Strength Evaluation of Piezoelectric Ceramics under Transient Thermal Environments

The strength of piezoelectric ceramics is analyzed for a plate suddenly exposed to an environmental medium of different temperatures. The admissible temperature jump the material can sustain is studied using the stress- and fracture-toughness-based failure criteria. The critical parameters governing the level of the transient thermal stress in piezoelectric ceramics are identified. Solutions are obtained for the maximum thermal shock that the plate can sustain without failure, under the conditions that (i) maximum local tensile stress equals the tensile strength of the ceramic, and (ii) maximum stress intensity factor for representative pre-existing cracks equals the fracture toughness of the ceramic.     

陶瓷圆柱体的抗热震参数

通过求解第三类边界条件下无限长圆柱体的瞬态温度场及瞬态热应力场，研究了陶瓷圆柱体的抗热冲击行为，建立了引起无限长陶瓷圆柱体表面临界热应力的临界温差表达式，并以此作为陶瓷圆柱体的抗热震参数。计算结果表明，无限长陶瓷圆柱体的临界温差大于具有相同Biot模数的无限大陶瓷平板的临界温差，但其表面达到临界热应力的时间小于无限大平板的数值。     

复合材料层合板低速冲击承载能力的细观力学有限元模型

将复合材料细观力学桥联模型与有限元软件ABAQUS结合,用于分析层合板受低速冲击作用的极限承载能力.通过确定组分材料是否破坏来判断单层板是否破坏,对破坏后的单层实施一种常系数刚度衰减.将细观力学本构模型、针对组分材料的破坏判据以及刚度衰减模式编制成用户子程序VUMAT,为ABAQUS求解层合板的极限冲击响应提供一种自定义材料模型.只需要输入纤维和基体的材料参数、纤维体积含量等有限数据并且无须单层板的实验数据,就能顺利实施复合材料层合板结构的冲击承载能力分析.所计算的层合板的挠度-时间曲线以及横向冲击力-时间曲线与实验值吻合良好,说明本文的方法是有效的.     

陶瓷涂层三明治板的抗热震性

采用解析法研究了第3类边界条件下双面陶瓷涂层三明治板的瞬态温度场及瞬态热应力场.对不同Biot模数的热冲击过程中,Al2O3涂层/硬质合金(WC-8%Co,质量分数)基体/Al2O3涂层三明治板的瞬态热应力进行了数值计算.分析了涂层/基体厚度比、涂层与基体热-物理性能匹配对陶瓷涂层三明治板表面热应力峰值的影响.结果表明:陶瓷涂层三明治板的基体的热导率、线膨胀系数和弹性模量应高于涂层,这样可以降低其表面热应力,获得高抗热震性陶瓷涂层三明治板.此外,涂层厚度应尽可能小,以利于改善涂层的抗热震性.     

Analysis of Thermal Stress Resistance of Partially Absorbing Ceramic Plate Subjected to Asymmetric Radiation, I: Convective Cooling at Rear Surface

An analysis is presented of the thermal stresses in a partially absorbing brittle ceramic flat plate asymmetrically heated by radiation on the front surface and cooled by convection on the rear surface with a heat transfer coefficient, h , being finite or zero. For finite A, the transient thermal stresses are a function of h , whereas the steady-state thermal stresses are independent of h . The maximum value of tensile thermal stresses occurs at an optical thickness μ a = 2 and equals zero for μ a = 0 or ∞. For an optical thickness μ a <10.7, the steady-state thermal stresses exceed the transient stresses, with the converse being true for μ10.7. The maximum tensile thermal stresses occur in the front surface where the temperatures are highest. For h =0, the tensile thermal stresses increase with increasing value of optical thickness. The role of the material properties which control the thermal stress resistance under conditions of combined radiation heating and convection cooling are discussed. Appropriate thermal stress resistance parameters are proposed.     

Transient thermal stress analysis of threaded-adhesive joints applied in non-magnetic Dewar

A transient thermal stress analysis of threaded-adhesive joints applied in a non-magnetic Dewar at cryogenic temperature was conducted using the finite element method (FEM). A large temperature gradient was observed in the adhesive fillet region of the lower threaded-adhesive joint at the beginning of the cooling process. This caused a transient thermal stress that was much higher than that at the steady state. The peak von Mises stress of the lower adhesive joint reached the maximum value of 189 MPa at about 10 s after the introduction of liquid nitrogen into the Dewar and was 149% larger than the maximum thermal stress at the steady state. Attention should be paid on this serious transient thermal stress in the design and usage of non-magnetic Dewar.     

Thermal shock resistance of porous ceramic foams with temperature-dependent material properties

The impact of temperature dependence of material properties on thermal shock resistance of porous ceramic foams is studied in this paper. Two cases of thermal shock are carried out: sudden heating and sudden cooling. Finite difference method and weight function method are employed to get the thermal stress field at crack tip. The effects of time dependence and temperature dependence of material properties on thermal shock behavior are analyzed. The thermal shock resistance is acquired based on two different criteria: fracture mechanics criterion and stress criterion. By comparison analysis, results show that taking temperature dependence of the material properties into account is crucial in the assessment of thermal shock resistance of ceramic foams. Cold shock fracture experiments of Al₂O₃ foams with different relative densities are also made, and the obtained results are in coincidence with theoretical results very well.     

Two-Dimensional Transient Thermal Stress Analysis of Adhesive Butt Joints

Transient thermal stress distribution in an adhesive butt joint is considered. It is assumed that both the upper and lower end surfaces of the joint are maintained at different temperatures at a certain instant in time and that no heat transfers between the side surfaces of the joint and ambient air. In the analysis, two adherends were replaced with finite strips and unsteady temperature distribution in the joint was obtained theoretically. Then the transient thermal stress distribution in the joint was analyzed using a two-dimensional theory of elasticity. The effects of the ratios of the coefficient of thermal expansion and Young's modulus of the adherend to those of the adhesive on the thermal stress distribution were clarified from numerical calculations. Furthermore, the transient stress distribution in the adhesive was measured by a photoelastic experiment on a joint where the adhesive was modelled by an epoxy plate. The experimental results were consistent with the analytical results.     

考虑局部非热平衡的流体层流横掠多孔介质中恒热流平板的传热分析

对流体层流横掠多孔介质中恒热流加热的平板,应用Brinkman-Forchheime-extended Darcy流动模型和流体与多孔介质之间局部非热平衡理论建立守恒方程组,应用数量级分析和积分法,得出了速度边界层厚度、热边界层厚度、壁面黏性摩擦系数和对流传热系数、流体与多孔介质之间局部温差的计算公式。结果表明,速度边界层与光板时明显不同,其在平板前端迅速增长,之后越来越平坦,趋于一个恒定值;而热边界层则沿着流动方向不断增长,类似于光板时的情况;局部的表面对流传热系数在平板前端达最大值,之后逐渐减小,也类似于光板时的情况;多孔介质与流体间的局部温差在平板前端达最大值,之后呈现沿着流动方向逐渐减小的变化趋势。     

Analysis of Thermal Stress Resistance of Partially Absorbing Ceramic Plate Subjected to Asymmetric Radiation, II: Convective Cooling at Front Surface

Thermal stresses in a partially absorbing brittle ceramic plate asymmetrically heated by radiation and cooled by convection on the same surface with finite and infinite heat transfer coefficients are analyzed. Comparison of the results from this study with those obtained in Part I, where the plate is subjected to radiation heating in the front surface and cooled by convection at the rear surface, indicates that the magnitudes of the maximum steady-state tensile thermal stresses are nearly identical. Significant differences are found in the transient thermal stresses and the temperature distribution. The relative temperature levels in the present case are found to be significantly lower than those obtained in Part I. Implications of these results to the design and operation of engineering structures such as concentrated solar receivers are discussed.     

Analytical Solutions of Photo-Thermal-Elastic Waves in a Semiconductor Material Due to Pulse Heat Flux with Thermal Memory

In the present work, the interaction between the generalized thermoelasticity theory and Photothermal theory under the effect of volumetric source of heat with thermal memory is investigated. The governing equations for this model are taken of semiconductor medium in one dimension with pulse heat flux. The main goal is to study the overlap between the waves as plasma, thermal and elastic waves. The analytical solutions are obtained for some physical quantities as temperature, displacement, radial stress and carrier intensity in thin circular plate by using Laplace transformation method. To obtain the complete solutions, the inversion numerical method is used. The semiconductor silicon material is used to obtain numerical results. The obtained physical quantities are discussed and illustrated graphically.     

Temperature and Stress Distributions in a Hollow Cylinder of Functionally Graded Material: The Case of Temperature-Independent Material Properties

We have presented a numerical technique for analyzing one-dimensional transient temperature distributions in a circular hollow cylinder that was composed of functionally graded ceramic–metal-based materials, without considering the temperature-dependent material properties. The functionally graded material (FGM) cylinder was assumed to be initially in a steady state of gradient temperature; the ceramic inner surface was exposed to high temperature, and the metallic outer surface, which was associated with its in-service performance, was exposed to low temperature. Then, the FGM cylinder was cooled rapidly on the ceramic surface of the cylinder, using a cold medium. The transient temperature and related thermal stresses in the FGM cylinder were analyzed numerically for a model of the mullite–molybdenum FGM system. The technique for analyzing the temperature distribution is quite simple and widely applicable for various boundary conditions of FGMs, in comparison with methods that have been proposed recently by other researchers.     

升温速率对复合材料修补片固化过程热应力的影响

采用有限元法数值模拟了3234/T300B热固性树脂基复合材料修补片的热补仪加热固化过程,分析了工程应用范围内不同升温速率下的复合材料修补片固化历程中的温度、热应力分布和变化特征,并研究了升温速率对补片在不同时间点的残余热应力值的影响规律。研究结果表明:升温阶段热应力主要集中在补片表面中心区域及其与母板接触的区域,降温阶段复合材料修补片内部热应力高于表面热应力;升温速率越快,固化越迅速,在升温阶段修补片内部热应力及峰值热应力越大;在保温和降温阶段,修补片内热应力分布和大小不受升温速率的影响;对于较低升温速率,热应力最大值出现在升温结束时刻;对于较高的升温速率,热应力最大值出现在接近升温末期的时刻。研究结果为合理选择升温速率从而减小升温阶段的内部热应力并控制补片分层等缺陷提供了参数依据。     

Thermal Residual Stresses in Adhesively Bonded In-plane Functionally Graded Clamped Plates Subjected to an Edge Heat Flux

In this study we have carried out the thermal residual stress analyses of adhesively bonded functionally graded clamped plates for different edge heat fluxes. The material properties of the functionally graded plates were assumed to vary with a power law along an in-plane direction not through the plate thickness direction. The transient heat conduction and Navier equations describing the two-dimensional thermo-elastic problem were discretized using the finite-difference method, and the set of linear equations was solved using the pseudo singular value method. The plate material properties near the interfaces played an important role in the interfacial adhesive stresses. The compositional gradient affected considerably both in-plane temperature distributions and heat transfer periods. The type of in-plane heat flux had only a minor effect on the temperature profiles but affected both the temperature levels and heat transfer period. Both plates undergo considerable compressive normal strains and stresses, but shear strains were more effective. Peak equivalent strains were observed for a constant heat flux and plates with a metal-rich composition. The compositional gradient and direction played important role in the profiles and levels of normal, shear and equivalent stresses as well as strains. The equivalent stress and strains concentrated along the free edges of the adhesive layer. The adhesive layer experienced a considerable distortional deformation rather than volumetric deformation. The equivalent stress exhibited small changes through the adhesive thickness and along the overlap length. The equivalent stress remained uniform in a large region of the overlap length and increased to a peak level around the free edges of the first plate–adhesive interface, whereas it increased to a peak level in a large region of the overlap length from a minimum level around the free edges of the second plate–adhesive interface. The strains and equivalent strains were higher for a metal-rich material composition. The direction of the material composition of the plates affected both stress and strain levels; thus, the CM–CM and CM–MC plates exhibited lower strain and stress levels than those in the MC–CM and MC–MC plates. However, only the adhesively bonded CM–MC plate configuration could achieve the lowest deformations and stresses in both plates and adhesive layer.     

Thermal shock resistance behavior of auxetic ceramic honeycombs with a central crack or an edge crack

In this paper, the thermal shock resistance of an auxetic ceramic honeycomb plate is studied based on the fracture mechanics concept for the cases of a central crack or an edge crack. The transient temperature field and transient thermal stress field are obtained for both auxetic and non-auxetic structures. The relationship between the thermal stress intensity factor (TSIF) and the internal cell angle, crack length and time is determined and the critical temperature for the initiation of crack propagation is predicted. Results show that compared with the non-auxetic ceramic honeycombs which are at an internal cell angle of 30°, the critical temperature of the auxetic ceramic honeycombs whose cell are orientated at an angle of −30° increases by 78.5% and the TSIF at the crack tip decreases by 40%, respectively. Hence, the auxetic structures have better thermal shock resistance. This study indicates that auxetic ceramic honeycombs have significant potential applications in harsh temperature environments.     

Thermal residual stresses in adhesively bonded in-plane functionally graded clamped circular hollow plates

This study investigates the effects of in-plane compositional gradient exponent and direction on the thermal residual stress and deformations in adhesively bonded functionally graded clamped circular plates. The material composition was assumed to vary with a power law along an in-plane direction not through the plate thickness direction. The transient heat conduction and Navier equations in polar coordinates describing the two-dimensional thermo-elastic problem were discretized using finite-difference method, and the set of linear equations were solved using the pseudo-singular-value method. The material composition direction is designed as Ceramic-Metal (CM)–CM, CM–Metal-Ceramic (MC), MC–CM, and MC–MC for the inner and outer plates. The temperature decreased radially along the plates, but exhibited a sharp decrease across the adhesive layer. The compositional gradient exponent and direction affected evidently temperature levels and heat transfer period. The compressive radial and shear strains are more effective on the deformation in the adhesive layer and the plate regions near the plate–adhesive interfaces. The adhesive layer is subjected to considerable shear deformations. The equivalent strain and stresses are very low in a large region of the plates but exhibit sharp peaks on the plate regions near the plate–adhesive interfaces, and decrease towards the adhesive interfaces. These stress and strain peaks in the plates and adhesive layer are affected by the compositional gradient and direction. For an outer edge flux, the largest equivalent strain and stresses are observed in the CM–MC joint but the lowest levels occur in the MC–CM or secondly CM–CM joint. In addition, an inner edge flux results in the lowest and highest peak strains and stresses in the MC–CM and CM–MC joints, respectively. The MC–MC and CM–CM joints result in lower temperature, stress and strain levels around the adhesive layer and along the adhesive interfaces for outer and inner edge fluxes, respectively.     

NATURAL CONVECTION HEAT AND MASS TRANSFER FROM A VERTICAL FLAT PLATE WITH VARIABLE WALL TEMPERATURE AND CONCENTRATION TO POWER-LAW FLUIDS WITH YIELD STRESS IN A POROUS MEDIUM

The problem of natural convection coupled heat and mass transfer of non-Newtonian power law fluids with yield stress from a vertical flat plate in a fluid-saturated porous medium is analyzed under boundary layer approximations. Similarity solutions are obtained for the general case of power law variations of the wall temperature and concentration. Velocity, temperature, and concentration profiles as well as local heat and mass transfer rates are presented and discussed for different values of the rheological parameters of a power-law fluid, the Lewis number, and the thermal and concentration buoyancy ratio.     

箱装发射药储存时的安全性及能量分析

采用大型通用计算程序PHOENICS（1．4版本）对箱装发射药中含有内部热源的非稳态导热与自然对流换热及辐射换热的耦合问题进行了数值求解。分析和比较了在直角坐标和贴体坐标下发射药内部靠近中心处的最高温度随时间的变化趋势,并对发射药的安全性及发射药所含有的能量进行了分析。     

Approximate Theory of Thermal Stress Resistance of Brittle Ceramics Involving Creep

The effect of stress relaxation by creep on the thermal stress fracture of brittle ceramics at high temperature under conditions of quasi-static heat flow is discussed. It is shown that, to a good approximation, thermal stress relaxation rates can be calculated on the basis of creep rates which correspond to the minimum temperature of the ceramic workpiece. For materials exhibiting linear stress-creep rate dependence, expressions for the relaxation time and maximum temperature difference or heat flux to which ceramic bodies can be subjected are derived in terms of the material variables affecting thermal stress fracture and stress relaxation by creep. A numerical example shows that high-temperature creep can materially affect the thermal stress behavior of brittle ceramics. Appropriate thermal stress parameters are proposed to form the basis of proper material selection for high-temperature environments involving thermal stress and stress relaxation by creep. Conditions for which thermal stress calculations should be based on an elastic or viscoelastic analysis are outlined.     

ANALYSIS OF TRANSIENT TEMPERATURE DISTRIBUTIONS IN A PERFUSED MEDIUM DUE TO A SPHERICAL HEAT SOURCE WITH APPLICATION TO HEAT TRANSFER IN TUMORS: HOMOGENEOUS AND INFINITE MEDIUM

The role of conduction and convection in transferring heat through a perfused medium is quantified by analyzing the transient temperature field within and around a spherical heat source embedded in the medium, using the bio-heat transfer equation. Analytical expressions for transient temperature distributions are obtained in terms of the following dimensionless variables: ξ, the relative position; τ, the Fourier number; β²;, the Peclet number, and ratios of thermal conductivities and difFusivities. The perfused medium is assumed to be infinite, isotropic and homogeneous. Frequency response of the probe to sinusoidal power input is also analyzed. The analytical expressions obtained are used to estimate heat transfer characteristics of tumors from in vivo data describing blood flow and temperature distributions around a spherical probe.