Effect of heat conduction of penny-shaped crack interior on thermal stress intensity factors

Abstract

This paper analyzes the thermal stress induced by a penny-shaped crack in an elastic solid with uniform steady heat flux. Air inside an opening crack is taken as a thermally conducting medium and the crack is partially insulated. The Hankel transform technique is applied to convert the problem to a system of dual integral equations. Heat flux in the opening crack or temperature gradient across the crack depends on the crack opening displacement. Explicit expressions for the whole temperature change field and heat flux at any position in the cracked medium are given in terms of elementary functions. Thermal stresses and displacements are presented for a solid with a partially insulated crack under remote tensile loading and uniform heat flux. Stress intensity factors (SIFs) are determined. The mode-I SIFs depend only on external tensile loading, and are free of the material properties. The mode-II SIFs are related to both mechanical and thermal loading, in addition to the material properties. Numerical results for a cracked thermoelastic material are presented to show the influence of the thermal conductivity of air of the crack interior on the mode-II SIFs, and indicate that heat conduction of crack affects thermal SIFs. Insulated and isothermal cracks are two limiting cases of a partially insulated crack.