Measured Nonlinearity Parameters Research Articles

Experimental Evaluation Method of Carbonation in Concrete Structure Using Nonlinear Resonant Ultrasonic Spectroscopy

Carbonation is a typical type of concrete deterioration that can cause various physicochemical changes and adversely affects the performance of reinforced concrete structures, particularly in offshore structures. Nonlinear resonant ultrasonic spectroscopy (NRUS), which is a non-destructive test technique, is applied in this study to experimentally evaluate the degree of concrete carbonation without damaging the structure. Nonlinearity parameters of test specimens exposed to accelerated carbonation conditions are measured via NRUS. The measured nonlinearity parameters indicate lower values for longer carbonation durations. This is because internal microcracks are reduced by CaCO<sub>3</sub>, which is a carbonation product. The consistent trend of the experimental results shows that NRUS can be effectively applied to evaluate concrete carbonation.

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.

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.

A Pulse Inversion-Based Nonlinear Ultrasonic Technique using a Single-Cycle Longitudinal Wave for Evaluating Localized Material Degradation in Plates

General nonlinear ultrasonic techniques (NUTs) use tone-burst ultrasonic waves with a narrow bandwidth so that the fundamental frequency component and the second-order harmonic component can be clearly separated in the frequency domain. Meanwhile, when using a longitudinal wave propagating in the thickness direction, the number of cycles of tone-burst signals can be limited by the object thickness. In some cases, only a pulsed signal or a single-cycle signal, which has broad bandwidth, may be applicable to avoid superposition of the first transmitted wave and the multi-reflected waves. Such cases complicate the use of general NUTs, and it is necessary to apply a method to precisely extract the second-order harmonic component even in broadband signals to the NUT. In this study, the pulse inversion (PI) method, which can extract only even harmonics or odd harmonics by superposing or subtracting two wave signals obtained from 180° out-of-phase inputs, is applied to an NUT using broadband ultrasound. The performance of the PI-based NUT with respect to material degradation is verified using a series of heat-treated aluminum alloy specimens with various levels of precipitates. The experimental results show that the nonlinearity parameters measured with single-cycle signals agree well with the previous well-validated experimental results obtained using narrowband signals. Next, the PI-based NUT is used to assess the localized material degradation of a stainless steel plate subjected to high-cycle fatigue. The experimental results show that the profile of the measured nonlinearity parameters as a function of scan position is consistent with the intended distribution of localized fatigue damage, which demonstrates the potential feasibility of the proposed technique for evaluation of localized material degradation in plates.

In-situ fatigue monitoring procedure using nonlinear ultrasonic surface waves considering the nonlinear effects in the measurement system

Abstract Second harmonic generation using nonlinear ultrasonic waves have been shown to be an early indicator of possible fatigue damage in nuclear power plant components. This technique relies on measuring amplitudes, making it highly susceptible to variations in transducer coupling and instrumentation. This paper proposes an experimental procedure for in-situ surface wave nonlinear ultrasound measurements on specimen with permanently mounted transducers under high cycle fatigue loading without interrupting the experiment. It allows continuous monitoring and minimizes variation due to transducer coupling. Moreover, relations describing the effects of the measurement system nonlinearity including the effects of the material transfer function on the measured nonlinearity parameter are derived. An in-situ high cycle fatigue test was conducted using two 304 stainless steel specimens with two different excitation frequencies. A comprehensive analysis of the nonlinear sources, which result in variations in the measured nonlinearity parameters, was performed and the effects of the system nonlinearities are explained and identified. In both specimens, monotonic trend was observed in nonlinear parameter when the value of fundamental amplitude was not changing.

Nonlinear Effects in Three-minute Oscillations of the Solar Chromosphere. II. Measurement of Nonlinearity Parameters at Different Atmospheric Levels

Abstract Recent theoretical studies suggest that the nonlinearity of three-minute velocity oscillations at each atmospheric level can be quantified by the two independent parameters—the steepening parameter and the velocity amplitude parameter. For the first time, we measured these two parameters at different atmospheric levels by analyzing a set of spectral lines formed at different heights of sunspots ranging from the temperature minimum to the transition region. The spectral data were taken by the Fast Imaging Solar Spectrograph of the Goode Solar Telescope, and by the Interface Region Imaging Spectrograph. As a result, from the wavelet power spectra of the velocity oscillations at different heights, we clearly identified the growth of the second harmonic oscillations associated with the steepening of the velocity oscillation, indicating that higher-frequency oscillations of periods of 1.2 to 1.5 minutes originate from the nonlinearity of the three-minute oscillations in the upper chromosphere. We also found that the variation of the measured nonlinearity parameters is consistent with the theoretical expectation that the nonlinearity of the three-minute oscillations increases with height, and shock waves form in the upper chromosphere. There are, however, discrepancies as well between theory and observations, suggesting the need to improve both theory and the measurement technique.

Influence of surface roughness on the measurement of acoustic nonlinearity parameter of solids using contact piezoelectric transducers

The current article reports on the experimental study of the influence of surface roughness on the measurement of the acoustic nonlinearity parameter. The nonlinearity parameter was measured using contact piezoelectric transducers, which were calibrated using the reciprocity based technique. Aluminum and steel samples were chosen to study the influence of hardness of the sample on the measurement of the nonlinearity parameter. While, lower Ra value (average asperity height) aluminum samples were more susceptible to surface deformation and scratches from coupling the transducer to the sample, the same could not be observed for steel samples. Results demonstrate a large variation in nonlinearity parameter for aluminum (∼35%) compared to steel (∼2%) between two consecutive experiments, suggesting flattening of asperities after the first experiment. Experiments were also performed with 3 different setup configurations; (1) receiver and transmitter on rough sides, (2) receiver on smooth and transmitter on rough side and (3) receiver on rough and transmitter on smooth side. Results show that least variation in the measured nonlinearity parameter was observed when the receiver was placed on the smooth side, and a 10% variation was observed between the three setup configurations. Finally, a comparison of relative nonlinearity parameter calculated using current or voltage ratio and absolute nonlinearity parameter showed large discrepancies. Conclusions were drawn from the experimental observations.

Evaluation of Fire-Damaged Concrete: An Experimental Analysis based on Destructive and Nondestructive Methods

Fire damage to concrete causes contact-type defects that degrade its durability through impaired mechanical properties. Various nondestructive tests are used to evaluate defects induced by fire damage. Recently, nonlinear ultrasonic methods such as the nonlinear resonance vibration method and nonlinear modulation method have been introduced. These nonlinear methods are more sensitive to fire-induced contact-type defects than the linear ultrasonic method. This study involved an experimental analysis of the residual material properties of fire-damaged concrete, specifically, compressive strength, splitting tensile strength, and static elastic modulus. The residual material properties of 116 cylindrical concrete samples with various mix proportions and subjected to various heating temperatures were measured by a destructive method, and their nonlinearity parameters were measured by two nonlinear ultrasonic methods. Through regression analysis, correlated relationships that can facilitate the prediction of residual material properties of fire-damaged concrete using measured nonlinearity parameters were identified. In addition, the effect of fire damage on the mechanical strength of concrete was investigated by comparison with the relationships for undamaged concrete, and relationships for the evaluation of fire-damaged concrete were identified through regression analysis.

Evaluation of sensitization in stainless steel 304 and 304L using nonlinear Rayleigh waves

Austenitic stainless steels have a wide range of applications in the energy industry, but the corrosion resistance of these stainless steels can be reduced by sensitization, particularly in the heat affected zones in welds. Sensitization is the formation of chromium carbide precipitates along the grain boundaries, causing the formation of a zone of chromium depletion around the grain boundary. Since chromium is the primary alloying element that makes stainless steel corrosion resistant, this chromium depleted zone is susceptible to intergranular stress corrosion cracking (IGSCC). Sensitization occurs when a stainless steel is exposed to a high temperature for an extended time period, such as during welding. The objective of this research is to determine the sensitivity of nonlinear ultrasound to the presence of sensitization by using nonlinear Rayleigh waves to quantitatively track the sensitization of 304 and 304L stainless steels as a function of holding time at 675°C. The effect of the carbon content of the alloys (304 versus 304L) to the sensitization process and the measured nonlinearity parameter, β are investigated. Annealing of these specimens isolates the effect of just sensitization, removing the presence of cold work which can also affect the material nonlinearity. Complementary electrochemical potentiodynamic reactivation (EPR) measurements and microscopy are used to confirm the absence or presence of sensitization. The results show that the acoustic nonlinearity parameter is sensitive to the presence of chromium carbide precipitates in sensitized austenitic stainless steels.

Using nonlinear ultrasound to track microstructural changes due to thermal aging in modified 9%Cr ferritic martensitic steel

This research investigates second harmonic generation in Rayleigh surface waves propagating in 9%Cr ferritic martensitic steel. Previous experimental results show that nonlinear ultrasound is sensitive to certain microstructural changes in materials such as those due to thermal embrittlement and precipitation hardening. This research measures the ultrasonic nonlinearity parameter as an indicator of microstructural changes due to thermal aging in 9%Cr ferritic martensitic steel specimens. The specimens are isothermally aged for different holding periods to induce progressive changes in the microstructure and to obtain different levels of thermal damage. As thermal aging progresses, the existing dislocations are annihilated in the beginning and precipitates are formed; these microstructural evolutions lead to large changes in the measured nonlinearity parameter, β. Nonlinear ultrasonic experiments are conducted for each specimen using a wedge transducer for generation and an air-coupled transducer for detection of Rayleigh surface waves. The amplitudes of the first and second order harmonics are measured as a function of propagation distance, and these amplitudes are used to obtain the relative nonlinearity parameter at different aging stages. A possible scenario for the microstructural evolution during thermal aging is proposed based on the results from the nonlinear ultrasonic measurements, scanning electron microscopy (SEM), and Rockwell HRC hardness. These results indicate a clear trend that the measured nonlinearity parameter is sensitive to variations in dislocation and precipitate density, and thus can be useful in tracking microstructural changes in this material during thermal aging.

Acoustic nonlinearity parameters for transversely isotropic polycrystalline materials.

This article considers polycrystalline materials with macroscopic elastic anisotropy and the effect of the anisotropy on the quadratic nonlinearity parameter used to describe second harmonic generation in solids. The polycrystal is assumed to have transversely isotropic elastic symmetry, which leads to a directional dependence of the nonlinearity parameters. Additionally, the anisotropy leads to second harmonic generation from an input shear wave. Estimates of the longitudinal and shear wave nonlinearity parameters are given as a function of single-crystal elastic constants, macroscopic anisotropy constants, and propagation direction. An inverse model is presented that relates measured nonlinearity parameters to the macroscopic anisotropy constants. The estimates of the nonlinearity parameters can be used to approximate the damage-free or baseline nonlinearity parameter of structural components, which helps the effort toward absolute measures of material damage.

Quantitative evaluation of carbonation in concrete using nonlinear ultrasound

Abstract A new nonlinear ultrasonic technique for nondestructive evaluation of concrete components is developed and implemented to characterize the effects of carbonation on concrete. The physical principle of this method is the second harmonic generation (SHG) in propagating Rayleigh surface waves which are detected by a non-contact air-coupled transducer. The nonlinearity parameter, as an indicator of material properties, is experimentally obtained from measured Rayleigh wave signals and is used to quantitatively evaluate the progress of carbonation under accelerated conditions. The experimental results show that there is a significant decrease in the measured nonlinearity parameter, most likely originated from the deposit of the carbonation product, CaCO3, in pre-existing voids and microcracks. The sensitivity of the nonlinearity parameter is also verified by comparing with the measured Rayleigh wave velocity. The results in this paper demonstrate that the SHG technique using Rayleigh surface waves can be used to monitor carbonation in concrete.

Air-coupled detection of nonlinear Rayleigh surface waves to assess material nonlinearity

This research presents a new technique for nonlinear Rayleigh surface wave measurements that uses a non-contact, air-coupled ultrasonic transducer; this receiver is less dependent on surface conditions than laser-based detection, and is much more accurate and efficient than detection with a contact wedge transducer. A viable experimental setup is presented that enables the robust, non-contact measurement of nonlinear Rayleigh surface waves over a range of propagation distances. The relative nonlinearity parameter is obtained as the slope of the normalized second harmonic amplitudes plotted versus propagation distance. This experimental setup is then used to assess the relative nonlinearity parameters of two aluminum alloy specimens (Al 2024-T351 and Al 7075-T651). These results demonstrate the effectiveness of the proposed technique – the average standard deviation of the normalized second harmonic amplitudes, measured at locations along the propagation path, is below 2%. Experimental validation is provided by a comparison of the ratio of the measured nonlinearity parameters of these specimens with ratios from the absolute nonlinearity parameters for the same materials measured by capacitive detection of nonlinear longitudinal waves.

Characterization of thermally damaged concrete using a nonlinear ultrasonic method

Thermal damage in concrete usually induces contact-type defects, which result in degradation of the concrete's performance. This paper attempts to visualize the thermal damage in a multiscale, and characterizes the thermally damaged concrete using a nonlinear ultrasonic method. An impact-modulation method is used to obtain nonlinearity parameters, as a quantitative measure of contact-type defects, and shows better sensitivity than phase velocity variation as a linear ultrasonic method for thermally damaged concrete. The measured nonlinearity parameter is compared with the permeable pores, which reflect the occurrence of opening and pores in thermally damaged concrete. Degradation of concrete strength due to thermal damage is also assessed via the measurement.

THE NONLINEAR BIASING OF THE zCOSMOS GALAXIES UP TOz∼ 1 FROM THE 10k SAMPLE

We use the overdensity field reconstructed in the volume of the COSMOS area to study the nonlinear biasing of the zCOSMOS galaxies. The galaxy overdensity field is reconstructed using the current sample of ~8500 accurate zCOSMOS redshifts at I(AB)<22.5 out to z~1 on scales R from 8 to 12 Mpc/h. By comparing the probability distribution function (PDF) of galaxy density contrast delta_g to the lognormal approximation of the PDF of the mass density contrast delta, we obtain the mean biasing function b(delta,z,R) between the galaxy and matter overdensity field and its second moments b(hat) and b(tilde) up to z~1. Over the redshift interval 0.4<z<1 the conditional mean function <delta_g|delta> = b(delta,z,R) delta is of the following characteristic shape. The function vanishes in the most underdense regions and then sharply rises in a nonlinear way towards the mean densities. <delta_g|delta> is almost a linear tracer of the matter in the overdense regions, up to the most overdense regions in which it is nonlinear again and the local effective slope of <delta_g|delta> vs. delta is smaller than unity. The <delta_g|delta> function is evolving only slightly over the redshift interval 0.4<z<1. The linear biasing parameter increases from b(hat)=1.24+/-0.11 at z=0.4 to b(hat)=1.64+/-0.15 at z=1 for the M_B<-20-z sample of galaxies. b(hat) does not show any dependence on the smoothing scale from 8 to 12 Mpc/h, but increases with luminosity. The measured nonlinearity parameter b(tilde)/b(hat) is of the order of a few percent (but it can be consistent with 0) and it does not change with redshift, the smoothing scale or the luminosity. By matching the linear bias of galaxies to the halo bias, we infer that the M_B<-20-z galaxies reside in dark matter haloes with a characteristic mass of about 3-6 x 10^12 Msol, depending on the halo bias fit.

Theoretical evaluation of the temperature dependence of third order elastic constants and ultrasonic attenuation in NaCl

Abstract This paper presents a comprehensive calculation of ultrasonic attenuation in NaCl in the temperature range 80–300 K using the temperature dependent third order elastic constants (TOEC). A method is suggested here to evaluate the temperature dependence of the complete set of TOEC using the measured nonlinearity parameters in combination with the Varshney model for elasticity of alkali halides. Our calculations reproduce the measured combinations of TOEC reasonably well. This set is used to compute the temperature dependence of ultrasonic attenuation for longitudinal and shear waves along the [100] direction and for a longitudinal wave along the [111] direction. The orientation dependence of attenuation is also computed using this set for the [100], [110] and [111] directions. The calculation of attenuation is performed using both Mason's limited mode approach as well as by taking into account the interaction of the sound wave with a much wider spectrum of thermal phonon modes and incorporating the refinements suggested by Merkulov et al . regarding the dependence of Mason's integral on the cutoff frequency supported by the lattice. The results of our refined calculations show better agreement with the experiment than those obtained using Mason's scheme in most cases.

Prevention of alcohol-impaired driving : R. Hingson. Alcohol Health & Research World, 17(1), 28–34.

Thermal damage in concrete usually induces contact-type defects, which result in degradation of the concrete's performance. This paper attempts to visualize the thermal damage in a multiscale, and characterizes the thermally damaged concrete using a nonlinear ultrasonic method. An impact-modulation method is used to obtain nonlinearity parameters, as a quantitative measure of contact-type defects, and shows better sensitivity than phase velocity variation as a linear ultrasonic method for thermally damaged concrete. The measured nonlinearity parameter is compared with the permeable pores, which reflect the occurrence of opening and pores in thermally damaged concrete. Degradation of concrete strength due to thermal damage is also assessed via the measurement.

Temperature variation of some combinations of third-order elastic constants of silicon between 300 and 3 °K

The ultrasonic harmonic generation technique has been used to determine the nonlinearity parameters of silicon between room temperature and 3 °K. By measuring the amplitude of the second harmonic of an initially sinusoidal longitudinal ultrasonic wave propagating along the three principal directions, the temperature dependence of three linear combinations of third-order elastic (TOE) constants of silicon have been studied. Between room temperature and 77 °K, the magnitude of the TOE constants does not vary much as a function of temperature. Between 77 and 3 °K, C111 changes by 3.5%, C112+4C166 changes by 11.7%, and C123+6C144+8C456 changes by −207%. All these combinations are negative at room temperature as well as at low temperatures except C123+6C144+8C456 which is positive below 8 °K. Room-temperature values of the strain generalized Grüneisen parameters of silicon have been calculated from measured nonlinearity parameters and are compared with existing values. Complete sets of third-order elastic constants at 298, 77, and 4 °K have been calculated by combining our nonlinearity parameters with pressure derivatives of elastic constants measured by Beattie and Schirber [Phys. Rev. B 1, 1548 (1970)].