Interfacial spring model for ultrasonic interactions with imperfect interfaces: Theory of oblique incidence and application to diffusion-bonded butt joints

Abstract

The quasi-static distributed spring model is used to derive the ultrasonic reflectivity of an imperfectly-bonded interface as a function of frequency and angle of incidence. The results are then incorporated in a model for the corner reflection from a diffusion-bonded joint between two abutting plates, the corner being defined by the bond plane and the common lower surface plane of the plates. An immersion-inspection geometry is assumed, and seven categories of corner reflections are identified and examined in detail. These fall into two classes: those having parallel incident and exiting rays in water (φ′=φ), and those having nonparallel water rays (φ′ ≠ φ). The φ′ = φ categories are suitable for single probe (pulse-echo) inspections of the joint. Based on the amplitude of the outgoing corner-reflected signal, two φ = φ′ geometries appear promising. These employ, respectively, a corner reflection involving only longitudinal waves with the interface illuminated at near-grazing incidence (LLL), and a corner reflection involving only transverse waves with the interface illuminated at near 45° incidence (TTT). In addition, two practical φ′ ≠ φ geometries are indicated; these both involve mode conversion upon reflection from the interface, with the incident or outgoing longitudinal wave traveling nearly parallel to the interface. Model predictions for LLL and TTT reflections are compared to measurements on diffusion-bonded Inconel specimens, and techniques for applying the model results to more complicated bond geometries are discussed.