- Email: [email protected]
Fast X-ray tomography and acoustic emission study of damage in metals during continuous tensile tests
Available online at www.sciencedirect.com
Acta Materialia 55 (2007) 6806–6815 www.elsevier.com/locate/actamat
Fast X-ray tomography and acoustic emission study of damage in metals during continuous tensile tests Eric Maire a
a,*
, Vincent Carmona a, Joel Courbon a, Wolfgang Ludwig
a,b
Universite´ de Lyon, INSA-Lyon, MATEIS CNRS UMR5510, 7 avenue Jean Capelle, F-69621 Villeurbanne, France b ESRF ID19 beam line, BP 220, F-38043 Grenoble, France Received 6 July 2007; received in revised form 29 August 2007; accepted 29 August 2007 Available online 22 October 2007
Abstract Model AA-2124 matrix composites with two different reinforcement sizes were pulled with a strain rate of 105 using a dedicated tensile rig suitable for in situ tomography. Two main novelty aspects characterize the present study. First, tomography provides a new approach towards understanding the significance of AE signals, recorded simultaneously, during image acquisition on the same sample. The number of acoustic emission events is found to be in good agreement with the number of cracks as detected by image analysis and the energy of the signals is proportional to the dimension of the cracks. Secondly, fast tomography was used to perform the first continuous in situ tensile test. The continuous procedure is compared in the paper with the standard step by step procedure. 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Damage; Tomography; Metal–matrix composites; Acoustic emission
1. Introduction The rupture of a material is a complex process which has been widely studied experimentally and theoretically. The purpose of these studies is to describe the physics and mechanics of this process completely in order to help researchers predict the rupture or optimize the microstructure to delay it. In the case of many metallic materials, rupture occurs during ductile deformation. In such a process, involving a lot of plasticity, the damage mechanism has been shown to be composed of three different phases: initiation occurs by rupture of the fragile second phase inclusions always present in the matrix of standard metallic materials [1]; then these initiated microcracks grow by plastic deformation of the surrounding ductile matrix; and finally they coalesce, leading to the appearance of larger cracks in the matrix itself.
*
Corresponding author. E-mail address: [email protected] (E. Maire).
Acoustic emission (AE) is a non-destructive way of studying damage [2–4]. It is easy to implement but the information obtained is only global, so that it is desirable to obtain a more local picture of the damage process in parallel. One of the best methods for imaging a damage process is synchrotron X-ray tomography, which shows a non-destructive image in the bulk and without bias due to surface preparation and/or surface stress state [5,6]. The ductile rupture process has been imaged by several authors using tomography but with rather long exposure times, typically 1 s per radiograph and 1000 radiographs for one acquisition [5,6]. This requires the mobile grip of the tensile machine to be stopped during acquisition, so as to prevent blurring of the tomographic images due to the large tensile displacement during the scan acquisition. Depending on the material, during these stops where the displacement of the grip is fixed, plastic relaxation leading to a substantial reduction of the stress can be observed and it is not clear how this affects the complete rupture process. It has been observed in some polymer systems, for instance [7], that delayed rupture could be observed during these
1359-6454/$30.00 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2007.08.043
E. Maire et al. / Acta Materialia 55 (2007) 6806–6815
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Fig. 1. Tomographic reconstruction of both materials showing the good microstructure of the produced material. (a) Small particles, 2D tomographic slice; (b) large particles, 2D tomographic slice; (c and d) 3D rendering of the small particles.
stops due to relaxation probably accelerated by the X-ray irradiation. Metal systems are known to be less sensitive to X-rays, but those based on aluminum, for instance, are not far from their melting temperature when tested at room temperature. Relaxation in this case can be a nonnegligible contribution to the deformation. Three-dimensional (3D) imaging has not yet been achieved during a continuous tensile test. Recently, Pyzalla et al. [8] showed that fast tomography could be used to study the damage process during the creep of a metallic material. In the present paper we combine AE and, for the first time, fast tomography without stopping the tensile test. We show in the rest of this paper that this helps to obtain a more complete understanding of the damage evolution leading to the rupture of the sample.
Fig. 2. Geometry of the samples.
2. Materials and methods 2.1. Materials We have chosen model materials where damage occurs by particle fracture similar to these used in Ref. [6]. The materials were fabricated specifically for the present study. They are made of an age-hardenable standard AA-2124 matrix in the T4 state reinforced with spherical ceramic inclusions. The 2124 powder (size range 3–15 lm) was commercially provided by alpoco. The zirconia/silica spherical reinforcement is also a commercial product [6]. Two different materials were processed, each exhibiting a different size range for the reinforcement: one material was processed with so-called ‘‘small’’ particles (screened between 40 and 60 lm) and the other with ‘‘large’’ particles (screened between 125 and 250 lm). The choice of this kind of system was motivated by the ductility and X-ray transparency of the matrix and the sphericity, brittleness and X-ray absorption of the reinforcement. The two powders (reinforcement and matrix) were mixed using a turbulat, then cold-pressed in a cylindrical die (diameter 20 mm), hot-extruded at 450 C with a ratio of 16:1 to form bars of 10 · 2 mm in section and several decimeters in length, and finally heat-treated (in the T4 state for the matrix, i.e. 1 h at 530 C + water quench + at least 15 days at ambient temperature). The initial microstructure of the
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samples as seen by tomography is shown in Fig. 1. It can be seen from the figure that the spatial distribution of the spherical inclusions is rather homogeneous with both sizes of reinforcement. The matrix contains small pores. These fabrication defects are probably due to insufficient pressure being applied during the extrusion but do not modify the conclusions of the present study, because their size and fraction is much smaller than that of the inclusions. 2.2. Methods From the bars, dog-bone-shaped samples were cut according to the geometry given in Fig. 2. Acoustic emission sensors (two resonant micro-80 Physical Acoustics Corporation (PAC) sensors which have a large range of resonance, coupled on the samples with a thin layer of vacuum grease) were attached to both ends of each sample before it was mounted on a dedicated tensile rig, as shown in Fig. 3. A two-channel Mistras 2001 data acquisition system from PAC with a sampling rate of 4 MHz and a 40 dB pre-amplification was used to record AE data. The total amplification of the recording system was 80 dB. Ambient noise was filtered using a threshold of 40 dB. The structural part of the tensile rig used was a carefully polished PMMA tube [5] allowing the rotation of the entire stage without screening the X-ray beam. The tomograph used was the ID19 beam line at the European Synchrotron Radiation Facility (ESRF), Grenoble, France. The beam was monochromated to 38.5 keV. The radiographs were formed on a transparent luminiscent screen and an optical system magnified the visible light on a dedicated fast-readout low-noise camera. The isotropic pixel size was equal to 1.4 lm. Two different kinds of tomographic parameters were used to perform (i) high-quality slow acquisition and (ii) low-quality fast acquisition on two different samples cut from the same bar for each material. For the slow setup, the exposure time was 0.3 s and the number of radiographs (each 1536 · 820 pixels in size) was 1200. The total time required to record a scan was 20 min. For the fast setup, the number of radiographs was reduced down to 500, and each radiograph was binned (re-sized to 2.8 lm by binning 2 · 2 pixels into one). After binning, the size of the radiographs was 748 · 410 pixels and the exposure time was reduced to 0.1 s. The total scan time could therefore be reduced down to 1 min. The slow in situ tensile test tomography experiment was performed according to a standard step-by-step procedure. The initial microstructure of the sample was scanned using the slow tomography mode. The displacement rate was set to 103 and the sample was loaded up to a given strain level. At this stage, the rig displacement was stopped and the microstructure of the sample was scanned. This procedure was repeated at increasing strain levels up to the rupture of the sample. The novelty of the presented work is the use of continuous tensile test during tomography. For the continuous tensile test, the procedure was as follows. In order to save
beam time, the sample was first loaded at a standard strain rate (103) up to the elastic/plastic transition. It had been previously checked that only little damage was induced during this elastic part of the loading in these materials [5,6]. As further evidence, no acoustic emission could be recorded during this primary part of the loading in both kinds of materials. At this stage, the rig displacement rate was reduced to 0.05 lm s1 and the sample was loaded without stopping up to its rupture while scans were recorded every 2 min. The tensile curves obtained during these experiments are shown in Fig. 4. One can observe the perturbing effect of the stops on the tensile curves recorded during the two slow experiments compared with the smooth character of the two curves recorded without stopping during the fast experiments. The 3D images have to be properly treated and analyzed to obtain a quantification of the morphology of the particles and of the cracks, and their evolution during the test. The thresholding of the particles in the initial state is straightforwardly based on the gray level. As for the cracks, their very small opening just after initiation and the value of their gray level very close to that of the matrix
Fig. 3. The acoustic emission sensors mounted on the sample.
E. Maire et al. / Acta Materialia 55 (2007) 6806–6815
implies that a special procedure must be used to isolate them. This procedure, based on a sequence of thresholding, closing and screening (using the position of the particles) operations, is exemplified in the case of the small particles material in Fig. 5. We double checked that the proposed procedure for segmenting the cracks was in excellent agreement with the number of observed cracks by manual counting on a small but representative portion of the material. Once binarized, the images were labeled and the 3D morphology of each label (i.e. each crack or each particle) could be measured. All these operations, performed using real 3D algorithms, were applied to the images using plugins written in Java for the ImageJ free software [9]. The acoustic waves emitted by one single event being recorded simultaneously by two piezoelectric sensors, it was possible to locate the origin of each of these signals and also to reject the ones emanating from regions other than the useful part (gauge length) of the sample. For each of these signals several parameters (energy, amplitude, duration, etc.) were measured directly by the software used. Our purpose in the present study is to relate the characteristics of these signals to the tomographic observation. 3. Experimental results Figs. 6 and 7 show, for the slow and fast modes, respectively, but in the case of the small particles only, two series of slices extracted from the middle of the reconstructed block. These slices were extracted in the same location of the sample for increasing values of the plastic strain. They were sampled parallel to the tensile axis in order to show
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the effect of damage. These two figures show that the quality is slightly worse with the fast setup but that it is still sufficient to allow the observation of the damage mechanism in the studied material. Fig. 8 shows the microstructure before failure in the case of the large particles. All these figures reveal that damage initiates by particle fracture inducing penny-shaped cracks perpendicular to the direction of the applied load. During the plastic deformation of the sample, the number of these cracks increases and the previously initiated ones grow in the direction of loading, but hardly at all in the two directions perpendicular to the tensile stress. Further fragmentation of already broken particles can often be seen, especially in the case of the large particles. This leads to the formation of multi-fragmented particles. Note that, for this reason, the number of cracks counted by image processing in our following analysis is the exact number of cracks (for instance, two cracks in the same particle counting twice) and not the number of damaged particles. During the last deformation stages, neighboring cracks coalesce through the appearance of secondary cracks inside the matrix and this leads to the final rupture of the sample. Fig. 9 plots the location of the origin of the position of the different AE signals along the length of the specimen. This plot is given as a function of the global stress in the composite. The case of the small particles material has been chosen as a representative example of such a plot. The graph demonstrates that the spatial distribution of damage is rather homogeneous along the length of the two samples. The same observation has been made for the large particles. It can be understood from this figure that damage is distributed rather homogeneously in the strained volume of the sample
Fig. 4. Tensile curves recorded during the slow and fast experiments for both materials.
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(this is consistent with the visual impression given by Figs. 6–8). Note also in this figure the effect of the perturbation of the AE results induced by the stops during the slow experiment. This perturbation appears just after each of the stops during which the stress relaxes at constant strain. No AE event is observed before the sample is restrained up to a stress equivalent to the maximum stress reached before the stop. This explains the portion of the interrupted curves where the strain increases while no AE event is detected. Fig. 10 shows the evolution of the events counted in acoustic emission, as a function of those counted using image analysis, for the two materials and for the two types
of experiments (fast and slow). The principal conclusion of this figure is that, in terms of the number of events detected, acoustic emission concurs rather well with direct observation. This is probably the first time that this kind of direct relation has been shown. 4. Discussion 4.1. Relaxation effects Fig. 11 compares, in the case of the small particles (although the same observation can be made for the large
Fig. 5. Image analysis steps used to select the particles and the cavities.
E. Maire et al. / Acta Materialia 55 (2007) 6806–6815
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particles), the counting of AE events plotted as a function of the stress in the fast and slow experiments. During the stops in the slow experiments, the stress on the sample drops because the displacement is fixed and the sample relaxes its internal strain (see also Figs. 4 and 9 for the perturbing effect of the stops). When the sample is reloaded the stress and strain increase, but it is observed that AE
does not increase until a stress higher than the maximum stress during the previous loading is reached. This shows how stopping the experiment for tomographic acquisition slightly perturbs the acoustic emission measurement. Although only a few stops were performed, the strain accumulated during the different reloading stages can, for example, be estimated to about 10% of the total rupture
Fig. 6. Reconstructed tomographic slices of a same region of the small particle material at three different strain levels (a, b and c) acquired using the slow setup. The tensile direction is vertical in the figure.
Fig. 7. Reconstructed tomographic slices of a single region of the small particle material at three different strain levels (a, b and c) acquired using the fast setup. The strain levels were chosen as being equivalent to the ones shown in Fig. 1. The tensile direction is vertical in the figure.
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precise picture of the process involved during rupture. Increasing the number of stops during the slow experiment is, of course, a possibility, but it is experimentally more tedious and the previously discussed effect of the relaxation would be more pronounced. 4.2. Energy of the AE signals
Fig. 8. Reconstructed tomographic slices of a region of the large particles material just before rupture. The tensile direction is vertical in the figure.
strain in the case of the material reinforced with small particles. One of the main purpose of the fast experiment is the higher number of scans which allows to give a more
The energy of each recorded pulse was measured by the AE processing software. Fig. 12 shows that the correlation between the cumulated surface of the cracks perpendicular to the tension axis (measured using the 3D images) and the accumulated energy of the AE signals is extremely good, especially in the case of the continuous experiment. The acoustic energy is then remarkably proportional to the surface of the cracks projected in the plane perpendicular to the loading axis which in turn is somehow related to the energy released during the creation of the crack at the origin of the signal. It must be stated clearly here that the energy measured by the AE software is only a small fraction of the mechanical energy released during the fracture of the particles. This is due to the fact that the signals are only partially
Fig. 9. Position along the length of the sample of the new AE events recorded during the test as a function of stress. Damage is clearly diffuse in this material before rupture occurs.
E. Maire et al. / Acta Materialia 55 (2007) 6806–6815
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Fig. 10. Comparison between the number of events measured by acoustic emission and those measured by direct tomographic observation.
Fig. 11. AE counts as a function of stress in the case of the small particles, showing the perturbing effect of the stops during the slow experiment.
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collected by the imperfect sensors and are also attenuated during their transport from the source to the sensor (although this probably has a weaker effect as the energy of the signal does not seem to be correlated with the distance between the source and the detector). The ratio of these two energies is an important parameter as the knowledge of the energy involved during the rupture of such a ceramic particle is a key issue for the determination of a nucleation criterion which can then be used to predict the nucleation in a subsequent modeling of the rupture process. An upper bound of the rupture energy can be estimated as follows. It has been shown in Ref. [6] that the behaviour of the particles is purely elastic, with a Young’s modulus E of the order of 120 GPa, and that the particles break under a stress rr of the order of 700 MPa. The amount of energy released during the cracking of one single particle of radius r cannot exceed wr, the stored elastic energy before cracking, which is the available driving energy. wr can be calculated as follows: wr ¼ 2pr3 r2r =3E
ð1Þ 7
wr is of the order of 2 · 10 J in the case of the small particles and 2.5 · 106 J for the large particles. The average value of the AE energy of one signal is about wAE = 5 · 1014 J for the small and 8 · 1013 J for the large
particles. The ratio between the released elastic energy and the measured acoustic energy can be estimated to be of the order of 5 · 106 for the small and 3 · 106 for the large particles. This remarkably close value of the ratio is an interesting finding of the present study because one can now simply link the energy of the signal to the mechanical energy released by a rupture. This, of course, needs to be double checked on different materials, but would be important information in the field of damage nucleation characterization. 4.3. Multi-fragmentation of the particles The above-mentioned analysis assumes that all the energy stored in the particle is released during the rupture. The multi-fragmented particles found in the damaged material are clear evidence that, in reality, some energy can remain stored in the particle after it is broken by the first crack. This kind of process has already been observed and commented on, for instance, by Gammage et al. [10]. These authors developed a simple analytical model of the multi-fragmentation. Some other experiments on the multi-fragmentation of ceramic fibers in metallic matrices, reported in Ref. [11], also suggest that after the first crack has occurred in a particle the rupture properties of the
Fig. 12. Correlation between the cumulated AE energy per cubic millimeter vs. the cumulated surface of cracks projected in the plane perpendicular to the tensile axis in the case of the slow and fast experiments.
E. Maire et al. / Acta Materialia 55 (2007) 6806–6815
remaining ceramic might be lowered by the shockwave induced by the first cracking. This might result in the second crack becoming nucleated rather more easily than the first one. These different reports show that a more complete micromechanical analysis of the fracture process would help to confirm the results found by the simple approach used in the present study. 5. Conclusion In conclusion, the set of observations made possible by this simultaneous AE and fast tomography experiment during a continuous tensile test help us to improve our comprehension of the rupture process of materials. Fast tomography is feasible during continuous loading, and the obtained images compare quite well with the ones made when stopping the tensile displacement during scanning. After image processing, the amount of new cracks can be counted using the images obtained in the fast mode. For the first time the direct comparison of the results of the two complementary techniques used on two different materials show a fairly good agreement. The measurements also clearly show the detrimental effect of the relaxation that occurs during stops in the slow experiment. Finally, it is shown that the energy of the acoustic signals is directly proportional to the cumulated surface of new cracks projected in the plane perpendicular to the loading axis. The ratio between the mechanical rupture energy and the AE energy for one crack is of the order of 3 · 106 to 5 · 106 in the two studied materials.
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Acknowledgements The authors are grateful to Luc Salvo for his help during the extrusion experiments at the GPM2 Laboratory in Grenoble, to James Gore for improving the English and to Elodie Boller from the ESRF for the help for the fast setup. We acknowledge the ESRF for beamtime on ID19 and financial support of traveling expenses. V.C. acknowledges the French Ministry of Research for his PhD grant. References [1] Sarkar J, Kutty TRG, Conlon KT, Wilkinson DS, Embury JD, Lloyd DJ. Mater Sci Eng A 2001;316:52–9. [2] Rabiei A, Enoki M, Kishi T. Mat Sci Eng A 2000;293(1–2):81–7. 20 November. [3] Mummery PM, Derby B, Scruby CB. Acta Metall Mater 1993;41(5):1431–45. [4] Niklas A, Froyen L, Wevers M, Delaey L. Metall Mater Trans A 1995;26A(12):3183–9. December. [5] Buffie`re J-Y, Maire E, Cloetens P, Lormand G, Fouge`res R. Acta Mater 1999;47:1613. [6] Babout L, Maire E, Fouge`res R. Acta mater 2004;52:2475–87. [7] Raz-Ben Aroush D, Maire E, Gauthier C, Youssef S, Cloetens P, Wagner HD. Composites Sci Technol 2006;66(10):1348–53. [8] Pyzalla A, Camin B, Buslaps T, Di Michiel M, Kaminski H, Kottar A, et al. Science 2005;308:92–5. [9] http://rsb.info.nih.gov/ij/. [10] Gammage JJ, Wilkinson DS, Embury JD, Maire E. Philos Mag 2005;85:3191–206. [11] Maire E, Owen A, Buffie`re J-Y, Withers PJ. Acta Mater 2001;49(1):143–53.
Acta Materialia 55 (2007) 6806–6815 www.elsevier.com/locate/actamat
Fast X-ray tomography and acoustic emission study of damage in metals during continuous tensile tests Eric Maire a
a,*
, Vincent Carmona a, Joel Courbon a, Wolfgang Ludwig
a,b
Universite´ de Lyon, INSA-Lyon, MATEIS CNRS UMR5510, 7 avenue Jean Capelle, F-69621 Villeurbanne, France b ESRF ID19 beam line, BP 220, F-38043 Grenoble, France Received 6 July 2007; received in revised form 29 August 2007; accepted 29 August 2007 Available online 22 October 2007
Abstract Model AA-2124 matrix composites with two different reinforcement sizes were pulled with a strain rate of 105 using a dedicated tensile rig suitable for in situ tomography. Two main novelty aspects characterize the present study. First, tomography provides a new approach towards understanding the significance of AE signals, recorded simultaneously, during image acquisition on the same sample. The number of acoustic emission events is found to be in good agreement with the number of cracks as detected by image analysis and the energy of the signals is proportional to the dimension of the cracks. Secondly, fast tomography was used to perform the first continuous in situ tensile test. The continuous procedure is compared in the paper with the standard step by step procedure. 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Damage; Tomography; Metal–matrix composites; Acoustic emission
1. Introduction The rupture of a material is a complex process which has been widely studied experimentally and theoretically. The purpose of these studies is to describe the physics and mechanics of this process completely in order to help researchers predict the rupture or optimize the microstructure to delay it. In the case of many metallic materials, rupture occurs during ductile deformation. In such a process, involving a lot of plasticity, the damage mechanism has been shown to be composed of three different phases: initiation occurs by rupture of the fragile second phase inclusions always present in the matrix of standard metallic materials [1]; then these initiated microcracks grow by plastic deformation of the surrounding ductile matrix; and finally they coalesce, leading to the appearance of larger cracks in the matrix itself.
*
Corresponding author. E-mail address: [email protected] (E. Maire).
Acoustic emission (AE) is a non-destructive way of studying damage [2–4]. It is easy to implement but the information obtained is only global, so that it is desirable to obtain a more local picture of the damage process in parallel. One of the best methods for imaging a damage process is synchrotron X-ray tomography, which shows a non-destructive image in the bulk and without bias due to surface preparation and/or surface stress state [5,6]. The ductile rupture process has been imaged by several authors using tomography but with rather long exposure times, typically 1 s per radiograph and 1000 radiographs for one acquisition [5,6]. This requires the mobile grip of the tensile machine to be stopped during acquisition, so as to prevent blurring of the tomographic images due to the large tensile displacement during the scan acquisition. Depending on the material, during these stops where the displacement of the grip is fixed, plastic relaxation leading to a substantial reduction of the stress can be observed and it is not clear how this affects the complete rupture process. It has been observed in some polymer systems, for instance [7], that delayed rupture could be observed during these
1359-6454/$30.00 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2007.08.043
E. Maire et al. / Acta Materialia 55 (2007) 6806–6815
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Fig. 1. Tomographic reconstruction of both materials showing the good microstructure of the produced material. (a) Small particles, 2D tomographic slice; (b) large particles, 2D tomographic slice; (c and d) 3D rendering of the small particles.
stops due to relaxation probably accelerated by the X-ray irradiation. Metal systems are known to be less sensitive to X-rays, but those based on aluminum, for instance, are not far from their melting temperature when tested at room temperature. Relaxation in this case can be a nonnegligible contribution to the deformation. Three-dimensional (3D) imaging has not yet been achieved during a continuous tensile test. Recently, Pyzalla et al. [8] showed that fast tomography could be used to study the damage process during the creep of a metallic material. In the present paper we combine AE and, for the first time, fast tomography without stopping the tensile test. We show in the rest of this paper that this helps to obtain a more complete understanding of the damage evolution leading to the rupture of the sample.
Fig. 2. Geometry of the samples.
2. Materials and methods 2.1. Materials We have chosen model materials where damage occurs by particle fracture similar to these used in Ref. [6]. The materials were fabricated specifically for the present study. They are made of an age-hardenable standard AA-2124 matrix in the T4 state reinforced with spherical ceramic inclusions. The 2124 powder (size range 3–15 lm) was commercially provided by alpoco. The zirconia/silica spherical reinforcement is also a commercial product [6]. Two different materials were processed, each exhibiting a different size range for the reinforcement: one material was processed with so-called ‘‘small’’ particles (screened between 40 and 60 lm) and the other with ‘‘large’’ particles (screened between 125 and 250 lm). The choice of this kind of system was motivated by the ductility and X-ray transparency of the matrix and the sphericity, brittleness and X-ray absorption of the reinforcement. The two powders (reinforcement and matrix) were mixed using a turbulat, then cold-pressed in a cylindrical die (diameter 20 mm), hot-extruded at 450 C with a ratio of 16:1 to form bars of 10 · 2 mm in section and several decimeters in length, and finally heat-treated (in the T4 state for the matrix, i.e. 1 h at 530 C + water quench + at least 15 days at ambient temperature). The initial microstructure of the
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samples as seen by tomography is shown in Fig. 1. It can be seen from the figure that the spatial distribution of the spherical inclusions is rather homogeneous with both sizes of reinforcement. The matrix contains small pores. These fabrication defects are probably due to insufficient pressure being applied during the extrusion but do not modify the conclusions of the present study, because their size and fraction is much smaller than that of the inclusions. 2.2. Methods From the bars, dog-bone-shaped samples were cut according to the geometry given in Fig. 2. Acoustic emission sensors (two resonant micro-80 Physical Acoustics Corporation (PAC) sensors which have a large range of resonance, coupled on the samples with a thin layer of vacuum grease) were attached to both ends of each sample before it was mounted on a dedicated tensile rig, as shown in Fig. 3. A two-channel Mistras 2001 data acquisition system from PAC with a sampling rate of 4 MHz and a 40 dB pre-amplification was used to record AE data. The total amplification of the recording system was 80 dB. Ambient noise was filtered using a threshold of 40 dB. The structural part of the tensile rig used was a carefully polished PMMA tube [5] allowing the rotation of the entire stage without screening the X-ray beam. The tomograph used was the ID19 beam line at the European Synchrotron Radiation Facility (ESRF), Grenoble, France. The beam was monochromated to 38.5 keV. The radiographs were formed on a transparent luminiscent screen and an optical system magnified the visible light on a dedicated fast-readout low-noise camera. The isotropic pixel size was equal to 1.4 lm. Two different kinds of tomographic parameters were used to perform (i) high-quality slow acquisition and (ii) low-quality fast acquisition on two different samples cut from the same bar for each material. For the slow setup, the exposure time was 0.3 s and the number of radiographs (each 1536 · 820 pixels in size) was 1200. The total time required to record a scan was 20 min. For the fast setup, the number of radiographs was reduced down to 500, and each radiograph was binned (re-sized to 2.8 lm by binning 2 · 2 pixels into one). After binning, the size of the radiographs was 748 · 410 pixels and the exposure time was reduced to 0.1 s. The total scan time could therefore be reduced down to 1 min. The slow in situ tensile test tomography experiment was performed according to a standard step-by-step procedure. The initial microstructure of the sample was scanned using the slow tomography mode. The displacement rate was set to 103 and the sample was loaded up to a given strain level. At this stage, the rig displacement was stopped and the microstructure of the sample was scanned. This procedure was repeated at increasing strain levels up to the rupture of the sample. The novelty of the presented work is the use of continuous tensile test during tomography. For the continuous tensile test, the procedure was as follows. In order to save
beam time, the sample was first loaded at a standard strain rate (103) up to the elastic/plastic transition. It had been previously checked that only little damage was induced during this elastic part of the loading in these materials [5,6]. As further evidence, no acoustic emission could be recorded during this primary part of the loading in both kinds of materials. At this stage, the rig displacement rate was reduced to 0.05 lm s1 and the sample was loaded without stopping up to its rupture while scans were recorded every 2 min. The tensile curves obtained during these experiments are shown in Fig. 4. One can observe the perturbing effect of the stops on the tensile curves recorded during the two slow experiments compared with the smooth character of the two curves recorded without stopping during the fast experiments. The 3D images have to be properly treated and analyzed to obtain a quantification of the morphology of the particles and of the cracks, and their evolution during the test. The thresholding of the particles in the initial state is straightforwardly based on the gray level. As for the cracks, their very small opening just after initiation and the value of their gray level very close to that of the matrix
Fig. 3. The acoustic emission sensors mounted on the sample.
E. Maire et al. / Acta Materialia 55 (2007) 6806–6815
implies that a special procedure must be used to isolate them. This procedure, based on a sequence of thresholding, closing and screening (using the position of the particles) operations, is exemplified in the case of the small particles material in Fig. 5. We double checked that the proposed procedure for segmenting the cracks was in excellent agreement with the number of observed cracks by manual counting on a small but representative portion of the material. Once binarized, the images were labeled and the 3D morphology of each label (i.e. each crack or each particle) could be measured. All these operations, performed using real 3D algorithms, were applied to the images using plugins written in Java for the ImageJ free software [9]. The acoustic waves emitted by one single event being recorded simultaneously by two piezoelectric sensors, it was possible to locate the origin of each of these signals and also to reject the ones emanating from regions other than the useful part (gauge length) of the sample. For each of these signals several parameters (energy, amplitude, duration, etc.) were measured directly by the software used. Our purpose in the present study is to relate the characteristics of these signals to the tomographic observation. 3. Experimental results Figs. 6 and 7 show, for the slow and fast modes, respectively, but in the case of the small particles only, two series of slices extracted from the middle of the reconstructed block. These slices were extracted in the same location of the sample for increasing values of the plastic strain. They were sampled parallel to the tensile axis in order to show
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the effect of damage. These two figures show that the quality is slightly worse with the fast setup but that it is still sufficient to allow the observation of the damage mechanism in the studied material. Fig. 8 shows the microstructure before failure in the case of the large particles. All these figures reveal that damage initiates by particle fracture inducing penny-shaped cracks perpendicular to the direction of the applied load. During the plastic deformation of the sample, the number of these cracks increases and the previously initiated ones grow in the direction of loading, but hardly at all in the two directions perpendicular to the tensile stress. Further fragmentation of already broken particles can often be seen, especially in the case of the large particles. This leads to the formation of multi-fragmented particles. Note that, for this reason, the number of cracks counted by image processing in our following analysis is the exact number of cracks (for instance, two cracks in the same particle counting twice) and not the number of damaged particles. During the last deformation stages, neighboring cracks coalesce through the appearance of secondary cracks inside the matrix and this leads to the final rupture of the sample. Fig. 9 plots the location of the origin of the position of the different AE signals along the length of the specimen. This plot is given as a function of the global stress in the composite. The case of the small particles material has been chosen as a representative example of such a plot. The graph demonstrates that the spatial distribution of damage is rather homogeneous along the length of the two samples. The same observation has been made for the large particles. It can be understood from this figure that damage is distributed rather homogeneously in the strained volume of the sample
Fig. 4. Tensile curves recorded during the slow and fast experiments for both materials.
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(this is consistent with the visual impression given by Figs. 6–8). Note also in this figure the effect of the perturbation of the AE results induced by the stops during the slow experiment. This perturbation appears just after each of the stops during which the stress relaxes at constant strain. No AE event is observed before the sample is restrained up to a stress equivalent to the maximum stress reached before the stop. This explains the portion of the interrupted curves where the strain increases while no AE event is detected. Fig. 10 shows the evolution of the events counted in acoustic emission, as a function of those counted using image analysis, for the two materials and for the two types
of experiments (fast and slow). The principal conclusion of this figure is that, in terms of the number of events detected, acoustic emission concurs rather well with direct observation. This is probably the first time that this kind of direct relation has been shown. 4. Discussion 4.1. Relaxation effects Fig. 11 compares, in the case of the small particles (although the same observation can be made for the large
Fig. 5. Image analysis steps used to select the particles and the cavities.
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particles), the counting of AE events plotted as a function of the stress in the fast and slow experiments. During the stops in the slow experiments, the stress on the sample drops because the displacement is fixed and the sample relaxes its internal strain (see also Figs. 4 and 9 for the perturbing effect of the stops). When the sample is reloaded the stress and strain increase, but it is observed that AE
does not increase until a stress higher than the maximum stress during the previous loading is reached. This shows how stopping the experiment for tomographic acquisition slightly perturbs the acoustic emission measurement. Although only a few stops were performed, the strain accumulated during the different reloading stages can, for example, be estimated to about 10% of the total rupture
Fig. 6. Reconstructed tomographic slices of a same region of the small particle material at three different strain levels (a, b and c) acquired using the slow setup. The tensile direction is vertical in the figure.
Fig. 7. Reconstructed tomographic slices of a single region of the small particle material at three different strain levels (a, b and c) acquired using the fast setup. The strain levels were chosen as being equivalent to the ones shown in Fig. 1. The tensile direction is vertical in the figure.
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precise picture of the process involved during rupture. Increasing the number of stops during the slow experiment is, of course, a possibility, but it is experimentally more tedious and the previously discussed effect of the relaxation would be more pronounced. 4.2. Energy of the AE signals
Fig. 8. Reconstructed tomographic slices of a region of the large particles material just before rupture. The tensile direction is vertical in the figure.
strain in the case of the material reinforced with small particles. One of the main purpose of the fast experiment is the higher number of scans which allows to give a more
The energy of each recorded pulse was measured by the AE processing software. Fig. 12 shows that the correlation between the cumulated surface of the cracks perpendicular to the tension axis (measured using the 3D images) and the accumulated energy of the AE signals is extremely good, especially in the case of the continuous experiment. The acoustic energy is then remarkably proportional to the surface of the cracks projected in the plane perpendicular to the loading axis which in turn is somehow related to the energy released during the creation of the crack at the origin of the signal. It must be stated clearly here that the energy measured by the AE software is only a small fraction of the mechanical energy released during the fracture of the particles. This is due to the fact that the signals are only partially
Fig. 9. Position along the length of the sample of the new AE events recorded during the test as a function of stress. Damage is clearly diffuse in this material before rupture occurs.
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Fig. 10. Comparison between the number of events measured by acoustic emission and those measured by direct tomographic observation.
Fig. 11. AE counts as a function of stress in the case of the small particles, showing the perturbing effect of the stops during the slow experiment.
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collected by the imperfect sensors and are also attenuated during their transport from the source to the sensor (although this probably has a weaker effect as the energy of the signal does not seem to be correlated with the distance between the source and the detector). The ratio of these two energies is an important parameter as the knowledge of the energy involved during the rupture of such a ceramic particle is a key issue for the determination of a nucleation criterion which can then be used to predict the nucleation in a subsequent modeling of the rupture process. An upper bound of the rupture energy can be estimated as follows. It has been shown in Ref. [6] that the behaviour of the particles is purely elastic, with a Young’s modulus E of the order of 120 GPa, and that the particles break under a stress rr of the order of 700 MPa. The amount of energy released during the cracking of one single particle of radius r cannot exceed wr, the stored elastic energy before cracking, which is the available driving energy. wr can be calculated as follows: wr ¼ 2pr3 r2r =3E
ð1Þ 7
wr is of the order of 2 · 10 J in the case of the small particles and 2.5 · 106 J for the large particles. The average value of the AE energy of one signal is about wAE = 5 · 1014 J for the small and 8 · 1013 J for the large
particles. The ratio between the released elastic energy and the measured acoustic energy can be estimated to be of the order of 5 · 106 for the small and 3 · 106 for the large particles. This remarkably close value of the ratio is an interesting finding of the present study because one can now simply link the energy of the signal to the mechanical energy released by a rupture. This, of course, needs to be double checked on different materials, but would be important information in the field of damage nucleation characterization. 4.3. Multi-fragmentation of the particles The above-mentioned analysis assumes that all the energy stored in the particle is released during the rupture. The multi-fragmented particles found in the damaged material are clear evidence that, in reality, some energy can remain stored in the particle after it is broken by the first crack. This kind of process has already been observed and commented on, for instance, by Gammage et al. [10]. These authors developed a simple analytical model of the multi-fragmentation. Some other experiments on the multi-fragmentation of ceramic fibers in metallic matrices, reported in Ref. [11], also suggest that after the first crack has occurred in a particle the rupture properties of the
Fig. 12. Correlation between the cumulated AE energy per cubic millimeter vs. the cumulated surface of cracks projected in the plane perpendicular to the tensile axis in the case of the slow and fast experiments.
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remaining ceramic might be lowered by the shockwave induced by the first cracking. This might result in the second crack becoming nucleated rather more easily than the first one. These different reports show that a more complete micromechanical analysis of the fracture process would help to confirm the results found by the simple approach used in the present study. 5. Conclusion In conclusion, the set of observations made possible by this simultaneous AE and fast tomography experiment during a continuous tensile test help us to improve our comprehension of the rupture process of materials. Fast tomography is feasible during continuous loading, and the obtained images compare quite well with the ones made when stopping the tensile displacement during scanning. After image processing, the amount of new cracks can be counted using the images obtained in the fast mode. For the first time the direct comparison of the results of the two complementary techniques used on two different materials show a fairly good agreement. The measurements also clearly show the detrimental effect of the relaxation that occurs during stops in the slow experiment. Finally, it is shown that the energy of the acoustic signals is directly proportional to the cumulated surface of new cracks projected in the plane perpendicular to the loading axis. The ratio between the mechanical rupture energy and the AE energy for one crack is of the order of 3 · 106 to 5 · 106 in the two studied materials.
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Acknowledgements The authors are grateful to Luc Salvo for his help during the extrusion experiments at the GPM2 Laboratory in Grenoble, to James Gore for improving the English and to Elodie Boller from the ESRF for the help for the fast setup. We acknowledge the ESRF for beamtime on ID19 and financial support of traveling expenses. V.C. acknowledges the French Ministry of Research for his PhD grant. References [1] Sarkar J, Kutty TRG, Conlon KT, Wilkinson DS, Embury JD, Lloyd DJ. Mater Sci Eng A 2001;316:52–9. [2] Rabiei A, Enoki M, Kishi T. Mat Sci Eng A 2000;293(1–2):81–7. 20 November. [3] Mummery PM, Derby B, Scruby CB. Acta Metall Mater 1993;41(5):1431–45. [4] Niklas A, Froyen L, Wevers M, Delaey L. Metall Mater Trans A 1995;26A(12):3183–9. December. [5] Buffie`re J-Y, Maire E, Cloetens P, Lormand G, Fouge`res R. Acta Mater 1999;47:1613. [6] Babout L, Maire E, Fouge`res R. Acta mater 2004;52:2475–87. [7] Raz-Ben Aroush D, Maire E, Gauthier C, Youssef S, Cloetens P, Wagner HD. Composites Sci Technol 2006;66(10):1348–53. [8] Pyzalla A, Camin B, Buslaps T, Di Michiel M, Kaminski H, Kottar A, et al. Science 2005;308:92–5. [9] http://rsb.info.nih.gov/ij/. [10] Gammage JJ, Wilkinson DS, Embury JD, Maire E. Philos Mag 2005;85:3191–206. [11] Maire E, Owen A, Buffie`re J-Y, Withers PJ. Acta Mater 2001;49(1):143–53.