|NDT.net - February 2000, Vol. 5 No. 02|
|TABLE OF CONTENTS|
This paper deals with the application of acoustic emission analysis techniques including localization, and more sophisticated procedures such as moment tensor inversion methods to characterize the fracture mechanisms in concrete and steel reinforced concrete. After a description of the analysis techniques, an example for the application of these techniques to pullout tests with a single steel bar will be reported. Experiments on steel fibre reinforced concrete are reported in a different paper (Weiler et al.) in this volume.
The software called Hypo AE to localize the sources of acoustic emissions was developed in co-operation with the Institute of Geophysics at the University of Karlsruhe in Germany (Oncescu and Grosse, 1996). The program is a derivative of the Hypo71 program for the localization of earthquake hypocenters and is based on an idea developed by Ludwig Geiger (1910). For the determination of the hypocenter by extraction of the arrival times, at least 4 stations are necessary; having more than 4 stations, the problem is over determined and the calculation is done using an iteration algorithm (Buland, 1976). Formerly, the arrival times of the compression waves of all channels have to be read off by hand. Assuming a time resolution of at least 1 µs, a localization accuracy of 8 to 10 mm has to be accepted. To reduce the time consuming P-wave onset picking, an automatic picker (Grosse and Reinhardt, 1999) was developed.
Automatic Extraction of the Onset-Time of Acoustic Emissions
To establish a procedure to analyze a large number of acoustic emission signals it is necessary to reduce the time of manual efforts by an automatic picking algorithm. This algorithm is supposed to extract the onset-times fully automatically - at least it should support the operator as far as possible, because the hundreds of events recorded during a typical experiment result in several thousand signals to be analyzed. It is important that the accuracy of the automatic picking is not significantly differing from the manual picking. Under all circumstances this procedure should therefore result in saving time and not in a significant loss of precision. The most useful solution would be an automatic detection working in real-time or close to this.
We therefore have extensively worked on a software solution to meet these requirements. The program package called FreshCon is based on a sophisticated picking algorithm, which will be described in the paper by Grosse and Reinhardt (1999). Analyzing the energy content of an event, the problem is solved using Hinkley's criterion to discriminate between signal and noise and to pick the arrival time (Fig. 1). Assuming reasonable noise conditions, the accuracy of the picking algorithm is better than ten samples related to the manual picking. According to the signal quality and the signal-to-noise ratio, a butterworth bandpass filter as well as different other options can be set (Fig. 2). A proper setting of the filter parameters will result in an increasing precision.
|Fig 1: Hinkley's criterion to determine the onset-time of an acoustic emission event; refer to Grosse and Reinhardt (1999) for more details.|
Fig 2: Setup for program FreshCon.
Taking the experimental conditions (defined by the sensor characteristics and the noise conditions, for instance) and the requested degree of accuracy into account, the picking program provides three different modes of interaction.
The realtime execution of the 3D-localization routine HypoAE after each picking process is implemented. Besides the automatic picking mode where the experimentalist has less possibilities of interaction, the semi-automatic picking mode is of special interest. It allows full control and correction of the supposed onset times in a very fast way. This is shown in Fig. 3 for an acoustic emission event which was recorded with eight broadband sensors. The program allows to display all channels (up to 18) filtered or unfiltered and enlarge one selected channel of interest. In this way, a large number of signals can be evaluated.
|Fig 3: Acoustic emission event recorded with eight sensors. The calculated onset-time is marked by a vertical line. A certain channel can be zoomed in the detail window.The result of the localization program HypoAE is displayed at the bottom.|
The broadband recording of acoustic emissions during the loading of a specimen together with the three-dimensional localization of the sources facilitates different analysis tools. One is the waveform comparison in terms of pattern recognition. This assumes that similar fracture mechanisms cause similar waveforms and allow the classification of signals. As a first step, a method to determine the coherence function of two signals was employed. This technique was adapted from the field of telecommunications. Similar events can be separated from less similar in the frequency domain by extracting one parameter called the coherence sum (Grosse, 1996). The mathematical background together with some applications was presented in Grosse et al. (1997). Although a classification of the signals can be done using the coherence method, this does not lead to the determination of crack type and orientation. To meet these requirements, usually an inversion of the moment tensor is performed.
|Fig 4: From failure to analysis - stages of quantitative acoustic emission analysis.|
There are several ways to determine the crack type and orientation of AE sources. One concept is the determination of the polarity of the initial P-wave pulses. The distribution of the two senses of the wave polarity around the focus is determined by the radiation pattern of the source. This way, it is possible to estimate the orientation of the nodal planes and thus the mechanism of the source. Unfortunately, it is not possible to quantify the deviation from a pure shear dislocation source (Double Couple DC) with this method.
The analysis of the moment tensor is a different approach to the problem. The symmetric moment tensor with six independent components mathematically defines the strength and the 3D radiation pattern of a general seismic point source. The diagonal and the off-diagonal elements of the moment tensor represent force dipoles without or with moment, respectively. It was shown by several authors (Shigeishi and Ohtsu, 1992; Landis and Shah, 1993) that a determination of the crack orientation in concrete can be performed by the eigenvalue analysis of the moment tensor, picking the P-wave amplitudes of AE signals. With this method, deviations of DC mechanisms can be extracted as well as the radiation pattern of the whole damage process. A determination of the DC, compensated linear vector dipole (CLVD) (Knopoff and Randall, 1970), and the isotropic tensile components are the basis for the fracture mechanics analysis. To estimate the six moment tensor components, the amplitude informations of at least six AE recordings have to be used - a reasonable number in acoustic emission experiments.
Solving the problem with this method, the Green's functions of the specimen, describing the wave propagation in a medium, and the transfer function of the recording system have to be known. Considering the wave propagation in concrete, a unique Green's function is hardly to be found for a specimen because of the heterogeneity of the medium. Consequently, a moment tensor inversion based on P-wave amplitudes was employed in a relative way to eliminate the influences of inhomogeneity and anisotropy. The method was developed for the determination of the radiation pattern using cluster analysis (Dahm, 1993 and 1996). This relative approach is suitable for the requirements in AE experiments, as will be demonstrated in the next chapter. Up to hundreds of acoustic emissions are recorded which occur commonly in certain regions. This is called clustering. The travel path from different events of a cluster to a certain sensor is approximately the same, and thus the dynamic part of the Green's functions can be eliminated. A description of the mathematical procedure can be found in Grosse et al. (1997). For the application of this method to acoustic emission experiments, the following assumptions are made:
Due to uncertainties regarding the last item, deviations of pure shear mechanisms have not been investigated during the experiments described below.
With a 3D localization some first statements about the failure process can be made. As reported (Grosse et al., 1994), the spatial distribution of the events give some indications about the stress accumulation in the specimen. A more detailed analysis of travel time residuals can even be used to locate significant inhomogeneities in terms of a passive tomography.
Another interesting result is concerning the spatial and time dependent distribution of the events. During the experiment, the specimen had cracked into two parts due to the load before debonding led to failure. In Fig. 5, the AE sources are repesented in the x/z plane by numbers according to their appearance. The reinforcement bar was located in the middle of the figure and was pulled out upwards.
|Fig 5: Localization of acoustic emission events. Projection to the x/y plane with events numbered according to their appearance.|
At first glance, this representation seems somehow bewildering, but it becomes obvious that the numbers do not show an assorted pattern. As expected, most of the sound bondsources are located near the bar or in the area slightly above, which is the area of highestload amplitude in the cube. Assuming a failure process extending from the middle to the edges of the cube upwards, parallel to the trajectories of the stress, the AE accumulation should follow this direction. Obviously this is not the case for the time dependent appearance of the events. Examining for instance the signals along the two dashed lines, a discontinuous AE pattern (mixed numbers) can be observed. Destructive tests of the specimen indicated that not only the cementitious matrix but also the aggregates have been fractured. This effect and the failure of the specimen depend apparently on the quality of the bond between cement and aggregates as well as between the concrete and the steel bar. Zones with a higher porosity show earlier acoustic emissions than homogenious regions with a better bond. In case of a good bond between concrete and reinforcement, the specimen is splitting before a debonding of the bar occurs.
Results of the moment tensor inversion
The steel bar reinforcement of a concrete cube (100 mm side length) was pulled out of the specimen as described. Because of the load history, cracks with fault planes parallel to the pullout direction are expected as the dominant failure mechanisms. On the basis of the 3D localization, the AE signals were separated into clusters of up to ten events. A moment tensor inversion of every single event of the clusters resulted in numerous P/T diagrams as reported earlier (Grosse, 1996).
|Fig 6: Example of a Mode-II-fracture - moment tensor inversion and interpretation.|
In conclusion, considering the polarity constraints, it seems that shear faults in downward direction are predominant. The P-axes, pointing to the principal stress axes, are generally vertical with a shift between 10 and 25°. Regarding the T-axes, east-west directions are dominant but are not as well-fixed as the P-axes. Obviously, fractures of the Mode-II-type (normal shear faults) are the sources of these acoustic emissions. This is illustrated by Fig. 6, showing the results of a moment tensor inversion for a single event of a cluster with nine signals. The best solution for the P and T axis is indicated with a cross and a star, respectively. The estimated P and T axis are the eigenvectors corresponding to the minimal and maximal eigenvalue of the moment tensor. For pure shear dislocation sources, the fault plane normal is at 45° between the P and T axis, which are also the principal stress axes if the fault plane is a plane of maximum shear. The errors of the decomposed source components are estimated with a bootstrap analysis (Efron and Tibshirani, 1986) and are shown as small circles. This representation differs from the commonly used graphs of the nodal planes but, since errors are visualized, it helps to estimate the quality of the results. Additionally, from simulation studies Dahm (1996) concluded that P and T axes are the best resolved source parameters in the case of statistical noise in the data. The values below the graphs indicate the relative values (expressed as a percentage) for the shear component (DC), the extensional component (ISO) and the relative strength (MR). In addition, the relative seismic moment (SM) was calculated, which is proportional to the energy emitted by the source. The data quality and hence the scattering of the error points is closely related to the seismic moment (SM). The scattering of the error points is smaller with higher SM-values. In the middle of fig. 3, the fault plane solution resulting from the inversion of the moment tensor is shown, indicating the regions of pressure and dilatation. On the right, the fracture mechanical interpretation is represented summarizing the results of the fault plane solution and taking into account the polarity informations of the AE recordings. In this example, the normal fault is inclined by 20°. Some events of the examined clusters show variations of normal faulting. As represented in Fig. 7, very few events had to be interpreted as Double-Couple mechanisms with a strong strike slip component. This could be explained as a turn around of a matrix crack formation caused by the aggregates in concrete.
|Fig 7: Example of strike slip faulting - moment tensor inversion and interpretation.|
Even though these interpretations seem plausible, it is important to know that this conclusions are based on an insufficient and inherent data base (disfavourable hypocenter distance to wavelength relation). A summary of the results of the relative moment tensor inversion for the events and clusters of this experiment is reported in Grosse et al. (1997). Experiments investigating the fracture mechanisms in more detail as well as enhancing and improving the data basis are conducted nowadays.
For example, the interaction between concrete and a reinforcement bar under load was studied including the dynamic aspects of concrete failure. A significant AE activity around the steel bar has been recorded caused by normal faults with slip parallel to the load direction or up to 20° shifted.
Still in progress is work done on beams of steel fibre reinforced concrete, starting with a few, aligned fibres and ending up with an industrial volume fraction of randomly distributed fibres. First tests indicate good results with respect to the localization of matrix cracks and difficulties in the identification of fibre pullouts within the beams. For more details refer to the paper by Weiler et al. In this volume.
Acoustic emission analysis as represented in this paper can be used to understand the failure process in concrete and to optimize the bond between matrix and reinforcement. In the next future the presented analysis methods will be supplemented by ultrasound techniques using B- and C-Scan as well as certain imaging algorithms. In addition Finite-Difference methods will be used to understand the wave propagation in the material.
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