Characterizing open and non-uniform vertical heat sources: towards the identification of real vertical cracks in vibrothermography experiments

摘要

Lock-in vibrothermography is used to characterize vertical kissing and open cracks in metals. In this technique the crack heats up during ultrasound excitation due mainly to friction between the defect's faces. We have solved the inverse problem, consisting in determining the heat source distribution produced at cracks under amplitude modulated ultrasound excitation, which is an ill-posed inverse problem. As a consequence the minimization of the residual is unstable. We have stabilized the algorithm introducing a penalty term based on Total Variation functional. In the inversion, we combine amplitude and phase surface temperature data obtained at several modulation frequencies. Inversions of synthetic data with added noise indicate that compact heat sources are characterized accurately and that the particular upper contours can be retrieved for shallow heat sources. The overall shape of open and homogeneous semicircular strip-shaped heat sources representing open half-penny cracks can also be retrieved but the reconstruction of the deeper end of the heat source loses contrast. Angle-, radius- and depth-dependent inhomogeneous heat flux distributions within these semicircular strips can also be qualitatively characterized. Reconstructions of experimental data taken on samples containing calibrated heat sources confirm the predictions from reconstructions of synthetic data. We also present inversions of experimental data obtained from a real welded Inconel 718 specimen. The results are in good qualitative agreement with the results of liquids penetrants testing.