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Study of Propagation of Ion Acoustic Waves in Argon Plasma
Fukuoka, H. Toda, and H. Naka, Exp. CrossRef Google Scholar. King and C. Fortunko, J. Thompson, S. Lee and J. Smith, J. Man and W. Lu, J. Elasticity 17 , CrossRef Google Scholar. Kino, et al. Fisher and G. Thompson and D. Timoshenko and J. Goodier, Theory of Elasticity , 3rd ed. The existing literature does not throw much light on this aspect. Based on the triangulation technique the location of acoustic sources has been reported over the last three decades.
Using the analysis of the arrival times of the acoustic waves at three arbitrarily positioned AE sensors Tobias, reported a methodology to locate the acoustic source in two dimensional workspace i. Based on the path differences for the 1st , 2nd and 1st ,3rd sensors that were calculated by multiplying the differences in arrival times to the sensors and the wave velocity, the location of the acoustic source was determined analytically using the polar coordinates relative to a reference sensor.
Asty, proposed an arrangement of three sensors on a spherical surface and derived the formulae to identify the location of the acoustic source on the spherical surface by using the difference in arrival times of the acoustic signal between the sensors. However, this method can be extended to identify the source location on a plane surface by increasing the radius of the sphere to infinity; this results in Tobias's solution. A similar approach as used by Asty has been used by Barat et al. Axinte et al. Kosel et al. They have shown that estimation of time delay between AE signals by the cross-correlation function CCF is only applicable for one active AE source.
The conventional triangulation technique for detecting AE source assumes that the wave speed is independent of the direction of propagation. This is not true in case of anisotropic plate as well as in case of isotropic plates with some impact point. Castagnede et al. Their method works well for thick structures but fails for thin plates when sensors are placed far away from the impact point. Kundu et al. It has been observed that for impact point loading the optimization method is better than triangulation technique for predicting AE sources.
Expression of the objective function for multiple sensors is also redefined to maximize the efficiency of detecting the impact point. Using this modified objective function the impact point in an anisotropic but homogeneous graphite epoxy composite plate is correctly predicted. Hajzargerbashi et al. The modified objective function was found to be more computationally effective and the prediction accuracy has been significantly improved by the use of four sensors instead of three.
In their formulation clusters of three sensors are placed at two different locations in a plate. From the difference in arrival time at the sensors in each of the clusters the angular direction of a particular sensor of a cluster with horizontal referential axis can be known. From the angles of two sensors in the clusters two straight lines can be plotted and such lines will intersect at a point; which will give the location of the source.
The source localisation is found to be more accurate if instead of six sensors nine sensors are used by arranging them into three clusters. Aljets et al.
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Tests were conducted on a composite CFRP plate with anisotropic lay-up with a novel configuration of three sensors which are closely arranged in a triangular array with the sensors just a few centimeters apart. The main benefit of a closely arranged sensor array is the possibility to install all sensors in one housing such that mounting and wiring up of the AE system becomes simplified. Since the sensors are installed very close to each other, the signal of an event should look fairly similar at all sensors. This makes it easier to identify exactly the same wave feature in all three sensor signals.
The accuracy of the source location in this method decreases with distance of the sensor array from the source. Giridhara et al. Through this method it has been shown that with the use of information regarding Lamb wave propagation along with triangulation scheme the rapid location of damage is possible without using all of the sensor data. This methodology has been validated experimentally by studying hole and corrosion type damages.
Salamone et al. Using three such sensors arranged as rosettes the principal strain directions were obtained. With minimum of two rosettes i. The advantage of this approach is that it does not require knowledge of the wave speed in the material and can be applied for isotropic material. However, there are difficulties in applying this technique for an anisotropic plate since the wave propagation direction does not coincide with the principal strain direction for the anisotropic plate.
The proposed technique does not rely on the constraint condition that the principal strain direction must coincide with the wave propagation direction and is an improvement over the proposed approach by Salamone et al. McLaskey et al. The basic principle of beamforming technique is based on the delay-and-sum algorithm. They have applied this technique for large plates and it also requires the knowledge of the wave velocity.
He et al. The original beamforming method proposed by McLaskey et al. Nakatani et al. Xiao et al. The accurate x and y coordinates of AE source are determined by the two arrays respectively.
It has been shown that even if the velocity error is large, the AE source location can still be localized accurately. They have validated their approach with analysis using finite elements and experiments with generating AE source using pencil-lead-break. In complex geometry structures such assumptions may not be valid. To improve upon these Baxter et al.
This method does not require knowledge of the sensor location or wave speed. It uses an artificial source namely the Hsu-Neilsen source or H-N source which provides an easy, repeatable, consistent, broadband AE source. This method does not require information about sensor location or time of occurrence of source. The source location is defined with regards to a user defined grid, rather than sensor location. Hensman et al. They proposed one artificial source instead of ten artificial sources and thus the requirement of training data is reduced. Eaton et al. They performed a thorough assessment to check the performance and the robustness of the ''Delta T Mapping'' approach and compared them with traditional techniques.
The experiments were conducted on two carbon fibre composite specimens and a wide tensile specimen with a circular cut out to assess the performance of "Delta T Mapping" technique using both artificial H-N sources and real fatigue test data. An improvement in location accuracy over the traditional TOA approach was observed in nearly all cases. Ernst and Dual, proposed a method which allows the detection and localisation of multiple acoustic emission source with only a single, one point, unidirectional measurement using the time reversal principle and dispersive behavior of the flexural wave mode.
The difficulties of distortion of elastic wave due to phase dispersion while using the TOA method are overcome by this method. In this method the dispersive behaviour of the guided wave is used to locate the origin of the acoustic emission event. Therefore, the localisation of source depends solely on the measured wave form and not on arrival time estimation. This method can successfully localise the source on anisotropic structures as well as structures having geometrical complexities like notches.
Kundu, classified different source localisation techniques using geometric method and specified their advantages and limitations.
Laser-Generated Surface Acoustic Wave Technique for Crack Monitoring – A Review
Broadly the source localisation can be classified into three categories: Source localisation in isotropic plates, Source localisation in anisotropic plates and localisation in complex and three dimensional structures. For isotropic and homogeneous structures; if the speed of propagation of the wave is known then triangulation technique can be used effectively. By solving a set of nonlinear equations source localisation can be done in isotropic homogeneous structures even if the wave speed is not known. However, solution of the nonlinear equations makes this method less attractive.
To overcome this, three unknowns i. Major shortcoming of this method is that sometimes the objective function becomes infinite and special care needs to be taken to avoid such singularities. Beamforming array technique can be used effectively for isotropic plate which is based on the delay-and-sum algorithm. The advantage of this method is that it does not require the exact time of arrival of a specific wave mode and thus can handle noisy signals. For isotropic plate with unknown wave speed, strain rossette technique using Micro-Fiber-Composite sensors is another one technique which can provide good result for localisation of source.
Using modal analysis of the propagation of the elastic waves and calculating the time difference between the extensional and flexural plate wave modes at a sensor the acoustic source in isotropic plate can also be localised. Advantages of this technique are that the acoustic source can be localised with fewer sensors and characteristics of the source can be predicted.
However, the limitation of this approach is that the plate properties must be known for the theoretical analysis; which is very difficult to get accurately for anisotropic plates. For anisotropic plates beamforming array technique and the optimization technique can be used.
However, both these techniques require direction dependent velocity profile in the anisotropic plate. For monitoring a critical region for any crack formation hit by a foreign object in anisotropic plate, without knowing its materials properties, Poynting vector technique is useful. However, exact location of acoustic source cannot be predicted by this technique. In complex three dimensional or two dimensional structures straight line propagation of the generated wave from the acoustic source to the sensor is not possible. In such situations alternate techniques such as Artificial Neural Network ANN or time reversal technique based on impulse response function IRF or placing of densely distributed acoustic sensors on structure can be used.
However, since these methods are either labour intensive or require a large number of sensors, these techniques should be followed when all other methods fail. The uncertainties in source localisation arising from the wrong recording of the arrival time during different experimental techniques can be filtered out by the extended Kalman filter in case of isotropic plates as proposed by Niri and Salamone, and Non-linear Kalman Filter in case of anisotropic plate as proposed by Niri et al.
From the available literature as above, it is found that geometric methods are mostly used for damage localisation only in plates of regular shape. However, effectiveness of such methods for plates of irregular shape and other type of structures like shells and frames are yet to be investigated. Besides, the sensitivity of geometric methods to minute deficiencies of the structure at the elementary level needs further investigation. Moreover, validation of such methods against field data is rare in literature.
On the other hand, data recorded in the sensors contain structural information and it is only logical that such data be used directly to obtain the damage related information. However in geometrical method, the sensor data are processed through purely geometrical procedure which is not related to performance of the structure. Hence, this process seems to be practically cumbersome and technically undesirable especially for large and complex structures.
In recent years researchers have tried to apply the Finite Element Analysis for damage localisation using AE technique. Gary and Hamstad, proposed a two dimensional cylindrical symmetric dynamic finite element method DFEM for thin plate specimens to model AE source in a more general way than the Pencil-lead-break.
The pencil-lead break is a valuable source for simulation of AE source experimentally. However, the limitations for this source are that it can be only applied to outer surface as out-of-plane source and the range of the source rise times and source dimensions are limited. To overcome these limitations, in the proposed model the source force versus time characteristics are varied and the time dependent displacement fields for the far-filed are captured.
Most of the numerical experiments are carried out for an aluminium plate of 0. The numerical method was followed as described by Blake and Bond, The element sizes were varied across the plate depth from 0.
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The out of plane displacement responses were captured at a distance of 0. The numerical simulated results for displacement response were found to be in good agreement with the experimental result carried out with pencil-lead-break. The input source function for AE has been varied for different rise times and the time dependent displacement responses were found. It was observed that with the increase in the rise time there is loss of amplitude, however the spectral shapes are roughly same.
To simulate the AE source in more relevant way a force of constant intensity applied to a circular region with increasing radius. The applied force was kept constant across the source and dropped to zero at its edge for different diameters 0. The time dependent vertical displacements at 0. The use of the DFEM helped to find out the vertical out-of-plane as well as radial in-plane displacement response easily. From the study it has been observed that the meshing needs to be denser in the neighbourhood of the source to launch the wave properly and intensity of the applied force than the source size is of considerable interest for AE studies of source effects on resulting AE signals.
The material modelled in this case was steel in all cases. The source was considered at the centre and the time response of vertical displacements is captured at 8 d from the source. Comparisons between the out-of-plane displacement outputs for the 2-D and 3-D model are found to be in good agreement. The 3-D model vertical displacement time response is found to be in good agreement when it was compared with the laboratory experiment data for a 1.
The study indicated that to properly represent the Rayleigh wave the mesh density away from the source needs to be increased. To model AE sources that generate Rayleigh wave frequencies, the source size must be less than 3 mm diameter having a rise time of less than 1 ms and the element sizes of about 0. The study on the dependence on the plate edge source position with 3-D model indicated that below the mid-plane, the out-of-plane top surface displacement waveforms vary significantly; however at the mid-plane of the plate the low amplitude flexural part of the observed waveform disappeared and the sources above the mid-plane the waveforms are almost same as the mid-plane source.
However, a real AE source in general is a buried source. To model a buried dipole, two closely spaced body forces were applied simultaneously along opposite directions. The applied body forces were step-like in nature and considered to be a cosine bell curve. The dipole was equivalent to two small but finite, simultaneous monopole sources in close proximity. The dipole strength was determined by multiplying the force of each of the equal and opposite monopoles by the small distance dipole spacing between the centres of the two monopoles.
In the modeling they have considered that the minimum wave length must be bigger than the source size i. They have checked for convergence with respect to the ratio of the minimum wavelength to source size of the dipole and found that a ratio of 2. The study also suggested that for ratio of the minimum wavelength to element size more than 15 the convergence is well achieved.
Their observation indicated that the dipole can be of minimum size of 3 cells, 1 each for the monopoles with 1 cell space between. The time dependent displacements obtained using the proposed model were compared with the other previously published analytical results and they are found to be in good agreement with the results obtained by the proposed model. DFEM can provide time dependent displacements at selected times after the operation of the AE source. They have studied the lead breaks on the surface and edge of the thin aluminium plate and found that the surface lead breaks generate A0 zero order anti-symmetric Lamb mode while the edge lead breaks generate S0 zero order symmetric Lamb mode.
The edge lead break source also generates Rayleigh wave and propagates along the plate edge. All these experimental observations were also validated by theoretical DFEM analysis. Their theoretical studies indicated that the Rayleigh wave generated interacts at the plate corner to produce a mode converted S0 wave. The Rayleigh waves were mode converted at the sides of the plate upon reflection to longitudinal waves, which then propagated through the thin plate as the S0 mode. The experimental studies found to be in good agreement with the theoretical studies. However, they identified that this method can be used effectively if the flexural mode is present only.
Sause and Horn, a used finite element simulation approach for investigating the acoustic emission waveforms resulting from failure due to matrix cracking, fibre breakage and fibre matrix interface failure during mechanical loading of carbon fibre reinforced plastic CFRP specimens. They have used a new emission source model based on principle of virtual work and D'Alembert principle and used the Structural Mechanics Module of Comsol Multiphysics software for finite element modelling and simulation. Sause and Horn, b investigated the influence of microscopic elastic properties and the geometry of the AE source by finite element simulation.
Through their model they have compared between the Lamb wave formation of the anisotropic, homogeneous model specimen and those of an anisotropic, microscopically inhomogeneous model and demonstrated that microscopic conditions close to the source influence the excitation of distinct Lamb wave modes significantly. This can help in distinguishing different modes of fracture in fibre reinforced materials. The interpretation of dominant Lamb wave propagation modes for thin plate becomes more challenging in case of composite specimen with discontinuity.
Their investigation pointed out that the AE source localisation is largely impacted by internal damage as these damages significantly alters the emitted wave fields of the original source and affects the initial arrival time of different wave modes. Study of literature on AE techniques in damage analysis reveals that there is an ample opportunity for making the technique practically implementable.
In the response based damage investigation it is well understood that response recorded at a proper location can produce useful information on the behaviour of structure. Hence, placing the sensors at such critical locations is crucial for damage identification by AE technique. Some researchers have tried to simulate the procedure of damage detection using sensor data by using FEM. This technique is useful as a researcher can perform parametric study on various types of structures by introducing artificial wave functions simulating AE wave at varied locations.
Subsequently, the response recorded at each location can be analysed for finding out the critical locations of sensors. Using FEM as above many researchers, in the recent past, have tried to study damage on simple structures like plates using simplified sources of AE. However, further investigation is required to make it implementable in real life structures. Structural damage localisation by AE technique is an active area of research interest in structural engineering worldwide. The technique has evolved through the last few decades and researchers have tried quite a few different methods of AE for damage localisation.
The present study makes an effort to review such methods of AE under five broad categories and discuss chronological advancements in each such category along with its pros and cons. Subsequently, the following general conclusions are drawn:. However analytical techniques can provide damage localisation details and type of damage for simple geometry which can be effectively used to validate the results obtained by other numerical analysis technique like FEA. By analysing the good quality recorded AE signals structural information can be available which helps in localisation of damage.
However, damage localisation by signal processing requires expertise in signal processing. In absence of such expertise included noise in the AE signals may be wrongly interpreted as the original signal which may result in incorrect localisation of damage.
Damage localisation by soft computing technique like ANN has got tremendous potential for detecting an AE source. However, the huge amount of data required for ANN requires a large number of sensors which is not feasible for big civil engineering structures. Techno-economical feasibility study has a potential amount of research scope in this regard. Damage localisation by geometric technique has been studied for regular geometric plate structures.
However, the effectiveness of the damage localisation by geometric techniques for plates of irregular shape and other type of structures like shells and frames are yet to be investigated. Moreover, this localization method does not throw any light on the more detailed investigation e. Thus, there is scope for more rigorous studies on the geometric technique to address the above issues. Parametric studies have been carried out on simple plate structures by the researchers by introducing artificial AE wave function as AE source. More detailed investigations are required for the FEM to make it implementable for real life structures.
The use of AE Technique is an attractive option and is increasing in use for SHM of structures such as steel and concrete bridges. Among the various NDTs, acoustic emission AE monitoring is arguably based on the simplest physical concepts AE in the form of popping and cracking noises from materials under stress. High sensitivity to crack growth, ability to locate source, passive nature no need to supply energy from outside; but energy from damage source itself is utilised and possibility to perform real time monitoring detecting crack as it occurs or grow are some attractive features of AE.
However, it is one of the most difficult techniques to practically implement due to the challenges in the area of analysis of recorded data. For effective SHM the need is for effective data analysis linked with three main aims of monitoring; accurately locating the source of damage, identifying and discriminating signals from the sources of AE and quantifying the level of damage of AE source for severity assessment. The study of the effectiveness of AE in the quantification of damage, severity assessment and predicting the remaining capacity of a structure still remains the critical area of research.
The sensitivity to scaling, geometry, material properties, degradation state, and AE sensor layout for SHM requires more detailed investigations to make this implementable for real life structures. Moreover, under critical dynamic loading condition like earthquake the SHM using AE techniques is very challenging as AE wave signal frequencies due to any damage during such events are to be separated out from the dynamic load frequencies which is very complex and have quite high potential for further research.
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by Warren P. Mason
Castagnede, B. Location of pointlike acoustic emission sources in anisotropic plates. The Journal of the Acoustical Society of America 86 3 : Eaton, M. Acoustic emission source location in composite materials using Delta T Mapping.
Ernst, R. Acoustic emission localization in beams based on time reversed dispersion. Ultrasonics 54 6 : Gary, J. On the far-field structure of waves generated by a pencil break on a thin plate. Journal of Acoustic Emission 12 : Giridhara, G. Rapid localisation of damage using a circular sensor array and Lamb wave based triangulation. Mechanical Systems and Signal Processing 24 8 : Gorman, M.
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