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On deformation peculiarities of two thin strips with a microcrack at the interface

НазваOn deformation peculiarities of two thin strips with a microcrack at the interface
Назва англійськоюOn deformation peculiarities of two thin strips with a microcrack at the interface
АвториOleksandr Kletskov, Valentine Silich-Balhabaieva, Alla Sheveleva, Volodymyr Loboda, Yuri Lapusta
ПринадлежністьOles Honchar Dnipro National University, Dnipro, Ukraine Université Clermont Auvergne, Clermont Auvergne INP, SIGMA Clermont, CNRS, Institut Pascal, Clermont-Ferrand, F-63000, France
Бібліографічний описOn deformation peculiarities of two thin strips with a microcrack at the interface / Oleksandr Kletskov, Valentine Silich-Balhabaieva, Alla Sheveleva, Volodymyr Loboda, Yuri Lapusta // Scientific Journal of TNTU. — Tern.: TNTU, 2025. — Vol 118. — No 2. — P. 153–167.
Bibliographic description:Kletskov O., Silich-Balhabaieva V., Sheveleva A., Loboda V., Lapusta Y. (2025) On deformation peculiarities of two thin strips with a microcrack at the interface. Scientific Journal of TNTU (Tern.), vol 118, no 2, pp. 153–167.
УДК

539.3

Ключові слова

microcrack, stress-strain state, singular integral equations, energy release rate, crack opening.

This study examines the problem of plane strain in a crack between two isotropic, linearly elastic layers, one of which is rigidly fixed. The Fourier integral transform method was applied, reducing the initial system of differential equations to a system of ordinary differential equations. A system of singular integral equations (SIE) was constructed to satisfy the boundary conditions of the problem. By discretizing this system, it was further reduced to a system of linear algebraic equations (SLAE). Analytical expressions were obtained for the crack opening and stress distribution along the interface, allowing the calculation of the energy release rate (ERR) at the crack tips. A numerical illustration of the results was conducted, including graphs of crack opening and stress dependence for various layer thicknesses and Young's moduli. Comparison between analytical and numerical solutions, obtained using the finite element method (FEM), showed good agreement for the case of a microcrack with variable characteristics of the thin coating and the lower layer. A significant influence of the coating thickness on the energy release rate was identified.

ISSN:2522-4433
Перелік літератури
  1. Hu K. Q., Jin H., Yang Z., Chen X. (2019) Interface crack between dissimilar one-dimensional hexagonal quasicrystals with piezoelectric effect. Acta Mechanica, 230, pp. 2455–2474. Doi: 10.1007/s00707-019-02404-z.
  2. Pei P., Yang G., Shi Y., Gao C.-F. (2020) Periodic interfacial cracks in dissimilar piezoelectric materials under the influence of Maxwell stress. Meccanica, 55, pp. 113–124.
  3. Verma P. R. (2022) Magnetic-yielding zone model for assessment of two mode-III semi-permeable collinear cracks in piezo-electro-magnetic strip. Mechanics of Advanced Materials and Structures, 29, pp. 1529–1542.
  4. Hu K. Q., Gao C-F., Zhong Z., Chen Z. T. (2021) Interaction of collinear interface cracks between dissimilar one-dimensional hexagonal piezoelectric quasicrystals. Journal of Applied Mathematics and Mechanics, 101 (11). Available at: https://doi.org/10.1002/zamm.202000360.
  5. Onopriienko O. D., Govorukha V. B., Kagadii T. S., Shporta А. H. (2023) Analysis of cracks and shielding effects in modern materials. Computer Science and Applied Mathematics, 2, pp. 59–95. (In Ukrainian).
  6. Erdogan F., Gupta G. D. (1971) Layered composites with an interface flaw. International Journal of Solids and Structures, no. 7, pp. 1089–1107.
  7. Delale F., Erdogan F. (1983) The crack problem for a nonhomogeneous plane. Journal of Applied Mechanics, , 50, pp. 609–614.
  8. Delale F., Erdogan F. (1988) Interface crack in a nonhomogeneous elastic medium. International Journal of Engineering Science, 26 (6), pp. 559–568.
  9. Birinci A., Birinci F., Cakiroglu F. L., Erdol R. (2010) An internal crack problem for an infinite elastic layer. Archive of Applied Mechanics, 80, pp. 997–1005. Available at: https://doi.org/10.1007/s00419-009-0355-5.
  10. Sheveleva A., Loboda V., Lapusta Y. (2020) A conductive crack and a remote electrode at the interface between two piezoelectric materials. Applied Mathematical Modeling, 87, pp. 287–299.
  11. Loboda V., Lapusta Y., Sheveleva A. (2006) Analysis of pre-fracture zones for an electrically permeable crack in an interlayer between piezoelectric materials. International Journal of Fracture, 142 (3–4), pp. 307–313. Available at: https://doi.org/10.1007/s10704-006-9034-5.
  12. Boyko A., Valiashek V., Kryven V., Kaplun A. (2014) Development of plastic areas in angle points zone under concentrated force. Scientific Journal of TNTU, 76 (4), pp. 34–43. (Mechanics and materials science).
  13. Yasniy P., Dyvdyk O., Semenets O., Iasnii V., Antonov A. (2020) Fatigue crack growth in aluminum alloy from cold expanded hole with preexisting crack. Scientific Journal of TNTU, 99 (3), pp. 5–16.
  14. Kryven V., Blashchak N., Valiashek V., Kryva N., Tsymbaliuk L. (2019) Elastic-plastic deformation of a half-layer with a notch at rigid loading. Scientific Journal of TNTU, 96 (4), pp. 5–13.
  15. Zhang A. B., Wang B. L. (2013) An opportunistic analysis of the interface crack based on the modified interface dislocation method. International Journal of Solids and Structures, 50, pp. 15–20.
References:
  1. Hu K. Q., Jin H., Yang Z., Chen X. (2019) Interface crack between dissimilar one-dimensional hexagonal quasicrystals with piezoelectric effect. Acta Mechanica, 230, pp. 2455–2474. Doi: 10.1007/s00707-019-02404-z.
  2. Pei P., Yang G., Shi Y., Gao C.-F. (2020) Periodic interfacial cracks in dissimilar piezoelectric materials under the influence of Maxwell stress. Meccanica, 55, pp. 113–124.
  3. Verma P. R. (2022) Magnetic-yielding zone model for assessment of two mode-III semi-permeable collinear cracks in piezo-electro-magnetic strip. Mechanics of Advanced Materials and Structures, 29, pp. 1529–1542.
  4. Hu K. Q., Gao C-F., Zhong Z., Chen Z. T. (2021) Interaction of collinear interface cracks between dissimilar one-dimensional hexagonal piezoelectric quasicrystals. Journal of Applied Mathematics and Mechanics, 101 (11). Available at: https://doi.org/10.1002/zamm.202000360.
  5. Onopriienko O. D., Govorukha V. B., Kagadii T. S., Shporta А. H. (2023) Analysis of cracks and shielding effects in modern materials. Computer Science and Applied Mathematics, 2, pp. 59–95. (In Ukrainian).
  6. Erdogan F., Gupta G. D. (1971) Layered composites with an interface flaw. International Journal of Solids and Structures, no. 7, pp. 1089–1107.
  7. Delale F., Erdogan F. (1983) The crack problem for a nonhomogeneous plane. Journal of Applied Mechanics, , 50, pp. 609–614.
  8. Delale F., Erdogan F. (1988) Interface crack in a nonhomogeneous elastic medium. International Journal of Engineering Science, 26 (6), pp. 559–568.
  9. Birinci A., Birinci F., Cakiroglu F. L., Erdol R. (2010) An internal crack problem for an infinite elastic layer. Archive of Applied Mechanics, 80, pp. 997–1005. Available at: https://doi.org/10.1007/s00419-009-0355-5.
  10. Sheveleva A., Loboda V., Lapusta Y. (2020) A conductive crack and a remote electrode at the interface between two piezoelectric materials. Applied Mathematical Modeling, 87, pp. 287–299.
  11. Loboda V., Lapusta Y., Sheveleva A. (2006) Analysis of pre-fracture zones for an electrically permeable crack in an interlayer between piezoelectric materials. International Journal of Fracture, 142 (3–4), pp. 307–313. Available at: https://doi.org/10.1007/s10704-006-9034-5.
  12. Boyko A., Valiashek V., Kryven V., Kaplun A. (2014) Development of plastic areas in angle points zone under concentrated force. Scientific Journal of TNTU, 76 (4), pp. 34–43. (Mechanics and materials science).
  13. Yasniy P., Dyvdyk O., Semenets O., Iasnii V., Antonov A. (2020) Fatigue crack growth in aluminum alloy from cold expanded hole with preexisting crack. Scientific Journal of TNTU, 99 (3), pp. 5–16.
  14. Kryven V., Blashchak N., Valiashek V., Kryva N., Tsymbaliuk L. (2019) Elastic-plastic deformation of a half-layer with a notch at rigid loading. Scientific Journal of TNTU, 96 (4), pp. 5–13.
  15. Zhang A. B., Wang B. L. (2013) An opportunistic analysis of the interface crack based on the modified interface dislocation method. International Journal of Solids and Structures, 50, pp. 15–20.
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