Quantitative simulation of ultrasonic time of flight diffraction technique in 2D geometries using Huygens–Fresnel diffraction model: Theory and experimental comparison

Abstract

This article presents an analytical approach for simulation of ultrasonic diffracted wave signals from cracks in two-dimensional geometries based on a novel Huygens–Fresnel Diffraction Model (HFDM). The model employs the frequency domain far-field displacement expressions derived by Miller and Pursey in 2D for a line source located on the free surface boundary of a semi-infinite elastic medium. At each frequency in the bandwidth of a pulsed excitation, the complex diffracted field is obtained by summation of displacements due to the unblocked virtual sources located in the section containing a vertical crack. The time-domain diffracted wave signal amplitudes in a general isotropic solid are obtained by standard Fast Fourier Transform (FFT) procedures. The wedge based finite aperture transducer refracted beam profiles were modelled by treating the finite dimension transducer as an array of line sources. The proposed model is able to evaluate back-wall signal amplitude and lateral wave signal amplitude, quantitatively. The model predicted range-dependent diffracted amplitudes from the edge of a bottom surface-breaking crack in the isotropic steel specimen were compared with Geometrical Theory of Diffraction (GTD) results. The good agreement confirms the validity of the HFDM method. The simulated ultrasonic time-of-flight diffraction (TOFD) A-scan signals for surface-breaking crack lengths 2mm and 4mm in a 10mm thick aluminium specimen were compared quantitatively with the experimental results. Finally, important applications of HFDM method to the ultrasonic quantitative non-destructive evaluation are discussed.