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The quantitative non-destructive evaluation (NDE) of interface adhesion has long been a challenge for the safe use of bonding structures. It is difficult to predict the adhesion resistance force between adhesive and adhered material without performing destructive testing. Ultrasonic approach seems to be the only potential way for its NDE based on the reason of mechanical nature of the problem. Different ultrasonic techniques, such as bulk wave echography, reflection resonance, and Lamb guided waves, have been used to evaluate the interface adhesion strength. But no direct relation between the interfacial bonding strength and the ultrasonic measurement has been established. The most used compression wave echography and resonance at normal incidence are less sensitive to the interface condition, except for a disbond. It is essential that the interface should be excited with a shear stress component to increase the measurement sensibility. But it is not easy to excite the interface by using shear waves in experiment, while the use of guided waves will encounter the problems of high attenuation and mode selection as all modes are not sensitive to a certain interface in a bonded structure. A previous study has shown that the V (z) inversion technique can be used to perform a multimode measurement on a layered structure, where both compression and shear stress resonance occur. This method has the advantage in using a simple experimental setup working at the normal incidence with a focus transducer of large angular aperture. The inversed angular-frequency reflectance function R(; f) gives the resonance modes which are equivalent to the Lamb type guided modes, while it is a local determination of the wave mode, thus the difficulty in guided wave measurement above mentioned can be avoided. The first part of the paper contains the development of the theoretical model for wave propagation in a multilayered structure where three-layer sandwich bonded structures can be considered as a particular case. A weak interfacial adhesion is described by two interface compression and shear stiffness parameters, namely km and kt. By integrating the transfer matrix formalism under the non-ideal boundary conditions, the plane wave angular (incident angle) and frequency reflection coefficient function R(; f) for a liquid immersed asymmetric metal-adhesive-metal three-layer and its dispersion curves of guided mode waves with or without charge are calculated. It is confirmed that the evolutions of the reflection zeros (mode resonances) correspond to the dispersion curves of the guided waves of the same structure without charge. Furthermore, the resonance modes observed in R(; f) can be considered as a combination of the respective Lamb modes of the top and bottom single metal layers coupled through the modes conditioned by the middle adhesive layer and the its interface conditions. The second part of the paper shows the behaviors of the resonance modes by changing the parameters related to the bonding strength. The acoustical impedance, the mass density and the thickness of the adhesive layer, which are related to the cohesive property, and the shear interfacial stiffness coefficient kt which conditions the adhesive property, are changed respectively to observe the resonance mode evolutions. The mode evolutions due to each parameter are analyzed and differentiated. It can be concluded that the change in the adhesion strength of the bonding structure does not affect significantly the modes belonging to those inherent to the two adhered aluminum layers, while the coupling modes will be shifted in frequency and exchange with or replace the said inherent modes. It is expected that the obtained results in this study will be of significance for quantitatively characterizing the interfacial properties of an adhesively bonded layered structure by using the V (z) inversion technique.
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Keywords:
- bonding structure /
- interface adhesion /
- acoustic reflection resonance function /
- mode dispersion
[1] Maeva E, Severina I, Bondarenko S, Chapman G, O'Neill B, Severin F, Maev R G 2004 Can. J. Phys. 82 981
[2] Li M X 2009 10000 Selected Problems in Sciences: Physics (Beijing: Science Press) p356 (in Chinese) [李明轩 2009 10000个科学难题 物理学卷 (北京: 科学出版社) 第356页]
[3] Awaja F, Gilbert M, Kelly G, Fox B, Pigram P J 2009 Prog. Polym. Sci. 34 948
[4] Baik J M, Thompson R B 1984 J. Nondestr. Eval. 4 177
[5] Titov S A, Maev R G, Bogachenkov A N 2008 Ultrasonics 48 537
[6] Zhou H M, Liu G W 2012 Measurement 45 1414
[7] Pilarski A, Rose J L 1988 J. Appl. Phys. 63 300
[8] Pilarski A, Rose J L 1988 NDT International 21 241
[9] Vine K, Cawley P, Kinloch A J 2002 NDT & E Int. 35 241
[10] Drinkwater B, Cawley P 1997 Ultrasonics 35 479
[11] Baltazar A, Wang L, Xie B, Rokhlin S I 2003 J. Acoust. Soc. Am. 114 1424
[12] Leiderman R, Braga A M B, Barbone P E 2005 J. Acoust. Soc. Am. 118 2154
[13] Belloncle V V, Rousseau M, Terrien N 2007 NDT & E Int. 40 419
[14] Akker S, Arman J 1997 Ultrasonics 35 287
[15] Pilarski A, Rose J L 1992 J. Nondestr. Eval. 11 237
[16] Singher L, Segal Y, Segal E, Shamir J 1994 J. Acoust. Soc. Am. 96 2497
[17] Xu P C, Datta S K 1990 J. Appl. Phys. 67 6779
[18] Karpur P, Kundu T, Ditri J J 1999 Review of Progress in Quantitative Nondestructive Evaluation (Vol. 18A-18B) (NewYork: Springer US) 18 pp1533-1542
[19] Castaings M 2014 Ultrasonics 54 1760
[20] Ren B, Lissenden C J 2013 Int. J. Adhes. Adhes. 45 59
[21] Gao G J, Deng M X, Li M L, Liu C 2015 Acta Phys. Sin. 64 224301 (in Chinese) [高广健, 邓明晰, 李明亮, 刘畅 2015 物理学报 64 224301]
[22] Zhang R, Wan M X, Cao W W 2000 Acta Phys. Sin. 49 1297 (in Chinese) [张锐, 万明习, Cao Wen-Wu 2000 物理学报 49 1297]
[23] Vinh P C, Giang P T H 2011 Wave Motion 48 647
[24] Bar-Cohen Y, Mal A K, Lih S S 1993 Materials Evaluation 51 1285
[25] Rokhlin S I, Wang W 1989 J. Acoust. Soc. Am. 86 1876
[26] Liang K K, Kino G S, Khuri-Yakub B T 1985 IEEE Trans. Sonics. Ultrason. 32 213
[27] X W J, Ourak M 1997 NDT & E Int. 30 75
[28] X W J, Ourak M, Lematre M, Bourse G 2000 AIP Conference Proceedings Montreal, Canada, July 25-30, 1999 p1183
[29] Bourse G, X W J, Mouftiez A, Vandevoorde L, Ourak M 2012 NDT {& E Int. 45 22
[30] Liu J, Xu W J, Hu W X, Ourak M, Dubois A 2015 Chin. Phys. Lett. 32 124303
[31] Thomson W T 1950 J. Appl. Phys. 21 89
[32] Lowe M J S 1995 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 42 525
[33] Rokhlin S I, Wang Y J 1991 J. Acoust. Soc. Am. 89 503
[34] Rokhlin S I, Wang L 2002 J. Acoust. Soc. Am. 112 822
[35] Chimenti D E, Rokhlin S I 1990 J. Acoust. Soc. Am. 88 1603
[36] Crom B L, Castaings M 2010 J. Acoust. Soc. Am. 127 2220
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[1] Maeva E, Severina I, Bondarenko S, Chapman G, O'Neill B, Severin F, Maev R G 2004 Can. J. Phys. 82 981
[2] Li M X 2009 10000 Selected Problems in Sciences: Physics (Beijing: Science Press) p356 (in Chinese) [李明轩 2009 10000个科学难题 物理学卷 (北京: 科学出版社) 第356页]
[3] Awaja F, Gilbert M, Kelly G, Fox B, Pigram P J 2009 Prog. Polym. Sci. 34 948
[4] Baik J M, Thompson R B 1984 J. Nondestr. Eval. 4 177
[5] Titov S A, Maev R G, Bogachenkov A N 2008 Ultrasonics 48 537
[6] Zhou H M, Liu G W 2012 Measurement 45 1414
[7] Pilarski A, Rose J L 1988 J. Appl. Phys. 63 300
[8] Pilarski A, Rose J L 1988 NDT International 21 241
[9] Vine K, Cawley P, Kinloch A J 2002 NDT & E Int. 35 241
[10] Drinkwater B, Cawley P 1997 Ultrasonics 35 479
[11] Baltazar A, Wang L, Xie B, Rokhlin S I 2003 J. Acoust. Soc. Am. 114 1424
[12] Leiderman R, Braga A M B, Barbone P E 2005 J. Acoust. Soc. Am. 118 2154
[13] Belloncle V V, Rousseau M, Terrien N 2007 NDT & E Int. 40 419
[14] Akker S, Arman J 1997 Ultrasonics 35 287
[15] Pilarski A, Rose J L 1992 J. Nondestr. Eval. 11 237
[16] Singher L, Segal Y, Segal E, Shamir J 1994 J. Acoust. Soc. Am. 96 2497
[17] Xu P C, Datta S K 1990 J. Appl. Phys. 67 6779
[18] Karpur P, Kundu T, Ditri J J 1999 Review of Progress in Quantitative Nondestructive Evaluation (Vol. 18A-18B) (NewYork: Springer US) 18 pp1533-1542
[19] Castaings M 2014 Ultrasonics 54 1760
[20] Ren B, Lissenden C J 2013 Int. J. Adhes. Adhes. 45 59
[21] Gao G J, Deng M X, Li M L, Liu C 2015 Acta Phys. Sin. 64 224301 (in Chinese) [高广健, 邓明晰, 李明亮, 刘畅 2015 物理学报 64 224301]
[22] Zhang R, Wan M X, Cao W W 2000 Acta Phys. Sin. 49 1297 (in Chinese) [张锐, 万明习, Cao Wen-Wu 2000 物理学报 49 1297]
[23] Vinh P C, Giang P T H 2011 Wave Motion 48 647
[24] Bar-Cohen Y, Mal A K, Lih S S 1993 Materials Evaluation 51 1285
[25] Rokhlin S I, Wang W 1989 J. Acoust. Soc. Am. 86 1876
[26] Liang K K, Kino G S, Khuri-Yakub B T 1985 IEEE Trans. Sonics. Ultrason. 32 213
[27] X W J, Ourak M 1997 NDT & E Int. 30 75
[28] X W J, Ourak M, Lematre M, Bourse G 2000 AIP Conference Proceedings Montreal, Canada, July 25-30, 1999 p1183
[29] Bourse G, X W J, Mouftiez A, Vandevoorde L, Ourak M 2012 NDT {& E Int. 45 22
[30] Liu J, Xu W J, Hu W X, Ourak M, Dubois A 2015 Chin. Phys. Lett. 32 124303
[31] Thomson W T 1950 J. Appl. Phys. 21 89
[32] Lowe M J S 1995 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 42 525
[33] Rokhlin S I, Wang Y J 1991 J. Acoust. Soc. Am. 89 503
[34] Rokhlin S I, Wang L 2002 J. Acoust. Soc. Am. 112 822
[35] Chimenti D E, Rokhlin S I 1990 J. Acoust. Soc. Am. 88 1603
[36] Crom B L, Castaings M 2010 J. Acoust. Soc. Am. 127 2220
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