The solution to the problem for the acoustic-emission field of displacements in an elastic bimaterial consisting of two half-spaces generated by a time-harmonic given displacement of opposite surfaces of an internal circular torsion crack parallel to the interfacial plane is obtained using the method of boundary integral equations. The effect on the parameters of displacement amplitudes of different types of contact conditions on the interface plane—perfect mechanical contact and contact through a thin compliant gap, which is modeled using effective spring boundary conditions—is investigated. The effect on the amplitudes of displacements in space, the frequency of displacements of the crack surfaces, the ratio of stiffnesses of the bimaterial components, and the location of the point of observation of displacements are analyzed numerically. The effect of shielding dynamic displacements by a layer in comparison with their analogs for half-spaces with perfect contact is determined. A decrease in the displacement amplitudes (relative to the case of a homogeneous body with a crack) in the defect-free component of the bimaterial is found with an increase in the ratio of stiffnesses of the contacting materials.
Similar content being viewed by others
References
H. T. Sulym and Y. Z. Piskozub, “Conditions of contact interaction (review),” Math. Methods Physicomechanical Fields, 47, 110–125 (2004).
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Wiley-Interscience Publ., Washington (1993).
J. -M. Baik and R. B. Thompson, “Ultrasonic scattering from imperfect interfaces: A quasi-static model,” J. Nondestr. Eval., 4, No. 3–4, 177–196 (1984).
V. M. Bystrov, V. A. Dekret, and V. S. Zelens’kyi “Edge effect and near-surface buckling in layered composite material with imperfect contact between layers,” Int. Appl. Mech., 58, No. 6, 695–705 (2022).
M. V. Golub, O. V. Doroshenko, and Y. Gu, “Effective boundary conditions and stochastic crack distribution for modelling guided waves scattering by a partially closed interfacial delamination in a laminate,” Materials, 16, No. 6, 2415 (2023).
M. V. Golub, S. I. Fomenko, A. N. Shpak, Y. Gu, Y. Wang, and Ch. Zhang, “Semi-analytical hybrid approach for modelling smart structures and guided wave-based SHM systems for a laminate with multiple delaminations and surface-mounted inhomogeneities,” Appl. Math. Model., 120, 812–832 (2023).
I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, Academic Press, London (2007).
J. Lei, Y.-S. Wang, and D. Gross, “Dynamic interaction between a sub-interface crack and the interface in a bi-material: time-domain BEM analysis,” Arch. Appl. Mech., 73, 225–240 (2003).
H. Lekesiz, N. Katsube, S. I. Rokhlin, and R. R. Seghi, “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).
O. V. Menshykov, M. V. Menshykova, and I. A.Guz, “Boundary integral equations in the frequency domain for interface linear cracks under impact loading,” Acta Mech., 231, No. 8, 3461–3471 (2020).
V. O. Men’shikov, O. V. Men’shikov, and O. Yu. Kladova, “Interfacial Crack with Frictionless and Frictional Contact of Faces in a Bimaterial under a Shear Wave,” Int. Appl. Mech., 58, No. 1, 102–110 (2022).
V. Mykhas’kiv, V. Stankevych, 2. Zhbadynskyi, and C. Zhang, “3-D dynamic interaction between a penny-shaped crack and a thin interlayer joining two elastic half-spaces,” Int. J. Fract., 159, 137–149 (2009).
M. Ohtsu, Acoustic Emission and Related Non-destructive Evaluation Techniques in the Fracture Mechanics of Concrete: Fundamentals and Applications, Woodhead Publ., Kidlington (2020).
V. Skalskyi, Z. Nazarchuk, and O. Stankevych, “Mathematical models for displacement fields caused by the crack in an elastic half-space,” in: Acoustic Emission. Fracture Detection in Structural Materials. Series: Foundations in Engineering Mechanics, Springer, Cham (2022), pp. 51–86.
V. Z. Stankevich, “Computation of certain double integrals those are characteristic of dynamic problems of the theory of cracks in a semi-infinite body,” J. Math. Sci., 81, No. 6, 3048–3052 (1996).
V. Z. Stankevych, V. M. Boiko, and Yu. V. Tereshchak, “Steady vibrations of an elastic bimaterial with a thin compliant layer and a circular crack,” Mater. Sci., 58, No. 3, 377–384 (2022).
A. O. Vatul’yan and O. V. Yavruyan, “Vibrations of a layer with delamination in the framework of the gradient elasticity theory,” Russ. J. Nondestr. Test., 57, 825–837 (2021).
J. Yang, S. Han, and W.-R. Yu, “Detection of delamination of steel–polymer sandwich composites using acoustic emission and development of a forming limit diagram considering delamination,” Heliyon, 9, No. 6, e16942 (2023).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Prykladna Mekhanika, Vol. 60, No. 2, pp. 91–99, March–April 2024
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Stankevych, V.Z., Stankevych, O.M. Acoustic Emission in Elastic Bimaterial with Crack Under Different Contact Conditions on Interface Plane. Int Appl Mech 60, 203–211 (2024). https://doi.org/10.1007/s10778-024-01274-w
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10778-024-01274-w