LOCAL BUCKLING OF THIN-FILM COATING UNDER PRESSURE ALONG INTERPHASE CRACK UNDER VARIOUS CONTACT CONDITIONS
DOI:
https://doi.org/10.15407/dopovidi2025.06.074Keywords:
thin film, coated materials, buckling, interfacial crack, hyperelastic material, critical strainAbstract
Within the framework of three-dimensional linearized stability theory for deformable bodies, the influence of weakened adhesion between components of a piecewise-homogeneous half-plane (thin-film structure, coated material) on critical instability parameters during compression along an interphase crack is investigated. For this purpose, two types of contact along the interface outside the crack are considered, modeling, respectively, the “strongest” and “weakest” types of interphase adhesion — perfect adhesion and frictionless sliding. Critical parameters are determined by solving eigenvalue problems for Fredholm integral equations of the first kind (or their systems), to which the initial boundary value problems are reduced. For cracks that are sufficiently long compared to the thickness of the coating, limits of applicability of the approximate formula for critical deformation loss of stability are established.
Downloads
References
Biot, M. A. (1965). Mechanics of incremental deformations. New York: John Wiley & Sons. 504 p.
Schultheisz, C. R. & Waas, A. M. (1996). Compressive failure of composites, part I: Testing and micromechanical theories. Prog. Aerosp. Sci., 32, No. 1, pp. 1-42. https://doi.org/10.1016/0376-0421(94)00002-3
Waas, A. M. & Schultheisz, C. R. (1996). Compressive failure of composites, part II: Experimental studies. Prog. Aerosp. Sci., 32, No. 1, pp. 43-78. https://doi.org/10.1016/0376-0421(94)00003-4
Guz, A. N. (2008). Fundamentals of the fracture mechanics of compressed composites. Kyiv: Litera (in Russian).
Mei, H., Landis, C. M. & Huang, R. (2011). Concomitant wrinkling and buckle-delamination of elastic thin films on compliant substrates. Mech. Mater., 43, pp. 627-642.
Nikravesh, S., Ryu, D. & Shen, Y.-L. (2020). Instabilities of thin films on a compliant substrate: Direct numerical si- mulations from surface wrinkling to global buckling. Sci. Rep., 10, 5728. https://doi.org/10.1038/s41598-020-62600-z
Kipnis, A. L. (2025). Wrinkling of hyperelastic thin film on hyperelastic semibounded substrate in cases of rigid connection and frictionless sliding of components. J. Elast., 157, 40. https://doi.org/10.1007/s10659-025-10130-y
Yu, H.-H. & Hutchinson, J. W. (2002). Influence of substrate compliance on buckling delamination of thin films. Int. J. Fract., 113, pp. 39-55. https://doi.org/10.1023/A:1013790232359
Gu, P. & Chen, X. (2022). Role of an interface crack for the blistering mode of a stiff film on a compliant subst- rate. J. Coat. Technol. Res, 19, pp. 661-669. https://doi.org/10.1007/s11998-021-00556-z
Cotterell, B. & Chen, Z. (2000). Buckling and cracking of thin film on compliant substrates under compression. Int. J. Fract., 104, pp. 169-179. https://doi.org/10.1023/A:1007628800620
Bogdanov, V., Dovzhyk, M. & Nazarenko, V. (2024). Analysis of the beam approximation applicability in problems on compression of bodies along closely spaced cracks. In: Altenbach, H., Bogdanov, V., Grigorenko, A. Y., Kush- nir, R. M., Nazarenko, V. M. & Eremeyev, V. A. (eds.). Selected problems of solid mechanics and solving methods. Advanced Structured Materials, vol. 204 (pp. 59-80). Cham: Springer. https://doi.org/10.1007/978-3-031-54063-9_5
Cao, Y., Jiang, Y., Li, B. & Feng, X. (2012). Biomechanical modeling of surface wrinkling of soft tissues with growth-dependent mechanical properties. Acta Mech. Solida Sin., 25, pp. 483-492. https://doi.org/10.1016/ S0894-9166(12)60043-3
Stewart, P. S., Waters, S. L., Sayed, T. E., Vella, D. & Goriely, A. (2016). Wrinkling, creasing, and folding in fiber- reinforced soft tissues. Extreme Mech. Lett., 8, pp. 22-29. https://doi.org/10.1016/j.eml.2015.10.005
Dimmock, R. L., Wang, X., Fu, Y., Haj, A. J. L. & Yang, Y. (202). Biomedical applications of wrinkling polymers. Recent Prog. Mater., 2, No. 1, 005. https://doi.org/10.21926/rpm.2001005
Dowson, D. (2012). Bio-tribology. Faraday Discuss., 156, pp. 9-30. https://doi.org/10.1039/c2fd20103h
Dunn, A. C., Tichy, J. A., Urueña, J. M. & Sawyer, W. G. (2013). Lubrication regimes in contact lens wear during a blink. Tribol. Int, 63, pp. 45-50. https://doi.org/10.1016/j.triboint.2013.01.008
Bereznick, D. E., Ross, J. K. & McGil, S. M. (2002). The frictional properties at the thoracic skin-fascia interface: implications in spine manipulation. Clin. Biomech., 17, No. 4, pp. 297-303. https://doi.org/10.1016/s0021- 9290(02)00014-3
Guz, A. N. (1999). Fundamentals of the three-dimensional theory of stability of deformable bodies. Berlin, Heidelberg, New York: Springer. https://doi.org/10.1007/978-3-540-69633-9
Guz, A. N. (2014). Establishing the foundations of the mechanics of fracture of materials compressed along cracks (review). Int. Appl. Mech., 50, No. 1, pp. 1-57. https://doi.org/10.1007/s10778-014-0609-y
Guz, A. N., Bogdanov, V. L. & Nazarenko, V. M. (2020). Two-dimensional problems on the fracture of bodies under compression along cracks. In: Guz, A. N., Bogdanov, V. L. & Nazarenko, V. M. (eds.). Fracture of materials under compression along cracks (pp. 149-248). Cham: Springer. https://doi.org/10.1007/978-3-030-51814-1_3
Bogdanov, V.L., Nazarenko, V.M. & Kipnis, O.L. (2024). Compression of semibounded body with thin coating layer along interface near-surface crack. Part I. Int. Appl. Mech., 60, No. 5, pp. 511-524. https://doi.org/10.1007/ s10778-025-01303-2
Bogdanov, V. L., Nazarenko, V. M. & Kipnis, O. L. (2024). Compression of semibounded body with thin coating layer along interface near-surface crack. Part II. Int. Appl. Mech., 60, No. 6, pp. 641-652. https://doi.org/10.1007/ s10778-025-01316-x
Kipnis, A. L. (2025). Stability of a piecewise-homogeneous half-plane with sliding components under compression along an interface crack. Mech. Compos. Mater., 61, No. 2, pp. 409-424. https://doi.org/10.1007/s11029-025-10283-w
Mikhlin, S. G. (1964). Variational methods in mathematical physics. Oxford: Pergamon Press.
Bartenev, G. M. & Khazanovich, T. N. (1960). On the law of highly elastic deformations of network polymers. Vysokomolekulyarnyye Soyedineniya, 2, No. 1, pp. 21-28 (in Russian).
John, F. (1960). Plane strain problems for a perfectly elastic material of harmonic type. Commun. Pure Appl. Math., 13, No. 2, pp. 239-296. https://doi.org/10.1002/cpa.3160130206
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Reports of the National Academy of Sciences of Ukraine
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
