Dual Element Transducer Approach for Second Harmonic Generation and Material Nonlinearity Measurement of Solids in the P
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Dual Element Transducer Approach for Second Harmonic Generation and Material Nonlinearity Measurement of Solids in the Pulse‑Echo Method Sungjong Cho1 · Hyunjo Jeong1 · Shuzeng Zhang2 · Xiongbing Li2 Received: 7 January 2020 / Accepted: 4 August 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract A planar stress-free boundary is known to destructively alter the nonlinear wave generation process including the second harmonic component. This is the reason why the harmonic generation measurements in the study of nonlinear fluids and solids have been limited to the through-transmission setup. Recently, we have found through acoustic modeling and simulation that a dual element transducer composed of the annular ring emitter and the inner disk receiver improves the second harmonic generation in the pulse-echo mode with the stress-free boundary. This paper utilizes a dual element transducer for nonlinearity parameter (β) measurements of solid specimens in the pulse-echo testing configuration. The theoretical derivation provides the received beam fields and the formula for β determination with all necessary corrections incorporating diffraction, attenuation and boundary reflection. The dual element transducer is applied to pulse-echo β measurements of aluminum alloy samples, and the results are found to be in good agreement with the through-transmission method. Keywords Material nonlinearity · Harmonic generation · Pulse-echo testing · Stress-free boundary · Dual element transducer · Total correction
1 Introduction The acoustic nonlinearity parameter becomes a powerful tool in the nondestructive evaluation toolbox as a measure of material nonlinearity and damage state in structural components [1]. This parameter can quantitatively be obtained by harmonic generation measurements. The most commonly used technique is the finite amplitude method, in which a high power wave of a monochromatic frequency propagates through a nonlinear solid medium introduces distortions, resulting in the generation of higher harmonics. Finite amplitude technique requires the knowledge of absolute displacement of the fundamental and second harmonic waves to calculate the nonlinearity parameter (β).
* Hyunjo Jeong [email protected] 1
Department of Mechanical Engineering, Wonkwang University, Iksan, Jeonbuk 54538, Republic of Korea
School of Traffic and Transportation Engineering, Central South University, Changsha 410075, Hunan, China
2
Harmonic generation measurements for β determination can be conducted using multiple wave types, different generation and detection methods, and a variety of experimental set-ups [2]. The practical implementation of the measurement technique has been limited to the through-transmission setup for determining the nonlinearity parameter (β) of longitudinal elastic waves propagating in solids [3–6]. For practical applications, pulse echo measurement techniques that enable single-sided access to test components are more desirable. When using second harmonic waves reflected f
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