Thin-skin analysis technique for interaction of arbitrary-shape inducer field with long cracks in ferromagnetic metals

In using the AC field measurement (ACFM) technique for non-destructive evaluation (NDE) of metals, a current-carrying wire structure is used to induce eddy current within a thin layer of the metal and a magnetic field sensor to measure the field perturbations in the vicinity of the metal. The sensitivity of ACFM crack detection and sizing relies on an appropriate design of the wire structure geometry together with a dully placement of the sensor. This paper presents an analytical modeling technique for evaluating the electromagnetic field interaction of an ACFM probe with a long uniform crack in a ferromagnetic metallic slab. The probe in the proposed model can have an arbitrary-shape wire inducer with no restrictions on its relative sensor position. The technique is accurate and very efficient computationally. It first uses the two-dimensional Fourier transform to obtain the field distribution at the metal surface. The Laplacian field distribution above the metal is then determined by satisfying the so-obtained boundary condition at air–metal interface. To demonstrate the accuracy of the model, we consider the special case of a rhombic wire inducer. The comparison of our results with those obtained using the conventional algorithm in the literature validates the accuracy of the model introduced in this paper. To show the generality of the model, we also present theoretical and experimental results associated with a solenoid inducer with a three-dimensional geometry for which no analytical solution is available in the literature. The theoretical prediction of crack signal supported by experimental results is used to develop a model-based method for inverting crack signal into crack depth.