Characterization of Microcracking in Polymer Concrete Using Multiple Scattered Waves Under Steady-State Vibration Conditions

Transcription

1 RESEARCH IN NONDESTRUCTIVE EVALUATION 2017, VOL. 28, NO. 1, Characterization of Microcracking in Polymer Concrete Using Multiple Scattered Waves Under Steady-State Vibration Conditions S. Toumi a,b, C. Mechri a,c, M. Bentahar a, F. Boubenider b, and R. El Guerjouma a a Laboratoire d Acoustique de l Université du Maine (LAUM), UMR CNRS 6613, Université du Maine, Le Mans, France; b Laboratoire de Physique des Matériaux, Ondes et Acoustique, USTHB, Alger, Algeria; c Centre de Transfert de Technologie du Mans, Le Mans, France ABSTRACT This work presents the development of an ultrasonic method based on the use of multiple-scattered waves to detect and image microcracks in polymer concrete samples under steadystate bending vibrations. The sensitivity of the multiple-scattered waves to microcracks revealed to be dependent on the plane in which bending vibrations were excited. In order to understand the origin of such a sensitivity, acoustic emission measurements were performed under the same vibration conditions to verify the existence of a structural anisotropy related to microcrack distribution. Results revealed that, depending on the considered plane, acoustic emission signatures are very different and therefore can be used to understand the involved mechanisms and to identify the vibration planes that offer the optimal imaging conditions. KEYWORDS Acoustic emission; air-coupled ultrasound imaging; damage anisotropy; polymer concrete; ultrasonic multiple scattering 1. Introduction The study of multiple scattering of elastic waves in complex media has started since more than half a century in geosciences, where the late part of the diffuse field was termed coda [1]. Being more sensitive to changes created in the propagating medium than the direct ballistic waves, coda waves were used to monitor velocity variations of two successive signals, which are nearly alike, in the case of an earthquake [2] or an active source [3]. The term Coda Wave Interferometry (CWI) was given by Snieder et al. where they proved the possibility of detecting weak velocity changes in solids using seismic and ultrasonic coda waves [4]. Later, thermal CWI was applied on concrete and revealed to be of high sensitivity compared to time-of-flight techniques [5,6].Atthetimewhentechniquesbasedonthe intensity fluctuations created by isolated scatterers proved to have limited detection capabilities [7], other techniques based on the linear interaction CONTACT Dr. M. Bentahar mourad.bentahar@univ-lemans.fr Laboratoire d Acoustique de l Université du Maine (LAUM), UMR CNRS Université du Maine. Av. Olivier Messiaen, 72085, Le Mans Cedex 9, France. Color versions of one or more of the figures in the article can be found online at American Society for Nondestructive Testing

2 RESEARCH IN NONDESTRUCTIVE EVALUATION 19 with defects revealed to be very sensitive to detect weak changes [8 10]. On the other hand, stress-induced CWI experiments were performed to determine third order elastic constants of complex solids in the frame of the acoustoelastic theory [11]. Results revealed that in the case of concrete samples, the acoustoelastic coefficients increase as a function of the cracks density [12]. The nonlinear interaction of the coda wave with defects was also determined in multiply scattering media through the nonlinear mixing with a pump wave [13]. In general, when the interaction coda/micro-scatterers is weak, it can be enhanced by increasing the dynamic strain. However, such a procedure is usually at the origin of nonlinear phenomena in many types of materials, especially in the case of consolidated granular media. Indeed, conditioning and relaxation effects might appear even in the absence of micro-cracks [14] and disturb the defect characterization procedure. In this work, we present a method to predispose microcracks to interact with a high frequency wave when the propagating medium is under steadystate vibration conditions. In particular, we propose contact and contactless air-coupled ultrasonic methods to detect and image defects using an original non invasive approach. Since the proposed technique revealed to be sensitive to the plane in which vibrations were applied, we performed acoustic emission (AE) measurements when samples were under vibration in two orthogonal planes in order to obtain the acoustic signatures of the vibrating damaged medium, with a consequent wealth of information on the response of microcracks to the imposed vibration. 2. Materials and method The polymer concrete (PC) samples, whose dimensions are 160 x 40 x 11 mm 3, consist of an epoxy resin matrix reinforced by sand and aggregates at 40%, 30%, and 30% volume fraction, respectively. The Young modulus and the Poisson ratio of the used epoxy resin (SR 1500 /SD 25 05) are E ¼ 2:8 GPa and ν ¼ 0:3, respectively. PC samples are submitted to a three-point bending fatigue test. The sinusoidal fatigue cycle is performed using a frequency corresponding to 10 Hz at 3 kn loading forceamplitude,wherethedistancebetweenthesupportingpinsissetat 120 mm (Fig. 1). In such a medium one can take advantage of the interaction between an ultrasonic wave and the created microchanges by analyzing the multiple-scattered part of a propagating ultrasonic wave. In general, the analysis is performed in the time domain by cross-correlating two waveforms taken before and after the fatigue test or at low and high

3 20 S. TOUMI ET AL. Figure 1. The polymer based concrete sample is submitted to a three-point bending fatigue test performed in the (XY) plane (a). The PC sample is mounted on the shaker where ultrasonic waves are emitted and received at different positions along x-axis using two identical ultrasonic transducers (b). The insert shows the evolution of the resonance frequency as a function of the induced dynamic strain, where the arrow shows the strain at which the steady-state vibration condition is obtained (c). excitation amplitudes. The time-windowed normalized cross-correlation function is expressed as Rt ð s Þ ¼ ð Þeu ðt 0 þ t s Þdt 0 q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (1) ò tþt t T u2 ðt 0 Þdt 0 ò tþt t T eu2 ðt 0 þ t s Þdt 0 ò tþt t T ut0 where ut ðþis the waveform corresponding to the initial state (or low excitation) and eu ðþis t the waveform obtained at fatigued state (or high excitation). The cross-correlation is performed on a time window of length 2T, which is centered around t (t T). t s is the time shift of the perturbed waveform relative to the unperturbed waveform. When waves are not perturbed, i.e., ut ðþ¼eu ðþ, t the time shift is zero ðt s ¼ 0Þ and the cross-correlation is consequently Rðt s ¼ 0Þ ¼1[4 6]. The decorrelation coefficient Kðt s Þ between the waveforms ut ðþand eu ðþcan t be determined as Kðt s Þ¼1 Rðt s Þ. 3. Results and discussion 3.1. Contact ultrasound detection of microcracks To detect and locate the created scatterers or microcracks within the weaklyfatigued PC samples, the application of the CWI for different ultrasonic paths did not show any clear time delay between ut ðþand eu ðþ,evenforincreasingexcitation amplitudes. Indeed, the correlation function produced a sequence of auto- t correlations, i.e., Kðt s ¼ 0Þ ¼0. In order to increase the sensitivity of the CWI, we used a shaker controlled by a power amplifier (see Fig. 1). Vibration modes of the polymer concrete sample generated in a clamped-free configuration were detected

4 RESEARCH IN NONDESTRUCTIVE EVALUATION 21 using an accelerometer attached to the free side of the sample. Since the aim of these experiments is not to create nonlinear resonances, we performed preliminary fast and slow nonlinear dynamics measurements in order to probe the conditioning of the consolidated granular sample and its subsequent relaxation. For the first three flexural resonances, results showed that the material was vibrating in the linear regime as long as the excitation amplitude was kept below 20 mv before amplification, which is equivalent to a strain level corresponding to ε ffi 10 7.Theinsert(Fig. 1c) is an example of the frequency variation corresponding to the fundamental bending mode as a function of the dynamic strain. In the present work, we did not measure the stress level in the area affected by microcracks. Indeed, since we were working in the linear regime and since the dynamic strain level measured at a given x coordinate is the same, we can reasonably consider that the generated strain fields in both planes are identical. Moreover, since we are exciting samples in the linear domain, the generated strain field is not affected by conditioning and relaxation effects. Under the abovementioned steady-state vibration conditions, we performed through transmission measurements of ultrasonic pulses generated using identical large band transducers, whose center frequency is around 500 khz, mounted opposite each other (Fig. 1b). Under the steady-state vibration conditions, the ultrasonic emitter transducer was excited by a pulse generator adjusted to deliver a 50 mvpp signal amplified at 46 db. The experimental setup was calibrated through a set of measurements, where different aspects such as the positioning of sensors and coupling were taken into account. The numerous measurements showed that for a given position of the transducers, the reproducibility of the delay between the multiply scattered signals did not exceed 50 ns, which corresponds to the sampling period of the acquisition system. On the other hand, due to the sensitivity of the coda wave to the environmental conditions (that may change between two measurements), reference signals were recorded at every position when the material was at rest (i.e., in the absence of the linear vibration). Evolution of the decorrelation coefficient as a function of the transducers position along the x-axis is presented in Fig. 2. The latter shows that as a function of the excited resonance, the strain distribution at the microcracks changes with a consequent impact on the coda part of the recorded waveforms observed through the decorrelation coefficient K. Recall that the reference signal is recorded at every position when the material is at rest. This point highlights the fact that despite the sensitivity of coda waves to environmental changes (temperature, humidity, etc.); the new reference signal we obtain at every position in the absence of the low frequency vibration takes into account all the environmental changes that might appear between two measurements. Furthermore, Fig. 2 shows that microcracks created during the fatigue test do not seem to propagate along a single line but were diffused between the supporting pins. This result is in accordance with

5 22 S. TOUMI ET AL. Decorrelation coefficient (K) st Flexural mode 2 nd Flexural mode 3 rd Flexural mode Transducers Position (cm) Figure 2. Decorrelation coefficient K determined at different positions along X-axis when the polymer concrete is submitted to a linear flexural resonance. Results show that the distribution of microcracks is not symmetric to the middle of the concrete beam (around 8 cm). previous works on the fracture behavior of inhomogeneous materials submitted to three-point bending tests. In such materials, microcracks resulted from the interaction between the gradient of the stress field and the distribution of the fracture stresses, where the stress can be higher than the lower limit of the fracture distribution even at the end of the linear domain [15,16] Contactless ultrasound imaging of the microcracked area In the view of imaging the microcracked area through the scattering of the ultrasonic waves, we used air-coupled ultrasonic transducers whose frequency bandwidth goes from ~ 300 khz to ~ 700 khz. Air-coupled transducers were excited with a Sine-Gaussian profile signal emitted at 1 khz repetition frequency. Received signals were sampled at 15 MHz over a dynamic range of 16 bits and amplified at 60 db. Due to the acoustic impedance mismatch at the interface air/polymer concrete, where Z air ffi 216Rayl and Z PC ffi 9MRayl, the reflection coefficient of the ultrasonic waves is importantr ffi 99:98%. However, the high voltage of the excitation amplitude (~ 200 V) associated to an averaging of the received signals (~50) improves the signal-to-noise ratio (SNR), which is around 30 db for the ballistic wave. In the coda region, the SNR of the recorded signals was above 12 db. Under these conditions, reference signals corresponded to the propagation through the polymer concrete before activating the shaker. Received signals were then recorded under weak vibrations, as explained above. The acquired waveforms (ballistic and coda parts) are 250 µs long. This length is very short compared to the period of the fundamental bending modes, which

6 RESEARCH IN NONDESTRUCTIVE EVALUATION 23 is around 4ms. For these measurements ultrasonic pulses and the low frequency vibrations were synchronized. Coda waves were analyzed by considering a time window corresponding to ~20 µs (8 periods). The effect of the displacements induced by the bending mode on the coda wave measurements was limited. This was verified on an intact (reference) sample where the time-shift induced by the bending mode displacements was less than 50 ns. This experimental procedure allows getting a through transmission C-Scan of the polymer concrete based on the decorrelation coefficient K determined at every position as shown in Fig. 3. Indeed, the latter shows that under steady-state vibrations, the sensitivity of the CWI to microcracks is improved and allows an active and simple imaging of the microcracked area using a non-invasive contactless approach. This result confirms the one obtained using the contact ultrasound approach (see Fig. 2), since it shows that microcracks created during the fatigue test are mainly distributed between the supporting pins. Figure 3. Air-coupled ultrasonic imaging of the microcracks created within the polymer concrete, where the colorbar corresponds to the values of the decorrelation coefficient K determined at every scan position. The dimension of the pixels is 1 mm. Results are obtained when the concrete beam is excited at the fundamental bending resonance where the sample is vibrating along the Z-axis. The A-Scan signals show that microcracks effect can only be observed in the coda of the recorded signals. Equivalent images, performed in the same vibration direction were found for the 2nd and 3rd bending resonances.

7 24 S. TOUMI ET AL. It is important to notice that when the steady-state vibrations are generated in the (XY) plane (i.e., the sample is vibrating along the Y-axis) the decorrelation coefficient does not allow to detect and locate in a clear way the damaged area (see Fig. 3), which seriously affects the detection capabilities of the air-coupled imaging technique. Indeed, the damaged area is clearly visible in the XZ plane, where the travel path of the ultrasonic waves within the polymer concrete sample is important, at the time where it is barely visible in the XY plane despite the small propagating distance. The influence of the vibration axis on the microcracks behavior seems to be of great importance and deserves a better attention. In order to understand the reasons of such a weak interaction, we present in the next section acoustic emission measurements performed in the same vibration conditions in both (XY) and (XZ) planes, when samples are vibrating in the Y-axis and Z-axis, respectively Acoustic emission under linear resonance The weak interaction between the ultrasonic waves and the existing microcracks is mainly due to the direction along which the mechanical force is applied during the fatigue bending test. Indeed, in the present study the cracks are mainly in the force direction [17] and located in the polymer matrix and at aggregates/matrix interfaces. In addition, important cracks kinking angles exist away from the beam center with a local influence of the aggregate s size and distribution [16]. Therefore, it is expected that mechanisms at the microcracks are changing depending on the plane in which steady-state vibrations are excited. This can be verified with the help of AE measurements performed when microcracked samples are submitted to the same bending resonances in both (XY) and (XZ) planes. For that purpose, broadband ultrasonic piezoelectric sensors were used to detect AE hits, which are pre-amplified (40 db) and sampled at 5 MHz. First, we should point out that the complex material we are analyzing can generate AE signals with different characteristics and nature (shear, compression, etc.) depending on the particular stacking sequence, which decides on the principal failure mechanism, and the experimental configuration. Therefore, one should expect the excited mechanisms to overlap. However, since most of the information about the underlying mechanisms is typically hidden in the frequency content of the detected waveforms, the dynamic analysis we are performing is mainly focused on the evolution of the Fourier transform of the AE signals emitted by the vibrating complex material. Figures 4(a) and 4(b) show, on one hand, that the frequency range oftheaesignalsisordersofmagnitudeshigherthantheonesusedto generate the steady-state vibrations. On the other hand, the same figures show that the frequency contents of the AE signals recorded in both planes are very different. Indeed, AE hits recorded during the steady-state

8 RESEARCH IN NONDESTRUCTIVE EVALUATION a b 80 Frequency (khz) Frequency (khz) Number of recorded hits Number of recorded hits Figure 4. Frequency contents of the acoustic emission signals recorded during one steady-state vibration cycle (resonance cycle) in the XY (a) and XZ (b) planes. The colorbar corresponds to the AE amplitudes in db (0 db corresponds to 1 µv). The inserts show the possibility to study the mechanisms (the main ones) generated at the microcracks using the characteristics of the recorded acoustic emission hits. vibration in the (XY) plane, are around 600 and have two main frequency components at ~ 40 khz and ~ 100 khz generated at amplitudes lower than 50 db. Here it is important to note that when the material is at resonance, the AE activity is not showing any particular evolution. However, the number of AE hits recorded when the vibrations are performed in the (XZ) plane is more important (~ 3000 hits) with amplitudes ranging between20dband70db,where0dbcorrespondsto1µv.thefrequency contents of these AE signals have new components (especially when the material is near resonance), which are irregularly distributed along the considered resonance cycle. These AE events show that microcracks behave differently depending on the plane in which vibrations are excited. Indeed, in view of their orientation, microcracks are submitted to shear and/or compression forces, which can generate mechanisms as different as clapping and sliding with different frequency components. At the time when we think that changing a vibration plane will mainly favor one mechanism over another, we believe that the understanding of the experimental observations need a deeper analysis. Indeed, the presence of memory effects beside the aforementioned activated mechanisms (clapping or sliding) makes the analytical formulation of the relationship between stress and strain not feasible. As an alternative, a multistate statistical description of the microcracked polymer concrete, based on the generalized Preisach Mayergoyz (PM) formalism, seems to be a promising approach in order to link the behavior of simple mesoscopic elements (at the microscopic scale to describe the microcracks behavior) to the observations performed at the macroscopic scale [18,19].

9 26 S. TOUMI ET AL. 4. Conclusions and prospects In this contribution, we developed a contact ultrasound technique to probe the existence of microcracks created in polymer concrete samples. This technique showed that, under steady-state vibrations, the sensitivity of coda waves to microcracks is improved, where the influence of the environmental conditions was considerably limited using a new reference signal at every position. Besides, air-coupled ultrasound imaging of the weakly damaged PC sample has been performed under the same steady-state bending vibrations. Results showed that the efficiency of the imaging depends on the considered vibration plane. In order to verify the structural anisotropy of the created microcracks within the PC sample, AE measurements were performed when vibrations are generated in both (XY) and (XZ) planes. The existing differences between the recorded AE signals show that we are exciting different micro-mechanisms whose presence and/or absence has an important impact on the interaction between the propagating ultrasonic wave and the microcracks. Therefore, our future work will be focused on the study of AE signatures related to micro-mechanisms when damaged materials are submitted to linear and/ or nonlinear vibrations in order to study the AE activity generated during the conditioning and relaxation of different materials. References [1] K. Aki. J. Phys. Earth 4:71 79 (1956). [2] G. Poupinet, W. L. Ellsworth, and J. Frechet. J. Geophys. Res. 89: (1984). [3] P. M. Roberts, W. S. Phillips, and M. C. Fehler. J. Acoust. Soc. Am. 91: (1992). [4] R. Snieder, A. Grêt, and H. Douma. Science 295:2253 (2002). [5] E. Larose, J. DeRosny, L. Margerin, D. Anache, P. Gouedard, M. Campillo, and B. VanTiggelen. Phys. Rev. E 73:16609 (2006). [6] Y. Zhang, O. Abraham, F. Grondin, A. Loukili, V. Tournat, A. Le Duff, B. Lascoup, and O. Durand. Ultrasonics 53: (2013). [7] T. M. Nieuwenhuizen and M. C. W. van Rossum. Physics Letters A 177: (1993). [8] C. Pacheco and R. Snieder. J. Acoust. Soc. Am. 118: (2005). [9] A. Aubry and A. Derode. Phys. Rev. Lett. 102: (2009). [10] Larose T. Planes, V. Rossetto, and L. Margerin. Appl. Phys. Lett. 96: (2010). [11] C. Payan, V. Garnier, J. Moysan, and P. A. Johnson Appl. Phys. Lett. 94: (2009). [12] D. Schurr, J.-Y. Kim, K. Sabra, and L. J. Jacobs. NDT & E International 44: (2011). [13] Y. Zhang, V. Tournat, O. Abraham, A. Le Duff, B. Lascoup, and O. Durand. J. Appl. Phys. 113: (2013). [14] M. Bentahar, H. El Aqra, R. El Guerjouma, M. Griffa, and M. Scalerandi. Phys. Rev. B 73: (2006). [15] J.-M. Berthelot and L. Fatmi. Engineering Fracture Mechanics 71: (2004).

10 RESEARCH IN NONDESTRUCTIVE EVALUATION 27 [16] A. Yin, X. Yang, S. Yang, and W. Jiang. Engineering Fracture Mechanics 78: (2011). [17] H. Kim and W. G. Buttlar. Composites Science and Technology 69: (2009). [18] M. Scalerandi, S. Idjimarene, M. Bentahar, and R. El Guerjouma. Commun. Nonlinear Sci. Numer. Simulat. 22: (2015). [19] P. Antonaci, C. L. E. Bruno, A. S. Gliozzi, and M. Scalerandi. International Journal of Solids and Structures 47: (2010).