Wujun Zhu

Generation of cumulative second-harmonic ultrasonic guided waves with group velocity mismatching: Numerical analysis and experimental validation

The generation of second-harmonic Lamb waves in a homogeneous, isotropic, stress-free elastic plate is analytically and experimentally investigated. The numerical analyses show that whether the matching condition of the group velocity is satisfied or not, the integrated amplitude of a second-harmonic Lamb wave accumulates with the propagation distance when both the finite duration of the primary Lamb wave tone burst and the phase velocity matching are given. The theoretical analyses are validated by experimental measurements of an aluminium plate. Our conclusions are different from those of the previous works that reported that the group velocity matching is required for the generation of the cumulative second-harmonic Lamb waves with the finite duration of tone bursts.

Lamb Wave-Based Structural Health Monitoring on Composite Bolted Joints under Tensile Load

Online and offline monitoring of composite bolted joints under tensile load were investigated using piezoelectric transducers. The relationships between Lamb wave signals, pre-tightening force, the applied tensile load, as well as the failure modes were investigated. Results indicated that S0/A0 wave amplitudes decrease with the increasing of load. Relationships between damage features and S0/A0 mode were built based on the finite element (FE) simulation and experimental results. The possibility of application of Lamb wave-based structure health monitoring in bolted joint-like composite structures was thus achieved.

Modeling of ultrasonic nonlinearities for dislocation evolution in plastically deformed materials: Simulation and experimental validation

A nonlinear constitutive relationship was established to investigate nonlinear behaviors of ultrasonic wave propagation in plastically damaged media based on analyses of mixed dislocation evolution. Finite element simulations of longitudinal wave propagation in plastically deformed martensite stainless steel were performed based on the proposed nonlinear constitutive relationship, in which the contribution of mixed dislocation to acoustic nonlinearity was considered. The simulated results were validated by experimental measurements of plastically deformed 30Cr2Ni4MoV martensite stainless steels. Simulated and experimental results both reveal a monotonically increasing tendency of the normalized acoustic nonlinearity parameter as a function of plastic strain. Microscopic studies revealed that the changes of the acoustic nonlinearity are mainly attributed to dislocation evolutions, such as dislocation density, dislocation length, and the type and fraction of dislocations during plastic loading.

Second Harmonic Generation of Lamb Wave in Numerical Perspective

The influences of phase and group velocity matching on cumulative second harmonic generation of Lamb waves are investigated in numerical perspective. Finite element simulations of nonlinear Lamb wave propagation are performed for Lamb wave mode pairs with exact and approximate phase velocity matching, with and without group velocity matching, respectively. The evolution of time-domain second harmonic Lamb waves is analyzed with the propagation distance. The amplitudes of primary and second harmonic waves are calculated to characterize the acoustic nonlinearity. The results verify that phase velocity matching is necessary for generation of the cumulative second harmonic Lamb wave in numerical perspective, while group velocity matching is demonstrated to not be a necessary condition.

Numerical Perspective of Second-Harmonic Generation of Circumferential Guided Wave Propagation in a Circular Tube*

The effect of second-harmonic generation (SHG) by primary (fundamental) circumferential guided wave (CGW) propagation is investigated from a numerical standpoint. To enable that the second harmonic of the primary CGW mode can accumulate along the circumferential direction, an appropriate mode pair of primary and double frequency CGWs is chosen. Finite element simulations and evaluations of nonlinear CGW propagation are analyzed for the selected CGW mode pair. The numerical simulations performed directly demonstrate that the response of SHG is completely generated by the desired primary CGW mode that satisfies the condition of phase velocity matching at a specific driving frequency, and that the second harmonic of the primary CGW mode does have a cumulative effect with circumferential angles. The numerical perspective obtained yields an insight into the complicated physical process of SHG of primary CGW propagation unavailable previously.

A feasibility study on fatigue damage evaluation using nonlinear Lamb waves with group-velocity mismatching

HighlightsFatigue damage evaluation is verified by mode pairs with group‐velocity mismatching.A parameter is proposed to quantify the cumulative efficiency of SHG.The proposed parameter is validated in both experiments and simulations.Mode pair S3‐s6 is demonstrated to be sensitive to material damage evolution. ABSTRACT The feasibility of fatigue damage evaluation has been investigated using nonlinear Lamb waves with group‐velocity mismatching. To choose an efficient mode pair, a parameter is proposed to quantify the efficiency of cumulative second‐harmonic generation (SHG) of Lamb waves based on the normal modal analysis. Experiments and simulations are performed to verify the proposed parameter, which demonstrates that whether the matching condition of group velocity is satisfied or not, the efficiency of cumulative SHG increases with the order of Lamb mode for the five low‐order Lamb waves investigated. Then, S3‐s6 mode pair with group‐velocity mismatching is chosen to characterize the fatigue damage of an aluminium alloy for the high efficiency of cumulative SHG. Results show that S3‐s6 mode pair is sensitive to fatigue damage evolution and the integrated amplitude of second harmonics increases by nearly 300% with fatigue cycles. Nonlinear Lamb waves with group‐velocity mismatching are validated to be a candidate to efficiently evaluate the fatigue damage.

Fatigue Damage Evaluation Using Nonlinear Lamb Waves with Quasi Phase-Velocity Matching at Low Frequency

Due to the dispersive and multimode natures, only nonlinear Lamb waves with exact phase-velocity matching were generally used in previous studies to evaluate the evenly distributed microstructural evolution in the incipient stage of material degradation, because of the cumulative generation of second harmonics, which was also found within a significant propagation distance for mode pair S0-s0 with quasi phase-velocity matching at low frequency. To explore the feasibility of fatigue damage evaluation by using this mode pair and fully utilize its unique merits, the cumulative second harmonic analysis was performed on aluminum alloy specimens with various material damage produced by the continuous low cycle fatigue tests. Similar to mode pair S1-s2 with exact phase-velocity matching, a mountain shape curve between the normalized acoustic nonlinearity parameter and the fatigue life was also achieved with the peak point at about 0.65 fatigue life for mode pair S0-s0, even though a relatively higher sensitivity to fatigue damage was observed for mode pair S1-s2. The excited frequency selection was further analyzed in a certain frequency range, where the quasi phase-velocity matching condition was satisfied for mode pair S0-s0 owing to the less dispersive property. Results show that the fatigue damage can be effectively detected using the mode pair S0-s0, and a relatively lower excited frequency was preferred due to its higher sensitivity to microstructural evolution.

Symmetry properties of second harmonics generated by antisymmetric Lamb waves

Symmetry properties of second harmonics generated by antisymmetric primary Lamb waves are systematically studied in this work. In theory, the acoustic field of second harmonic Lamb waves is obtained by using the perturbation approximation and normal modal method, and the energy flux transfer from the primary Lamb waves to second harmonics is mainly explored. Symmetry analyses indicate that either the symmetric or antisymmetric Lamb waves can merely generate the symmetric second harmonics. Finite element simulations are performed on the nonlinear Lamb wave propagation of the antisymmetric A0 mode in the low frequency region. The signals of the second harmonics and the symmetric second harmonic s0 mode are found to be exactly equivalent in the time domain. The relative acoustic nonlinearity parameter A2/A12 oscillates with the propagation distance, and the oscillation amplitude and spatial period are well consistent with the theoretical prediction of the A0-s0 mode pair, which means that only the second har...

Numerical and experimental investigations of nonlinear S0 Lamb mode for detection of fatigue damage

Nonlinear Lamb wave has been widely acknowledged as an efficient nondestructive method for evaluating early stage of fatigue damage. The previous studies focused on the evaluation of fatigue damage using the particular mode pairs, such as S1-S2 mode pair. Recently, the nonlinear S0 Lamb mode with low-frequency was considered for its unique features of less dispersion and easy to be generated, and was indicated may as sensitive to fatigue damage as other mode pairs reported before. However, few researches were performed on experimental measurement. In this work, the S0 mode is demonstrated as an alternative for fatigue damage evaluation.

Experimental and numerical studies of nonlinear ultrasonic responses on plastic deformation in weld joints

The experimental measurements and numerical simulations are performed to study ultrasonic nonlinear responses from the plastic deformation in weld joints. The ultrasonic nonlinear signals are measured in the plastic deformed 30Cr2Ni4MoV specimens, and the results show that the nonlinear parameter monotonically increases with the plastic strain, and that the variation of nonlinear parameter in the weld region is maximal compared with those in the heat-affected zone and base regions. Microscopic images relating to the microstructure evolution of the weld region are studied to reveal that the change of nonlinear parameter is mainly attributed to dislocation evolutions in the process of plastic deformation loading. Meanwhile, the finite element model is developed to investigate nonlinear behaviors of ultrasonic waves propagating in a plastic deformed material based on the nonlinear stress–strain constitutive relationship in a medium. Moreover, a pinned string model is adopted to simulate dislocation evolution during plastic damages. The simulation and experimental results show that they are in good consistency with each other, and reveal a rising acoustic nonlinearity due to the variations of dislocation length and density and the resulting stress concentration.