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

应力集中效应是指在瞬时加热下，从球体或圆柱体的自由表面反射的应力波在中心处产生非常高的应力的现象，即使初始热应力相对较小。这种现象可以在受到球对称加热的实心球和受到柱对称加热的实心柱中观察到。这种加热可能是由电磁辐射能或激光的吸收引起的.本文综述了球和柱中热冲击问题，特别是球和柱中热应力聚焦效应问题的分析方法的最新发展.首先，考虑在一个空心球受到快速均匀加热的热冲击的问题，如果外半径与内半径的球体的比例增加，峰值切向应力的内表面变得越来越高。作为极限情况，对于实心球，可以观察到应力集中效应。其次，对于长圆柱杆，由于瞬时加热，应力波也显示出应力集中效应。射线理论方法在分析球体的应力集中效应时是有效的，而射线级数方法在分析圆柱体的应力集中效应时是有效的。本文在分析球的应力集中效应的基础上，引入应力集中强度因子S_i，并将其<Fi>表示为σ_i=S_<Fi>/r^3（i=r，rheta，phi）。该因子表示应力集中的强度。

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.