P.-Y. Le Bas

Quantification of material nonlinearity in relation to microdamage density using nonlinear reverberation spectroscopy: Experimental and theoretical study

High amplitude vibrations induce amplitude dependence of the characteristic resonance parameters (i.e., resonance frequency and damping factor) in materials with microscopic damage features as a result of the nonlinear constitutive relation at the damage location. This paper displays and quantifies results of the nonlinear resonance technique, both in time (signal reverberation) and in frequency (sweep) domains, as a function of sample crack density. The reverberation spectroscopy technique is applied to carbon fiber reinforced plastic (CFRP) composites exposed to increasing thermal loading. Considerable gain in sensitivity and consistent interpretation of the results for nonlinear signatures in comparison with the linear characteristics are obtained. The amount of induced damage is quantified by analyzing light optical microscopy images of several cross-sections of the CFRP samples using histogram equalization and grayscale thresholding. The obtained measure of crack density is compared to the global macroscopic nonlinearity of the sample and explicitly confirms that the increase in nonlinearity is linked to an increased network of cracks. A change from 1% to 3% in crack density corresponds to a tenfold increase in the signature of nonlinearity. Numerical simulations based on a uniform distribution of a hysteretic nonlinear constitutive relation within the sample support the results.

Quantitative linear and nonlinear resonance inspection techniques and analysis for material characterization: Application to concrete thermal damage

Developed in the late 1980s, Nonlinear Resonant Ultrasound Spectroscopy (NRUS) has been widely employed in the field of material characterization. Most of the studies assume the measured amplitude to be proportional to the strain amplitude which drives nonlinear phenomena. In 1D resonant bar experiments, the configuration for which NRUS was initially developed, this assumption holds. However, it is not true for samples of general shape which exhibit several resonance mode shapes. This paper proposes a methodology based on linear resonant ultrasound spectroscopy, numerical simulations and nonlinear resonant ultrasound spectroscopy to provide quantitative values of nonlinear elastic moduli taking into account the 3D nature of the samples. In the context of license renewal in the field of nuclear energy, this study aims at providing some quantitative information related to the degree of micro-cracking of concrete and cement based materials in the presence of thermal damage. The resonance based method is validated as regard with concrete microstructure evolution during thermal exposure.

Experimentally identifying masked sources applying time reversal with the selective source reduction method

This paper describes a time reversal (TR) method of spatially illuminating a source signal which has been masked by another source signal. This masking occurs as a result of inherent limitations in the traditional TR process. The selective source reduction (SSR) method employs a subtraction technique where one TR focus is selectively reduced to illuminate the masked focus. Experimental results and considerations are presented to demonstrate the SSR method for two elastic wave pulses emitted simultaneously from two spatially separated surficial sources and to examine the limitations of the method. A blind test was conducted to demonstrate that no a priori information about the source(s) is required. Spatial and/or temporal characteristics of multiple close-proximity sources can be resolved with the use of the illumination method. The measurements show that the SSR method’s limitations are chiefly due to imperfect temporal reconstruction of the source function in the time reversed focal signal, which conseq...

Damage imaging in a laminated composite plate using an air-coupled time reversal mirror

We demonstrate the possibility of selectively imaging the features of a barely visible impact damage in a laminated composite plate by using an air-coupled time reversal mirror. The mirror consists of a number of piezoelectric transducers affixed to wedges of power law profiles, which act as unconventional matching layers. The transducers are enclosed in a hollow reverberant cavity with an opening to allow progressive emission of the ultrasonic wave field towards the composite plate. The principle of time reversal is used to focus elastic waves at each point of a scanning grid spanning the surface of the plate, thus allowing localized inspection at each of these points. The proposed device and signal processing removes the need to be in direct contact with the plate and reveals the same features as vibrothermography and more features than a C-scan. More importantly, this device can decouple the features of the defect according to their orientation, by selectively focusing vector components of motion into the object, through air. For instance, a delamination can be imaged in one experiment using out-of-plane focusing, whereas a crack can be imaged in a separate experiment using in-plane focusing. This capability, inherited from the principle of time reversal, cannot be found in conventional air-coupled transducers.

Probing material nonlinearity at various depths by time reversal mirrors

In this Letter, the time reversal mirror is used to focus elastic energy at a prescribed location and to analyze the amplitude dependence of the focus signal, thus providing the nonlinearity of the medium. By varying the frequency content of the focused waveforms, the technique can be used to probe the surface, by penetrating to a depth defined by the wavelength of the focused waves. The validity of this concept is shown in the presence of gradual and distributed damage in concrete by comparing actual results with a reference nonlinear measurement and X ray tomography images.

Probing the interior of a solid volume with time reversal and nonlinear elastic wave spectroscopy

A nonlinear scatterer is simulated in the body of a sample and demonstrates a technique to locate and define the elastic nature of the scatterer. Using the principle of time reversal, elastic wave energy is focused at the interface between blocks of optical grade glass and aluminum. Focusing of energy at the interface creates nonlinear wave scattering that can be detected on the sample perimeter with time-reversal mirror elements. The nonlinearly generated scattered signal is bandpass filtered about the nonlinearly generated components, time reversed and broadcast from the same mirror elements, and the signal is focused at the scattering location on the interface.

Three-dimensional modeling and numerical predictions of multimodal nonlinear behavior in damaged concrete blocks

In this paper, the multimodal nonlinear elastic behavior of concrete, which is representative of a consolidated granular material, is modeled numerically. Starting from a local three-dimensional softening law, the initial stiffness properties are re-estimated according to the local strain field. The experiments deal with samples of thermally damaged concrete blocks successively excited around their first three modes of vibration. The geometry of these samples cannot be described by a one-dimensional approximation in these experiments where compressional and shear motions are strongly coupled. Despite this added complexity, the nonlinear behavior for the three modes of vibration of the samples is well captured by the simulations using a single scalar nonlinear parameter appropriately integrated into the elasticity equations. It is shown that without sufficient attention paid to the latter, the conclusions would have brought erroneous statements such as nonlinearity dispersion or strain type dependence.

Correction to “Nonlinear dynamical triggering of slow slip on simulated earthquake faults with implications to Earth”

[1] Among the most fascinating, recent discoveries in seismology are the phenomena of dynamically triggered fault slip, including earthquakes, tremor, slow and silent slip—during which little seismic energy is radiated—and low frequency earthquakes. Dynamic triggering refers to the initiation of fault slip by a transient deformation perturbation, most often in the form of passing seismic waves. Determining the frictional constitutive laws and the physical mechanism(s) governing triggered faulting is extremely challenging because slip nucleation depths for tectonic faults cannot be probed directly. Of the spectrum of slip behaviors, triggered slow slip is particularly difficult to characterize due to the absence of significant seismic radiation, implying mechanical conditions different from triggered earthquakes. Slow slip is often accompanied by nonvolcanic tremor in close spatial and temporal proximity. The causal relationship between them has implications for the properties and physics governing the fault slip behavior. We are characterizing the physical controls of triggered slow slip via laboratory experiments using sheared granular media to simulate fault gouge. Granular rock and glass beads are sheared under constant normal stress, while subjected to transient stress perturbation by acoustic waves. Here we describe experiments with glass beads, showing that slow and silent slip can be dynamically triggered on laboratory faults by ultrasonic waves. The laboratory triggering may take place during stable sliding (constant friction and slip velocity) and/or early in the slip cycle, during unstable sliding (stick-slip). Experimental evidence indicates that the nonlinear-dynamical response of the gouge material is responsible for the triggered slow slip.