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Ultrasonic Propagation and Scattering in Pearlitic Steel


Diffuse ultrasonic backscatter measurements have been especially useful for extracting microstructural information and for improving flaw detection in materials. In this dissertation, this approach is applied to inspection of railroad wheels. To improve the wear resistance, the tread surfaces of railroad wheels are usually quenched with  water  to increase the hardness.

The pearlite phase of iron, characterized by alternating ferrite and cementite phases, is created by the quenching and the lamellar spacing within grains increases progressively from the quenched tread surface to deeper locations due to the non-uniform cooling rate. The quench depth is an important parameter governing the wheel performance.

In this dissertation, several aspects of ultrasonic methods are studied. A new singly-scattered response (SSR) model that includes lamellar duplex microstructure within  grains is developed to investigate the dependence of ultrasonic backscatter on such a microstructure in pearlitic wheel steel. An ultrasonic attenuation model is developed to study the influence of pearlite phase on ultrasonic attenuation.

The experimental results show that both ultrasonic scattering amplitudes and longitudinal attenuation drop dramatically near the tread surface of a quenched wheel due to the presence of pearlite. The quench depth is measured by fitting the variance curve from the tread surface with the SSR model that includes the graded lamellar spacing on the propagation path.

A mode-converted (longitudinal-to-transverse, or L-T) SSR model that includes duplex microstructure within grains is also developed to examine the preferred orientation of microstructure in a quenched sample. Finally, the dependence of ultrasonic backscatter on stress is verified by observing the decrease of backscatter amplitudes measured from a 1018 steel block under a uniaxial load.

The experimental results show a trend that is similar to the theoretical prediction. The residual stress in a quenched steel sample is estimated by quantifying the change of  backscatter amplitudes with and without residual stress. Diffuse ultrasonic backscatter techniques exhibit strong sensitivity to duplex microstructure, texture and stress,  outcomes that can be applicable for quality control including microstructure evaluation, measurement of quench depth and residual stress.

An Example Ultrasonic Signal Reflected From a Foreign Object in a Steel Sample.

An Example Ultrasonic Signal Reflected From a Foreign Object in a Steel Sample.


Ultrasonic energy in the form of elastic waves is extensively used for measuring the quality of structural components in the manufacturing process or during service. Applications are comprised of detecting the size of discrete flaws that cause failure (e.g., inclusion or cracks), characterizing the degradation of materials during the service time (e.g., fatigue of aircraft components or embrittlement of pressure vessels in nuclear power plants), monitoring the structural changes of materials that occur during manufacturing processes (e.g., grain size, microstructure and porosity) to provide information to modify the manufacturing process.

Pearlitic Steel:

Pearlite is a two-phase, lamellar (or layered) structure composed of alternating layers of α-ferrite (88 wt%) and cementite (Fe3C, 12 wt%) that occurs in some steels and cast irons. Fig. 2.1 shows a phase diagram of carbon steel.

When an iron-carbon alloy containing eutectoid composition of 0.76 % carbon is heated up to 727◦C (1030◦F, the eutectoid temperature), the structure contains only austenite (γ) phase. The eutectoid reaction begins when the sample temperature cools to 727◦C. The iron-iron carbide eutectoid reaction.

Phase Diagram of Carbon Steel.

Phase Diagram of Carbon Steel.

Attenuation Model:

When an ultrasonic wave propagates in polycrystalline materials, it scatters on grain boundaries due to the relative misorientation of the crystallites. The lost energy due to scattering is typically described in terms of the ultrasonic scattering attenuation, a quantity that can be measured and can serve as a metric to characterize the microstructure of polycrystalline materials. Many previous studies of ultrasonic scattering in polycrystals focused on scattering-induced attenuation as a function of  frequency and microstructure.

Statistical Backscatter Model:

The main focus here is the analysis of the received signals collected in a typical Cscan scan rather than on each waveform by itself to extract the microstructural information of the test sample. Statistical methods are usually used to quantify the diffuse scattering from the heterogeneities to infer microstructural information.

Backscatter Applications:

The developed statistical models are utilized for analyzing the backscatter signals measured by experiments, through which the microstructure, or grain size can be evaluated.

A significant number of experimental backscatter studies have been performed by Thompson and coworkers. Thompson et al. gave a brief review of the classical understanding of how elastic waves are scattered by grain boundaries in randomly oriented polycrystalline materials.

Wheel Inspections:

Flaws in railroad wheels can act as stress concentrators during service, which can result in the initiation of fatigue cracks, and ultimately cause the rim to split from a wheel. Ultrasound inspection techniques are widely used for detecting flaws in railroad wheels. Previous standards for the manufacturing inspection of railroad wheels using ultrasound have been replaced by new standards, for example EN 13262 and RD32.144-2000,  both requiring ultrasonic testing by means of the immersion.


In this chapter, ultrasonic scattering within heterogeneous media is reviewed. The mean and mean square signals from a model source and receiver in a random medium are investigated.

The mean signal or the mean square signal is related to a convolution between the mean Green’s function or Green’s function covariance and the model transducer functions, respectively. The Dyson equation is achieved to describe the mean Green’s function and the Bethe-Salpeter equation results from consideration of the covariance.

 Dyson Equation and the Mean Green’s Function:

The analysis begins with the governing partial differential equation (PDE) for the Green’s function Giα(x,y,t) of an elastic medium with constant material density (set to unity) and modulus that varies randomly in space.

 Bethe-Salpeter Equation and Green’s Function Covariance:

It is not sufficient to calculate the mean response 〈G〉for diffuse field measurements in which signals are squared before averaging.  The Green’s function covariance is defined as 〈Gαβ(x,x′,ω)G∗ij(y,y′,ω+ Ω)〉, in which the asterisk impliesω+ Ω as well as the complex conjugate.

Wigner Transform of a Piston Transducer:

The square of the variance of the signal obtained from a typical ultrasonic C-scan is a typical diffuse ultrasonic result.  In such experiments, the signals are collected at various positions of the transducer and the scattering from the local depth is analyzed to extract the microstructural information by examining the statistics of the signals.


In this chapter, a new singly-scattered model is proposed based on the previous SSR model given by Eq. (3.43) in chapter 3 for application to pearlitic wheel steel. In this case, the material is assumed to have a lamellar duplex microstructure within grains (pearlite phase) so that the dependence of ultrasonic backscatter on the duplex microstructure can be examined.

Model Results:

In this section, trends predicted by the model with respect to the microstructural parameters are examined.  Several parameters given in Eq.(4.13) required for the model must first be specified (including the pulse width σ, the single-crystal elastic constants of steel, the sound speeds in water and steel). Table 4.1 shows some of the values used in the model for the results that follow.


Backscatter Measurements

The tread surface of railroad wheels is typically quenched to improve the hardness and wear resistance. In order to examine the microstructure difference between an unquenched wheel (20 mm thickness) and a quenched wheel (25 mm thickness), eight rectangular regions (15 mm × 5 mm) were scanned.

Cross Section Mapping:

To examine the variation of microstructure, both cross sections of the unquenched
and quenched wheel samples were scanned using a 10 MHz focused transducer (Pana-metrics V327, 2-inch focal length, Olympus Panametrics, Inc., Waltham, MA) focused at a depth of 10 mm.


The increase of lamellar spacing with depth from the tread surface was observed in  chapter 4. The developed SSR model that includes the effects of the lamellar spacing given by Eq.(4.13) is not applicable for the measurement from the tread surface  due to the increase of lamellar spacing on the propagation path.

In  this chapter, the developed SSR model is expanded to include the gradation of lamellar duplex microstructure on the propagation path for application to railroad wheels. The effects of the graded duplex microstructure on ultrasonic scattering are investigated by comparing the spatial variance curve measured from the tread surface with that measured from the cross section.


The dependence of ultrasonic attenuation on the microstructure of materials has been investigated for many years. Attenuation in materials can be caused by both dissipation and scattering. The attenuation by dissipation is attributed to the transformation of energy into heat due to the damping, viscosity, etc. The attenuation induced by scattering is caused by the grain boundaries due to the relative misorientation of the grains. In polycrystalline metals, scattering from grain boundaries is a major source of attenuation.


In chapters 4, 5 and 6, the effects of lamellar duplex microstructure within grains on ultrasonic scattering were studied using the L-L mode in a pulse-echo configuration.  In this chapter, a new mode-converted (longitudinal-to-transverse, L-T) singly scattered response (SSR) model is expanded based on the previous L-T SSR model developed by Hu et al. for application to pearlitic steel.

The effects of lamellar spacing on ultrasonic  scattering are investigated using both the L-L ultrasonic backscatter and the L-T ultrasonic backscatter measured in two different directions,respectively. The experimental results show that the L-T variance amplitudes measured on the cross section of a quenched wheel sample exhibit a large dependence on the measurement direction, a result which is attributed to an angular variation of the effective interaction lengths in different directions.


The theory of acoustoelasticity refers to the relationship between wave propagation speed in a deformable medium and the state of stress present. This relationship considers  the influence of finite strains or wave displacements superimposed on a deformed medium.

Usually, linear-elastic approximations are not adequate to describe material responses in applications experiencing sufficiently large strains. In such cases, the acoustoelastic formalism considers nonlinear strain energy terms up to thethird-order to describe the effect properly.


In this dissertation, diffuse ultrasonic backscatter techniques were used to inspect railroad wheels. A new singly-scattered response (SSR) model that accounted for pearlitic microstructure within grains was developed based on the previous SSR model to evaluate lamellar duplex microstructure.

The spatial variance amplitudes of the collected  ultrasonic backscatter signals captured at many positions dropped dramatically near the tread surface of a quenched wheel due to the creation of the fine pearlite phase during quenching.

The lamellar spacing was estimated using the developed SSR model, and the results showed a good agreement with optical micrograph observations. A graded SSR model was also developed to investigate the effects of the graded duplex microstructure within grains on ultrasonic scattering along the propagation path.

The quench depth was measured accurately by fitting the variance curve measured from the tread surface with the graded SSR model using the least squares error method. In addition, expressions of ultrasonic attenuation in pearlitic steel were developed. The ultrasonic attenuation measured in a pearlitic wheel steel showed a good agreement with theoretical predictions.

The future work will target the limitations and problems as listed above. The objectives of the future theoretical research will focus on the modification of the SSR and  attenuation models by including the different elastic properties of ferrite and cementite phases, and by considering the preferred orientations of duplex microstructure at deeper locations due to the non-uniform cooling rate to make the theoretical predictions match better with the experimental results.

Other methods of simplifying the duplex crystallites within a grain, such as circular plates with varying position dependent diameter dimensions within a grain, will also be applied for comparison with the current simplified approach. The major objectives of the future experimental research will focus on investigating the appropriate frequency range and applying different frequencies to obtain the parameters that define the lamellar spacing.

Then multiple ultrasonic backscatter measurements will be  made to extract the lamellar spacing, the factor M, the correlation length and the residual stress simultaneously using multiple frequencies (7.5 MHz, 10 MHz, 15 MHz and so on) and multiple modes (including L-L, L-T and T-T). In addition, other techniques such as X-ray diffraction or neutron diffraction will be used for measuring residual stress in  quenched steel samples to compare with ultrasonic backscatter measurements.

Source: University of Nebraska-Lincoln
Author: Hualong Du

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