Ultrasonic Nonlinearity Parameter Research Articles

Weibull parameter based probability distribution for predicting creep life of power plant materials: A non-destructive approach

The knowledge of remaining useful life and the probability of failure at any point of time in the life cycle of any power plant component is an important information for the plant operators to take preventive action. This paper focuses on life data evaluation of creep-exposed power plant material based on statistical probability distribution through Weibull analysis. The probability distribution was obtained considering the change in non-linear ultrasonic (NLU) parameter measured in P92 steel at different creep test conditions. The material was creep tested at 650⁰C for three different applied stresses. The NLU parameter (β), which indicates the extent of damage, is the ratio of the amplitude of the fundamental frequency of the transmitted signal to the square of the amplitude of the second harmonic of a sinusoidal wave propagated into the material. The two-parameter based Weibull distribution function was adopted for evaluating the cumulative distribution function and failure rate. A sudden increase in NLU parameter was observed at ∼ 80% of creep damage followed by a drop in its value indicating the specimen failure. With increase in applied stress, failure rate increase was also observed. Microstructural observations revealed that with creep progress, the growth and coarsening of precipitates, micro crack formation and their coalescence were the major cause for increase in failure rate. Therefore, application of this technique can be useful for evaluating the creep life and probability of failure of any plant component in a non-invasive way.

Ultrasonic nonlinear parameter based on Hollomon hardening model

The Hollomon hardening model is introduced into the wave equation of ultrasound and the ultrasonic nonlinear parameter βn based on hardening index n is obtained. Subsequently, tensile tests and ultrasonic nonlinear tests are carried out on AA6061-T6 aluminum alloy specimens under different pre-deformations and strain rates. The results show that under unloading condition, the normalized βn based on n and the normalized βtest based on ultrasonic nonlinear test both increase with the increasing pre-deformation and strain rate. The growth rate of the former is about 77% of the latter. The results show that it is possible to evaluate the hardening state of materials quantitatively based on ultrasonic nonlinear technology.

Nonlinear ultrasonic testing for evaluation of fracture toughness in 4130 steel

An estimation of plane strain fracture toughness [endif]--> is essential to assess the operational safety of fracture-critical systems; loss of [endif]-->can lead to catastrophic failure. However, it is not possible to quantify [endif]-->in situ; the laboratory testing to determine [endif]-->is destructive. Here, we investigate nonlinear ultrasonic testing as a nondestructive method to evaluate [endif]-->. This is based on a hypothesized correlation between the nonlinear ultrasonic parameters and [endif]-->characteristics of a material given their mutual dependence on microstructure. Using Second Harmonic Generation (SHG), surface and bulk waves are used to measure the (relative) nonlinearity parameter for tempered 4130 steel samples. Coupons made of the same materials are also tested for their [endif]-->characteristics using Charpy V-Notch testing, providing a direct comparison between destructive and nondestructive measures. Our results show correlations between ultrasonic parameters and [endif]-->characteristics of 4130 steel samples, but different relations are observed for bulk and surface waves. The observed differences are possibly due to sample heterogeneity and different wave structures of the two wave modes and should be further investigated. We demonstrate the potential of nonlinear ultrasonic testing for [endif]-->estimation. The ultimate goal is developing a nondestructive method to assess [endif]--> in situ.

Thermal damage evaluation of nickel-based superalloys based on ultrasonic nondestructive testing

Ultrasonic nondestructive technique was used to assess the thermal degradation in a nickel-based superalloy in this research. Thermal exposure tests were carried out at an elevated temperature of 1050 °C to introduce controlled levels of damage, while the linear ultrasonic parameters (sound velocity and attenuation coefficient) and nonlinear ultrasonic parameters were observed. The evolution of the microstructure and the subsequent degradation in macro-mechanical properties of the material were quantitatively researched. The results suggest that the nonlinear parameters show hypersensitivity and high-credibility compared with the traditional linear parameters. The monotonic increase of the ultrasonic nonlinear parameters was explained by the evolution of the lattice mismatch and the volume fraction of the γ′ and carbide precipitated phase based on the dislocation precipitation interaction model.

Nonlinear Analysis Method of High-Strength Steel Based on Local Buckling Fiber Hinge

Based on the analysis and summary of the research and application status of domestic and foreign high-strength steel local buckling fiber hinged rod stability and ordinary steel local buckling fiber hinged rod stability control, this paper proposes a fiber hinged rod suitable for spatial structures subject to local buckling. The new type is high-strength steel composite local buckling fiber hinged pressure rod. The influence of related parameters in the dislocation string model and the dislocation couple model on the ultrasonic nonlinear parameters is deeply analyzed. And, from the perspective of contact nonlinear acoustics, the mechanism of the ultrasonic nonlinear response of the crack is analyzed, and the finite element software ABAQUS is used to simulate it. The relationship between the nonlinear parameter and the internal crack shape of the material is simulated and analyzed, which proves the nonlinearity. A series of nonlinear ultrasonic testing was performed on three groups of FV520B high-strength steel fatigue specimens using a nonlinear testing system. Analyzing the results, it is found that the material has a good ultrasonic nonlinear cumulative effect, and the microcracks have a greater impact on the ultrasonic nonlinear response. The β-N curves under three sets of fatigue tests are obtained. The results show that the nonlinear parameters are very sensitive to the fatigue damage of FV520B high-strength steel, and the ultrasonic nonlinear parameters generally increase with the increase in the number of fatigue cycles.

Linear and Nonlinear Ultrasonic Techniques for Monitoring Stress-Induced Damages in Concrete

Abstract When stress in concrete exceeds certain threshold value, microcracks are nucleated, these microcracks can propagate and coalesce forming macrocracks, resulting in the gradual decay of the mechanical properties of concrete and eventual failure of the concrete structures. For safety concerns, one needs to develop suitable nondestructive testing methods capable of detecting past overloads of concrete structures during its service life. In this work, the stress-induced damage in concrete is monitored using ultrasonic techniques, exploiting the coupling between the stress level experienced by concrete and its wave propagation parameters. Cyclic compression tests with increasing maximum load level have been performed on specimens made of concrete with coarse-grained (CG) aggregates. Experimental results have been analyzed by two different ultrasonic methods—the linear and the nonlinear ultrasonic techniques. In linear ultrasonic technique, the stress level experienced by the specimens is related to the variations in signal amplitude and velocity of ultrasonic waves. In nonlinear ultrasonic method, the sideband peak count (SPC) technique is used for revealing the stress-induced damage corresponding to each load step. In comparison to linear ultrasonic parameters, the nonlinear ultrasonic parameter SPC-I appears to be more sensitive to the variations of the internal material structures during both loading and unloading phases. Moreover, the SPC technique has shown to be capable of identifying both the initial damage due to the evolution and nucleation of microcracks at the microscopic scale, and the subsequent damages induced by high overload, resulting in an irreversible degradation of the mechanical properties.

Determination of the Ultrasonic Non-linearity Parameter B/A versus Frequency for Water

For tissue characterization, it is desirable to determine B/A using high-frequency transducers. Moreover, an accurate estimate of B/A at elevated frequencies (or at least the assumption of frequency independence of B/A) is required to evaluate the safety of high-frequency systems. However, common finite-amplitude approaches become increasingly inaccurate at high frequencies. In this article, a practical variation of the finite-amplitude method is proposed which combines experiments with numerical simulations of the Khokhlov–Zabolotskaya–Kuznetsov equation and can be used at elevated frequencies. The results at low frequencies show that the proposed approach is accurate with lower uncertainties compared with the finite-amplitude method because it avoids assumptions and approximations. The measured values of B/A versus frequency for water at 2.25–20 MHz show that there is no statistically significant variation in B/A values with frequency, and therefore the assumption of frequency independence of B/A is realistic.

Analysis of the Influence of Surface Roughness on Measurement of Ultrasonic Nonlinearity Parameter Using Contact-Type Transducer

The ultrasonic nonlinearity parameter is used to evaluate the nonlinear elasticity of a material, which is determined from the displacement amplitude of the fundamental and second-order frequencies components in an ultrasonic wave propagating through a material. However, the displacement amplitude of the second-order harmonic component generated during propagation through a material is very weak because it is easily affected by measurement conditions such as surface roughness. In this study, we analyzed the influence of surface roughness on the measurement of the ultrasonic nonlinearity parameter. For this purpose, Al6061-T6 and SUS304 specimens were prepared with different surface roughness ranging from 0.5 to 2.9 μm. Then, the absolute and relative ultrasonic nonlinearity parameter measurements were conducted using a through-transmission technique involving two cases: both surfaces being rough, and one being a rough surface and the other being a smooth surface. The experimental results showed that the surface roughness had a lesser influence on the absolute measurement than on the relative measurement and that the transmission surface was less affected by the reception surface. These results were similar regardless of the types of specimens. Therefore, to perform accurate measurements, it is desirable to measure the nonlinearity parameter after polishing the material surface.

Use of combined linear and nonlinear ultrasound to examine microstructural and microchemical variations in highly irradiated 304 stainless steel

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.

A study on Al 2219 alloy precipitate growth rates by non-linear ultrasonic technique

A non-linear ultrasonic study has been carried out to characterise the variation in precipitation phase. An age-hardenable aluminium alloy (2219) has been taken as a model alloy for the present investigation. It is shown that there is a strong correlation between the change in the non-linear coefficient and the change in the precipitated phase. The observed variations in the non-linear ultrasonic parameter have been explained by modifying an existing dislocation-coherent precipitate interaction model for the generation of harmonics in order to account for a weaker dislocation-semicoherent precipitate interaction. In general, the model proposed can be applicable to all precipitation-hardenable alloy systems undergoing coherent to incoherent precipitate phase transition.

Research on Fatigue Damage in High-Strength Steel (FV520B) Using Nonlinear Ultrasonic Testing

In view of the early fatigue damage of high-strength steel FV520B, a nonlinear ultrasonic detection was performed on two types of fatigue samples using nonlinear Lamb waves. The experimental results indicated that the ultrasonic nonlinear parameter is highly sensitive to early fatigue damage in high-strength FV520B. For plate specimens, the ultrasonic nonlinear parameter increased with the number of fatigue cycles. Scanning electron microscopy (SEM) observations of the fatigue specimens revealed that as the number of fatigue cycles increased, the microstructure of the material gradually deteriorated, and the ultrasonic nonlinear parameter increased. For notched specimens, the ultrasonic nonlinear parameter increased as the size of the main crack increased. SEM observations of the fracture indicated that the ultrasonic nonlinear parameters were more consistent with the equivalent microcrack length (defined as the sum of microcrack lengths in the statistical area), as compared with the length of the main crack. It was determined that the nonlinear effect of the Lamb wave is related to the equivalent microcrack length inside the material and that the ultrasonic nonlinear parameter can effectively characterize the fatigue damage state of high-strength FV520B.

Monitoring damage in composite plates from crack initiation to macro-crack propagation combining linear and nonlinear ultrasonic techniques

In this article, a holistic technique for sensing damage initiation, as well as damage progression in composite plates, is presented combining linear and nonlinear ultrasonic techniques. For this investigation, multiple sets of composite plate specimens made of two different composite materials were fabricated to check if the proposed technique works for different types of specimens. The specimens were damaged by impact loading and then inspected by propagating Lamb waves through them. Different failure mechanisms, such as fiber breaks, matrix cracking, debonding, and delamination, cause composite damage. Two groups of composite specimens that were fabricated and damaged were glass fiber–reinforced polymer composite and basalt fiber–reinforced polymer composite. A chirp signal excited by PZT (lead zirconate titanate) transducer was propagated through undamaged and damaged specimens to investigate the effects of varying degrees of damage on the recorded signals. Both linear and nonlinear ultrasonic parameters were extracted from the recorded signals and analyzed. The change in the linear ultrasonic parameters such as the wave speed and attenuation with damage progression were recorded. A new nonlinear ultrasonic parameter, the sideband peak count or sideband peak count-index, is also introduced and calculated from the recorded signals. It is observed that the nonlinear ultrasonic parameter can monitor the early stage of damage progression better than the linear ultrasonic parameters, while some linear ultrasonic parameters are more effective than the nonlinear ultrasonic parameter for monitoring the advanced stage of damage. Therefore, a combination of linear ultrasonic and nonlinear ultrasonic analyses is ideal for the holistic monitoring of the composite panels from the crack nucleation stage to the structural failure stage.

Nonlinear ultrasonic nondestructive detection and modelling of kissing defects in high voltage composite insulators

This paper investigates a feasible nondestructive method for micron-sized kissing defects in the composite insulators, which are commonly utilized in ultra-high voltage (UHV) power grid. In this paper, cylindrical adhesive contact model was established to describe the obvious distortion of ultrasound propagation caused by kissing defects on the polymeric interface of composite insulators. The ultrasonic nonlinearity parameter was measured for each of the kissing defective and intact specimens. Moreover, the theoretical analysis has been proved by the test results on the kissing defective samples, which indicates that the 0.7 μm kissing defects existed in the composite insulators could be successfully recognized by the nonlinear ultrasonic methods and the nonlinearity is reduced by interface roughness.

Influence of Microstructural Changes’ Effects on the Linear and Nonlinear Ultrasonic Parameters of Cast Stainless Steels

In this research, some nondestructive ultrasonic techniques were employed to inquire into the effect of microstructural changes induced by thermal aging and cold work on the ultrasonic response. As thermal embrittlement is a risk to the safety of nuclear power plants, a nondestructive detection method has to be developed for on-site monitoring. The austenitic stainless steel with δ-ferrite specimens were used to study the behavior of microstructural changes caused by age-treating and cold work and then examined by the velocity, attenuation, and nonlinear ultrasonic technique. The variations of the linear and the nonlinear ultrasonic parameters were related to the microstructural changes. Additionally, the experimental results suggest that the ultrasonic nonlinearity parameter of cast stainless steel is determined by the microstructure evolution caused by spinodal decomposition and the phase precipitation process.

Retardation Effect of Tin Multilayer on Sn-3.0Ag-0.5Cu (SAC305)-Based Solder Joint Interface

Transient liquid phase-like soldering technique has been successfully applied to prepare lead-free solder joints at 230 °C. Multiple interlayers of tin thin films in combination with a Sn-3.0Ag-0.5Cu (SAC305) solder paste have been used as filler for joining. Microstructural analysis was carried out by electron microscopy and energy-dispersive spectroscopy. For interlayer containing samples (Cu-Sn-SAC305-Sn-Cu), interfacial intermetallics layers found to be more homogeneous compared to the samples without interlayers (Cu-SAC305-Cu). Quality of the joints has been investigated nondestructively by ultrasonic method. On measuring the electrical resistivity by four-probe method, Cu-Sn-SAC305-Sn-Cu solder joint shows lower electrical resistivity compared to that of the Cu-SAC305-Cu solder joint, wherein nonlinear ultrasonic parameters confirm the superiority of former over later.

Evaluation of yield strength by ultrasonic reconstruction of quadratic nonlinear Stress–Strain curve

The ultrasonic nonlinearity parameter β defined by the ratio of the second-order harmonic amplitude to the square of fundamental frequency amplitude, has been considered as a potential index to evaluate material degradation. However, the yield strength obtained from destructive tensile testing is still widely adopted for this purpose since it is a more intuitive concept to the field engineer than the parameter β. Therefore, this study proposes a nondestructive method to evaluate the yield strength directly from the ultrasonic measurements. In this regard, the tensile stress–strain curve is represented in the form of a quadratic nonlinear stress–strain equation within the elastic range, which includes the linear elastic modulus and the second-order nonlinearity parameter βt. The linear elastic modulus is obtained by measuring the propagation velocity of longitudinal and transverse waves using a traditional ultrasonic pulse-echo method, and the second-order nonlinearity parameter is obtained by measuring the Murnaghan constants using acoustoelastic effects. Then, the tensile stress–strain curve is reconstructed to estimate the 0.01% offset yield strength. To demonstrate the application of the proposed algorithm, the experiments were performed for heat-treated SA508 specimens. The results indicate that the 0.01% offset yield strength obtained using the proposed algorithm exhibit a good agreement with that obtained via destructive tensile testing.

Device and method for nonlinear ultrasonic measurements on highly irradiated 304 stainless steel specimens in a hot cell environment.

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.

Comparison of Linear and Nonlinear Ultrasonic Parameters in Characterizing Grain Size and Mechanical Properties of 304L Stainless Steel

Ultrasonic nondestructive techniques can be used to characterize grain size and to evaluate mechanical properties of metals more practically than conventional destructive optical metallography and tensile tests. Typical ultrasonic parameters that can be correlated with material properties include ultrasonic velocity, ultrasonic attenuation coefficient, and nonlinear ultrasonic parameters. In this work, the abilities of these ultrasonic parameters to characterize the grain size and the mechanical properties of 304L stainless steel were evaluated and compared. Heat-treated specimens with different grain sizes were prepared and tested, where grain size ranged from approximately 40 to 300 μm. The measurements of ultrasonic velocity and ultrasonic attenuation coefficient were based on a pulse-echo mode, and the nonlinear ultrasonic parameter was measured based on a through-transmission mode. Grain size, elastic modulus, yield strength, and hardness were measured using conventional destructive methods, and their results were correlated with the results of ultrasonic measurements. The experimental results showed that all the measured ultrasonic parameters correlated well with the average grain size and the mechanical properties of the specimens. The nonlinear ultrasonic parameter provided better sensitivity than the ultrasonic velocity and the ultrasonic attenuation coefficient, which suggests that the nonlinear ultrasonic measurement would be more effective in characterizing grain size and mechanical properties than linear ultrasonic measurements.

A Novel Multi-frequency Nonlinear Ultrasonic Approach for the Characterization of Annealed Polycrystalline Microstructure

A multi-frequency nonlinear ultrasonic measurement is used to characterize grain size variations and distributions unambiguously. The ultrasonic nonlinearity parameter varies linearly with grain size in the Rayleigh scattering regime but deviates from linear behavior at the Rayleigh-to-stochastic transition zone. Frequency dependence of this parameter is found to be a reliable tool for rapid screening of materials where grain size varies widely.

Applicability of nonlinear ultrasonic technique to evaluation of thermally aged CF8M cast stainless steel

Abstract Cast austenitic stainless steel (CASS) is used for fabricating different components of the primary reactor coolant system of pressurized water reactors. However, the thermal embrittlement of CASS resulting from long-term operation causes structural safety problems. Ultrasonic testing for flaw detection has been used to assess the thermal embrittlement of CASS; however, the high scattering and attenuation of the ultrasonic wave propagating through CASS make it difficult to accurately quantify the flaw size. In this paper, we present a different approach for evaluating the thermal embrittlement of CASS by assessing changes in the material properties of CASS using a nonlinear ultrasonic technique, which is a potential nondestructive method. For the evaluation, we prepared CF8M specimens that were thermally aged under four different heating conditions. Nonlinear ultrasonic measurements were performed using a contact piezoelectric method to obtain the relative ultrasonic nonlinearity parameter, and a mini-sized tensile test was performed to investigate the correlation of the parameter with material properties. Experimental results showed that the ultrasonic nonlinearity parameter had a correlation with tensile properties such as the tensile strength and elongation. Consequently, we could confirm the applicability of the nonlinear ultrasonic technique to the evaluation of the thermal embrittlement of CASS.