Reduced thermal stress in composites via negative thermal expansion particulate fillers

The use of negative thermal expansivity (NTE) particles as composite fillers is relatively new and the particle–matrix interface is not well studied. This lack of understanding of the particle–matrix interface is further complicated as in many engineering applications, such as microchip packaging, the composite is constrained by its surroundings and is not free to expand upon heating; an important consideration that is often not taken into account. This paper presents a systematic theoretical study of the behaviour at the particle–matrix interface under varying particle coefficient of thermal expansivity (CTE), Poisson’s ratios (including negative Poisson’s ratios), Young’s moduli, boundary conditions and particle separation distances via finite element modelling, and describes how to optimise composite formulation for problems of thermal mismatch through tailoring of particle–matrix interaction. The effects of reduced CTE are explored via models of electronic chip package assembly.     

Negative thermal expansion: a review

Most materials demonstrate an expansion upon heating, however a few are known to contract, i.e. exhibit a negative coefficient of thermal expansivity (NTE). This naturally occurring phenomenon has been shown to occur in a range of solids including complex metal oxides, polymers and zeolites, and opens the door to composites with a coefficient of thermal expansion (CTE) of zero. The state of the art in NTE solids is reviewed, and understanding of the driving mechanisms of the effect is considered along with experimental and theoretical evidence. The various categories of solids with NTE are explored, and experimental methods for their experimental characterisation and applications for such solids are proposed. An abstraction for an underlying mechanism for NTE at the supramolecular level and its applicability at the molecular level is discussed.     

Composites with needle-like inclusions exhibiting negative thermal expansion: A preliminary investigation

In this work a simple cylindrical structure with a stiff needle-like inclusion embedded within a much softer matrix is presented and analysed with the aim of obtaining a system with tunable thermal expansion properties. It is shown that by the correct combination of the thermal and mechanical properties of the matrix and inclusion, it is possible to design a system which can be tailor-made to exhibit particular values of the coefficient of thermal expansion (CTE) in the radial direction and also negative thermal expansion (NTE). In particular an analytical model to quantify the radial strain with changes in temperature is derived and verified through finite element analysis. The model is used to find correct property combinations which lead to particular values of thermal expansion which could also be negative or zero.     

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。     

Zirconium tungstate/cyanate ester nanocomposites with tailored thermal expansivity

The dimensional stability of polymer matrix composites can be enhanced by reducing the mismatch in the coefficient of thermal expansion (CTE) between the high CTE polymer matrix and low CTE fiber reinforcements, which leads to development of residual stresses and matrix microcracking. A potential strategy to diminish these residual stresses involves development of polymer nanocomposites with well dispersed nanoparticles that reduce the extent of mismatch in CTE. In this work, we explore the potential for development of bulk polymer nanocomposites with tailored thermal expansivity through incorporation of zirconium tungstate nanoparticles that are characterized by a negative CTE in a unique low viscosity bisphenol E cyanate ester (BECy) thermosetting polymer matrix. Incorporation of up to 10 vol.% whisker-like nanoparticles, synthesized by a hydrothermal method, results in a 20% reduction in the CTE of the polymer matrix. However, the nanoparticles exert a dramatic catalytic effect on the cure reaction of BECy resin and subsequently decrease the onset temperature of the glass transition for the cured polymer network, at high filler loadings.     

Study on the thermal expansion properties of C/C composites

Two different woven (2D and 3D) carbon/carbon composites (C/C) and a block carbon have been prepared by chemical vapor infiltration (CVI). The effects of the density and porosity of composites, preform architectures and heat treatment on the thermal expansion properties of the C/C composites were investigated. It is revealed that the coefficient of thermal expansion (CTE) of C/C composites is negative below 100 °C, and the CTE values are inversely proportion to its porosity. Comparing with 2D C/C composites, 3D C/C composites have a better thermal stability. Heat treatment can increase the thermal stability of composites by changing interfacial thermal stress. The thermal expansion behavior of C/C composites is considered as the result of interaction between fibers and matrix.     

Thermal expansion behavior of plasma sprayed cordierite

Bulk cordierite has unusually low thermal expansivity. We here report on a study of the thermal expansion behavior of cordierite formed by plasma spraying. It is found that the thermal expansivity is strongly influenced by crystal structure and that the thermal expansion coefficient of the high-cordierite structure is very low (1.84 × 10⁻⁶/°C). Furthermore, the as-sprayed cordierite expands 27% in volume when it is placed next to zirconia in a high-temperature furnace. This expanded structure results in even lower thermal expansivity in the later thermal cycling.     

Carbon fiber-reinforced cyanate ester/nano-ZrW2O8 composites with tailored thermal expansion

Fiber-reinforced composites are widely used in the design and fabrication of a variety of high performance aerospace components. The mismatch in coefficient of thermal expansion (CTE) between the high CTE polymer matrix and low CTE fiber reinforcements in such composite systems can lead to dimensional instability and deterioration of material lifetimes due to development of residual thermal stresses. The magnitude of thermally induced residual stresses in fiber-reinforced composite systems can be minimized by replacement of conventional polymer matrices with a low CTE, polymer nanocomposite matrix. Zirconium tungstate (ZrW(2)O(8)) is a unique ceramic material that exhibits isotropic negative thermal expansion and has excellent potential as a filler for development of low CTE polymer nanocomposites. In this paper, we report the fabrication and thermal characterization of novel, multiscale, macro-nano hybrid composite laminates comprising bisphenol E cyanate ester (BECy)/ZrW(2)O(8) nanocomposite matrices reinforced with unidirectional carbon fibers. The results reveal that incorporation of nanoparticles facilitates a reduction in CTE of the composite systems, which in turn results in a reduction in panel warpage and curvature after the cure because of mitigation of thermally induced residual stresses.     

A strain energy model for the prediction of the effective coefficient of thermal expansion of composite materials

In this paper, a strain energy model is developed for the prediction of the effective coefficient of thermal expansion (CTE) of composite materials. This model is based on the relationship established between the strain energy of the microstructure and that of the homogenized equivalent model under specific thermo-elastic boundary conditions. Expressions in closed-form are derived for the effective CTE in terms of the strain energy and effective elastic tensor. Different kinds of composites are tested to validate the model. Representative unit cells with specific boundary conditions are used to evaluate effective CTEs that are compared with available results obtained numerically and experimentally.     

Negative thermal expansion of laminates

Measurements have been carried out on the in-plane and through the thickness thermal expansion coefficients of glass polypropylene fibre composites of 50% volume fraction between room temperature and 120°C. Only in the temperature range 20° to 75°C are reproducible results obtained. It is confirmed that in-plane negative values may be obtained in specific directions. The physical reason for this and its connection with the necessary appearance of a large Poisson ratio is pointed out. The expansivity of the matrix material depends strongly on temperature. Very good agreement between the experimental values and those predicted from the properties of the two constituents is found provided that the value for the expansivity of the polyoropylene is that within the temperature range considered. It is shown that the polypropylene matrix does not provide a matrix which is stable enough in its properties to enable the system to yield consistent negative values of expansivity. An alternative system is proposed and a single experiment confirms that a negative value of the thermal expansivity of as large as –50 × 10^–6 K^–1 may be obtained.     

Measurement of volumetric thermal expansion coefficient of various nanofluids

Experiments were carried out for studying volumetric thermal expansion behavior of various nanofluids in order to evaluate their potential application in heat removal systems employing natural convection as mode of heat removal. For this purpose, various nanoparticles such as Al₂O₃, CuO, SiO₂ and TiO₂ were used, which were suspended in the base fluid (water) by ultrasonication. All nanofluids had the same concentration of 1 wt %. Each nanofluid was heated from room temperature to a maximum of about 60°C and the increase in volume due to heat addition was recorded. The volumetric thermal expansion due to heating for each nanofluid was compared to that for the base fluid for same increase in the temperature. The volumetric thermal expansion coefficient was evaluated from the measured data. Surprisingly, it was found that the nanofluids have greater volumetric thermal expansion coefficients as compared to that of the base fluid. 1The text was submitted by the authors in English.     

二维编织 C/ SiC复合材料的热膨胀系数预测

根据二维编织 C/ SiC复合材料的细观结构及其制备工艺特点 , 提出了一种预测该材料面内热膨胀系数的单胞模型。模型充分考虑了编织结构复合材料中的纤维束弯曲和 CVI工艺制备陶瓷基复合材料产生的孔洞对热膨胀系数的影响。利用单胞模型预测了二维编织 C/ SiC的结构参数、 纤维体积含量、 孔洞含量对复合材料热膨胀系数的影响规律 , 结果表明 : 随着纤维束扭结处产生间隙与纱线宽度比值的增大 , 热膨胀系数增大 ; 当其它参数不变时 , 随着纤维体积含量的增大 , 热膨胀系数反而下降; 随着孔洞含量的增加 , 热膨胀系数也出现了下降的趋势。利用 DIL402C热膨胀仪测试了二维编织 C/ SiC复合材料纵向热膨胀系数 , 试验结果与模型预测结果吻合较好。     

泡沫塑料材料的低温线膨胀系数测定

采用自行研制的高精度低温位移传感器测量出泡沫塑料材料从室温到液氢温度的微应变情况,对试验结果的可靠性进行分析.实验结果表明:低温位移传感器可准确、稳定地得出泡沫塑料材料的线膨胀系数,是一种简单实用的线膨胀系数测试方法.     

Elastic constants and thermal expansion of aluminum-SiC metal-matrix composites

The elastic behavior and the thermal expansivity of metal-matrix composites have been investigated using ultrasonic velocity and strain gage measurements. The composites used in this study consisted of three aluminum alloys reinforced with different concentrations of SiC particles. The results show that the elastic constants increase and the coefficients of thermal expansion decrease with particle content. The results also show that the behavior of elastic constants with reinforcement can be best represented by the calculations of the upper and lower bounds of Hashin and Shtrikman. The behavior of thermal expansion, however, agrees with bounds developed by Schapery. In addition, both properties are found to be related through a model linking the strain to the elastic and thermal stresses in the composite. This relationship gives promise for the nondestructive characterization of the composites using these measurements.     

Preparation and properties of polyimide nanocomposites with negative thermal expansion nanoparticle filler

Nanocomposites with tunable coefficient of thermal expansion (CTE) were prepared by incorporating cubic zirconium tungstate (ZrW₂O₈) nanoparticles at various volume percentages in a polyimide (PI). Rod-shaped nanoparticles of cubic ZrW₂O₈, which has isotropic negative thermal expansion, were synthesized using a hydrothermal method. The interfacial interaction between the PI and ZrW₂O₈ was enhanced by covalently bonding different organic moieties, including a short aliphatic silane and PI oligomer, to the surface of ZrW₂O₈. Structure–property relationships for the PI–ZrW₂O₈ nanocomposites were investigated for thermal degradation, glass transition, tensile and thermal expansion properties. Addition of ZrW₂O₈ nanoparticles did not alter the thermal degradation and glass transition temperature of the base PI. The addition of ZrW₂O₈ nanoparticles increased the Young's modulus of the polymer, indicating stiffening of the polyimide matrix. The increase was higher for nanocomposites with engineered interfaces due to the efficient load transfer achieved through the presence of linker groups. The addition of ZrW₂O₈ reduced the in-plane CTE of the base PI at all loadings studied. The CTE of the base PI was reduced by around 22% with the addition of ZrW₂O₈ at 15 volume% loading.     

Effect of annealing on the thermal expansion and residual stresses of bidirectional thermoplastic composite laminates

Thermal expansion measurements have been conducted on various [(±30)_N]_S laminates fabricated by combining different types of matrix and fibers. The main objective was to link the coefficient of thermal expansion (CTE) of these laminates to the thermophysical characteristics of the matrix. The results show how these laminates can be used to analyze the influence of annealing and glass transition temperatures on the CTE and the release of residual stresses. It is shown that to ensure a reproductive expansion during thermal cycling, the composite must be annealed at a temperature high enough over T_g of the matrix (below the melt temperature) in order to completely release the residual stresses induced during the molding phase and uniformize the crystalline structure of the matrix. Once this is done, the response of the material under thermal cycling gives reproducible coefficient of thermal expansion (CTE) with almost no distortion after each cycle.     

Thermal expansion behaviour of barium and strontium zirconium phosphates

Ba_1.5-xSr_xZr₄P₅SiO₂₄ compounds withx = 0, 0.25, 0.5, 0.75, 1.0, 1.25 and 1.5, belonging to the low thermal expansion NZP family were synthesized by the solid state reaction method. The XRD pattern could be completely indexed with respect to space group indicating the ordering of vacancy at the divalent cation octahedral sites. The microstructure and bulk thermal expansion coefficient from room temperature to 800°C of the sintered samples have been studied. All the samples show very low coefficient of thermal expansion (CTE), withx = 0 samples showing negative expansion. A small substitution of strontium in the pure barium compound changes the sign of CTE. Similarly,x = 1.5 sample (pure strontium) shows a positive CTE and a small substitution of barium changes its sign.X = 1.0 and 1.25 samples have almost constant CTE over the entire temperature range. The low thermal expansion of these samples can be attributed to the ordering of the ions in the crystal structure of these materials     

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.     

A theoretical approach for the thermal expansion behavior of the particulate reinforced aluminum matrix composite Part I A thermal expansion model for composites with mono-dispersed spherical particles

Microstructural observation revealed that the increase in the volume fraction of SiC particles lowers the coefficient of thermal expansion (CTE) of the composite, and the CTE of the metal matrix composites is proportional to the size of the Si phase. To analyze the thermal expansion behavior of aluminum matrix composites, a new model for the CTE of the mono-dispersed binary composite on the basis of Ashelby's cutting and welding approach was proposed. In the theoretical model, it was considered that during cooling relaxation of residual stresses could create an elasto-plastic deformation zone around a SiC or Al₂O₃ particle in the matrix. The size of reinforced particles and other metallurgical factors of the matrix alloy and composite were also considered. In this model, the interacting effect between the reinforced hard particle and the soft matrix is considered by introducing the influence of the elasto-plastic deformation zone around a particle, which is distinguished from the previous models. It was revealed that the CTE of the composite are influenced by the particle volume fraction, the elastic modulus and Poisson's ratio as well as the elasto-plastic deformation zone size and the particle size.     

SiO2-TiO2/聚四氟乙烯复合材料的制备及热膨胀性能

为了使微波基板材料与Cu金属衬底的热膨胀性能匹配,对陶瓷/聚四氟乙烯（PTFE）微波复合基板材料的热膨胀性能进行了研究。采用湿法工艺制备了以SiO₂和TiO₂为填料的SiO₂-TiO₂/PTFE复合材料,研究了复合材料密度、填料粒度和填料体积分数对SiO₂-TiO₂/PTFE复合材料热膨胀性能的影响。结果表明,当SiO₂的体积分数由0增至40%（TiO₂ ：34%~26%）时,SiO₂-TiO₂/PTFE复合材料的线膨胀系数（CTE）由50.13×10^-6 K^-1减小至10.03×10^-6K^-1。陶瓷粉体粒径和复合材料密度减小会导致CTE减小。通过ROM、Turner和Kerner模型计算CTE发现,ROM和Kerner模型与实验数据较相符,而实验值与Turner模型预测值之间的差异随PTFE含量的升高而逐渐增大。