Effective spring boundary conditions modelling wave scattering by an interface with a random distribution of aligned interface rectangular cracks. (English) Zbl 1473.74074
Summary: In the present study frequency-dependent effective spring boundary conditions are introduced to describe wave propagation through an interface between two elastic isotropic media with a distribution of rectangular aligned micro-cracks. The explicit analytic formulae are obtained for stiffnesses in effective spring boundary conditions modelling the distribution of rectangular cracks employing the boundary integral equation method, the ensemble averaging technique and Boström-Wickham approach. Three diagonal components of the introduced stiffness matrix are expressed in terms of the elastic properties of materials, the frequency, and dimensions of rectangular cracks. The analysis of the derived relations for stiffnesses shows the low influence of density on stiffnesses. If the area of rectangular cracks is constant, but the elongation of rectangular cracks increases then stiffnesses become larger. On the other hand, stiffnesses get smaller if one side is constant and the second side of rectangular crack increases. Examples demonstrating the influence of material properties and the elongation of rectangular cracks on three components of the stiffness matrix are provided. Effective stiffnesses for the distribution of square cracks are nearly proportional to the corresponding stiffnesses obtained for the distribution of circular cracks.
MSC:
| 74J20 | Wave scattering in solid mechanics |
| 74R10 | Brittle fracture |
| 74S60 | Stochastic and other probabilistic methods applied to problems in solid mechanics |
| 74S15 | Boundary element methods applied to problems in solid mechanics |
Keywords:
imperfect contact; distributed spring; stiffness; adhesive zone; delamination; boundary integral equation method; ensemble averaging techniqueReferences:
| [1] | Achenbach, J. D.; Li, Z. L., Reflection and transmission of scalar waves by a periodic array of screens, Wave Motion, 8, 225-234 (1986) · Zbl 0581.73030 |
| [2] | Baik, J. M.; Thompson, R. B., Ultrasonic scattering from imperfect interfaces: A quasi-static model, J. Nondestruct. Eval., 4, 177-196 (1984) |
| [3] | Baltazar, A.; Rokhlin, S. I.; Pecorrari, C., On the relationship between ultrasonic and micromechanical properties of contacting rough surfaces, J. Mech. Phys. Solids, 50, 1397-1416 (2002) · Zbl 1071.74663 |
| [4] | Balvantin, A.; Diosdado-De-la Pena, J.; Limon-Leyva, P.; Hernandez-Rodriguez, E., Study of guided wave propagation on a plate between two solid bodies with imperfect contact conditions, Ultrasonics, 63, 137-145 (2018) |
| [5] | Boström, A.; Golub, M. V., Elastic SH wave propagation in a layered anisotropic plate with interface damage modelled by spring boundary conditions, Q. J. Mech. Appl. Math., 62, 39-52 (2009) · Zbl 1156.74339 |
| [6] | Boström, A.; Wickham, G. R., On the boundary conditions for ultrasonic transmission by partially closed cracks, J. Nondestruct. Eval., 10, 139-149 (1991) |
| [7] | Castaings, M., SH ultrasonic guided waves for the evaluation of interfacial adhesion, Ultrasonics, 54, 1760-1775 (2014) |
| [8] | Esmaeel, R.; Taheri, F., Delamination detection in laminated composite beams using the empirical mode decomposition energy damage index, Compos. Struct., 94, 1515-1523 (2012) |
| [9] | Glushkov, E. V., Energy distribution of a surface source in an inhomogeneous half-space, J. Appl. Math. Mech., 47, 70-75 (1984) · Zbl 0526.73019 |
| [10] | Glushkov, Y. V.; Glushkova, N. V., Diffraction of elastic waves by three-dimensional cracks of arbitrary shape in a plane, J. Appl. Math. Mech., 60, 277-283 (1996) · Zbl 0883.73023 |
| [11] | Glushkov, E. V.; Glushkova, N. V.; Ekhlakov, A. V., A mathematical model of the ultrasonic detection of three-dimensional cracks, J. Appl. Math. Mech., 66, 141-149 (2002) · Zbl 1150.74593 |
| [12] | Golub, M. V.; Boström, A., Interface damage modelled by spring boundary conditions for in-plane elastic waves, Wave Motion, 48, 2, 105-115 (2011) · Zbl 1283.74049 |
| [13] | Golub, M. V.; Doroshenko, O. V., Boundary integral equation method for simulation scattering of elastic waves obliquely incident to a doubly periodic array of interface delaminations, J. Comput. Phys., 376, 675-693 (2019) · Zbl 1416.65490 |
| [14] | Golub, M. V.; Doroshenko, O. V., Effective spring boundary conditions for modelling wave transmission through a composite with a random distribution of interface circular cracks, Int. J. Solids Struct., 165, 115-126 (2019) |
| [15] | Golub, M. V.; Doroshenko, O. V., Wave propagation through an interface between dissimilar media with a doubly periodic array of arbitrary shaped planar delaminations, Math. Mech. Solids, 24, 483-498 (2019) · Zbl 1447.74022 |
| [16] | Golub, M. V.; Doroshenko, O. V.; Boström, A., Effective spring boundary conditions for a damaged interface between dissimilar media in three-dimensional case, Int. J. Solids Struct., 81, 141-150 (2016) |
| [17] | Grinchenko, V. T.; Meleshko, V. V., Harmonic Vibrations and Waves in Elastic Bodies (1981), Naukova Dumka: Naukova Dumka Kiev · Zbl 0499.73018 |
| [18] | Ishii, Y.; Biwa, S.; Adachi, T., Second-harmonic generation in a multilayered structure with nonlinear spring-type interfaces embedded between two semi-infinite media, Wave Motion, 76, 28-41 (2018) · Zbl 1524.35619 |
| [19] | Kurt, I.; Akbarov, S. D.; Sezer, S., Lamb wave dispersion in a PZT/metal/PZT sandwich plate with imperfect interface, Waves Random Complex Media, 26, 301-327 (2016) · Zbl 1366.35179 |
| [20] | Lakes, R.; Lee, T.; Bersie, A.; Wang, Y., Extreme damping in composite materials with negative stiffness inclusions, Nature, 410, 565-567 (2001) |
| [21] | Leiderman, R.; Braga, A., Scattering of guided waves by defective adhesive bonds in multilayer anisotropic plates, Wave Motion, 74, 93-104 (2017) · Zbl 1524.74258 |
| [22] | Lekesiz, H.; Katsube, N.; Rokhlin, S. I.; Seghi, R. R., Effective spring stiffness for a planar periodic array of collinear cracks at an interface between two dissimilar isotropic materials, Mech. Mater., 43, 87-98 (2011) |
| [23] | Lekesiz, H.; Katsube, N.; Rokhlin, S. I.; Seghi, R. R., Effective spring stiffness for a periodic array of interacting coplanar penny-shaped cracks at an interface between two dissimilar isotropic materials, Int. J. Solids Struct., 50, 2817-2828 (2013) |
| [24] | Li, S.; Wang, G.; Morgan, E., Effective elastic moduli of two dimensional solids with distributedcohesive microcracks, Eur. J. Mech. A Solids, 23, 925-933 (2004) · Zbl 1063.74083 |
| [25] | Margetan, F. J.; Thompson, R. B.; Gray, T. A., Interfacial spring model for ultrasonic interactions with imperfect interfaces: Theory of oblique incidence and application to diffusion-bonded butt joints, J. Nondestruct. Eval., 7, 131-152 (1988) |
| [26] | Matsushita, M.; Mori, N.; Biwa, S., Transmission of lamb waves across a partially closed crack: numerical analysis and experiment, Ultrasonics, 92, 57-67 (2019) |
| [27] | Memmolo, V.; Monaco, E.; Boffa, N.; Maio, L.; Ricci, F., Guided wave propagation and scattering for structural health monitoring of stiffened composites, Compos. Struct., 184, 568-580 (2018) |
| [28] | Mikata, Y.; Achenbach, J. D., Interaction of harmonic waves with a periodic array of inclined cracks, Wave Motion, 10, 59-72 (1988) · Zbl 0626.73106 |
| [29] | Mykhas’kiv, V.; Zhbadynskyi, I.; Zhang, C., Dynamic stresses due to time-harmonic elastic wave incidence on doubly periodic array of penny-shaped cracks, J. Math. Sci., 203, 114-122 (2014) |
| [30] | Mykhas’kiv, V. V.; Zhbadynskyi, I. Y.; Zhang, C., On propagation of time-harmonic elastic waves through a double-periodic array of penny-shaped cracks, Eur. J. Mech. A Solids, 73, 306-317 (2019) · Zbl 1406.74601 |
| [31] | Pecorari, C.; Kelly, P., The quasistatic approximation for a cracked interface between a layer and a substrate, J. Acoust. Soc. Am., 107, 2454-2461 (2000) |
| [32] | Prudnikov, A. P.; Brychkov, Y. A.; Marichev, O. I., (Integrals and Series. Integrals and Series, More Special Functions, vol. 3 (1989), Gordon and Breach Science Publishers) · Zbl 0728.26001 |
| [33] | Remizov, M. Y.; Sumbatyan, M. A., Three-dimensional one-mode penetration of elastic waves through a doubly periodic array of cracks, Math. Mech. Solids, 23, 636-650 (2018) · Zbl 1395.74047 |
| [34] | Rucka, M.; Wojtczak, E.; Lachowicz, J., Damage imaging in lamb wave-based inspection of adhesive joints, Appl. Sci., 8, 522 (2018) |
| [35] | Scarpetta, E.; Sumbatyan, M. A., Wave propagation through elastic solids with a periodic array of arbitrarily shaped defects, Math. Comput. Modelling, 37, 19-28 (2003) · Zbl 1069.74028 |
| [36] | Sherafat, M.; Guitel, R.; Quaegebeur, N.; Lessard, L.; Hubert, P.; Masson, P., Guided wave scattering behavior in composite bonded assemblies, Compos. Struct., 136, 696-705 (2016) |
| [37] | Shifrin, E. I., Inverse spectral problem for a non-uniform rod with multiple cracks, Mech. Syst. Signal Process., 96, 348-365 (2017) |
| [38] | Siryabe, E.; Renier, M.; Meziane, A.; Galy, J.; Castaings, M., Apparent anisotropy of adhesive bonds with weak adhesion and non-destructive evaluation of interfacial properties, Ultrasonics, 79, 34-51 (2017) |
| [39] | Sotiropoulos, D. A.; Achenbach, J. D., Ultrasonic reflection by a planar distribution of cracks, J. Nondestruct. Eval., 7, 123-129 (1988) |
| [40] | Zhao, Y.; Qiu, Y.; L. J, A.; J, J.; Qu, J., Frequency-dependent tensile and compressive effective moduli of elastic solids with randomly distributed two-dimensional microcracks, J. Appl. Mech., 82, 081006-081006-13 (2015) |
| [41] | Zotov, V. V.; Popuzin, V. V.; Tarasov, A. E., An Experimental Model of the Ultrasonic Wave Propagation Through a Doubly-Periodic Array of Defects, 189-204 (2017), Springer: Springer Singapore |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
