Time of flight diffraction for rough planar defects

Ultrasonic non-destructive evaluation techniques, such as time-of-flight diffraction (ToFD) for which the arrival times of waves diffracted from crack tips are analysed to locate and size defects, are well understood for smooth defects. In environments where extreme changes in temperature and pressure occur, the damage that may arise is often non-uniform and more difficult to characterise when designing and qualifying an inspection. This article investigates the implementation of ToFD methods for sizing rough defects using a purely theoretical approach. High-fidelity finite element modelling and stochastic Monte Carlo methods are used to provide physical and statistical insights for the dependence on both incident beam angle and degree of roughness for the case of planar defects. Optimal incident angles for ultrasonic ToFD techniques were determined in the 1980s but largely based on theoretical and experimental investigations for smooth defects. However, rough defects produce tip-diffracted signatures that are more complicated than for their smooth counterparts, largely due to multiple scattering effects related to mode conversion and propagation of surface waves along the rough surface. It is shown that roughness may cause larger diffraction amplitude values at different angles, which leads to increased uncertainty when sizing, with illustrative examples and physical interpretations provided. Comparisons of amplitudes for smooth and rough defects of the same size are also demonstrated. The ToFD method, using envelope peak detection and autocorrelation approaches, is implemented to estimate the size of rough cracks, and the effects of roughness on the accuracy of this sizing are investigated with statistical analysis.