Analysis technique for interaction of high-frequency rhombic inducer field with cracks in metals

In the nondestructive evaluation (NDE) involving the ac field measurement (ACFM), a current carrying structure is required to induce the eddy current in the work-piece and a probe to sample the field. Due to its flat profile, slender shape, and other advantages, the rhombic wire loop is a suitable inducer for developing linear flexible arrays for the ACFM inspection of large surfaces of ferrous and nonferrous metals. This paper introduces an analysis technique for the evaluation of the interaction of the field of the rhombic inducer carrying a high-frequency current, with long surface cracks of uniform depth in flat metal plates. The technique is accurate and very efficient computationally. It uses the two-dimensional Fourier transform together with a special boundary condition at the metal surface. The boundary condition takes into account the thin-skin nature of the eddy current in the metal as well as the flux leakage at the crack mouth. The analysis technique benefits from the use of scalar potential functions and can be extended to simply or multiply connected wire loops. Also, it is applicable to high-frequency (thin-skin) eddy current problems. Using the analysis technique, the tangential field below a rhombic inducer along its long diagonal when the inducer is located above the surface of aluminum and steel is given in the presence and absence of a crack. This field was found to have a nonuniform phase distribution. Near a crack, the phase change is significant, even for shallow cracks. The role of the nonuniform phase in the detection sensitivity is addressed. Also, simulated ACFM crack responses using an inducer with a linear probe attached along the long diagonal are presented and discussed. To support the validity of the analysis technique, experimental results obtained for some of the simulations are also reported. In addition to its application in predicting crack responses, the technique can be used for model-based inversion of crack signals.