THERMAL STRESSES IN COMPOSITE CYLINDERS

Abstract

This paper is concerned with the static problem of the linear theory of thermo-elasticity for a composite cylinder. The cylinder is assumed to be occupied by different inhomogeneous and anisotropic elastic materials. The method described is also used to study the deformation of a circular cylinder made of two different homogeneous and isotropic materials.     

某型汽轮机转子热应力的计算和分析

本文运用有限元子结构法和有限元-边界元联合计算法,在IBM微型机上计算和分析了某舰用主机全锻转子冷态紧急启动时的热应力变化情况,得到了一些有益的初步结论。     

THERMAL STRESSES IN THE EARLY STAGE OF SOLIDIFICATION OF STEEL

Abstract

A numerical model for calculation of thermal stresses and strains during solidification of steel is presented. Creep deformations are included. Stresses and strains during the early stage of solidification are studied for different steels under different cooling conditions. The results obtained may explain some observed cracking in continuously cast steel.     

ANALYSIS ON TRANSIENT THERMAL STRESSES IN AN ANNULAR FIN

Transient thermal stresses are an important consideration in production processes involving large temperature changes. Recently, thermal stresses have also become significant in design problems related to microelectronic devices through their effects on material properties and system parameters. To calculate the thermal stresses, three kinds of methods are available. The first is the analytical method, in which the elastic theory is used to find the exact solution. The second approach consists of some kind of approximate technique, such as a perturbation procedure. The third method is the use of a numerical process, such as a finite-difference or a finite-element method.

This article investigates the transient thermal stresses in an annular fin with its base subjected to a heat flux of a decayed exponential function of time. In order to obtain the solution of the governing equation, which is a partial differential equation, the following procedures of analysis are used.

1. Normalize the governing partial differential equation subject to appropriate initial and boundary conditions.

2. Take the Laplace transform of the resulting equation with respect to time.

3. Utilize the exponential-like solutions introduced by Keller and Keller to solve the transformed system.

4. Achieve the inverse Laplace transform by means of complex contour integration and the residue theorem.

5. Substitute the temperature distribution function into the governing equation of thermal stresses. Then use Simpson's rule to obtain the thermal stress distribution as a function of time and position of the fin.     

ANALYSIS OF TRANSIENT THERMAL BENDING MOMENTS AND STRESSES OF THE WORKPIECE DURING SURFACE GRINDING

Geometrical inaccuracy is often induced by heat generated during grinding. Furthermore, the transient thermal process is the main cause for the residual stresses on theground surface. The objective of this article is to investigate the three-dimensional transient temperature distribution of the workpiece using the finite difference method,and based on the acquired temperature and beam theory, the thermal moment and thermoelastic stress as calculated using Simpson's multiple numerical integral method. The energypartition is the key factor in accurately predicting the temperature distribution, on which the solution of the thermal moment and stress rely. As the heat conductivity of the workpiece decreases, the stress and moment increase near the wheel-workpiece contact zone and the peaks move closer to the contact position. A smaller thickness results in higher thermal stress and lower thermal moment. Enhancing cooling in grinding effectively reduces temperature and the induced stress.     

THERMAL STRESSES IN BONDED SOLAR CELLS-THE EFFECT OF THE ADHESIVE LAYER

A two-dimensional, rectangular model of a proposed solar cell structure is analyzed as two plate elements bonded with an elastic continuum. The governing equations are formulated using the principle of minimum potential energy, with displacement components that vary linearly through the thickness of the adhesive layer. An approximate solution is constructed for a particular class of material properties and is characterized by a boundary layer near the unloaded edge. Both interface stress components achieve their largest values at the edge, and the maximum shear stress is independent of the Young's Modulus of the substrate.     

退火过程对硅锭热应力与位错影响的数值分析

利用CGSim软件对定向凝固多晶硅从长晶过程开始到退火过程结束进行瞬态数值模拟,研究不同退火温度和退火时间对多晶硅锭内热应力及位错密度的影响。通过软件中热弹性应力非稳态模型（Haasen-Alexander-Sumino模型）计算出位错和Von-Mises应力。结果表明：随着退火温度的升高和退火时间的增加,热应力及位错增殖速率的逐渐减小,在退火1 h后热应力和位错增殖速率大幅减小,退火3 h后减小效果减弱。高温退火时热应力和位错密度低于低温退火,在1250℃下退火3 h是比较合适的方案。     

ANALYSIS OF THERMAL STRESSES IN A FLAT PLATE SUBJECTED TO CONDUCTIVE HEAT TRANSFER WITH THERMAL BOUNDARY CONDUCTANCE

An analysis is presented of the effect of a finite boundary conductance on the magnitude of the thermal stresses in a flat plate subjected to symmetric and asymmetric conductive heat transfer from an infinite, mechanically noninteracting medium.     

EVALUATION OF THERMAL STRESSES INDUCED IN ANISOTROPIC MATERIAL DURING THERMAL SHOCK

In machines and structures operating in a high-temperature environment, such as a turbine blade or a cutting tool, repeated thermal shock is known to induce damage and fracture. Such damages are big problems in technical fields. In developing a good material with a high resistance to thermal shock, it is essential to conduct a quantitative evaluation of the thermal stresses induced in the material during the thermal shock. However, until recently, there have been few methods to evaluate the thermal stresses quantitatively at a given instant of the thermal shock. As an experimental method for the quench-type thermal shock, the present authors proposed the new method that enables us to evaluate the thermal stresses quantitatively. Using this method, we succeeded in clarifying the characteristics of thermal shock of several materials, such as ceramics, cemented carbide, and cermets. However, the influence of the material anisotropy on the thermal stresses induced by the thermal shock is still unknown. In the present study, we perform the thermal shock experiment using two kinds of materials with different degrees of the material anisotropy. From the experiment, it is clarified that the thermal stresses induced by the thermal shock vary with the material anisotropy. A similar result was also obtained using the finite element method (FEM) simulation, which covers a wide range of the material anisotropy. A simple expression was found via simulations used to evaluate the thermal stresses when the material has anisotropies in physical properties, such as Young's modulus and a linear expansion coefficient.     

THERMAL STRESSES OF ROTATING ROLLS IN ROLLING PROCESSING

In a modern rolling mill, proper roll cooling has been identified as a critical factor in the problems of excessive roll wear and poor surface finish of rolled product. In this paper, an analytical solution to determine the cyclic stresses produced in the roll is developed. An understanding of the cyclic stresses can be utilized to evaluate roll wear and leads to proper cooling practices for increasing roll life and better product surface quality. In the present analysis, a rotating roll subjected to surface heat fluxes and convective cooling is considered under the assumption that it rotates at high speeds. The methods of the thermoelastic displacement potential and the general stress function are used to solve the governing partial differential equations in order to calculate the thermal stresses. Examples of typical rolling conditions are given to demonstrate the feasibility and applicability of the model developed     

APPLICATION OF TAYLOR TRANSFORMATION TO THE THERMAL STRESSES IN ISOTROPIC ANNULAR FINS

This article presents the stresses distribution in a perfectly elastic isotropic annular fin. The Taylor transformation method is used to solve the nonlinear temperature field equation. The stresses distribution are integrated obtain the results. The thickness of the fins is assumed to be sufficiently small so as to have a state of plane stress and one-dimensional heat conduction.     

NUMERICAL ANALYSIS OF THERMAL STRESSES IN A NONLINEAR THERMOELASTIC THICK CYLINDRICAL SHELL AND CUBE

Numerical analysis of static thermal stresses in a nonlinear, isotropic, thermaelas-tic, thick cylindrical shell and a cube is presented using the nonlinear thermoelas-ticity. The geometrical relations, equilibrium equations, and Fourier's law are linear while the constitutive relations accounting for the id-order elastic moduli and the temperature-dependent 2d-order elastic moduli and coefficient of thermal expansion are nonlinear. Nonlinear effects are numerically investigated for a cylindrical shell and a cube made of D54S aluminum alloy.

     

ANALYSIS OF THERMAL STRESSES IN A SOLID CIRCULAR CYLINDER SUBJECTED TO CONDUCTIVE HEAT TRANSFER WITH THERMAL BOUNDARY CONDUCTANCE

An analysis is presented of the effect of a finite boundary conductance on the magnitude of the thermal stresses in a solid circular cylinder, subjected to conductive heat transfer from an infinite mechanically noninteracting surrounding medium.     

THERMAL STRESSES IN LAMINATED BEAMS

This paper considers laminated beams consisting of layers of different materials fastened together by thin adhesives. The stresses that result from subjecting the beam to temperature stimuli are calculated. The problem is treated by two-dimensional elasticity theory in conjunction with the variational theorem of complementary energy. A pair of governing differential equations is developed, and boundary conditions concerning stress-free surfaces and ends of the beam are satisfied. The calculation of the distributions of interlaminar normal and shear stresses shows that high stress intensity occurs in the end zones of the beam. Thus, the satisfaction of end conditions is of prime importance in the analysis of laminated structural elements. Delamination failure-when it occurs - will probably start at the ends of the beam, This agrees with observed failures of laminated structural elements subjected to stress-free end conditions.     

THERMAL STRESSES IN A FLAT PLATE SUBJECTED TO CONVECTIVE HEATING INDUCED BY PIECEWISE LINEAR VARIATION OF AMBIENT TEMPERATURE

The problem of determining the stress state in a plate subjected to a thermal transient is often encountered in engineering practice. Available solutions are limited to special cases and are not easy to use. The aim of this work is to provide a simple tool for stress and strain calculations due to piecewise linear variation of ambient temperature. A variational approach is applied to obtain approximate temperature and stress distributions within the plate in a simple analytic form. Stress diagrams derived from the exact temperature distribution are used to assess the accuracy of the method. The method is finally used to determine the magnitude of thermal stresses induced by thermal cycling. The results are shown to be in agreement with those of previous studies     

CYCLIC LOADING OF THERMAL STRESSES

The isotropic and kinematic hardening theories of plasticity are used to evaluate the cyclic loading behavior of structures under thermal stresses. The material of the structures used in this article is assumed to follow nonlinear strain hardening property. The material's strain hardening curve in tension and compression is assumed to be both identical for isotropic material and different for anisotropic material. The method of successive approximation is used to calculate the stresses and plastic strains in the structure due to cyclic loadings. The results of the analysis are checked with the known experimental test. The thermal stresses are categorized into load- and deformation-controlled stresses. It is concluded that the isotropic hardening theory, excluding creep, will always result in structural shakedown. The kinematic hardening theory under deformation-controlled conditions, excluding creep, will result in reversed plasticity. The load-controlled cyclic loading under kinematic hardening theory with isotropy assumption results in reversed plasticity. Under the anisotropy assumption of tension/compression curve, the load-controlled stress based on kinematic hardening theory predicts ratcheting behavior. When creep deformation is considered, the load-controlled thermal stresses results in ratcheting, and the deformation-controlled thermal stresses result in shakedown behavior, regardless of the material's isotropic and anisotropic properties or the hardening theories.     

THERMAL STRESSES IN MICROSTRETCH ELASTIC CYLINDERS

The present paper is concerned with the problem of thermal stresses in isotropic microstretch elastic cylinders. The temperature distribution is assumed to be a general polynomial in the axial coordinate. As in classical theory, the problem is reduced to solving the plane strain problem.     

THERMAL STRESSES IN JOINED SEMI-INFINITE SOLIDS

The elastic stress field caused by an ellipsoidal inclusion with uniform dilatational eigenstrains in one of two perfectly bonded semi-infinite solids is investigated. The thermal stress in domain z induced by the temperature variation j T could be simulated effectively by pure dilatational eigenstrain. The solutions are obtained using the method of dilatation centers. The potential functions for the problem solved are the harmonic potential functions of attracting matter filling the element of volume and expressed in terms of derivatives of elliptic integrals. Numerical examples are given to show the normal and tangential stresses along the boundary of the ellipsoidal inclusion and the maximum principle stresses along the major and minor axes in the inclusion that are important to the fracture problems. The effects of the inclusion depth from the interface, the ratio of elastic moduli of joined semi-infinite solids, the shapes of the inclusion and the rotation angle of the ellipsoidal inclusion are also studied. They are of great significance in physical applications pertaining to thermal stress problems.     

THERMAL STRESSES IN FUNCTIONALLY GRADED MATERIALS

The thermal stress problems of functionally graded materials (FGMs), as one of the advanced high-temperature materials capable of withstanding the extreme temperature environments, are discussed. The FGMs consist of the continuously changing composi tion of two different materials. For example, one is an engineering ceramic to resist the severe thermal loading from the high-temperature environment, and the other is a light metal to maintain the structural rigidity. When the FGMs are subjected to extremely severe thermal loading, large thermal stresses are produced in the FGMs. Therefore, one of the most important problems of FGMs is how to decrease thermal stresses and how to increase heat resistance. The optimal composition profile problems of the FGMs in decreasing thermal stresses are discussed in detail. When FGMs are subjected to extremely severe thermal loading, the FGMs are damaged. The crack initiates on the ceramic surface and propagates in the FGMs. It is important to discuss the thermal stresses in the FGMs with various types of cracks. The thermal stress intensity factors in the FGMs with various types of crack are treated analytically and numerically. The optimal composition profile problems of the FGMs in decreasing thermal stress intensity factor are studied. Finally, the crack propagation paths due to thermal shock are discussed.     

BEHAVIOR OF THERMAL STRESSES IN A RAPIDLY HEATED THIN PLATE

Using the hyperbolic heat conduction model, thermal stresses generated within a rapidly heated thin metal plate are investigated numerically. The effects of different parameters such as the form, duration, amplitude, and penetration depth of the heating source on the temperature, thermal moment, deflection, and thermal stresses are studied. It is found that under ultra-fast heating of very thin plates, the hyperbolic heat conduction model must be adopted to model the thermal behavior.