Explicit relations between elastic and conductive properties of materials containing annular cracks

The impact of annular cracks on the effective elastic and conductive properties of a material is analysed. The compliance contribution tensor of an annular crack the quantity that determines the increase in compliance of a solid due to introduction of such a crack-is derived analytically. The resistivity contribution tensor of an annular crack is calculated numerically. It is shown that an effective circular crack, i.e. a crack which yields the same change in elastic/conductive properties of a material as the given annular crack, can be chosen to match both of these tensors. Using this result, the explicit relation between elastic and conductive properties of a material containing annular cracks is obtained. The relation is derived using a non-interaction approximation. Applicability of the derived formulae to real materials (to plasma-sprayed coatings, in particular) is discussed.