Abstract
The through-transmission (TT) method is mainly used to measure the amplitude of the second harmonic from which the acoustic nonlinear parameter is determined for early damage detection of materials. The pulse echo (PE) method, however, has been excluded from nonlinear studies of solid materials because the stress-free boundary suppresses the generation of second harmonics. It is more demanding to develop the PE method for practical applications and this paper considers a novel phase shift technique of annular array transducers to improve second harmonic generation (SHG) at the stress-free boundary. The fundamental and second harmonic fields after phase-shifted radiation are calculated, and their received amplitudes are investigated. The phase difference between the two second harmonic components after reflection from the stress-free boundary is analyzed to explain the enhanced SHG. The PE method with optimal phase shift can generate an improved second harmonic amplitude as high as about 45% of the TT method. Four element array transducers are also found to be more efficient in improved SHG than two element transducers.
Highlights
Ultrasonic nondestructive evaluation allows the detection of defects within a material or structure
This paper investigates the efficient second harmonic generation (SHG) from the stress-free boundary of a nonlinear solid by control of the transmission phase shift of array elements
We studied a novel phase shift technique to enhance SHG reflected at the stress−free boundaries of thin solid samples, using annular array transducers
Summary
Ultrasonic nondestructive evaluation allows the detection of defects within a material or structure. Measurements of conventional linear ultrasonic parameters, such as sound velocity, attenuation, and backscattering, are not sensitive to these inhomogeneities and do not provide quantitative information on material condition [2] Nonlinear acoustic methods, such as second harmonic generation (SHG) and measurement of acoustical nonlinear parameters, have proven useful for detecting these types of material defects [3,4,5]. When a sound beam radiates from annular array elements with different phase shifts, the fundamental and second harmonic waves, which are reflected from the rigid or stress-free boundary, are calculated in the pulse-echo setup and their characteristic behavior are examined based on the magnitude of received amplitudes. Optimal phase shifts for a given sample thickness and frequency are illustrated in terms of SHG and nonlinear parameter determination
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