Analysis technique for interaction of rectangular open-ended waveguides with surface cracks of arbitrary shape in metals

The use of microwave technique has proved to be a viable means for crack detection and sizing surface cracks in metals. In this technique, the surface of the specimen is interrogated with a radiating open-ended waveguide probe and a crack is assumed to be a simple short-circuited rectangular waveguide, causing peturbations in the probe reflection coefficient. Since the growth of fatigue in metals is a stochastic process, the cracks do not have a constant predetermined shape. We describe a new formulation to model the problem of an open-ended waveguide probe radiating into a conducting metal with a surface-breaking crack of arbitrary shape. In this formulation, the crack is first modeled by an appropriate number of short rectangular waveguides. The generalized scattering matrix technique is then used to calculate the scattering matrix of the new segmented waveguide structure. The probe reflection coefficient of the dominant mode, TE₁₀, is finally calculated for various positions of the crack in order to predict the probe output signal. To demonstrate the accuracy of the model, we consider two special cases of a long and an elliptical-shape cracks. The comparison of our results with those available in the literature substantiates the model introduced in this paper. To further validate the model, we present results associated with a fatigue crack of complex geometry which are compared with those obtained using a finite element code.