Low-Frequency Guided Wave Quantitative Reconstruction of Corrosion in Plates, 1D Diffraction Problem

Guided Wave Tomography is a nondestructive imaging technique that consists in inverting guided wave propagation data to localize defects. In particular, this technique should provide quantitative information about the corrosion state of metallic plates by reconstructing a thickness map from diffraction or time-of-flight measurements. In this paper we first present an analytical framework for corrosion profile reconstruction considering the 1D case. Due to the fact that, in practice, the low frequency ultrasound range (typically 50 to 100 kHz) is used for long range inspections, the first-order shear deformation approximation is relevant for plate thicknesses encountered in metallic structures. This leads to an analytical description of guided wave phenomena: diffraction, refraction and mode conversion, for 5 modes: A0, S0, SH0, A1 and SH1. The validity of an analytical approach to modeling thickness loss defects, in particular the validity of the first Born approximation, is discussed by comparing with elastodynamic numerical results. The comparison results show that the nonlinear behavior with depth increase, or width increase, of the defects (distortion) can be fully described using a multimodal high order Born series. Consequently, a consistent iterative inversion Born series based algorithm can be used to deal with the reconstruction of strong thickness losses.