Ultrasonic inspection of steam-generator tube axial cracking using Lamb wave

Abstract

In this study, the interaction of Lamb wave propagating thin tube structure with finite vertical discontinuity was studied using both modal decomposition method (MDM) and experimental method. For MDM, a global matrix formulation and orthogonality of Lamb mode was employed to describe the boundary condition of finite vertical discontinuity of the tube and the mode conversion phenomenon respectively. The final form of governing equation by MDM was a linear matrix equation which could be solved using a simple matrix identity. The calculation result showed that, below the cut-off frequency, reflection amplitudes of both A0 and S0 Lamb mode increase as the depth of discontinuity increased beyond the threshold value. An experimental investigation was performed using a Hertzian-contact transducer and steam-generator tubes to verify the calculation results by MDM. A0 Lamb mode was selected as a test signal considering the characteristics of the transducer and previous studies. The experiment for mode identification using half-sectioned tube verified that the Hertzian-contact transducer effectively generated A0 Lamb mode. Tests performed using steam-generator tubes with EDM (electric discharge machined) axial notches showed that the deeper notches produced the higher reflection echo. A0 Lamb mode interacted with the notch having a depth larger than 1/40 of wave length, or corresponding to 30% of the wall thickness. This finding was in good agreement with previous studies and the prediction by MDM. The experiment using real crack specimens to estimate the deviation of reflection amplitude showed that the reflection cross-section of real crack was very similar with that of EDM notch. Therefore, specimens with EDM notches can be used as reference blocks for Lamb wave UT calibration.