Material properties in thermal-stress analysis

With simple techniques and not too-costly laboratory equipment, the significant material properties in modeling transient thermal stresses by photothermoelasticity are evaluated. The results are presented for a room-temperature-cured epoxy, a hot-cured epoxy and a polycarbonate. The materials tested are also evaluated on their applicability to a transient-thermal-stress analysis.     

Analytical Study of Fluid Flow and Heat Transfer during Forced Convection in a Composite Channel Partly Filled with a Brinkman–Forchheimer Porous Medium

In this paper, the problem of fully developed forced convection in a parallel-plate channel partly filled with a homogeneous porous material is considered. The porous material is attached to the walls of the channel, while the center of the channel is occupied by clear fluid. The flow in the porous material is described by a nonlinear Brinkman–Forchheimer-extended Darcy equation. Utilizing the boundary-layer approach, analytical solutions for the flow velocity, the temperature distribution, as well as for the Nusselt number are obtained. Dependence of the Nusselt number on several parameters of the problem is extensively investigated.     

Thermally induced natural-frequency variations in a thin disk

A number of studies has shown that natural frequencies and, accordingly, the minimum critical speed for the formation of a standing wave in thin, rotating, circular disks can be beneficially altered by purposely induced initial membrane stresses. The possibility of controlling natural frequencies by induced thermal membrane stresses, rather than initial stresses, has received some previous theoretical attention and is experimentally examined here for a stationary, constant-thickness, centrally clamped, circular disk. The primary advantages of thermal membrane stresses are manifested in the inherent flexibility in adjustment of the thermal as opposed to the initial stresses. Increases in the minimum critical speed, which is proportional here to the zero nodal circle—two nodal-diameter natural frequency, of 20 percent were determined with moderate heating. This can be considered a relatively small critical-speed increase when compared with variations expected in many common rotating disk environments. A thermal model, which utilizes as input the peripheral disk heat flux and the controlled disk temperature at some known radius, is shown to predict the temperature distribution and natural frequencies with reasonable accuracy. The applicability of this model enhances the potential practicality of the induced thermal-membrane-stress method of natural frequency and/or critical speed control.     

Temperature and thermal stresses in material of a pad during braking

The transient temperature field and corresponding quasi-static thermal stresses are analysed in a system consisting of a semi-space and a strip. The strip is heated on its outer surface by a heat flux with the intensity equal to the specific power of friction during braking with a uniform retardation. The evolution and distribution in depth from a surface of friction for temperatures and thermal stresses were investigated for the metal-ceramic FMK-11 material of the strip.     

Measurement of thermal stresses in the S.S. “Boulder Victory”

A lack of comprehensive experimental measurements of thermal stresses induced in a ship's hull structure by diurnal temperature changes prompted this study. Its essential purpose was to provide reliable prototype measurements of thermal-stress patterns around a complete transverse section of a ship. These results are compared with stresses computed by the theory of simple beams under arbitrary temperature distributions across their section. Bridge-type SR-4 strain-gage assemblies were developed for attachment directly to the structure. A variety of temperature conditions were observed and corresponding strain measurements taken. The results are consistent and give a reliable picture of thermal-stress conditions in a ship. They also verify the prediction of thermal stresses afforded by the simple-beam theory.     

Thermal Stresses in an Elastic Rectangle

The paper addresses the method of determining the two-dimensional thermal stresses in a rectangular isotropic plate or a long bar with arbitrary temperature distribution in the plane and with no variation in temperature through the thickness is presented. The thermal stress have been obtained by the superposition method in terms of Fourier series that satisfy the differential equation and the boundary conditions. The method is illustrated by two examples. The distribution of stresses along some typical lines in the rectangle are computed and the possibilities of approximate solutions are estimated.     

2-D problem of a Mode-I crack for a generalized thermoelasticity under Green-Naghdi theory

A general model of the equations of the generalized thermoelasticity for an infinite space weakened by a finite linear opening Mode-I crack is solved. The crack is subjected to prescribed temperature and stress distribution in the context of Green-Naghdi theory. The normal mode analysis is used to obtain the exact expressions for the displacement components, the force stresses, the temperature and the couple stresses. Comparisons are made with the results predicted in the both type II, III of Green-Naghdi theory. It is found that a Mode-I crack has great effects on the distribution of field quantities with energy dissipation.     

Theoretical study and experimental verification of the behaviour of a passive conditioning system for electronic components

 The paper describes the theoretical determination of the flow and the temperature distribution in a water natural circulation loop for passive conditioning of a big shelter for electronic components. A cylinder filled with phase change material in thermal connection with the inner of the shelter and with the ambient by a water natural circulation loop forms the system. The system operates in natural convection, consequently during the daytime the water flow in the exchanger is stopped because the external temperature is greater then the melting temperature. During the night the situation is reversed, thus the convective flow begins allowing the water circulating and exchanging heat with the ambient. The paper presents a simulation model which describes the flow and the temperature field of the water in the loop during the night. Moreover the theoretical values of temperature are compared with the experimental data obtained in a climatic chamber. Received on 17 January 2000     

Thermo-mechanical solution of film/substrate systems under local thermal load and application to laser lift-off of GaN/sapphire structures

Film/substrate structures may undergo a localized thermal load, which can induce stresses, deformation and defects. In this paper, we present the solutions of temperature and stresses in a film/substrate structure under a local thermal load on the film surface. Then, the generalized Stoney formula, which connects the curvature of deformation and the stress field is obtained. The present solution takes into account the non-uniformity of the temperature field both in the width and thickness directions of the film. The thermo-mechanical solution is applied to the analysis of the temperature distribution, stresses, and damage of a GaN/sapphire system during the laser lift-off (LLO) process. It is shown that the laser with the Gaussian distribution of energy density causes much smaller tensile stresses at the edge of the heated area in the film than the laser with the uniform distribution of energy density, and thus can avoid damage to the GaN films separated from the substrate.     

具有半边裂纹导电薄板放电瞬间的温度场数值模拟

采用数值模拟方法 ,模拟计算了具有半边裂纹的导电薄板在放电瞬间的温度场分布。计算结果表明 :在裂纹尖端附近由于电磁热的集中效应 ,可使材料熔化形成焊口 ,裂纹尖端处的曲率半径显著增大 ,并且焊口的温度分布与形状是不完全对称的。裂纹尖端焊口形状的模拟计算结果与试验结果非常吻合。从温度梯度的分布结果可知 ,裂纹前缘附近在放电过程中将产生很大的压应力 ,可显著减少甚至是消除裂纹前缘处的扩展应力数值 ,抑制了裂纹主干线的形成 ,可达到遏制裂纹扩展的目的     

Pressure waves in a tube filled with a bubbly mixture with a nonuniform cross-sectional bubble distribution

The evolution of pressure waves in a tube filled with a gas-liquid medium with a stepped cross-sectional bubble distribution is investigated. The calculations are compared with experimental data. It is shown that in the case of a nonuniform bubble distribution, due to the appearance of transverse flows, the pressure pulse is damped faster than for a uniform distribution. The interaction of pressure waves with a bubble cluster in a tube filled with liquid is also analyzed.     

Effect of fiber geometry on stress in fiber-reinforced composite materials

Eleven two-dimensional photoelastic models of fiber-reinforced composite-material configurations were designed for the purpose of investigating the effects of various fiber-end shapes, various fiber arrangements and broken fibers on the shear-stress distribution in an elastic matrix. Maximum shear stresses in the matrix in the vicinity of fiber discontinuities are presented. The peak stress resulting from a gradually tapered fiber was found to be slightly higher than that from a square-ended fiber, and a round-ended fiber produced a peak stress which was slightly lower than that from the square-ended fiber. Peak stresses resulting from two square-ended fibers butted closely together were considerably higher and decreased with increasing gap length between fiber ends. It made little difference whether the gap between the butted fiber ends was open, simulating a void resulting from a broken fiber, or filled with matrix material.Paper was presented at 1966 SESA Spring Meeting held in Detroit, Mich., on May 4–6.     

导电圆柱薄壳的热磁弹性效应分析

研究了磁场环境中受机械载荷作用的导电圆柱薄壳的热磁弹性问题．首先,根据电动力学方程和广义Ohm定律,得到了导电薄壳电流密度的分布,考虑到Joule热效应及热平衡方程,得到了导电薄壳的温度分布．其次,通过几何方程、物理方程、运动方程和电动力学方程导出了导电薄壳在机械场、电磁场以及温度场作用下的基本方程．最后,采用差分法及准线性化方法,得到了可以应用离散正交法求解的准线性微分方程组．对于导电圆柱薄壳,得到了Lorentz力表达式,并且推导了温度场积分特征值．讨论了导电圆柱薄壳应力、温度及变形随外加电磁参量的变化规律,并通过实例证实了可以通过改变电、磁、力场的参数来实现对薄壳的应力、应变、温度的控制．     

High-rate start-up behaviour of unvulcanised rubber compounds

The recently developed machines, which are shown to be comparable with “established” devices, are used to perform the start-up of uniaxial extension and simple shear at high constant deformation rates. Henky strains in excess of 8 at constant strain rates of over 100 s^?1 are achieved for two highly filled unvulcanised rubber compounds of Butyl and Chloroprene rubbers. In general no steady state is attained in uniaxial extension; the stress reaches a maximum and then declines. It is shown that the time—temperature superposition principle holds for start-up flows resulting in a family of master curves. It is established that the extensional stresses are one or two orders of magnitude greater than the shear stresses at corresponding deformation rates over a wide rate range.     

Magnetothermoelastic stress and perturbation of magnetic field vector in a functionally graded hollow sphere

In this article, a closed-form solution for one-dimensional magnetothermoelastic problem in a functionally graded material (FGM) hollow sphere placed in uniform magnetic and temperature fields subjected to an internal pressure is obtained using the infinitesimal theory of magnetothermoelasticity. Hyper-geometric functions are employed to solve the governing equation. The material properties through the graded direction are assumed to be nonlinear with an exponential distribution. The nonhomogeneity of the material in the radial direction is assumed to be exponential. The temperature, displacement and stress fields and the perturbation of magnetic field vector are determined and compared with those of the homogeneous case. Hence, the effect of inhomogeneity on the stresses and the perturbation of magnetic field vector distribution are demonstrated. The results of this study are applicable for designing optimum FGM hollow spheres.     

The vapour–liquid interface and stresses in dried bodies

The paper presents a contribution to modelling the problem of vapour–liquid interface receding into dried body and stresses induced by drying of capillary-porous bodies. A complex algorithm comprising the specific mechanisms of drying in the first and second periods of drying is constructed. It enables calculation and drawing of the body temperature and drying curves for the whole drying process and identification of the vapour–liquid interface receding into the body. The drying induced stresses caused by the receding vapour–liquid interface and the non-uniform distribution of moisture content and/or temperature are analyzed. Numerical calculations of the temperature and drying curves and the drying induced stresses are carried out for the example of a finite dimensional kaolin cylinder dried convectively.     

有限长厚壁管在过冷沸腾状态下的热应力响应

在求得有限长厚壁管水淬时瞬态温度分布的基础上［１］，引入了包含相变的热弹塑性本构方程的增量形式．用有限元法求得了瞬态热应力和残余应力．对影响热应力和残余应力的各种因素进行了分析和讨论．     

Finite-element solutions for thermal stresses in steel-concrete composite bridges

The objective was to determine experimentally and analytically steady-state temperature distributions produced in the cross-sectional planes of steel-concrete composite simple-span bridges. The upper and lower surfaces were exposed to different temperatures. The research included the development of finite-element solutions for steady-state temperature distributions from known boundary conditions and the calculation of strains and stresses. Temperature and stress distributions were generally nonlinear with linear strains through the finite elements. Temperatures were predicted to ±1° F (±0.6° C). The experimental strains are linear through the composite section, with the computed finite-element strains generally giving slightly higher stresses. The concrete-slab stresses were overestimated for positive curvature and slightly underestimated for negative curvature. Concrete-slab stresses were relatively small when compared to their permissible stress. Temperature stresses in the steel beam were shown to be significantly large to warrant consideration in the design of these bridges. Stresses were calculated for short-term steady-state temperatures. Transient field conditions producing greater thermal stresses are now under investigation.     

Biaxial fracture stresses for filled-epoxy tubes

Strength results for a filled epoxy are reported for biaxial stresses. Three test methods and several specimen configurations were employed. Strength magnitudes were quite dependent upon specimen geometry under compression-compression stresses. For other stress states, this dependence disappeared and the modified Coulomb-Mohr theory fit the data well. Similar data for graphite are cited.     

Thermoelastic interaction with energy dissipation in a transversely isotropic thin circular disc

The distribution of stresses due to step input of temperature on the boundaries of a homogeneous transversely isotropic circular disc is investigated by applying Laplace transform technique in the context of generalized theories of thermo-elasticity. The inverse of the transformed solution is carried out by applying a method of Bellman et al. The stresses are computed numerically and presented graphically in a number of figures. A comparison of the results for different theories (CTE, CCTE, TRDTE(GL), TEWED(GN)) and the effect of anisotropy on the stresses are also presented. When the material is isotropic and outer radius of the disc tends to infinity, the corresponding result agrees with that of existing literature.