Optimum material design for functionally gradient material plate

Summary Steady thermal stresses in a plate made of a functionally gradient material (FGM) are analyzed theoretically and calculated numerically. An FGM plate composed of PSZ and Ti-6Al-4V is examined, and the temperature dependence of the material properties is considered. A local safety factor is used for evaluation of the FGM's strength. It is assumed that top and bottom surfaces of the plate are heated and kept at constant thermal boundary conditions. The pairs of the surface temperatures, for which the minimum local safety factor can be of more than one, are obtained as available temperature regions. The temperature dependence of the material properties diminishes, available temperature region as compared with that for an FGM plate without it. The available temperature region of the FGM plate is wider than that of the two-layered plate, especially for the surface temperatures which are high at the ceramic surface and low at the metal side. The influence of different mechanical boundary conditions is examined, and available temperature regions are found to be different, depending on the mechanical boundary conditions. The influence of the intermediate composition on the thermal stress reduction is also investigated in detail for the surface temperatures which are kept at 1300 K at the ceramic surface and 300K at the metal side. Appropriate intermediate composition of the FGM plate can yield the local safety factor of one or more for the four mechanical boundary conditions at once. For the two-layered plate there does not exist, however, any appropriate pair of metal and ceramic thicknesses which would yield the local safety factor of one or more for the four mechanical boundary conditions at once. The influence of the intermediate composition on the maximization of the minimum stress ratio depends on the mechanical boundary conditions. Finally, the optimal FGM plates are determined.     

材料高温力学性能理论表征方法研究进展

随着科学技术的迅猛发展,材料在高温领域的应用越来越广泛。然而高温下材料的力学性能和常温相比有很大差异,材料的高温力学性能研究和表征已成为当前的研究热点。论文文对材料在高温下力学行为理论表征方法研究的最新进展进行了总结和回顾。着重介绍了近年来高温陶瓷材料的断裂强度、金属材料的屈服强度、弹性模量与本构关系的温度相关性理论表征方法的研究进展。最后,总结已有研究工作的特点和不足之处,对材料高温力学性能理论表征方法的后续研究进行了展望,就进一步研究提供建议。     

Influence of surfactant addition on the rheological properties of aqueous Welan matrices

In the present work the effects produced by the presence of two different surfactants (Abil B 8842 and Triton N 101) on the rheological properties of aqueous welan matrices are studied, both in steady and in oscillatory shear conditions. Welan is an acidic microbial polysaccharide having high thermal, pH, and salt stability. At sufficiently low concentrations it forms aqueous weak gel matrices which can be profitably used to regulate the rheological properties of disperse systems and improve their stability. Different systems are examined, having the same polysaccharide concentration (0.25 wt%) and different surfactant concentrations (up to 40 wt%, far beyond the range of practical interest for emulsion preparation). All the systems exhibit marked shear-thinning properties which can be described quite satisfactorily by the Cross equation. The concentration dependence of the zero-shear-rate viscosity as well as the mechanical spectra confirm that, in the concentration range considered, the aqueous welan systems are typically weakly structured fluids. The influence of both surfactants is examined in detail by comparing the behavior of the different classes of systems. Both surfactants reduce the polymer contribution at low shear, whereas an opposite action is exerted at high concentration and shear. These contrasting effects are ascribed to the different structural features of the polymer matrix under low stresses and high shear conditions, respectively. Received: 6 February 2000 Accepted: 1 November 2000     

Residual Stress Analysis on Thick Film Systems by the Incremental Hole-Drilling Method – Simulation and Experimental Results

The residual stress state in thick film systems, as for example thermal spray coatings, is crucial for many of the component’s properties and for the evaluation of the integrity of the coating under thermal and/or mechanical loading. Therefore it is necessary to be able to determine the local residual stress distribution in the coating, at the interface and in the substrate. The incremental hole-drilling method is a widely used method for measuring residual stress depth profiles, which was already applied for thermally sprayed coatings. But so far no reliable hole-drilling evaluation method exists for layered materials having a stress gradient in depth. The objective was to investigate, how far existing evaluation methods of the incremental hole-drilling method that are only valid for residual stress analysis of homogenous material states can be applied to thick film systems with coating thicknesses between 50 μm and 1000 μm and to point out the application limits for these already existing methods. A systematic Finite Element (FE) study was carried out for coating systems with an axisymmetric residual stress state σ₁?=?σ₂. It is shown that conventional evaluation methods developed for homogeneous, non-layered material states can be successfully applied for a stress evaluation in the substrate and the coating for small and for sufficiently large coating thicknesses, respectively, regardless of the type of evaluation algorithm used i.e. the differential or the integral method. The same accounts for material combinations that have a Young’s modulus ratio close to one, between 0.8 and 1.2. The studies indicated that outside the given ranges case specific calibration must be applied to calculate reliable results. Further, calibration data were determined case specifically for a selected model coating system. The accuracy of a residual stress determination using these case specific calibration data was examined and the sensitivity of the evaluation with respect to an accurate knowledge of the boundary conditions of the coating system i.e. the coating thickness and the Young modulus was studied systematically. Finally, the calibration data were applied on a thermally sprayed aluminium coating on a steel substrate analysis and the results for using the incremental hole drilling method were compared to results from X-ray stress analysis.     

A new method of high-temperature strain measurement

A new technique for measuring strain at temperatures from room temperature to at least 3000 K has been developed and evaluated. The system was developed for measuring strain during studies of the short-time (seconds to minutes), high-temperature mechanical properties of materials heated by self resistance, but it has general applicability. The technique consists of optically tracking two small ceramiccement targets on the specimen with a digital line scan camera. The targets are illuminated with a laser and viewed through a narrow-band (1-nm) interference filter which eliminates specimen thermal radiation. Experimental testing of the system has been performed on stainless steel and graphite at temperatures up to 1477 K and 3000 K, respectively. With the present lens arrangement, the strain measurement system has a maximum displacement range of 4.24 mm and an overall inaccuracy at temperature of ±4.14 μm. The unique features of this system are: (1) the sensitivity to variations in light level in the tracking range has been substantially reduced; (2) the system is dynamic in that it can operate during heatup and on short-time scales; (3) the nodules are stable and have no adverse effects on the test results; and (4) the system is reliable and easy to use.     

Stress intensity factors for glass-fiber reinforced plastics with an infinite row of parallel cracks at low temperatures

Stress intensity factors are determined for glass-fiber reinforced plastics with an infinite row of parallel cracks at low temperatures under tension. A state of generalized plane strain is assumed. The thermal and mechanical properties as functions of temperature are obtained from the experimental data. Fourier transforms are used to reduce the problem to the solution of a pair of dual integral equations. The solution of the dual integral equations is then expressed in terms of a Fredholm integral equation of the second kind. Numerical calculations are carried out, and the stress intensity factors at different temperatures are shown graphically.     

铝-镁合金5A06在瞬态热冲击条件下的力学性能研究

通过热强度试验,测试并确定航空航天材料在复杂高速热冲击条件下的强度极限等关键参数,对于航空航天材料和结构的可靠性评定、寿命预测以及高速飞行器的安全设计具有重要的意义。针对强度设计手册中没有航空航天材料在高速热冲击环境下的强度极限等表征参数的现状,使用自行研制的高速飞行器瞬态气动热试验模拟系统,对铝-镁合金材料5A06在多种不同的瞬态热冲击条件下,进行气动加热模拟与热载联合试验研究,得到在瞬态热、力学环境的共同作用下铝-镁合金5A06材料的强度极限、承载时间等力学性能变化状况。为研究分析航空航天材料和结构在高速热冲击环境下的承载能力和结构减重提供了可靠依据。     

A finite deformation thermomechanical constitutive model for triple shape polymeric composites based on dual thermal transitions

Shape memory polymers (SMPs) have gained strong research interests recently due to their mechanical action that exploits their capability to fix temporary shapes and recover their permanent shape in response to an environmental stimulus such as heat, electricity, irradiation, moisture or magnetic field, among others. Along with interests in conventional “dual-shape” SMPs that can recover from one temporary shape to the permanent shape, multi-shape SMPs that can fix more than one temporary shapes and recover sequentially from one temporary shape to another and eventually to the permanent shape, have started to attract increasing attention. Two approaches have been used to achieve multi-shape shape memory effects (m-SMEs). The first approach uses polymers with a wide thermal transition temperature whilst the second method employs multiple thermal transition temperatures, most notably, uses two distinct thermal transition temperatures to obtain triple-shape memory effects (t-SMEs). Recently, one of the authors’ group reported a triple-shape polymeric composite (TSPC), which is composed of an amorphous SMP matrix (epoxy), providing the system the rubber-glass transition to fix one temporary shape, and an interpenetrating crystallizable fiber network (PCL) providing the system the melt-crystal transition to fix the other temporary shape. A one-dimensional (1D) material model developed by the authors revealed the underlying shape memory mechanism of shape memory behaviors due to dual thermal transitions. In this paper, a three-dimension (3D) finite deformation thermomechanical constitutive model is presented to enable the simulations of t-SME under more complicated deformation conditions. Simple experiments, such as uniaxial tensions, thermal expansions and stress relaxation tests were carried out to identify parameters used in the model. Using an implemented user material subroutine (UMAT), the constitutive model successfully reproduced different types of shape memory behaviors exhibited in experiments designed for shape memory behaviors. Stress distribution analyses were performed to analyze the stress distribution during those different shape memory behaviors. The model was also able to simulate complicated applications, such as a twisted sheet and a folded stick, to demonstrate t-SME.     

D-c electric-potential method applied to thermal/mechanical fatigue crack growth

The paper describes a d-c electric potential system for measuring crack length under thermal/mechanical fatigue-crack-growth (TMFCG) test conditions. A programmable d-c current supply and precision multimeter produce reliable electric-potential readings. H.H. Johnson's formula is used to calculate crack length from electric potential for the center-crack-tensionM(T) geometry. Calibration constants for the formula are determined from an initial optical crack-length measurement. The resolution of the system is 1.0 microvolt which corresponds to a crack extension of approximately 0.002 mm for the center-crack-tension geometry using a current of 10.00 amps. Good crack-length accuracy and low data scatter are achieved by taking special precautions to minimize or eliminate errors in potential measurement due to thermal effects. Material resistivity changes are identified as the cause of short and long term changes in the measured electric potential for uncracked specimens. Crack-length accuracy is discussed in terms of short-term scatter and longterm drift.     

用具有负定矩阵的梯度系统构造稳定的变质量力学系统

随着科学技术的发展,对喷气飞机、火箭等变质量系统动力学的研究显得越来越重要, 并且总是希望变质量系统的解是稳定的或渐近稳定的. 而通用的研究稳定性的Lyapunov直接法有很大难度, 因为直接从微分方程出发构造Lyapunov函数往往很难实现. 本文给出一种研究稳定性的间接方法, 即梯度系统方法. 该方法不但能揭示动力学系统的内在结构, 而且有助于探索系统的稳定性、渐进性和分岔等动力学行为. 梯度系统的函数V通常取为Lyapunov函数, 因此梯度系统比较适合用Lyapunov函数来研究. 列写出变质量完整力学系统的运动方程,在系统非奇异情形下,求得所有广义加速度. 提出一类具有负定矩阵的梯度系统, 并研究该梯度系统解的稳定性. 把这类梯度系统和变质量力学系统有机结合,给出变质量力学系统的解可以是稳定的或渐近稳定的条件, 进一步利用矩阵为负定非对称的梯度系统构造出一些解为稳定或渐近稳定的变质量力学系统. 通过具体例子,研究了变质量系统的单自由度运动,在怎样的质量变化规律、微粒分离速度和加力下,其解是稳定的或渐近稳定的. 本文的构造方法也适合其它类型的动力学系统.      

Thermal buckling analysis of truss-core sandwich plates

Truss-core sandwich plates have received much attention in virtue of the high values of strength-to-weight and stifness-to-weight as well as the great ability of impulseresistance recently. It is necessary to study the stability of sandwich panels under the influence of the thermal load. However, the sandwich plates are such complex threedimensional(3D) systems that direct analytical solutions do not exist, and the finite element method(FEM) cannot represent the relationship between structural parameters and mechanical properties well. In this paper, an equivalent homogeneous continuous plate is idealized by obtaining the efective bending and transverse shear stifness based on the characteristics of periodically distributed unit cells. The first order shear deformation theory for plates is used to derive the stability equation. The buckling temperature of a simply supported sandwich plate is given and verified by the FEM. The efect of related parameters on mechanical properties is investigated. The geometric parameters of the unit cell are optimized to attain the maximum buckling temperature. It is shown that the optimized sandwich plate can improve the resistance to thermal buckling significantly.     

Widerstandsverminderung in turbulenten Rohrströmungen: Stabilitätsverhalten wäßriger Polyacrylamidlösungen bei mechanischer und thermischer Beanspruchung

Experimental results on the drag reduction efficiency of polymers based on acrylamide are represented and discussed. The measurements were carried out on a laboratory and a pilot plant scale. Points of main interest are the mechanical and thermal stability of the polymers. The laboratory tests, which were performed under well defined conditions, show the decisive influence of wall shear stress on degradation. These results explain the good stability, which has been measured in a technical pipeline. In the case of suspensions of coal in water a drag reduction efficiency interesting for technical applications has been observed, too. The thermal degradation of the polymer is accelerated by oxygen solved in the water. Under inert conditions only very small degradation effects occur even at temperatures up to 150 °C. GPC measurements give instructive results for an understanding of the thermal and mechanical degradation of the polymers on a molecular base.     

Conservation laws in classical mechanics for quasi-coordinates

Noether's theorem and Noether's inverse theorem for mechanical systems with gauge-variant Lagrangians under symmetric infinitesimal transformations and whose motion is described by quasi-coordinates are established. The existence of first integrals depends on the existence of solutions of the system of partial differential equations — the so-called Killing equations. Non-holonomic mechanical systems are analysed separately and their special properties are pointed out. By use of this theory, the transformation which corresponds to Ko Valevskaya first integral in rigid-body dynamics is found. Also, the nature of the energy integral in non-holonomic mechanics is shown and a few new first integrals for non-conservative problems are obtained. Finally, these integrals are used in constructing Lyapunov's function and in the stability analyses of nonautonomous systems. The theory is based on the concept of a mechanical system, but the results obtained can be applied to all problems in mathematical physics admitting a Lagrangian function.     

Transient heat conduction in non-homogeneous spherical systems

A comprehensive study encompassing a general analytical development and an archival presentation of results is made for transient heat conduction in thermally coupled spherical regions. The system consists of a sphere and its surrounding environment, each region having different thermal properties and different initial temperatures. The general closed form solution, which accommodates an arbitrary inital temperature distribution in the sphere, is specialized to apply to a number of interesting problems. Among these, the situation in which the sphere and the surroundings are initially at different uniform temperatures constitutes a basic problem in the theory of heat conduction. Correspondingly, a comprehensive presentation of transient temperature histories is made for various locations in the sphere and in the surroundings, with relevant thermal property ratios serving as parameters. Characteristics such as the duration of the transient period and the penetration depth of the temperature field into the surroundings are illuminated. Another interesting situation is that in which the thermal conductivity of the sphere is much greater than that of the surroundings, so that the sphere temperature may be regarded as being spatially uniform. In addition to a presentation of temperature histories, the conditions are identified under which the assumed spatial uniformity of the sphere temperature is valid. For the case of a metallic sphere situated in a gaseous environment, it is demonstrated that the transient response can be represented by a single universal curve.     

Axially symmetric thermal stress of an external circular crack under general thermal conditions

Summary The paper presents a solution for the linear thermoelastic problem of determining axisymmetric stress and displacement fields in an isotropic elastic solid of infinite extent weakened by an external circular crack under general mechanical loadings and general thermal conditions. The mechanical loadings and thermal conditions applied on the crack faces are axisymmetric, being non-symmetric about the crack plane. In similar lines of [7], equations of equilibrium of an elastic solid conducting heat have been solved using Hankel transforms and Abel operators of the first kind. Expressions for stress, displacement, temperature and heat flux functions are obtained in terms of Abel transforms of the first kind of the jumps of stress, displacement, temperature and heat flux at the crack plane. Two types of thermal conditions, that is, general surface temperatures and general heat flux on faces of the crack are considered. In both the cases, closed form solutions have been obtained for the unknown functions solving Abel type of integral equations. Explicit expressions for stresses, displacements, temperature fields, stress intensity factors have been obtained. Two special cases of thermal conditions in which: (i) crack faces are subjected to constant non-symmetric temperatures over a circular ring area, (ii) crack faces are subjected to constant non-symmetric heat flux over a circular ring area, have been considered. In some special cases, results have been compared with those from the literature.     

On the effect of gravity on the bifurcation of rectangular closed-loop thermosyphon

Closed-loop thermosyphons are systems in which heat is transferred from a source to a sink by means of a natural convective flow, i.e. without the help of mechanical pumping. In fact, the dynamics of such systems strongly depend both on the thermal boundary conditions and on the gravitational field in which they operate. While the effect of variations of the boundary conditions has been extensively analysed in the last decades, the dependence on gravity has never been explicitly studied.The aim of this paper is to examine the effect of variations of gravity as well as that of thermal boundary conditions on the dynamics of natural circulation loops. Such an analysis might point out some useful applications for the cooling of a generic source in reduced gravity conditions.To this purpose an experimental campaign was performed on a natural circulation operating under a gravity field varying in the range between 10^–2 g and 1.8 g, with g = 9.81 ms^–2. The dynamical behaviour detected during the experiment was used for the validation of a mathematical model, previously validated under terrestrial gravity conditions. Model simulations were found to satisfactorily reproduce the dynamics of the system under variable gravity. This proved the possibility to use the model for the construction of bifurcation diagrams describing the behaviours of natural circulation loops under variations of both the gravitational field and the thermal boundaries.     

Dissipative heating of elastomers: a new modelling approach based on finite and coupled thermomechanics

Especially in the automotive industries, elastomers take an important role. They are used in different types of bearings, where they inhibit vibration propagation and thereby significantly enhance driving performance and comfort. That is why several models have already been developed to simulate the material’s mechanical response to stresses and strains. In many cases, these models are developed under isothermal conditions. Others include the temperature-dependent mechanical behaviour to represent lower stiffness’s for higher temperatures. In this contribution it is shown by some exemplary experiments that viscoelastic material heats up under dynamic deformations. Hence, the material’s properties change due to the influence of the temperature without changing the surrounding conditions. With some of these experiments, it is shown that a fully coupled material model is necessary to predict the behaviour of bearings under dynamic loads. The focus of this contribution lies on the modelling of the thermoviscoelastic behaviour of elastomers. In a first step, a twofold multiplicative split of the deformation gradient is performed to be able to describe both mechanical and thermal deformations. This concept introduces different configurations. The stress tensors existing on these configurations are used to formulate the stress power in the first law of thermodynamics which allows to simulate the material’s self-heating. To formulate the temperature dependency of the mechanical behaviour, the non-equilibrium part of the Helmholtz free energy function is formulated as a function of the temperature and the deformation history. With the introduced model, some FE calculations are carried out to show the model’s capability to represent the thermoviscoelastic behaviour including the coupling in both directions.     

Improved tri-layered interfacial stress model with the effect of different temperatures in the layers

The study of thermal mismatch induced stresses and their role in mechanical failure is one relevant topic to composite materials and electronic packages. An understanding of the nature of the interfacial stresses under different temperature conditions is necessary in order to minimize or eliminate the risk of mechanical failure. An accurate estimate of thermal stresses in the interfaces plays an important role in the design and reliability studies of micro-electronic devices. In the microelectronic industry, from a practical point of view, there is a need for simple and powerful analytical models to determine interfacial stresses in layered structures quickly and accurately. In the present paper, a model is proposed for the shearing and peeling stresses occurring at the interface of three bonded thin plates of dissimilar materials to account for different uniform temperatures in the layers by incorporating two temperature ratios. The model is then further upgraded to accommodate the effect of thickness wise linear temperature gradients in the layers by incorporating three linear temperature gradients at the interfaces. This upgraded model can be viewed as a more generalized form to take care of different temperature conditions which may occur in a tri-layered structure. The improved uniform temperature model of tri-material assembly provided by Sujan (Int Microelectron Packag Soc JMEP 5(1):37–42, 2008) is utilized to develop the proposed tri-layered model. The selected shearing stress results are presented for the case of die, die attach and substrate as commonly found in electronic packaging.     

On the coupling mechanism between nonlinear solitary waves and slender beams

This paper describes the coupling mechanism between highly nonlinear solitary waves propagating along a granular system and slender beams in contact with the granular medium. Nonlinear solitary waves are compact non-dispersive waves that can form and travel in nonlinear systems such as one-dimensional chains of particles, where they are conventionally generated by the mechanical impact of a striker. These waves have a constant spatial wavelength and their speed, amplitude, and duration can be tuned by modifying the particles’ material or size, or the velocity of the striker. In the study presented in this article we investigated numerically the interaction between solitary waves propagating along a chain of granular particles and a slender beam. Some of the numerical findings were validated experimentally. We found that the geometric and mechanical properties of the beam or thermal stress applied to the beam alter certain features of the solitary waves. In the future, these findings may be used to develop a novel sensing system for the nondestructive assessment of beams.     

用具有负定非对称矩阵的梯度系统构造稳定的广义Birkhoff系统1）

Birkhoff系统是一类比Hamilton系统更广泛的约束力学系统,可在原子与分子物理,强子物理中找到应用.非定常约束力学系统的稳定性研究是重要而又困难的课题,用构造Lyapunov函数的直接方法来研究稳定性问题有很大难度,其中如何构造Lyapunov函数是永远的开放问题.本文给出一种间接方法,即梯度系统方法.提出一类梯度系统,其矩阵是负定非对称的,这类梯度系统的解可以是稳定的或渐近稳定的.梯度系统特别适合用Lyapunov函数来研究,其中的函数V通常取为Lyapunov函数.列出广义Birkhoff系统的运动方程,广义Birkhoff系统是一类广泛约束力学系统.当其中的附加项取为零时,它成为Birkhoff系统,完整约束系统和非完整约束系统都可纳入该系统.给出广义Birkhoff系统的解可以是稳定的或渐近稳定的条件,进一步利用矩阵为负定非对称的梯度系统构造出一些解为稳定或渐近稳定的广义Birkhoff系统.该方法也适合其他约束力学系统.最后用算例说明结果的应用.