T. J. Ulrich

Imaging nonlinear scatterers applying the time reversal mirror

Nonlinear elastic wave spectroscopy (NEWS) has been shown to exhibit a high degree of sensitivity to both distributed and isolated nonlinear scatterers in solids. In the case of an isolated nonlinear scatterer such as a crack, by combining the elastic energy localization of the time reversal mirror with NEWS, it is shown here that one can isolate surfacial nonlinear scatterers in solids. The experiments presented here are conducted in a doped glass block applying two different fixed frequency time-reversed signals at each focal point and scanning over a localized nonlinear scatterer (a complex crack). The results show a distinct increase in nonlinear response, via intermodulation distortion, over the damaged area. The techniques described herein provide the means to discriminate between linear and nonlinear scatterers, and thus to ultimately image and characterize damaged regions.

The time reversed elastic nonlinearity diagnostic applied to evaluation of diffusion bonds

With the recent application of time reversed acoustics and nonlinear elasticity to imaging mechanical damage, the development of time reversal based nondestructive evaluation techniques has begun. Here, diffusion bonded metal disks containing intentionally disbonded regions are analyzed using the time reversed elastic nonlinearity diagnostic. The nonlinear results are compared with linear ultrasonic imaging (C scan). Scanning electron microscopy is shown to illustrate the differences between the features seen by the linear and nonlinear methods.

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.

Three component time reversal: Focusing vector components using a scalar source

In acoustics, it is known that, for a given response signal at an arbitrary location, reciprocity and time reversal (TR) can be used to focus high levels of acoustic energy at that position. In solid media, elastic waves generally induce different disturbances in three directions. In this paper, both experimental and numerical wave propagation results for solid materials demonstrate the ability to use a scalar source, a three component detector and the reciprocal TR process to selectively focus each of the different vector components, either individually or collectively. The principle is explained from an analytical point of view. The numerical and experimental study demonstrates excellent temporal and spatial focalization. Applications of the selective vector component focusing can be found in damage imaging techniques using both linear or nonlinear ultrasonic waves.

Application of nonlinear dynamics to monitoring progressive fatigue damage in human cortical bone

In this work, the results of applying nonlinear dynamics to study progressive material fatigue in human bone are described. Material nonlinear dynamical response has been shown to be associated with mechanical damage. The progressive mechanical damage experiments were conducted in cortical bone extracted from a human femur. After each damage step, the material dynamical nonlinear response was measured by applying wave modulation and extracting a nonlinear parameter proportional to the sideband amplitude. The nonlinear parameter increases rapidly with damage step, indicating increased damage after the initial cycling procedure, while the quasistatic stiffness taken from the cycling experiments shows little change.

Resonant ultrasound spectroscopy for materials with high damping and samples of arbitrary geometry

Resonant ultrasound spectroscopy (RUS) is a powerful and established technique for measuring elastic constants of a material with general anisotropy. The first step of this technique consists of extracting resonance frequencies and damping from the vibrational frequency spectrum measured on a sample with free boundary conditions. An inversion technique is then used to retrieve the elastic tensor from the measured resonance frequencies. As originally developed, RUS has been mostly applicable to (i) materials with small damping such that the resonances of the sample are well separated and (ii) samples with simple geometries for which analytical solutions exist. In this paper, these limitations are addressed with a new RUS approach adapted to materials with high damping and samples of arbitrary geometry. Resonances are extracted by fitting a sum of exponentially damped sinusoids to the measured frequency spectrum. The inversion of the elastic tensor is achieved with a genetic algorithm, which allows searching for a global minimum within a discrete and relatively wide solution space. First, the accuracy of the proposed approach is evaluated against numerical data simulated for samples with isotropic symmetry and transversely isotropic symmetry. Subsequently, the applicability of the approach is demonstrated using experimental data collected on a composite structure consisting of a cylindrical sample of Berea sandstone glued to a large piezoelectric disk. In the proposed experiments, RUS is further enhanced by the use of a 3-D laser vibrometer allowing the visualization of most of the modes in the frequency band studied.

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.

Selective source reduction to identify masked sources using time reversal acoustics

The presence of strong sources of elastic waves often makes it impossible to localize weaker ones, which are sometimes the most meaningful, e.g. in the characterization of complexity of active Earth faults or of microdamage in a composite structural material. To address this problem, a selective source reduction method is proposed here which, applied in conjunction with time reversal acoustics (TRA), provides the means to selectively reduce the contribution of strong sources allowing full illumination of the weak ones. The method is complementary to other methods based on TRA which aim at the selective illumination of scatterers in the propagation medium. In this paper, a description of the method is given along with presentation of a few numerical results to demonstrate its usefulness for localization of sources. Validation and some experimental results are also presented.

Time reversed elastic nonlinearity diagnostic applied to mock osseointegration monitoring applying two experimental models

This study broadens vibration-like techniques developed for osseointegration monitoring to the nonlinear field. The time reversed elastic nonlinearity diagnostic is applied to two mock models. The first one consists of tightening a dental implant at different torques in a mock cortical bone; the second one allows one to follow glue curing at the interface between a dental implant and a mock jaw. Energy is focused near the implant interface using the time reversal technique. Two nonlinear procedures termed pulse inversion and the scaling subtraction method, already used successfully in other fields such as contrast agents and material characterization, are employed. These two procedures are compared for both models. The results suggest that nonlinear elasticity can provide new information regarding the interface, complementary to the linear wave velocity and attenuation. The curing experiment exhibits an overall low nonlinear level due to the fact that the glue significantly damps elastic nonlinearity at the interface. In contrast, the torque experiment shows strong nonlinearities at the focus time. Consequently, a parallel analysis of these models, both only partially reflecting a real case, enables one to envisage future in vivo experiments.