Nonlinear Resonant Ultrasound Spectroscopy Research Articles

Profiling the thermal damage gradient in concrete using linear and non-linear ultrasonics

Processes such as carbonation and thermal damage result in a depth-dependent variation in concrete mechanical properties, which are typically characterized by invasive sampling and destructive testing. In this study, several ultrasonic testing methods are employed to nondestructively measure gradients in elastic properties within concrete and mortar slabs, induced by varying amount of exposure to elevated temperatures. The slabs are subjected to two distinct heat exposures, carefully chosen to create different gradients within the first few centimeters below the surface. The first exposure scenario following the ISO fire standard led to superficial damage. Deeper damage was achieved with radiant panels. We use linear and non-linear ultrasonic testing, with the aim of characterizing the resulting property gradients including refracted P-waves, analysis of surface wave dispersion and higher harmonic generation. Additionally, we employ NRUS (nonlinear resonant ultrasound spectroscopy) to test slices extracted from the different depths within the slabs. The ultrasonic test results are benchmarked and interpreted in relation to a suite of other multiphysical measurements (resistivity, capacity, temperature). This work represents a first crucial step towards the development of a new method for measuring gradients of nonlinear elastic properties within concrete through nondestructive ultrasonic testing.

Nonlinear resonant bar of approximate Ramberg–Osgood type modulus defect

This study investigates the nonlinear vibration of a material bar with a modulus defect that causes observable hysteresis in the elastic regime. The Ramberg–Osgood equation is used to obtain an approximate model of the quasi-static stress–strain relationship for such a material, from which a phenomenological dynamic hysteresis function of arbitrary order is constructed. The nonlinear hysteresis is described with two parameters. Applying the hysteresis function leads to a nonlinear wave equation which is then solved for the longitudinal vibration of the bar using a perturbation method. The leading-order solution provides the strain-dependent resonance frequency and damping factor which are the two quantities measured in the nonlinear resonance ultrasound spectroscopy (NRUS). It is shown that the resonance frequency shift and damping increment hold, in general, a power-law dependence on the strain amplitude and the conventional linear dependence is a special case for the quadratic hysteresis. The derived formula is applied to existing data from bending and torsional NRUS-type experiments where the conventional linear fit appears to be clearly inadequate. Experimental resonance frequency shift data are fitted to determine the two hysteresis parameters, both of which vary with the changes in the material state. It is shown that the nonlinear damping ratio is a more general measure of the energy dissipation due to the increasing hysteresis and thus can be taken as a damage index. Consequently, this paper proposes a general procedure to analyze NRUS data for a wider range of materials. The present analysis is valid up to the yield strain which is sufficient to cover the strain amplitudes used in NRUS measurements.

Impact of relative humidity variations on Carrara marble mechanical properties investigated by nonlinear resonant ultrasound spectroscopy

Like many other stones, marble mechanical properties can be significantly changed in presence of water. Water most often induces a weakening which can lead to marble degradation when coupled to temperature variations. Yet, marble artefacts are more frequently subjected to relative humidity (RH) variations than episodes of water imbibition and/or drastic temperature variations. Thus, one could wonder how do variations of RH alone impact marble mechanical state. In this study, Carrara Gioia marble samples are subjected to adsorption-desorption cycles. They were previously thermally-damaged between 40 and 105 °C, and their microstructure was characterized for each heating temperature. The evolution of their mechanical properties is monitored non-destructively with two parameters measured by Nonlinear Resonant Ultrasound Spectroscopy. The resonant frequency decreases weakly with increasing RH, indicating a diminution in sample stiffness due to low moisture-induced softening. The nonlinear parameter increases strongly, probably due to higher capillary pressure associated to a capillary condensation increase with RH. However, these phenomena are reversible: during adsorption-desorption cycling both parameters remain quite constant for a given RH. Therefore, while a RH increase impacts the mechanical properties of Carrara marble, adsorption-desorption cycling shows a reversible behavior which does not induce any permanent change in mechanical properties.

Nonlinear resonant ultrasound spectroscopy using white-noise excitation

Nonlinear resonant ultrasound spectroscopy (NRUS) is a technique for non-destructive sample evaluation by which a strain-dependent nonlinear parameter is quantified that exhibits heightened sensitivity to defects as compared to monitoring of linear resonance attributes. As NRUS measurements have traditionally used a controlled sweep of sinusoidal inputs, applications of the method have been largely limited to laboratory experiments. Here we present NRUS results which utilized a white noise signal as input, in order to better approximate ambient excitation and facilitate efficient validation using time-domain models. Studied samples were chosen to reflect a range of nonlinear responses and underlying mechanisms (acrylic, sandstone, fractured steel). We excited the studied samples using bonded piezoelectric transducers which delivered white-noise inputs at increasing amplitudes, with the nonlinear response measured with a laser doppler vibrometer. By comparing results against those obtained from traditional NRUS, we find comparable trends in the nonlinear parameter under white-noise excitation, including similar relative differences in magnitude across the samples and consistent values across similar mode shapes. While we note that white-noise strain estimation is complicated by simultaneous excitation of multiple resonant modes, NRUS results from white-noise excitation demonstrate promising viability of the technique for (1) in-situ inspection, and (2) a more-tractable approach to model the physics of various NRUS signals.

Nonlinear/linear resonance ultrasound spectroscopy (N/RUS) of additively manufactured 316L stainless steel samples using in-contact and non-contact excitation

Due to their sensitivities to defects and microstructural changes, the linear and nonlinear parameters measured with nonlinear resonance ultrasound spectroscopy (NRUS) have the potential to evaluate the quality of additively manufactured parts. Here, NRUS with in-contact and non-contact excitation configurations is used to test a set of 316L stainless steel samples manufactured by laser powder bed fusion. Subgroups of the samples are heat treated to three temperatures to alter the samples' microstructure and mechanical performance. Results show that the hysteretic nonlinearity parameter measured with in-contact NRUS demonstrates sensitivity to heat-treatment-induced microstructural changes. However, due to the unwanted nonlinearity introduced by the bonding, variations in the repeated in-contact measurements of a single sample are almost as large as the differences between the heat treatment subgroups. The non-contact configuration allows measurement of two linear parameters (resonance frequency and damping) with exceptional repeatability, and results show clear distinction between samples in different heat treatment groups. The non-contact NRUS configuration could not produce a sufficient dynamic strain amplitude to allow a reliable measurement of the samples’ nonlinear response. In-contact and non-contact NRUS results are analyzed in relation to independently measured mechanical properties and microstructural information to investigate the feasibility of NRUS for the nondestructive evaluation of additively manufactured metals.

Toward In-situ Characterization of Additively Manufactured Parts Using Nonlinear Resonance Ultrasonic Spectroscopy

ABSTRACT In this study, we investigate the feasibility of using nonlinear resonance ultrasound spectroscopy (NRUS) for in-situ monitoring of additively manufactured (AM) parts i.e., while they are still on the build plate. In NRUS, the test specimen is excited around one or more of its resonance frequencies with increasing driving amplitude. The linear shift in resonance frequency with the increasing driving amplitude is a measure of the constituent material’s hysteretic nonlinearity (α), which is itself related to some degree of micro-damage in the test specimens. We conduct NRUS on test specimens glued to a thick plate. The specimens are excited using a piezoelectric transducer (PZT) adhered to the bottom of the plate. We use this setup to measure the hysteretic nonlinearity parameters ( and ) of several cylindrical AM specimens fabricated by laser powder bed fusion technique as well as a few non-AM metallic specimens. The measured nonlinearity parameters for the specimens on the build plate (process monitoring mode) are compared to those measured without the build plate (quality control mode). We observe a systematic decrease in the measured nonlinearity when the specimens are tested on the build plate. An analytical study demonstrates that we measure the weighted average nonlinearity of the specimen and build plate, which itself has a lower nonlinearity. Despite the observed difference, the measured nonlinearity parameters of the specimens with and without the build plate are highly correlated. With further investigations, the proposed test setup can potentially be used for characterization of AM parts in situ.

From force chains to nonclassical nonlinear dynamics in cemented granular materials.

In this letter, we present evidence for a mechanism responsible for the nonclassical nonlinear dynamics observed in many cemented granular materials that are generally classified as mesoscopic nonlinear elastic materials. We demonstrate numerically that force chains are created within the complex grain-pore network of these materials when subjected to dynamic loading. The interface properties between grains along with the sharp and localized increase of the stress occurring at the grain-grain contacts leads to a reversible decrease of the elastic properties at macroscopic scale and peculiar effects on the propagation of elastic waves when grain boundary properties are appropriately considered. These effects are observed for relatively small amplitudes of the elastic waves, i.e., within tens of microstrain, and relatively large wavelengths, i.e., orders of magnitude larger than the material constituents. The mechanics are investigated numerically using the hybrid finite-discrete-element method and match those observed experimentally using nonlinear resonant ultrasound spectroscopy.

Nonlinear reverberation spectroscopy with phase-sensitive superheterodyne reception

A technique is presented for determining elastic nonlinearity of materials from resonant frequency shifts as a function of signal amplitude during free vibrational decay after tone-burst excitation. The technique differs from previous nonlinear reverberation spectroscopy (NRS) techniques in that it employs phase-sensitive superheterodyne reception. Time-dependent amplitudes of in-phase and out-of-phase components of signals, relative to a reference sinusoid at the excitation frequency, are provided through analog hardware processing in the absence of digitization of the signal from the vibrational sensor. The time-dependent phase and amplitude of the signal are determined through software analysis of these in-phase and out-of-phase components, and the instantaneous frequency during free decay is then determined from the time derivative of the phase. With this approach, superheterodyne reception and low-pass filtering of the phase-detector outputs lead to a great reduction in noise and computation effort, relative to direct digitization and software processing of the sensor signal, while retaining information on frequency shifts on a relevant time scale during ringdown. As with other NRS techniques, rapid acquisition of data on amplitude dependence of the resonant frequency during ringdown leads to minimization of systematic errors from temperature drift. The technique is demonstrated with noncontacting electromagnetic-acoustic transduction on custom alloyed Al (0.2 at.% Zn) and commercial Al 7075 cylinders with axial-shear resonant frequencies between 658 kHz and 659 kHz. The precision of measurements of relative frequency shifts is found to be on the order of 0.1 parts per million (ppm), exceeding by two orders of magnitude the best reported precision of nonlinear resonant ultrasound spectroscopy (NRUS).

Nonlinear resonant ultrasound spectroscopy (NRUS) for nondestructive evaluation

Nonlinear Resonant Ultrasound Spectroscopy (NRUS) is a simple yet effective technique for nondestructive evaluation of incipient damage in a wide range of materials. NRUS combines the advantages of resonance-based testing and nonlinear ultrasonic or acoustic testing in that it can be used for testing complex-shaped objects and detection of microscopic defects. In this talk, I describe several applications of NRUS in: (1) monitoring of microcracking in concrete materials due to various damage processes; (2) monitoring the growth of microscopic fatigue cracks in aluminum; and (3) predicting the fatigue life of additively manufactured metallic alloys. In addition, I provide a snapshot of our ongoing research in developing non-contact NRUS test set up and using NRUS for in-process monitoring of additively manufactured parts. I close with describing the limitations of NRUS and possible directions for future research to realize NRUS potential in nondestructive evaluation (NDE) applications.

Variations of Classical and Nonclassical Ultrasound Nonlinearity Parameters during Heat-Induced Microstructural Evolution in an Iron-Copper Alloy

This research demonstrates and compares the potential of two nonlinear ultrasound techniques, second harmonic generation (SHG) and nonlinear resonant ultrasound spectroscopy (NRUS). This research examines a set of thermally aged iron-copper (Fe-1.0% Cu) alloy specimens, which are used as surrogate specimens for radiation damage. It is found that both SHG and NRUS are sensitive to the growth of the copper precipitates, while the changes in the respective nonlinearity parameters are due to different mechanisms. This research demonstrates the potential use of both of these nonlinear ultrasound techniques.

Sensitivity Assessment of the Nonlinear Resonant Ultrasonic Spectroscopy for Concrete Damage Detection

Nonlinear Resonant Ultrasound Spectroscopy is a nondestructive acoustic method which is able to measure the bulk hysteretic nonlinearity. This method monitors the shift of the resonant frequency in response of variations in the excitation frequency amplitudes. Measurements were performed on concrete samples exposed to temperatures of 200, 400, 600, 800, 1000, 1200 °C. The elastic modulus values are given to compare the Nonlinear Resonant Ultrasound Spectroscopy (NRUS) sensitivity. These are calculated from the measured velocities of ultrasonic pulses (linear acoustic method) and from the bulk density. The strengths of the samples obtained by destructive methods are also given. Based on these results, the NRUS method can be described as a very sensitive indicator of damage in concrete.

Investigation of the relationship between classical and nonclassical ultrasound nonlinearity parameters and microstructural mechanisms in metals.

This research studies two nonlinear ultrasound techniques: second harmonic generation and nonlinear resonant ultrasound spectroscopy, and the relationship to microstructural mechanisms in metals. The results show that there is a large change in both the classical, β, and nonclassical, α, ultrasound nonlinearity parameters in response to three specific microstructural mechanisms: precipitate growth in and along the grain boundaries, dislocations, and precipitate pinned dislocations. For example, both β and α increase with the growth of the precipitate radii (precipitate-pinned-dislocations). Additionally, both β and α increase when there is a growth of precipitates in and along the grain boundaries. As expected, β and α decrease when there is a removal of dislocations in the material. The relationship between β and α, and the microstructural mechanisms studied provide a quantitative understanding of the relationship between measured nonlinearity parameters and microstructural changes in metals, helping to demonstrate the possibility of using these two independent, but complementary, nonlinear ultrasound procedures to monitor microstructural damage.

Cover Picture: Nonlinear Resonant Ultrasound Spectroscopy for Predicting Sensitivity to Initiation in Granular High Explosives (Prop., Explos., Pyrotech. 3/2020)

Cover Picture: Nonlinear Resonant Ultrasound Spectroscopy for Predicting Sensitivity to Initiation in Granular High Explosives (Prop., Explos., Pyrotech. 3/2020)

Comparison of changes in nonclassical (α) and classical (β) acoustic nonlinear parameters due to thermal aging of 9Cr–1Mo ferritic martensitic steel

The objective of this research is to demonstrate the sensitivity of the hysteretic, nonclassical acoustic nonlinear parameter, α to track changes in the microstructure of 9Cr–1Mo ferritic martensitic steel due to thermal aging. The α parameter is measured with a non-contact nonlinear resonance ultrasound spectroscopy (NRUS) system with an air-coupled source and a laser Doppler vibrometer (LDV) receiver. This NRUS setup is used to track changes in multiple 9Cr–1Mo specimens subjected to different aging times at the same 650∘C temperature. These α results are shown to be highly sensitive to the associated changes in the microstructure of the 9Cr–1Mo specimens, and are then compared to three different parameters – Rockwell hardness, Young's modulus, E and the classical acoustic nonlinear parameter, β – all measured in the same specimens. These results are then combined to infer microstructure changes such as the removal of dislocations and the formation of carbide precipitates occurring in the 9Cr–1Mo specimens during thermal aging.

Nonlinear Resonant Ultrasound Spectroscopy for Predicting Sensitivity to Initiation in Granular High Explosives

AbstractNonlinear Resonant Ultrasound Spectroscopy (NRUS) is a technique that can measure bulk nonlinear coefficients of the nonlinear elastic modulus for a material. NRUS has been used to identify damage in a variety of granular materials including rocks and concrete. Some energetic materials, such as Pentaerythritol Tetranitrate (PETN), are commonly fielded as pressed granular compacts. It is well known that the sensitivity to initiation of these materials is heavily dependent on their microstructure, and that microstructure changes naturally (becomes damaged) over time. In this study, we examine the use of NRUS to identify changes in microstructure between pristine and thermally aged PETN pellets. In particular, we examine the relationship between the bulk hysteretic nonlinearity, α, of the pellets and time spent at temperature, powder specific surface area (SSA), and sensitivity to initiation. We find that, in general, α does not increase uniformly for all pellets within a single thermal aging condition. However, when the pellets are test fired to determine sensitivity to initiation, there is a strong correlation between α and firing voltage threshold. NRUS‐measured α has the added benefit that the measurements can be made in situ and on benchtop scales.

Detecting and imaging stress corrosion cracking in stainless steel, with application to inspecting storage canisters for spent nuclear fuel

One of the primary concerns with the long-term performance of storage systems for spent nuclear fuel (SNF) is the potential for corrosion due to deliquescence of salts deposited as aerosols on the surface of the canister, which is typically made of austentic stainless steel. In regions of high residual weld stresses, this may lead to localized stress-corrosion cracking (SCC). The ability to detect and image SCC at an early stage (long before the cracks are susceptible to propagate through the thickness of the canister wall and leaks of radioactive material may occur) is essential to the performance evaluation and licensing process of the storage systems. In this paper, we explore a number of nondestructive testing techniques to detect and image SCC in austenitic stainless steel. Our attention is focused on a small rectangular sample of 1 × 2 in2 with two cracks of mm-scale sizes. The techniques explored in this paper include nonlinear resonant ultrasound spectroscopy (NRUS) for detection, Linear Elastodynamic Gradient Imaging Technique (LEGIT), ultrasonic C-scan, vibrothermography, and synchrotron X-ray diffraction for imaging. Results obtained from these techniques are compared. Cracks of mm-scale sizes can be detected and imaged with all the techniques explored in this study.

Electromagnetic excitation technique for nonlinear resonant ultrasound spectroscopy

Nonlinear resonant ultrasound spectroscopy (NRUS) is a method that can be used to determine the amount of microcracking in structures. The nonlinear parameter extracted in NRUS is based on the dependence of the resonance frequency on vibration amplitude in the presence of damage. NRUS measurements typically are excited with a piezoelectric transducer, but here the application of an electromagnetic transducer is explored as an alternative. The electromagnetic transducer, unlike a single piezoelectric, allows selective excitation of longitudinal, torsional, and bending vibrations in a rod-shaped sample. Measurement of the nonlinear properties of the sample for each type of vibration is therefore possible. This electromagnetic technique involves gluing a coil of wire onto the end of a rod sample and placing it in a magnetic field. By controlling which part of the coil is inside the strongest region of the magnetic field, the principal direction of the driven oscillations in the rod can be controlled. Both piezoelectric and electromagnetic excitation techniques are tested by measuring the parameter of nonlinearity for longitudinal motion, αE, in a sample of Berea sandstone. The electromagnetic technique was shown to measure a 30% higher mean value for αE than the piezoelectric technique.

Investigation of the nonlinearity of transducer acoustic couplants for nonlinear elastic measurements

The study of nonlinear elasticity of materials often relies on attaching contact transducers to a sample to achieve the required strain amplitudes. When measuring and quantifying the degree of nonlinearity, it is assumed that the nonlinearity of the bond between the material and the transducer is negligible. Here, we aim to characterize the nonlinearity of common acoustic couplants used in nonlinear measurements. Other factors are also reported since bond nonlinearity is not the only important property when choosing an acoustic couplant, i.e., amount of energy transfer, thermal properties, cure time, toxicity, and ease of application and/or removal. Various types of acoustic couplants including, epoxies, glues, thermal adhesives, and coupling agents were studied using Nonlinear Resonance Ultrasound Spectroscopy (NRUS), which is a measure of the hysteretic nonlinearity of a material. Measurements were made on cylindrical samples of acrylic, aluminum alloy 6061-T651, and Crab Orchard sandstone, chosen for their range of sound speeds, attenuation, and nonlinearity.

Nonlinear resonant ultrasound spectroscopy of stress corrosion cracking in stainless steel rods

Stainless steel containers are susceptible to stress corrosion cracking (SCC) under certain stress and corrosion conditions. Nonlinear ultrasonic techniques are very sensitive to the early presence of damage, more so than linear techniques. Nonlinear Resonant Ultrasound Spectroscopy (NRUS) is used here to measure a nonlinear shift in the resonance frequency due to a cumulative amount of SCC. Steel rods are immersed in a heated magnesium chloride solution and removed after different exposure times. NRUS measurements are conducted using the fundamental longitudinal mode of vibration. Rods exposed longer generally have a larger resonance frequency shift and are therefore more nonlinear. Thus NRUS might offer a means of detecting a cumulative SCC damage in a sample.

Linear Versus Nonlinear Acoustic Probing of Plasticity in Metals: A Quantitative Assessment.

The relative dislocation density of aluminum and copper samples is quantitatively measured using linear Resonant Ultrasound Spectroscopy (RUS). For each metallic group, four samples were prepared with different thermomechanical treatments in order to induce changes in their dislocation densities. The RUS results are compared with Nonlinear Resonant Ultrasound Spectroscopy (NRUS) as well as Second Harmonic Generation (SHG) measurements. NRUS has a higher sensitivity by a factor of two to six and SHG by 14–62%. The latter technique is, however, faster and simpler. As a main result, we obtain a quantitative relation between the changes in the nonlinear parameters and the dislocation density variations, which in a first approximation is a linear relation between these differences. We also present a simple theoretical expression that explains the better sensitivity to dislocation content of the nonlinear parameters with respect to the linear ones. X-Ray diffraction measurements, although intrusive and less accurate, support the acoustics results.