Thermal conductivity of a material containing cracks of arbitrary shape

The problem of thermal conductivity of a material containing microcracks of arbitrary shape (including non-flat ones) is considered. The resistivity contribution tensor of a crack – the quantity that determines the decrease in the overall conductive properties of a solid due to introduction of such cracks – is derived on the basis of the solution for the strength of a singularity of the heat flux near a crack tip (heat flux intensity factor). The approach is illustrated with several examples. It is also shown how the resistivity contribution tensor can be used to calculate effective conductive properties in the framework of various self-consistent schemes – effective media, effective field and differential scheme.