Investigation of the Stress-Focusing Effect and Determination of Stress Focusing Intensity Factor

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The stress-focusing effect is the phenomenon that, under an instantaneous heating, stress waves reflected from the free surface of the sphere or the cylinder result in very high stresses at the center, even though the initial thermal stress is relatively small. This plenomenon may be observed in the solid spheres subjected to the spherical symmetric heating and in the solid cylinders subjected to the cylindrical symmetric feating. This type of heating may be caused by the absorption of electromagnetic radiant energy or laser rays.This paper reviews recent extensions of the analytical methods for the problem of thermal shock in spheres and cylinders, especially, for the problem of thermal stress-focusing effect in spheres and cylinders. 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. As a limit case, for a solid sphere, it might be possible to observe the stress-focusing effect.Next, as for the analysis of a long cylindrical rod due to the instantaneous heating, stress waves also show the stress-focusing effect. While the method of ray theory is effective in the analysis of stress-focusing effect in a sphere, the method of ray series is effective in the analysis of stress-focusing effect in a cylinder. Therefore, the major accomplishment of this study has been in gaining a better understanding of the stress-focusing effect in the solid spheres and long cylindrical rods.In this study, analyzing the behavior of the stress focusing effect in a sphere, we introduce the stress focusing intensity factor S_<Fi>, which is expressed by the relation sigma_i=S_<Fi>/r^3 (i=r, rheta, phi) at the focusing points. This factor denotes the strength of stress focusing.