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 malt 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.