Elastic Thermal Stress Research Articles

Modeling of Thermal Stresses in Joining Two Layers with Multi‐ and Graded Interlayers

The technique of introducing interlayers has been used extensively to mitigate residual thermal stresses in joining dissimilar materials. Finite‐element analyses have often been used to quantify thermal stresses in these layered structures in case‐by‐case studies. Recently, simple analytical models containing only three unknowns have been developed to derive closed‐form solutions for elastic thermal stresses in both multilayer systems and two layers joined by a graded junction. The analytical solutions are exact for locations away from the free edges of the system. Application of these solutions is shown here to provide a systematic study of thermal stresses in Si3N4 and Al2O3 layers joined by various sialon polytypoid‐based multi‐ and graded interlayers. The effects of the thickness, stiffness, and coefficient of thermal expansion of the interlayer on thermal stresses in the system are examined. The differences in thermal stresses resulting from multi‐ and graded interlayers are shown.

An analytical model for predicting thermal residual stresses in multilayer coating systems

An analytical model based on force and moment balances was developed to predict the thermal residual stresses in elastic multilayer coating systems due to differential thermal contraction. A closed-form solution was obtained which is independent of the number of coating layers. Specific results were obtained for the distribution of elastic thermal residual stresses within ZrO 2/NiCoCrAlY thermal barrier coating systems. Furthermore, the effects of thickness and porosity of ZrO 2 ceramic layer on the residual stress and the curvature of coating systems due to cooling process were discussed. It has been found that the curvature almost increased linearly with increasing thickness or decreasing porosity of ceramic layer. Finally, the contribution of bending strain to the thermal stress was examined and the accuracy of approximate solution was estimated.

Thermal Residual Stress Analysis of Ni–Al2O3, Ni–TiO2, and Ti–SiC Functionally Graded Composite Plates Subjected to Various Thermal Fields

This study investigates the thermal elastic residual stresses occurring in Ni–Al2O3, Ni–TiO2, and Ti–SiC functionally graded plates due to uniform, linear, and parabolic temperature fields through the plate thickness. A 3D eight-noded isoparametric layered (no limit layer number) finite element with three degrees of freedom at each node was implemented to the residual stress problem analogous to the shell elements proposed by Ahmad et al. (Ahmad, S., Irons, B.M. and Zienkiewicz, O.C. (1970). Analysis of Thick and Thin Shell Structures by Curved Finite Elements, Int. J. of Numerical Methods in Engineering, 2: 419–451.) and Yunus and Khonke (Yunus, S.M. and Khonke, P.C. (1989). An Efficient Through-Thickness Integration Scheme in an Unlimited Layer Doubly Curved Isoparametric Composite Shell Element, Int. J. of Numerical Methods in Engineering, 28: 2777– 2793.). The longitudinal stresses (11, 22) and transverse shear stresses (13, 23) were dominant. The shear stresses become important especially at the free edges of the plate. As the compositional gradient was increased the normal and shear stresses increased. Whereas the normal stresses become tensile in both ceramic-rich and metal-rich regions; the shear stresses, which are not severe in both the regions, change their directions and become a maximum inside the plate. The thermal and mechanical properties of constituents played an important role on the stress magnitudes rather than on the profiles of the through-thickness variations of normal and shear stresses. Thus, the difference of the coefficients of thermal expansion of the ceramic and metal phases affected the magnitudes of the normal and shear stresses. In addition, the continuous temperature fields through the plate thickness resulted in similar normal and shear stress variations.

Dynamics of melt–crystal interface and thermal stresses in rotational Bridgman crystal growth process

The growth process of potassium bromide (KBr) single crystals in a vertical Bridgman furnace has been studied numerically using an integrated model that combines formulation of global heat transfer and thermal elastic stresses. The global heat transfer sub-model accounts for conduction, convection and interface movement in the multiphase system. Using the elastic stress sub-model, thermal stresses in the growing crystal caused by the non-uniform temperature distribution is predicted. Special attention is directed to the interaction between the crystal and the ampoule. The global temperature distribution in the furnace, the flow pattern in the melt and the interface shapes are presented. We also investigate the effects of the natural convection and rotational forced convection on the shape of the growth fronts. Furthermore, the state of the thermal stresses in the crystal is studied to understand the plastic deformation mechanisms during the cooling process. The influence of the wall contact on thermal stresses is also addressed.

Modeling of elastic thermal stresses in two materials joined by a graded layer

The distribution of elastic thermal stresses in two dissimilar materials joined by a graded layer is a critical issue and has been analyzed previously. However, numerical methods have often been used. The difficulty in obtaining an analytical solution in existing analyses is discussed, and an exact closed-form solution is derived in the present study. To illustrate applications of the present solution, results are calculated for elastic thermal stresses in thermal barrier coatings, which consist of substrate, graded bond coat, and top coat. Different profiles of the thermomechanical properties in the bond coat are considered to examine how the graded interlayer modifies the elastic thermal stress distribution in the system.

Growth kinetics and thermal stress in AlN bulk crystal growth

Group III nitrides, such as GaN, AlN and InGaN, have attracted great attention due to their applications in blue-green and ultraviolet light emitting diodes and lasers. In this paper, an integrated model has been developed based on the conservation of momentum, mass, chemical species and energy together with boundary conditions that account for heterogeneous chemical reactions both at the source and seed surfaces. The predicted temperature profiles have been compared with measurements for different power levels and flow rates in a reactor for AlN crystal growth at the North Carolina State University. We have found that the heat power level affects the entire temperature distribution greatly while the flow rate has insignificant effect on the temperature distribution; the overall thermal stress level is higher than the critical resolved shear stress, indicating that thermal elastic stress can be a major source to induce high dislocation density in the as-grown crystal. The stress level is strongly dependent on the temperature gradient in the as-grown crystal. Results are correlated well with defects showing in an X-ray topograph for the AlN plate crystal.

Thermal stresses in elastic multilayer systems

Thermal stresses in elastic multilayer systems have been previously modelled. However, because the displacement compatibility condition at interfaces between layers must be satisfied, the complexity in obtaining a closed-form solution increases with the number of layers in the system. As a result, existing analyses often adopt simplifications (e.g. assuming a constant elastic modulus throughout the system) to obtain closed-form solutions or are solved numerically by computer. The present study develops an analytical model, in which the complexity in obtaining a closed-form solution is independent of the number of layers and an exact closed-form solution can be concisely formulated. Specific results are calculated for elastic thermal stresses in (AlGa)As laser diodes, which consist of five layers. Also, the zero-order and the first-order approximations are formulated based on the exact closed-form solution, and their accuracy is examined. The acceptability of assuming a constant elastic modulus in the system in existing analyses is also discussed.

Design of an improved vacuum vessel protection for very long pulse operation in Tore Supra

The present concept of Tore Supra vacuum vessel wall protection, by means of actively cooled stainless steel cooling panels, will be improved in order to cope with the CIEL project requirements (radiated power of at least 10 MW yielding heat flux up to 0.3 MW/m 2 for up to 1000 s). Therefore, new die formed stainless steel cooling panels have been developed and their performance were compared with different design solutions. Results of 3-D thermal and thermomechanical elastic stress analysis associated with fatigue estimates of the corrugated vacuum vessel structure are presented. They take into account especially the effect of heat deposition on the vessel wall due to radiating plasma power losses through an unavoidable very small fraction of unprotected area remaining in the improved vessel covering.

Minimization of elastic thermal stresses during laser machining of ceramics using a dual-beam arrangement

Lasers are emerging as a valuable tool for shaping and cutting hard and brittle ceramics. Unfortunately, the large, concentrated heat flux rates that allow the laser to efficiently cut and shape the ceramic also result in large localized thermal stresses in a small heat-affected zone. These notable thermal stresses can lead to microcracks, a decrease in strength and fatigue life, and possibly catastrophic failure. In order to assess where, when, and what stresses occur during laser scribing, an elastic stress model has been incorporated into a two-dimensional drilling as well as a three-dimensional scribing and cutting code. The results of the analysis for a single Gaussian laser source show that substantial tensile stresses develop over a thick layer below and parallel to the surface, which may be the cause of experimentally observed subsurface cracks. In this work the effect of splitting the beam into two parts is discussed: a highly focused beam that does the actual drilling or scribing, and a partially defocused beam, used to heat the material ahead of, around, or behind the laser beam. Different secondary beam scenarios are investigated, and their effect on reducing the damaging tensile stresses is evaluated.

Transient Elastic Thermal Stress Development During Laser Scribing of Ceramics

Lsaers are emerging as a valuable tool for shaping and cutting hard and brittle ceramics. Unfortunately, the large, concentrated heat flux rates that allow the laser to efficiently cut and shape the ceramic also result in large localized thermal stresses in a small heat-affected zone. These notable thermal stresses can lead to micro-cracks, a decrease in strength and fatigue life, and possibly catastrophic failure. In order to assess where, when, and what stresses occur during laser scribing, an elastic stress model has been incorporated into a three-dimensional scribing and cutting code. First, the code predicts the temporal temperature fields and the receding surface of the ceramic. Then, using the scribed geometry and temperature field, the elastic stress fields are calculated as they develop and decay during the laser scribing process. The analysis allows the prediction of stresses during continuous wave and pulsed laser operation, a variety of cutting speeds and directions, and various shapes and types of ceramic material. The results of the analysis show substantial tensile stresses develop over a thick layer below and parallel to the surface, which may be the cause of experimentally observed subsurface cracks.

Grain boundary strength in non-cubic ceramic polycrystals with misfitting intragranular inclusions (nanocomposites)

The residual stress distribution in polycrystalline ceramics with thermal expansion anisotropy and misfitting intragranular dispersion is studied through micromechanical simulation. The effective grain boundary strength under remote tension is derived from the stability of a grain-boundary microcrack with thermal elastic residual stresses. This result is then applied to the strength and fracture properties of a two-phase nanocomposite (5 vol% SiC-Al2O3). The residual stresses from misfitting dispersion increase the effective grain boundary strength of the nanocomposite from 1.5 to 5 times more than that of the single-phase polycrystal, depending on the grain size of the matrix phase. The residual stresses reduce the instability range of microcrack precursors at grain junctions and increase the initial level of driving force for critical microcrack extension. Predicted strengthening of grain boundaries leads, in turn, to the superior inert strength of unnotched nanocomposite.

Re/W/Mo and Ir/W/Ta Graded-Structure Emitters of Thermionic Energy Converter

Rhenium and iridium exhibit excellent thermionic electron emission characteristics in a cesium plasma converter, owing to their low work function in cesium vapor. The maximum power density and output characteristics of an emitter surface with iridium or thenium layers were simulated, and the surface was expected to be improved compared with other refractory metals such as polycrystalline rhenium, tungsten and molybdenum. The rhenium/tungsten/molybdenum graded structure was fabricated by chemical vapor deposition. In order to improve the thermal stability of the rhenium layer at elevated temperatures, tungsten layer was inserted between the rhenium layer and the molybdenum substrate to form graded-composition interfaces. The iridium/tungsten/ tantalum graded-structure emitter has been successfully produced by annealing at high temperature following hot isostatic pressing. When the tantalum component reacted with the iridium emitter, a 2226 K low-melting-point phase appeared. A three-layer structure with tungsten as the intermediate layer was selected to enhance the thermal stability of the emitter. The procedure of an elastic thermal stress analysis of functionally graded emitters by the axisymmetric finite-element method is presented. Thermal stresses are reduced to form graded-composition interfaces of rhenium/tungsten/molybdenum and iridium/tungsten/tantalum systems in the simulated model. The maximum power of a thennionic energy converter of a rhenium/tungsten/molybdenum emitter is 7.9 W/cm 2 and that of an iridium/tungsten/tantalum emitter is 2.6 W/cm 2 .

Macro-segregation, dynamics of interface and stresses in high pressure LEC grown crystals

High dislocation density and strong dopant inhomogeneities have been found in high pressure liquid-encapsulated Czochralski (HPLEC) grown crystals. The origin and underlying mechanisms of these defects are attributed to the complex nature of transport phenomena in the HPLEC system. Our integrated computer model (MASTRAPP) can simulate this process by calculating the flow and heat transfer in both the melt and the gas, and thermal-elastic stress in the crystal. In this work, this model has been further extended to investigate the development of thermal stress in the growing crystal and the redistribution of dopant in the melt. The results for InP growth show complex gas flow and heat transfer pattern in the system. Two large stress spots are predicted by the model, one at the edge of the crystal just above the encapsulant layer and the other in the top corner of the crystal. Although the stress always remains largest at the first location, its value decreases as the crystal grows, due to the enhanced cooling of the crystal. A curved crystal/melt interface is also found to introduce high thermal stresses in its vicinity, which may be dangerous because of a high temperature at the interface and thus a low strength of the crystal. The model also predicts both radial and longitudinal dopant segregation in the growing crystal, and shows that the dopant redistribution in the melt is caused by the complex flow pattern in the melt. This is the first time, that a strong radial dopant segregation has been predicted based on a comprehensive flow model for a HPLEC growth.

Characterization of defect structures in magnetic liquid encapsulated Kyropoulos grown InP single crystals

Synchrotron White Beam X-ray Topography (SWBXT) has been used as a nondestructive diagnostic technique for the characterization of defect structures in large wafers cut from S and Fe-doped InP single-crystal boules. Wafers cut both longitudinally and laterally with respect to the growth axis were studied in order to reveal the overall defect distribution in the boules. Studies carried out on longitudinally cut S-doped crystals enabled information to be obtained on interface shape, from the observation of growth striations, as well as defect distribution. The conditions for optimal visibility of the growth striations were determined and it was found that the morphology of the growth interface was a sensitive function of local growth conditions. The formation of extensive slip bands from peripheral regions was also observed. This indicates that large thermal stresses were generated during crystal growth leading to such significant plastic deformation processes. Studies carried out on a series of laterally sliced, Fe-doped wafers cut from the same boule revealed dislocations in well-defined fourfold symmetric distributions. A finite element thermal-elastic stress analysis was performed for an intermediate growth stage to investigate the nature of the stress which causes this fourfold distribution. The calculated excess shear stress from this analysis agrees qualitatively with the observed dislocation distribution and slip system activity. The influence of an applied magnetic field on precipitate distributions in InP boules was preliminarily studied by examining a longitudinal cut, heavily Fe-doped InP wafer, which was grown in the presence of an intermittent applied field. Topographs recorded from this wafer revealed that no formation of large precipitates was discernible in either the initial or intermediate growth stages when the magnetic field was applied. On the other hand, the formation of large precipitates was observed in regions near the final stage of crystal growth when the magnetic field was turned off. Further such investigations are underway.

A new model for analysing thermal stress in granular composite

A double embedding model of inletting reinforcement grain and hollow matrix ball into the effective media of the particulate-reinforced composite is advanced. And with this model the distributions of thermal stress in different phases of the composite during cooling are studied. Various expressions for predicting elastic and elastoplastic thermal stresses are derived. It is found that the reinforcement suffers compressive hydrostatic stress and the hydrostatic stress in matrix zone is a tensile one when temperature decreases; when temperature further decreases, yield area in matrix forms; when the volume fraction of reinforcement is enlarged, compressive stress on grain and tensile hydrostatic stress in matrix zone decrease; the initial temperature difference of the interface of reinforcement and matrix yielding rises, while that for the matrix yielding overall decreases.

Thermal Stress Failure of Water-Cooled Zinc Fuming Furnace Jackets

The failure of zinc slag fuming furnace jackets is a common industrial problem that has received little attention in the literature. During service the water-cooled jackets develop cracks in the working panel that initiate on the slag face and propagate towards the water cavity. In-plant measurements revealed the presence of large thermal transients or temperature “spikes” in the panel approximately 20 cm above the tuyere line. The transients were observed during charging and tapping of the furnace and are associated with slag fall-off due to surface wave action and gas injection effects when the bath level is low. Temperatures at the panel mid-thickness were seen to rise by as much as 180°C above the steady-state level. A mathematical modelling analysis of the transient freezing phenomena has been coupled with an elastic thermal stress model. The experimental and modelling results indicate that the temperature spikes are associated with the sudden removal of patches of the frozen slag layer and molten slag coming into contact with the jacket. The temperature increases are large enough to generate compressive stresses that cause yielding of the material in the exposed area which upon cooling results in tensile stresses. It is postulated that cycling between compressive and tensile stress states leads to failure by low-cycle fatigue. Examination of the crack surfaces reveals features that support this mechanism. Résumé La rupture du chemisage des fours à scories de zinc fumants est un problème industriel commun, peu étudié jusqu'à présent. Pendant l'utilisation de chemisage refroidi par eau, on voit se développer des fissures dans les panneaux en cours de fonctionnement, e1les débutent à la surface des scories et se propagent vers les cavités remplies d'eau. Des mesures effectuées en usine révèlent la présence de transferts thermiques importants, ou pics de température, dans un panneau situé approximativement à 20 cm au-des sus de la ligne des tuyères. On a observé des états transitoires pendant le chargement et le déchargement des fours, on les a associées à des chutes de scories causées par des ondes de surface et l'injection de gaz lorsque le niveau du bain est bas. On a pu observer, à mi-épaisseur des panneaux, une augmentation de température de 180°C au-dessus du niveau de l'état stable. Une analyse de modélisation mathématique du phénomène transitoire de solidification a été couplé à un modèle de contrainte thermique élastique. Les résultats expérimentaux ainsi que ceux de la modélisation indiquent que les pics de température sont associés au retrait brutal de morceaux de scories en couches solides, mettant ainsi en contact scories en fusion et chemisage. L'augmentation de température est suffisamment importante pour être cause de contraintes de compression, à l' origine de déformations plastiques du matériau dans la surface exposée et par conséquence des contraintes de tension, lors du refroidissement. On postule que le cycle contraintes en compression, contraintes en tension, conduit à des ruptures par fatigue sous cycle lent. L'examen de surfaces fissurées montre des caractéristiques qui appuient ce mécanisme.

Approximate Evaluation of the Elastic Thermal Stresses in a Thin Film Fabricated on a Very Thick Circular Substrate

Approximate Evaluation of the Elastic Thermal Stresses in a Thin Film Fabricated on a Very Thick Circular Substrate

Elastic fields due to centers of dilatation and thermal inhomogeneities in plane-layered solids

A n image method for obtaining the solution for a center of dilatation in a three-layer elastic solid with planar interfaces is presented. The three-layered elastic solid consists of an elastic slab sandwiched between two semi-infinite elastic solids. The three elastic solids are perfectly bonded together at the two planar interfaces. The solution is given in terms of Galerkin vectors which are in terms of an infinite series of the Newtonian potential function of a mass point at the center of dilatation, its mirror images and their derivatives. As an application, the solution for the center of dilatation is used to obtain the elastic solution due to thermal inhomogeneities. The thermoelastic solution is obtained by a method which is based on the integration of properly weighted centers of dilatation over the volume occupied by the inhomogeneity. The potential functions for the problem solved are the harmonic potential functions of attracting matter filling the volume of the thermal inhomogeneity and its mirror images. The solution for the thermal elastic stresses due to an expanding (or contracting) thermal inhomogeneity (inclusion) of any shape embedded in one of the solids is given as an example. Numerical results for a spherical inclusion with pure dilatation eigenstrain are also presented and discussed.

Centre of dilatation and thermal stresses in an elastic plate

The elastic field caused by a centre of dilatation in a plate is given in terms of Galerkin vectors. The field caused by a thermal inhomogeneity is obtained by a method which is based on the integration of properly weighted centres of dilatation over the volume occupied by the plate. The potential functions for the problem solved are the harmonic potential functions of attracting matter filling the element of volume and its mirror images. One of the applications, the thermal elastic stresses due to an expanding (or contracting) inclusion of any shape embedded in the plate, is given as an example. Numerical results for a spherical inclusion with pure dilatation eigenstrain are also presented.

Approximate evaluation of the elastic interfacial stresses in thin films with application to high-Tc superconducting ceramics

The mechanical strength and structural integrity of a high-Tc superconductor may play a decisive role when a superconducting material is used for practical purposes. In this analysis, we suggest a simple analytical model for an approximate evaluation of the elastic thermal stresses in elongated thin films in application to high-Tc superconducting ceramics. The emphasis is on interfacial shearing and peeling stresses responsible for the integrity of the film-substrate composite and the strength of the intermediate material, if any. A numerical example is performed for a superconducting ceramic YBa2Cu3O7-δ deposited on a Si. GaAs, Al2O3 or MgO substrate. It is shown that the thermally-induced stresses und strains can be brought down by reducing the thermal expansion (contraction) mismatch of the film and the substrate, the fabrication temperature, and Young's modulus of the film material. Our theory is equally applicable to other film structures as long as the materials involved can be treated as linearly elastic.