Ultrasonic Nonlinearity Parameter Research Articles

Nonlinear Lamb wave for the evaluation of creep damage in modified 9Cr–1Mo steel

Higher harmonic generation using nonlinear ultrasonic is known to be very sensitive to microstructural degradation. This technique relies on nonlinear stress-strain relation i.e. nonlinear Hooke's law. The quantitative measurement to characterize the materials degradation is done by the nonlinear ultrasonic parameter, β. The objective of this work is to use nonlinear ultrasonic using Lamb wave to evaluate creep damage in modified 9Cr–1Mo steel. Relative change in β was seen to be dependent on the higher order elastic constants that evolve with microstructure as creep progresses as well as sub-structural changes. The extent of damage in the material due to creep exposure was evaluated by Kernel Average Misorientation (KAM) from EBSD and co-related with nonlinear acoustic parameter.

Damage assessment of concrete using a non-contact nonlinear wave modulation technique

This paper presents the development of a nonlinear vibro-acoustic modulation technique based on non-contact piezoelectric sensors to detect the crack progression of concrete subjected to both mechanical and thermal load. Two types of crack are investigated in the work including the isolated single crack induced by the three point bending test and distributed mapping cracks caused by heating treatment. Experimental results show that the damage index defined in the air-coupled wave modulation method – ultrasonic nonlinear parameter presents a positive correlation with the growth of single crack in bending test and the accumulation of mapping crack in thermal test. The sensitivity of developed method is validated through a comparison between the ultrasonic nonlinear parameter and two traditional linear parameters namely the phase velocity of Rayleigh wave and resonance frequency of vibrations. X-ray Computed Tomography (CT) technique and three-dimensional (3D) image reconstruction method are used to visualize microstructure of thermal damage. The CT images show that proposed nonlinear parameter is reliable and well correlated with the microstructural defects of concrete specimen. The repeatability of the air-coupled method is better than the contact method because the coefficient of variation of non-contact measurements is averagely about 43.2% of the contact measurements. Due to the advantage of removable characteristic of non-contact ultrasonic measurements, the developed air-coupled nonlinear wave modulation method could be promising for fast damage assessment of concrete structures in engineering practice.

A multi-parameter ultrasonic evaluation of mean grain size using optimization

An evaluation model based on multiple ultrasonic parameters was developed to control mean absolute error between an actual measured value and a model calculation value. Superalloy GH4169 was used to validate the presented model. A multi-dimensional ultrasonic parameter set was built for each sample by ultrasonic and nonlinear ultrasonic test and parameter calculation. The feature scale of different parameters was restricted to the same range using normalization. The dimensionality of the parameter set was descended by a correlation metric with grain size. A new one-dimensional ultrasonic characteristic parameter was comprised of the select normalized set of ultrasonic parameters by quadratic polynomial, exponential, Gauss kernel and linear mapping functions with undetermined coefficients. The relationship between the new ultrasonic multiple eigenvalues mapping parameter and estimated grain size was expressed using a linear fitting function. An optimization problem aimed at minimizing the mean absolute error between the estimated and quantitative measured grain size was solved using evolutionary algorithms to obtain coefficients for the mapping and fitting functions. These calculations were used to generate four full multi-parameter ultrasonic evaluation models, which were benchmarked against three single parameter evaluation models (i.e. velocity, attenuation coefficient, and backscattering). The performance analysis and verification using leave-one-out cross-validation demonstrate the utility of the MUE model through its high precision, good stabilization, super anti-interference and practicality.

Ultrasonic nonlinearity parameter in uniaxial stress condition

The ultrasonic nonlinearity parameter derived for one-dimensional propagation of a longitudinal wave in an isotropic material has been considered useful in the evaluation of material degradation. To demonstrate this, many researchers have reported on the correlation with the yield strength obtained from a tensile test. However, there is an essential issue with this procedure – which is that the ultrasonic nonlinearity parameter is derived in a state where the lateral strain is restrained, whereas the tensile test to measure the yield strength is carried out under uniaxial stress conditions, where lateral deformation is free. In this study, to address this issue, the authors have defined the ultrasonic nonlinearity parameter under uniaxial stress conditions which were the same as the tensile test, and showed that the correlation with the yield strength was higher than the currently used ultrasonic nonlinearity parameter. To verify the validity of the proposed ultrasonic nonlinearity parameter, experiments were carried out for Al6061-T6 alloy specimens heat-treated with different aging times. Results showed that the proposed ultrasonic nonlinearity parameter exhibited a much higher correlation with yield strength than the currently used nonlinearity parameter.

Characterization of Microstructural Evolution by Ultrasonic Nonlinear Parameters Adjusted by Attenuation Factor

The use of an acoustic nonlinear response has been accepted as a promising alternative for the assessment of micro-structural damage in metallic solids. However, the full mechanism of the acoustic nonlinear response caused by the material micro-damages is quite complex and not yet well understood. In this paper, the effect of material microstructural evolution on acoustic nonlinear response of ultrasonic waves is investigated in rolled copper and brass. Microstructural evolution in the specimens is artificially controlled by cold rolling and annealing treatments. The correlations of acoustic nonlinear responses of ultrasonic waves in the specimens corresponding to the microstructural changes are obtained experimentally. To eliminate the influence of attenuation, which was induced by microstructural changes in specimens, experimentally-measured nonlinear parameters are corrected by an attenuation correction term. An obvious decrease of nonlinearity with the increase of grain size is found in the study. In addition, the influences of material micro-damages introduced by cold rolling on the acoustic nonlinear response in specimens are compared with the ones of grain boundaries controlled by heat treatment in specimens. The experimental results show that the degradation of material mechanical properties is not always accompanied by the increase of acoustic nonlinearity generated. It suggested that the nonlinear ultrasonic technique can be used to effectively characterize the material degradations, under the condition that the variations of grain sizes in the specimens under different damage states are negligible.

Characterization of Tempering Behaviour of Modified 9Cr-1Mo Steel by Ultrasonic Lamb wave Mixing

This work demonstrates the use of mixing of ultrasonic Lamb waves to characterize the tempering behaviour in metallic plate. Lamb wave mixing has been used to measure the generated second harmonic during tempering of mod.9Cr-1Mo steel plate. As-received material is normalized at 1080°C and then tempered in the temperature range of 600 - 850°C with a step size of 50°C for 1.5hrs and followed by furnace cooling. Lamb wave mixing technique has been used to assess the tempering behaviour of this material. Nonlinear ultrasonic parameter β which is the ratio of 2nd harmonic amplitude to the multiplication of the fundamental amplitudes is determined from the mixing wave at each temperature and correlated with microstructural characteristics. It is seen that this nonlinear acoustic parameter (β) is sensitive towards coherency strain generated between precipitate and matrix during tempering.

Self-Sensing Nonlinear Ultrasonic Fatigue Crack Detection under Temperature Variation †.

This paper proposes a self-sensing nonlinear ultrasonic technique for fatigue crack detection under temperature variations. Fatigue cracks are identified from linear (α) and nonlinear (β) ultrasonic parameters recorded by a self-sensing piezoelectric transducer (PZT). The self-sensing PZT scheme minimizes the data acquisition system’s inherent nonlinearity, which often prevents the identification of fatigue cracks. Also, temperature-dependent false alarms are prevented based on the different behaviors of α and β. The proposed technique was numerically pre-validated with finite element method simulations to confirm the trends of α and β with changing temperature, and then was experimentally validated using an aluminum plate with an artificially induced fatigue crack. These validation tests reveal that fatigue cracks can be detected successfully in realistic conditions of unpredictable temperature and that positive false alarms of 0.12% occur.

Characterization of microstructural changes due to prolonged thermal exposure of directionally solidified Ni-base super alloy CM 247LC using ultrasonic

The high temperature strength of directionally solidified Ni-base super alloy CM 247LC strongly depends on the morphology, volume fraction, size and size distribution of γ′ precipitate (Ni3Al) in the FCC γ matrix. The microstructure of the alloy is engineered to achieve the right combination of these parameters that provides the required high temperature strength and creep resistance. The alloy contains high volume fraction of coherent γ′ precipitates having near cubic shape. High temperature exposure of gas turbine components made out of the alloy leads to coarsening of the γ′ precipitates and broadening of the γ matrix channel. This in turn, adversely affects the high temperature mechanical properties of the alloy. The present study endeavours to non-destructively characterize such detrimental changes in the microstructure that controls the mechanical properties and limits the life of components. The microstructural changes of the fully heat treated alloy exposed at 980 °C for different hours (100–1200) of thermal exposure have been characterized using ultrasonic methods. Changes in microstructural parameters due to different hours of thermal exposure have been correlated with changes in ultrasonic velocity, ultrasonic attenuation coefficient and second order acoustic nonlinearity parameter. It is observed that the change in attenuation is predominantly by absorption of the ultrasonic wave due to dislocation damping in the γ channels. Nonlinear ultrasonic parameter changes with thermal exposure predominantly due to the alteration of dislocation precipitate interaction. A dislocation precipitation interaction model for ultrasonic wave distortion has been used to explain the observed variation in nonlinear parameter. A microstructural parameter has been identified that varies in a similar way as ultrasonic attenuation and second order ultrasonic parameter. It is shown that variations in the acoustic non-linearity parameter follow the trend more closely with the identified microstructural parameter.

Stress evaluation of metallic material under steady state based on nonlinear critically refracted longitudinal wave

Abstract This paper presents the study of applying the nonlinear ultrasonic wave to evaluate the stress state of metallic materials under steady state. The pre-stress loading method is applied to guarantee components with steady stress. Three kinds of nonlinear ultrasonic experiments based on critically refracted longitudinal wave are conducted on components which the critically refracted longitudinal wave propagates along x, x1 and x2 direction. Experimental results indicate the second and third order relative nonlinear coefficients monotonically increase with stress, and the normalized relationship is consistent with simplified dislocation models, which indicates the experimental result is logical. The combined ultrasonic nonlinear parameter is proposed, and three stress evaluation models at x direction are established based on three ultrasonic nonlinear parameters, which the estimation error is below 5%. Then two stress detection models at x1 and x2 direction are built based on combined ultrasonic nonlinear parameter, the stress synthesis method is applied to calculate the magnitude and direction of principal stress. The results show the prediction error is within 5% and the angle deviation is within 1.5°. Therefore the nonlinear ultrasonic technique based on LCR wave could be applied to nondestructively evaluate the stress of metallic materials under steady state which the magnitude and direction are included.

First-principles calculations of electronic, acoustic and anharmonic properties of Mn2RuZ (Z = Si and Ge) Heusler compounds

The electronic, acoustic and anharmonic properties of Mn2RuZ (Z = Si and Ge) Heusler compounds were systematically studied by first-principles calculations combined with homogeneous deformation theory. The calculated lattice constants, electronic, magnetic and elastic properties were found to agree with the available experimental and theoretical values. Based on the obtained elastic properties, the acoustic velocities, Debye temperatures and thermal conductivities were calculated for both compounds. Their acoustic velocities and thermal conductivities were found to exhibit anisotropic behavior. Mn2RuSi has larger acoustic velocities, higher Debye and thermal conductivities for its lower density and larger second-order elastic constants. The pressure derivatives of second-order elastic constants, mode Grüneisen constants of long-wavelength acoustic modes, and nonlinear ultrasonic parameters were also obtained. The predictions on the acoustic and anharmonic properties are useful for further study of the related materials in the near future.

Nonlinear Electromagnetic Acoustic Testing Method for Tensile Damage Evaluation

This paper describes an approach for measuring material plasticity using contactless electromagnetic acoustic method. Harmonic generation from noncumulative fundamental longitudinal wave in specimen is studied based on numerical method, and the contribution to harmonic generation from tensile damage is shown to be higher than that from a geometric factor; more serious damages increase the amplitude of second harmonics. These two experimental setups (nonlinear piezoelectric method and nonlinear electromagnetic acoustic method) are used to assess the relative nonlinearity parameters of tensile damage of five aluminum alloy specimens along the thickness direction, and the proposed technique is as effective with the traditional nonlinear piezoelectric method. This result demonstrates that the ultrasonic nonlinear parameter can represent tensile damage with ultrasonic nonlinear parameter by noncontact electromagnetic acoustic method.

Application of Wavelet and EEMD Joint Denoising in Nonlinear Ultrasonic Testing of Concrete

The health state of concrete is deteriorating during its service. Nonlinear ultrasonic detection based on the amplitude of the fundamental and the second harmonic is considered to be a powerful tool for the discovery of the microcrack in concrete. However, the research on processing the nonlinear ultrasonic signal is still insufficient. In order to highlight the real frequency domain components in the nonlinear ultrasonic signal, wavelet and ensemble empirical mode decomposition (EEMD) were joined to denoise the numerical and measured signal. The optimal wavelet base and the decomposition level were determined by the signal‐to‐noise ratios (SNRs). Then, the wavelet threshold denoising signal was decomposed by EEMD, omitting the high‐frequency components and ultimately achieving the desired denoising effect. The denoising result of the test signals demonstrates that this method is effective in denoising the details of the ultrasonic signal and improving the reliability and adaptability of the nonlinear ultrasonic testing. In this experiment, the concrete with the microcrack was tested by linear and nonlinear ultrasonic methods. Based on the variation regularity of the nonlinear ultrasonic coefficient β and velocity v, we can conclude that the nonlinear ultrasonic parameter β is more sensitive to the microcrack in concrete than the traditional wave velocity v. The nonlinear ultrasonic testing can be an important supplement to the current nondestructive testing technique of the concrete.

Assessment of the Low-Cycle Strain-Induced Martensite Transformation in AISI 316 Stainless Steel by Magnetic and Acoustic Nondestructive Methods

The strain-induced martensite transformation during the low-cycle fatigue in austenitic AISI 316 stainless steel was investigated by magnetic and acoustic nondestructive methods. The low-cycle fatigue test was performed at various strain amplitudes. The volume fraction of α′-martensite was determined for the fatigue-failed specimens by magnetic property measurements with further microstructure detection. The cyclic hardening behavior was discussed in terms of the α′-martensite transformation. The volume fraction of α′-martensite was growing with the strain amplitude. An increase in the α′-martensite fraction was evaluated with the nonlinear ultrasonic parameter. The α′-martensite fraction may distort the lattice in austenitic stainless steel, resulting in the distortion of an ultrasonic wave. From this distortion, superharmonics may be generated with the α′-martensite nucleation, which strongly depends on the strain amplitude. The relationship between nonlinear acoustic characteristic and the volume fraction of α′-martensite is linear.

Nondestructive Evaluation of Strain-Induced Phase Transformation and Damage Accumulation in Austenitic Stainless Steel Subjected to Cyclic Loading

Strain-induced phase transformation and damage accumulation in austenitic stainless steel subjected to cyclic loading were investigated by nondestructive evaluation. The cyclic loading test was performed at various strain amplitudes at the same strain rate. The volume fraction of the strain-induced phase transformation (α′-martensite) was determined by ferrite scope and magnetic coercivity measurement. The damage accumulation and microstructure of cyclic loading specimens were characterized by microstructural observation. The cyclic hardening and cyclic softening behavior are discussed in terms of the generation of strain-induced martensite phases and a dislocation substructure at each strain amplitude. The volume fraction of the strain-induced phase increased with the strain amplitude. The increase in α′-martensite was evaluated by measuring the ultrasonic nonlinearity parameter. The presence of α′-martensite is sufficient to distort the austenitic matrix due to an interface misfit between the austenite matrix and α′-martensite, resulting in wave distortion of the longitudinal wave. From this wave distortion, super-harmonics may be generated with nucleation of the strain-induced martensite, a process that strongly depends on the strain amplitude.

First-Principles Calculations of Acoustic and Anharmonic Properties of Ferromagnetic Cu2MnZ (Z = Al and In) Heusler Alloys

The acoustic and anharmonic properties of ferromagnetic Cu2MnZ (Z = Al and In) Heusler alloys have been investigated by first-principles calculations method. The obtained lattice parameters, magnetic moments, elastic properties are found to be in good agreement with the available experimental values. From the elastic properties, the sound velocities and the related Debye temperatures and minimum thermal conductivities have been obtained for the two alloys. The sound velocities and thermal conductivities of both alloys are found to show significant anisotropy, and the Cu2MnAl with small density and large elastic constants has large sound velocities, high Debye temperature, and large thermal conductivities. Also, the effective second-order elastic constants, generalized Gruneisen constants, and nonlinear ultrasonic parameters to characterize anharmonic properties have been studied for the two alloys. These predictions on the acoustic and anharmonic properties can provide a valuable guidance or reference for further related investigations.

Dependence of nonlinear ultrasonic characteristic on second-phase precipitation in heat-treated Al 6061-T6 alloy

It is well known that nonlinear ultrasound is sensitive to certain microstructural features in materials such as dislocations and precipitates. This paper investigates the dependence of the nonlinear ultrasonic characteristic on MgnSim precipitation in heat-treated Al 6061-T6 alloy specimens. The specimens were heat-treated at a constant temperature of 220°C for different exposure times up to 6000min. The accuracy of the ultrasonic measurement setup that determines the absolute ultrasonic nonlinearity parameter βu was first validated. The nonlinearity parameter and the yield strength were measured for each of the artificially aged specimens. The experimental results show fluctuations in the nonlinearity parameter and yield strength over the aging time, but with an interesting correlation between the nonlinearity parameter and the yield strength over the aging time. Microstructural observations confirmed that those fluctuations are due to the formation and evolution of precipitates that occurs in a unique precipitation sequence in this alloy. These results suggest that the nonlinear ultrasonic measurement can be useful for monitoring second phase precipitation and related mechanical properties in the Al 6061-T6 alloy.

Rayleigh Surface wave based non linear ultrasound to assess effect of precipitation hardening during tempering in P92 steel

This study presents the generation and variation of second harmonic of Rayleigh surface wave due to the change in precipitation morphology during tempering of P92 steel. The specimens from P92 steel were normalized at 1075°C and then tempered in the temperature range of 745–835°C at a step of 30°C for 3hrs followed by air cooling. Non linear ultrasonic (NLU) parameter which is defined as the ratio of the amplitude of second harmonic to the square of the amplitude of the transmitted signal frequency was measured at each temperature and was correlated with the changes in precipitates number density, volume fraction and dislocation density. It was observed that the measured non linearity parameter is sensitive to the precipitate coherency strain. Similar trend in the variation of mechanical properties and NLU parameter with the tempering temperature suggests that this technique can be useful in monitoring material strengthening due to the precipitation hardening and precipitation-dislocations interactions.

Fatigue Life Prediction of Metallic Materials Based on the Combined Nonlinear Ultrasonic Parameter

The fatigue life prediction of metallic materials is always a tough problem that needs to be solved in the mechanical engineering field because it is very important for the secure service of mechanical components. In this paper, a combined nonlinear ultrasonic parameter based on the collinear wave mixing technique is applied for fatigue life prediction of a metallic material. Sweep experiments are first conducted to explore the influence of driving frequency on the interaction of two driving signals and the fatigue damage of specimens, and the amplitudes of sidebands at the difference frequency and sum frequency are tracked when the driving frequency changes. Then, collinear wave mixing tests are carried out on a pair of cylindrically notched specimens with different fatigue damage to explore the relationship between the fatigue damage and the relative nonlinear parameters. The experimental results show when the fatigue degree is below 65% the relative nonlinear parameter increases quickly, and the growth rate is approximately 130%. If the fatigue degree is above 65%, the increase in the relative nonlinear parameter is slow, which has a close relationship with the microstructure evolution of specimens. A combined nonlinear ultrasonic parameter is proposed to highlight the relationship of the relative nonlinear parameter and fatigue degree of specimens; the fatigue life prediction model is built based on the relationship, and the prediction error is below 3%, which is below the prediction error based on the relative nonlinear parameters at the difference and sum frequencies. Therefore, the combined nonlinear ultrasonic parameter using the collinear wave mixing method can effectively estimate the fatigue degree of specimens, which provides a fast and convenient method for fatigue life prediction.

Effect of Precipitation Morphology on the Second Harmonic Generation of Ultrasonic Wave During Tempering in P92 Steel

This paper reports the generation of second harmonic of ultrasound wave and the variation of its amplitude with the precipitation morphology in P92 steel. P92 steel samples were normalized at 1075 °C and tempered in a range of 715–835 °C at a step of 30 °C to study the effect of nucleation and growth of precipitates on the amplitude of second harmonic of ultrasound wave. It has been observed that the non linear ultrasonic (NLU) parameter which is defined as the ratio of the amplitude of second harmonic to the square of the amplitude of the transmitted signal frequency increases with the nucleation and growth of precipitates. Whereas when the growth of precipitate is restricted and fine secondary precipitates start to nucleate, it decreases. The maximum of NLU parameter corresponds to the optimum tempering temperature for the studied material.

Correlation between Ultrasonic Nonlinearity and Elastic Nonlinearity in Heat-Treated Aluminum Alloy

The nonlinear ultrasonic technique is a potential nondestructive method to evaluate material degradation, in which the ultrasonic nonlinearity parameter is usually measured. The ultrasonic nonlinearity parameter is defined by the elastic nonlinearity coefficients of the nonlinear Hooke's equation. Therefore, even though the ultrasonic nonlinearity parameter is not equal to the elastic nonlinearity parameter, they have a close relationship. However, there has been no experimental verification of the relationship between the ultrasonic and elastic nonlinearity parameters. In this study, the relationship is experimentally verified for a heat-treated aluminum alloy. Specimens of the aluminum alloy were heat-treated at <TEX>$300^{\circ}C$</TEX> for different periods of time (0, 1, 2, 5, 10, 20, and 50 h). The relative ultrasonic nonlinearity parameter of each specimen was then measured, and the elastic nonlinearity parameter was determined by fitting the stress-strain curve obtained from a tensile test to the 5th-order-polynomial nonlinear Hooke's equation. The results showed that the variations in these parameters were in good agreement with each other.