Breaking of window glass close to fire,II: Circular panes

A heat-conduction equation with linearized radiation cooling boundary conditions is used to calculate the thermal field in a circular window pane heated by thermal radiation (fire) but screened on narrow strips along edges built into the frame. This temperature field is used to calculate a quasi-static thermal stress field in the pane in the first-order planar thermal stresses build up at the edges in a narrow strip of a few times the pane thickness. As the radius of the pane grows the edge stresses quickly approach those of the linear strip pane. The round window does not differ much from the strip window in the geometrical region of practical utility in windows. The results also indicate, without explicit calculations, that in rectangular windows the stresses do not concentrate in the corner regions. As the final result of the theoretical work it seems plausible to use simple, general relationships obtained for the strip window as well for all geometries deviating from linear to evaluate approximately the danger of thermal breakage of a pane.     

Interfacial Peeling Moments and Shear Forces at Free Edges of Multilayers Subjected to Thermal Stresses

Stresses normal to interfaces, i.e., interfacial peeling stresses and interfacial shear stresses, exist locally at edges of multilayers because of both the thermal mismatch between layers and the free-edge effect. These peeling and shear stresses can result in modes I and II edge delamination, respectively. However, because of the complexity of the problem, exact closed-form solutions for these stresses are very difficult if not impossible to derive even for bilayered systems. Hence, instead of the detailed stress field at edges, both the interfacial peeling moment resulting from the localized peeling stresses and the interfacial shear force resulting from the localized shear stresses are analyzed here. Exact closed-form solutions for the peeling moment and the shear force at each interface in elastic multilayered systems are derived. To illustrate the application of present closed-form solutions, specific results are calculated for five-layered thermal barrier coating systems, and a finite-element analysis is also performed to confirm the analytical results.     

Stresses Due to Temperature Gradients in Ceramic-Matrix-Composite Aerospace Components

Ceramic-matrix composites (CMCs) are being considered as replacement materials for divergent flaps and seals in advanced aerospace turbine engines. During service, these components are subjected to severe temperature gradients across the width of the flaps. This paper discusses an analytical procedure to estimate the stresses generated in the CMC flaps due to the temperature gradients. The analytical procedure can be used for a material with nonlinear temperature-dependent stress–strain behavior. This procedure was used to predict the thermal stresses in four candidate CMC systems due to temperature gradients. The thermal stresses along the edges typically exceed the proportional limit, and sometimes the fatigue limit of the CMC.     

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.     

长水口热机械应力研究

长水口是实现钢水无氧化浇注的重要元件 ,在使用过程中常常因为热机械应力过大而损坏。运用有限单元法 ,模拟长水口在工作状态下的热应力场 ,研究了热冲击时间、预热温度以及材料的热导率对热应力的影响。计算结果表明 :热冲击时间的长短不影响应力峰值的大小 ;提高预热温度可以降低应力峰值 ;不同的热导率不会改变应力峰值的大小 ,只会改变应力的变化快慢。     

Thermal Stresses in Circular Ceramic Rod Specimens Subjected to Sudden Radiative Cooling

The thermal stresses which result from sudden radiation heat losses in a ceramic circular cylinder were calculated by the finite-element method. It was shown that, for a given value of coefficient of thermal expansion and Young's modulus, the magnitude of the maximum stress increases with increasing emissivity and cylinder diameter and decreasing thermal conductivity. In terms of the initial temperature, T, the maximum stress was found to be proportional to T^x, with 3.3 ≤ x ≤ 3.5.     

Functionally Graded Materials Under Severe Thermal Environments

Thermal shock strengths of a plate of a functionally graded material (FGM) are analyzed when the plate is suddenly exposed to an environmental medium of different temperature. A finite element/mode superposition method is proposed to solve the time-dependent temperature field. The admissible temperature jump that the material can sustain is studied using the stress-based and fracture mechanics-based criteria. The critical parameters governing the level of the transient thermal stress in the medium are identified. The strength of FGMs under transient thermal stresses is analyzed using both maximum local tensile stress and maximum stress intensity factor criteria.     

Thermal Stress Analysis of Partially Absorbing Brittle Ceramics Subjected to Symmetric Radiation Heating

An analysis is presented of the thermal stresses in partially absorbing ceramics, in the form of flat plates symmetrically heated by thermal radiation and cooled by convection. The absorption coefficient is introduced as a material property, which affects thermal stress resistance. For zero heat transfer coefficient and optical thickness μa→0 the tensile thermal stresses are proportional to (μa)³. For h =∞ and μa→0, the tensile thermal stresses are a linear function of μa. Appropriate thermal stress resistance parameters were derived.     

Residual Stress in Singly and Doubly Ion-Exchanged Glass

Photoelastic measurement on rings sliced from soda-lime glass tubes, ion-exchanged with electric field assistance, were used to calculate the residual stress in this material. Account was taken of the effect of sample distortion due to slicing. Well below the glass transition the measured surface stresses were independent of time of exchange but increased markedly with decreasing temperature of exchange for both singly and doubly exchanged specimens.     

Analysis of the Effect of Piezoelectric Patches on the Behavior of Adhesively Bonded Scarf Joints — An Analytical Study

In order to reduce the maximum peel and shear stress concentrations in the adhesive layer, a smart adhesively bonded scarf joint system was developed by surface bonding of piezoelectric patches onto a typical scarf joint. The forces and bending moments at the edges of the developed smart joint system can be adaptively controlled by adjusting the applied electric field on the piezoelectric patches, thus reducing the peel and shear stresses concentration in the adhesive layer. In order to verify the effect of surface bonding of piezoelectric patches in smart scarf adhesive joints, an analytical model was developed to evaluate the shear stress distribution and to predict the peel stress. It was established that the piezoelectric patched joint could reduce the stress concentrations at the scarf joint edges. The influence of the electric field and the effects of the scarf angle and the adherend Young's modulus on the peel and shear stresses were investigated. It was found that the effect of scarf angle is more significant at higher angles to raise the stresses. The effect of the electric field on the shear stress is more significant than on the peel stress.     

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.     

Edge Stresses in Alumina/Zirconia Laminates

Using the technique of fluorescence piezospectroscopy, we determine the distribution of thermal residual stresses across the edges of three laminated alumina/zirconia composites. We develop a methodology for separating the measured stress state into microstresses that result from grain-to-grain thermal mismatch and macrostresses that result from lamination-induced thermal mismatch between individual plies. Comparison between the measured edge-stress distributions and those calculated based on a simple force-superposition model shows good agreement, indicating that the laminate system is well approximated as linear elastic. Given the experimental confirmation of significant edge stresses in multi-ply laminates, the possibility of failure initiating at composite edges must be considered in the design of surface-compressed laminate structures with the aim of mediating the detrimental effect of surface flaws.     

Finite element model of thermal stress effects onstress distributions in rubber modified glassy polymers. Part 1 – Single particle model

Abstract

A single particle finite element model has been used to analyse the effects of thermal stresses on the stress distributions near the interface between the rubber particle and the matrix in rubber modified polymers. The thermal stresses are due to the mismatch of thermal contraction between the rubber particle and the matrix during cooling. The study is to determine whether the thermal stresses are significant enough to affect the distribution of normal stress and von Mises stress at the particle/matrix interface. Results from the single particle model show that a temperature decrease of 60 K, i.e. from 100 to 40°C, can generate a circumferential compressive stress at the particle/matrix interface, which is of the same magnitude as the tensile stress required to cause failure in most of the glassy polymers. Although the effect on the circumferential normal stress is significant, its effect on the von Mises stress is very small. The results also show that when the cavitation occurs in the rubber particle, the thermal stress effect is drastically reduced. This study provides encouraging evidence for the importance of thermal stresses in determining the stress distributions in rubber modified polymers and suggests that thermal stresses should be considered in the deformation analysis of these materials.     

实心轮胎材料动态温升特性有限元分析与试验

应用ANSYS有限元分析软件建立橡胶和聚氨酯弹性体两种轮胎材料的应力场有限元模型，计算出节点生热率，再将其作为负载导入到温度场有限元模型中，进行温升有限元计算，得到两种轮胎材料的动态温升规律。台架试验结果很好地验证了有限元分析的温升规律，证实建模选用模块合理有效。     

Thermomechanical simulations of the transient coupled effect of thermal cycling and oxidation on residual stresses in thermal barrier coatings

Failures in thermal barrier coatings (TBCs) are associated with the build-up of residual stresses that result from thermal cycling, growth strain, and stress relaxation associated with high temperatures. To address these highly coupled processes, three aspects were examined. The first was concerned with the effect of thermal cycling and thermal gradients on the resulting residual stress fields. The second with the dynamic growth of thermally grown oxide (TGO) layer using novel finite volume-finite element algorithms. In the third, we examined the effect of stress relaxation on the (TC/TGO) interface. We modelled these highly coupled processes using transient thermomechanical finite element simulations. The temperature profile and state of oxidation variation with time were imported as a predefined field and solved in ANSYS nonlinear platform. Our results revealed that stress relaxation of the TGO stresses at high temperatures leads to a reduction in the TC/TGO interfacial stresses. They also revealed that the use of the isotropic hardening rule limits the increase in plastic deformation of the bond coat (BC), while the use of kinematic hardening rule leads to ratcheting. Furthermore, we highlighted the importance of considering uneven growth of TGO on the resulting stress field.     

碳化硅晶体生长炉辐射换热特性的数值模拟

采用C语言搭建了碳化硅(SiC)晶体生长炉三维温度场数值模拟平台,基于柱坐标系构建生长炉物理模型,采用有限体积法离散数学模型,利用S2S(Surface to Surface)辐射模型考察了生长室内的辐射换热特性,提出判断辐射面可视性的最短距离法. 模拟了电流强度1250 A、电流频率16 kHz条件下的生长炉温度场,定量揭示了生长室内的辐射换热强度;采用标准偏差法研究了线圈结构对晶体内部温度及温度梯度均匀性的影响. 结果表明,螺旋电磁加热线圈容易导致生长炉内部温度场呈非轴对称特性分布;辐射热流较导热热流大102~103倍,辐射换热促使生长室内温度分布均匀;螺旋线圈的布置方式使晶体截面温度呈非轴对称分布,造成温度梯度的均匀性变差,晶体生长过程中容易产生热应力,影响晶体质量.     

Residual Stress Development in Adhesive Joints Subjected to Thermal Cycling

The effect of thermal cycling on the state of residual stress in thermoviscoelastic polymeric materials bonded to stiff elastic substrates was investigated using numerical techniques, including finite element methods. The work explored the relationship between a cyclic temperature environment, temperature-dependent viscoelastic behavior of polymers, and thermal stresses induced in a bimaterial system. Due to the complexity of developing a closed-form solution for a system with time- and temperature-dependent material properties, and time-varying temperature and coupled boundary conditions, numerical techniques were used to acquire approximate solutions.

The results indicate that residual stresses in an elastic-viscoelastic bimaterial system incrementally shift over time when subjected to thermal cycling. Potentially damaging tensile axial and peel stresses develop over time as a result of viscoelastic response to thermal stresses induced in the polymeric layer. The applied strain energy release rate at the ends of layered or sandwich specimens is shown to increase as axial stress develops. The rate of these changes is dependent upon the thermal cycling profile and the adhesive's thermo-mechancial response. Discussion of the results focuses on the possiblility that the increasing tensile residual stresses induced in an adhesive bond subjected by thermal cycling may lead to damage and debonding, thus reducing bond durability.     

Transient Thermal Stress Calculation of a Shell and Tube Condenser with Fixed Tubesheet

The present article deals with transient thermal stress calculation on a safety horizontal shell and tube condenser. This condenser is used in a power plant for cooling of hot steam diverted from the turbine in the case of its emergency shutdown. The standard stress calculation was provided according to the EN 13445 standard in steady regime. As consistent with this calculation, an expansion joint must be used on the shell. The main aim of this article is to describe a detailed calculation of the transient temperature field on the shell and tubes, using finite element method analysis, and longitudinal thermal stresses on the shell and tubes during the start-up process. Transient analyses are useable for more accurate EN 13445 calculation and, furthermore, for fatigue calculation.     

X-Ray Stress Analysis of WC-Co Cermets: I,Procedures

The factors that influence the measurement of stress by the “two-exposure” X-ray diffractometer technique in the WC phase of WC-Co cermets were studied. Chromium Karadiation was used on the (1012) line of WC (2θ= 135.8°). The X-ray values of Young's modulus and Poisson's ratio are 105×10⁶ psi and 0.19, respectively, and the X-ray stress factor is 1.51 × 10⁸ psi/Å. The measured stresses are biaxial. Because penetration is limited to less than 5 μm for CrKa radiation, extreme care in surface preparation and heat treatment is required. A suitable preparation is metallographic polishing with 6 μm diamond followed by annealing in hydrogen at 750°C. This treatment allows measurement of about 40, 000 psi compressive temperature stress inherent in the WC particles resulting from differences in coefficients of thermal expansion between WC and Co. Mechanical stresses can also be measured; they arise from external forces such as grinding, polishing, and sand blasting. Mechanical and temperature stresses cannot always be clearly distinguished, however.     

The Stresses in an Adhesive Layer

A simple method has been developed for calculating the stresses near the ends of a parallel-sided adhesive layer. The method can be applied to adhesive layers having aspect ratios of 10 or greater, and Poisson's ratios of 0.49 or less. For a layer subject to uniform boundary conditions of displacement at the adhering surfaces, the stress fields at distances greater than about five layer thicknesses from the free surfaces are uniform. The stress field throughout the layer is uniquely determined by the stresses in the uniform stress region. If the stress field is expressed by functions of reduced coordinates of position, obtained by dividing the cartesian coordinates by the layer thickness, these functions are for practical purposes independent of the aspect ratio or the thickness.

The method has been used to calculate shrinkage stresses, the stresses in a joint under tension perpendicular to the plane of the adhesive layer, and the stresses in a joint under shear. The features of the stress fields are described, and where necessary, shown in the form of graphs or contour plots.