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.

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.

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.

Planar bi-metallic lattice with tailorable coefficient of thermal expansion

A mechanical metamaterial that has a tailorable coefficient of thermal expansion(CTE)is promising for guaranteeing the reliability of electrical and optical instruments under thermal fluctuations.Despite growing research on the design and manufacturing of metamaterials with extraordinary CTEs,it remains challenging to achieve a nearly isotropic tailorable CTE while ensuring a sufficient load bearing capacity for applications,such as mechanical supporting frames.In this research,we propose a type of bi-metallic lattice whose CTE is artificially programmed from positive(75 ppm/K)to negative(−45 ppm/K),and whose equivalent modulus can be as high as 80 MPa.The bi-metallic lattice with a tailorable CTE in two orthogonal directions can be readily assembled without special modifications to construct large-scale planar structures with desired isotropic CTEs.A theoretical model that considers the actual configuration of the bi-metallic joint is developed;the model precisely captures the thermal deformations of lattice structures with varied geometries and material compositions.Guided by our theoretical design method,planar metallic structures that were manufactured using Al,Ti,and Invar alloy were experimentally characterized;the structures exhibited outstanding performance when compared with typical engineering materials.

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.

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.

Microstructure and thermal properties of copper matrix composites reinforced with titanium-coated graphite fibers

Milled form of mesophase pitch-based graphite fibers were coated with a titanium layer using chemical vapor deposition technique and Ti-coated graphite fiber/Cu composites were fabricated by hot-pressing sintering. The composites were characterized with X-ray diffraction, scanning/transmission electron microscopies, and by mea- suring thermal properties, including thermal conductivity and coefficient of thermal expansion （CTE）. The results show that the milled fibers are preferentially oriented in a plane perpendicular to the pressing direction, leading to anisotropic thermal properties of the composites. The Ti coating reacted with graphite fiber and formed a continuous and uniform TiC layer. This carbide layer establishes a good metallurgical interracial bonding in the composites, which can improve the thermal properties effectively. When the fiber content ranges from 35 vol% to 50 vol%, the in-plane thermal conductivities of the composites increase from 383 to 407 W.（m.K）-~, and the in-plane CTEs decrease from 9.5 x 10-6 to 6.3 10-6 K-1.

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.

Effects of boron on the microstructure and thermal properties of Cu/diamond composites prepared by pressure infiltration

Diamond reinforced copper（Cu/diamond） composites were prepared by pressure infiltration for their application in thermal management where both high thermal conductivity and low coefficient of thermal expansion（CTE） are important.They were characterized by the microstructure and thermal properties as a function of boron content,which is used for matrix-alloying to increase the interfacial bonding between the diamond and copper.The obtained composites show high thermal conductivity（660 W/（m·K）） and low CET（7.4×10-6 K-1） due to the formation of the B13C2 layer at the diamond-copper interface,which greatly strengthens the interfacial bonding.Thermal property measurements indicate that in the Cu-B/diamond composites,the thermal conductivity and the CTE show a different variation trend as a function of boron content,which is attributed to the thickness and distribution of the interfacial carbide layer.The CTE behavior of the present composites can be well described by Kerner＇s model,especially for the composites with 0.5wt% B.

Evaluation of the microstructure,thermal and mechanical properties of Cu/SiC nanocomposites fabricated by mechanical alloying

Nano-sized silicon carbide(SiC:0wt%,1wt%,2wt%,4wt%,and 8wt%)reinforced copper(Cu)matrix nanocomposites were manufactured,pressed,and sintered at 775 and 875℃in an argon atmosphere.X-ray diffraction(XRD)and scanning electron microscopy were performed to characterize the microstructural evolution.The density,thermal expansion,mechanical,and electrical properties were studied.XRD analyses showed that with increasing SiC content,the microstrain and dislocation density increased,while the crystal size decreased.The coefficient of thermal expansion(CTE)of the nanocomposites was less than that of the Cu matrix.The improvement in the CTE with increasing sintering temperature may be because of densification of the microstructure.Moreover,the mechanical properties of these nanocomposites showed noticeable enhancements with the addition of SiC and sintering temperatures,where the microhardness and apparent strengthening efficiency of nanocomposites containing 8wt%SiC and sintered at 875℃were 958.7 MPa and 1.07 vol%^(−1),respectively.The electrical conductivity of the sample slightly decreased with additional SiC and increased with sintering temperature.The prepared Cu/SiC nanocomposites possessed good electrical conductivity,high thermal stability,and excellent mechanical properties.

Effects of Chemical Treatments on Thermal Expansion Properties of Cordierite Ceramics

Cordierite honeycomb ceramics was treated with 1.5 M HNO3 , followed with 1.5 M NaOH at 93 ℃. The combination of acid treatment with alkali treatment significantly diminished the rebounding of coefficient of thermal expansion （CTE） caused by heat treatment, a phenomenon observed in samples treated solely with acid. Inductively coupled plasma （ICP） analysis results reveal that the alkali treatment preferentially dissolved ＂free＂ SiO2 left in the acid-treated samples, which is considered to be a key factor responsible for the CTE rebounding.

Study on thermal expansion behavior of Dy_2O_3-Al_2O_3-SiO_2 glass

Employing Dy2O3, Al2O3, and SiO2 as starting materials, several series of Dy2O3-Al2O3-SiO2 sealing glass were prepared. The relationship between their coefficients of thermal expansion and the contents of Dy2O3, Al2O3, and SiO2 were studied respectively. Experimental results showed that Dy2O3 and Al2O3 had a positive effect on the coefficient of thermal expansion of glass, whereas, SiO2 had a negative effect. The coefficient of thermal expansion of glass showed an apparent linear relation to the contents of these three raw materials, from which an estimation model was built, to calculate the coefficient of thermal expansion of sealing glass. Relative errors of the calculating results to testing results were no more than 2%, which suggested that the estimation model was reasonable. This study provides a good theory reference for the practical utilizing of this sealing material, through which a proper glass composition for good sealing could be easily found.

Mechanical, electrical, and thermal expansion properties of carbon nanotube-based silver and silver–palladium alloy composites

The mechanical, electrical, and thermal expansion properties of carbon nanotube（CNT）-based silver and silver–palladium（10：1, w/w） alloy nanocomposites are reported. To tailor the properties of silver, CNTs were incorporated into a silver matrix by a modified molecular level-mixing process. CNTs interact weakly with silver because of their non-reactive nature and lack of mutual solubility. Therefore, palladium was utilized as an alloying element to improve interfacial adhesion. Comparative microstructural characterizations and property evaluations of the nanocomposites were performed. The structural characterizations revealed that decorated type-CNTs were dispersed, embedded, and anchored into the silver matrix. The experimental results indicated that the modification of the silver and silver–palladium nanocomposite with CNT resulted in increases in the hardness and Young＇s modulus along with concomitant decreases in the electrical conductivity and the coefficient of thermal expansion（CTE）. The hardness and Young＇s modulus of the nanocomposites were increased by 30%？40% whereas the CTE was decreased to 50%-60% of the CTE of silver. The significantly improved CTE and the mechanical properties of the CNT-reinforced silver and silver–palladium nanocomposites are correlated with the intriguing properties of CNTs and with good interfacial adhesion between the CNTs and silver as a result of the fabrication process and the contact action of palladium as an alloying element.

Thermal Expansion and Mechanical Properties of Middle Reinforcement Content SiCp/Al Composites Fabricated by PM Technology

Middle reinforcement content SiCp/Al composites（Vp=30%, 35% and 40%） for precision optical systems applications were fabricated by powder metallurgy technology. The composites were free of porosity and SiC particles distributed uniformly in the composites. The mean linear coefficients of thermal expansion（20-100 ℃） of SiCp/Al composites ranged from 11.6×10-6 to 13.3×10-6 K-1 and decreased with an increase in volume fraction of SiC content. The experimental coeffi cients of thermal expansion agreed well with predicted values based on Kerner＇s model. The Brinell hardness increased from 116 to 147, and the modulus increased from 99 to 112 GPa for the corresponding composites. The tensile strengths were higher than 320 MPa, but no signifi cant increasing trend between tensile strength and SiC content was observed.

Na_(2)O/Li_(2)O Ratio Dependency on the Thermal,Mechanical,Dielectric Properties and Chemical Stabilities of Li_(2)O-Al_(2)O_(3)-SiO_(2) Glass

Li_(2)O-Al_(2)O_(3)-SiO_(2) based glasses were investigated as potential protection glass for electronic devices due to their excellent mechanical properties,such as high hardness,toughness,and scratch resistance.In this paper,Li_(2)O-Na_(2)O-Al_(2)O_(3)-SiO_(2) glass with different Li_(2)O/Na_(2)O ratio components were prepared by meltquenching method,and the effects of Na_(2)O/Li_(2)O ratio on the glass densities,structure,thermal,mechanical properties,and chemical stabilities were studied.The experimental results indicate that the glass transition temperature increases with the increases in Na_(2)O/Li_(2)O ratios,due to larger ion radius.While the thermal expansion coefficient slightly decreases from 11.4×10^(-6) to 11.09×10^(-6)/℃.The elastic modulus increases from 57 to 72 GPa.The bending strength reaches maximum 80.90 MPa when the Na_(2)O/Li_(2)O ratio is 1.7,then decreases as the ratio further increases.In addition,the Vicker’s hardness gets to 7.37 GPa with largest Na_(2)O/Li_(2)O ratio.Moreover,the dielectric loss and dielectric constant increases as the ratio increases.The Raman structure analysis shows the Q4[Si-O-Si]decreases as Na_(2)O/Li_(2)O ratio increases,which is responsible for the characteristic properties change.Moreover,the glass shows lowest mass loss in 10vol%HF solutions when the ratio is 1.4,while 1.7 in 5wt%NaOH solution.

Research for Optimizing Porosity of Porous Thermal-insulating Materials

With the energy crisis and ecological environment deterioration, porous thermal-insulating materials become an advanced research hotspot, and the influence of pore distribution cannot be ignored. The mathematical model is established basing on the heat transfor theory, regarding the minimum heat flux density as the objective function, the constant total porosity as a constraint condition, using the BFGS method to optimize the pore distribution. The results show that when the heat flux is the minimum, in the case of the fixed total porosity, the high temperature zone has high porosity, the low temperature zone has low porosity; the maximal fluctuating amplitude of porosity between the adjacent discrete points has great impact on the thermal insulating performanee, the greater the fluctuating amplitude, the better the thermal insulating ability. After calculating the temperature field of the corresponding physical model, it can be found that the temperature gradient is non-uniform, the temperature gradient of the high temperature zone is steep, and that of the low temperature zone is gentle. These results have guiding significance for preparation of porous thermal-insulating materials.

Microstructure and properties of electronic packaging box with high silicon aluminum-base alloy by semi-solid thixoforming

The electronic packaging box with high silicon aluminum-base alloy was prepared by semi-solid thixoforming technique.The flow characteristic of the Si phase was analyzed.The microstructures of different parts of the box were observed by optical microscopy and scanning electron microscopy,and the thermophysical and mechanical properties of the box were tested.The results show that there exists the segregation phenomenon between the primary Si phase and the liquid phase during thixoforming,the liquid phase flows from the box,and the primary Si phase accumulates at the bottom of the box.The volume fraction of primary Si phase decreases gradually from the bottom to the walls.Accordingly,the thermal conductivities of bottom center and walls are 107.6 and 131.5 W/（m·K）,the coefficients of thermal expansion（CTE） are 7.9×10-6 and 10.6×10-6 K-1,respectively.The flexural strength increases slightly from 167 to 180 MPa.The microstructures and properties of the box show gradient distribution overall.

Elevating the comprehensive thermal properties of rare-earth cerates through high-entropy design

In the rapidly evolving aerospace sector,the quest for sophisticated thermal barrier coating(TBC)materials has intensified.These materials are primarily sought for their superior comprehensive thermal characteristics,which include a low thermal conductivity coupled with a high coefficient of thermal expansion(CTE)that synergizes with the substrate.In our study,we adopt a solid-state method to synthesize a series of high-entropy rare-earth cerates:La_(2)Ce_(2)O_(7)(1RC),(La_(1/2)Nd_(1/2))2Ce_(2)O_(7)(2RC),(La_(1/3)Nd_(1/3)Sm_(1/3))_(2)Ce_(2)O_(7)(3RC),(La_(1/4)Nd_(1/4)Sm_(1/4)Eu_(1/4))_(2)Ce_(2)O_(7)(4RC),and(La_(1/5)Nd_(1/5)Sm_(1/5)Eu_(1/5)Gd_(1/5))_(2)Ce_(2)O_(7)(5RC),all sintered at 1,600℃ for 10 h.We thoroughly examine their phase structure,morphology,elemental distribution,and thermal properties.Our in-depth analysis of the phonon scattering mechanisms reveals that 4RC and 5RC exhibit exceptional thermal properties:high CTEs of 13.00×10^(−6) K^(−1) and 12.77×10^(−6) K^(−1) at 1,400℃,and low thermal conductivities of 1.55 W/(m·K)and 1.68 W/(m·K)at 1,000℃,respectively.Compared to other TBC systems,4RC and 5RC stand out for their excellent thermal characteristics.This study significantly contributes to the development of high-entropy oxides for TBC applications.

Mixed Alkali-zinc Effects on Thermo-mechanical Properties in Borosilicate Glasses

A series of mixed alkali-zinc borosilicate glasses with various r values(r=molar ratio of[ZnO]/([R^(2)O]+[ZnO]))from 0.00 to 1.00 were fabricated to probe the mixed alkali-zinc effects on thermo-mechanical properties.The nonlinear evolution of glass transition temperature(T_(g))with the addition of ZnO is ascribed to the competition of two converse factors,i e,the T_(g)depression as one of the colligative properties for a solution,on the one hand,and the enhancement of T_(g)due to the higher field strength of zinc cations compared to that of alkali ions.However,the nonlinear evolution of elastic moduli and coefficients of thermal expansion with r is attributed to the variance of intermediate-range clusters,which is confirmed by infrared and Raman scattering spectra.These findings are very helpful in tailoring the performance of borosilicate glasses.