THERMAL STRESS-FOCUSING EFFECT IN A TRANSVERSELY ISOTROPIC SPHERICAL ZIRCONIA INCLUSION IN AN INFINITE ELASTIC MEDIUM CAUSED BY IMPACT COOLING

When an isotropic infinite elastic medium with a transversely isotropic spherical zirconia inclusion is suddenly subjected to a uniform temperature fall, stresswavesoccur at the interface of the spherical inclusion the moment thermal impact is applied. The stress wave in a transversely isotropic spherical inclusion proceeds radially inward to the center of the inclusion. The wave may accumulate at the center and cause very large stress magnitudes, even though the initial thermal stress should be relatively small. This phenomenon is called the stress-focusing effect. The stress wave in an inclusion may be affected by phase transformation during the tempering process. The stress-focusing effects are analyzed in an exact manner, and a clear indication of the mechanism of thermal and phase transformational stress-focusing effects in a transversely isotropic spherical Zirconia inclusion in the isotropic infinite elastic domain is given.     

THERMAL STRESS-FOCUSING EFFECT IN A TRANSVERSELY ISOTROPIC SPHERICAL INCLUSION EMBEDDED IN AN ISOTROPIC INFINITE ELASTIC MEDIUM

When an isotropic infinite elastic medium with a transversely isotropic spherical inclusion is suddenly subjected to a uniform temperature rise, stress waves occur at the interface of spherical inclusion at the moment thermal impact is applied. The stress wave in a transversely isotropic inclusion proceeds radially inward to the center of the inclusion. The wave may accumulate at the center and cause very large stress magnitudes even though the initial thermal stress should be relatively small. This phenomenon is called the stress-focusing effect. The stress wave in an infinite elastic medium proceeds radially to infinity. This paper analyzes, in an exact manner, the effects of these waves using the ray integrals. The results give a clear indication of the mechanism of the thermal stress-focusing effect in a transversely isotropic inclusion embedded in the isotropic infinite elastic medium.     

THERMAL STRESS-FOCUSING EFFECT FOLLOWING RAPID NONUNIFORM HEATING OF LONG CYLINDRICAL RODS

When a cylinder is suddenly subjected to an instantaneous heating on its cross-section, stress waves occur at the surface of the cylinder the moment thermal impact is applied. The stress waves in a cylinder proceed radially inward to the center of the cylinder. The wave may accumulate at the center and give rise to very large stress magnitudes, even though the initial thermal stress may be relatively small. This phenomenon is called the stress-focusing effect. In this article, we show that the phenomenon of thermal stress-focusing effect should occur in a cylinder heated by rapid nonuniform heat. The analytical results give a clear indication of the mechanism of thermal stress-focusing effects and clarify the order of singularity of the stress-focusing effects in a cylinder caused by instantaneous nonuniform heating.     

THERMAL STRESS-FOCUSING EFFECT FOLLOWING RAPID UNIFORM HEATING OF SPHERES AND LONG CYLINDRICAL RODS

Stress waves that develop following the rapid uniform heating of linear-elastic spheres and long cylindrical rods display a stress-focusing effect as they proceed radially toward the center in these geometries. The stress-focusing effect is the phenomenon that, under a rapid uniform heating, stress waves reflected from the free surface of the sphere or the cylindrical rod result in very high stresses at the center, even though the initial thermal stress might be relatively small. This phenomenon may be observed in the solid spheres subjected to the spherical symmetric heating and in the cylindrical rods subjected to the cylindrical symmetric heating. This type of heating may be caused by the absorption of infrared rays radiation or electromagnetic radiant energy. This article reviews recent extensions of the analytical methods for the problem of thermal shock in spheres and cylindrical rods, especially for the problem of the thermal stress-focusing effect in spheres and cylindrical rods. First, considering the problem of thermal shock in a hollow sphere subjected to the rapid uniform heating, if the ratio of the outer radius to the inner radius of the sphere increases, the peak tangential stress at the internal surface becomes higher and higher. In the limit case, for a solid sphere, it might be possible to observe the stress-focusing effect. Next, as for the analysis of a cylindrical rod due to the rapid uniform heating, stress waves also show the stress-focusing effect. Hence, the major accomplishment of this study is in gaining a better understanding of the thermal stress-focusing effect in solid spheres and cylindrical rods.     

STRESS-FOCUSING EFFECT DUE TO AN INSTANTANEOUS CONCENTRATED HEAT SOURCE IN A SPHERE

The stress-focusing effect is the phenomenon in which, due to an instantaneous concentrated heat source, stress waves propagating from the free surface of the sphere result in very high stresses at the center. Using the ray theory, the Fourier transformed solution of stress waves in the sphere is sorted out into rays according to the ray path of multiply reflected waves. In the study, in order to denote the strength of the stress focusing, we introduce the stress-focusing intensity factor, S_Fi, which is defined by the relation σ _i = S_Fi/r^?3 (i = r, θ, ?) at the focusing point. The numerical results reveal that stresses peak out periodically with a constant period.     

Effect of FGM core on dynamic response of a buried sandwich cylindrical shell in poroelastic soil to harmonic body waves

The two-dimensional dynamic interaction of progressive plane seismic waves with an arbitrarily thick, isotropic, and functionally graded cylindrical shell of infinite extent embedded in a boundless fluid-saturated porous elastic medium is investigated. The inhomogeneous shell is approximated by a laminate model, for which the solution is expected to gradually approach the exact one as the number of layers increases. Continuity of the displacement and stress components at the interfaces of neighboring layers is applied to form a system global transfer matrix, ultimately leading to determination of the modal scattering and transmission coefficients. The analytical results are illustrated with numerical examples in which an air-filled steel–zirconia FGM shell, buried in a water-saturated Ridgefield Sandstone formation, is insonified by fast compressional or shear waves at normal incidence. The effects of material compositional gradient and FGM layer thickness on the basic dynamic field quantities are evaluated and discussed. Limiting cases are considered and good agreements with the solutions available in the literature are obtained.     

Thermo-mechanical stress analyses of solid oxide fuel cell anode based on three-dimensional microstructure reconstruction

During high-temperature operation of a solid oxide fuel cell, the stresses caused by mismatch of thermal expansion coefficients between different materials and external mechanical loads may cause the rising of damage risk of nickel-yttria-stabilized zirconia anode. It is quite difficult to quantify the mechanical characteristics of a composite anode without investigating on the stress distribution in its real microstructure. However, the high operating temperature and extremely complex microstructure in micro-scale determine the high difficulty in in-situ measurement of thermo-mechanical stress distribution. In this work, the microstructures of six different anode samples, fabricated by using identical nickel oxide-yttria-stabilized zirconia powder mixture, are reconstructed in three-dimension based on the dual-beam focused-ion-beam-scanning-electron-microscopy. The three-dimensional thermo-mechanical stress distributions of different microstructures are conducted at operating temperature based on the finite element method. The effects of both thermal expansion coefficients mismatch between nickel and yttria-stabilized zirconia and external mechanical loads are analyzed. The mechanical failure probabilities of yttria-stabilized zirconia phase in different reconstructions are estimated based on the obtained stress distributions to investigate the influence of microstructure characterizations on nickel-yttria-stabilized zirconia anode strength.     

UNSTEADY HEAT TRANSFER FROM A ROTATING DISK WITH SOLIDIFICATION

Abstract

Unsteady heat transfer from an infinite rotating disk when phase change from liquid to solid occurs is investigated numerically. The moving boundary is fixed for all times by a coordinate transformation, and a finite difference method is used to obtain the instantaneous location of the solid-Uquid interface and the heat transfer from the surfaces of solid and liquid. It is observed that the instantaneous heat flux at the surface of the solid can be obtained with sufficient accuracy by measuring the thickness of the solid, or vice versa, When the Prandtl number is varied, the minimum response time of heat transfer in both solid and liquid phases occurs around Pr = 1.     

Effect of phase transformation of zirconia on the fracture behavior of electrolyte-supported solid oxide fuel cells

Zirconia solid electrolyte provides the functions of mechanical support, electronic insulation and oxygen ions conductivity for electrolyte-supported solid oxide fuel cell. Ferritic stainless steel is used as current collector to study the structural stability of the two cells during the cooling process. The sample using fully-stabilized zirconia is cracked after the cooling process, while the partially-stabilized zirconia sample has no obvious changes. Thermal expansion coefficient of the two samples is similar, which exhibits that TEC is not the main factor to result in the fracture. In-situ X-ray diffraction results indicated that the conflict between the compression state in cell due to TEC and the volume expansion of the fully-stabilized zirconia sample due to phase transformation can cause cracking. Partially-stabilized zirconia sample can be transformed from tetragonal to cubic phase during the temperature rising, while can be recovered to its initial state during cooling. Even much more cubic phase can be transformed to the tetragonal phase induced by pressure stress during cooling, which plays an important role on the anti-cracking performance.     

Thermal Stress Analysis for an Inclusion with Nonuniform Temperature Distribution in an Infinite Kirchhoff Plate

Abstract

An elliptic inclusion with prescribed polynomial eigenstrains in an infinite Kirchhoff plate is analyzed. The integral type general solutions for the in-plane and out-of-plane displacements on the mid-plane of the plate were derived. The integrals were simplified by using Green's function for the Kirchhoff plate. The integrals could be explicitly expressed by calculating two potential functions defined in this work. After some manipulation of Ferrers and Dyson's formula related to the integration of the harmonic potential for the three-dimensional ellipsoid, we evaluated the potential functions, which can be algebraically expressed by the I-integrals. The results were applied to the analysts of the thermal stress for an inclusion with non uniform temperature distribution that might be approximated by a polynomial. For mathematical convenience, we consider an inclusion with a linear temperature distribution. The expressions for the displacements were decomposed in order to separately investigate the effects of the constant and the first-order term of the temperature distribution. The elastic fields caused by an elliptic inhomogeneity with polynomial eigenstrains, which is called the inhomogeneous inclusion, were also determined by the equivalent eigenstrain method.     

GENERALIZED THERMOELASTICITY: CLOSED-FORM SOLUTIONS

A study of the one-dimensional thermoelastic waves produced by an instantaneous plane source of heat in homogeneous isotropic infinite and semi-infinite bodies of the Green-Lindsay (G-L) type is presented. Closed-form Green's functions corresponding to the plane heat source are obtained using the decomposition theorem for a potential-temperature wave of the G-L theory. Qualitative analysis of the results is included.     

Thermal stress induced by electric current in the vicinity of an elliptic inclusion in an infinite plate

We consider an elliptic inclusion embedded in an infinite plate subjected to the simultaneous effects of electric current and energy flux at infinity. Using complex variable methods, we analyze the resulting mechanical properties of the composite, in particular around the perimeter of the inclusion. In doing so, we find that thermal stress can exist even in a simply connected region as a result of Joule heating which can therefore be used to preset stress in manufactured devices. In the particular case of the elliptic inclusion, we find that the electric current has the ability to transfer thermal stress to regions of lower temperature thereby improving security and reliability of the corresponding devices.     

Transient response analysis of a spherical shell embedded in an infinite thermoelastic medium based on a memory-dependent generalized thermoelasticity

In the context of a memory-dependent generalized thermoelasticity, the thermal-induced transient response in an infinite elastic body containing a spherical shell is investigated. A thermal shock is applied on the inner surface of the spherical shell. The infinite body and the spherical shell are assumed to be isotropic but two dissimilar materials. By using an analytical technique based on the Laplace transform along with its numerical inversion, the governing equations of the problem are solved and the non-dimensional physical quantities in the two materials, i.e., temperature, displacement and stress, are obtained and illustrated graphically respectively. In simulation, the accuracy of memory-dependent derivative (MDD) is verified by degrading the present model into L-S model to compare the results obtained from the cases with interfacial thermal resistance and without interfacial thermal resistance. In addition, the effects of the different kernel functions as well as the ratios of the two materials, including the ratios of the density, the thermal-conductivity and the time-delay, on the distributions of the considered variables are obtained and demonstrated graphically respectively.     

Plane waves in nonlocal thermoelastic solid with voids

This work is concerned with the propagation of time harmonic plane waves in an infinite nonlocal thermoelastic solid having void pores. Three sets of coupled dilatational waves and an independent transverse wave may travel with distinct speeds in the medium. All these waves are found to be dispersive in nature, but the coupled dilatational waves are attenuating, while transverse wave is nonattenuating. Coupled dilatational waves are found to be influenced by the presence of voids, thermal field and elastic nonlocal parameter. While the transverse wave is found to be influenced by the nonlocal parameter, but independent of void and thermal parameters. For a particular model, the effects of frequency, void parameters, thermal parameter and nonlocality have been studied numerically on the phase speeds, attenuation coefficients and specific losses of all the propagating waves. All the computed results obtained have been depicted graphically and explained.     

Thermoelastic Wave with Energy Dissipation in an Unbounded Medium with a Spherical Cavity

The generalized linear theory of thermoelasticity has been used to study waves emanating from the boundary of a spherical cavity in a homogeneous and isotropic infinite thermoelastic body. The basic equations are written in the form of a vector-matrix differential equation and solved by an eigenvalue approach. Solutions in closed form have been achieved in the Laplace transform domain, and the inversion in the space-time domain for the field variables are done numerically. Finally, the results are analyzed and represented graphically.     

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.     

SOLUTION OF AN ELLIPTICAL RIGID INCLUSION WITH DEBONDINGS IN AN INFINITE PLANE UNDER THE UNIFORM HEAT FLUX

A problem of an elliptical rigid inclusion in an infinite plane subjected to uniform heat flux in an arbitrary direction and with a number of debondings on the interface of the elliptical rigid inclusion and the elastic matrix is solved. The rotation of the inclusion under the uniform heat flux is considered. The complex variable method is used, and the closed-form solution is obtained. The stress intensity of debonding at the debonding tips is calculated and the extension of debonding is investigated. Examples of stress distributions and resultant moments on the inclusion are shown for the inclusion with two debondings.     

AN INFINITE PLATE WITH A FLAW AND SUBJECTED TO UNIFORM HEAT FLOW

The thermoelastic problem of an infinite plate which has a crack or a ribbonlike inclusion and is subjected to remotely uniform heat flow is analyzed under the assumption of linear heat transfer across the flaw. Numerical calculations show that the insulated crack causes an overestimation of the stress singularity, and the insulated inclusion produces an underestimation.     

Effect of Rotation and Initial Stress on an Infinite Generalized Magneto-Thermoelastic Diffusion Body with a Spherical Cavity

This study examines one-dimensional problem in a generalized magneto-thermoelastic diffusion in an infinite rotating medium with a spherical cavity subjected to a time dependent thermal shock at its internal boundary, which is assumed to be traction free. The chemical potential is also assumed to be a known function of time at the boundary of the cavity. The analytical expressions for the displacements, stresses, temperature, concentration and chemical potential are obtained in the physical domain using the harmonic vibrations. Effect of rotation, initial stress, magnetic field and diffusion are analyzed theoretically and computed numerically. Comparisons were made with the results; obtained in the presence and absence of rotation, magnetic field and diffusion. Numerical results determine the finite speeds of propagation for thermoelastic and diffusive waves. The results indicate that the effect of rotation, magnetic field, relaxation time and diffusion relaxation time are very pronounced.     

Three-Dimensional Fundamental Solution for Transversely Isotropic Electro-Magneto-Thermo-Elastic Materials

Fundamental solutions play an important role in the analyses of coupled fields in electro-magneto-thermo-elastic material. However, most works available on this topic address the case of uniform temperature. Based on the compact general solution of transversely isotropic electro-magneto-thermo-elastic material, which is expressed in harmonic functions, and employing the trial-and-error method, the three-dimensional fundamental solution for a steady point heat source in an infinite transversely isotropic electro-magneto-thermo-elastic material is presented by five newly induced harmonic functions. Numerical results are given graphically by contours.