZ91D and M40/ZM6 composites in the temperature range from 20 to 490 °C were investigated. The results show that the interfacial species and thermal stress have significant influence on the thermal expansion behavior of the composites. Simultaneously, the longitudinal coefficient of thermal expansion of Grf/Mg composites are affected by the thermal stress, interfacial species and yield strength of matrix alloy, it also decreases with increasing temperature and descending rate of longitudinal coefficient of thermal expansion(CTEs) of Grf/Mg composites changed in different temperature ranges. In terms of different descending rates, the curve of coefficient of thermal expansion vs temperature can be divided into three stages. The matrix alloys M40/AZ91D and M40/ZM6 yield at 170 and 155°C in the thermal expansion, respectively.

Transverse and longitudinal coefficient of thermal expansion of carbon fibers at high temperatures (300–2500 K)

The transverse and longitudinal coefficients of thermal expansion (CTE) of carbon fibers are important parameters in C/C composites behaviour. In this study, the measurements of CTE are presented at very high temperatures (up to 2500 K). Experimental validations are first realised on isotropic metallic (tungsten) fiber. Then, measurements are performed on four carbon fibers (rayon-based, PAN-based and pitch-based). The results show that the mean transverse CTE varies from 5 × 10 −6 K −1 to 10 × 10 −6 K −1 and the longitudinal one from 1.6 × 10 −6 K −1 to 2.1 × 10 −6 K −1 depending on the fiber structural properties. For that, the relationships between the structural properties and the heat treatment temperature of the carbon fibers are discussed in relation to thermal expansion behaviour. A calculation of the ratio between the transverse and the longitudinal measured CTE as a function of the temperature allows us to classify fibers from the most isotropic to the most anisotropic in relation with the structural properties measured at room temperature.