# Anisotropy Corrected FMC/TFM Based Phased Array Ultrasonic Imaging in an Austenitic Buttering Layer
## 4 Results and Discussion
### Angle Dependent Ultrasonic Velocity  
In order to validate the phased array TT method for angle-dependent velocity measurement, the method was first applied to a ferrite steel specimen. Then, the same method was adapted to measure angle dependent ultrasonic velocities in the buttering material. Ultrasonic velocity measured using the TT method in the ferritic steel and the buttering layer specimens is shown in Figure 5a,b, respectively. Ultrasonic velocities measured for all 64 transmission and 64 reception conditions, i.e., 64 \(\times\) 64 velocity values, are shown in Figure 5a,b. For the ferritic steel specimen of thickness \(\sim\)19.27 mm and 63 mm total aperture of the transducer, velocity values for angles in the range of \(\pm\)73\({}^{\circ}\) are obtained. Similarly, for the buttering layer specimen of \(\sim\)23.38 mm thickness, velocity values for angles in the range of \(\pm\)68\({}^{\circ}\) are obtained. Figure 4: EBSD images and grain orientation: (**a**) schematic of the sample extracted for the EBSD study and EBSD image location in the buttering layer, (**b**) image quality map, and (**c**-**e**) inverse pole figure (IPF) maps corresponding to the buttering thickness, circumferential and radial directions, respectively. Figure 5: Variations in ultrasonic longitudinal wave velocity with the angle from the surface normal for: (**a**) the ferritic steel; (**b**) the buttering layer. The maximum variation in the average ultrasonic velocity with the angle in the ferritic steel specimen is observed to be within about 40 m/s (Figure 5a). However, about 600 m/s variation in the average ultrasonic velocity is observed in the buttering layer (Figure 5b). The average ultrasonic velocity is observed to be minimum (\(\sim\)5650 m/s) at an angle close to 0\({}^{\circ}\), i.e., close to the buttering thickness direction (perpendicular to the buttering layer-10 Cr steel interface). Further, the variation in ultrasonic velocity with angle is observed to be almost symmetrical about the vertical plane, i.e., the radial-thickness plane of the buttering. Alloy 617 buttering is a single-phase face-centered cubic (FCC) structure. In an FCC single crystal, the minimum and maximum ultrasonic velocities are expected to be along \(<\)100\(>\) and \(<\)111\(>\) directions, respectively, with an intermediate value in the \(<\)110\(>\) direction [6]. The minimum ultrasonic velocity observed in the direction close to the buttering thickness direction (perpendicular to the interface) is in line with the grain orientation observed by EBSD. Further, a notable variation in ultrasonic velocity is not expected in the depth direction of the buttering layer due to similar grain orientations at different depths. The variation in ultrasonic velocity with the angle from the buttering thickness direction could be fitted with a sixth-order polynomial as shown by the solid black line in Figure 4b:  
\[V_{\rm 6 th}(\theta)=5652-5.075\theta+0.567\theta^{2}+0.00369\theta^{3}-1.64 \times 10^{-4}\theta^{4}-5.069\times 10^{-7}\theta^{5}+1.266\times 10^{-8} \theta^{6} \tag{3}\]  
where \(\theta\) (in degree) is the angle of the beam propagation direction from the buttering thickness direction in the circumference-thickness plane, and \(V_{\rm 6 th}(\theta)\) is the angle dependent velocity in m/s. Further, the velocity profile in the buttering layer in the range of \(\pm\)68\({}^{\circ}\) resembles a sine curve (shown by the dashed black line in Figure 5b), and hence it has also been approximated by a simple equation as given below:  
\[V_{\rm sine}(\theta)=5960+300\times\sin(3.75^{\circ}(\theta-28)) \tag{4}\]  
It is to be noted that extrapolations of Equations (3) and (4) beyond \(\pm\)68\({}^{\circ}\) will not provide correct ultrasonic velocities, as ultrasonic velocities at \(\pm\)90\({}^{\circ}\) should be higher than that at 0\({}^{\circ}\) due to \(<\)110\(>\) orientation at 90\({}^{\circ}\) and \(<\)100\(>\) orientation at 0\({}^{\circ}\).