Modeling and Imaging of Ultrasonic Array Inspection of Side Drilled Holes in Layered Anisotropic Media
Abstract
:1. Introduction
2. Background Theory
2.1. Transfer and Stiffness Matrix Method for Multilayer Wave Propagation
2.2. Modeling of the Transducer Gaussian Beams
2.3. Equivalent Homogeneous Anisotropic Properties of a Thick Laminate
2.4. Scattering Coefficient of a SDH
3. Development of a Model to Facilitate Scattering of SDH in a Layered Anisotropic Medium
3.1. Reflection and Transmission Coefficients of Layered Structure Bounded by Anisotropic Media
3.2. Calculation of the Scattering from SDH Embedded in the Medium
3.3. TFM Imaging
3.4. Quantitative Comparison of the Images
- Simulate the response from the embedded scatterer and calculate the peak amplitude of the scatterer.
- Simulate the response of the laminate without the scatterer and calculate the root mean square of the amplitudes of the signal in a chosen region around the scatterer, which is the “noise” of the image.
- Use Equation (57) to calculate the SNR of the SDH. The same procedure is carried out for the experimental TFM image, wherein the laminate FMC signals are processed before and after the SDH has been drilled into the laminate.
4. Simulation and Results
4.1. Calculation of Equivalent Homogeneous Properties
4.2. SDH Embedded in Aluminum Inspected by a 2.25 and 5 MHz Array
4.3. SDH Embedded in CFRP Inspected by Arrays with Center Frequencies of 2.25 and 5 MHz
5. Discussion
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Conflicts of Interest
References
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Centre Frequency (MHz) | Pitch (mm) | Number of Elements | |
---|---|---|---|
Array 1 | 2.25 | 1 | 64 |
Array 2 | 5 | 0.6 | 16 |
Properties | Aluminum (GPa) | Carbon/Epoxy >65% Fiber-Volume Fraction (GPa) |
---|---|---|
C11 | 110 | 13.89(1+0.02i) |
C22 | 110 | 13.89(1+0.02i) |
C33 | 110 | 121.7(1+0.001i) |
C12=C21 | 60 | 6.43(1+0.011i) |
C13=C31 | 60 | 5.5(1+0.007i) |
C23=C32 | 60 | 5.5(1+0.007i) |
C44 | 25 | 5.1(1+0.066i) |
C55 | 25 | 5.1(1+0.066i) |
C66 | 25 | 3.73(1+0.027i) |
Properties | Values in GPa |
---|---|
54.76(1+0.002i) | |
54.76(1+0.002i) | |
13.89(1+0.02i) | |
18.53(1+0.01i) | |
5.96(1+0.004i) | |
5.96(1+0.005i) | |
4.3(1+0.06i) | |
4.3(1+0.06i) | |
18.12(1+0.03i) |
Central Frequency of Array | SNR of SDH in Simulated Image | SNR of SDH in Experimental Image | Difference |
---|---|---|---|
2.25 MHz | −42.9 dB | −39.5 dB | −3.4 dB |
5 MHz | −26.1 dB | −33.4 dB | −7.3 dB |
Central Frequency of Array | SNR of SDH in Simulated Image | SNR of SDH in Experimental Image | Difference |
---|---|---|---|
2.25 MHz | −42.9 dB | −25.6 dB | −17.3 dB |
5 MHz | −35.48 dB | −21 dB | −14.48 dB |
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Anand, C.; Groves, R.M.; Benedictus, R. Modeling and Imaging of Ultrasonic Array Inspection of Side Drilled Holes in Layered Anisotropic Media. Sensors 2021, 21, 4640. https://doi.org/10.3390/s21144640
Anand C, Groves RM, Benedictus R. Modeling and Imaging of Ultrasonic Array Inspection of Side Drilled Holes in Layered Anisotropic Media. Sensors. 2021; 21(14):4640. https://doi.org/10.3390/s21144640
Chicago/Turabian StyleAnand, Chirag, Roger M. Groves, and Rinze Benedictus. 2021. "Modeling and Imaging of Ultrasonic Array Inspection of Side Drilled Holes in Layered Anisotropic Media" Sensors 21, no. 14: 4640. https://doi.org/10.3390/s21144640
APA StyleAnand, C., Groves, R. M., & Benedictus, R. (2021). Modeling and Imaging of Ultrasonic Array Inspection of Side Drilled Holes in Layered Anisotropic Media. Sensors, 21(14), 4640. https://doi.org/10.3390/s21144640