Effect of axial stresses on longitudinal guided waves in a fluid-filled pipe.

This paper describes the study of the acoustic field of a fluid-filled pipe subjected to axial stress based on the acoustoelastic theory. The pipe with applied axial stresses can be approximated as a transversely isotropic pipe, and hence, its acoustic fields can be expressed using potential functions. The velocity changes of longitudinal wave modes with applied stresses are analyzed for the pipe filled with oil by an analytical method. It was found that the longitudinal mode velocity changes almost uniformly with the applied stresses. The high speed and low frequency plateaus of longitudinal wave modes are sensitive to stress. The relationship between stress and the velocity change of the guided wave is given. The results indicate that non-destructive testing techniques using longitudinal wave modes have strong potential to identify and monitor the stress levels in pipe structures.

Detection of initiation of corrosion induced damage in concrete structures using nonlinear ultrasonic techniques.

Structural failure caused by corrosion of the reinforcing steel in concrete structures is quite common. In most cases, corrosion cracks appear on the surface at a late stage, leaving inadequate time for taking any measures. This paper investigates the detection of corrosion damage in reinforced concrete elements by using nonlinear ultrasonic (NLU) techniques. Various linear ultrasonic and NLU techniques were adopted to identify the most sensitive technique and ultrasonic parameters for corrosion induced damage detection at its early stage. It is observed that the linear techniques are not very effective in detecting corrosion induced damage. The sideband peak count-index (or SPC-I), a relatively new and promising technique, has been found to be an excellent indicator for the detection of corrosion induced damage initiation. However, its efficacy for detecting corrosion induced damage has not yet been reported. The present study shows that the SPC-I-based NLU technique outperforms (with the highest sensitivity) all other NLU techniques for detecting the onset of corrosion in steel and micro-crack formation in the surrounding material. As the corrosion progresses and cracks appear on the surface of the concrete, the efficiency of the SPC-I slowly weakens and other technique(s) are found to be quite efficient at that stage.

Sideband peak count-index technique for monitoring multiple cracks in plate structures using ordinary state-based peri-ultrasound theory.

This work presents a peri-ultrasound theory based on ordinary state-based peridynamics for modeling elastic waves propagating in three-dimensional (3-D) plate structures and interacting with multiple cracks. A recently developed nonlinear ultrasonic technique called sideband peak count-index (or SPC-I) is adopted for monitoring one or more cracks with thickness values equal to 0 mm (crack-free), 1, 2, and 4 mm. Three separate scenarios-one crack, two cracks, and four cracks in 3-D plate structures-are investigated. These cracks can be classified as thin and thick cracks depending on the horizon size, which is mentioned in peri-ultrasound theory. Computed results for all three cases show larger SPC-I values for thin cracks than for thick cracks and the case of no cracks. This observation is in line with the previously reported results in the literature and proves that the state-based peri-ultrasound theory can capture the expected nonlinear response of elastic waves interacting with multiple cracks without changing the cracks' surface locations artificially, and this is always needed in most of the other numerical methods. The proposed state-based peri-ultrasound theory is more flexible and reliable for solving 3-D problems, and the out-of-plane wave field can be obtained for engineering analysis.

Modelling and simulation of borehole seismoelectric response with an impermeable wall.

In this paper, we construct a borehole model with an impermeable/permeable wall and study the seismoelectric responses. First, we define the boundary conditions at the borehole wall, then the acoustic field and electric field are simulated by the real axis integral method. In order to have a comprehensive analysis of the body wave components, we use the secant integral method to simulate the body waves and give the excitation intensity spectrum in the frequency domain. The results show that the impermeability of the borehole wall significantly increases the amplitude of the acoustic field generated by Stoneley waves. This is because the closed pores at the boundary make Stoneley waves energy leak more slowly and hence attenuating less. The impermeable borehole wall weakens the electromagnetic interface response. Besides, both P wave and S wave and their accompanying electric field properties are affected by boundary connectivity. This investigation provides a theoretical basis for qualitatively judging borehole wall permeability by the seismoelectric signals.

Experimental Research on Rapid Localization of Acoustic Source in a Cylindrical Shell Structure without Knowledge of the Velocity Profile.

Acoustic source localization in a large pressure vessel or a storage tank-type cylindrical structure is important in preventing structural failure. However, this can be challenging, especially for cylindrical pressure vessels and tanks that are made of anisotropic materials. The large area of the cylindrical structure often requires a substantial number of sensors to locate the acoustic source. This paper first applies conventional acoustic source localization techniques developed for the isotropic, flat plate-type structures to cylindrical structures. The experimental results show that the conventional acoustic source localization technique is not very accurate for source localization on cylindrical container surfaces. Then, the L-shaped sensor cluster technique is applied to the cylindrical surface of the pressure vessel, and the experimental results prove the applicability of using this technique. Finally, the arbitrary triangle-shaped sensor clusters are attached to the surface of the cylindrical structure to locate the acoustic source. The experimental results show that the two acoustic source localization techniques using sensor clusters can be used to monitor the location of acoustic sources on the surface of anisotropic cylindrical vessels, using a small number of sensors. The arbitrarily triangle-shaped sensors can be arbitrarily placed in a cluster on the surface of the cylindrical vessel. The results presented in this paper provide a theoretical and experimental basis for the surface acoustic source localization method for a cylindrical pressure vessel and lay a theoretical foundation for its application.

Multipole borehole acoustic field in a transversely isotropic medium induced by stress.

A borehole multipole acoustic field in a pre-stressed formation is investigated. The pre-stressed formation is modeled as a transversely isotropic medium induced by uniaxial stress. The formation is assumed to be isotropic in absence of any static stress and then becomes anisotropic due to the applied stress parallel to the borehole axis. The approximate equivalent elastic constants of the stress-induced anisotropic medium are derived from the theory of acoustoelasticity. The nonlinear static stress-strain relation is used for both small and large static deformations. This problem can be solved analytically because of uniformity of deformation induced by static stress applied parallel to the borehole axis. The stress effects on the velocity of guided waves and amplitude of waveforms excited by monopole, dipole, and quadrupole sources are investigated. Numerical results show that the velocities of guided waves increase with uniaxial stress. The uniaxial stress affects both amplitude and arrival time of the acoustic waves in the borehole. The integral amplitude of full waveforms varies almost in a parabolic manner with the increasing stress level and thus shows sensitivity to the uniaxial stress. This result may be helpful for remote stress measurements in boreholes.

Fatigue crack localization using noncontact laser ultrasonics and state space attractors.

A fatigue crack and its precursor often serves as a source of nonlinear mechanism for ultrasonic waves, and the resulting nonlinear features are often much more sensitive to the fatigue crack than their linear counterparts. Among various nonlinear ultrasonic techniques, the proposed laser nonlinear wave modulation spectroscopy (LNWMS) is unique in that (1) it utilizes a pulse laser to exert a single broadband input instead of conventional two distinctive sinusoidal waves, and (2) a complete noncontact measurement can be realized based on LNWMS. Under a broadband excitation, a nonlinear source exhibits modulations due to interactions among various input frequency components. These modulations are often weak and can be hardly directly detected. In this paper, a damage feature called Bhattacharyya distance is extracted from the ultrasonic time signal corresponding to a pulse laser input and used to quantify the degree of damage-induced nonlinearity and localize the crack. This feature is a measure of a statistical distance used to detect the geometrical changes between state space attractors reconstructed before and after damage formation. It has been successfully used for localizing fatigue cracks in metallic plates.

Mesh-free distributed point source method for modeling viscous fluid motion between disks vibrating at ultrasonic frequency.

The distributed point source method (DPSM) is extended to model wave propagation in viscous fluids. Appropriate estimation on attenuation and boundary layer formation due to fluid viscosity is necessary for the ultrasonic devices used for acoustic streaming or ultrasonic levitation. The equations for DPSM modeling in viscous fluids are derived in this paper by decomposing the linearized viscous fluid equations into two components-dilatational and rotational components. By considering complex P- and S-wave numbers, the acoustic fields in viscous fluids can be calculated following similar calculation steps that are used for wave propagation modeling in solids. From the calculations reported the precision of DPSM is found comparable to that of the finite element method (FEM) for a fundamental ultrasonic field problem. The particle velocity parallel to the two bounding surfaces of the viscous fluid layer between two rigid plates (one in motion and one stationary) is calculated. The finite element results agree well with the DPSM results that were generated faster than the transient FEM results.

Ultrasonic wave characteristics in multiscale cementitious materials at different stages of hydration.

Monitoring the microstructural change in cementitious materials during hydration is an essential but challenging task. Therefore, a non-invasive and sophisticated technique is warranted to understand the microscopic behaviour of the multiphase cementitious materials (where the length scale of the constituents varies from centimeters to micrometers) in different stages of hydration. Due to exothermic hydration reactions, different hydration products start to evolve with individual mechanical properties. In concrete, an interface transition zone (ITZ) appears between the aggregate surface and paste matrix, which influences the overall properties of concrete material. In the present research, 1) several wave characteristics, such as wave velocity, energy distribution, and signal phase are found out using Ultrasonic Pulse Velocity (UPV), Wavelet Packet Energy (WPE) and Hilbert Transform (HT) methods, to monitor the hydration mechanism (1d-28d) in cement-based materials with two levels of heterogeneities (cement paste and concrete, representing microscale and mesoscale, respectively). Also, the unique nonlinear behaviour is studied in the frequency domain using the promising Sideband Energy Ratio (SER) and Sideband Peak Count Index (SPC-I) methods. 2) Numerical simulations are carried out to understand the wave interaction in the developing microstructure. A discretized microstructure of cement shows microscopic details of each phase at any instant of hydration (e.g., formation stage and after complete maturity level). The experimental and numerical investigations on the characteristics of the nonlinear ultrasonic wave propagation show the impact of microstructural development of multi-scale cementitious materials during hydration.

Monitoring fatigue cracks in riveted plates using a sideband intensity based nonlinear ultrasonic technique.

Aluminum structures are routinely used in aircraft due to their lightweight and corrosion resistance properties. Multi-layered aluminum plates are generally joined by rivets forming regions which are prone to fatigue crack formation in an aircraft. Therefore, the detection and monitoring of fatigue cracks at rivet joints in aluminum structures are crucial for ensuring flight safety. In this study, piezoelectric sensors were utilized to generate and detect Lamb waves on aluminum plates with rivet joints to investigate the feasibility of a newly developed Sideband Peak Count (SPC) technique for detecting fatigue cracks around these joints. To overcome the limitations of existing SPC-I (Sideband Peak Count - Index) and SPI (Sideband Peak Intensity) techniques in capturing harmonic and modulating wave frequencies due to material nonlinearity, a comprehensive index, the Sideband Intensity Index (SII) is introduced. Comparative analysis with existing SPC-I and SPI techniques confirm the effectiveness of the SII technique. This investigation shows that the SII technique significantly improves the detection capability of initial fatigue cracks around rivet joints on aluminum plates. This study offers a more efficient method for detecting critical fatigue cracks in rivet joints.

Monitoring damage growth and topographical changes in plate structures using sideband peak count-index and topological acoustic sensing techniques.

Some topographies in plate structures can hide cracks and make it difficult to monitor damage growth. This is because topographical features convert homogeneous structures to heterogeneous one and complicate the wave propagation through such structures. At certain points destructive interference between incident, reflected and transmitted elastic waves can make those points insensitive to the damage growth when adopting acoustics based structural health monitoring (SHM) techniques. A newly developed nonlinear ultrasonic (NLU) technique called sideband peak count - index (or SPC-I) has shown its effectiveness and superiority compared to other techniques for nondestructive testing (NDT) and SHM applications and is adopted in this work for monitoring damage growth in plate structures with topographical features. The performance of SPC-I technique in heterogeneous specimens having different topographies is investigated using nonlocal peridynamics based peri-ultrasound modeling. Three types of topographies - "X" topography, "Y" topography and "XY" topography are investigated. It is observed that "X" and "XY" topographies can help to hide the crack growth, thus making cracks undetectable when the SPC-I based monitoring technique is adopted. In addition to the SPC-I technique, we also investigate the effectiveness of an emerging sensing technique based on topological acoustic sensing. This method monitors the changes in the geometric phase; a measure of the changes in the acoustic wave's spatial behavior. The computed results show that changes in the geometric phase can be exploited to monitor the damage growth in plate structures for all three topographies considered here. The significant changes in geometric phase can be related to the crack growth even when these cracks remain hidden for some topographies during the SPC-I based single point inspection. Sensitivities of both the SPC-I and the topological acoustic sensing techniques are also investigated for sensing the topographical changes in the plate structures.

A damage localization technique using wave front shapes in composite laminates without knowing the velocity profile.

Composite laminates are widely used in various fields, but their structures are prone to cracks and damage. Due to the difference in angles of the instantaneous direction of the wave front propagation and the direction of the energy flow in an anisotropic material, the use of Lamb waves for damage localization in composite laminates is a challenging task. Establishing the wave front shape equation can overcome the difficulty of damage localization caused by anisotropy, but this usually requires a priori knowledge of the acoustic velocity distribution of the laminates, which is not convenient for efficient damage localization. In this paper, a damage localization method based on wave front shapes for composite laminates without any knowledge of the velocity profile is presented. Numerical simulation and experimental results show that the proposed method works. This method shows good damage localization accuracy and has broad application prospects in non-destructive testing for plate structures with strong anisotropy.

Numerical modeling with experimental verification investigating the effect of various nonlinearities on the sideband peak count-index technique.

A newly developed nonlinear ultrasonic (NLU) technique called sideband band peak count-index (or SPC-I) measures the degree of nonlinearity in materials by counting the sideband peaks above a moving threshold line - larger the SPC-I values, higher is the material nonlinearity. In various published papers, the SPC-I technique has shown its effectiveness in structural health monitoring (SHM) applications. However, the effects of different types of nonlinear phenomenon on the sideband peak generation is yet to be investigated in depth. This work addresses this knowledge gap and investigates the effects of different types of nonlinearity on the SPC-I technique. Three types of nonlinearity (material nonlinearity, structural nonlinearity and contact nonlinearity) are investigated separately through numerical modeling. In this investigation the material nonlinearity and the contact nonlinearity are modeled by finite element method (FEM) using the commercial Abaqus/CAE software. The structural nonlinearity arising from stationary cracks is modeled using nonlocal peridynamics based peri-ultrasound modeling technique. Numerical modeling shows that the sideband peak values do not increase proportional to the input signal strength thus indicating nonlinear response, and different types of nonlinearities affect the SPC-I measurements differently. For the experimental verification a composite plate with impact-induced damage is considered for investigating the material nonlinearity and structural nonlinearity while a linear elastic aluminum plate is used to examine the contact nonlinearity between the transducers and the plate. The trends observed in the experimental observations matched with the numerical model predictions.

A modified sideband peak count based nonlinear ultrasonic technique for material characterization.

The ultrasonic Non-Destructive Testing and Evaluation (NDT&E) has been widely used for Structural Health Monitoring (SHM). The conventional linear ultrasonic technique which is suitable for detecting macro-scale defects is routinely used in industry; however, it often fails to detect the micro-scale defects. Generally, micro-defects in a material appear first due to dislocations at grain boundaries. These micro-defects then grow and coalesce to form macro-defects. The crack growth rate is much faster for macro-defects than micro-defects. Therefore, monitoring micro-defects is important to avoid catastrophic failures of structures. Nonlinear ultrasonic techniques help to detect micro-defects. A recently developed nonlinear ultrasonic technique called Sideband Peak Count - Index (SPC-I) technique has some inherent advantages over other nonlinear techniques for monitoring progression of micro-defects. In this research, the SPC-I technique is further modified. This modified technique, Sideband Peak Intensity (SPI) technique, is shown to be more robust and easier to implement. Both SPC-I and SPI techniques are used to monitor the damage progression in impact induced damages in metals. Similarities and dissimilarities between these two techniques are investigated. Then it is concluded that the SPI technique is good as a general-purpose robust damage monitoring tool that can be used by less skilled users while the SPC-I technique although requires more skills has more sensitivity and has the flexibility for an in-depth damage analysis in materials.

Ordinary state-based peri-ultrasound modeling to study the effects of multiple cracks on the nonlinear response of plate structures.

Since it is almost impossible to carry out a comprehensive parametric investigation experimentally for internal cracks with different geometry and orientation, a good numerical modeling and simulation technique is necessary to have a clear understanding of the physics of wave propagation and its interaction with cracks. Such investigation is helpful for structural health monitoring (SHM) with ultrasonic techniques. This work presents a nonlocal peri-ultrasound theory based on ordinary state-based (OSB) peridynamics for modeling elastic wave propagation in three-dimensional (3-D) plate structures containing multiple cracks. A relatively new and promising nonlinear ultrasonic technique called Sideband Peak Count - Index (or SPC-I) is adopted to extract the nonlinearity generated from the interactions between elastic waves and multiple cracks. Effects of three main parameters - the distance between the acoustic source and the crack, the crack spacing and the number of cracks are investigated using the proposed OSB peri-ultrasound theory together with the SPC-I technique. For each of these three parameters investigation, different crack thicknesses were considered - 0 mm (crack-free), 1 mm (thin crack), 2 mm (intermediate thickness) and 4 mm (thick crack); thin and thick cracks are defined after comparing the crack thickness value with the horizon size mentioned in the peri-ultrasound theory. It is found that for obtaining consistent results the acoustic source should be placed at least one wavelength away from the crack and crack spacings also play an important role on the nonlinear response. It is concluded that the nonlinear response diminishes when the cracks become too thick, and thin cracks show higher nonlinearity than that of thick cracks and no cracks. Finally, the proposed method which is combining the peri-ultrasound theory and SPC-I technique is used for monitoring cracks' evolution process. The numerical modeling results are compared with the experimental findings reported in the literature. Consistent qualitative trends in SPC-I variations predicted numerically and obtained experimentally are observed, thus it gives confidence in the proposed method.

Acoustic source localization using L-shaped sensor clusters: A review.

Acoustic source localization (ASL) plays an important role in structural health monitoring (SHM). The L-shaped sensor cluster (LSSC) is very convenient for ASL, and hence SHM. Various techniques based on LSSC have been developed rapidly in the past decade. LSSC can be conveniently used for damage detection and localization, a necessary step for monitoring structures through non-destructive testing (NDT). After ten years of development, LSSC still has a wide development space. In this paper, the fundamental roles of LSSC in developing different techniques within last ten years and its future potentials are discussed. The LSSC-based time difference of arrival localization techniques and the wave front shape-based localization techniques are reviewed in detail in this paper. This paper aims to give readers a more comprehensive and clear understanding of these techniques. The discussion on the advantages and disadvantages of these techniques and various sources of the errors will give the readers the current limitations and future development prospects of ASL and damage detection techniques using LSSC.

Detection of interface flaws in Concrete-FRP composite structures using linear and nonlinear ultrasonics based techniques.

Timely and appropriate retrofitting of existing structures holds paramount importance to ensure the structural integrity and sustainability. Fiber Reinforced Polymer (FRP) composites with high corrosion resistance, strength and durability, have been increasingly used in recent years for retrofitting of concrete infrastructure. The effectiveness of retrofitting is primarily dependent on the appropriate integrity at the interface between FRP and concrete substrate. Presence of any interface flaw can jeopardize the structural performance. In the present study, investigations are carried out to detect the early stage flaws at the FRP-concrete interface using ultrasonic waves. Artificial flaws of different size are introduced in the adhesive (epoxy) layer of carbon based FRP composite concrete beam. Rayleigh waves (at different frequencies) are generated for measuring the response from different FRP composite-concrete specimens. The specimens consist of three different types of materials, namely, concrete, epoxy and FRP. Two different input excitation frequencies, i.e., 75 KHz and 250 KHz, are tried out during the experimental investigations. The output signals are processed using different linear and nonlinear ultrasonic methods. Numerical simulations are also performed to better understand the wave signals' interactions with the multi-layer composite medium. The results showed that the linear ultrasonic methods are not able to provide a consistent information on presence and extent of flaws. Nonlinear ultrasonic methods showed significantly better performance for characterizing both small and large flaws considered in this investigation. Sensitivity analysis reveals that relatively new and promising nonlinear ultrasonic technique, namely, the Sideband Peak Count-Index (SPC-I) performs remarkably well for detection of flaws in FRP-concrete interface.

Theoretical error formation and evaluation of acoustic source localization for cluster-based techniques.

In this paper, the formation of theoretical error is presented to investigate the acoustic source localization (ASL) error that can be expected from traditional L-shaped, cross-shaped, square-shaped, and modified square-shaped sensor cluster arrangements. The response surface model based on the optimal Latin hypercube design is developed to theoretically study the effects of sensor placement parameters on the error evaluation index of root mean squared relative error (RMSRE) for the four techniques. The ASL results from the four techniques with the optimal placement parameters are analyzed theoretically. The relevant experiments are conducted for verifying the above theoretical research. The results show that the theoretical error, formed by the difference between the true and the predicted wave propagation directions is related to arrangement of sensors. The results also show that the sensor spacing and the cluster spacing are the two parameters that affect the ASL error most. Between these two parameters the sensor spacing has the stronger influence. The RMSRE increases with an increasing sensor spacing and a decreasing cluster spacing. Meanwhile, the interaction effect of placement parameters should be also emphasized, especially that between the sensor spacing and the cluster spacing for the L-shaped sensor cluster-based technique. Among the four cluster-based techniques, the newly modified square-shaped sensor cluster-based technique shows the smallest RMSRE and not the largest number of sensors. This research on error generation and analysis will provide guidance for the optimal sensor arrangements in cluster-based techniques.

Scattering of focused ultrasonic beams by cavities in a solid half-space.

The ultrasonic field generated by a point focused acoustic lens placed in a fluid medium adjacent to a solid half-space, containing one or more spherical cavities, is modeled. The semi-analytical distributed point source method (DPSM) is followed for the modeling. This technique properly takes into account the interaction effect between the cavities placed in the focused ultrasonic field, fluid-solid interface and the lens surface. The approximate analytical solution that is available in the literature for the single cavity geometry is very restrictive and cannot handle multiple cavity problems. Finite element solutions for such problems are also prohibitively time consuming at high frequencies. Solution of this problem is necessary to predict when two cavities placed in close proximity inside a solid can be distinguished by an acoustic lens placed outside the solid medium and when such distinction is not possible.

Fast Fourier transform method for determining velocities of ultrasonic Rayleigh waves using a comb transducer.

A convenient, accurate and precise method is proposed to determine velocities of ultrasonic Rayleigh waves in different materials by extracting central frequencies of signals, which are measured by a comb transducer and converted to the frequency domain using the fast Fourier transformation (FFT). The velocities can be calculated as cr = fl, where f is the central frequency of the wave signal and l is the teeth spacing or period of the comb transducer. The experimental measurements are easy to do, as long as the Rayleigh wave reflected from the standard reflectors are measured using one comb transducer, without knowing the wave propagation distances and times. Results show that the proposed technique has a high level of precision, as the central frequencies are very stable. The same comb transducer is used to measure the Rayleigh wave velocities in different materials where the velocities vary from 2100 m/s to 3400 m/s. Comparison of the experimental results with those measured using the time-of-flight method showed a high level of accuracy - all relative errors were found to be less than 1%.