Fracture of films caused by uniaxial tensions: a numerical model

doi:10.1007/s10483-023-3061-7

Abstract

Abstract: Surface cracks are commonly observed in coatings and films. When structures with coatings are subject to stretching, opening mode cracks are likely to form on the surface, which may further lead to other forms of damage, such as interfacial delamination and substrate damage. Possible crack forms include cracks extending towards the interface and channeling across the film. In this paper, a two-dimensional numerical model is proposed to obtain the structural strain energy at arbitrary crack lengths for bilayer structures under uniaxial tension. The energy release rate and structural stress intensity factors can be obtained accordingly, and the effects of geometry and material features on fracture characteristics are investigated, with most crack patterns being confirmed as unstable. The proposed model can also facilitate the analysis of the stress distribution in periodic crack patterns of films. The results from the numerical model are compared with those obtained by the finite element method (FEM), and the accuracy of the theoretical results is demonstrated.

Key words: surface crack, numerical model, stress intensity factor, periodic crack, finite element method (FEM)

2010 MSC Number:

Chenxue JIA, Zihao WANG, Donghui ZHANG, Taihua ZHANG, Xianhong MENG. Fracture of films caused by uniaxial tensions: a numerical model. Applied Mathematics and Mechanics (English Edition), 2023, 44(12): 2093-2108.

TrendMD

References

[1] FU, H. R., NAN, K. W., BAI, W. B., HUANG, W., BAI, K., LU, L. Y., ZHOU, C. Q., LIU, Y. P., LIU, F., WANG, J. T., HAN, M. D., YAN, Z., LUAN, H. W., ZHANG, Y. J., ZHANG, Y. T., ZHAO, J. N., CHENG, X., LI, M. Y., LEE, J. W., LIU, Y., FANG, D. N., LI, X. L., HUANG, Y. G., ZHANG, Y. H., and ROGERS, J. A. Morphable 3D mesostructures and microelectronic devices by multistable buckling mechanics. Nature Materials, 17(3), 268–276(2018)
[2] LI, D. D., LAI, W. Y., ZHANG, Y. Z., and HUANG, W. Printable transparent conductive films for flexible electronics. Advanced Materials, 30(10), 1704738(2018)
[3] YU, Y., NYEIN, H. Y. Y., GAO, W., and JAVEY, A. Flexible electrochemical bioelectronics: the rise of in situ bioanalysis. Advanced Materials, 32(15), e1902083(2020)
[4] LU, Z. X., GUO, L., and ZHAO, H. Y. Mechanics of nonbuckling interconnects with prestrain for stretchable electronics. Applied Mathematics and Mechanics (English Edition), 42(5), 689–702(2021) https://doi.org/10.1007/s10483-021-2715-7
[5] RAUT, H. K., GANESH, V. A., NAIR, A. S., and RAMAKRISHNA, S. Anti-reflective coatings: a critical, in-depth review. Energy & Environmental Science, 4(10), 3779–3804(2011)
[6] HARUN, W. S. W., ASRI, R. I. M., ALIAS, J., ZULKIFLI, F. H., KADIRGAMA, K., GHANI, S. A. C., and SHARIFFUDDIN, J. H. M. A comprehensive review of hydroxyapatite-based coatings adhesion on metallic biomaterials. Ceramics International, 44(2), 1250–1268(2018)
[7] HORNBERGER, H., VIRTANEN, S., and BOCCACCINI, A. R. Biomedical coatings on magnesium alloys: a review. Acta Biomaterialia, 8(7), 2442–2455(2012)
[8] LIU, Y. J. and YIN, H. M. Elastic thermal stresses in a hollow circular overlay/substrate system. Mechanics Research Communications, 55, 10–17(2014)
[9] THOULESS, M. D., LI, Z., DOUVILLE, N. J., and TAKAYAMA, S. Periodic cracking of films supported on compliant substrates. Journal of the Mechanics and Physics of Solids, 59(9), 1927– 1937(2011)
[10] LI, J., AN, Y., HUANG, R., JIANG, H., and XIE, T. Unique aspects of a shape memory polymer as the substrate for surface wrinkling. ACS Applied Materials & Interfaces, 4(2), 598–603(2012)
[11] COTTERELL, B. and CHEN, Z. Buckling and cracking of thin films on compliant substrates under compression. International Journal of Fracture, 104(2), 169–179(2000)
[12] CHEN, Z. B., KIM, Y. Y., and KRISHNASWAMY, S. Anisotropic wrinkle formation on shape memory polymer substrates. Journal of Applied Physics, 112(12), 124319(2012)
[13] GOEHRING, L. Evolving fracture patterns: columnar joints, mud cracks and polygonal terrain. Philosophical Transactions of the Royal Society A: Mathematical Physical and Engineering Sciences, 371(2004), 20120353(2013)
[14] NANDAKISHORE, P. and GOEHRING, L. Crack patterns over uneven substrates. Soft Matter, 12(8), 2253–2263(2016)
[15] YIN, H. M., PAULINO, G. H., and BUTTLAR, W. G. An explicit elastic solution for a brittle film with periodic cracks. International Journal of Fracture, 153(1), 39–52(2008)
[16] ALACA, B. E., OZCAN, C., and ANLAS, G. Deterministic assembly of channeling cracks as a tool for nanofabrication. Nanotechnology, 21(5), 055301(2010)
[17] HUANG, Y., YUAN, J. H., ZHANG, Y. C., and FENG, X. Interfacial delamination of inorganic films on viscoelastic substrates. Journal of Applied Mechanics, 83(10), 101005(2016)
[18] NAZIR, M. H. and KHAN, Z. A. A review of theoretical analysis techniques for cracking and corrosive degradation of film-substrate systems. Engineering Failure Analysis, 72, 80–113(2017)
[19] CHAI, H. and FOX, J. On delamination growth from channel cracks in thin-film coatings. International Journal of Solids and Structures, 49(22), 3142–3147(2012)
[20] BALDELLI, A. A. L., BABADJIAN, J. F., BOURDIN, B., HENAO, D., and MAURINI, C. A variational model for fracture and debonding of thin films under in-plane loadings. Journal of the Mechanics and Physics of Solids, 70, 320–348(2014)
[21] MEN, L., YU, Y. L., HOU, Z. Y., LI, X., and WANG, Z. J. Cracking modes in layered hyperelastic structures. Journal of the Mechanics and Physics of Solids, 174, 105254(2023)
[22] LI, T. and SUO, Z. Ductility of thin metal films on polymer substrates modulated by interfacial adhesion. International Journal of Solids and Structures, 44(6), 1696–1705(2007)
[23] XIANG, Y., LI, T., SUO, Z. G., and VLASSAK, J. J. High ductility of a metal film adherent on a polymer substrate. Applied Physics Letters, 87(16), 161910(2005)
[24] LI, J. C., DOZIER, A. K., LI, Y. C., YANG, F. Q., and CHENG, Y. T. Crack pattern formation in thin film lithium-ion battery electrodes. Journal of the Electrochemical Society, 158(6), A689(2011)
[25] ZHANG, X., ZHAO, M. H., FAN, C. Y., LU, C. S., and DANG, H. Y. Three-dimensional interfacial fracture analysis of a one-dimensional hexagonal quasicrystal coating. Applied Mathematics and Mechanics (English Edition), 43(12), 1901–1920(2022) https://doi.org/10.1007/s10483-022-2942-7
[26] BEUTH, J. L. Cracking of thin bonded films in residual tension. International Journal of Solids and Structures, 29(13), 1657–1675(1992)
[27] XIA, Z. C. and HUTCHINSON, J. W. Crack patterns in thin films. Journal of the Mechanics and Physics of Solids, 48(6-7), 1107–1131(2000)
[28] LIU, W. D., LIU, M., and ZHANG, L. C. Oxidation-induced mechanical deterioration and hierarchical cracks in glassy carbon. Carbon, 100, 178–186(2016)
[29] MALZBENDER, J., DEN TOONDER, J. M. J., BALKENENDE, A. R., and DE WITH, G. Measuring mechanical properties of coatings: a methodology applied to nano-particle-filled solgel coatings on glass. Materials Science and Engineering, 36(2-3), 47–103(2002)
[30] MCGUIGAN, A. P., BRIGGS, G. A. D., BURLAKOV, V. M., YANAKA, M., and TSUKAHARA, Y. An elastic-plastic shear lag model for fracture of layered coatings. Thin Solid Films, 424(2), 219–223(2003)
[31] WEI, X., NARAGHI, M., and ESPINOSA, H. D. Optimal length scales emerging from shear load transfer in natural materials: application to carbon-based nanocomposite design. ACS Nano, 6(3), 2333–2344(2012)
[32] YU, Z. L., LIU, J. J., and WEI, X. D. Unraveling crack stability and strain localization in staggered composites by fracture analysis on the shear-lag model. Composites Science and Technology, 156, 262–268(2018)
[33] HARVEY, C. M., WOOD, J. D., and WANG, S. Brittle interfacial cracking between two dissimilar elastic layers: part 1-analytical development. Composite Structures, 134, 1076–1086(2015)
[34] HARVEY, C. M., WOOD, J. D., and WANG, S. Brittle interfacial cracking between two dissimilar elastic layers: part 2-numerical verification. Composite Structures, 134, 1087–1094(2015)
[35] MENG, X. H., WANG, Z. H., VINNIKOVA, S., and WANG, S. D. Mechanics of periodic film cracking in bilayer structures under stretching. Journal of Applied Mechanics, 85(7), 071006(2018)
[36] YIN, H. M. Fracture saturation and critical thickness in layered materials. International Journal of Solids and Structures, 47(7-8), 1007–1015(2010)