The Effect of Thermal Conductivity on the Singular Behavior of the Near-Tip Temperature Gradient

The singular behavior of the temperature gradient in the vicinity of a macrocrack tip is studied in this work. The emphasis is placed on the effect of thermal conductivity on the power of singularity of the near-tip temperature gradient. Both the temperature dependency and the inhomogeneity of the thermal conductivity are investigated analytically. In the near-tip region, they are the sensitive factors influencing the singular behavior of the temperature gradient. The physical conditions under which their effect dominates over the geometric singularity at the crack tip are studied in detail. In some cases, their strong effects can even make the singularity of the temperature gradient diminished at the crack tip. Consequently, the thermal energy intensification disappears.