Appraising a stationary phase-based diffraction theory for elastic wave diffraction from three-dimensional rough crack edges

Surface roughness of crack-like defects strongly influences ultrasonic edge diffraction, thereby affecting defect detectability and characterization in ultrasonic nondestructive evaluation. Although most existing studies have focused on two-dimensional cracks where the edge reduces to a point, the more complex case of three-dimensional (3D) rough-crack edges has rarely been addressed. This work extends a previously proposed stationary phase-based theory of diffraction (SPTD), originally validated for smooth-surface cracks, to 3D rough cracks and evaluates its region of validity using high-fidelity finite element-boundary integral (FEBI) simulations combined with Monte Carlo analyses. A general SPTD formulation is derived to incorporate both surface roughness and in-plane crack-edge perturbations. Ensembles of rough-crack models with varying roughness levels are generated, and their edge diffractions are analyzed using both FEBI and SPTD. The results establish the validity region of SPTD with respect to roughness parameters and incident angles. The distinct effects of surface-height gradients and in-plane edge perturbations are clarified, showing that they modify the diffracted field in different ways. Near-surface head and Rayleigh waves are further identified as key mechanisms limiting SPTD applicability. In summary, this study extends SPTD to realistic 3D rough-crack edges, providing an efficient framework for ultrasonic diffraction prediction in defect characterization.