Propagation of Non-Linear Lamb Waves in Adhesive Joint with Micro-Cracks Distributing Randomly

Abstract

With the advantages of uniform stress transfer and weight reduction, adhesive joints are widely used in engineering. The propagation of non-linear Lamb waves in an adhesive joint with micro-cracks distributing in a random way is systematically investigated by using the numerical simulation method in this paper. A finite element model of the tri-layer adhesive structure with micro-cracks distributing randomly is established, and the Lamb wave mode pair with a matching condition of the phase velocity is chosen to examine the interaction of the micro-cracks with Lamb waves. The results show that the micro-cracks within the adhesive layer will lead to the generation of second harmonics. We also find that the Acoustic Non-linearity Parameters (ANP) increase with the propagation distance in the micro-crack damage zone and the density of the micro-cracks. However, ANPs are less concerned with the friction coefficients of the surface of micro-cracks. This numerical research reveals that non-linear Lamb waves can be employed to effectively characterize the micro-cracks related damages within an adhesive joint.

Advances in nonlinear ultrasonic detection of microcracks

“…数相关性不大。 类似地， Li 等人 [66] 研究了三层胶粘结构中粘接层随机分布微裂纹对非线性 Lamb 波传播的影响，粘接层微裂纹会生成 Lamb 波二次谐波，且非线性参量随微裂纹区域大小和微 裂纹密度的增加而增加。对于非线性 Lamb 波混频响应，Yin 等人 [67] 研究发现，板中随机分布 微裂纹可以生成 Lamb 波和频和差频信号。非线性参量对微裂纹密度有很强的依赖性，当密度 不变时，非线性参量随微裂纹区域的增大呈线性增加。 (4)方向 在二次谐波方面，Yang 等人 [50] 对不同裂纹长度的疲劳裂纹产生 Lamb 波二次谐波的方向性 开展了仿真研究，如图 5 所示。研究发现，疲劳裂纹产生的二次谐波主要分布在裂纹前向和后 向的散射方向， 且仅前向散射方向的二次谐波幅值随裂纹长度的增大而单调增大。Wang 等人 [68] 研究了横波与微裂纹相互作用生成二次谐波的方向性，结果表明，二次谐波的方向性随微裂纹 取向角的变化而变化。在非线性混频方面，Lv 等人 [69] 数值分析了两列横波和裂纹之间的非共线 混频作用，结果表明，生成最大混频纵波幅值对应的两列横波相互作用角与裂纹的方向相关。 Lv 等人 [70] 分析了两列 A0 模式 Lamb 波与微裂纹的非线性混频作用，结果表明，两列 A0 模式 Lamb 波与微裂纹相互作用产生了透射和反射和频 S0 模式 Lamb 波， 两种和频 S0 模式 Lamb 波 的传播方向随微裂纹方向的变化呈现不同的趋势：透射和频的传播方向角与微裂纹的取向基本 一致，而反射和频的传播方向角则随微裂纹的取向线性增加。 图 5 疲劳裂纹归一化非线性参量的方向性 [50] Figure 5 Directivity pattern of normalized nonlinear parameters for fatigue cracks [50] 此外，关于接触压力对裂纹非线性的影响也有报道 [71][72][73] 。Yang 等人 [71] 研究了拉伸载荷作用 下裂纹面张开对不同长度疲劳裂纹非线性响应的影响，结果表明，施加在板上的载荷能明显改 变裂纹的非线性响应。Saidoun 等人 [72,73] 分析了纵波与单向接触界面的相互作用，建立了界面接 触压力与生成二次谐波的对应关系，结果表明，随着界面接触压力的增加，二次谐波先增加后 减小。 A c c e p t e d https://engine.scichina.com/doi/10.1360/TB-2021-0798…”

Mathematical Modeling and Computer-Aided Simulation of the Acoustic Response for Cracked Steel Specimens

“…Studies employing finite element model simulations of a structure with micro-cracks study the interaction of the microcracks with Lamb waves. The results indicate that the micro-cracks lead to the generation of second harmonics [44]. For internal defect detection, some studies extract and combine spatial and temporal features to estimate the physical properties such as Young's modulus [45].…”

Detection of Micro-Cracks in Metals Using Modulation of PZT-Induced Lamb Waves

“…Guan et al numerically identified the direction of the micro-crack with the change of nonlinearity parameter [ 31 ]. Li et al numerically investigated the second harmonic amount change from the Lamb wave passing through a micro-crack in the adhesive layer [ 32 ].…”