Perturbation technique for the finite element modelling of differential probes in non-destructive eddy-current testing

The paper deals with a new finite element scheme for non-destructive eddy-current testing (ECT) problems involving multiply connected test pieces and differential probes. It concerns a perturbation technique applied to the magnetodynamic h - phi formulation. The unperturbed field (in the absence of the flaw) is conventionally computed in the complete domain. The source of the perturbation problem is then determined by the projection of the unperturbed field in a relatively small region around the defect, the optimum size of which depends on the working frequency. The discretisation of this reduced domain is well adapted to the size of the defect and chosen independently of the dimensions of the excitation probe and the specimen under study. At a discrete level, the voltage change is efficiently computed by integration only over the defect and a layer of elements in the reduced domain that touches the defect's boundary. The accuracy of the proposed perturbation model is illustrated by comparison of the results obtained for different dimensions of the reduced domain with those achieved in the conventional way. The considered test case involves a differential probe scanning the outer surface of a metal tube for the detection of through-wall cracks.