Average grain size evaluation using scattering-induced attenuation of coda waves

Grain size is one of the key microstructural factors affecting the mechanical properties of polycrystalline metal materials. In this study, a novel method for grain size evaluation using ultrasonic coda waves is proposed. Different from conventional bulk wave methods that require a point-by-point scanning of the structure, the proposed method allows for a rapid evaluation of the average grain size of the whole part from a single inspection location using one-pass testing data. A piecewise energy attenuation function dealing with different attenuation mechanisms is proposed to obtain the effective attenuation coefficient of coda waves. A power-law model is constructed to correlate the effective attenuation coefficient with the average grain size. Ultrasonic testing on nickel-based superalloy plate specimens with different average grain sizes is performed for model calibration and method verification. The applicability and robustness of the proposed method are further validated using a realistic turbine disk specimen with an irregular shape and non-uniform grain sizes. Results show that the proposed method yields a reliable and accurate estimation of the average grain size with a maximum relative error less than 20 %.

Multi-parameter optimization of attenuation data for characterizing grain size distributions and application to bimodal microstructures

In this paper, the effect on the ultrasonic attenuation of the grain size heterogeneity in polycrystals is analyzed. First, new analytical developments allowing the extension of the unified theory of Stanke and Kino to general grain size distributions are presented. It is then shown that one can additively decompose the attenuation coefficient provided that groups of grains are defined. Second, the study is specialized to a bimodal distribution of the grain size for which microstructures are numerically modeled by means of the software Neper. The additive partition of the attenuation coefficient into contributions coming from large and small grains motivates the derivation of an optimization procedure for characterizing the grain size distribution. The aforementioned approach, which is based on a least squares minimization, is at last presented and illustrated on both analytical and numerical attenuation data. It is thus shown that the method provides satisfying approximations of volume fractions of large grains and modal equivalent diameters from the frequency-dependent attenuation coefficient.

Comparison of ultrasonic attenuation within two- and three-dimensional polycrystalline media

An analytical approach to develop explicit formulas of attenuation coefficient in both 2D and 3D cases is proposed. It results in a better understanding of the grain scattering mechanisms within a polycrystalline material and the grain size effects on the attenuation of an ultrasonic wave. It is based on the Stanke and Kino's model and uses the Born approximation. An explicit formula is deduced for untextured polycrystals with equiaxed grains of cubic symmetry and allows a rigorous comparison of the attenuation coefficient between both 2D and 3D cases. It confirms that the attenuation in the Rayleigh region is higher in 2D simulation than in 3D one, while very similar coefficients are obtained in the stochastic region for both cases. The study of the explicit formula allows the decomposition of the attenuation coefficient into various scattering-induced components, which leads to a better understanding of different grain scattering mechanisms. The reflection/transmission at grain boundaries between wave modes of a same type mainly explains a same attenuation coefficient in the stochastic region for both 2D and 3D modelings. The conversion at grain boundaries between different types of wave modes provides some explanations for a higher attenuation value given by the 2D modeling in the Rayleigh region. The effect of the grain size on the attenuation coefficient is then predicted by the 2D analytical calculation and by the FE simulation. The analytical-numerical comparison validates the numerical calculations and the approach suggests a way of using the 2D FE calculations to predict the evolution of the attenuation coefficient with the wave frequency in 3D.

Numerical prediction of ultrasonic attenuation in concentrated emulsions and suspensions using Monte Carlo method

For the study of predicting ultrasonic attenuation of mixed particles and probing the effect of interaction between neighboring particles, the Monte Carlo method was investigated to establish a submicron particle size characterization model in concentrated particulate two-phase system and serve as a probability and statistics technique to evaluate the underlying ultrasonic events during the ultrasound propagation. The numerical simulation method was proposed to predict the ultrasonic attenuation characteristics in the two-phase system of silica suspensions and corn oil-in-water emulsions with different particle sizes, ultrasonic frequencies and concentrations. Furthermore, an extension of the well-established single-particle theory of Epstein-Carhart and Allegra-Hawley (ECAH) was carried out, by incorporated in the couple phase model from a hydrodynamic point of view and effective hypothesis both accounted for the ultrasonic wave overlapping effect for the close proximity of particles. The simulation result shows agreement with the results of the ECAH model, the Lloyd & Berry (LB) model and the Waterman model in the dilute limitation, corresponding to glass beads and silica particles respectively. Afterwards, such a method was then applied into mixed particle system, where the mixed iron particles and glass beads with various ratios were set as examples for the purpose of predicting ultrasonic attenuation for the mixed particle systems. After comparing with the experimental results, it is shown that as a function of frequency, the variation of the ultrasonic attenuation coefficient with different mixing ratio manifests a nonlinear tendency. Also noteworthy is that the physical properties of particles play a dramatic impact in influencing ultrasonic attenuation. At higher concentrations, it was validated both in two-phase system of silica suspensions and corn oil-in-water emulsions that the attenuation predicted by Monte Carlo method agreed well with the experimental results of literature, yielding a theoretically increasing but less than linear expected attenuation with particle concentration. Particularly, the critical concentration of deviation from the linear change was obtained and interpreted using the thermal and viscous overlapping theory. The proposed Monte Carlo method presents a novel approach in calculating the attenuation in high particle volume concentration of more than 40% and provides a numerical modeling of particle size measurement in the complex particle-particle interaction condition.

Ultrasonic wave propagation in ternary intermetallic CeCuGe compound

The elastic and ultrasonic properties of the hexagonal intermetallic CeCuGe ternary compound have been evaluated along unique axis at room temperature. Higher order elastic constants have been calculated for CeCuGe compound using Lennard-Jones interaction potential model. The ultrasonic velocity, Debye average velocity, thermal relaxation time and acoustic coupling constant are evaluated along unique axis of the crystal and the temperature dependent ultrasonic velocities are evaluated along different angles with unique axis of the crystal. Finally temperature dependent ultrasonic attenuation is evaluated to extract important information about the material.

Evaluating grain size in polycrystals with rough surfaces by corrected ultrasonic attenuation

Surface roughness of a sample has a great effect on the calculated grain size when measurements are based on ultrasonic attenuation. Combining modified transmission and reflection coefficients at the rough interface with a Multi-Gaussian beam model of the transducer, a comprehensive correction scheme for the attenuation coefficient is developed. An approximate inverse model of the calculated attenuation, based on Weaver's diffuse scattering theory, is established to evaluate grain size in polycrystals. The experimental results showed that for samples with varying surface roughness and matching microstructures, the fluctuation of evaluated average grain size was ±1.17μm. For polished samples with different microstructures, the relative errors to optical microscopy were no more than ±3.61%. The presented method provides an effective nondestructive tool for evaluating the grain size in metals with rough surfaces.

Attenuation of laser generated ultrasound in steel at high temperatures; comparison of theory and experimental measurements

This article reexamines some recently published laser ultrasound measurements of the longitudinal attenuation coefficient obtained during annealing of two steel samples (DP600 and S550). Theoretical attenuation models based on perturbation theory are compared to these experimental measurements. It is observed that the Rayleigh attenuation formulas provide the correct qualitative agreement, but overestimate the experimental values. The more general theoretical attenuation model considered here demonstrates strong quantitative agreement, which highlights the applicability of the model during real-time metal processing.

Effect of Frequency-Dependent Attenuation on Predicted Histotripsy Waveforms in Tissue-Mimicking Phantoms

Tissue-mimicking phantoms are employed for the assessment of shocked histotripsy pulses in vitro. These broadband shock waves are critical for tissue ablation and are influenced by the frequency-dependent attenuation of the medium. The density, sound speed and attenuation spectra (2-25 MHz) were measured for phantoms that mimic key histotripsy targets. The influence of non-linear propagation relative to the attenuation was described in terms of Gol'dberg number. An expression was derived to estimate the bandwidth of shocked histotripsy pulses for power law-dependent attenuation. The expression is independent of the fundamental frequency of the histotripsy pulse for linear frequency-dependent attenuation.

Dependence of diffuse ultrasonic backscatter on residual stress in 1080 steel

In this article, the effects of residual stress on the ultrasonic scattering in a quenched steel sample are investigated by calculating the change of spatial variance amplitudes of ultrasonic signals after removing residual stress via annealing. The experimental results show that the average spatial variance amplitude decreases by about 11.89% for a scan area on the quenched surface after removing residual stress. This quantity was used to estimate the residual stress based on the developed stress-dependent backscatter model. In addition, the residual stress on the whole scan area was mapped by calculating the change of the spatial variance amplitude for each subarea after annealing, respectively. Diffuse ultrasonic backscatter signals show a high sensitivity to residual stress such that this technique has potential as a non-destructive method for measuring residual stress.

Effect of alumina composition and surface integrity in alumina/epoxy composites on the ultrasonic attenuation properties

We report a method of fabricating backing blocks for ultrasonic imaging transducers, using alumina/epoxy composites. Backing blocks contain scatterers such as alumina particles interspersed in the epoxy matrix for the effective scattering and attenuation of ultrasound. Here, the surface integrity can be an issue, where the composite material may be damaged during machining because of differences in strength, hardness and brittleness of the hard alumina particles and the soft epoxy matrix. Poor surface integrity results in the formation of air cavities between the backing block and the piezoelectric element upon assembly, hence the increased reflection off the backing block and the eventual degradation in image quality. Furthermore, with an issue of poor surface integrity due to machining, it is difficult to increase alumina as scatterers more than a specific mass fraction ratio. In this study, we increased the portion of alumina within epoxy matrix by obtaining an enhanced surface integrity using a net shape fabrication method, and verified that this method could allow us to achieve higher ultrasonic attenuation. Backing blocks were net-shaped with various mass fractions of alumina to characterize the formability and the mechanical properties, including hardness, surface roughness and the internal micro-structure, which were compared with those of machined backing blocks. The ultrasonic attenuation property of the backing blocks was also measured.

Beyond Cervical Length: A Pilot Study of Ultrasonic Attenuation for Early Detection of Preterm Birth Risk

The purpose of this study was to determine whether cervical ultrasonic attenuation could identify women at risk of spontaneous preterm birth. During pregnancy, women (n = 67) underwent from one to five transvaginal ultrasonic examinations to estimate cervical ultrasonic attenuation and cervical length. Ultrasonic data were obtained with a Zonare ultrasound system with a 5- to 9-MHz endovaginal transducer and processed offline. Cervical ultrasonic attenuation was lower at 17-21 wk of gestation in the SPTB group (1.02 dB/cm-MHz) than in the full-term birth groups (1.34 dB/cm-MHz) (p = 0.04). Cervical length was shorter (3.16 cm) at 22-26 wk in the SPTB group than in the women delivering full term (3.68 cm) (p = 0.004); cervical attenuation was not significantly different at this time point. These findings suggest that low attenuation may be an additional early cervical marker to identify women at risk for SPTB.

Development of an ultrasonic method to detect cervical remodeling in vivo in full-term pregnant women

The objective of this study was to determine whether estimates of ultrasonic attenuation could detect changes in the cervix associated with medically induced cervical remodeling. Thirty-six full-term pregnant women underwent two transvaginal ultrasonic examinations separated in time by 12 h to determine cervical attenuation, cervical length and changes thereof. Ultrasonic attenuation and cervical length data were acquired from a zone (Zonare Medical Systems, Mountain View, CA, USA) ultrasound system using a 5-9 MHz endovaginal probe. Cervical attenuation and cervical length significantly decreased in the 12 h between the pre-cervical ripening time point and 12 h later. The mean cervical attenuation was 1.1 ± 0.4 dB/cm-MHz before cervical ripening agents were used and 0.8 ± 0.4 dB/cm-MHz 12 h later (p < 0.0001). The mean cervical length also decreased from 3.1 ± 0.9 cm before the cervical ripening was administered to 2.0 ± 1.1 cm 12 h later (p < 0.0001). Cervical attenuation and cervical length detected changes in cervical remodeling 12 h after cervical ripening administration.

Use of ultrasonic back-reflection intensity for predicting the onset of crack growth due to low-cycle fatigue in stainless steel under block loading

The present study proposes the use of ultrasonic back-reflected waves for evaluating low cycle fatigue crack growth from persistent slip bands (PSBs) of stainless steel under block loading. Fatigue under high-low block loading changes the back-reflected intensity of the ultrasonic wave that emanates from the surface. Measuring the change in ultrasonic intensity can predict the start of crack growth with reasonable accuracy. The present study also proposes a modified constant cumulative plastic strain method and a PSB damage evolution model to predict the onset of crack growth under block loads.

Elastic and ultrasonic properties of single crystalline nickel nanowires

In the present paper, we have theoretically calculated the non linear elastic constants of single crystalline Ni NWs at very broad temperature range 20-300K validating simple interaction potential model. The temperature dependent ultrasonic attenuation and other related properties are determined using their second and third order elastic constants (SOECs/TOECs). Where possible, the results are compared with experiments from literature. There is a correlation between the thermal conductivity and ultrasonic attenuation in the temperature range 100-300K. Also, a correlation between the resistivity and ultrasonic attenuation in the temperature range 40-100K has been established validating the theoretical approach.

Ultrasonic attenuation in pearlitic steel

Expressions for the attenuation coefficients of longitudinal and transverse ultrasonic waves are developed for steel with pearlitic microstructure. This type of lamellar duplex microstructure influences attenuation because of the lamellar spacing. In addition, longitudinal attenuation measurements were conducted using an unfocused transducer with 10 MHz central frequency on the cross section of a quenched railroad wheel sample. The dependence of longitudinal attenuation on the pearlite microstructure is observed from the changes of longitudinal attenuation from the quenched tread surface to deeper locations. The results show that the attenuation value is lowest and relatively constant within the quench depth, then increases linearly. The experimental results demonstrate a reasonable agreement with results from the theoretical model. Ultrasonic attenuation provides an important non-destructive method to evaluate duplex microstructure within grains which can be implemented for quality control in conjunction with other manufacturing processes.

Interaction of ultrasonic waves with domain walls on nanocrystalline YIG

The nanocrystalline YIG samples with different particle sizes (20-40 nm) has been prepared using microwave-hydrothermal method. As synthesized powders were characterized using XRD and TEM. The powders were pressed and sintered at three different temperatures i.e., 700 °C/30 min, 800 °C/30 min, 900 °C/30 min, using microwave furnace. The sintered samples were characterized using XRD and TEM. The sintered samples are monophasic in nature with average grain size ranging in between 72 nm and 90 nm. The thermal variation of ultrasonic velocities [longitudinal (V(l)) and transverse (V(S))] and longitudinal attenuation (α(l)) has been measured on sintered samples by the pulse transmissionmethod at 1 MHz, in the temperature range of 300-600 K. The room temperature velocity is found to be grain size dependent and decreases with increasing temperature, except near the Curie temperature, T(C), where a small anomaly is observed. The longitudinal attenuation (α(1)) at room temperature is also found to be more sample dependent. The temperature variation of ultrasonic longitudinal attenuation exhibits a sharp maximum just below Curie temperature (T(C)). The above observations were carried on in the demagnetized state, on the application of a saturation field of 380 mT, the anomaly observed in the thermal variation of velocities (longitudinal and transverse) and attenuation is found to disappears. The observed interaction of ultrasonic velocity with domain walls has been qualitatively explained with the help oftemperature variation of magneto-crystalline anisotropy constant (k(1)) and Landau's theory.