Enhancement of Guided Wave Detection and Measurement in Buried Layers of Multilayered Structures Using a New Design of V(z) Acoustic Transducers
Abstract
:1. Introduction
2. Theoretical Considerations and Methods
2.1. Principles of V(z) Signature with Single and Multi-Element Focused Transducers
2.2. V(z) Curve Modelling for Single and Multi-Element Focused Transducers
- is the horizontal component of the wave vector in the coupling fluid;
- is the angular spectrum of the incident field of the piezoelectric source (s) defined at the focal plane (f);
- is the angular spectrum of the transducer response when a plane wave of unit amplitude is emitted from the focal plane (f) to the piezoelectric source (s);
- is the reflection coefficient of the fluid-loaded sample, as a function of the incident wave number component ;
- is the phase shift applied to the spectrum when the surface sample is located at a distance (−z) from the focal plane during defocusing process, where is the vertical component of the wave vector in the coupling fluid, thus given by .
2.3. V(z) Processing and Associated Spectral Representation
3. Results and Comparison
3.1. Transducer and Material Properties
3.2. Detection and Measurement of Guided Waves on the Three-Layer Structure
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
- Rokhlin, S.I.; Huang, W. Ultrasonic wave interaction with a thin anisotropic layer between two anisotropic solids: Exact and asymptotic-boundary-condition methods. J. Acoust. Soc. Am. 1992, 92, 1729–1742. [Google Scholar] [CrossRef]
- Ismaili, N.A.; Chenouni, D.; Lakhliai, Z.; El-Kettani, M.E.C.; Morvan, B.; Izbicki, J.L. Determination of epoxy film parameters in a three-layer metal/adhesive/metal structure. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 2009, 56, 1955–1959. [Google Scholar] [CrossRef] [PubMed]
- Mustapha, S.; Ye, L. Propagation behaviour of guided waves in tapered sandwich structures and debonding identification using time reversal. Wave Motion 2015, 57, 154–170. [Google Scholar] [CrossRef]
- Balvantín, A.J.; Diosdado-De-la-Peña, J.A.; Limon-Leyva, P.A.; Hernández-Rodríguez, E. Study of guided wave propagation on a plate between two solid bodies with imperfect contact conditions. Ultrasonics 2018, 83, 137–145. [Google Scholar] [CrossRef] [PubMed]
- Guo, Z.; Achenbach, J.D.; Madan, A.; Martin, K.; Graham, M.E. Modeling and acoustic microscopy measurements for evaluation of the adhesion between a film and a substrate. Thin Solid Films 2001, 394, 188–200. [Google Scholar] [CrossRef]
- Baltazar, A.; Wang, L.; Xie, B.; Rokhlin, S.I. Inverse ultrasonic determination of imperfect interfaces and bulk properties of a layer between two solids. J. Acoust. Soc. Am. 2003, 114, 1424–1434. [Google Scholar] [CrossRef]
- Boström, A.; Golub, M. Elastic SH wave propagation in a layered anisotropic plate with interface damage modelled by spring boundary conditions. Q. J. Mech. Appl. Math. 2009, 62, 39–52. [Google Scholar] [CrossRef] [Green Version]
- Golub, M. Propagation of elastic waves in layered composites with microdefect concentration zones and their simulation with spring boundary conditions. Acoust. Phys. 2010, 56, 848–855. [Google Scholar] [CrossRef]
- Leiderman, R.; Figueroa, J.C.; Braga, A.M.B.; Rochinha, F.A. Scattering of ultrasonic guided waves by heterogeneous interfaces in elastic multi-layered structures. Wave Motion 2016, 63, 68–82. [Google Scholar] [CrossRef]
- Leiderman, R.; Braga, A.M.B. Scattering of guided waves by defective adhesive bonds in multilayer anisotropic plates. Wave Motion 2017, 74, 93–104. [Google Scholar] [CrossRef]
- Siryabe, E.; Rénier, M.; Meziane, A.; Galy, J.; Castaings, M. Apparent anisotropy of adhesive bonds with weak adhesion and non-destructive evaluation of interfacial properties. Ultrasonics 2017, 79, 34–51. [Google Scholar] [CrossRef] [PubMed]
- Fraisse, P.; Schmit, F.; Zarembowitch, A. Ultrasonic inspection of very thin adhesive layers. J. Appl. Phys. 1992, 72, 3264–3271. [Google Scholar] [CrossRef]
- Xu, P.C.; Lindenschmidt, K.E.; Meguid, S.A. A new high-frequency analysis of coatings using leaky lamb waves. J. Acoust. Soc. Am. 1993, 94, 2954–2962. [Google Scholar] [CrossRef]
- Rogers, J.A.; Dhar, L.; Nelson, K.A. Noncontact determination of transverse isotropic elastic moduli in polyimide thin films using a laser based ultrasonic method. Appl. Phys. Lett. 1994, 65, 312–314. [Google Scholar] [CrossRef]
- Rokhlin, S.I.; Ganor, M.; Degtyar, A.D. Ultrasonic characterization of plasma spray coating. In Review of Progress in Quantitative Nondestructive Evaluation; Springer: New York, NY, USA, 1997; pp. 1585–1591. [Google Scholar] [CrossRef] [Green Version]
- Van de Rostyne, K.; Glorieux, C.; Gao, W.; Gusev, V.; Nesladek, M.; Lauriks, W.; Thoen, J. Investigation of elastic properties of CVD-diamond films using the lowest order flexural leaky lamb wave. Phys. Stat. Sol. A 1999, 172, 105–111. [Google Scholar] [CrossRef]
- Alleyne, D.; Cawley, P. A 2-dimensional Fourier transform method for the measurement of propagating multimode signals. J. Acoust. Soc. Am. 1991, 89, 1159–1168. [Google Scholar] [CrossRef]
- Abbate, A.; Koay, J.; Frankel, J.; Schroeder, S.C.; Das, P. Application of wavelet transform signal processor to ultrasound. Proc. IEEE Ultrason. Symp. 1994, 2, 1147–1152. [Google Scholar] [CrossRef]
- Titov, S.A.; Maev, R.G.; Bogachenkov, A. Measurements of velocity and attenuation of leaky waves using an ultrasonic array. Ultrasonics 2006, 44, 182–187. [Google Scholar] [CrossRef]
- Titov, S.A.; Maev, R.G.; Bogachenkov, A. Lens multielement acoustic microscope in the mode for measuring the parameters of layered objects. Acoust. Phys. 2017, 63, 583–589. [Google Scholar] [CrossRef]
- Titov, S.A.; Maev, R.G. An Ultrasonic Array Technique for Material Characterization of Plate Samples. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 2013, 60, 1435–1445. [Google Scholar] [CrossRef]
- Lemons, R.A.; Quate, C.F. Acoustic microscope. Phys. Acoust. 1979, XIV, 1. [Google Scholar] [CrossRef]
- Kushibiki, J.I.; Chubachi, N. Material characterization by line-focus beam acoustic microscopy. IEEE Trans. Son. Ultrason. 1985, 32, 189–212. [Google Scholar] [CrossRef]
- Nayfeh, H.; Chimenti, D.E. Propagation of guided waves in fluid-coupled plates of fiber-reinforced composite. J. Acoust. Soc. Am. 1988, 83, 1736–1743. [Google Scholar] [CrossRef]
- Nagy, P.B.; Adler, L. Adhesive joint characterization by leaky guided interface waves. In Review of Progress in Quantitative Nondestructive Evaluation; Springer: New York, NY, USA, 1989; pp. 1417–1424. [Google Scholar] [CrossRef] [Green Version]
- Philibert, M.; Yao; Gresil, M.; Soutis, C. Lamb waves-based technologies for structural health monitoring of composite structures for aircraft applications. Eur. J. Mater. 2022, 2, 436–474. [Google Scholar] [CrossRef]
- Gorgin, R.; Luo, Y.; Wu, Z. Environmental and operational conditions effects on Lamb wave based structural health monitoring systems: A review. Ultrasonics 2020, 105, 106114. [Google Scholar] [CrossRef]
- Liu, G.R.; Achenbach, J.D.; Kim, J.O.; Li, Z.I. A combined finite element method/boundary element method technique for V(z) curves of anisotropic-layer/substrate configurations. J. Acoust. Soc. Am. 1992, 92, 2734–2740. [Google Scholar] [CrossRef]
- Lee, Y.C.; Kim, J.O.; Achenbach, J.D. V(z) curves of layered anisotropic materials for the line-focus acoustic microscope. J. Acoust. Soc. Am. 1993, 94, 923–930. [Google Scholar] [CrossRef]
- Achenbach, J.D.; Kim, J.O.; Li, W. Measuring thin-film elastic constants by line-focus acoustic microscopy. Adv. Acoust. Micros. 1995, 129, 153–208. [Google Scholar] [CrossRef]
- Guo, Z.; Achenbach, J.D.; Madan, A.; Martin, K.; Graham, M.E. Integration of modeling and acoustic microscopy measurements for thin films. J. Acoust. Soc. Am. 2000, 107, 2462–2471. [Google Scholar] [CrossRef]
- Lee, Y.C.; Cheng, S.W. Measuring Lamb wave dispersion curves of a bi-layered plate and its application on material characterization of coating. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 2001, 48, 830–837. [Google Scholar] [CrossRef]
- Bourse, G.; Xu, W.J.; Mouftiez, A.; Vandevoorde, L.; Ourak, M. Interfacial adhesion characterization of plasma coatings by V(z) inversion technique and comparison to interfacial indentation. NDT E Int. 2012, 45, 22–31. [Google Scholar] [CrossRef]
- Lematre, M.; Benmehrez, Y.; Bourse, G.; Xu, W.J.; Ourak, M. Acoustic microscopy measurement of elastic constants by using an optimization method on measured and calculated SAW velocities: Effect of initial Cij values on the calculation convergence. NDT E Int. 2002, 35, 279–286. [Google Scholar] [CrossRef]
- Loukkal, A.; Lematre, M.; Bavencoffe, M.; Lethiecq, M. Modeling and numerical study of the influence of imperfect interface properties on the reflectance function for isotropic multilayered structures. Ultrasonics 2020, 103, 106099. [Google Scholar] [CrossRef] [PubMed]
- Vijaya Kumar, R.I.; Bhat, M.R.; Murthy, C.R.I. Some studies on evaluation of degradation in composite adhesive joints using ultrasonic techniques. Ultrasonics 2013, 53, 1150–1162. [Google Scholar] [CrossRef] [PubMed]
Material | Mass Density (kg/m3) | Longitudinal Wave Velocity (m/s) | Transversal Wave Velocity (m/s) | Longitudinal Attenuation (Np/m) | Transverse Attenuation (Np/m) |
---|---|---|---|---|---|
Aluminum | 2740 | 6190 | 3128 | - | - |
Epoxy | 1548 | 2380 | 1400 | 20 | 53 |
Steel | 7850 | 5940 | 3240 | - | - |
Water | 1000 | 1500 | - | - | - |
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Lematre, M.; Lethiecq, M. Enhancement of Guided Wave Detection and Measurement in Buried Layers of Multilayered Structures Using a New Design of V(z) Acoustic Transducers. Acoustics 2022, 4, 996-1012. https://doi.org/10.3390/acoustics4040061
Lematre M, Lethiecq M. Enhancement of Guided Wave Detection and Measurement in Buried Layers of Multilayered Structures Using a New Design of V(z) Acoustic Transducers. Acoustics. 2022; 4(4):996-1012. https://doi.org/10.3390/acoustics4040061
Chicago/Turabian StyleLematre, Michaël, and Marc Lethiecq. 2022. "Enhancement of Guided Wave Detection and Measurement in Buried Layers of Multilayered Structures Using a New Design of V(z) Acoustic Transducers" Acoustics 4, no. 4: 996-1012. https://doi.org/10.3390/acoustics4040061