Toshiaki Hata

Thermal Shock in a Hollow Sphere Caused by Rapid Uniform Heating

Adopting the Goodiers concept, the dynamic thermoelastic problem in a sphere is decomposed into a particular form of dynamic stress problem corresponding to the thermoelastic displacement potential and the homogeneous form of dynamic stress problem corresponding to the stress functions. Applying the ray theroy to the homogeneous form, we obtain the general solution for transient waves induced by sudden heating

Stress-Focusing Effect in a Uniformly Heated Solid Sphere

Using the ray theory, the Laplace transformed solution of stress waves in the sphere is sorted out into rays according to the ray path of multiply-reflected waves. Inverse transform of each ray gives rise to theexact solution of the transient response up to the arrival time of the next ray

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

Abstract 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 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 spheric 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, SFi, which is defined by the relation σ i = SFi/r−3 (i = r, θ, ϕ) at the focusing point. The numerical results reveal that stresses peak out periodically with a constant period.

THERMOELASTIC PROBLEM FOR A GRIFFITH CRACK IN A PLATE WITH TEMPERATURE-DEPENDENT PROPERTIES UNDER A LINEAR TEMPERATURE DISTRIBUTION

This paper is concerned with a method for calculating the thermal-stress distribution in a plate exhibiting temperature-dependent properties. Using the perturbation method, general equations for the displacements are found. The equations can be solved by using four displacement functions. Following this method, a solution is derived for calculating the stress intensity factor for a Griffith crack in a temperature-sensitive plate under a linear temperature distribution, where we assume that the temperature field is not disturbed by the crack. (Under these conditions, if a plate is temperature-insensitive, the stress intensity factor for the crack is zero.) In this case, whether the stress intensity factor is zero or not depends only on the temperature variation of the coefficient of thermal expansion. A numerical example is given for a plate made of steel.

Stress-Focusing Effects in a Spherical Inclusion Embedded in an Infinite Medium Caused by Instantaneous Phase Transformation

Recently, transformation toughening of ceramics has attracted considerable attention in several works [1]. The mechanism in the toughening of ceramics is the stress-induced phase transformation of a Zirconia particle [2], which is accompanied by volumetric expansion under cooling process. Due to this expansion, the composite material consisting of Zirconia particles within a brittle matrix becomes more resistant to thermal fracture. While in the dynamic state the mechanism in the toughening of ceramics is not well understood. Therefore the interaction between a thermal shock and a possible phase transformation in the transformation-toughened ceramics with Zirconia particles should be studied. In this paper a phenomenological model is proposed to describe the situation, which involves the interaction between a thermal shock and a dynamic inhomogeneity with a stress-induced martensitic transformation in a spherical particle of Zirconia embedded in an infinite elastic matrix.

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 IN A SOLID SPHERE SUBJECTED TO INSTANTANEOUS HEATING

When an isotropic solid sphere is suddently subjected to a uniform temperature rise on the surface of the sphere, a stress wave occurs at the surface the moment thermal impact is applied. The stress wave at the surface proceeds radially inward to the center of the sphere. The wave may accumulate at the center and give rise to very large stress magnitudes, even though the initial thermal stress is relatively small. This phenomenon is called the stress-focusing effect. This paper analyzes, in an exact manner, the effects of these waves using the ray series. The results give a clear indication of the mechanism of stress-focusing effect in a solid sphere.

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.