Determination of third-order elastic constants using change of cross-sectional resonance frequencies by acoustoelastic effect

Abstract

This investigation presents a new measurement technique for third-order elastic constants using the acoustoelastic effect. The cross-sectional resonance frequencies of a cylindrical rod are measured while the rod is stressed under tensional load. The Murnaghan's third-order elastic constants of the rod are determined by matching experimentally obtained resonance frequencies with those numerically obtained by a finite element model. Electromagnetic acoustic transducers (EMATs) are employed to measure cross-sectional resonance frequencies, enhancing the repeatability to minimize the variation of the contact condition between the transducer and the specimen. The present method was applied to specimens made of carbon steel (JIS-S20C) and aluminum (Al7075-T651), whose third-order elastic constants were calculated. It should be emphasized that the estimated Murnaghan's constants obtained by the proposed method showed very small coefficients of variation (CVs), less than 6.54%, for repeated tests conducted on several specimens, showing excellent repeatability and reproducibility that is almost unattainable by conventional methods using wave speeds or higher harmonics of an input wave.

Distinctive trembling features following resonance peaks at zero group velocity frequencies in harmonic analysis

“…Considering the peculiarity of ZGV modes, the actuation, measurement, and extraction of ZGV modes are therefore of great significance. Various sensors have been utilized for the excitation and measurement of ZGV resonances, classified as contact and noncontact approaches, and encompassing PVDF-based transducers [10], EMAT [11], accelerometer/microphone [12], air-coupled transducers [13], laser interferometers [9], interdigital transducer (IDT) [14], and laser doppler vibrometers [15]. To name a few, Zhu et al exploited piezoelectrical wafer active sensors (PWAS) to selectively actuate ZGV resonances and utilized Physical Acoustics NANO-30 sensor to measure temporal vibration signals at different locations [7].…”

“…The exploitation of ZGV resonances enabled the non-contact evaluation of the deposited thin layer thickness by the shift of resonance frequency [33]. The potential application of ZGV modes for material properties determination were demonstrated, encompassing elastic constant [11], Poisson's ratio [34], interfacial stiffness [24], and bulk acoustic wave velocity [16]. Regarding various damage types, the characterization of progressive fatigue damage in solid plates was proposed utilizing a monotonous increasing relation between the ZGV mode frequency and fatigue loading cycles [27].…”