Abstract

A novel and effective method is proposed to determine the temperature and thermal stresses in the case of a finite Griffith crack lying perpendicular to the surface of an isotropic half-plane under uniform remote heat flux or a surface heat source. The surface of the half-plane and the two faces of the crack are otherwise thermally insulating and traction-free. For the heat conduction problem, the thermally insulating crack is simulated by a continuous distribution of heat dipoles, and the resulting Cauchy singular integral equation (SIE) is solved numerically to arrive at the associated density function. The original thermoelastic problem can be treated equivalently as a mode II Zener-Stroh crack (ZSC) under isothermal conditions. The net dislocation of ZSC is determined by the aforementioned density function and the crack is modeled by a pileup of edge dislocations. The resulting SIE is solved numerically leading to the mode II stress intensity factors at the two crack tips induced by uniform remote heat flux or surface heat source. The net dislocation of an actual Zener-Stroh crack can be designed in such a way that the crack will become neutral to the uniform heat flux or surface heat source.

摘要

提出了一种新颖有效的方法来确定在均匀远程热通量或表面热源下垂直于各向同性半平面表面的有限格里菲斯裂纹情况下的温度和热应力。半平面的表面和裂纹的两个面在其他方面是绝热和无牵引的。对于热传导问题，绝热裂纹是通过热偶极子的连续分布来模拟的，并且对由此产生的柯西奇异积分方程 (SIE) 进行数值求解以获得相关的密度函数。原始热弹性问题可以等效地视为等温条件下的 II 型 Zener-Stroh 裂纹 (ZSC)。ZSC 的净位错由上述密度函数确定，裂纹由边缘位错堆积建模。由此产生的 SIE 被数值求解，导致由均匀远程热通量或表面热源引起的两个裂纹尖端处的模式 II 应力强度因子。实际齐纳-斯特罗裂纹的净位错可以这样设计，使裂纹对均匀的热通量或表面热源变得中性。