A novel implementation algorithm of asymptotic homogenization for predicting the effective coefficient of thermal expansion of periodic composite materials

Asymptotic homogenization (AH) is a general method for predicting the effective coefficient of thermal expansion (CTE) of periodic composites. It has a rigorous mathematical foundation and can give an accurate solution if the macrostructure is large enough to comprise an infinite number of unit cells. In this paper, a novel implementation algorithm of asymptotic homogenization (NIAH) is developed to calculate the effective CTE of periodic composite materials. Compared with the previous implementation of AH, there are two obvious advantages. One is its implementation as simple as representative volume element (RVE). The new algorithm can be executed easily using commercial finite element analysis (FEA) software as a black box. The detailed process of the new implementation of AH has been provided. The other is that NIAH can simultaneously use more than one element type to discretize a unit cell, which can save much computational cost in predicting the CTE of a complex structure. Several examples are carried out to demonstrate the effectiveness of the new implementation. This work is expected to greatly promote the widespread use of AH in predicting the CTE of periodic composite materials.

PREPARATION OF HIGH THERMAL EXPANSION COEFFICIENT PORCELAINS FUSED TO METALS

Usually the thermal expansion coefficients (TEC) of metals are higher than that of porcelains. In order to match the TECs in the case of coating porcelains on metals, high TEC porcelains are needed. In this research, the high TEC phase leucite (KAlSi2 O6) in the high TEC porcelain was prepared by sol-gel method. The crystal size of leucite made by sol-gel is about 77nm through controlling the process parameters. The process from xerogel to leucite was investigated by means of DSC (differential scanning calorimetry), TG (thermogravimetry), XRD ( X-ray diffraction) and IR (infrared absorption spectrum). Leucite had been detected after the gel was treated at 900℃, this formation temperature is about 250℃ lower than that of melting method. The porcelain made from 50% of the leucite powder and 50% of low fused temperature frit has an average TEC of 19.2×10-6/℃ C from room temperature to 450℃, which is much higher than the common porcelains.

Thermal Expansion Coefficients of Thin Crystal Films

The formulas for atomic displacements and Hamiltonian of a thin crystal film in phonon occupation number representation are obtained with the aid of Green's function theory. On the basis of these results, the formulas for thermal expansion coefficients of the thin crystal film are derived with the perturbation theory, and the numerical calculations are carried out. The results show that the thinner films have larger thermal expansion coefficients.

Effect of colouring green stage zirconia on the adhesion of veneering ceramics with different thermal expansion coefficients

This study evaluated the adhesion of zirconia core ceramics with their corresponding veneering ceramics, having different thermal expansion coefficients （TECs）, when zirconia ceramics were coloured at green stage. Zirconia blocks （N=240; 6 mm x 7 mm x 7 mm） were manufactured from two materials namely, ICE Zirconia （Group 1） and Prettau Zirconia （Group 2）. In their green stage, they were randomly divided into two groups. Half of the specimens were coloured with colouring liquid （shade A2）, Three different veneering ceramics with different TEC （ICE Ceramic, GC Initial Zr and IPS e.max Ceram） were fired on both coloured and non-coloured zirconia cores. Specimens of high noble alloys （Esteticor Plus） veneered with ceramic （VM 13） （n= 16） acted as the control group. Core-veneer interface of the specimens were subjected to shear force in the Universal Testing Machine （0.5 mm-min-1）. Neither the zirconia core material （P=0.318） nor colouring （P=0.188） significantly affected the results （three-way analysis of variance, Tukey＇s test）. But the results were significantly affected by the veneering ceramic （P=0.000）. Control group exhibited significantly higher mean bond strength values （45.7__.8） MPa than all other tested groups （（27.1__.4.1）-（39.7__.4.7） and （27.4__.5.6）-（35.9___4.7） MPa with and without colouring, respectively） （P^0.001）. While in zirconia-veneer test groups, predominantly mixed type of failures were observed with the veneering ceramic covering ~ 1/3 of the substrate surface, in the metal-ceramic group, veneering ceramic was left adhered 1/3 of the metal surface. Colouring zirconia did not impair adhesion of veneering ceramic, but veneering ceramic had a significant influence on the core-veneer adhesion. Metal-ceramic adhesion was more reliable than all zirconia-veneer ceramics tested.

Measurement Method of Compressibility and Thermal Expansion Coefficients for Density Standard Liquid at 2329 kg/m^3 based on Hydrostatic Suspension Principle

The accurate measurement on the compressibility and thermal expansion coefficients of density standard liquid at 2329kg/m3（DSL-2329） plays an important role in the quality control for silicon single crystal manufacturing. A new method is developed based on hydrostatic suspension principle in order to determine the two coefficients with high measurement accuracy. Two silicon single crystal samples with known density are immersed into a sealed vessel full of DSL-2329. The density of liquid is adjusted with varying liquid temperature and static pressure, so that the hydrostatic suspension of two silicon single crystal samples is achieved. The compression and thermal expansion coefficients are then calculated by using the data of temperature and static pressure at the suspension state. One silicon single crystal sample can be suspended at different state, as long as the liquid temperature and static pressure function linearly according to a certain mathematical relationship. A hydrostatic suspension experimental system is devised with the maximal temperature control error ±50 μK; Silicon single crystal samples can be suspended by adapting the pressure following the PID method. By using the method based on hydrostatic suspension principle, the two key coefficients can be measured at the same time, and measurement precision can be improved due to avoiding the influence of liquid surface tension. This method was further validated experimentally, where the mixture of 1, 2, 3-tribromopropane and 1,2-dibromoethane is used as DSL-2329. The compressibility and thermal expansion coefficients were measured, as 8.5′10–4 K–1 and 5.4′10–10 Pa–1, respectively.

Microstructure evolution,mechanical properties and tailoring of coefficient of thermal expansion for Cu/Mo/Cu clad sheets fabricated by hot rolling

The law of microstructure evolution and mechanical properties of hot roll bonded Cu/Mo/Cu clad sheets were systematically investigated and the theoretical prediction model of the coefficient of thermal expansion(CTE)of Cu/Mo/Cu clad sheets was established successfully.The results show that the deformation of Cu and Mo layers was gradually coherent with an increase in rolling reduction and temperature and excellent interface bonding was achieved under the condition of a large rolling reduction.The development of the microstructure and texture through the thickness of Cu and Mo layers was inhomogeneous.This phenomenon can be attributed to the friction between the roller and sheet surface and the uncoordinated deformation between Cu and Mo.The tensile strength of the clad sheets increased with increasing rolling reduction and the elongation was gradually decreased.The CTE of Cu/Mo/Cu clad sheets was related to the volume fraction of Mo.The finite element method can simulate the deformation and stress distribution during the thermal expansion process.The simulation result indicates that the terminal face of the clad sheets was sunken inward.

Analytical Model of Elastic Modulus and Coefficient of Thermal Expansion for 2.5D C/SiC Composite

To make better use of 2.5D C/SiC composites in industry, it is necessary to understand the mechanical properties. A finite element model＇of 2.5D composites is established, by considering the fiber undulation and the porosity in 2.5D C/SiC composites. The fiber direction of warp is defined by cosine function to simulate the undulation of warp, and based on uniform strain assumption, analytical model of the elastic modulus and coefficient of thermal expansion （CTE） for 2.5D C/SiC composites were established by using dual- scale model. The result is found to correlate reasonably well with the predicted results and experimental results. The parametric study also demonstrates the effects of the fiber volume fraction, distance of warp yarn, and porosity in micro-scale on the mechanical properties and the coefficients of thermal expansion.

Density and thermal expansion coefficients of liquid and austenite phase in lamellar cast iron

Volume change related defects formation mechanisms are an important detracting phenomenon in production of complex shaped cast components.Among different technical alloys,cast iron behaves in a complex manner due to the combined volume change of the formed phases.The liquid and the austenitic phase are contracting while the graphite phase is expanding during the solidification.The complex volume change in combination with complex casting shapes causes a considerable deviation from isotropy in the solidification domain.The mentioned difficulties are considered the main reason why an extensive research work is condensed in the literature within this topic.The multitude of reported experimental set up and the various efforts to interpret the volume change phenomena in terms of density and thermal expansion coefficients makes the results difficult to compare from different sources.With these difficulties in mind,the present paper presents a broad experimental series and measures unidirectional linear deformation of an industrially spread lamellar cast iron alloy system(Fe-C-2Si)using the push-rod based dilatometer technique.The measurements are divided into two major groups with respect to the liquid iron deformation over the liquidus temperature line,and the austenite deformation below the solidus temperature line.The obtained results are interpreted as thermal expansion coefficients,density variation slopes,and density data at the liquids and solidus temperature.The obtained results are compared with literature data and with calculated values by the Thermo Calc software.

The Approach of Compensation of Air Refractive Index in Thermal Expansion Coefficients Measurement Based on Laser Feedback Interferometry

We present the thermal expansion coefficient （TEC） measurement technology of compensating for the effect of variations in the refractive index based on a Nd： YA G laser feedback system, the beam frequency is shifted by a pair of aeousto-optic modulators and then the heterodyne phase measurement technique is used. The sample measured is placed in a muffle furnace with two coaxial holes opened on the opposite furnace walls. The measurement beams hit perpendicularly and coaxially on each surface of the sample. The reference beams hit on the reference mirror and the high-refiectivity mirror, respectively. By the heterodyne configuration and computing, the influences of the vibration, distortion of the sample supporter and the effect of variations in the refractive index are measured and largely minimized. For validation, the TECs of aluminum samples are determined in the temperature range of 29-748K, confirming not only the precision within 5 × 10-7 K-1 and the accuracy within 0.4% from 298K to 448K but also the high sensitivity non-contact measurement of the lower reflectivity surface induced by the sample oxidization from 448 K to 748 K.

Effects of heat treatment temperature on crystallization and thermal expansion coefficient of Li_2O-Al_2O_3-SiO_2

The basic glass of Li2O-Al2O3-SiO2 system using P2O5 as nucleator was prepared by means of conventional melt quenching technology, and the heat-treatment process was determined by using differential thermal analysis. The crystalline phases and the microstructure of the glass-ceramics were investigated by using X-ray diffraction and scanning electron microscopy. The results show that the glass based on Li2O-Al2O3-SiO2 oxides using P2O5 as nucleator can be prepared at lower melt temperature of 1 450 ℃ and the glass-ceramics with lower thermal expansion coefficient of 21.6×10-7 ℃-1 can also be obtained at 750 ℃. The glass-ceramics contain a few crystal phases in which the main crystal phase is β-quartz solid solution and the second crystal phase is β-spodumene solid solution. When the heat treatment temperature is not higher than 650 ℃, the transparent glass-ceramics containing β-quartz solid solution can be prepared. β-quartz solid solution changes into β-spodumene solid solution at about 750 ℃. And the appearance of the glass-ceramics changes from translucent, part opaque to complete opaque with increasing （temperature.）

Superplastic forming of Ti6Al4V alloy using ZrO_(2)-TiO_(2) ceramic die with adjustable linear thermal expansion coefficient

Firstly,the relation between the coefficient of thermal expansion(CTE)and the volume fraction of TiO_(2) was investigated, and also the influence of relative density of ceramic on the CTE was studied.The results show that the volume fraction of TiO_(2) and the relative density both make influence on the CTE of ZrO_(2)-TiO_(2) ceramic.According to the results,the ZrO_(2)-TiO_(2)(volume fraction of TiO_(2) is 27%)ceramic die with the similar CTE(8.92×10^(-6) ℃^(-1))to Ti6Al4V was fabricated.Secondly,to evaluate the dimensional accuracy of the workpiece superplastically formed,the Ti6Al4V impression experiment was performed.The result shows that the dimensional inaccuracy of workpiece is 0.003.Thirdly,in order to evaluate the practicability,the experiment of superplastic forming Ti6Al4V using ZrO_(2)-TiO_(2) cylinder ceramic die was carried out.The Ti6Al4V cylinder shows good shape retention and surface quality,and high dimensional accuracy.The ceramic dies seem to be adequate for superplastic forming the high accuracy Ti6Al4V, and the trials have confirmed the potential of the ZrO_(2)-TiO_(2) ceramic die.

High Performance ZrNbAl Alloy with Low Thermal Expansion Coefficient

Thermal expansion is a common phenomenon in both metals and alloys, which is important for metallic material applications in modern industry, especially in nuclear and aerospace industries. A lower thermal expansion coefficient may cause lower thermal stress and higher accuracy. A new Zr-based alloy is developed and presented.The XRD diffraction results demonstrate that only a close-packed hexagonal phase（α or α＇ phase） exists in the microstructure. The thermal expansion and mechanical properties are studied. According to the experimental results, the new Zr-based alloy presents a low thermal expansion coefficient and good mechanical properties.Also,its thermal expansion coefficient is stable through solution treatment.

Study on Thermal Expansion Coefficient of Sealing Materials for Ceramic Metal Halide Lamps

With Al2O3, Dy2O3, and SiO2 as starting materials, the basic glass of Al2O3-Dy2O3-SiO2 system was prepared by conventional melting technology, and their thermal expansion coefficients （TECs） at different anneal time were investigated. TECs of the basic glass, which were heat-treated under different temperature, were also investigated. The result showed that TECs of the basic glass gradually approached a fixed value as the anneal time was extended, which suggested that most of the inner stress had been eliminated. After heat treatment, the contents of Dy2O3, Dy2Si2O7, and a new crystal increased up to 1200 ℃ and decreased below 1250 ℃, which was consistent with the TEC change of crystallized samples. This suggests that the crystal has a direct effect on TECs of the crystallized samples.

Determination of the Thermal Expansion Coefficient of Concrete at Early Ages by Using Temperature-stress Testing Machine

By using the uptodate temperatuer-stress testing machine, the thermal expansion coefficient of concrete at early ages was studied and indicative conclusions were achieved ： temperature rising due to hydration heat is not directly correlated with cracking, but the temperature and stress evolation process should be taken into consideration in the same time. Proper chemical admixtures and mineral cornpasitions can improve the mechanical properties of concrete such as thermal expansion coefficient, which is very indicative in practice.

Determination Method of Thermal Expansion Coefficient of Cordierite

Cordierite ceramics were prepared by using talc, bauxite and kaolin clay as starting materials. According to the detected resuh of XRD step-scanning from 25° to 35° by a high temperature X-ray diffractometer, 20 and d values of five peaks of cordierite crystal were ascer- rained. Then the least squares technique was used to cal- culate the crystal parameters ： at 25 ℃ , a = b = O. 981 8 nm, c =0. 927 4 nm, V=O. 774 3 nm3 ; at 600 ℃ , a =b =O. 982 0 nm, c=0.9252 nm, V=O. 773 5 nm3. The crystal volumetric coefficient of thermal expansion （CTE） and linear CTE along a and c axes were calcu- lated, αv = 2. 33 × 10-6℃-1, αa = αb, = 3. 27 × 10-6℃ -1 , αc = -4.19 ×10-6℃ -1. The average CTE of cordierite crystal is as low as O. 78 × 10-6℃ -1

Coefficient of thermal expansion of stressed thin films

A new technique was proposed to determine the coefficient of thermal expansion (CTE) of thin films at low temperature. Different pre-stress could be applied and the elastic modulus of materials at different temperatures was measured with CTE simultaneously to eliminate the influence of mechanical deformation caused by the pre-stress. By using this technique, the CTEs of polyimide/silica nanocomposite films with different silica doping levels were experimentally studied at temperature from 77 K to 287 K, and some characteristics related to this new technique were discussed.

Microstructure evolution and thermal expansion of Cu-Zn alloy after high pressure heat treatment

The thermal expansion coefficients of Cu-Zn alloy before and after high pressure treatment were measured by thermal expansion instrument in the temperature range of 25？700 ℃,and the microstructure and phase transformation of the alloy were examined by optical microscope,X-ray diffractometer（XRD） and differential scanning calorimeter（DSC）.Based on the experimental results,the effects of high pressure treatment on the microstructure and thermal expansion of Cu-Zn alloy were investigated.The results show that the high pressure treatment can refine the grain and increase the thermal expansion coefficient of the Cu-Zn alloy,resulting in that the thermal expansion coefficient exhibits a high peak value on the α-T curve,and the peak value decreases with increasing the pressure.

DEVELOPMENT OF INCONEL~ ALLOY 783，A LOW THERMAL EXPANSION，CRACK GROWTH RESISTANT SUPERALLOY

Low thermal expansion superalloys have been used for a number of years in a variety of applications, including gas turbine engines. The low thermal expansion characteristics of the most widely used class of materials are derived from the ferromagnetic characteristics of Ni, Fe, and Co-based austenitic matrices containing little or no Cr.Alloy developments have been aimed at improving the oxidation resistance and stress accelerated grain boundary oxygen (SAGBO) attack.INCONEL alloy 783 is an oxidation resistant, low coefficient of thermal expansion superalloy developed for gas turbine applications. Alloy 783 represents a culmination in the development, of an alloy system with very high alumtnum content that, in addition to forming γ′,causes βaluminide phase precipitation in the austenitic matrix.This type of structure can be processed to resist both SAGBO and general oxidation,while providing low thermal expansion and useful mechanical properties up to 700℃.Key aspects of the alloy's development are presented.

Interface and thermal expansion of carbon fiber reinforced aluminum matrix composites

Two kinds of unidirectional PAN M40 carbon fiber （55%, volume fraction） reinforced 6061Al and 5A06Al composites were fabricated by the squeeze-casting technology and their interface structure and thermal expansion properties were investigated. Results showed that the combination between aluminum alloy and fibers was well in two composites and interface reaction in M40/5A06Al composite was weaker than that in M40/6061Al composite. Coefficients of thermal expansion （CTE） of M40/Al composites varied approximately from （1.45-2.68）×10^-6 K^-1 to （0.35-1.44）×10^-6 K^-1 between 20℃ and 450℃, and decreased slowly with the increase of temperature. In addition, the CTE of M40/6061Al composite was lower than that of M40/SA06Al composite. It was observed that fibers were protruded significantly from the matrix after thermal expansion, which demonstrated the existence of interface sliding between fiber and matrix during the thermal expansion. It was believed that weak interracial reaction resulted in a higher CTE. It was found that the experimental CTEs were closer to the predicted values by Schapery model.

Thermal expansion and mechanical properties of high reinforcement content SiC_(p)/Cu composites fabricated by squeeze casting technology

High reinforcement content SiCp/Cu composites (φp=50%, 55% and 60%) for electronic packaging applications were fabricated by patent cost-effective squeeze-casting technology. The composites appear to be free of pores, and the SiC particles are distribute uniformly in the composites. The mean linear coefficients of thermal expansion (CTEs, 20-100 ℃ ) of as-cast SiCp/Cu composites range from 8.8×10-6 ℃-1 to 9.9×10-6 ℃-1 and decrease with the increase of SiC content. The experimental CTEs of as-cast SiCp/Cu composites agree well with the predicted values based on Kerner model. The CTEs of composites reduce after annealing treatment due to the fact that the internal stress of the composite is released. The Brinell hardness increases from 272.3 to 313.2, and the modulus increases from 186 GPa to 210 GPa for the corresponding composites. The bending strength is larger than 374 MPa, but no obvious trend between bending strength and SiCp content is observed.