Modelling nonlinearity of guided ultrasonic waves in fatigued materials using a nonlinear local interaction simulation approach and a spring model

The Study of Localized Crack-Induced Effects of Nonlinear Vibro-Acoustic Modulation

The nonlinear interaction of longitudinal vibration and ultrasound in beams with cracks is investigated. The central focus is on the localization effect of this interaction, i.e., the locally enhanced nonlinear vibro-acoustic modulation. Both numerical and experimental investigations are undertaken. The finite element (FE) method is used to investigate different crack models, including the bi-linear crack, open crack, and breathing crack. A parametric study is performed considering different crack depths, locations, and boundary conditions in a two-dimensional beam model. The study shows that observed nonlinearities (i.e., nonlinear crack-wave modulations) are particularly strong in the vicinity of the crack, allowing not only for crack localization but also for the separation of the crack-induced nonlinearity from other sources of nonlinearity.

Mechanic-Electric-Thermal Directly Coupling Simulation Method of Lamb Wave under Temperature Effect

Lamb Wave (LW)-based structural health monitoring method is promising, but its main obstacle is damage assessment in varying environments. LW simulation based on piezoelectric transducers (referred to as PZTs) is an efficient and low-cost method. This paper proposes a multiphysics simulation method of LW propagation with the PZTs under temperature effect. The effect of temperature on LW propagation is considered from two aspects. On the one hand, temperature affects the material parameters of the structure, the adhesive layers and the PZTs. On the other hand, it is considered that the thermal stress caused by the inconsistency of thermal expansion coefficients among the structure, the adhesive layers, and the PZTs affect the piezoelectric constant of the PZTs. Based on the COMSOL Multiphysics, the mechanic-electric-thermal directly coupling simulation model under temperature effect is established. The simulation model consists of two steps. In the first step, the thermal-mechanic coupling is carried out to calculate the thermal stress, and the thermal stress effect is introduced into the piezoelectric constant model. In the second step, mechanic-electric coupling is carried out to simulate LW propagation, which considers the piezoelectric effect of the PZTs for the LW excitation and reception. The simulation results at -20 °C to 60 °C are obtained and compared to the experiment. The results show that the A₀ and S₀ mode of simulation signals match well with the experimental measurements. Additionally, the effect of temperature on LW propagation is consistent between simulation and experiment; that is, the amplitude increases, and the phase velocity decreases with the increment of temperature.

Advanced numerical simulations considering crack orientation for fatigue damage quantification using nonlinear guided waves

A numerical study including a fatigue crack trajectory simulation was undertaken by means of separating morphing and adaptive remeshing technology (SMART) Crack Growth in ANSYS, on the basis of which the simulations of nonlinear ultrasonic waves for fatigue damage detection using the precise fatigue crack trajectory was achieved. The simulated crack trajectory was first validated by experimental results in terms of crack initiation angle and number of fatigue cycles and was subsequently utilised for crack quantification based on second harmonic method. The results revealed that the nonlinearity in terms of the trend and magnitude with respect to crack length in the advanced simulation is closer to that in the experimental results than the common simulation approach where damage was modelled as a straight line crack. Given that the influence of crack orientation on contact acoustic nonlinearity (CAN) was taken into consideration, the developed advanced simulation could further enhance the capability of numerical modelling for simulating the interaction between nonlinear guided waves and fatigue crack, facilitating the fundamental investigation of CAN mechanism.

Nonlinear electromechanical impedance spectroscopy: A powerful tool for studying amplitude dependent internal frictions of solids

Strain amplitude dependent effects of materials/structures are very important in the field of material science and engineering and have been found to be extremely sensitive to defects or damage. In this work, a nonlinear electromechanical impedance spectroscopy (N-EMIS) technique is proposed to characterize the amplitude dependent internal frictions (ADIFs) and modulus defects (or resonance shift) of materials. First, a new experimental scheme called the on/off parallel resistor capacitor circuit is proposed to measure the N-EMIS of a piezoelectric transducer (PZT)-specimen composite system under high driving levels. Second, based on the N-EMIS, the formulas for calculating the ADIF are derived and validated by vibration measurement using a laser vibrometer. To further enlarge the strain amplitude, a PZT-stepped horn-specimen three-component system is then introduced, with which the maximum strain amplitude can reach 10^-3. Finally, ADIF tests are conducted on polycrystalline pure copper and 1045-steel. The results show that at high strain levels, the internal frictions of both materials can reach several times than those at low driving levels, while the modulus drops only slightly. The proposed N-EMIS technique can effectively assess the strain amplitude dependent properties of materials and is expected to be widely used in the near future for evaluation of plasticity, fatigue, and damage.

Numerical parametric study of Nonlinear Coda Wave Interferometry sensitivity to microcrack size in a multiple scattering medium

This paper reports a numerical study of the sensitivity and applicability of the Nonlinear Coda Wave Interferometry (NCWI) method in a heterogeneous material with a localized microcracked zone. We model the influence of a strong pump wave on the localized microcracked zone as a small average increase in the length of each crack. Further probing of this microcracked zone with a multiply scattered ultrasonic wave induces small changes to the coda-type signal, which are quantified with coda wave interferometry. A parametric sensitivity study of the CWI observables with respect to the changes in crack length is established via numerical simulations of the problem using a 2D spectral element method (SEM2D). The stretching of the signal, proportional to the relative variation in effective velocity, is found to be linearly proportional to the global change in crack length, while the other CWI parameter, the remnant decorrelation coefficient, is found to be quadratically proportional to the crack length change. The NCWI method is shown to be relevant for the detection of different damaged material states in complex solids. The reported numerical results are especially significant in the context of quantitative nondestructive evaluation of micro-damage level of a heterogeneous materials using nonlinear ultrasound signals.

Measurement of the Acoustic Non-Linearity Parameter of Materials by Exciting Reversed-Phase Rayleigh Waves in Opposite Directions

The acoustic non-linearity parameter of Rayleigh waves can be used to detect various defects (such as dislocation and micro-cracks) on material surfaces of thick-plate structures; however, it is generally low and likely to be masked by noise. Moreover, conventional methods used with non-linear Rayleigh waves exhibit a low detection efficiency. To tackle these problems, a method of exciting reversed-phase Rayleigh waves in opposite directions is proposed to measure the acoustic non-linearity parameter of materials. For that, two angle beam wedge transducers were placed at the two ends of the upper surface of a specimen to excite two Rayleigh waves of opposite phases, while a normal transducer was installed in the middle of the upper surface to receive them. By taking specimens of 0Cr17Ni4Cu4Nb martensitic stainless steel subjected to fatigue damage as an example, a finite element simulation model was established to test the proposed method of measuring the acoustic non-linearity parameter. The simulation results show that the amplitude of fundamentals is significantly reduced due to offset, while that of second harmonics greatly increases due to superposition because of the opposite phases of the excited signals, and the acoustic non-linearity parameter thus increases. The experimental research on fatigue damage specimens was carried out using this method. The test result was consistent with the simulation result. Thus, the method of exciting reversed-phase Rayleigh waves in opposite directions can remarkably increase the acoustic non-linearity parameter. Additionally, synchronous excitation with double-angle beam wedge transducers can double the detection efficiency.

Nonlinear scattering and mode conversion of Lamb waves at breathing cracks: An efficient numerical approach

This article presents an efficient numerical approach to the investigation of nonlinear scattering and mode conversion phenomena of Lamb waves as they interact with breathing cracks. A Local Interaction Simulation Approach (LISA) is adopted, which possesses the versatility to capture arbitrary damage profiles. The stick-slip contact dynamics is implemented in the LISA model via the penalty method, which captures the nonlinear interactions between Lamb waves and breathing cracks. The LISA framework achieves remarkable computational efficiency with its parallel implementation using Compute Unified Device Architecture (CUDA) executed on powerful GPUs. A small-size LISA model with absorbing boundaries is tailored for the purpose of extracting the Lamb wave scattering and mode conversion features. Due to the explicit parallel CUDA implementation and the small-size model setup, the computation is highly efficient. Numerical case studies on nonlinear scattering of Lamb waves from breathing cracks are given. Distinctive higher harmonic generation and selective mode conversion phenomena are presented using the complex-valued Wave Damage Interaction Coefficients (WDICs) containing both amplitude and phase information of the scattered wave field. The effect of oblique incident angle on nonlinear scattering phenomenon is investigated. The rough crack surface feature with initial openings and closures is also considered to better approximate fatigue cracks in practical engineering scenarios. In addition, the wave amplitude effect on the nonlinear scattering and mode conversion is studied. This research may provide guidelines for the effective design of sensor arrays utilizing nonlinear Lamb waves for fatigue crack detection.

Experimental and Numerical Study of Nonlinear Lamb Waves of a Low-Frequency S₀ Mode in Plates with Quadratic Nonlinearity

This paper investigates the propagation of low-frequency S₀ mode Lamb waves in plates with quadratic nonlinearity through numerical simulations and experimental measurements. Both numerical and experimental results manifest distinct ultrasonic nonlinear behavior which is mainly presented by the second harmonics. Meanwhile, we find that both the acoustic nonlinearity parameter and dispersion distance show the exponential decay trend with the increase of frequency-thickness. Moreover, the results reveal that the frequency is key to affect the acoustic nonlinearity parameter and dispersion distance with the same frequency-thickness. This study theoretically and experimentally reveals that nonlinear Lamb waves of the low-frequency S₀ mode are feasible to quantitatively identify material weak nonlinearity in plates.

Monitoring Steel Bolted Joints during a Monotonic Tensile Test Using Linear and Nonlinear Lamb Wave Methods: A Feasibility Study

The structural integrity of steel bolted joints may be compromised due to excessive loading. Therefore, condition assessment and the detection of potential defects before they cause a failure have become a major issue. The paper is focused on the condition monitoring of a bolted lap joint subjected to progressive degradation in a tensile test. The inspection used Lamb waves propagated through the overlap area. Wave propagation signals were registered automatically by means of piezoelectric transducers. Two damage indices were defined based on linear and nonlinear features of Lamb waves. The use of a network of piezoelectric transducers and the analysis of multiple signals instead of single ones was proved to effectively monitor the state of the bolted joint. The obtained results showed that the method enabled to detect selected stages of the degradation process and to characterize the reduction of the contact area between the plates in the overlap area.