Al_2O_3-Ti系梯度功能材料残余热应力的有限元分析

采用有限元方法（ＦｉｎｉｔｅＥｌｅｍｅｎｔＭｅｔｈｏｄ）对Ａｌ２Ｏ３－Ｔｉ系梯度功能材料在制备过程中产生的残余热应力进行了线弹性分析。详细讨论了梯度层数目、梯度层厚度和成分梯度指数对应力大小和分布的影响，确定了各项最佳参数。非梯度功能材料（ＮＦＧＭ）与优化后的梯度功能材料的残余热应力对比结果显示：梯度功能材料缓和热应力的效果十分显著。     

Thermal shock analysis for a functionally graded plate with a surface crack

Summary The fracture behavior of a functionally graded material (FGM) plate subjected to a thermal shock is studied. A surface crack is considered. The thermomechanical properties of the FGM plate are assumed to vary along the thickness direction. By using a perturbation method, the transient temperature field is solved. Then the transient thermal stresses and the corresponding thermal stress intensity factor (TSIF) are obtained. The transient thermal stresses and TSIF in an FGM ceramic/metal (ZrO₂/Ti-6Al-4V) plate are shown in figures. Dedicated to Professor Franz Ziegler on the occasion of his 70th birthday     

Al₂O₃ and γAl₂O₃ Nanomaterials Based Nanofluid Models with Surface Diffusion: Applications for Thermal Performance in Multiple Engineering Systems and Industries

Thermal transport investigation in colloidal suspensions is taking a significant research direction. The applications of these fluids are found in various industries, engineering, aerodynamics, mechanical engineering and medical sciences etc. A huge amount of thermal transport is essential in the operation of various industrial production processes. It is a fact that conventional liquids have lower thermal transport characteristics as compared to colloidal suspensions. The colloidal suspensions have high thermal performance due to the thermophysical attributes of the nanoparticles and the host liquid. Therefore, researchers focused on the analysis of the heat transport in nanofluids under diverse circumstances. As such, the colloidal analysis of H₂O composed by γAl₂O₃ and Al₂O₃ is conducted over an elastic cylinder. The governing flow models of γAl₂O₃/H₂O and Al₂O₃/H₂O is reduced in the dimensionless form by adopting the described similarity transforms. The colloidal models are handled by implementing the suitable numerical technique and provided the results for the velocity, temperature and local thermal performance rate against the multiple flow parameters. From the presented results, it is shown that the velocity of Al₂O₃–H₂O increases promptly against a high Reynolds number and it decreases for high-volume fraction. The significant contribution of the volumetric fraction is examined for thermal enhancement of nanofluids. The temperature of Al₂O₃–H₂O and γAl₂O₃–H₂O significantly increases against a higher ϕ. Most importantly, the analysis shows that γAl₂O₃–H₂O has a high local thermal performance rate compared to Al₂O₃–H₂O. Therefore, it is concluded that γAl₂O₃–H₂O is a better heat transfer fluid and is suitable for industrial and technological uses.     

Nonlinear thermal bending response of FGM plates due to heat conduction

Nonlinear thermal bending analysis is presented for a simply supported, shear deformable functionally graded plate without or with piezoelectric actuators subjected to the combined action of thermal and electrical loads. Heat conduction and temperature-dependent material properties are both taken into account. The temperature field considered is assumed to be a uniform distribution over the plate surface and varied in the thickness direction and the electric field considered only has non-zero-valued component E_Z. The material properties of functionally graded materials (FGMs) are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents, and the material properties of both FGM and piezoelectric layers are assumed to be temperature-dependent. The governing equations of an FGM plate are based on a higher order shear deformation plate theory that includes thermo-piezoelectric effects. A two step perturbation technique is employed to determine the thermal load–deflection and thermal load–bending moment curves. The numerical illustrations concern nonlinear bending response of FGM plates without or with surface bonded piezoelectric actuators due to heat conduction and under different sets of electric loading conditions. The results reveal that for the case of heat conduction the nonlinear thermal bending responses are quite different to those of FGM plates subjected to transverse mechanical loads, and the temperature-dependency of FGMs could not be neglected in the thermal bending analysis.     

Nonlinear free and forced vibration behavior of functionally graded plate with piezoelectric layers in thermal environment

In the present study, finite element formulation based on higher order shear deformation plate theory is developed to analyze nonlinear natural frequencies, time and frequency responses of functionally graded plate with surface-bonded piezoelectric layers under thermal, electrical and mechanical loads. The von Karman nonlinear strain–displacement relationship is used to account for the large deflection of the plate. The material properties of functionally graded material (FGM) are assumed temperature-dependent. The temperature field has uniform distribution over the plate surface and varies in the thickness direction. The considered electric field only has non-zero-valued component E_z. Numerical results are presented to study effects of FGM volume fraction exponent, applied voltage in piezoelectric layers, thermal load and vibration amplitude on nonlinear natural frequencies and time response of FGM plate with integrated piezoelectric layers. In addition, nonlinear frequency response diagrams of the plate are presented and effects of different parameters such as FGM volume fraction exponent, temperature gradient, and piezoelectric voltage are investigated.     

含FGM的涂层结构中热残余应力的分析与优化

本文利用有限元方法和优化理论,对含FGM(Functionally Graded Materials)层的热喷涂构件中的残余应力进行了数值分析,并获得了FGM内各组份体积含量分布的最优化形式和参数p.同时,我们也研究了喷涂构件的几何形状、涂层及基底的材料性能对于p的影响规 律。在本文的分析中,考虑了基底材料和FGM的塑性变形以及其性能对于温度的依赖。本文 的工作将有利于含FGM层的热喷涂构件的设计与生产。     

Thermomechanical bending analysis of functionally graded sandwich plates with both functionally graded face sheets and functionally graded cores

The bending response of functionally graded material (FGM) sandwich plates subjected to thermomechanical loads is investigated using a four-variable refined plate theory. A new type of FGM sandwich plate, namely, both FGM face sheets and an FGM hard core, is considered. Containing only four unknown functions, the governing equations are deduced based on the principle of virtual work and then these equations are solved via the Navier approach. Analytical solutions are obtained to predict the deflections and stresses of simply supported FGM sandwich plates. Benchmark comparisons of the solutions obtained for a degradation model (functionally graded face sheets and homogeneous cores) with ones computed by several other theories are conducted to verify the accuracy and efficiency of the present approach. The influences of volume fraction distribution, geometrical parameters, and thermal load on dimensionless deflections and normal and shear stresses of the FGM sandwich plates are studied.     

Effective elastic properties and residual stresses in directionally solidified eutectic Al<Subscript>2</Subscript>O<Subscript>3</Subscript>/YAG/ZrO<Subscript>2</Subscript> ceramics estimated by finite element analysis

Effective elastic properties and residual stresses were assessed in directionally solidified ternary eutectic ceramic, Al₂O₃/YAG/ZrO₂, by finite element analyses. A 3D finite element model was generated from a CT scan, representative of the microstructure and with a similar volume fraction. Effective elastic properties were calculated by numerical homogenisation. They highlight a quasi-isotropic behaviour of the ternary eutectic ceramics. Despite the difficulties to measure the strain, the dispersion observed in the results and the limited reliability of the materials properties, the results constitute a step towards a better understanding of the material behaviour. Thermal residual stresses induced by the manufacturing were also evaluated. Tensile residual stresses in yttria-stabilised zirconia and compressive residual stresses in YAG and alumina were highlighted. This evaluation also shed light on the influence of the phase morphology in the microstructure. Indeed, the computed spatial distribution of the residual stresses showed that they are different from one position to another due to the variation in phase morphology and also to material properties variability. Therefore, it is important when numerically assessing the thermomechanical properties to take into account the microstructure morphology as well as the variability of material properties.     

Geometry effects of substrate and coating layers on the thermal stress response of FGM structure

Summary Due to transient temperature change, the plane strain elastic-plastic problem for a functionally graded material (FGM) bonded to a homogeneous coating layer and a metal substrate is considered by the use of the finite element method (FEM). The substrate and the coating are assumed to be aluminum and partially stabilized zirconia, respectively. The FGM layer is a particulate composite of aluminum and partially stabilized zirconia with volume fractions continuously varying through the thickness. Generally in high temperature applications, the FGM system is sandwiched between a substrate layer and a coating layer. The coating layer increases the protection from heat but decreases the thermal shock resistance while the substrate layer increases the rigidity of the structure and decreases strength-related properties at high temperature. In order to compromise the thickness of both the coating and substrate layers, different values of the substrate and coating thickness are studied in order to evaluate their effects on the thermal stress response of the FGM structure. Since the main objective of the FGMs is using them in different applications with severe thermal loading conditions, the thermal stresses may be so high that some reinforcements may be fractured and/or debonded from the matrix giving a weakening effect instead of a reinforcing one. Hence, the behaviors of the reinforcements and the matrix are essential to be studied. In this regard, microscopic constitutive equations along with the temperature-dependent properties of the constituent materials are considered to enable us obtaining more realistic results of thermal stresses. Since the FGM structures are fabricated at high temperatures, thermal residual stresses are produced. In order to find out the importance of the consideration of the residual stresses arising from the fabrication process, the FGM structure with stress-free conditions is heated to the operating temperature, and its thermal stress response is compared with that one where the residual stresses are taken into account. Also, several functional forms of gradation of the constituents in the FGM layer are examined to reach the optimum profile giving the minimum stress level for the FGM structure under thermo-elasto-plastic behavior.     

Electronic Structure and Magnetic Properties of New Rare-earth Half-metallic Materials AcFe₂O₄ and ThFe₂O₄: Ab Initio Investigation

Electronic structure and magnetism of the rare-earth metals Ac and Th doped Fe₃O₄ Fe_1-xRe_xFe_2-yRe_yO₄(Re=Ac, Th; x=0, 0.5, 1; y=0, 0.5, 1.0, 1.5, 2.0) are investigated by first-principle calculations. AcFe₂O₄, FeAc₂O₄ and ThFe₂O₄ are found to be II B-type half-metals. The large bonding-antibonding splitting is believed to be the origin of the gap for AcFe₂O₄, FeAc₂O₄ and ThFe₂O₄, resulting in a net magnetic moment of 9.0μ_B, 4.0μ_B and 8.1μ_B, respectively, compared with 4.0μ_B of Fe₃O₄. Also, the conductance of AcFe₂O₄ and ThFe₂O₄ are both slightly larger than that of Fe3O4. It can be predicted that the new rare-earth half-metals AcFe₂O₄ and ThFe₂O₄ have wider application ground in spin electronic devices due to their larger magnetoresistance and higher conductivity than that of Fe₃O₄. The half-metallic feature can be maintained up to the lattice contraction of 8%, 3% and 4% for Fe₃O₄, AcFe₂O₄ and ThFe₂O₄, respectively.     

Analyzing the ZnO and CH₃NH₃PbI₃ as Emitter Layer for Silicon Based Heterojunction Solar Cells

Today, it has become an important task to modify existing traditional silicon-based solar cell factory to produce high-efficiency silicon-based heterojunction solar cells, at a lower cost. Therefore, the aim of this paper is to analyze CH₃NH₃PbI₃ and ZnO materials as an emitter layer for p-type silicon wafer-based heterojunction solar cells. CH₃NH₃PbI₃ and ZnO can be synthesized using the cheap Sol-Gel method and can form n-type semiconductor. We propose to combine these two materials since CH₃NH₃PbI₃ is a great light absorber and ZnO has an optimal complex refractive index which can be used as antireflection material. The photoelectric parameters of n-CH₃NH₃PbI₃/p-Si, n-ZnO/p-Si, and n-Si/p-Si solar cells have been studied in the range of 20–200 nm of emitter layer thickness. It has been found that the short circuit current for CH₃NH₃PbI₃/p-Si and n-ZnO/p-Si solar cells is almost the same when the emitter layer thickness is in the range of 20–100 nm. Additionally, when the emitter layer thickness is greater than 100 nm, the short circuit current of CH₃NH₃PbI₃/p-Si exceeds that of n-ZnO/p-Si. The optimal emitter layer thickness for n-CH₃NH₃PbI₃/p-Si and n-ZnO/p-Si was found equal to 80 nm. Using this value, the short-circuit current and the fill factor were estimated around 18.27 mA/cm² and 0.77 for n-CH₃NH₃PbI₃/p-Si and 18.06 mA/cm² and 0.73 for n-ZnO/p-Si. Results show that the efficiency of n-CH₃NH₃PbI₃/p-Si and n-ZnO/p-Si solar cells with an emitter layer thickness of 80 nm are 1.314 and 1.298 times greater than efficiency of traditional n-Si/p-Si for the same sizes. These findings will help perovskites materials to be more appealing in the PV industry and accelerate their development to become a viable alternative in the renewable energy sector.     

Design of Si<Subscript>3</Subscript>N<Subscript>4</Subscript>-based ceramic laminates by the residual stresses

Ceramic laminates with strong interfaces between layers are considered a very promising material for different engineering applications because of the potential for increasing fracture toughness by designing high residual compressive and low residual tensile stresses in separate layers. In this work, Si₃N₄/Si₃N₄-TiN ceramic laminates with strong interfaces were manufactured by rolling and hot pressing techniques. The investigation of their mechanical properties has shown that the increase in apparent fracture toughness can be achieved for the Si₃N₄/Si₃N₄-20 wt.%TiN composite, while further increase of TiN content in the layers with residual tensile stresses lead to a formation of multiple cracks, and as a result, a significant decrease in the mechanical performance of the composites. Micro-Raman spectroscopy was used to measure the frequency shift across the Si₃N₄/Si₃N₄-20 wt.%TiN laminate. These preliminary Raman results can be useful for further analysis of residual stress distribution in the laminate.     

Femtosecond laser-induced damage of HfO₂/SiO₂ mirror with different stack structure

Laser-induced damage of the "standard" (λ/4 stack structure) and "modified" (reduced standing-wave field) HfO₂/SiO₂ mirrors were investigated by a commercial 800?nm Ti:sapphire laser system. Three kinds of pulse duration of 50?fs, 105?fs, and 135?fs were chosen. The results show that the single-shot damage threshold of the "modified" mirror was about 14%-23% higher compared to that of the "standard" mirror. A model based on the rate equation for free electron generation was adopted to explain the threshold results. It took in account the transient changes in the dielectric function of material during the laser pulse. The simulated threshold agreed with the experimental very well. Besides, for two kinds of mirror, typical breakdown craters for both the single-shots and multi-shots damage tests reveal striking distinct characteristics. Interestingly, the multi-shots damage crater with zigzag-like edge was observed only on the "standard" mirror. These phenomena were illustrated reasonably by the distribution features of the electric field intensity within the mirrors.     

Thermo-elasto-plastic stresses in functionally graded materials subjected to thermal loading taking residual stresses of the fabrication process into consideration

Functionally graded materials (FGMs) have recently been received with considerable interest, primarily as high temperature resistant materials for space vehicles subjected to high temperature environment. FGMs are one of the composite materials and consist of continuous change of composition of different material components from one surface to the other. FGMs usually fabricated at high temperature at which the FGMs have stress free condition. After the FGMs cooled from the fabrication temperature to the room temperature residual thermal stresses produced. In this paper, elasto-plastic thermal stresses in a rectangular plate (FGP) of a particle reinforced composite FGM are treated by finite element method due to the microscopic combination law when the FGP is subjected to three kinds of temperature conditions, first is cooling from the fabricated temperature to the room temperature, second is heating and last is heating after cooling from the fabricated temperature. In the analysis, the thermal stress constitutive equation of a particle-reinforced composite taking temperature change and damage process into consideration is used. The effects of the particle volume fraction and the three kinds of temperature conditions on the stresses in the matrix, stresses in the particle and macroscopic stress are discussed.     

HA-Ti生物功能梯度材料微观组织及热应力缓和特性

本文用粉末冶金法制备了ＨＡ－Ｔｉ系生物ＦＧＭ,并测定了ＨＡ－Ｔｉ复合体材料的弹性模量和热膨胀系数．应用经典叠层板理论和热弹性力学理论分析了ＨＡ－Ｔｉ系ＮＦＧＮ双层板和ＨＡ－Ｔｉ系ＦＧＭ的制备残余热应力和热应变．结果表明,ＨＡ－Ｔｉ系生物ＦＧＭ呈现出宏观不均匀性与微观连续性的组织特征．ＨＡ－Ｔｉ系复合体材料的弹性模量在Ｔｉ－ＨＡ８０达到谷值,并受到气孔率的影响．其热膨胀系数随着ＨＡ含量和测试温度的升高而增大．残余热应力和残余热应变强烈依赖于组成分布,ＦＧＭ由于组成梯度化减小了成分变化幅度,其最大残余拉应力只有ＨＡ／Ｔｉ直接叠合体（ＮＦＧＭ）的１／３,具有显著缓和热应力的功能.     

Optimization of material composition to minimize the thermal stresses induced in FGM plates with temperature-dependent material properties

A hybrid genetic algorithm with the complex method is developed for the optimization of the material composition of a multi-layered functionally graded material plate with temperature-dependent material properties in order to minimize the thermal stresses induced in the plate when it is subjected to steady-state thermal loads. In the formulation, the plate is artificially divided into an n _l -layered plate, and a weak-form-based finite layer method is developed to obtain the displacement and stress components induced in the n _l -layered plate using the Reissner mixed variational theorem. Two thermal conditions, namely the specified temperature and heat convection conditions, imposed on the top and bottom surfaces of the plate are considered. The through-thickness distributions of the volume fractions of the constituents are assumed as certain specific/non-specific function distributions, such as power-law, sigmoid, layerwise step and layerwise linear function distributions, and the effective material properties of the plate are estimated using the Mori–Tanaka scheme. Comparisons with regard to the minimization for the peak values of the stress ratios induced in the FGM plates with various optimal material compositions are conducted.     

Stress intensity factors of two diametrically opposed edge cracks in a thick-walled functionally graded material cylinder

A method is developed to evaluate stress intensity factors for two diametrically-opposed edge cracks emanating from the inner surface of a thick-walled functionally graded material (FGM) cylinder. The crack and the cylinder inner surfaces are subjected to an internal pressure. The thermal eigenstrain induced in the cylinder material due to nonuniform coefficient of thermal expansion after cooling from the sintering temperature is taken into account. First, the FGM cylinder is homogenized by simulating its nonhomogeneous material properties by an equivalent eigenstrain, whereby the problem is reduced to the solution of a cracked homogenized cylinder with an induced thermal and an equivalent eigenstrains and under an internal pressure. Then, representing the cracks by a continuous distribution of edge dislocations and using their complex potential functions, generalized formulations are developed to calculate stress intensity factors for the cracks in the homogenized cylinder. The stress intensity factors calculated for the cracks in homogenized cylinder represents the stress intensity factors for the same cracks in the FGM cylinder. The application of the formulations are demonstrated for a thick-walled TiC/Al₂O₃ FGM cylinder and some numerical results of stress intensity factors are presented for different profiles of material distribution in the FGM cylinder.     

Guided thermoelastic waves in functionally graded plates with two relaxation times

Functionally graded material (FGM) is a promising heat insulation material. Wave propagation in FGM structures has received much attention for the purpose of non-destructive testing and evaluation. Few literatures dealt with the thermoelastic wave in FGM structures although the thermal effect would cause attenuations of elastic waves. In this paper, guided thermoelastic waves in FGM plates subjected to stress-free, isothermal boundary conditions are investigated in the context of the Green–Lindsay (GL) generalized thermoelastic theories (with two relaxation times). Coupled wave equations and heat conduction equation are solved by the Legendre polynomial approach. Dispersion curves for a pure elastic graded plate are calculated to make a comparison with the published data. For the thermoelastic graded plate, dispersion curves of thermal modes and elastic modes are illustrated simultaneously. Attenuation curves for graded plates with different relaxation times are compared. The influences of different material gradient shapes are discussed. Two homogeneous thermoelastic plates with different volume fractions are obtained to show their differences from graded plates. Finally, thermoelastic wave dispersion curves for a homogeneous plate and a graded plate are calculated in the context of the classical coupled thermoelastic theory (CT) to show its differences and similarities to the generalized theory.     

Raman spectral analysis of TiO₂ thin films doped with rare-earth samarium

TiO₂ thin films doped with rare-earth samarium were prepared on a quartz plate by the sol-gel/spin-coating technique. The samples were annealed at 700?°C to 1100?°C, and the Raman spectra of the samples were obtained. Analyses of Raman spectra show that samarium doping can inhibit the anatase-rutile phase transition. Samarium doping can refine grains of TiO₂ thin films and increase the internal stress, thereby preventing lattice vibration. Nanocrystalline TiO₂ thin films obviously show the phonon confinement effect, i.e., the blueshift of characteristic Raman peak and full width at half-height increase, and the peak shapes asymmetrically broaden with a decrease in the grain sizes of the samples.     

An Approximation for the Entropy Measuring in the General Structure of<i>SGSP</i>₃

In this article, we calculate various topological invariants such as symmetric division degree index, redefined Zagreb index, VL index, first and second exponential Zagreb index, first and second multiplicative exponential Zagreb indices, symmetric division degree entropy, redefined Zagreb entropy, VL entropy, first and second exponential Zagreb entropies, multiplicative exponential Zagreb entropy. We take the chemical compound named Proanthocyanidins, which is a very useful polyphenol in human’s diet. They are very beneficial for one’s health. These chemical compounds are extracted from grape seeds. They are tremendously anti-inflammatory. A subdivision form of this compound is presented in this article. The compound named subdivided grape seed Proanthocyanidins is abbreviated as SGSP₃. This network SGSP₃, is converted and modeled into its mathematical graphical formation with the support of the latest mathematical tools. We have also developed many closed formulas for the measurement of entropy for the general chemical structure of the subdivided grape seed Proanthocyanidins network. The achieved outcomes can be correlated with the chemical version of SGSP₃ to get a better understanding of its biological as well as physical features.