Finite Element Simulation of Nonlinear Acoustic Behavior at Minute Cracks Using Singular Element

Abstract

A finite element method (FEM) simulation of wave propagation is performed for a model plate which includes minute cracks nucleated by spallation. The minute cracks are modeled by singular elements which express nonlinear stress-strain at the crack surfaces. The transmitted wave through these cracks is simulated and the 2nd harmonic amplitude is processed by fast fourier transform (FFT). The ratio of the 2nd harmonic component to the fundamental one increases with an increase in the incident wave of amplitude for the incident wave of amplitude 5-20 nm. The simulated results qualitatively confirm the measured nonlinear acoustic response on spalled samples.

Finite element modeling of heating phenomena of cracks excited by high-intensity ultrasonic pulses

“…It can be seen that the force spectrum also consists principally of 20 kHz and its harmonics. However, owing to the contact interaction (contact nonlinearity) of both crack faces, [20,21] the amplitude ratio between the harmonics and the fundamental component becomes larger compared with that in Fig. 3(b).…”

Advances in nonlinear ultrasonic detection of microcracks

“…波混频的数值模拟均表明：非线性参量随微裂纹长度单调增加，随微裂纹宽度单调减小 [48,[57][58][59][60][61] ， 如图 4(a)和(b)。 Hirata 等人 [57] 和 Okada 等人 [58] 分别采用有限元模型和奇异单元模型模拟微裂纹与 体波的非线性相互作用，结果表明，裂纹越长、裂纹宽度越小，高次谐波幅值越大。Wan 等人 [59] 和 Xie 等人 [48] 针对金属材料和骨材料中的微裂纹开展了 Lamb 波二次谐波数值模拟研究。Jiao 等 人 [60] 和 Aslam 等人 [61] 分别采用 Lamb 波同向和对向混频信号表征了不同长度和宽度的微裂纹。 Lamb 波二次谐波和混频信号幅值随微裂纹长度和宽度的变化趋势与体波高次谐波一致。Wang 等人 [46] 进一步研究表明，Lamb 波传播方向与裂纹的夹角和激励信号周期数可以有效影响非线性 参量随裂纹长度的增加速率。 此外， 针对微裂纹引起的非线性信号弱、 易被背景噪声掩盖等问题，…”

Detection and Imaging of Nonmetallic Inclusions in Continuously Cast Steel Plates by Higher Harmonics

“…Higher harmonics are measured in every measurement configuration by using a longitudinal, transverse, or surface wave. The higher harmonic amplitude excited at the solid interface is less than 1% of the fundamental wave amplitude; 8,9) however, we can easily extract higher harmonics by using band-pass or high-pass filters. In contrast, subharmonics are excited only at a particular measurement configuration.…”