基于等效弹性模量的微裂纹-超声波非线性作用多阶段模型

Modelling of multi-stage nonlinear interaction of micro-crack and ultrasonic based on equivalent elastic modulus

提出了一种基于等效弹性模量的微裂纹-超声波非线性作用多阶段模型.该模型将微裂纹微观层面的界面几何特征和宏观层面的界面相对运动统一为介观单元弹性模量的变化,利用等效弹性模量表征损伤区域的"应力-应变",然后利用分段函数来描述微裂纹-超声波非线性相互作用,最后通过有限元仿真对波动方程进行求解,验证了模型的有效性,获得了超声波在经过微裂纹后传播的非线性波动规律.仿真结果表明本文提出的模型相比于双线性刚度模型、接触面模型,能更好地体现一个谐波周期内超声波经过微裂纹损伤区域时波形会发生畸变.同时,仿真实验还分析了裂纹倾角、裂纹长度和超声波激励幅值对超声波经过微裂纹后产生的二次和三次谐波的幅值的影响.最后,对比分析了该模型的仿真计算结果与实验测试结果,表明本文提出的多阶段模型与实验测试均能较好地体现微裂纹-超声波非线性作用产生的二次谐波信号,且结果基本一致,验证了模型的有效性.该模型为开展超声波非线性效应定量检测微裂纹提供了一种新的仿真手段.

A multi-stage model of nonlinear interaction between micro-crack and ultrasound based on equivalent elastic modulus 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 used to characterize the ＂stress-strain＂ of the damage region. Then piecewise function is used to describe the nonlinear 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 interaction of micro-crack and ultrasound, and the second harmonic amplitudes of the experimental test are basically the same as the simulation calculations based on the proposed multi-stage model. Thus, the effectiveness of the proposed multi-stage model is verified. The model provides a new simulation method to quantitatively detect the micro-crack by ultrasonic nonlinear effect.