Elsevier

Ultrasonics

Volume 54, Issue 6, August 2014, Pages 1470-1475
Ultrasonics

Air-coupled detection of nonlinear Rayleigh surface waves to assess material nonlinearity

https://doi.org/10.1016/j.ultras.2014.04.020Get rights and content

Highlights

  • An air coupled transducer is used to detect nonlinear Rayleigh waves.

  • This technique is highly repeatable, robust, accurate with a high SNR.

  • The technique is validated with measurements on aluminum 7075 and 2024 samples.

  • The results are consistent with published data obtained with capacitive detection.

Abstract

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.

Introduction

An ultrasonic wave propagating in an elastic material generates higher harmonics through its interaction with various sources of nonlinearity in a material. The non-dimensional acoustic nonlinearity parameter, β relates the amplitudes of the fundamental and second harmonic waves, providing information on the microstructure of a material. The acoustic nonlinearity parameter has proven to be sensitive to certain microstructural changes such as those due to precipitation [1], creep [2], fatigue [3], thermal [4] or radiation damage [5], and is therefore a powerful indicator of the material state.

The most commonly used nonlinear wave technique uses through-transmitted longitudinal waves, which is often difficult to apply in the field since access to both sides of the specimen is required. Rayleigh surface waves have the advantage, as compared to longitudinal waves, that they require access to only one side of a component. In addition, diffraction and attenuation effects are smaller, and Rayleigh surface waves travel a long distance without a significant loss of acoustic energy. Most importantly, it is possible to effectively isolate the material contribution in the measured second harmonic component by varying the propagation distance; here the unwanted nonlinearity from the measurement system will remain constant (or decrease), while the material nonlinearity will increase with increasing propagation distance. These features make Rayleigh waves an efficient method for measuring the material nonlinearity and thus this technique can be used for the nondestructive, in situ surveillance of complex components.

Experimental setups that employ wedge transducers for both transmission and detection have been used [6], [7], [4] to perform nonlinear Rayleigh surface wave measurements. However, these have shown to be time consuming and can suffer from large variations due to the inconsistent contact conditions at the wedge-specimen interface. These circumstances lead to opportunities for measurement improvements, and non-contact methods can potentially make nonlinear Rayleigh wave measurements more flexible, less time consuming, and more accurate. A Michelson interferometer detection setup to perform nonlinear Rayleigh wave measurements was used by Hurley and Fortunko [8], which had the advantage of having a broadband response and simple calibration, and made absolute displacement measurements. Herrmann et al. [9] used a heterodyne laser interferometer detection setup for nonlinear Rayleigh wave measurements. However, the laser based detection of ultrasonic waves suffers from variations in optical reflectivity of the specimen surface and is only feasible for specimens with highly reflective surfaces. A recent study of Cobb et al. [10] makes use of electromagnetic acoustic transducers (EMATs) to perform fully non-contact nonlinear Rayleigh wave measurements, but they did not achieve the desired consistency.

The objective of the current research is to explore the feasibility of a non-contact, air-coupled detection technique to assess the acoustic nonlinearity parameter using Rayleigh surface waves. In principle, the assessment of the absolute acoustic nonlinearity parameter, β is possible using Rayleigh surface waves by making a series of electroacoustic calibrations and diffraction corrections. However, for the purpose of demonstrating the efficiency of using air-coupled detection, this study considers a relative acoustic nonlinearity parameter β and compares the relative nonlinearities between two different specimens when all other experimental parameters are kept constant.

Section snippets

Theoretical Background

Consider a Rayleigh wave propagating in the x direction, where the z direction is pointing out of the half-space. The displacement field ui(ω0) of the fundamental wave is given byux(ω0)=A1eb1z-2b1b2kR2+b22eb2zexp[ikR(x-cRt)],uz(ω0)=iA1b1kReb1z-2kR2kR2+b22eb2zexp[ikR(x-cRt)],where b12=kR2-kL2 and b22=kR2-kT2. Note that kR,kL, and kT denote the wavenumber of the Rayleigh surface wave, the longitudinal wave and the shear wave in the material.

As shown by Herrmann et al. [9], the displacement field u

Experimental setup using air-coupled receiver

A function generator is used (see Fig. 1) to obtain a sinusoidal signal at the excitation frequency of 2.1 MHz with a peak to peak voltage of 800 mV. The source signal consists of 20 cycles, and provides a sufficiently long steady-state portion, which is important for the subsequent signal processing. The internal trigger of the function generator is used to synchronize the source with the RITEC amplifier and the oscilloscope. The desired high-voltage excitation signal for the generating

Specimen preparation

An aluminum 2024-T351 plate and an aluminum 7075-T651 plate, both 25.4 mm thick are used to demonstrate the accuracy of the proposed non-contact air-coupled Rayleigh wave measurements since there are results available for comparison in the published literature. The Al 2024-T351 plate is heat treated at 325 °C for three hours and air cooled in an uncontrolled atmosphere to reduce the influence of cold work associated with the T351 tempering process. Note that the Al 7075-T651 alloy is solution

Results and discussion

Nonlinear Rayleigh surface wave measurements along the rolling direction of the Al 2024-T351 and Al 7075-T651 plates are performed with the proposed setup. The standard deviation of the linear fit to the normalized second harmonic A2el/(A1el)2 over the propagation distance is calculated to be below 2% for three different sets of measurements in which the generating wedge transducer is removed and reattached for each measurement set. This shows that the measurement based on the non-contact

Conclusions

This research demonstrates the robustness and high accuracy of using a non-contact, air-coupled receiver for the measurement of the acoustic nonlinearity parameter with Rayleigh surface waves. The experimental setup provides an output signal with sufficiently high SNR and potential experimental inconsistencies due to the coupling variability of the generating wedge transducer are shown to be negligible. An additional advantage is that the surface condition of the specimen is relatively

Acknowledgements

This work is supported by the German Academic Exchange Service (DAAD) through a Graduate Research Assistantship for Sebastian Thiele and is being performed using funding received from the DOE Office of Nuclear Energy’s Nuclear Energy University Programs. Additional funding has been provided by the Electric Power Research Institute (EPRI).

References (16)

  • J.S. Valluri et al.

    Acta Mater.

    (2010)
  • A. Ruiz et al.

    NDT&E Int.

    (2013)
  • S.V. Walker et al.

    NDT&E Int.

    (2012)
  • M. Liu et al.

    NDT&E Int.

    (2011)
  • M.O. Deighton et al.

    Ultrasonics

    (1981)
  • J.H. Cantrell et al.

    J. Appl. Phys.

    (1997)
  • J.-Y. Kim et al.

    J. Acoust. Soc. Am.

    (2006)
  • K.H. Matlack et al.

    J. Appl. Phys.

    (2012)
There are more references available in the full text version of this article.

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