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One of the consequences of the 475 °C embrittlement of duplex stainless steels is the reduction of the resistance to localized corrosion. Therefore, the detection of this type of embrittlement before the material exhibits significant loss in toughness, and corrosion resistance is important to ensure the structural integrity of critical components under corrosion threats. In this research, conductivity measurements are performed using the alternating current potential drop (ACPD) technique with using a portable four-point probe as a nondestructive evaluation (NDE) method for detecting the embrittlement in a 2507 (UNS S32750) super duplex stainless steel (SDSS) aged at 475 °C from as-received condition to 300 h. The electric conductivity results were compared against two electrochemical tests namely double loop electrochemical potentiokinetic reactivation (DL-EPR) and critical pitting temperature (CPT). Mechanical tests and the microstructure characterized using scanning electron microscopy (SEM) imaging are conducted to track the progress of embrittlement. It is shown that the electric conductivity correlates with the changes in impact energy, microhardness, and CPT corrosion tests result demonstrating the feasibility of the four-point probe as a possible field-deployable method for evaluating the 475 °C embrittlement of 2507 SDSS.

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.

This study employs nonlinear ultrasonic techniques to track microstructural changes in additively manufactured metals. The second harmonic generation technique based on the transmission of Rayleigh surface waves is used to measure the acoustic nonlinearity parameter, β. Stainless steel specimens are made through three procedures: traditional wrought manufacturing, laser-powder bed fusion, and laser engineered net shaping. The β parameter is measured through successive steps of an annealing heat treatment intended to decrease dislocation density. Dislocation density is known to be sensitive to manufacturing variables. In agreement with fundamental material models for the dislocation-acoustic nonlinearity relationship in the second harmonic generation, β drops in each specimen throughout the heat treatment before recrystallization. Geometrically necessary dislocations (GNDs) are measured from electron back-scatter diffraction as a quantitative indicator of dislocations; average GND density and β are found to have a statistical correlation coefficient of 0.852 showing the sensitivity of β to dislocations in additively manufactured metals. Moreover, β shows an excellent correlation with hardness, which is a measure of the macroscopic effect of dislocations.

This paper proposes a low-cost and efficient piezoelectric tuned mass damper (Piezo-TMD) for structural vibration reduction and energy harvesting. The Piezo-TMD consists of not only a proof mass, piezoelectric materials deforming in the d33 mode, and an electrical resistance, but also a spring and an inductor which enable the mechanical frequency and electrical frequency of the Piezo-TMD to be tuned to the structural resonance frequency. The equations of motion of a structure with the Piezo-TMD are derived, and an optimal design procedure for the Piezo-TMD is proposed to achieve a simultaneous maximum vibration reduction and energy harvesting. The performance of the Piezo-TMD is compared with that of a conventional optimal TMD installed in a footbridge under a pedestrian loading. The simulation results show that the Piezo-TMD performs better than the optimal conventional TMD in terms of vibration reduction while efficiently converting the absorbed mechanical energy to electricity with a high energy harvesting ratio. The innovative development of simultaneously tuning the mechanical and electrical systems leads to a much lower number of PZT stacks (saving 88% of piezoelectric materials in an illustrated case). The parametric study shows that the Piezo-TMD achieves the best performance when the optimal values for the spring stiffness, resistance, inductance, and the number of piezoelectric stacks are adopted from the proposed optimal design. If the selected spring stiffness and inductance are uncertain in a range between 0.94-1.07 times the optimal values, the vibration reduction performance of the Piezo-TMD remains similar, and the energy harvesting performance reduces less than 5%, as compared to the optimal performance. The effect of the number of piezoelectric stacks was also investigated. An insufficient number of piezoelectric stacks reduces the Piezo-TMD performance, and an excessive stack number does not improve the Piezo-TMD performance but increases the Piezo-TMD cost. Finally, the proposed Piezo-TMD employs inductance to significantly reduce the PZT stack number, thereby significantly reducing the cost of Piezo-TMDs.

This research demonstrates the feasibility of using a non-collinear wave mixing technique to image internal microscale damage throughout the interior volume of a relatively large (28 cm thick) concrete component. By exploiting the underlying mechanics of nonlinear wave mixing, it is possible to mix two incident waves with frequencies low enough to propagate without being scattered by the inherently heterogenous, concrete microstructure, while still being sensitive to damage features with length scales well below these incident wavelengths. For this study, scanning and imaging is accomplished by manually adjusting the locations of the two incident waves, while a knowledge of the wave speeds in concrete plus synchronization identifies the location of the mixing zone—the specific volume of concrete being imaged. The viability of the proposed technique is demonstrated by examining a concrete prism specimen with known, embedded internal microscale damage.

Nonlinear Rayleigh surface waves are used to monitor the damage state due to alkali-silica reaction (ASR) in full-scale reinforced concrete block specimens created as part of a full-scale testing program for concrete nuclear containment structures. The measurement technique uses a wedge/transducer source to generate and a non-contact, air-coupled receiver to detect nonlinear Rayleigh surface waves to obtain the acoustic nonlinearity parameters for three different reinforced block concrete specimens – a confined and an unconfined ASR specimen, plus a control specimen – at three different time intervals. These results further validate the utility of nonlinear Rayleigh waves to quantify the progress of microscale damage due to ASR in full-scale, concrete structures.

The objective of this research is to use nonlinear resonance ultrasound spectroscopy (NRUS) to evaluate the sensitivity of the nonclassical hysteretic nonlinearity parameter, α to microscopic material damage in metallic specimens. The proposed NRUS procedure uses both a noncontact source and receiver – an air-coupled piezoelectric transducer source and a laser vibrometer receiver – to excite and detect the axial motion of a slender rod. This fully noncontact configuration avoids mechanical contact which can adversely influence the measurements. This NRUS procedure measures α f and α Q by calculating the amount of the shift of the resonance frequency and the change of quality factor (Q) as a function of increasing excitation amplitudes. The sensitivity of this NRUS measured α parameters to small changes in microstructure is demonstrated on a series of thermally aged 17-4 PH stainless steel samples. These hysteretic nonlinearity ( α f and α Q ) results are then compared to (quadratic) acoustic nonlinearity parameter (β) values previously measured on these same 17-4 PH samples to demonstrate the sensitivity of the hysteretic nonlinearity parameters to changes in microstructure due to precipitate formation.

This research explores five available signal processing methods: discrete Fourier transform (DFT); least squares method; original Prony method; least squares (LS) Prony method; and known poles (KP) Prony method, to accurately analyze the harmonic content of a tone-burst signal obtained from the second harmonic generation (SHG) measurement. Accurately obtaining the correct frequency content is especially important when the number of cycles is limited by the thickness or high attenuation of a specimen. Results from both numerically generated synthetic signals and experimental data from a specimen demonstrate that the least squares and KP Prony methods provide the most consistent and accurate results for tone-burst signals with low number of cycles. The conventional DFT provides accurate harmonic amplitudes only when the effective number of cycles (neff) is eight or higher. The least squares and KP Prony methods are then applied to a set of thin binary Fe-1.0% Cu alloy specimens where the changes in the nonlinearity parameter, β, as a function of heat treatment time is determined. The β parameters processed with these two methods produce trends that make better physical sense than processing with the original Prony method.

With the increase of aggregate quarrying to meet the growing need for concrete construction comes a risk associated with new aggregate sources, which may not have uniform compositions and contain potentially harmful substances, such as sulfate and sulfide. To provide insights into the impact of sulfate- and sulfide-bearing sand on susceptibility to delayed ettringite formation (DEF), this study measures the evolution of expansion, acoustic nonlinearity (representing microscale damage), and dynamic elastic modulus of mortars prepared with varying cement compositions and exposed to an early-age high-temperature curing cycle. Samples containing sulfate- and sulfide-bearing sand show substantially higher initial levels of damage, with expansion starting at earlier ages than control samples. Damage in mortars using this sand can be attributed to accelerated decomposition of alkali-feldspar, microcracking due to relative thermal deformation between phases, early release of alkali that increases the amount of sulfate in the pore solution, and release of sulfate ions from aggregates.

The structural integrity of components that operate at elevated temperatures can be compromised by the precipitation of second phases during long-term service. In industry, the 475 °C embrittlement phenomenon due to spinodal decomposition of the ferrite phase that results in the formation of Cr-rich α′ precipitates at a relatively low temperature has been a concern because of its adverse effects on ferritic, duplex and super duplex stainless steels; this precipitation causes a rapid decrease in the impact and corrosion resistance of these steels. Some of the precipitates have micro or nanometer dimensions, which makes them difficult to detect with conventional ultrasonic nondestructive evaluation (NDE) methods. In contrast to the conventional linear ultrasonic NDE, nonlinear ultrasound offers a unique advantage of high sensitivity to microstructural changes such as those due to the precipitation of second phases, fatigue damage, plastic deformation, and thermal damage in metallic alloys. In this research, ultrasonic measurements were conducted to determine the nonlinearity parameter (β) of thermally embrittled 2507 SDSS specimens. The β parameters of these specimens were measured by exploiting two different nonlinear effects: the acoustoelastic effect and second harmonic generation in Rayleigh waves. Experimental results indicate that nonlinear parameters obtained from these independent experiments are consistent and sensitive to the 475 °C embrittlement process.

Austenitic stainless steels are subject to the precipitation of chromium carbides (M23C6) during exposure to high temperatures, causing these alloys to be susceptible to intergranular corrosion due to chromium depletion along grain boundaries. The acoustic nonlinearity parameter, β, shows sensitivity to the formation of carbides in these alloys. The Thermo-Calc TC-PRISMA module was used to model the nucleation and growth of grain boundary M23C6 carbides. The model was verified with scanning transmission electron microscopy analysis that allowed measurements of the grain boundary precipitates. The paper introduces a reduced-order model of the acoustic nonlinearity based on the formation of misfit dislocations at the interface of the grain boundary precipitate and matrix to explain the change in β during isothermal aging. A direct relationship between the radius of the M23C6 grain boundary carbides and β was observed and verified with nonlinear ultrasound measurements on 304L and 316L stainless steels.

Our work employs nonlinear ultrasonic techniques to track microstructural changes in additively manufactured metals. One study is based on the use of the second harmonic generation technique with Rayleigh surface waves used to measure the acoustic nonlinearity parameter, β. Stainless steel specimens made through laser-powder bed fusion and laser engineered net shaping were compared with traditional wrought manufactured specimens. The β parameter is measured through successive steps of an annealing heat treatment intended to decrease dislocation density. In agreement with fundamental material models for the dislocation-acoustic nonlinearity relationship in the second harmonic generation, β drops for each specimen throughout the heat treatment before recrystallization. Geometrically necessary dislocations (GNDs) are measured from electron back-scatter diffraction as a quantitative indicator of dislocations; average GND density and β are found to have a statistical correlation coefficient of 0.852 showing the sensitivity of β to dislocations in additively manufactured metals. Moreover, β shows an excellent correlation with hardness, which is a measure of the macroscopic effect of dislocations. Ongoing work continues trying to characterize additively manufactured stainless steels with nonlinear ultrasound through non-collinear mixing.

Two kinds of thermally aged Fe-Cu alloys with different Cu proportions 0.05% and 0.45% were prepared and their magnetic properties were investigated to apply magnetic nondestructive testing techniques for the assessment of irradiation embrittlement of materials. Initially, the alloy is 10% cold rolled and then isothermally aged at 500 °C and 400 °C with different aging time up to 1000 h in order to create Cu-precipitates in the Fe metal matrix. The hysteresis loop (HL), Barkhausen noise (BN) and Magnetic Adaptive Testing (MAT) parameter were measured for magnetic properties studies and mechanical properties were investigated by Vickers hardness. The HL, BN were decreased and the MAT parameter was increased by thermal aging. The changes of these parameters were explained by copper rich precipitations (CRPs) formation, interaction with domain walls and dislocation movement pinned by CRPs. It was confirmed by TEM and EDX analysis.

This research explores the sensitivity of nonlinear ultrasound (NLU) to the changes in microstructure of heat treated Fe-1.0 at.% Cu binary alloy. Results from experimental measurements and a theoretical model each show that the acoustic nonlinearity parameter, β increases with increasing Cu-precipitate radius. The iron-copper material investigated in this research serves as a surrogate material to simulate the evolution of radiation damage as a result of copper nanocluster precipitation that occurs in reactor pressure vessels (RPV) of light water nuclear power reactors. With RPVs seeing more neutron cycles than originally anticipated, it is imperative to develop nondestructive evaluation (NDE) techniques capable of evaluating the integrity of these structures.

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.

A nonlinear acoustic approach for the detection and quantification of damage in mortars affected by delayed ettringite formation (DEF) is used to provide insights into the degradation mechanism at the microscale and its correlation with bulk expansion. The nonlinear acoustic technique, Nonlinear Impact Resonance Acoustic Spectroscopy (NIRAS) successfully differentiates among mortars experiencing various amounts of expansion and microstructurally-evident distress due to DEF. Results indicate that mortars are damaged both during the early-age high-temperature curing and subsequent 23 °C-limewater curing. However, the time of initiation of expansion occurs earlier for samples showing higher damage level (as measured by average nonlinearity parameter) at the end of high-temperature curing. During the exposure period, the ratio of absolute maximum to the initial average nonlinearity parameter of DEF-affected mortars varies from 3 to 30, indicating that the DEF damage can increase more than an order of magnitude greater than that experienced during the high-temperature curing.

This paper theoretically analyzes the nonlinear torsional vibration of a granular material specimen in the resonant column test (RCT). The RCT is a material testing method that has been well established in geotechnical engineering. The test provides some important dynamic properties of granular materials including the shear wave speed, effective dynamic shear modulus and damping capacity. Both the elastic modulus and damping capacity show a strong dependence on the amplitude of excitation, which is the essential behavior of materials with hysteretic nonlinearity. The analysis, starting with a constitutive relationship that describes the hysteretic nonlinear behavior of granular materials, is performed specifically on the forced torsional vibration of a circular bar with a fixed and inertia-loaded boundary condition as a model for the specimen in the RCT. Self-interaction of a single resonance mode is assumed in the perturbation analysis to obtain an approximate solution for near-resonance response. The theoretical results predict linear dependences of the resonance frequency and damping ratio on the shear strain; these are in agreement with the existing experimental observations. Notable is that the present model describes the hysteretic nonlinear behaviors with a single parameter, i.e., the hysteresis nonlinearity parameter in the constitutive relationship. The derived equations are applied to a jointed gneiss specimen where how the hysteresis nonlinearity parameter is determined from RCT data is demonstrated.

Because of their ability to probe the material properties at different penetration depths, surface acoustic waves (SAW) are considered for nondestructively characterizing the near-surface properties of a component that has been previously modified. During long-term service, microstructural changes are unavoidable, which in many cases promote the formation of deleterious phases in a material that operates at elevated temperatures impacting the mechanical response of the component. This research investigates the behavior of the nonlinearity parameter (βR) measured using the second harmonic generation of Rayleigh surface waves propagating in the free surface of aged Inconel 718 (IN 718) superalloy specimens with and without laser shock processing (LSP). Also, microstructural and mechanical characterizations were conducted to track first the sole effect of aging time, and secondly, the combined effects of aging + LSP on microhardness, residual stress, and tensile properties of the samples. Our experimental results obtained from aged samples with and without LSP processing indicate that a superposition of different effects of aging and surface treatment in the material contribute to the βR parameter, including microstructure, compressive residual stress, and cold work effects. The experimental results also indicate that it is feasible to observe a perceivable change in the βR parameter of the SAW when the specimen is heat-treated at different temperatures, which has no perceivable effect on the surface roughness. The changes on the βR parameter in aged samples are due to the gradual precipitation of γ′ and γ" hardening phases and the further precipitation of δ-phase, and in aged samples with LSP, electron backscatter diffraction (EBSD) analysis showed that changes are due to microstructural, near-surface residual stresses and texture effects. These results indicate a distinctive trend that shows that the measured βR can be useful in tracking microstructural changes in this material during high-temperature operations.

Nonlinear ultrasound (NLU) has been shown to be sensitive to microstructural features including precipitates and dislocations. The heat-affected zone (HAZ) of welded austenitic stainless steels can be susceptible to intergranular stress corrosion cracking (IGSCC). This research uses NLU to evaluate the microstructure of the HAZ with an emphasis on dislocations, precipitates, grain size/morphology and sensitization, which is the formation of chromium carbide precipitates at the grain boundaries. The results show that there is a large increase in the measured acoustic nonlinearity parameter in the vicinity of the HAZ, which can be used to monitor changes in microstructure such as sensitization.

This research develops a nonlinear ultrasonic (NLU) technique, second harmonic generation (SHG), to monitor the time-dependent microstructural evolution and shrinkage in concrete over a period from 28 to 55 days of age. Drying shrinkage by moisture migration from concrete to its environment causes stress and microcracking and can lead to larger crack formation, which compromises performance. Here, the process of drying is monitored by the SHG method using nonlinear Rayleigh surface waves to obtain the acoustic nonlinearity parameter. The results show large changes in the measured acoustic nonlinearity parameter which is attributed to damage generated during drying shrinkage. Finally, the measured acoustic nonlinearity parameter is used to compare the microstructural condition in hardened concrete as affected by shrinkage mitigation (through the use of shrinkage-reducing admixture) and crack filling (or self-healing) by carbonation.

This paper investigates thermal damage in sandstone using linear and nonlinear ultrasonic methods. The nonlinear ultrasonic method is based on the higher harmonic generation in non-resonant standing waves; the nonlinearity parameter is defined as the ratio of the second harmonic amplitude to the square of the fundamental amplitude. This parameter is highly sensitive to the damage evolution/microstructural changes in sandstone. The longitudinal ultrasonic velocity and dynamic elastic modulus are also measured as representative linear ultrasonic parameters. Both the linear and nonlinear parameters exhibit a peculiar reverse trend in the temperature range 100–150 ℃. This effect is thought to be due to the filling of pre-existing microcracks by the clay component in sandstone, which swells and migrates with the temperature elevation. The nonlinearity parameter shows an accelerated increase at temperatures higher than 200 ℃. Variations of the wave velocity and elastic modulus are up to 49%, while the nonlinearity parameter increases as much as 19 times during the thermal process. The nonlinearity parameter is more sensitive to the microstructural changes in sandstone (microcracking and clay swell and migration) due to thermal loading than the linear parameters, and thus the present nonlinear ultrasonic technique can serve as a promising tool for characterizing damage progress in rock materials.

This paper presents an analytical method for designing a spatial filter that processes the data from an array of two-dimensional guided wave transducers. An inverse problem is defined where the spatial filter coefficients are determined in such a way that a prescribed beam shape, i.e., a desired array output is best approximated in the least-squares sense. Taking advantage of the 2 π -periodicity of the generated wave field, Fourier-series representation is used to derive closed-form expressions for the constituting matrix elements. Special cases in which the desired array output is an ideal delta function and a gate function are considered in a more explicit way. Numerical simulations are performed to examine the performance of the filters designed by the proposed method. It is shown that the proposed filters can significantly improve the beam quality in general. Most notable is that the proposed method does not compromise between the main lobe width and the sidelobe levels; i.e. a narrow main lobe and low sidelobes are simultaneously achieved. It is also shown that the proposed filter can compensate the effects of nonuniform directivity and sensitivity of array elements by explicitly taking these into account in the formulation. From an example of detecting two separate targets, how much the angular resolution can be improved as compared to the conventional delay-and-sum filter is quantitatively illustrated. Lamb wave based imaging of localized defects in an elastic plate using a circular array is also presented as an example of practical applications.

A multi-physics approach for the assessment of alkali silica reaction (ASR) generates new foundational understanding of the nature of the reaction, which ultimately can be used for the development of techniques and tools for the assessment and monitoring of existing concrete structures. The approach combines two nondestructive evaluation techniques: (1) nonlinear acoustic measurements, which are sensitive to microcracking; and (2) microwave materials characterization measurements, which are sensitive to moisture including the transition of water from its free state in the pore solution to a bound state within accumulating ASR gel. Comparison with assessment of expansion and damage rating index obtained from petrographic analysis on standard mortar bars shows a correlation between all of the measures. Specifically, a strong correlation is found between the cumulative average nonlinearity parameter and expansion, and there is also agreement of the microwave measurements with the damage rating index.

This research develops a nondestructive evaluation (NDE) technique to obtain images of two types of defects, delamination and debonding, in a thick laminate composite plate as a laboratory material system for wind turbine blades. The technique uses focused shear waves which are generated and detected by a set of noncontact, air-coupled ultrasonic transducers. The noncontact nature of the air-coupled method facilitates rapid scanning/inspection of large composite structures. Ray-tracing simulations are performed which visualize the focusing behavior of the focused shear waves in the specimen, from which the experimental parameters are determined. The proposed focused shear wave technique is compared with a Lamb-wave based technique, showing that the present technique is more appropriate for direct imaging of these defects. The obtained images of delamination and debonding defects agree well with the estimated defect locations and dimensions. This demonstrates the feasibility of further developing the present technique for specific field applications in wind turbine blades.

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.

This research combines linear and nonlinear ultrasound to examine the microstructural and microchemical changes in five large, highly irradiated cold-worked ANSI 304 stainless steel coin specimens cut from two hexagonal cross section blocks with radiation damage levels ranging from ~0.4 to ~33 dpa following irradiation in the EBR-II fast reactor. Both linear (velocity) and nonlinear ultrasonic (β) measurements were conducted in a hot cell using an automated fixture device specially designed to hold the sensor for repeatable measurements in an environment where direct human access is limited, demonstrating their potential to more fully investigate the complex defect ensemble introduced by irradiation. The measurements were performed at the Westinghouse Churchill site hot cell facility. The linear measurements agree very well with previous measurements employing a different sensor application technique. The ultrasonic nonlinearity parameters measured after irradiation increased by more than 100% from the unirradiated state and show a level of random variation below 4.7%. These ultrasonic nonlinearity parameters also show a spatial dependence on measurement location across each of the specimens in agreement with the spatial inhomogeneity of microstructure and microchemical distribution previously observed in adjacent, nominally identical specimens using transmission electron microscopy (TEM) and atom probe tomography (APT). It is proposed that the inhomogeneous distribution of microstructural and microchemical features including Frank loops, and both intragranular and grain boundary precipitates, as well as their different nonlinearity generation efficiencies are responsible for the spatial dependence of the measured ultrasonic nonlinearity parameters. The major and dominant component of the microstructure of these specimens at 20–30 dpa is vacancy agglomerations called voids, previously observed by microscopy and measurable using either linear ultrasonic velocity or linear attenuation, but which are not readily visible using nonlinear ultrasound. Components such as Frank loops, which are one of the other major microstructural components, do not contribute significantly to changing the linear ultrasonic velocity. Using this combination of linear and nonlinear measurements allows for the examination of microstructural/microchemical components whose linear ultrasonic interactions are overshadowed by voids, especially Frank loops and various radiation-induced precipitates. The changes in ultrasonic nonlinearity parameters in these specimens are thought to arise from two major sources. The smaller contribution is due to carbide pinning of dislocations in the grain boundary walls and the few line dislocations present in the grain interior. The largest contribution appears to come from segregation of Ni and Si to the perimeter of the very high density of Frank loops, leading to the formation of Ni3Si precipitates which are thought to be very efficient at pinning the Frank loops. These results on two hex blocks provide an ideal, though not completely realistic, test case to demonstrate the sensitivity of nonlinear ultrasound to two different microstructure sources.

The goal of inspection and continuous health monitoring of engineering structures is to detect defects particularly during their early stages of development. In this work, a method using an optimization scheme for localization of a target using ultrasonic guided waves in a thin plate and data sampled from a beamforming is studied. The proposed optimization scheme finds the target by using a search algorithm based on random and chaotic walk search to reduce the number of evaluation points within the search space. The data used for the scheme is extracted from the using only a reduced number of evaluation points from the energy reconstruction map of a delay and sum beamforming algorithm. The proposed approach is numerically studied and implemented experimentally for discontinuity detection in a plate using guided Lamb waves. The combined experimental and numerical analysis indicates that the searching algorithm was able to find an acoustic target generated by a discontinuity in a plate even when the signals were contaminated by noise.

This research uses nonlinear Rayleigh waves to examine different levels of plastic strain in samples made from legacy X52 pipeline material. Here the plastic strain is used as a surrogate for the damage associated with a pipeline dent. Tension specimens are subjected to a static, mechanical load. Nonlinear Rayleigh waves are used to measure the relative acoustic nonlinearity parameter, β ′ in these specimens as a function of the accumulated plastic strain in the specimens. These results are then compared to previous β ′ measurements made in A36 steel specimens, and a scenario based on the formation of dislocations is proposed to explain the increase in β ′ observed. These measurements demonstrate the sensitivity of β ′ to the microstructural changes caused by plastic deformation in X52 pipeline steel.

It is well known that microcracks generate strong higher harmonics in propagating monochromatic waves. There is a large amount of literature on modeling this phenomenon, but most of these existing papers only describe one specific mechanism. For example, Zhao et al. [1] assumes that the crack faces are either open under tension or closed under compression, and in the latter case they may slide against each other. On the other hand, the Nazarov and Sutin [2] model assumes microcracks as an elastic contact of two rough surfaces, which are never completely separated by an external load. All these mechanisms depend on the level of excitation. In this research, a micromechanical model for the acoustic nonlinearity generation of microcracks is developed by combining the bilinear stiffness model and the rough surface contact model to describe the excitation-dependent nonlinear behavior of distributed microcracks. It is shown that the first and second harmonic amplitudes have the relationship: A2~A1n, with n dependent on the amplitude of excitation, and 2 ≥ n ≥ 1 for non-adhesive crack surfaces. Nanostructured ferritic alloys (NFAs) [3] are considered as an example. These materials exhibit outstanding high-temperature properties, irradiation tolerance and thermal stability, making them a leading candidate for advanced nuclear fission and fusion applications. One characteristic property of mechanically processed NFAs is their layer-like structure, with a large number of microcracks aligned in a specific direction. Nonlinear ultrasound measurements (acoustic nonlinearity, β) with longitudinal waves are used to characterize this material. The results show that these measurement techniques are sensitive to the orientation of the cracks. The model developed in this research is then used to interpret these experimental measurements and used to characterize the microcracks in a NFA specimen.

This research applies nonlinear ultrasonic techniques for the quantitative characterization of additively manufactured materials. The characterization focuses on identifying the dislocation density produced during the additive constructive process in order to increase confidence on a part’s performance and the success of the manufacturing process. Second harmonic generation techniques based on the transmission of Rayleigh surface waves are used to measure the ultrasonic nonlinearity parameter, β, which has proven a quantitative indicator of dislocations but has not been fully proven in additive manufactured materials. 316L and 304L stainless steel parts made from Powder Bed Fusion and Laser Engineered Net Shaping are compared between AM techniques and with wrought manufactured counterparts. β is consistently higher for additive manufactured parts. An annealing heat treatment is applied to each specimen to reduce dislocation density. β expectedly decreases by annealing in all specimens. A linear ultrasonic measurement is made to evaluate the effectiveness of using nonlinear techniques. The ultrasonic attenuation is higher for additive manufactured parts and increases at higher frequencies.

This chapter considers both the theoretical aspects of the nonlinear ultrasonic phenomena in elastic solids and their applications to materials characterization; it has been demonstrated that nonlinear ultrasound (NLU) measurements can provide quantitative inputs to determine the material state and measure damage in engineering components. It has recently been shown that NLU can be used to develop the framework for accurate life prediction of components under mechanical and thermo-mechanical loading. These NLU measurements are done at the material level, before the formation of macroscopic damage. The traditional NDE of damage of a material subject to, for example, fatigue starts from the time when a small crack initiates because there is no measurable macroscopic change in the material prior to the crack initiation. In most metallic materials, however, cracks of a measurable size appear late in the fatigue life (typically after 80%), while the material toughness and strength decreases gradually due to the microplasticity (dislocations) and associated change in the material’s microstructure. Starting from mechanics fundamentals, we first develop the theoretical equations of wave motion in an elastic solid with quadratic nonlinearity, covering bulk, surface, and guided waves. Various nonlinear acoustic phenomena occurring in the infinite and bounded elastic solids are described in a consistent mathematical framework. The next section considers measurement techniques for NLU, including examples of the assessment of fatigue and thermal damage in metals with NLU.

Non Destructive Testing (NDT) methods that are capable of detecting the wall thinning and defects through insulation and cladding sheets are necessary. In this study we developed a Pulsed Eddy Current (PEC) system to detect wall thinning of ferro magnetic steel pipes covered with 95 ㎜ thick fiber glass thermal insulator and shielded with aluminum plate of thickness 0.4 ㎜. In order to confirm the thickness change due to wall thinning, two different sensors, a hall sensor and a search coil sensor were used as a detecting element. In both the cases, the experimental data indicates a considerable change in the detected pulse corresponding to the change in sample thickness. The thickness of the tube was made to change such as 2.5 ㎜, 5 ㎜ and 8 ㎜ from the inner surface to simulate wall thinning. Fast Fourier Transform (FFT) was calculated using window approach and the results were summarized which shows a clear identification of thickness change in the test specimen by comparing the magnitude spectra.

Recent years have seen growing adoption of wireless structural sensor nodes that can significantly reduce the cost and installation effort of a structural health monitoring system. While previous wireless sensor development has mainly focused upon dynamic and vibration measurements at lower frequency domains, in this study, a new wireless ultrasonic sensing node capable of megahertz excitation and sampling is proposed. In addition to presenting the design of the wireless ultrasonic sensing node, experimental notch test and fatigue test of a dog-bone specimen are described in this article. The experimental results demonstrate that the ultrasonic characteristics of surface cracks can be identified in both scenarios with the proposed wireless sensor node. Furthermore, a signal processing procedure is proposed to obtain an accurate estimation of the ultrasonic signal amplitude, which can be a key indicator for crack identification. The procedure involves signal reconstruction with the cardinal sine function and envelope detection using discrete Hilbert transform.

In the area of robotic sensing, determination of parameters of a solid object, such as contact area, pressure distribution, or deformation, is an important step for the sensing and manipulation of an object with an unknown mechanical behavior. In this paper, a soft contact probe based on ultrasound is developed using a commercial elastomer. The emphasis is placed on the study of the contact mechanics of the probe. The probe is equipped with an ultrasonic sensor and then implemented in a 3 degrees of freedom manipulator robotic system. The correlation between the normal contact force and the ultrasonic signal reflected from the interface between the soft probe and the object is precisely studied. Experimental results are presented for loading and unloading cycles of the soft contact probe against a flat surface. Tests are performed on aluminum, elastomer, and plasticine test samples. It is shown that the probe can potentially be used as an end effector of a robotic system which will use the recorded ultrasonic signal as the feedback to a force control algorithm.

This research is part of a broader effort to develop a nondestructive evaluation technique to monitor radiation damage in reactor pressure vessel steels, the main contributor being copper-rich precipitates. In this work, 17-4PH stainless steel is thermally aged to study the effects of copper precipitates on the acoustic nonlinearity parameter. Nonlinear ultrasonic measurements using Rayleigh waves are performed on isothermally aged 17-4PH. Results showed a decrease in the acoustic nonlinearity parameter with increasing aging time, consistent with evidence of copper precipitation from hardness, thermo-electric power, transmission electron microscopy, and atom probe tomography measurements.

This research considers the effects of diffraction, attenuation, and the nonlinearity of generating sources on measurements of nonlinear ultrasonic Rayleigh wave propagation. A new theoretical framework for correcting measurements made with air-coupled and contact piezoelectric receivers for the aforementioned effects is provided based on analytical models and experimental considerations. A method for extracting the nonlinearity parameter β 11 is proposed based on a nonlinear least squares curve-fitting algorithm that is tailored for Rayleigh wave measurements. Quantitative experiments are conducted to confirm the predictions for the nonlinearity of the piezoelectric source and to demonstrate the effectiveness of the curve-fitting procedure. These experiments are conducted on aluminum 2024 and 7075 specimens and a β 11 7075 / β 11 2024 measure of 1.363 agrees well with previous literature and earlier work. The proposed work is also applied to a set of 2205 duplex stainless steel specimens that underwent various degrees of heat-treatment over 24 h, and the results improve upon conclusions drawn from previous analysis.

This research conducts in situ nonlinear ultrasonic (NLU) measurements for real time monitoring of load-induced damage in concrete. For the in situ measurements on a cylindrical specimen under sustained load, a previously developed second harmonic generation (SHG) technique with non-contact detection is adapted to a cylindrical specimen geometry. This new setup is validated by demonstrating that the measured nonlinear Rayleigh wave signals are equivalent to those in a flat half space, and thus the acoustic nonlinearity parameter, β can be defined and interpreted in the same way. Both the acoustic nonlinearity parameter and strain are measured to quantitatively assess the early-age damage in a set of concrete specimens subjected to either 25 days of creep, or 11 cycles of cyclic loading at room temperature. The experimental results show that the acoustic nonlinearity parameter is sensitive to early-stage microcrack formation under both loading conditions - the measured β can be directly linked to the accumulated microscale damage. This paper demonstrates the potential of NLU for the in situ monitoring of mechanical load-induced microscale damage in concrete components.

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.

This paper reports on the first successful nonlinear ultrasonic measurement on highly irradiated specimens in a hot cell environment. The specimens are ANSI 304 stainless steel specimens for which the microstructure characterization and ultrasonic velocity measurement have been previously conducted. The critical part of this research is the development of an automatic fixture device that can facilitate repeatable loading and unloading to place the contact ultrasonic transducers on and off of the specimen. The key step to achieve high measurement repeatability is a careful adjustment of the support-spring constants such that the contact force at the interface between the transducer face and specimen surface is as uniform and constant as possible. The longitudinal ultrasonic velocities, which are obtained as a by-product of the nonlinear ultrasonic measurements, show a level of random variation in terms of (max-min)/average (%) below 0.2%, and the velocity distributions and magnitudes are in good agreement with those from the previous work. The ultrasonic nonlinearity parameters show the level of random variation below 4.7%, which is extremely low, considering that the measurements are conducted in a hot cell environment. The nonlinearity parameters also show a strong dependence on the measurement location in a particular specimen with respect to the radiation source, demonstrating a possible inhomogeneous microstructure evolution in these 12.7 mm thick specimens. This research demonstrates the feasibility of making nonlinear ultrasonic measurement on highly radioactive materials and/or in a highly radioactive environment using the device and procedure developed.

This paper investigates thermal damage (microcracking) in sandstone using ultrasonic methods. Previous investigations have demonstrated that microcracks and lightly compressed interfaces in solids can generate strong higher harmonic signals in a propagating time-harmonic wave. Distributed cracks in rock will generate such nonlinearity and thus measurements of the acoustic nonlinearity can be a useful experimental means to quantify microcracking damage. In fact, experimental results have shown that the acoustic nonlinearity increases with the progress of microcracking in different rocks and concrete. This research attempts to experimentally determine the relation between the crack density and the acoustic nonlinearity in thermally damaged sandstone. The dynamic Young's modulus and longitudinal wave velocity are measured in sandstone specimens that are exposed to high temperatures, from which the crack density is calculated using a micromechanics model . A recently proposed standing wave based ultrasonic technique is employed to measure the acoustic nonlinearity parameters in these specimens. It is shown that the relation between the crack density and the acoustic nonlinearity are approximately linear. This result indicates that the acoustic nonlinearity measurement can be useful for evaluating thermal damage in rock materials.