Keywords: 
• 微裂纹 /
• 超声波 /
• 等效弹性模量 /
• 多阶段

Abstract: A multi-stage model of nonlinear interaction between micro-crack and ultrasound based on equivalent elastic modu-lus is presented in this paper. In this model, the interface characteristics of micro-cracks at a micro-level and the relative motion at a macro-level are unified into an elastic modulus of the mesoscopic element. The equivalent elastic modulus is usedtocharacterizethe"stress-strain"ofthedamageregion.Thenpiecewisefunctionisusedto describethenonlinear interaction between ultrasound and micro-crack. Finally, the wave equation is solved by the finite element simulation. In this manner, the nonlinear interaction law between ultrasound and micro-crack is obtained, and the validity of the model is verified. The simulation results also show that compared with bilinear stiffness model and contact surface model, the multi-stage model can well reflect the distortion of the waveform in one period of ultrasonic wave passing through the micro-crack. In addition, the influences of the crack angle, the crack length and the input amplitude on the second harmonics generation and the third harmonics generation are analyzed. In the end, the comparison and analysis of the experimental test and simulation calculations based on the proposed multi-stage model show that the proposed multi-stage model and the experimental test can well reflect the second harmonic signal produced by the nonlinear in-teraction of micro-crack and ultrasound, and the second harmonic amplitudes of the experimental test are basically the sameasthesimulationcalculationsbasedontheproposedmulti-stagemodel.Thus,theeffectivenessofthe proposed multi-stagemodelisverified. Themodelprovidesanewsimulationmethodtoquantitativelydetectthemicro-crackby ultrasonic nonlinear effect.