ABSTRACT. This paper investigates the waveforms and frequency spectra of elastic emissions (ELE), or quasi-rigid body vibration pulses, due to the formation ...
Waveforms and frequency spectra of elastic emissions due to macrofractures in solids
A. Schiavi1, G. Niccolini1, P. Tarizzo1, A. Carpinteri2, G. Lacidogna2, A. Manuello2 1
INRiM - National Institute of Metrological Research, Strada delle Cacce 91, 10135 Torino, Italy. 2
Politecnico di Torino, Department of Structural Engineering & Geotechnics, C.so Duca degli Abruzzi 24, 10129 Torino, Italy
ABSTRACT This paper investigates the waveforms and frequency spectra of elastic emissions (ELE), or quasi-rigid body vibration pulses, due to the formation of macrofractures in perfectly brittle, quasi-brittle and ductile materials subjected to uniaxial compression. Elastic emissions, differently from acoustic emissions, are detected in a low frequency range (i.e. below 15-10 kHz) and are characterized by high levels of released energy. Approaching to the large fractures and the final collapse of the material bursts of ELE are observed indicating the solid elastic-mechanical properties degradation and its irreversible plastic deformation. Through waveform and time-frequency analysis of the ELE spectra, measured by calibrated transducers, it is possible to provide quantitative information on the damage evolution and the strain energy released during each ELE event.
INTRODUCTION The brittle fracture of materials is a complex phenomenon which occurs according to two broadly defined scenarios. In the first one, failure occurs by sudden propagation of a single fracture without appreciable precursors. In the latter, failure occurs as the culmination of progressive damage. The phenomenon of damage from a physical point of view represents surface discontinuities in the form of cracks, or volume discontinuities in the form of cavities due to decohesion between inclusions, debonding between fibers and matrix in composite materials, delamination, corrosion and other disruptive phenomena. The most advanced method of quantitative non-destructive evaluation of damage progression is the acoustic emission (AE) technique. Since many years the expression ‘‘acoustic emission” (AE) is used to mean a class of phenomena in which transient elastic waves are generated by the rapid release of energy from localised sources, typically developing cracks, within a material. AE waves, whose frequencies typically range from kHz to MHz, propagate through the material towards the surface of the structural element, where they can be detected by sensors which turn the released strain energy packages into electrical signals.
T. Proulx (ed.), Experimental and Applied Mechanics, Volume 6, Conference Proceedings of the Society for Experimental Mechanics Series 9999, DOI 10.1007/978-1-4614-0222-0_73, © The Society for Experimental Mechanics, Inc. 2011
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610 Traditionally, in AE testing a number of parameters are recorded from the signals, such as cumulate number, occurrence and amplitude. The condition of the specimen is determined from these parameters. Over the years, through more sophisticated analysis techniques, many spectral analysis of acoustic emissions generated by fracture in many typologies of materials were carried out. However, in general, the analysis are limited in frequency range greater than 100 kHz, regardless the signals in the audible range, and are mainly focused on the counting of events in time. More in deep analysis of the waveform and frequency on spectra of AE, allow to identified additional informations carried by elastic waves, such as the quantification of the energy released in the evolution of damage. The amplitude level increasing, the variation in frequency and the cumulative rate over time are signature of the damage evolution, from micro-crack to the meso- and macro-crack until to the collapse of the material.
SHORT BACKGROUND The first analytical studies on the AE signals are due to Egle and Tatro in 1967 [1]; the authors have discriminate the AE due to longitudinal waves by AE due to flexural waves, providing the first estimation of energy released for each AE event. Pollock [2], in 1971, had highlighted the question of broad-band spectrum of the acoustic emission claiming that these emissions source wave carries appreciable energy at low frequency. The analysis of the energy content and the frequency spectrum of the AE allows to provide relevant information on the fracture and on its evolution from the diffusion of microfractures to macrofractures in different materials experience evolving damage. In 1990 Bocca and Carpinteri [3] have shown that in rock and concrete specimens, with very high strength, the catastrophical failure gives rise to the release of a remarkable amount of energy quantifiable through a negative impulse produced by the specimen in the time interval immediately following the achievement of peak load. Bruneau and Potel [4], through a statistical analysis of the energy content of AE, showed the evolution of fracture in composite materials. AE signals, approaching to fracture, are characterized by different higher distribution and rate. Depending on the energy level of the signals two main stages of damage are classified: matricial-cracks and interfacial decohesion. Aggelis et al. [4] have also used the AE parameters to monitor the transition of the damage mechanism from transverse cracking to delamination of cross ply laminates degradation, through an analysis of the signal amplitudes and frequencies in a range between 100 kHz and 500 kHz, of acoustic emissions. Recently a spectral analysis of acoustic emission signals at very low frequency, i.e. between 1 kHz and 20 kHz has been proposed [6]. The evolution of the fracture has been investigated in a frequency range such as to exclude all AE due to purely vibration modes of the specimen. Actually, these emissions, defined elastic emissions (ELE), are quasi-rigid body vibrations resulting from the specimen flexibility and the constraints (specimen-platen contact with friction). In the next stages of the fracture, until to the final collapse, ELE with wavelengths much greater than the maximum size of the solid under consideration are detected. The hypothesis is that the formation of macrocrack generate pulses in the volume of the solid, which excite not only the vibration modes of the body (whose wavelengths, depending on the speed of elastic wave propagation in solid, are less than the size of the solid tested), but also actual dislocation of the entire parts of the solid.
611 ELASTIC EMISSIONS An ELE event would imply a rigid vibration of the body, while high-frequency AE are pure vibration modes of the body, including longitudinal (P-), shear (S-) and surface (Rayleigh) waves, due to micro-crack growth. Taking into account that the Rayleigh superficial waves velocity, cR, is about 0.92 of the S waves velocity cS and, at least, cS ≈ cL /√ 3, the propagation velocity cR of the Rayleigh superficial waves in the tested materials has been estimated to be roughly 0.531⋅cL, from the measured cL of the longitudinal elastic waves. On the basis on this restrictions, for the typology of the material and for the size, i.e. that the half-wavelengths λELE of detected signals fulfil the relationship λELE 2⋅dMAX, the upper limit for the ELE frequencies is defined as:
f ELE ≤
cR 0.92 ⋅ c L c ≈ ≈ 0.265 L 2 ⋅ d MAX 2 ⋅ 3 ⋅ d MAX d MAX
(1)
In order to verify that ELE were actually fracture phenomena and not random or spurious signals, such as extraneous noise and background vibration statistical analysis for specific this type of phenomenon has been carried out. All ELE were subjected to the Gutenberg-Richter and Omori laws [7]. These statistical methods show that the space-time organization of events of fracture (from seismic macro-scale to faintest acoustic emissions), is governed by well-defined scaling laws, as shown in some recent works. This result, comforted by other evidences, such as increase of rate and amplitude in time [8], allow the hypothesis that ELE are actually precursors of plastic deformation and irreversible damage in volume of the solid under compression to be confirmed. Besides a simple method to quantify the released energy in terms of kinetic energy of ELE has been also proposed [9]. However these emissions can be considered as precursor of large fractures or collapse, even if no change in slope can be recognized in the classical stress-strain curve. This consideration implies that, even if the material is undergoing a yielding or damage, for certain values of load, the elastic modulus does not seem to vary.
EXPERIMENTAL SET UP AND TESTED MATERIALS The test is performed in displacement control at constant piston velocity of 0.5·μm/s, using a servo-hydraulic press with a maximum capacity of 500 kN, equipped with control electronics. The specimen adheres to the press platens without any coupling material (specimen-platen contact with friction). The applied force is determined by measuring the pressure in the loading cylinder by means of a transducer. The margin of error in the determination of the force is 1%. The stroke of the press platen in contact with the test specimen is controlled by means of a wire type potentiometric displacement transducer. Two kind of “delta shear” accelerometers, with respectively the upper frequency limit of 10 kHz and 20 kHz, for detection of ELE events are used, depending on the typology and size of specimen tested. The events are characterized by the output response of the calibrated transducers (charge sensitivity 9.20 pC/m s–2 and 0.33 pC/m s–2), expressed in mm/s2. The accelerometer transducers are rigidly (fixed) coupled to the specimens in order to detect the surface acceleration.In order to filter out environmental background noise, we set appropriate detection thresholds for acquisition systems, i.e. 60 dB (referred to 1 μm/s2) for ELE signals and a pass-high filter in order to filter out any residual background vibration under 1 kHz. Tested materials are two specimen of concrete (with different features) and one specimen of Green Luserna Granite. As shown in Table 1, the physical quantities of interest
612 (specimen size, longitudinal wave velocity) indicate that the adopted transducer, working in the range of 1 to 10 kHz or in the range of 1 to 20 kHz, properly detects only ELE events. Table I. Tested materials and features
Specimen
Material
Density
Mass
Max size
[kg/m3]
[kg]
[m]
Longitudinal wave speed [m/s]
fELE [kHz]
1
Concrete
2500
0.146
5.3·10-2
4270
21.3
2
Luserna gran.
2480
0.580
10.6·10-2
2950
7.4
~ 4500
11.9
3
Concrete
2200
2.200
10
-1
EXPERIMENTAL RESULTS We analyzed the energy (in terms of global level amplitude) and frequency spectra of ELE during compression tests on three materials with different failure modes: ductile (concrete 1), quasi-brittle (Luserna 2) and perfectly brittle (concrete 3). In previous works such investigations were restricted to high-frequency AE. The increase of AE amplitudes as failure is approached were experimentally observed in [4]. Variation of AE frequencies during damage evolution has been studied in [10]. It has been observed that AE frequencies, as a function of increasing load, tend to decrease during “pre-failure” and “post-failure” stage, while tend to increase after the main fracture. These stages are separated by the so-called “seismic calm” stage, in which AE activity can be detected only in the MHz range. The behaviour of AE frequencies can be described through a “s-shape” curve, as shown in Fig.1. In this work analogous analysis on ELE spectra has been carried out.
Fig. 1: S-shape curve of AE during failure of rock specimen
Here, all ELE events detected during a compression test are shown as a function of time, amplitude and frequency. These 3D-graphs provide exhaustive information on the ELE activity. Each point represents the global level of a single ELE experimentally measured, and the frequency value is related to the peak of greatest amplitude in the considered spectrum. As an example, Fig. 2 shows the spectrum related to a single point in the time - energy - frequency diagram, where the X-axis represents the time in seconds, the Y-axis is the frequency in hertz, and the Z-axis is the amplitude in dB referred to1 μm/s2.
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Fig. 2: Example of spectrum extrapolated from the 3D-graph of a single ELE (detected on concrete 3 at 1209 s). Global level 113 dB, frequency peak 8.6 kHz.
Ductile fracture The duration of compression test on concrete-1 was 1600 s, with a change in the slope of the stress/strain curve 760 s since the beginning of the test. The failure behaviour of the specimen is ductile. In the graph a sporadic ELE activity at the beginning of the test and during the failure is detected. The ELE energy is spread over a range of about 15 dB. Frequency peaks are located around 4.5 kHz, both before and after the collapse of the sample. However, ELE activity both in pre-failure and in post-failure stages may be mainly due to frictional phenomena within the specimen. Failure occurs as the culmination of progressive damage without propagation of large fractures within the bulk of material. Therefore, ELE do not play as failure precursors in the specimens which exhibit ductile behaviour. In Fig. 3 distribution of ELE activity during compression test and distribution of amplitude/frequency are shown.
Fig. 3: ELE activity in ductile fracture on concrete 1.
614 Quasi brittle fracture The duration of compression on the granite Luserna specimen was 1420 s, and ELE activity started 600 s since the beginning of the test. ELE events concentrated when load drops occur. A burst of ELE activity can be recognized at about 1000 s, before the first significant load drop occurred at 1180 s. Although the slope of the stress/strain curve didn’t exhibit any significant variation between 600 s and 1180 s, the presence of ELE with high energy content (between 105 dB and 125 dB) indicated the growth of meso-and macro-fractures. Moreover, the range of signal amplitudes, i.e. 30 dB, was greater than the ductile specimen. Later on, between 1200 and 1400 s, the ELE rate increased with bursts of activity at each load drop. While in the stages shortly afterward each load drop (e.g. between load drops 3 and 4) no significant ELE bursts were detected, similarly to the AE “seismic calm”. The ELE frequencies of ELE were generally at 3.5 kHz, between 600 s 1200 s, while in the final stage, after 1200 s, ELE peaks appear at 1.9 kHz. 4.5 kHz and 6 kHz, as shown in the 3D diagram of Fig.4.
Fig. 4: ELE activity in quasi-fragile fracture on granite 2.
Perfectly brittle fracture The ELE activity, during the compression test on concrete-3 (high resistance concrete) was detected during all the test, although a significant increase was revealed after 1000 s. In this specimen a significant increase in the ELE amplitudes, and a concomitant decrease of peak frequencies can be detected, as shown in Fig. 5.
615
Fig.5: zoom selection of ELE activity (frequency in blue and amplitude in red) in the proximity of fracture.
Between 900 s and 1200 s, as the slope of stress/strain curve didn’t change appreciably, the ELE activity played a significant role both as a fracture precursor and as indicator of plastic deformation (or irreversible deformations). Moreover, ELE were detected in a very wide range of amplitude, extending approximately over 50 dB.
Fig. 6: ELE activity in perfectly brittle fracture on concrete 3.
CONCLUSIONS In this work the analysis of waveforms and frequency spectra of ELE has been proposed. Each spectrum (including the energy content as a function of frequency) was experimentally determined using calibrated accelerometers. A
616 quantitative analysis of the global level of acceleration (or velocity) of vibration can be carried out for all detected ELE events. The spectrum shape in the frequency region of interest and the energy released were measured as well. The variation of energy content and ELE frequency depend on the failure behaviour of the examined solids. In perfectly brittle materials, ELE energy increase is correlated with a frequency decrease until the specimen failure. In the case of brittle materials (such as granite) burst ELE seemed to show a random distribution of frequencies, although it is still possible to highlight significant increases in amplitude approaching the drop-load and the main fracture. In these materials, after the drop-load, the phenomenon of so-called “seismic calm” can be observed. At this stage it is assumed that AE are probably still present at frequencies too high to be detected with instruments used in these tests, but ELE are completely absent. Finally, in materials with ductile behaviour ELE events are due to internal frictional phenomena and appear during progressive damage until failure occurrence.
ACKNOWLEDGEMENTS The financial support provided by “Regione Piemonte” Re-Frescos project, is gratefully acknowledged.
REFERENCES [1] Egle, D. M., Tatro, C. A., Analysis of acoustic emission strain waves, J. Acoust. Soc. Am. 41 (2), 1967.
[2] Stephens, R. W. B., Pollock, A. A., Waveforms and frequency spectra of acoustic emissions, J. Acoust. Soc. Am. 50 (3) part 2, 1971.
[3] Bocca, P., Carpinteri, A., Snap-back fracture instability in rock specimens: experimental detection through a negative impulse, Engineering Fracture Mechanics, Vol. 35, n. 1/2/3, 1990.
[4] Bruneau, M., Potel, C., Materials and Acoustic Handbook, ISTE Ltd., London/John Wiley & Sons, Inc., Hoboken, NJ, 2009, Chap. 24.
[5] Aggelis, D. G., Barkoula, N. M., Matikas, T. E., Paipetis, A. S., Acoustic emission monitoring of degradation of cross ply laminates, J. Acoust. Soc. Am. 127 (6), 2010.
[6] Schiavi, A., Niccolini, G., Tarizzo, P., Lacidogna, G., Manuello, A., Carpinteri, A., Analysis of acoustic emissions at low frequency in brittle material under compression, Proceedings of the SEM Annual conference 2009, Albuquerque, New Mexico, USA.
[7] Niccolini, G., Schiavi, A., Tarizzo, P., Carpinteri, A., Lacidogna, G., Manuello, A., Scaling in temporal occurrence of quasi-rigid body vibration pulses due to macrofractures, Physical Review E, 82, 2010.
[8] Schiavi, A., Niccolini, G., Tarizzo, P., Carpinteri, A., Lacidogna, G., Manuello, A., Acoustic emissions at high and low frequencies during compression tests in brittle materials, Strain, 2010, doi: 10.1111/j.1475-1305.2010.00745.x.
617 [9] Schiavi, A., Niccolini, G., Tarizzo, P., Lacidogna, G., Manuello, A., Carpinteri, A., Analysis of energy released by elastic in brittle material under compression, Proceedings of the SEM Annual conference 2010, Indianapolis, Indiana, USA.
[10] Kukalov, G. I., Yakovitskaya, G. E., Acoustic Emission and stages of the crack-formation process in rock, Mining Institute, Siberian Branch, Russian Academy of Sciences, Novosibirsk 2, 111 (1993).
