Effects of Crack Surface Heat Conductance on Stress Intensity Factors

Abstract

Effects of crack surface heat conductance on stress intensity factors of modes I, II, and III are investigated. The crack problem is first solved by assuming perfect (infinite) heat conductance at crack surfaces. Finite heat conductance at crack surfaces is then accounted for by imposing a set of distributed dipoles at the crack surfaces. Distribution function of the dipoles is the solution of a Fredholm integral equation. It is shown that, for cracks in a homogeneous, isotropic, linear elastic solid, the degree of thermal conductivity at crack surfaces will affect the magnitude of mode I and mode II stress intensity factors but not mode III stress intensity factor. It is also shown that, for a geometrically symmetric cracked solid, only the mode II stress intensity factor will be influenced by different crack surface heat conductance even if the thermal loading is not symmetric. More importantly, for a given material thermal conductivity (K) and crack surface heat convection coefficient (h), effects of crack surface heat conductance on stress intensity factors is found to depend upon crack size. This “size effect” implies that, for a given set of K and h, an extremely small crack can be treated as if the crack surfaces are insulated and a very long crack can be treated as if the crack surfaces are perfectly heat conductive. As an example, the problem of a finite crack in an infinite plate subjected to a constant temperature gradient at infinity is studied.