A finite crack in a half-plane under uniform heat flux or surface heat source

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.

Keywords:

• Complex variable formulation
• conducting crack
• Griffith crack
• heat flux
• heat dipole
• insulating crack
• singular integral equation
• stress intensity factor
• surface heat source
• Zener-Stroh crack

Additional information

Funding

This work is supported by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada (Grant No: RGPIN – 2017 – 03716115112).