|NDT.net Dec 2004 Vol. 12 No.12|
Fracture process zone in notched concrete beams treated by using acoustic emissionH. Hadjab*, J.-Fr.Thimus
Professor and Head of the Arichitecture and Civil Engineering
and environnemental Departement of the Université catholique de Louvain,
Bâtiment Vinci, Place du Levant 1, 1348 Louvain-la- Neuve, Belgium.
*Hadda Hadjab is a PhD Student in the Civil Engineering and Environnemental Departement of the Université catholique de Louvain,, Belgium. Tel.(box):+32-10-472-125; fax: +32-10-472-179
AbstractIn the present paper, Acoustic Emission (AE) is used to investigate characteristic of the Fracture Process Zone (length, width and how macro crack propagation) in a concrete specimen subjected to four-point bending replying it to probability and statistics methods. To understand the process of the crack growth and fracture, a technique based on Acoustic Emission is developed. The results are treated according to probability and statistics laws. It is shown herein that these results agreed more or less in comparison to those obtained by the use of other techniques.
Keywords: Fracture Process Zone; quasi-brittle; Acoustic; Statistics; Probability; Concrete; propagation
1. IntroductionLinear elastic fracture mechanics allows the stress to approach infinity at a crack tip. Since infinite stress cannot be developed in materials, a certain range of inelastic zone must exist at the crack tip. For concrete, this inelastic zone surrounding the crack tip is being known as the Fracture Process Zone (FPZ) characterized by complex mechanisms[1-6] In brittle materials, macro cracks growth is associated with a Fracture Process Zone depending upon the material's microstructure, grain size, rate of loading, dimensions of specimen and other's parameters. The size of the FPZ can be significant. The FPZ can also be the result of micro cracking that occurs in front of the crack tip, somewhat similar to the plastic zone in metals or as the result of nonlinear phenomena existing behind the crack tip such as frictional interlocks between tortuous cracked surfaces and discontinuous fractures of unbroken aggregate bridging.
In the past, many authors have experimentally investigated growth of the Fracture Process Zone. They showed that its reported nature and exhibited dimensions are significant (see Table 1). Such discrepancies probably resulted from differences in observations, specimen geometry and dimensions. During their task, the following techniques have been used:
CT**: compact tension specimen
As the FPZ is considered as being one of the principal mechanisms in the fracture of quasibrittle materials, the main goal of this study is to obtain more data describing the FPZ characteristics (length, width and how macro cracks propagate) by using Acoustic Emission (AE). The interpretation of measurements is done by help of probability and statistics methods.
2. Description of the experimental investigation
2.1 Specimen preparationThe specimens are cast in steel molds of dimensions 60x15x15 cm according to the recommendations of ASTM. In order to create a notch, a fine plastic strip of 0.5x3cm was introduced during casting at the center and also at the base of the specimens.
The used concrete is composed of CEM I 42.5 R Portland Cement, 0/5 river sand and 7/14 crushed gravel. The mix proportions by weight are 1:2:3:0.5 (cement: aggregates: sand: water). All specimens are stored in air conditioned room at 20°C with 90 % humidity during 28 days. The average compression strength was about 52 MPa for cubes of 15x15x15 cm and 15.45 kN for the peak load for tests in four-points bending tests (FPB).
2.2 Tests performedFor this research, 24 specimens have been tested. Each test consists to a four-points bending test with one loading / unloading cycle until 70 % of the peak load value (15.45 kN). This peak value was determined by the performing of 5 four-points bending tests with similar specimens. For each specimen, the accelerometer sweeps the 6x4 locations (nodes as shown in Figure 1). For each location of the accelerometer, one performs the loading / unloading test (70 % of 15.45 kN). The maximum load capacity of the testing machine is 50 kN; the tests are performed with a displacement control of 0.01 mm/min. For a better follow-up of the test, a Crack Mouth Opening Displacement (CMOD) is recorded by using an extensometer MTS 632.02F-20.
2. 3 Acoustic emission measurementsAn Acoustic Emission (AE) is a localized and quick release of strain energy in a stressed material. The released energy causes stress waves, which propagate through the specimen. These waves can be detected at the specimen surface and analyzed to evaluate the magnitude and the nature of damage.
In the case of concrete specimens subjected to a mechanical loading, the AE results from a local fracture. Applications of AE to the detection of cracks and more particularly to the measurement of crack growth have been developed. The acoustic events are detected by a PCB quartz accelerometer (303 A02), having the following characteristics:
On the basis of the results a grid of 20x20 mm has been designed around the vertical plane of macro crack. In order to have more information about the FPZ during the test, the accelerometer moves from node to node and sweeps the grid area in a horizontal scanning. For every node in the grid, the AE signals are recorded.
The test measurements and data acquisition are managed by software developed at Civil Engineering Laboratory of UCL called AUSPICES (Acoustic & Ultrasonic Propagation Imaging Complementary to Elapsed Strength).
After amplification and filtration in a conditioner (frequency band from 0.1 to 50 kHz), signals greater than a preset threshold (chosen above the environmental noise) are transformed into impulses and counted. As many elastic waves can be generated by one event a certain duration is given to each event. That means that even if the threshold is exceeded several times during this time laps, only one event is counted. The signal of each event can moreover be recorded using an oscilloscope (sampling frequency of 500 Hz) for further analyzing. During the test, the noise threshold is fixed at 0.18 g, while the event duration is set to 1 s.
3. ResultsDevelopment and growth of micro cracks in front of the notch of all tested specimens were monitored to determine the extent of the FPZ in concrete.
Once the specimen is loaded, the AE signals resulting from micro cracking can be detected by the accelerometer mounted on the specimen at different location of the grid area. The signals are picked up by the data acquisition system. In order to treat the data, which are related to a certain number of random phenomena including a dispersion of the values, a probability and statistics approach is used to the 24 tests for each specimen. One thus has to seek to synthesize the observations, to test susceptible assumptions causing this dispersion, and finally to draw the conclusions on the basis of studied characteristic. The Poisson's law tests the probability of mode of fracture. Observation errors are then estimated by using a normal law of Gauss for the fields of the maximum amplitudes average and afterward one can obtain acceptable approximations.
3.1. Probability and statistics analysisUsing probability and statistics laws, results (amplitude of the AE) are discussed and interpreted in terms of probability. Since the repartition function F
According to probability and statistics approach, a quantile of 'q' order of a random continuous variable X and of a distribution function FX , is a value uq defined by this expression for a continuous case as:
and for a discreet case by the following relation:
One can define also the percentage number as:
During the tests campaign, for each 24 specimens and for the 6x4 locations of accelerometer, the amplitudes of the signals of acoustic emission are recorded and the maximum amplitudes Ami,j are calculated as:
where i, j denote the specimen number and the node location number respectively.
3.1.1 Procedure to estimate the length of FPZFor a horizontal row formed by four nodes, one calculates the average of maximum amplitudes noted as Ams (where the subscript 's' designs a given specimen); one obtains six values corresponding to different distances to the macro crack, more illustrated in Table 2.
3.1.2 Procedure to estimate the width of the FPZFor a given location, the average of maximum amplitudes for the 24 specimens is then noted as Amj. If we associate Amj to the continuous random variable X , the percentages events amplitudes number, Aq , are equivalent to the quantiles of 'q' order which is more illustrated in Figure 2 for the 6x4 nodes locations and 24 specimens. The values of amplitudes present, in terms of statistics, a population verifying Gauss's law (see detail in Figure 2) and well defining by the notion of quantile, which represents the percentage of the amplitudes dispersion and are given as:
where uq is the value of the quantile of 'q' order equivalent to Amj. On the basis of Aq values obtained for each location of accelerometer, the cumulative average percentage number noted by N is then calculated by the summation and average in the same vertical column all the six values.
3.2 Interpretation of resultsThe probable propagation of macro crack is then obtained by putting all results into the grid, and by assuming that this latest (i.e. probable propagation), corresponds at the maximum event percentage (as shown in Figure 3). The AE enables us to follow the process of the propagation of micro crack in such structures and defines the characteristic of the FPZ by the length and width measures.
4. DiscussionOnce the load increases and the main crack propagates, a very long Fracture Process Zone is developed ahead of the macro crack while the number of Acoustic Emission progresses dramatically.
4.1 length of FPZ
In light of the relationship between the average maximum of amplitudes point's events ( Ams ) and the distance to the macro crack tip (as shown in Figure 4), one can distinguish three regions:
On the other side, Figure 5 which presents load and AE events as a function of CMOD, shows four specific zones, that can be described as follows:
In summary, the evolution of the AE events permits to visualize the micro cracking zone as well as its characteristics. Then, the first micro crack appears at a point B (42 % of the peak load). At this particular point, a continuous zone is formed by a numerous micro cracks as defined in zone 2. The relationship between the applied load and the CMOD in a FPB specimen allows us to deduct that one can divide the curve in four zones based on initiation and the propagation of micro cracks. In order to study the FPZ, it is important to know what really happens into this zone.
This zone is delimited by two points B and C (about 68 % of the peak load). While micro cracks start to localize ahead of the macro crack, propagation of this latest begins in a proportion way with an increase of load. This phenomenon is referred to damage localization or strain localization characterizing the Fracture Process Zone. On the basis of these results shown in Figure 5, one can conclude that the FPZ length is limited between the point B and just before the peak load. On the other side, Figure 4 shows that using the AE events and precisely from 1 cm until 9 cm (vertical distance at the macro crack), the amplitudes increases by the rather small formation of micro cracks, which may be considered as constant (the uncertainty interval between two successively values is relatively constant in the two first intervals, compared to the third one). In this case, the FPZ is extending across the two first intervals represented above and its length is estimated appreciatively at a distance less than 9 cm.
4.2 width of FPZFigure 6 develops the method for measuring the width of FPZ. This one can be obtained while drawing the function N = f(x) where N is the cumulated average percentage of events for each vertical node and x is taken as the horizontal distance from the macro crack.
Figure 6 represents a curve with a top value at the point of co-ordinates (-1.0, 87.30 %) and a low value at the point of co-ordinates (3.0, 75.84 %). One may divide this curve in two areas:
Area 1 is limited by the more emissive vertical line (87.30 %) and the second emissive line (82.42 %). This area extends over a width of 3.3 cm. Its width defines a zone of confidence of events in which the amplitudes of the AE have low values, which are related to the material's damage.
Therefore, the width of this zone corresponds indeed to a so-called security value of a damaged zone occurring in front of the macro crack.
Area 2 is located below the second emissive line and is represented by a lower percentage, which corresponds of larger amplitudes.
If we adopt an arbitrary criterion that allows us to link up to a notion of damage, one considers that a vertical line is damaged if it contains more average percentages of events than the horizontal line dividing the curve in two areas.
It is important to remark that this line ( N = 82.42% ) gives us the width of the FPZ based at the confidence interval implying that the width of the FPZ is estimated at 3.3 cm. This latest is considered to be representing 2.75 times larger than the largest one in homogeneity of the structure (aggregate size).
4.3 Comparison with other approachesOn the basis of these results, a comparative study with theoretical models taking into account the characteristics of the FPZ is performed. These models are based on Dugdale- Barenblatt energy dissipation mechanism, or by the use of distinguished ones such as the Crack Band Model by Bazant and Fictitious Crack Model suggested by Hillerborg. Bazant modeled the Fracture Process Zone as a band of uniformly and continuously distributed micro cracks with a fixed width, hc, as follows;
where da is the maximum aggregates size and na is an empirical constant equals 3 for concrete. In this work, an approximate average value has been obtained (2.75, as explained above). For Hillerborg, the length of the FPZ is related to the length of the cohesive process zone which is a purely material property and is called the characteristic length given by:
in which ft , E and Gf are respectively the material tensile strength, the modulus of elasticity and the fracture energy. Hillerborg found that in concrete specimens subjected to uniaxial tension, the characteristic length is proportional to the length of the FPZ based on the fictitious crack model. The value of for concrete approximately ranges from 10 cm to 40 cm. According to the AE results of our study (see Figure 4), the value of the lchstudy can be considered as 11 cm and the FPZ length is 9 cm
. In this work, the length and width of the FPZ are estimated to be equal to 0.82 lch and 2.75 dagg , respectively.
5. ConclusionAnalyses of the load-CMOD and AE curves imply that macro cracks extends slightly before the load reaches to the peak, creating in this way the FPZ. The presence of this zone results in stable crack growth before the peak load and is also the main key responsible for the quasi brittle fracture response of concrete beyond the peak load. Then the behavior of concrete is greatly influenced by the existing of the Fracture Process Zone. To accurately quantify FPZ in concrete, it is important to determine experimentally its dimensions (width and length) as well as the propagation of the macro crack, which are considered important parameters to understand quasi-brittle fracture phenomenon of concrete.
The interpretation of the results in this study as well as the investigation of measurement by AE enable us to have qualitative information. From our point of view, it is a very delicate method, which, at the present time, does not lay out of any rigorous and objective criterion allowing us by stating from an uncertain number of acoustic events localized in the plan to determine, with a certain precision, the dimensions of the Fracture Process Zone. Thus, we are limited in this study to use only a qualitative approach, which consists to take in consideration only the information given during the various tests. On the basis of these latest, obtained results have shown more or less good agreements in comparison with those found by the use of other techniques.
AcknowledgementsThe authors are grateful to the Civil Engineering and Environnemental Laboratory at the Catholic University of Louvain. The first author was funded by the Commission Internationale pour la Coopération au Développement of the Catholic University of Louvain.