Analysis of Thermal Stress-Focusing Effect in a Solid Caused by Thermal Shock

近年来，各种特殊陶瓷对于计算机和许多其他电子设备的发展是必不可少的。当陶瓷材料受到快速的温度变化，如热冲击时，由于温度变化，会产生相当大的应力。在这些条件下，对断裂弱化的抗力称为耐热性、抗热应力或抗热震性。热应力对不同材料的影响不仅与材料特性有关，还与应力水平、体内应力分布和应力持续时间有关。因此，确定陶瓷材料在给定的热传递条件下的实际应力是非常重要的。在本研究中，我们精确地解决了球体和圆柱体等结构中的热冲击问题。当实心球体或圆柱体在其横截面上受到均匀的温升时，在施加热冲击的瞬间，表面会产生应力波。表面的应力波向内径向进入固体的中心。即使初始热应力相对较小，波也可能在中心积累并产生非常大的应力值。这种现象称为应力聚焦效应。最近，Hata应用射线理论精确地解决了均匀加热固体球体中的应力聚焦效应问题。结果表明，由应力聚焦效应引起的应力以固定的间隔周期性地达到峰值是一个有趣的现象。本文还用同样的方法对几种固体结构的热应力波效应进行了精确分析。数值结果给出了应力聚焦效应的明显迹象。这些结果对固体结构在热冲击作用下的设计具有一定的参考价值。

Recently, various special ceramics are essential to the development of computers and many other electronic devices. When ceramic materials are subjected to a rapid change in temperature, such as thermal shock, substantial stresses develop because of temperature changes. Resistance to weakening of fracture under these conditions is called thermal endurance, thermal stress resistance, or thermal shock resistance. The effect of thermal stresses on different kinds of materials depends not only on material characteristics but also on stress level, stress distribution in the body, and stress duration. Hence, it is very important to determine the actual stress in a ceramic material under given conditions of heat transfer.In this study we solve exactly the problem of thermal shock in structures, such as a sphere and a cylinder. When a solid sphere or cylinder is subjected to a uniform temperature rise over its cross section, 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 solid. 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.Recently Hata solved the problem of stress-focusing effects in a uniformed heated solid sphere exactly by applying the ray theory. The results show the interesting phenomenon that the stresses caused by the stress-focusing effects peak out periodically at a constant interval. This study also analyzes the effect of thermal stress waves in several solid structures precisely using the same method. The numerical results give clear indications of a stress-focusing effect. These results are useful for the design of solid structures under thermal impacts.