The influence of nonconductive disk-shaped inclusions on the DC conductivity of materials

The influence of non-conductive disk-like inclusions (fractures) on the conductivity of a conducting medium in direct current is considered. To find the additional specific electrical resistance due to cracks, a self-consistent problem for the current density has been solved. In this case, a hydrodynamic analogy was used between the motion of an ideal incompressible fluid during potential flow around solids and electric current flowing around fractures. The functional dependences of the resulting relative additional specific electrical resistance of the material on the fracturing coefficient for thick and thin samples are found. A graphical visualization of these dependences shows that for a thick specimen, for all real values of the coefficient of fracturing, it is linear and is determined by the shape of the fractures. For a thin sample, the dependence of the relative additional the specific electrical resistance of the material on the fracturing coefficient is proportional to the thickness of the sample and is nonlinear. The obtained dependences of the additional electrical resistivity can be used, in particular, as a non-invasive method for determining the fracturing coefficient of rock samples conducting electric current.