THERMAL-STRESS PROBLEMS IN INDUSTRY. 2: TRANSIENT THERMAL STRESSES IN A DISK BRAKE

A general solution is given for the transient thermal stresses in a disk brake caused by constant heat generation on both plane surfaces. The solution rigorously meets the traction-free boundary condition on both the lateral and plane surfaces of the disk. Numerical results for the stress fields are given.     

THERMAL-STRESS PROBLEMS IN INDUSTRY. 5: THREE-DIMENSIONAL TRANSIENT THERMAL STRESSES IN ROLLS UNDER ROTATING PARTIAL HEAT SOURCE

The problem of transient thermal stresses in rolls of CCP is solved using three-dimensional theory under the conditions of a rotating arc heat source of finite length in the axial direction.     

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.     

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.     

TRANSIENT THERMAL STRESSES OF A HOLLOW SPHERE DUE TO ROTATING HEAT SOURCE

Abstract

A three-dimensional theoretical treatment for the thermal-stress problems in spherical coordinates is developed. The first part is devoted to the relations of stress components in terms of thermoelastic displacement potential and a harmonic function. Next, a hollow sphere with a rotating heat source is considered as an illustrative example. The numerical calculations are then also carried out and the results shown graphically.     

COMPUTATION OF TRANSIENT THERMAL STRESSES IN ELASTIC-PLASTIC TUBES: EFFECT OF COUPLING AND TEMPERATURE-DEPENDENT PHYSICAL PROPERTIES

The objective of this study is to obtain the transient solution of the thermoelastic-plastic deformation of internal heat-generating tubes by considering the thermomechanical coupling effect and the temperature-dependent physical properties of the material. The previously developed steady-state model describing the elastic-plastic behavior of the tubes is modified to obtain the transient solution. The propagation of the elastic-plastic interface for a given heat load is obtained; and the corresponding stress, displacement, and plastic strain components are computed. The effect of the coupling is investigated using three different engineering materials, namely, steel, aluminum, and magnesium; and it has been found to be negligible. On the other hand, the temperature dependence of the mechanical and thermal properties affects the computed profiles significantly.     

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.     

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.     

APPLICATION OF THE FIVE-ELEMENTARY-FUNCTIONS METHOD TO TRANSIENT THERMAL-STRESS PROBLEMS IN MULTIPLY CONNECTED ORTHOTROPIC REGIONS

In a previous paper, we dealt with transient, plane, thermoelastic problems in a multiply connected isotropic region using the five-elementary-functions method. As an extension of this method to orthotropic bodies, this paper is concerned with transient, plane, thermal-stress problems in multiply connected orthotropic regions.     

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 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.     

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.     

THERMAL-STRESS PROBLEMS IN INDUSTRY. 1: ON THERMOELASTIC DISTORTION IN MACHINING METALS

Abstract

This paper is a theoretical analysis of the thermoelastic effect upon accuracy in the machining of metals. The problem is reduced to the unsteady thermoelastic analysis of a solid cylinder heated on the surface axisym-metrically by a moving heat source under an axial restraint. The thermal and elastic distortions of the workpiece are computed, and the error in the shape is plotted.

     

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     

THERMAL STRESSES IN PARTIALLY ABSORBING FLAT PLATE DUE TO SUDDEN INTERRUPTION OF STEADY-STATE ASYMMETRIC RADIATION,II: CONVECTIVE COOLING AT FRONT SURFACE

In Part II of this study the thermal stresses are analyzed in a partially absorbing flat plate, due to a sudden interruption of steady-state asymmetric radiation on the convectively cooled front face. As in the case of Part I, the maximum tensile stresses occur in the rear face. For the optical thickness μa ≥ 0.5, the maximum tensile stress initially rises to a peak and then decreases with time. On the other hand, for μa ≤ 0.5, the stresses decrease monotonically with time.

A comparison of the results for the front (Part II) and rear (Part I) cooling indicates that values of the maximum stress are numerically indentical for small values of heat transfer coefficient h, and plate thickness a. Increasing difference in the magnitude of the stresses for the two cases is found with increasing h and a.     

THERMAL STRESSES IN PARTIALLY ABSORBING FLAT PLATE DUE TO SUDDEN INTERRUPTION OF STEADY-STATE ASYMMETRIC RADIATION,I: CONVECTIVE COOLING AT REAR SURFACE

An analysis is presented of the thermal stresses in a partially absorbing flat plate due to sudden interruption of steady-state asymmetric thermal radiation on the front face with convection cooling at the rear face. Maximum transient tensile stresses occur in the rear surface and are almost independent of the heat transfer coefficient, h. For optical thicknesses of ≥ 0.5 μa, the maximum tensile stress initially rises to reach a peak and then decreases with time. In contrast, for thicknesses ≤ 0.5 μa, the stresses decrease monotonically. It is shown that a plot of nondimensional stress as a function of nondimensional time for a given value of pa and h does not result in a universal plot from which thermal stresses can be obtained for any value of plate thickness.     

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 DUE TO A UNIFORM HEAT FLOW PAST A CIRCULAR HOLE WITH A RADIAL EDGE CRACK

The problem solved in this paper is that of finding the stresses in a linear thermoelastic solid when a uniform heat flow is disturbed by the presence of an insulated circular hole with a radial edge crack. By using a Mellin transform technique the authors reduce the problem to a pair of singular integral equations, which are then solved numerically.     

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 A LONG CIRCULAR CYLINDER SUBJECTED TO SUDDEN COOLING DURING TRANSIENT CONVECTION HEATING

An analysis is presented of the thermal stresses encountered during cooling of a solid circular cylinder initially heated from uniform temperature by Newtonian convection, followed by sudden cooling prior to reaching thermal equilibrium during the heating phase of the cycle. The numerical results indicate that the magnitude of the stresses attained during the cooling phase increases with increasing duration of heating, but are less than the corresponding values encountered for convective cooling from a condition of initial uniform temperature. The relevance of these results to the prediction or interpretation of thermal fatigue behavior is noted.