Ultrasonic characterization of microstructural changes due to static recrystallization and grain growth in Inconel 625 and Inconel 718 superalloys.

In many metallic materials such as Inconel superalloys, the microstructure and grain size play an important role in their mechanical and physical properties and could impact the performance during long-term service at the operational temperature. Therefore, on-site detection of the microstructural transformation (such as recrystallization and grain growth) is of primary importance from a structural integrity point of view. Nondestructive evaluation methods such as the ultrasonic attenuation measurement offer a unique advantage that they can be used to evaluate the microstructure evolution of a component during fabrication or service operation. Nondestructive determination of the grain size could help predict the mechanical behavior of the component. In this study, the measured attenuation coefficient was fitted to a theoretical attenuation model to establish the grain size, which shows a strong quantitative agreement with the grain size determined from Electron Backscatter Diffraction (EBSD) analysis. Furthermore, the EBSD texture results confirmed the existence of a recrystallization temperature region previously established using hardness measurements. This experimental evidence demonstrates that ultrasonic attenuation can predict the grain transformation that could occur during material processing or operational service.

Nonlinear standing waves for assessing material nonlinearity in thin samples.

The second harmonic generation (SHG) technique offers a quantitative damage parameter known as the acoustic nonlinearity parameter (ß) capable of detecting the change in the inherent material nonlinearity. However, current SHG methods, in particular, those used for measuring ß in construction materials, have an unresolved issue in their application due to limited sample sizes. The restricted sample dimensions lead to the generation of boundary-reflected waves, which hinder the selective detection of propagating waves and thus the precise evaluation of material nonlinearity through ß. Furthermore, the use of large samples limits the compatibility of the SHG method with other characterization modalities, such as mechanical tests, X-ray diffraction, and computerized tomography. To address this issue, this paper introduces a new SHG method that is based on the use of nonlinear standing waves - the dominant longitudinal standing waves in a forced-free configuration. The corrections for phase delay and attenuation effect of each reflected wave are made, enabling accurate measurements of ß in thin samples with no requirement in the thickness-wavelength ratio. The measured ß is then employed to quantify the microstructural modification in cement paste induced by thermal damage, validating the proposed method as a promising tool for quantifying microstructural changes in materials.

Nonlinear ultrasonic technique for the characterization of microstructure in additive materials.

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, ß. Stainless steel specimens are made through three procedures: traditional wrought manufacturing, laser-powder bed fusion, and laser engineered net shaping. The ß 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, ß 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 ß are found to have a statistical correlation coefficient of 0.852 showing the sensitivity of ß to dislocations in additively manufactured metals. Moreover, ß shows an excellent correlation with hardness, which is a measure of the macroscopic effect of dislocations.

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, ß, 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 ß and α increase with the growth of the precipitate radii (precipitate-pinned-dislocations). Additionally, both ß and α increase when there is a growth of precipitates in and along the grain boundaries. As expected, ß and α decrease when there is a removal of dislocations in the material. The relationship between ß 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.

In situ nonlinear ultrasonic technique for monitoring microcracking in concrete subjected to creep and cyclic loading.

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, ß 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 ß 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.

Determination of absolute material nonlinearity with air-coupled ultrasonic receivers.

Quantitative evaluation of the microstructural state of a specimen can be deduced from knowledge of the sample's absolute acoustic nonlinearity parameter, ß, making the measurement of ß a powerful tool in the NDE toolbox. However, the various methods used in the past to measure ß each suffer from significant limitations. Piezoelectric contact transducers are sensitive to nonlinear signals, cheap, and simple to use, but they are hindered by the variability of the interfacial contact between transducer and specimen surface. Laser interferometry provides non-contact detection, but requires carefully prepared specimens or complicated optics to maximize sensitivity to the higher harmonic components of a received waveform. Additionally, laser interferometry is expensive and relatively difficult to use in the field. Air-coupled piezoelectric transducers offer the strengths of both of these technologies and the weaknesses of neither, but are notoriously difficult to calibrate for use in nonlinear measurements. This work proposes a hybrid modeling and experimental approach to air-coupled transducer calibration and the use of this calibration in a model-based optimization to determine the absolute ß parameter of the material under investigation. This approach is applied to aluminum and fused silica, which are both well-documented materials and provide a strong reference for comparison of experimental and modeling results.

Mixing of two co-directional Rayleigh surface waves in a nonlinear elastic material.

The mixing of two co-directional, initially monochromatic Rayleigh surface waves in an isotropic, homogeneous, and nonlinear elastic solid is investigated using analytical, finite element method, and experimental approaches. The analytical investigations show that while the horizontal velocity component can form a shock wave, the vertical velocity component can form a pulse independent of the specific ratios of the fundamental frequencies and amplitudes that are mixed. This analytical model is then used to simulate the development of the fundamentals, second harmonics, and the sum and difference frequency components over the propagation distance. The analytical model is further extended to include diffraction effects in the parabolic approximation. Finally, the frequency and amplitude ratios of the fundamentals are identified which provide maximum amplitudes of the second harmonics as well as of the sum and difference frequency components, to help guide effective material characterization; this approach should make it possible to measure the acoustic nonlinearity of a solid not only with the second harmonics, but also with the sum and difference frequency components. Results of the analytical investigations are then confirmed using the finite element method and the experimental feasibility of the proposed technique is validated for an aluminum specimen.

Diffraction, attenuation, and source corrections for nonlinear Rayleigh wave ultrasonic 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 ß11 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 ß11(7075)/ß11(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 24h, and the results improve upon conclusions drawn from previous analysis.

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.

Effects of beryllium coating layer on performance of the ultrasonic waveguide sensor.

Under-sodium viewing is one of the critical technical issues and requirements for the in-service inspection of the sodium-cooled fast reactor (SFR) that is currently under development. The waveguide sensor that uses leaky A(0) mode Lamb waves has shown its potential for high-resolution viewing/scanning of the reactor core and in-vessel structures. However, a few problems arise under a liquid sodium environment due to high sound speed in liquid sodium and dispersion in the long waveguide plate, which simultaneously deteriorate the reconstructed C-scan images. This paper proposes coating the surface of the waveguide sensor plate with a thin layer of material that has a very high ultrasonic wave velocity. It is shown that this coating layer can largely reduce the size (width) and radiation angle of the acoustic beam from the waveguide sensor. This paper precisely analyzes the effects of coating parameters on the beam quality. The proposed idea is validated through ultrasonic experiments in which the radiation beam profiles and group velocities in waveguide sensors with different surface treatments are measured and compared.

Theoretical and experimental study of the nonlinear resonance vibration of cementitious materials with an application to damage characterization.

This paper presents a theoretical and experimental study of the nonlinear flexural vibration of a cement-based material with distributed microcracks caused by an important deterioration mechanism, alkali-silica reaction (ASR). The general equation of motion is derived for the flexural vibration of a slender beam with the nonlinear hysteretic constitutive relationship for consolidated materials, and then an approximate formula for excitation-dependent resonance frequency is obtained. A downward shift of the resonance frequency is related to the nonlinearity parameters defined in the constitutive relationship. Vibration experiments are conducted on standard mortar bar samples undergoing progressive ASR damage. The absolute nonlinearity parameters are determined from these experimental results using the theoretical solution in order to investigate their dependence on the damage state of the material. With the progress of the ASR damage, the absolute value of the hysteresis nonlinearity parameter increases by as much as six times from the intact (undamaged) state in the sample with highly reactive aggregate; this is in contrast to a change of about 16% in the linear resonance frequency. It is demonstrated that the combined theoretical and experimental approach developed in this research can be used to quantitatively characterize ASR damage in mortar samples and other cement-based materials.

Detection of damage in concrete using diffuse ultrasound.

This letter demonstrates the potential for using diffuse ultrasound measurements to detect damage in concrete. Two different solutions to the diffusion equation, an infinite three-dimensional (3D) volume model that neglects geometric boundaries and a finite 3D cuboid model, are used for the required curve fitting procedure to determine the influence of geometric boundaries on the solution. The measurements consider two types of microcrack damage in concrete, alkali-silica reaction and thermal damage, and show that the measured diffusivity parameter is related to the amount of damage in each specimen.

Characteristics of second harmonic generation of Lamb waves in nonlinear elastic plates.

This paper investigates the characteristics of the second harmonic generation of Lamb waves in a plate with quadratic nonlinearity. Analytical asymptotic solutions to Lamb waves are first obtained through the use of a perturbation method. Then, based on a careful analysis of these asymptotic solutions, it is shown that the cross-modal generation of a symmetric second harmonic mode by an antisymmetric primary mode is possible. These solutions also demonstrate that modes showing internal resonance-nonzero power flux to the second harmonic mode, plus phase velocity matching-are most useful for measurements. In addition, when using finite wave packets, which is the case in most experimental measurements, group velocity matching is required for a cumulative increase in the second harmonic amplitude with propagation distance. Finally, five mode types (which are independent of material properties) that satisfy all three requirements for this cumulative increase in second harmonic amplitude-nonzero power flux, plus phase and group velocity matching-are identified. These results are important for the development of an experimental procedure to measure material nonlinearity with Lamb waves.

Models for wave propagation in two-dimensional random composites: A comparative study.

This paper provides a set of benchmark results on existing theoretical models for wave propagation in two-dimensional composite materials. This comparative study is motivated to investigate the reason why results from an accurate ultrasonic measurement often significantly contradict theoretical predictions. Eight different models are evaluated with their numerically calculated effective wave speeds and coherent attenuations. For computational simplicity, the problem of horizontal shear wave propagation in an elastic matrix containing parallel circular cylinders is considered. Numerical calculations are conducted for different composites in wide ranges of material properties, volume concentration, and frequency. Some of the numerical results are compared with experimental data. Judgments are made based on fundamental theoretical and physical criteria as well as relative agreements in the numerical results, and then possible causes of failures are discussed. The effect of microstructure, potentially as a major source of the observed disagreements between models, is also discussed.

Determination of elastic constants of generally anisotropic inclined lamellar structure using line-focus acoustic microscopy.

A methodology for measuring elastic constants of different phases in materials with lamellar microstructure by line-focus acoustic microscopy is developed. The material microstructure investigated is modeled by generally anisotropic multilayers arbitrarily inclined to the sample surface on which acoustic microscopy measurements are performed. To calculate surface acoustic wave (SAW) propagation in such structures quasi-static effective elastic constants are determined and compared with calculated frequency-dependent constants. As a model material, practically important, Ti-6Al-2Sn-4Zr-2Mo alloy is selected. Time-resolved line-focus acoustic microscopy experiments are performed on a Ti-6242 alpha/beta single colony (Ti-6Al-2Sn-4Zr-2Mo alloy) and on a Ti-6Al alpha-phase single crystal for which elastic constants of different phases are determined using inversion of measured SAW velocities. To validate the experimental methodology, SAW velocities in an X-cut quartz crystal are measured as a function of sample orientation angle and compared with predictions based on the known elastic moduli of quartz.

Correction for partial reflection in ultrasonic attenuation measurements using contact transducers.

This research investigates the influence of partial reflection on the measurement of the absolute ultrasonic attenuation coefficient using contact transducers. The partial, frequency-dependent reflection arises from the thin fluid-layer interface formed between the transducer and specimen surface. It is experimentally shown that neglecting this reflection effect leads to a significant overestimation in the measured attenuation coefficient. A systematic measurement procedure is proposed that simultaneously obtains the ultrasonic signals needed to calculate both the reflection coefficient of the interface and the attenuation coefficient, without disturbing the existing coupling conditions. The true attenuation coefficient includes a correction based on the measured reflection coefficient--this is called the reflection correction. It is shown that including the reflection correction also reduces the variation (random error) in the measured attenuation coefficient. The accuracy of the proposed method is demonstrated for a material with a known attenuation coefficient. The proposed method is then used to measure the high attenuation coefficient of a cement-based material.

Antiplane shear wave propagation in fiber-reinforced composites.

A self-consistent method for analyzing antiplane shear wave propagation in two-dimensional inhomogeneous media is presented. For applications in the high-frequency range, the self-consistent condition for the effective medium is solved being supplemented with the theory of quasidynamic effective density. Comparisons with other theoretical calculations and experimental data for fiber-reinforced composites demonstrate the merits of using the present method.