Since the identification of micro-cracks in engineering materials is very valuable in understanding the initial and slight changes in mechanical properties of materials under complex working environments, numerical simulations on the propagation of the low frequency S Lamb wave in thin plates with randomly distributed micro-cracks were performed to study the behavior of nonlinear Lamb waves. The results showed that while the influence of the randomly distributed micro-cracks on the phase velocity of the low frequency S fundamental waves could be neglected, significant ultrasonic nonlinear effects caused by the randomly distributed micro-cracks was discovered, which mainly presented as a second harmonic generation. By using a Monte Carlo simulation method, we found that the acoustic nonlinear parameter increased linearly with the micro-crack density and the size of micro-crack zone, and it was also related to the excitation frequency and friction coefficient of the micro-crack surfaces. In addition, it was found that the nonlinear effect of waves reflected by the micro-cracks was more noticeable than that of the transmitted waves. This study theoretically reveals that the low frequency S mode of Lamb waves can be used as the fundamental waves to quantitatively identify micro-cracks in thin plates.
This paper develops micromechanics models to estimate the tensile and compressive elastic moduli of elastic solids containing randomly distributed penny-shaped microcracks. The crack faces are open under tension and closed under compression. When the crack faces are closed, they may slide against one another following Coulomb's law of dry friction. The micromechanics models provide analytical expressions of the tensile and compressive moduli for both static and dynamic cases. It is found that the tensile and compressive moduli are different. Further, under dynamic loading, both compressive and tensile moduli are frequency dependent. As a by-product, the micromechanics models also predict wave attenuation in the dynamic case. Numerical simulations using the finite element method are conducted to validate the micromechanics models.
A non-collinear mixing technique to measure the acoustic nonlinearity parameter of an adhesive bond from one side of the sample AIP Conference Proceedings 1806, 020011 (2017) Corresponding author: now with Tufts University, jianmin.qu@tufts.eduAbstract. As a longitudinal wave propagates through a linearly elastic solid with distributed cracks, the solid is subjected to cyclic tension and compression. During the tensile cycles, a crack might be open and its faces are traction-free. During the compressive cycles, a crack might be closed and its faces are in contact. Such contact may also be frictional because of crack face roughness. Such tension and compression asymmetry causes acoustic nonlinearity. This paper develops a micromechanics model that relates the crack density to the acoustic nonlinearity parameter. The model is based on a micromechanics homogenization of the cracked solid under dynamic loading. It is shown that the acoustic nonlinearity parameter is proportional to the crack density. Furthermore, the acoustic nonlinearity parameter also depends on the frequency of the wave motion, and the coefficient of friction of the crack faces. Unlike the second harmonic generated by dislocations, the amplitude of the second harmonic due to crack face contact is proportional to the amplitude of the fundamental frequency. To validate the micromechanics model, the finite element method is used to simulate wave propagation in solid with randomly distributed microcracks. The micromechanics model predictions agree well with the finite element simulation results.
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