Verification of the new viscoelastic method of thermal stress calculation in asphalt layers of pavements

The new viscoelastic method of thermal stress calculations in asphalt layers has been developed and published recently by the author. This paper presents verification of this method. The verification is based on the comparison of the results of calculations with results of testing of thermal stresses in Thermal Stress Restrained Specimen Test. The calculations of thermal stresses according to the new method were based on rheological parameters of the Burgers model. The parameters were measured in laboratory at different low temperatures, at long time creep under constant loading. Five asphalt mixes were tested. Three of them were high modulus asphalt concretes and two conventional asphalt concretes. Specimens were prepared in exactly the same way both for rheological creep tests and for the Thermal Stress Restrained Specimen Test. The results of measured thermal stresses were compared with thermal stresses calculated from the new viscoelastic method developed by the author and in most cases a good agreement was found. For comparison, the measured stresses were compared with results of calculations according to the existing methods. The viscoelastic Monismith method failed in prediction of thermal stresses. The prediction from the quasi-elastic Hills and Brien method was underestimated, but better than from the Monismith method and worse than from the new viscoelastic method. The reasons of discrepancies were discussed.     

沥青混合料低温临界开裂温度的确定

为了同时考虑沥青混合料在降温过程中温度应力的累积和松弛作用,确定临界开裂温度,对试件进行了线收缩系数试验,并利用间接拉伸试验确定其抗拉强度和蠕变柔量,由蠕变柔量和松弛模量的关系得到松弛模量的Prony系列表达式;由Boltzmann叠加原理,得到温度应力公式,计算出不同降温速率下产生的温度应力,根据低温抗拉强度曲线,确定出沥青混合料的临界开裂温度,并对结果予以验证。结果表明:该方法考虑了应力累积和松弛二者的综合作用,能够较好地反映沥青混合料的低温开裂特性,其计算结果与约束试件温度应力试验结果相近;该方法不仅适用于恒定降温速率,还适用于现场连续变速降温工况;随温度的降低或降温速率的增加沥青混合料内部温度应力累积速度加快,临界开裂温度随降温速率增加而升高。      

Thermal stresses of asphalt pavement under dependence of material characteristics on reference temperature

This thesis presents an analytical study of thermal stresses of asphalt pavement under dependence of material characteristics on reference temperature. In the analysis, flexible pavement is regarded as a multi-layered elastic half-space axisymmetrical system. Firstly, thermo-elastic theory is used to describe thermal stresses of a multi-layered system, while the temperature-dependent material characteristics are considered. Then Laplace transformation and Hankel transformation with respect to time and radial, respectively, are utilized for thermo-elastic equations of equilibrium. In addition, the transfer matrix method is applied to derive general solutions for the multi-layered problem. Finally, the resulting formulation is applied to calculate thermal stresses in the low temperature cracking problem of asphalt pavement. Thermal stress is calculated and compared with the case that material characteristics are supposed to be constant to show the remarkable impact of temperature-dependent material characteristics on thermal stresses of asphalt pavement.     

Residual and thermoelastoplastic stress distributions in a heat treated solid cylinder

An important consideration in design is the determination of residual stresses developed during heat treatment of steel. By selecting an appropriate heat treatment technique, one can control the level of residual stresses in the components. Obviously beneficial residual stresses in the material increase the life of components. On the other hand, the unexpected failure of components that is later attributed to detrimental residual stresses is not uncommon.

In this paper, residual stress distribution in a quenched long solid cylinder with temperature dependent properties is evaluated. Using three different speeds of cooling, the level of residual stresses for each speed was determined and compared with the others. From the stresses calculated, it was found that the tensile and tangential residual stresses are more sensitive to the speed of cooling than the radial one. For theoretical analysis a quasi-static uncoupled thermoelastoplastic analysis, based on incremental theory of plasticity, is developed and a numerical procedure for successive elastic solution approximation is formulated.     

透水沥青混合料的热物特性与热阻功能

为研究透水沥青混合料的热物性,基于热力学理论计算比较了透水沥青混合料和密级配沥青混合料的热导率、比热容、热扩散率等指标,并对透水沥青混合料的热物性指标与空隙率、含水率的关系展开分析;通过设计室内光照试验,测得相同的传热条件下两种材料表面和底部的温度变化。理论计算结果表明同密级配沥青混合料相比,透水沥青混合料的热导率降低约20%,热扩散率降低约10%;室内温度测试结果显示,透水沥青混合料试件表面较密级配沥青混合料试件温度低2～2.5℃,底部温度低3～3.5℃,说明透水沥青混合料具有热阻功能,对气温荷载变化的抵抗能力较强,验证了理论计算结果。     

梯度功能材料薄板瞬态热弹性弯曲有限元分析

用层合板有限元法分析了由ZrO2和Ti-6Al-4V组成的新型梯度功能材料薄板的瞬态热弹性弯曲应力问题,并对本方法的正确性进行了检验。讨论了加热、 冷却热边界条件以及两种力学边界条件(固支和简支)对梯度功能材料薄板的瞬态热弹性弯曲应力分布的影响。发现：(1) 在加热过程中,简支板低温金属侧出现较大压应力;在冷却过程中,简支板高温陶瓷侧出现较大拉应力; 且其拉、压应力会随着板上、下表面温差的增大而增大。(2) 无论是简支板还是固支板, 在冷却过程中,沿整个厚度板内部压应力均较大。(3) 在本文的相同条件下,固支板比简支板更适合高温、大温差的使用环境。     

Development and partial relaxation of internal stresses in thin TiC layers chemically vapour deposited on Fe-C substrates

TiC layers were chemically vapour deposited at 1273 K mn Fe-C substrates with carbon contents between 0.06 and 1.20w%C. X-ray diffraction stress analyses showed that large compressive stresses are present in the IC coatings and that small tensile stresses any present in the substrates. The stresses developed during cooling from the deposition temperature to room temperature, owing to the difference in thermal shrink between coating and substrate. However, stress relaxation was also evident. This was provoked by the phase transformation processes occuring in the substrate on cooling. Stress relaxation was hindered when grain-boundary cementite formed in the substrates. The stresses present in the TiC coatings on substrates without grain-boundary cementite can be predicted quantitatively.     

Residual Stresses in Short-Fibre Reinforced Injection-Moulded Thermoplastic Parts

Having the prediction of the warpage and shrinkage behaviour of injection-moulded short-fibre reinforced thermoplastics in mind, a model is developed to calculate the residual stresses. In accordance with the structure and the behaviour of these materials, a layerwise orthotropic, viscoelastic constitutive equation is used. As a cause for the stress development, a process determining the history of cooling under pressure is considered. The volume expansion of the matrix is described using a time-dependent viscoelastic free volume concept. From this, the viscoelastic functions for thermal expansion are derived as well as a time-dependent temperature shift factor. The material law of the composite is developed with the help of micromechanical considerations assuming viscoelastic matrix and elastic fibre behaviour. The residual stresses are calculated for a specially designed testing device which possesses regions of different fibre orientation. Measured fibre orientation tensors are used as simulation input. In the following, the calculated stress profiles were compared with measured values, which were determined using the layer removal technique. The calculated and measured profiles are in good agreement and show a strong influence of the fibre orientation state. The highest occurring stresses are in the same order of magnitude as the long-term strength of these materials.     

沥青混合料热粘弹性本构关系试验测定及其力学应用

基于热粘弹性力学理论,就不同的温度条件下沥青混合料的应力松弛特征开展了试验研究,应用热流变简单材料的时温等效原理对试验结果进行了分析和参数拟合,根据试验结果建立了描述沥青混合料粘弹特性的广义Maxwell模型;通过理论推导提出了沥青混合料非定常和非均匀变温条件下增量型热粘弹性本构关系,在此基础上,给出应用本构关系进行沥青路面热粘弹性力学分析的数值实现方法;通过对TSRST试验的模拟,对得到的沥青混合料热粘弹性本构关系及其数值实现方法的合理性进行了验证,并给出一个工程计算实例。     

Application of Differential Transform Method to Thermoelastic Problem for Annular Disks of Variable Thickness with Temperature-Dependent Parameters

This article analyzes the one-dimensional steady temperature field and related thermal stresses in an annular disk of variable thickness that has a temperature-dependent heat transfer coefficient and is capable of temperature-dependent internal heat generation. The temperature dependencies of the thermal conductivity, Young’s modulus, and the coefficient of linear thermal expansion of the disk are considered, whereas Poisson’s ratio is assumed to be constant. The differential transform method (DTM) is employed to analyze not only the nonlinear heat conduction but also the resulting thermal stresses. Analytical solutions are developed for the temperature and thermal stresses in the form of simple power series. Numerical calculations are performed for an annular cooling/heating fin of variable thickness. Numerical results show that the sufficiently converged analytical solutions are in good agreement with the solutions obtained by the Adomian decomposition method and give the effects of the temperature-dependent parameters on the temperature and thermal stress profiles in the disk. The DTM is useful as a new analytical method for solving thermoelastic problems for a body with temperature-dependent parameters including material properties.     

Modeling of relaxation of viscoelastic stresses in multi-layered thin films/substrate systems due to thermal mismatch

Assume the ratio of the total axial rigidity of thin films to that of the substrate is smaller than 0.02, an approximate closed-form solution for viscoelastic stresses in multi-layered thin films/substrate systems due to thermal mismatch is derived. This is achieved by utilizing the analogy between the governing field equation of elasticity and the Laplace transform with respect to time of the viscoelastic field equation. Based on two solutions, simplified solutions for relaxation of residual stresses distributed in multiple layers of thin films deposited on a thick substrate are obtained. The effect of the thickness, thermal expansion coefficient, Young's modulus, and viscosity coefficient of the substrate and thin films on the relaxation of residual stresses is considered. This simplified solution can be applied to some special cases such as one layered or periodic multi-layered thin films on a thick substrate.     

Influence of selected WMA additives on viscoelastic behaviour of asphalt mixes and pavements

Warm mix asphalt additives are effective in decreasing production, laying and compaction temperatures of asphalt mixes. However, there are still questions concerning influence of warm mix additives on properties of asphalt mixes and pavement performance. This paper presents results of the comprehensive research of viscoelastic behaviour of asphalt mixes and pavement structures with layers made with warm mix asphalt additives at high temperatures. Two additives of significantly different effects on mixes at higher temperatures were selected for analysis, namely aliphatic synthetic wax produced with the use of Fisher–Tropsch method and formulation of surfactant- based molecules (ionic and non-ionic). Viscoelastic properties of mixes with these two additives and, as a reference mix, with neat unmodified asphalt binder were determined in uniaxial compression with sinusoidal loading using Asphalt Mixture Performance Test. The viscoelastic analysis of pavement structures was performed with use of the VEROAD software and data from laboratory testing. Two different pavement structures were analysed, for light and heavy traffic. The temperature distribution in pavement structure during the hottest summer day in northern Poland in 2012 was taken into account. The model of pavement was loaded with moving wheel at different speeds. The analysis has shown that two tested warm mix additives had different effect on viscoelastic transient response at high temperatures. One of them (Fischer–Tropsch wax) evidently caused an increase in resistance of asphalt mix and pavement structure to loading at high temperature. The second additive (formulation of surfactant-based molecules) slightly reduced resistance of asphalt mix and pavement to loading at high temperatures as compared with the reference mix.     

Thermal stresses of flexible pavement with consideration of temperature-dependent material characteristics using stiffness matrix method

The asphalt pavement is regarded as a multilayered elastic half space axisymmetrical body. By introducing the relationship between material characteristics and temperature into the fundamental equations of thermoelasticity and using mathematic methods of Laplace and Hankel integral transformation, the stiffness matrix for a layer is derived firstly. Then the global stiffness matrix is established for multilayered elastic half space using the finite element concepts in which layers are completely contacted. Therefore, explicit solution for thermal stresses of the asphalt pavement is obtained from the solution of the algebra equation formed by global stiffness matrix and the inverse Hankel and Laplace integral transformation. Because the elements of matrix do not include positive exponential function, the calculation is not overflowed and the shortages of transfer matrix method are overcome. This approach serves as a better model for real pavement structure as it takes into account the relationships between the material characteristics and temperature in the pavement system.     

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.     

Predicting crack initiation in composite material systems due to a thermal expansion mismatch

Residual stresses due to curing and thermal stresses due to differences between the thermal expansion coefficients of the matrix and fiber may have a major effect on the micro-stresses within a composite material system and must be added to the stresses induced by the external mechanical loads. Such microstresses are often sufficient to produce micro-cracking even in the absence of external loads, example during the cooling process. In this investigation, a micro-mechnics approach is used in which the fibers of a composite material system are modeled as cylindrical inclusions that are embedded into a matrix plate. The model is then used to predict, analytically, the residual stresses due to a thermal expansion mismatch, e.g. during a cooling process. Additionally, some critical effects due to a load transverse to the direction of the fibers are examined. The analysis provides a better understanding of how residual stresses are developed and how they may be controlled in material systems where small strains are present. Moreover, the results are used to identify locations of possible crack failure and to derive a fracture criterion for crack initiation at the local level. Comparison with experimental evidence for matrix cracking in intermetallic composites caused by thermal expansion mismatch shows a good agreement. This revised version was published online in July 2006 with corrections to the Cover Date.     

Thermal study of injection moulded ring

Application of CAD/CAM techniques to injection mould design is feasible and required now in view of the low cost of computers and the need to develop moulds in the shortest possible time. For this purpose a simpler thermal analysis of an injection mould is desirable, as most of the mould makers in Asia are in the category of small manufacturing units. This paper presents a thermal model of injection moulds for axisymmetric components using polar co-ordinates. This model could be utilised for studying the shrinkages, thermal residual stresses and cooling channels. A design example is presented to explain the method of application of the developed model.     

复合材料粘弹性本构关系与热应力松弛规律研究Ⅱ:数值分析

给出了预测复合材料粘弹性松弛模量、等效热应力松弛系数和等效时变热膨胀系数的均匀化方法的有限元数值实现步骤, 研究了单向纤维复合材料随温度变化的粘弹性本构关系, 以及热应力松弛规律和热膨胀系数的时变特征。单向纤维复合材料的一维热变形分析数据显示了热应变对时间的强烈依赖关系;以数值形式给出的等效热应力松弛模量对时间的依赖关系表明, 等效的热应力松弛模量对时间的依赖性较弱, 其冲击模量和渐近模量只相差0.4 %。     

Internal stress and solid solubility effects on the thermal expansivity of Al-Si eutectic alloys

Thermal expansion measurements are reported for a number of as-cast Al-Si eutectic alloys including a Sr-modified alloy which gives nearly spherical Si particles. The measurements were obtained by heating and cooling over repeated temperature cycles between room temperature and 500°C. In general, lower expansivity values were measured on the cooling cycle as compared with the heating cycle, resulting in a net positive permanent deformation at room temperature. Analytical solutions are described for the thermal expansivity of a concentric-spheres model for a Si particle contained within an Al matrix. The effect of plastic flow in the Al is included. Overall, the predictions show reasonable agreement with the measured expansivities. The observed differences between heating and cooling are of the same order as that which is predicted. At high temperatures, the measured increase in expansivities is smaller than calculated. The latter effect is explained by the decrease in expansivity which results from an increasing solid solubility of silicon in aluminum with increasing temperature.Paper presented at the Ninth International Thermal Expansion Symposium, December 8–10, 1986, Pittsburgh, Pennsylvania, U.S.A.     

金属基复合材料中热残余应力的分析方法及其对复合材料组织和力学性能的影响

对目前金属基复合材料热残余应力的分析方法进行了概述,并对热残余应力对金属基复合材料的性能影响进行了分析,提出了目前在复合材料热残余应力的实验分析和理论计算中仍存在的问题以供材料科学工作者共同研究解决.     

一种新型复合相变材料导热性能的实验研究

针对相变材料在实际应用过程中交替存在升温液化和降温固化的复杂传热过程,采用JW-Ⅲ建筑材料热流计式导热仪,分别对升温和降温过程中处于固态、混合态、液态的新型复合相变材料导热性能进行了测试和分析。研究结果表明,复合相变材料在加热和冷却过程中的导热系数随温度的变化存在明显的规律性差异,导热系数在混合态时差值达到20%;升温过程中,复合相变材料在混合态和液态时的导热系数值相差不大,但与固态时相比有明显减小;降温过程中,在液-固相变的过程中导热系数随温度减小而增大,有利于加速相变材料的固化。