THERMAL STRESSES IN A RAPIDLY HEATED PLATE USING THE PARABOLIC TWO-STEP HEAT CONDUCTION EQUATION

This work studies the thermal stresses generated within a rapidly heated thin metal plate when a parabolic two-step heat conduction equation is used. The effect of different design parameters on the thermal and stress behavior of the plate is investigated.     

TRANSIENT THERMAL SINGULAR STRESSES OF MULTIPLE CRACKING IN A W-Cu FUNCTIONALLY GRADED DIVERTOR PLATE

We consider the transient thermal singular stresses of multiple cracking in a functionally graded divertor plate due to a thermal shock. The plate is made of a graded layer bonded between a homogeneous substrate and a homogeneous coating, and it is subjected to a cycle of heating and cooling on the coating surface of the plate. The surface layer contains a parallel array of embedded or edge cracks perpendicular to the boundaries. The thermal and elastic properties of the material are dependent on the temperature and the position. Finite element calculations are carried out, and the transient thermal stress intensity factors are shown graphically.     

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.     

THERMAL STRESSES IN A PARTIALLY ABSORBING FLAT PLATE SYMMETRICALLY HEATED BY THERMAL RADIATION AND COOLED BY CONVECTION

The stresses due to “thermal trapping” of internally absorbed radiation in solid materials are analyzed for a flat plate symmetrically heated by radiation and cooled by convection for finite values of the heat transfer coefficient. The thermal-stress state consists of an initial transient followed by a steady-state stress at t -> ∞ and involves a reversal in the sign of the stresses. The maximum value of the transient stress increases with optical thickness, whereas the maximum value of the steady-state stress occurs at an optical thickness μa = 1·3 with zero stresses at μa. = 0 and ∞.     

TRANSIENT THERMAL STRESSES IN A THIN ELASTIC PLATE DUE TO A RAPID DUAL-PHASE-LAG HEATING

Thermal stresses generated within a thin plate as a result of a fast heating rate are investigated numerically using the dual-phase-lag heat conduction model. The quantitative and qualitative predictions of the dual-phase-lag model for the thermal stresses are compared with the predictions of the diffusion (parabolic) and wave (hyperbolic) heat conduction models. It is found that the predictions of the three models differ in the early stages of the heating process and then give almost the same predictions as they approach the steady-state limit.     

THERMAL STRESSES IN A PARTIALLY ABSORBING FLAT PLATE ASYMMETRICALLY HEATED BY CYCLIC THERMAL RADIATION AND COOLED BY CONVECTION

Abstract

An analysis is presented for the temperatures and thermal stresses in a partially absorbing flat plate subjected to normally incident cyclic thermal radiation on the front face, and cooled by convection on the rear face.

The resulting temperature and stress responses are cyclic in nature, with the temperatures and stresses in the center and the back face lagging behind those in the front face. The amplitude of the temperature fluctuation is found to be a maximum in the front face. During the initial thermal cycles the maximum stress in the plate is compressive. In contrast, when the plate approaches thermal equilibrium after many cycles, the maximum stress is tensile. The values of the maximum tensile and compressive stresses were found to depend on the frequency of the incident cyclic radiation.     

TRANSIENT VARIATIONS OF THERMAL STRESSES AND THE RESULTING RESIDUAL STRESSES WITHIN A THIN PLATE DURING WELDING PROCESSES

Variations of thermal and residual stresses are investigated inside a thin mild steel plate during welding processes. The temperature distribution is determined analytically using Green's functions. Transient thermal stresses developed within the plate are computed numerically. The resulting residual stresses, which remain after cooling of the plate, are found based on a method presented originally by Tall (L. Tall, Welding Journal, vol. 43, pp. 10–23, 1964). It is found that welding speed and heat source intensity are the main factors that affect the residual stress formation in the plate.     

THERMAL STRESSES IN A PARTIALLY ABSORBING FLAT PLATE ASYMMETRICALLY HEATED BY CYCLIC THERMAL RADIATION AND COOLED BY CONVECTION: ADDENDUM

This article is devoted to model and analyze the transverse deflection and thermal moment of transverse vibrations in a transversely isotropic, thermo-elastic beam resonator under the action of time harmonic concentrated load. The governing equations of flexural vibrations and thermal moment in a transversely isotropic, thermo-elastic Euler–Bernoulli beam have been derived in a closed form. A time harmonic point load is assumed to act on the beam at a given distance from the origin. The beam is assumed to be at either clamped-clamped (CC), simply supported-simply supported (SS), clamped-simply supported (CS), or clamped-free (CF) conditions at its ends. The Laplace transform technique has been used to find the transverse deflection and thermal moment in the transform domain due to the action of concentrated load in a beam under above conditions in case of both free and forced vibrations. The analytic expressions obtained in the physical domain after inversion of Laplace transforms have been computed numerically with the help of MATLAB software for silicon material beam. The results for coupled thermo-elastic, elastic, and isotropic beams have been deduced as special cases. The computer-simulated results have been presented graphically. The study may find applications in development and design of resonators (sensors), precision thermometers, and energy harvesters.     

THERMAL STRESSES IN A NONHOMOGENEOUS THICK PLATE UNDER STEADY DISTRIBUTION OF TEMPERATURE

This paper is concerned with a method for calculating the thermal-stress distribution in a nonhomogeneous medium whose shear modulus and coefficient of thermal expansion are assumed to be functions of z. The solution of the problem is determined by using displacement functions. A solution is then derived for the thermal-stress distribution in a nonhomogeneous, thick elastic plate under steady distribution of the surface temperature. Numerical results are presented.     

THERMAL STRESSES IN AN INFINITE PLATE WITH TWO ROWS OF HOLES

Abstract

A theoretical method is presented for a two-dimensional, steady thermoelastic problem of perforated plates with two rows of holes. The analysis is developed by the complex variable approach. The numerical results for stress concentration factors are given in the form of curves for a wide range of diameter/pitch. The extension of the present method to holes of arbitrary shape, number, and array is quite straightforward.     

TRANSIENT THERMAL STRESSES IN A RECTANGULAR PLATE DUE TO NONUNIFORM HEAT TRANSFER COEFFICIENTS

Abstract

The linear problems of transient temperature and thermal stresses in a thin, finite, rectangular plate subjected to heat losses due to nonuniform heat transfer coefficients on the upper and lower plate surfaces are solved by a direct power series approach through the application of the Lanczos-Chebyshev and the discrete least-squares methods. A numerical example demonstrates the accuracies that can be achieved by using only a small number of terms.     

FREQUENCY DEPENDENCE OF THE MAGNITUDE OF THERMAL STRESSES IN A FLAT PLATE SUBJECTED TO RAPID THERMAL CYCLING BY CONVECTIVE HEATING AND COOLING

Abstract

A study was conducted of the effect of the thermal stresses in a plate subjected to thermal cycling by changes in ambient temperature involving convective heat transfer, at frequencies sufficiently high that thermal equilibrium (;i.e., temperature uniformity) is not achieved within each cycle. The results obtained indicate that at any specific value of the Biot number the magnitude of maximum thermal stress within any cycle decreases with increasing frequency. Furthermore, at any given frequency the magnitude of the peak stress exhibits its maximum value during the first cycle and decreases to a constant value from cycle to cycle with increasing number of cycles     

ROLE OF ABSORPTION COEFFICIENT IN THE FREQUENCY DEPENDENCE OF THE THERMAL STRESSES IN A PARTIALLY ABSORBING PLATE SUBJECTED TO CYCLIC THERMAL RADIATION: A BRIEF NOTE

The frequency dependence of the thermal stresses in a partially absorbing plate subjected to cyclic thermal radiation is shown to be a function of optical thick ness.     

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     

THERMALLY INDUCED VIBRATION IN A THIN PLATE UNDER THE WAVE HEAT CONDUCTION MODEL

Thermally induced vibration in a thin plate under a thermal excitation is investigated. The excitation is in the form of a suddenly applied laser pulse (thermal shock). The resulting transient variations of temperature are predicted using the wave heat conduction model (hyperbolic model), which accounts for the phase lag between the heat flux and the temperature gradient. The resulting heat conduction equation is solved semianalytically using the Laplace transformation and the Riemann sum approximation to calculate the temperature distribution within the plate. The equation of motion of the plate is solved numerically using the finite difference technique to calculate the transient variations in deflections.     

DYNAMIC THERMAL STRESS IN A TRANSVERSELY ISOTROPIC HOLLOW SPHERE

A closed-form solution for the histories and distribution of dynamic themoelastic stress in a transversely isotropic hollow sphere is obtained. The field equation for a spherically symmetric transversely isotropic problem subjected to rapid arbitrary heating shock is derived and solved. Based on the results in this article, some phenomena in a transversely isotropic hollow sphere under thermal shock are shown.     

THERMAL-STRESS PROBLEMS IN INDUSTRY. 6: TRANSIENT THERMAL STRESSES IN A PLATE DUE TO ROLLING WITH CONSIDERATION OF COUPLING EFFECT

In this paper, the transient thermal-stress problem in a plate subjected to frictional heat generation in rolling ( or welding) is theoretically analyzed with the consideration of the thermomechanical coupling effect. Numerical evaluation is carried out for the temperature distribution, thermal stresses, and thermal deformation in a flat plate heated by linear heat sources which are located symmetrically on both surfaces and which move with constant velocity.     

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 AND DISPLACEMENTS INDUCED IN A FINITE,ORTHOTROPIC, CYLINDRICAL,THIN SHELL BY AN INSTANTANEOUS THERMAL SHOCK

The thermal responses in a thin cylindrical shell of graphite material with finite length, subjected to an instantaneous thermal shock, are investigated. Closed-form solutions for the thermal stresses and displacements caused by a line source along the circumferential direction are obtained by integrating the fundamental solutions for a point heat source acting on a finite, orthotropic, cylindrical, thin shell. Grade ZTA graphite is used in the numerical examples. As expected, orthotropic thermal and mechanical properties significantly affect the induced displacements and thermal stresses in the shell due to the thermal shocks.     

TRANSIENT THERMAL STRESSES IN A FINITE CYLINDER OF NONUNIFORM CROSS SECTION

Boundary fitted coordinate variables are used to map the region of interest into a square. The governing transient heat conduction and displacement equilibrium equations are rewritten in terms of the new coordinate variables and are solved by a direct power series approach through the application of the Lanczos-Chebyshev and the discrete least squares methods. A finite cylindrical cone section is used to demonstrate how numerical solutions can be obtained