Theory of thermal expansion of composites

The problem discussed is to find the overall thermal expansion of a composite consisting of inclusions in a matrix of material with different expansion coefficients and elastic moduli. The volume mismatch causes strain fields. The total strain energy must be a minimum. This problem was solved previously for inclusions which are either spheres or randomly oriented long cylinders. In these simple cases the matrix strain field consists of a short-range shear component and a uniform expansion; the inclusion suffers uniform strain. The matrix is replaced by an effective medium having the average properties of the composite. The overall expansion coefficient could be obtained in closed form. This separation of the strain field into short-range shear and long-range uniform dilation is valid, at least to a good approximation, for all inclusion shapes. Simple expressions can thus be obtained in terms of coefficients which, although not calculated exactly, can be deduced approximately or can be determined empirically. Plasticity can be accounted for by allowing the shear modulus to depend on the temperature and on the maximum shear strain. The size of the inclusions does not enter the theory except through the yield strain, which depends on the extent of the strain field.Paper presented at the Ninth International Thermal Expansion Symposium, December 8–10, 1986, Pittsburgh, Pennsylvania, U.S.A.     

Thermal expansion of selected graphite-reinforced polyimide-, epoxy-, and glass-matrix composites

The thermal expansion of continuous carbon-fiber reinforced composites with epoxy-, polyimide-, and borosilicate glass-matrices has been measured and compared. The expansion of a rubber-toughened epoxy-matrix/P75S carbon-fiber composite was very different from the expansion of two different single-phase epoxy-matrix/P75S composites, although all three had the same stacking sequence. Reasonable agreement was obtained between measured thermal expansion data and results from classical laminate theory. Microdamage in the graphite/polyimide laminate, induced by 250 cycles between –156 and 121°C, caused a 53% decrease in the coefficient of thermal expansion. The thermal expansion of the graphite/glass laminate was not changed after 100 thermal cycles from –129 to 38°C; however, a residual strain of about 10×10^–6 was observed for the laminate tested.     

Thermal expansion in metal/lithia-alumina-silica (LAS) composites

Lithia-alumina-silica (LAS) with metallic dispersions offers a new approach toward near-zero, isotropic, thermal expansion composites. The metallic phase contributes a positive coefficient of thermal expansion (CTE) to the negative CTE of the glass/ceramic matrix. In addition, the metal will increase the electrical and thermal conductivities over those of the matrix alone. The LAS system offers tailorable negative CTEs and light weight compared to other negative CTE ceramics. The most negative CTE phase is crystalline -eucryptite, whose proportion in an initially glassy matrix can be controlled by heat treatment. Dispersed metal powders were both hot-pressed and cold-pressed and sintered together with LAS matrices prepared by sol gel methods. Super Invar powder was studied for its minimal CTE mismatch, while titanium powders offered a compromise between light weight and low CTE. An ultralow-expansion (ULE) glass- and linear variable differential transducer (LVDT)-based differential dilatometer was developed for rapid screening of compositions, while a double-laser Michelson interferometer was used for precise near-zero CTE measurements. The reinforced -eucryptite glass/ceramic matrix exhibited both a U-shaped L/L curve with temperature and some thermal hysteresis, depending on the fabrication and heat treatment sequences. The temperature of the zero-CTE portion of this curve was found to change with increasing titanium powder content. Results are also given for mixtures of Super Invar powders in ULE glass and -eucryptite matrices. Negative CTEs in a LAS matrix above ambient temperatures were more difficult to obtain than below, although the use of petalite (high-silica LAS) appears promising.Paper presented at the Ninth International Thermal Expansion Symposium, December 8–10, 1986, Pittsburgh, Pennsylvania, U.S.A.     

Thermal expansion and stress relaxation of metal-matrix composites

The coefficient of thermal expansion (CTE) of a series of Al-6%Si matrix samples, with reinforcements of carbon, SiC, Al₂O₃, or boron fibres, cloths, or ceramic particles was measured in the range 60°–220°C with a dilatometer. The anisotropy of the CTE was measured and found to be very large for specimens unidirectionally reinforced with carbon fibre. Relaxation of stresses due to the different thermal expansion of matrix and reinforcement was studied by using the bending of asymmetrically reinforced samples and the magnitude of the stresses evaluated using bending beam theory.     

Thermal expansion of graphite fiber-reinforced metals

The presence of graphite fibers in metal matrices greatly influences the properties of the composites. Graphite fibers have been used in conjunction with aluminum, magnesium, and copper matrices. The type of graphite fiber, layup of the fiber, and volume percentage of the fibers are all important parameters in controlling the properties of the composites. The present status, particularly in the case of graphite/copper, can be considered to be the original developmental stage and is definitely far-removed from a matured technology. The present paper focuses on thermal expansion behavior of several graphite-metal matrix composites from –60 to +200°C.Paper presented at the Tenth International Thermal Expansion Symposium, June 6–7, 1989, Boulder, Colorado, U.S.A.     

Thermal expansion of a novel hybrid SiC foam–SiC particles–Al composites

A new type of hybrid SiC foam–SiC particles–Al composites (V_SiC = 53, 56.2 and 59.9%) to be used as an electronic packaging substrate material were fabricated by squeeze casting technique, and their thermal expansion behavior was evaluated. The coefficients of thermal expansion (CTEs) of the hybrid composites in the range of 20–100 °C were found to be between 6.6 and 7.7 ppm/°C. The measured CTEs are much lower than those of SiC particle-reinforced aluminum (SiC_p–Al) composites with the same content of SiC because of the characteristic interpenetrating structure of the hybrid composites. A material of such a low CTE is ideal for electronic packaging because of the low thermal mismatch (and therefore, low thermal stresses) between the electronic component and the substrate. To achieve similar CTEs in SiC_p–Al composites, the volume fraction of SiC would be much higher than that in the hybrid composites.     

Thermal expansion behaviour of aluminum matrix composites with densely packed SiC particles

The coefficient of thermal expansion (CTE) of Al-based metal matrix composites containing 70 vol.% SiC particles (AlSiC) has been measured based on the length change from room temperature (RT) to 500 °C. In the present work, the instantaneous CTE(T) of AlSiC is studied by thermo-elastic models and micromechanical simulation using finite element analysis in order to explain abnormalities observed experimentally. The CTE(T) is predicted according to analytical thermo-elastic models of Kerner, Schapery and Turner. The CTE(T) is modelled for heating and cooling cycles from 20 °C to 500 °C considering the effects of microscopic voids and phase connectivity. The finite element analysis is based on a two-dimensional unit cell model comparing between generalized plane strain and plane stress formulations. The thermal expansion behaviour is strongly influenced by the presence of voids and confirms qualitatively that they cause the experimentally observed decrease of the CTE(T) above 250 °C.     

Thermal expansion behaviour of unidirectional carbon-fibre-reinforced copper-matrix composites

Continuous carbon-fibre-reinforced copper-matrix composites prepared by diffusion bonding technology have been used for investigation of the coefficient of thermal expansion. For reasons of economy and ease of availability, continuous Torayca T300 fibres have been used for sample preparation. They were coated continuously with copper (galvanically and then chemically) and unidirectional composites were prepared by diffusion bonding in vacuum at 873 K for 30 min. The linear coefficient of thermal expansion (CTE) of samples with different volume fractions of carbon fibres was measured in directions parallel and perpendicular to the fibre direction. The samples were heat-treated for one temperature cycle in the range 293–573 K or cycled three times in a temperature range from 253 to 573 K. Measured CTE values are compared with those predicted by the well-known Schapery model and the model derived by Kural and Min. Better agreement was achieved with the predictions of the longitudinal CTE of the composite. Prediction of the transverse CTE was more difficult because of a lack of knowledge of the transverse CTE of carbon fibres. Models including the transverse CTE of carbon fibres (Kural–Min) gave better results for prediction of the transverse CTE of the unidirectional composite.     

Thermal expansion of TiAl + TiB2 alloys and model calculations of stresses and expansion of continuous fiber composites

Thermal expansion values for three TiAl alloys with different additions of TiB₂ can be represented using a third-order equation at temperatures between 20 and 800°C. Expansion values were obtained on both heating and cooling temperature cycles. The total expansion at 800°C is between 0.917 and 0.931% for three different samples. The expansivity increases from about 10×10^–6°C^–1 at 80°C to 14×10^–6°C^–1 at 750°C. A five-coaxial cylinder elastic model for multizone-coated continuous fiber composites is developed for predicting stresses and thermal expansion of composites. Either isotropic or transversely isotropic material properties can be assigned to the various cylinder zones.Paper presented at the Tenth International Thermal Expansion Symposium, June 6–7, 1989, Boulder, Colorado, U.S.A.     

Thermal expansion of composites

Coefficient of thermal expansion (CTE) has been determined for selected composite materials using differential thermal analysis. Variables evaluated were: type of material, with particular emphasis on filler content; annealing; thermal history, with particular attention being payed to the effects of multiple heating and cooling cycles; ageing in wet or dry conditions. Filler content was a major factor involved in controlling CTE, although clearly other factors such as the type of filler, resin and degree of conversion are important. For an inlay material, annealing at 120°C significantly reduced the value of coefficient of thermal expansion and this is most likely due to an increase in conversion of methacrylate groups. The findings of this study confirm those of previous studies regarding the reduction in CTE following an initial heating. This is most likely due to the relief of internal stress. New information reported here relates to the fact that stress release can occur slowly without heating and that rapid stress release can be achieved through water storage at mouth temperature. These results suggest that, clinically, internal stresses induced by polymerization will be dissipated rapidly. A further finding was that long-term water storage causes an increase in CTE, which may reflect changes at the resin-filler interface.     

Thermal expansion characteristics of cast Cu based metal matrix composites

Like any other metal/alloy, copper and its alloys also soften at elevated temperatures. Reinforcing with ceramic or carbon fibres is one of the suggested solutions to overcome this. Very limited literature is available on Cu based metal matrix composites (MMCs); none of these pertain to liquid phase fabrication. Hence, a systematic investigation was carried out on MMCs based on copper, with alumino-silicate fibres and carbon fibres as reinforcements. The MMCs thus produced exhibit a uniform distribution of reinforcement in the matrix. Coefficient of thermal expansion (CTE) values are lower than that of pure copper.     

Thermal expansivities in fibrous composites incorporating hybrid interphase regions

The aim of this paper is the prediction of coefficients of thermal expansion in unidirectional fiber-reinforced composites. The representative volume element is a three phase composite structure subjected to a uniform temperature change. The advanced hybrid interphase concept is introduced, in which the interphase thickness depends on the property under consideration. This model involves also imperfect adhesion by immediate softening of material properties. Equations for the prediction of coefficients of thermal expansion are presented. Results are illustrated and discussed in terms of fiber volume fraction and adhesion coefficient. To validate the accuracy of these results finite element analysis has also been utilized. Predictions of coefficients of thermal expansion are in good agreement with experimental, finite element analysis and previous published results. The coefficients of thermal expansion of the considered polymer matrix composites are affected significantly by the parameters characterizing interphase.     

Thermal expansion properties of 6061 Al alloy reinforced with SiC particles or short fibers

Thermal expansion measurements are reported for 6061 Al alloy and drawn composite materials reinforced with SiC particles or aligned short fibers. Samples with volume fractions of 5 and 20% SiC were measured in the drawing direction. The measurements were obtained from repeated heating and cooling cycles between room temperature and 500°C. Cumulative plastic strains were measured for the repeated thermal cycles, in association with the observation that lower expansivities generally occurred on cooling as compared with heating. Model calculations for particulate and an aligned fiber are presented for the combined elastic-plastic deformation properties of the Al/SiC composite systems. Lower expansivities and greater plastic strains are accounted for in the fiber-reinforced material.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Thermal mismatch induced disorder of beta-eucryptite and its effect on thermal expansion of beta-eucryptite/Al composites

In this paper, beta-eucryptite/Al composites with different volume fraction of beta-eucryptite particles (Euc/Al) were prepared by spark plasma sintering process. The microstructures of the composites were studied by transmission electron microscope. The phase compositions and thermal physical properties of the composites were analyzed by X-ray diffraction and thermal dilatometer. The change of peaks intensity ratio of beta-eucryptite (2 0 0) to beta-eucryptite (2 0 2) plane after 12 months of aging in room condition and at elevated temperature (40–300 °C) was used to characterize the disorder of beta-eucryptite, which was due to the high thermal mismatch stress in the composite. The results indicate that the disorder of beta-eucryptite can recover when the thermal mismatch stress in beta-eucryptite is released after 12 months of aging or at elevated temperature. Both compressive stress and tensile stress could induce the disorder of eucryptite (2 0 0) plane. The relationships among CTE behavior of the composite, the phase transformation of beta-eucryptite and the thermal mismatch stress were discussed.     

Cf/Mg复合材料的热膨胀系数及其理论计算

采用负压浸渗-液固挤压法制备了定向短切碳纤维（aligned Csf）及穿刺-2D碳纤维织物（2.5DCf）增强镁合金复合材料,观察了两种复合材料的微观组织结构,测定了其在30～350℃范围的热膨胀系数（α）,并在Schapery模型的基础上提出了计算定向Csf/Mg复合材料及2.5DCf/Mg复合材料α值的修正模型。结果表明,在30～200℃范围内,两种Cf/Mg复合材料的α值均表现出随温度的升高而升高的趋势,但在超过250℃以后,α值出现降低或稳定的现象,其原因为随着温度的升高,铝元素固溶度的增大、基体发生部分塑性变形等因素导致的;提出的修正模型理论计算值与其相应的实验测试α值之间的误差均在5%之内,表明该修正模型能够有效预测实验中的α值。     

3D C/C复合材料的热膨胀性能

通过测定热膨胀系数(CTE),分析了不同密度以及高温处理前后热解炭基三维编织炭/炭复合材料(3DC/C复合材料)的热膨胀行为,并与PAN基炭纤维以及热解炭的热膨胀性能作了比较。结果表明:PAN基炭纤维在1200℃以后,出现明显的负膨胀。从室温到100℃,C/C复合材料呈负膨胀状态,CTE与密度成正比;从100℃到1000℃,C/C复合材料的CTE-温度曲线基本遵循热解炭基体的热膨胀规律变化;超过1000℃以后,CTE-温度曲线出现峰值,表明热解炭的膨胀受纤维的限制。复合材料的热膨胀行为由纤维和基体二者决定。     

Thermal expansion behaviour of thermoplastic composites

The thermal-expansion behaviours of a variety of thermoplastic composites based on the ICI Victrex polymers PEEK, ITA, HTA and ITX are examined. It is shown that when each of the composites is raised above the glass-transition temperature, T _g, of the polymer matrix considerable permanent distortion occurs in the small samples used, though the effect is not evident below T _g. This is attributed to relaxation of process-induced residual stresses generated in the larger plates from which the samples were prepared. A number of models are used to calculate the thermal-expansion behaviour of the fibres transverse to their long axes; the results are shown to be inconsistent, and in poor agreement with directly measured properties. Finally, the utility of the data for calculation of thermal-expansion behaviour parallel to the fibres in the composites is considered.     

Thermal expansion characteristics of PEEK composites

The thermal expansion behaviour of several fibre-reinforced PEEK composites is assessed. It is shown that thermal expansion behaviour is consistent, and changes in a predictable manner with changes in fibre type. Using a composite manufactured such that no interfacial bonding took place, it is demonstrated that compressive forces caused by differential thermal contraction of fibre and matrix are sufficiently large to dominate behaviour in a direction parallel to the fibres. This suggests that PEEK composites should be resistant to changes in thermal expansion behaviour with repeated thermal cycling, and such resistance is demonstrated for AS4/PEEK (APC-2/AS4). It is shown that conventional models for predicting laminate response from unidirectional composite properties are valid for such materials, but it is also shown that the common analytical models for calculating transverse fibre behaviour from composite properties are inaccurate.     

Thermal expansion of high-modulus fibers

A resistance-heating technique was used to measure the axial thermal expansion of high-modulus boron and silicon carbide (SiC) fibers from room temperature to 700 and 1500°C, respectively. Both types of fibers investigated in this study were manufactured by a chemical vapor deposition (CVD) process. The boron fibers examined here are composed of boron and a tungsten boride core arising from reaction of deposited boron with a tungsten wire substrate. The composition of the SiC fibers consists of a SiC sheath with a carbon-rich outer coating surrounding an unreacted pyrolytic graphite coated carbon core. The thermal expansion of boron fibers was found to increase parabolically with temperature up to 700°C. Above this temperature the fiber contracted due to void migration and subsequent residual stress relaxation. For SiC fibers, a relatively small initial expansion from room temperature to 450°C was observed. Above 450°C the expansion was found to increase linearly with temperature up to 1300°C, where a hysteresis effect was observed involving a 50% reduction in expansion. Possible explanations for this hysteresis effect were considered and different theories presented. Volume percentage of carbon core was varied and found to have negligible effect on expansion. The conclusion was reached that expansion of these SiC fibers is controlled by the SiC sheath.Paper presented at the Tenth International Thermal Expansion Symposium, June 6–7, 1989, Boulder, Colorado, U.S.A.