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3.3.6 Nondestructive Determination of Residual Stress Using Electromagnetic-Acoustic Transducer

Kevin J. Coakley

Statistical Engineering Division, ITL

A.V. Clark

Materials Reliability Division, MSEL

Due to residual stress in a material, the velocity of sound depends on polarization state. Since the different polarization states travel at different velocities, interference occurs. As the propagation direction is varied relative to the polarization axes, the amplitude and phase of the transmitted wave varies. This is acoustic birefringence. Based on Electromagnetic-Acoustic transducer (EMAT) measurements of acoustic birefringence, stress can be determined.

In the experiment, the acoustic transducer is rotated. A sinusoidal signal enters the material and splits into two orthogonal polarization states. One state has a slow velocity of propagation. The other a fast velocity of propagation. In the ideal case, the measured signal is modeled as

\begin{eqnarray*}s(t_z,z) ~=~ A \cos ( k_s z - \omega t_z + \phi ) ~+~ B \cos (
k_f z - \omega t_z + \phi ) \end{eqnarray*}

where $A~=~ r \cos^2 ( \eta ) $and $B~=~ r \sin ^2 ( \eta ) $. Above, $\eta$ is the orientation of the slow velocity direction and the direction of the transducer. The transit time is tz and the pathlength is z. Let s =  Re( w )

where w is complex. We have

\begin{eqnarray*}w = A \exp( i
\theta _ 1 ) + B \exp( i \theta _ 2 ) \end{eqnarray*}


\begin{eqnarray*}\theta _ 1 = ( k_s z - \omega t_z + \phi )


\begin{eqnarray*}\theta _ 2 = ( k_f z - \omega t_z + \phi ) \end{eqnarray*}

The amplitude and phase of w are

\begin{eqnarray*}\vert w\vert = \sqrt{ A ^2 + B ^2
+ 2AB \cos( \theta_1 - \theta _ 2 ) } \end{eqnarray*}


\begin{eqnarray*}PHASE(w) ~=~ ATAN( { Im(w) }, { Re(w) } ) ~=~ ATAN( { A \sin \t...
...+ B
\sin \theta_2 } , { A \cos \theta _ 1 + B \cos \theta_2 } )

We developed statistical models to estimate ks and kffrom measured phase and amplitude. The model accounts for angle dependent effects due to material inhomogeneity and differential attenuation of the two polarization modes. A computer code for fitting the models to the data was developed for online data processing.

SED assisted in planning a study to compare EMAT and strain gauge measurements of stress. In the comparison study, ultrasound measurements will be made at many locations. However, strain gauge measurements will be made at just a few of these locations. We plan to compare ultrasound estimates with interpolated values of the strain gauge estimates. We developed a preliminary statistical model to predict the variance of the interpolated stress (from strain gauge measurements). Associated standard errors are also predicted.


Figure 19: Amplitude and phase of acoustic echo is measured as the transducer rotates with respect to polarization axes. Predicted amplitude and phase is based on a model which accounts for material inhomogeneity and differential attenuation in steel.

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Date created: 7/20/2001
Last updated: 7/20/2001
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