Alexander Sutin

Nonlinear Elastic Wave Spectroscopy (NEWS) Techniques to Discern Material Damage, Part I: Nonlinear Wave Modulation Spectroscopy (NWMS)

Abstract The level of nonlinearity in the elastic response of materials containing structural damage is far greater than in materials with no structural damage. This is the basis for nonlinear wave diagnostics of damage, methods which are remarkably sensitive to the detection and progression of damage in materials. Nonlinear wave modulation spectroscopy (NWMS) is one exemplary method in this class of dynamic nondestructive evaluation techniques. The method focuses on the application of harmonics and sum and difference frequency to discern damage in materials. It consists of exciting a sample with continuous waves of two separate frequencies simultaneously, and inspecting the harmonics of the two waves, and their sum and difference frequencies (sidebands). Undamaged materials are essentially linear in their response to the two waves, while the same material, when damaged, becomes highly nonlinear, manifested by harmonics and sideband generation. We illustrate the method by experiments on uncracked and cracked Plexiglas and sandstone samples, and by applying it to intact and damaged engine components.

Nonlinear acoustic interaction on contact interfaces and its use for nondestructive testing

Recent theoretical and experimental studies demonstrated that a weakly or incompletely bonded interfaces exhibit highly nonlinear behavior. One of acoustic manifestations of such nonlinearity is the modulation of a probing high-frequency ultrasonic wave by low-frequency vibration. The vibration varies the contact area modulating the phase and amplitude of higher frequency probing wave passing through the interface. In the frequency domain, the result of this modulation manifests itself as side-band spectral components with respect to the frequency of the probing wave. This modulation effect has been observed experimentally for various materials (metals, composites, concrete, sandstone, glass) with various types of contact-type defects (interfaces): cracks, debondings, delaminations, and microstructural material damages. Study of this phenomenon revealed correlation between the developed modulation criterion and the quantitative characteristics of the interfaces, such as its size, loading condition, and bonding strength. These findings have been used for the development of an innovative nondestructive evaluation technique, namely Vibro-Acoustic Modulation Technique. Two modifications of this technique have been developed: Vibro-Modulation (VM) and Impact-Modulation (IM), employing CW and impact-induced vibrations, respectively. The examples of applications of these methods include crack detection in steel pipes, aircraft and auto parts, bonded composite plates etc. These methods also proved their effectiveness in the detection of cracks in concrete.

Micro-damage diagnostics using nonlinear elastic wave spectroscopy (NEWS)

Nonlinear elastic wave spectroscopy (NEWS) represents a class of powerful tools which explore the dynamic nonlinear stress–strain features in the compliant bond system of a micro-inhomogeneous material and link them to micro-scale damage. Hysteresis and nonlinearity in the constitutive relation (at the micro-strain level) result in acoustic and ultrasonic wave distortion, which gives rise to changes in the resonance frequencies as a function of drive amplitude, generation of accompanying harmonics, nonlinear attenuation, and multiplication of waves of different frequencies. The sensitivity of nonlinear methods to the detection of damage features (cracks, flaws, etc.) is far greater than can be obtained with linear acoustical methods (measures of wavespeed and wave dissipation). We illustrate two recently developed NEWS methods, and compare the results for both techniques on roofing tiles used in building construction.

Slow dynamics and anomalous nonlinear fast dynamics in diverse solids.

Results are reported of the first systematic study of anomalous nonlinear fast dynamics and slow dynamics in a number of solids. Observations are presented from seven diverse materials showing that anomalous nonlinear fast dynamics (ANFD) and slow dynamics (SD) occur together, significantly expanding the nonlinear mesoscopic elasticity class. The materials include samples of gray iron, alumina ceramic, quartzite, cracked Pyrex, marble, sintered metal, and perovskite ceramic. In addition, it is shown that materials which exhibit ANFD have very similar ratios of amplitude-dependent internal-friction to the resonance-frequency shift with strain amplitude. The ratios range between 0.28 and 0.63, except for cracked Pyrex glass, which exhibits a ratio of 1.1, and the ratio appears to be a material characteristic. The ratio of internal friction to resonance frequency shift as a function of time during SD is time independent, ranging from 0.23 to 0.43 for the materials studied.

Vibro-Acoustic Modulation Nondestructive Evaluation Technique

Nonlinear acoustic technique has been recently introduced as a new tool for nondestructive inspection and evaluation of fatigued, defective, and fractured materials. Various defects such as cracks, debonding, fatigue, etc. lead to anomalous high levels of nonlinearity as compared with flawless structures. One of the acoustic manifestations of such nonlinearity is the modulation of ultrasound by low frequency vibration. Two methods employing the nonlinear interaction of ultrasound and vibration were developed, namely vibromodulation (VM) and impactmodulation (IM) methods. VM method employs forced harmonic vibration of a structure tested, while IM method uses impact excitation of structure natural modes of vibration. The feasibility tests were carried out for different objects and demonstrated high sensitivity of the methods for detection of cracks in steel pipes and pins, bonding quality in titanium and thermoplastic plates used for airspace applications, cracks in combustion engine, adhesion flaws in bonded composite structures, and cracks and corrosion in reinforced concrete. The model of the crack allowing to describe the modulation of sound by vibration is discussed. The developed nonlinear technique demonstrated certain advantages as compared with the conventional linear acoustic technique, specifically discrimination capabilities, sensitivity, and applicability to highly inhomogeneous structures.

Nonlinear resonant ultrasound spectroscopy (NRUS) applied to damage assessment in bone

Nonlinear resonant ultrasound spectroscopy (NRUS) is a resonance-based technique exploiting the significant nonlinear behavior of damaged materials. In NRUS, the resonant frequency(ies) of an object is studied as a function of the excitation level. As the excitation level increases, the elastic nonlinearity is manifest by a shift in the resonance frequency. This study shows the feasibility of this technique for application to damage assessment in bone. Two samples of bovine cortical bone were subjected to progressive damage induced by application of mechanical cycling. Before cycling commenced, and at each step in the cycling process, NRUS was applied for damage assessment. For independent assessment of damage, high-energy x-ray computed tomography imaging was performed but was only useful in identifying the prominent cracks. As the integral quantity of damage increased, NRUS revealed a corresponding increase in the nonlinear response. The measured change in nonlinear response is much more sensitive than the change in linear modulus. The results suggest that NRUS could be a potential tool for micro-damage assessment in bone. Further work must be carried out for a better understanding of the physical nature of damaged bone and for the ultimate goal of the challenging in vivo implementation of the technique.

Nonlinear elastic constants of solids with cracks

Experimental data on a cracked medium exhibiting high acoustic nonlinearity is a commonly observed phenomenon. Here a physical model of a medium with cracks is suggested to explain the observed phenomena. The model is based on the assumption of uniform stress that is valid for a low concentration of cracks. The crack behavior is described using the model in which a crack is represented as an elastic contact of two rough surfaces, pressed one to the other under the action of internal stresses in the surrounding solid. Linear and nonlinear acoustic constants of the fractured medium are calculated. It is shown that, in this medium, negative values of the Poisson’s ratio and anomalously high values of the nonlinear constants are possible.

Sensitive imaging of an elastic nonlinear wave-scattering source in a solid

We have developed an imaging method for locating isolated nonlinear scattering source(s) in solids. It relies on extracting the nonlinear response of a solid by modulation of a high by a low-frequency wave, and employing moving-window, synchronous detection. The resulting image consists of nonlinear wave reflection profiles with remarkable sensitivity to an isolated elastic nonlinear source(s). In creating the image, we can distinguish between a nonlinear scattering source and other wave scatterers in the material. The method should work equally well for imaging the relative nonlinearity of different regions within a volume.

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.

Single-channel time reversal in elastic solids

Reverberant volume time reversal in 3D elastic solids (doped glass and Berea sandstone) using a single channel are presented. In spite of large numbers of mode conversions (compressional to shear wave conversions at the walls), time reversal works extremely well, providing very good spatial and time focusing of elastic waves. Ceramics were bonded to the surface as sources (100–700 kHz); a broadband laser vibrometer (dc—1.5 MHz) was used as detector. Temporal and spatial time-reversal focusing are frequency dependent and depend on the dissipation characteristics of the medium. Doped glass (inverse dissipation Q between 2000 to 3000) shows time-reversed spatial focal resolution at about half of the shear wavelength. The Berea sandstone (Q=50) yields a wider focusing width (a bit more than the shear wavelength) due to its lower Q. Focusing in the doped glass is better because the time-reversal (virtual) array created by wave reflections is larger than in the highly attenuating sandstone. These are the first results reported in granular media, and are a first step toward geophysical and field applications.