THERMAL STRESSES INTENSITY FACTOR FOR FUNCTIONALLY GRADIENT PLATE WITH AN EDGE CRACK

Thermal stress problems of a functionally gradient plate as one of the advanced high-temperature materials capable of withstanding the extreme temperature environments, with and without an edge crack, are discussed One of the most important problems of the thermal stress in the functionally gradient plate with the crack are how to decrease the thermal stress intensity factor and how to determine the optimally continuous profile of the composition of the plate. The functionally gradient plate is subjected to a cycle of heating and cooling on the ceramics surface of the plate. The material properties of the functionally gradient plate are dependent on the temperature and the position. The optimally continuous profile of the composition of the plate is discussed. The numerical results for thermal stresses and the thermal stress intensity factor are shown for many temperature conditions and for many continuous profiles of the composition of the plate.     

STEADY THERMAL STRESSES IN AN INFINITE NONHOMOGENEOUS ELASTIC SOLID CONTAINING A CRACK

This article considers the crack problem for an infinite nonhomogeneous elastic solid subjected to steady heat flux over the crack surfaces. The aim is to understand the effect of nonhomogeneities of materials on stress intensity factors. By using the Fourier transforms, the problem is reduced to a Fredholm integral equation of the second kind which is solved numerically. Results are presented illustrating the influence of the nonhomogeneity of the material on the stress intensity factors. For some groups of the material constants, there exist minimum stress intensity factors, which is very interesting for the understanding of compositions of advanced functionally gradient materials.     

THERMAL STRESSES FOR AN INFINITE BODY WITH A SPHERICAL CAVITY WITH TWO RELAXATION TIMES

Thermoelastic interactions caused in a homogeneous and isotropic infinite body with a spherical cavity are considered for the two different theories of generalized thermoelasticity, that is, Lord, and Shulman's theory and Green and Lindsay's theory. Analytical expressions for the temperature, displacement, and thermal stress fields are obtained; and the results are compared with the classical dynamical coupled theory.     

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.     

THERMAL STRESSES IN A LONG ELASTIC CYLINDER CONTAINING A PENNY-SHAPED CRACK AND EMBEDDED IN A THERMALLY CONDUCTIVE ELASTIC INFINITE MEDIUM

This paper is concerned with- the state of stress in a long circular elastic cylinder with a concentric penny-shaped crack whose surfaces are subjected to a prescribed temperature. The plane of the crack is assumed to be perpendicular to the axis of the cylinder. The cylinder is bonded to a thermally conductive elastic infinite medium. The thermal and elastic constants of the cylinder and infinite medium are assumed to be different. By assuming suitable representations for the temperature function, the heat conduction problem is reduced to the solution of a Fredholm integral equation of the second kind. Similarly, the thermoelastic problem is also reduced to the solution of a Fredholm integral equation of the second kind. A closed-form expression is obtained for the stress-intensity factor. The integral equations are solved numerically, and the results are used to obtain numerical values for the stress intensity factor. These values are presented graphically.     

TRANSIENT THERMAL STRESSES IN A CHEMICALLY HARDENING MATERIAL CAST WITHIN AN ELASTIC CYLINDRICAL MOLD

Abstract

A method is formulated for determining the transient thermal stresses that evolve during the molding process within a material hardening as the result of an exothermic chemical reaction. The formulation is applied to the restricted case in which the shear-to-bulk-modulus ratio for the fully hardened material is small, and where the material is cast in the form of an infinitely long solid cylinder in a thermally thin elastic mold. The heat-generation rate and temperature variation are derived from a first-order chemical reaction. The solidification of the material is described by a transformation from an initial liquidlike state to an elastic solid, with thermoelastic constitutive rate equations during the hardening process based upon a two-component mixture model whose composition is related to the degree of reaction. Graphs for transient stresses and residual stress distributions are shown in terms of dimensionless variables, with hardening rate related to thermochemical constants, and with the elastic properties of the poured material and mold as parameters. Illustrative examples are analyzed to show the existence of tensile stresses that may be associated with cracking during the molding process, and containment stresses in the mold arising from thermal expansion of the hardening material. Material properties are listed to form numerical estimates of the dimensionless variables.     

THERMAL STRESS ANALYSIS IN THERMOPIEZOELASTIC STRIP WITH AN EDGE CRACK

The analysis of thermal stresses becomes important when the piezoelectric material has to be operated in either extremely cold or hot temperature environments. Hence, it is essential to know the interaction of mechanical defects with temperature changes. This investigation is concerned with a strip problem of transversely isotropic thermopiezoelastic material containing an edge crack under partial thermal and electric loading conditions. Thermopiezoelastic stresses are analyzed by introducing potential functions and Fourier transforms. The problem reduces to solving a singular integral equation, and the singular integral equation is solved. Numerical calculations of the thermal stress intensity factors are carried out for a cadmium selenide material.     

THERMAL STRESSES AROUND AN ELASTIC RIBBONLIKE INCLUSION WITH GOOD THERMAL CONDUCTIVITY

Plane-deformation problems of thermal stresses around an elastic ribbonlike conductor in an infinite, homogeneous, isotropic medium under uniform heat flow are analyzed by the method of continuous distribution of singular points. The line heat sources and concentrated forces are distributed continuously along the ribbonlike conductor. The boundary conditions yield a system of singular integral equations for density functions with Cauchy kernels and logarithmic singular kernel. A solution is assumed in the form of the product of a series of Chebyshev polynomials of the first kind and their weight function and is determined by transforming the singular integral equations into linear algebraic equations. One of the advantages of this method is that the strength of the thermal-stress singularity at the tips of the ribbonlike conductor can be easily evaluated. Numerical results for the strength of the thermal-stress singularity are plotted in terms of nondimensional parameters, consisting of the dimensions of the ribbonlike conductor and the material constants of the conductor and matrix.     

THERMAL STRESSES IN HETEROGENEOUS ELASTIC CYLINDERS WITH MICROSTRUCTURE

This article is concerned with the problem of thermoelastic equilibrium of cylinders with microstructure under action of a temperature variation that is a polynomial in the axial coordinate. The cylinder is occupied by different thermoelastic materials.     

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.     

CIRCUMFERENTIAL CRACK PROBLEM FOR AN FGM CYLINDER UNDER THERMAL STRESSES

The main objective of this study is to determine the stress intensity factors associated with a circumferential crack in a thin-walled cylinder subjected to quasi-static thermal loading. The cylinder is assumed to be a functionally graded material. In order to make the problem analytically tractable, the thin-walled cylinder is modeled as a layer on an elastic foundation whose thermal and mechanical properties are exponential functions of the thickness coordinate. Hence a plane strain crack problem is obtained. First temperature and thermal stress distributions for a crack-free layer are determined. Then using these solutions, the crack problem is reduced to a local perturbation problem where the only nonzero loads are the crack surface tractions. Both internal and edge cracks are considered. Stress intensity factors are computed as functions of crack geometry, material properties, and time.     

THERMAL STRESS ANALYSIS OF A RECTANGULAR PLATE AND ITS THERMAL STRESS INTENSITY FACTOR FOR COMPRESSIVE STRESS FIELD

Abstract

In this study, a transient thermal stress problem of a rectangular plate due to a nonuniform heat supply is treated theoretically and, thereafter, fracture behaviors of the plate with a crack are examined for compressive stress states. Assuming that a crack located on an arbitrary position, with an arbitrary direction, is sufficiently small and is closed because of the compressive stress field, a temperature field, in a transient state, is analyzed by taking into account the effect of relative heat transfer on both surfaces of the plate. Thereafter, the corresponding thermal stress analysis is developed on the basis of the two-dimensional plane stress problem using Airy's stress function method, and the stress intensity factor is analyzed for the biaxial stress state. As an analytical model, we consider mechanical boundary conditions of prescribed displacement and estimate the stress intensity factor of a crack tip using parameters of the crack configuration such as the location, direction, length, and coefficient of friction. These numerical results are shown in graphical form.     

NORMALIZED STRESS INTENSITY FACTOR RANGE SOLUTIONS OF AN INNER-SURFACE CIRCUMFERENTIAL CRACK IN THIN- TO THICK-WALLED CYLINDERUNDER THERMAL STRIPING BYSEMI-ANALYTICAL NUMERICAL METHOD

The normalized stress intensity factor (SIF) range of an inner-surface circumferential crack in a thin to thick-walled finite-length cylinder under thermal striping was considered in this paper. The edges of the cylinder were rotation-restrained and the outer surface was adiabatically insulated. The inner surface of the cylinder was heated by a fluid with sinusoidal temperature fluctuation. An analytical temperature solution for the problem and our semianalytical numerical SIF evaluation method for the crack were combined and, as a result, it was shown that the transient SIF solution can be expressed in a generalized form by dimensionless parameters such as mean-radius-to-wall-thickness ratio, Biot number, normalized striping frequency, and Fourier number. Finally, normalized SIF ranges for the first cycle and steady state were given for these dimensionless parameters in tables for mean-radius-to-wall-thickness ratio of 10, 5, and 1.     

CRITICAL STRESS INTENSITY FACTORS FOR CRACKED HOLLOW PIPES UNDER TRANSIENT THERMAL LOADS

Finite element analyses of a long hollow cylinder having an axisymmetric circumferential internal edge crack, subjected to convective cooling on the inner surface are performed. The transient thermal stress intensity factor is estimated using a domain version of the J-integral method. The effect of the thickness of the cylinder, crack length, and heat transfer coefficient on the stress intensity factor history are studied. The variations of critical normalized stress intensity factor with crack length-to-thickness ratio for different parameters are presented. The results show that if a small inner surface crack begins to grow, its stress intensity factor will increase with increase in crack length, reach a maximum, and then begin to drop. Based on the results, a fracture-based design methodology for cracked hollow pipes under transient thermal loads is discussed.     

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.     

TRANSIENT THERMOELASTIC PROBLEM FOR AN INFINITE PLATE CONTAINING A PENNY-SHAPED CRACK AT AN ARBITRARY POSITION

This article deals with the transient thermoelastic problem for an infinite plate containing a penny-shaped crack that is parallel to the surfaces of the plate but at an arbitrary position of the plate. The transient thermal stresses are set up by the heat generation on the surfaces and the sudden heat exchange on the surfaces. By using the finite difference method for the time variable, the analytical solution for spatial variables can be obtained. The numerical results for the temperature and stress intensity factor are obtained, and results are shown in graphs.     

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 AT ELLIPTICAL HOLES NEAR AN EDGE

Results are presented for the photothermoelastic analysis of the quasi-static problem of transient thermal stresses around elliptical holes near the edge of a plate. Extrapolation of a linear regression formula to an infinitely narrow ellipse predicts the tip stresses at cracks near free boundaries.     

THERMAL STRESSES IN HETEROGENEOUS ANISOTROPIC COSSERAT ELASTIC CYLINDERS

A method of solving the problem of thermal stresses for composite cylinders, where the cross section is occupied by different inhomogeneous and anisotropic Cosserat elastic materials is established. The temperature variation is assumed to be a polynomial in the axial coordinate. The method is used to study the deformation of a circular cylinder composite of two different isotropic materials.     

A MODE-I CRACK PROBLEM FOR AN INFINITE SPACE IN GENERALIZED THERMOELASTICITY

ABSTRACT

In this work, we solve a dynamical problem of an infinite space with a finite linear crack inside the medium. The Fourier and Laplace transform techniques are used. The problem is reduced to the solution of a system of four dual integral equations. The solution of these equations is shown to be equivalent to the solution of a Fredholm integral equation of the first kind. This integral equation is solved numerically using the method of regularization. The inverse Laplace transforms are obtained numerically using a method based on Fourier expansion techniques. Numerical values for the temperature, stress, displacement, and the stress intensity factor are obtained and represented graphically.