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Under certain conditions, the impedance of the crack can be modeled as a purely resistive part adiabatically coupled to a purely inductive part. One starts by modeling the properties of the crack as resistive, with an effective resistivity Rcr = ρbcn (length) where ρb is the crack bulk resistivity, with an equivalent full-length resistance approximately equal to Rb. One also models the crack as inductive, with an inductance Lcr = πb / ωc, where ωc is the angular frequency of the excitation current, and πb is a constant, which is estimated from endurance studies. This model treats the crack as a series inductive resistor. It does not take into account the eddy current loss. Therefore, its use must be considered as an approximate model.
The equation for Rcr is modified as follows: Renc = Rb + Rcr = Rb(ZT/Zp), and Rcn+crack = Rcneff = Rb(1 + ZT/Zp). The impedance of the crack is thus larger than the impedance Rl, which is without a crack.
It should be noted that this model does not work as an approximation if the excitation frequency is not much lower than the frequency of the crack; the crack model then becomes the limiting case for a small crack. In practice, the model works well if the frequency of the excitation current is at least 1000 Hz.
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