Calibrating Johnson's formula for applying DCPD method to an axial through-wall crack in a pipe

Direct current potential drop (DCPD) method is widely employed in the determination of crack length in conductive materials. It is based on the change of structure potential drop caused by the variation of the electrical resistance under a steady direct current. The accuracy of DCPD method depends on the calibration curve which describes the relationship between crack length and potential drop. Generally, the calibration curve for the crack in a plate sample is given by Johnson's formula analytically. However, the traditional Johnson's formula is only applicable to a center-cracked plate but not to a cracked pipe. In this paper, Johnson's formula has to be calibrated to estimate the length of a through-the-thickness crack in a pipe. Considering the geometrical difference between a pipe sample and a plate sample, the calibrated Johnson's formula is established based on the existence of parallel circuit in a pipe and the proposed unique reference sample. The calibration curve between axial through-wall crack length and potential drop is carried out by the calibrated Johnson's formula. The calibrated formula has been verified for the axial through-wall crack in a pipe sample by numerical and experimental approaches. Compared with the traditional Johnson's formula, the results illustrate that the present calibrated formula is successful to estimate the crack length in a pipe. This paper extends the applicability of the original formulation of Johnson's formula to cracked pipes.