Applied Mathematics and Mechanics >
Interfacial analysis of a penny-shaped one-dimensional hexagonal functionally graded piezoelectric quasicrystal film on a temperature-dependent substrate
Received date: 2025-07-27
Revised date: 2025-10-10
Online published: 2025-11-28
Supported by
Project supported by the National Natural Science Foundation of China (Nos. 11902293 and 12272353)
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In this paper, we investigate the interfacial behavior of a thin, penny-shaped, one-dimensional (1D) hexagonal functionally graded (FG) piezoelectric quasicrystal (PQC) film bonded on a temperature-dependent elastic substrate under thermal and electrical loads. The problem is modeled as axisymmetric based on the membrane theory, with the peeling stress and bending moment being disregarded. A potential theory method, combined with the Hankel transform technique, is utilized to derive the displacement field on the substrate surface. With perfect interfacial bonding assumption, an integral equation governing the phonon interfacial shear stress is formulated and numerically solved by the Chebyshev polynomials. Explicit expressions are derived for the interfacial shear stress, the internal stresses within the PQC film and the substrate, the axial strain, and the stress intensity factors (SIFs). Numerical simulations are conducted to investigate the effects of the film’s aspect ratio, material inhomogeneity, material mismatch, and temperature-dependent material properties on its mechanical response. The results provide insights for the functional design and reliability assessment of FG PQC film/substrate systems.
Kai LUO , Cuiying FAN , Minghao ZHAO , C. S. LU , Huayang DANG . Interfacial analysis of a penny-shaped one-dimensional hexagonal functionally graded piezoelectric quasicrystal film on a temperature-dependent substrate[J]. Applied Mathematics and Mechanics, 2025 , 46(12) : 2297 -2316 . DOI: 10.1007/s10483-025-3326-9
| [1] | HOSSEINI, M. J. M. and NAWROCKI, R. A. A review of the progress of thin-film transistors and their technologies for flexible electronics. Micromachines, 12(6), 655 (2021) |
| [2] | PETERS, M., LEYENS, C., SCHULZ, U., and KAYSSER, W. A. EB-PVD thermal barrier coatings for aeroengines and gas turbines. Advanced Engineering Materials, 3, 193–204 (2001) |
| [3] | SOMASUNDARAM, S. Silane coatings of metallic biomaterials for biomedical implants: a preliminary review. Journal of Biomedical Materials Research, Part B: Applied Biomaterials, 106(8), 2901–2918 (2018) |
| [4] | GULER, M. A. Mechanical modeling of thin films and cover plates bonded to graded substrates. Journal of Applied Mechanics, 75(5), 051105 (2008) |
| [5] | CHEN, P. J., CHEN, S. H., GUO, W., and GAO, F. The interface behavior of a thin piezoelectric film bonded to a graded substrate. Mechanics of Materials, 127, 26–38 (2018) |
| [6] | ALINIA, Y., ABBASZADEH-FATHABADI, S. A., and GULER, M. A. Stress analysis for a thin film bonded to an orthotropic substrate under thermal loading. Mechanics Research Communications, 109, 103594 (2020) |
| [7] | LONG, H., LIU, Y. W., and WEI, Y. G. Debonding characterization of stiff film/compliant substrate systems based on the bilinear cohesive zone model. Engineering Fracture Mechanics, 265, 108363 (2022) |
| [8] | NART, E., ALINIA, Y., and GüLER, M. A. The effect of material anisotropy on the mechanics of a thin-film/substrate system under mechanical and thermal loads. Mathematics and Mechanics of Solids, 27(4), 644–661 (2022) |
| [9] | DANG, H. Y., QI, D. P., ZHAO, M. H., FAN, C. Y., and LU, C. S. The thermally induced interfacial behavior of a thin two-dimensional decagonal quasicrystal film. International Journal of Fracture, 246(2-3), 103–116 (2024) |
| [10] | ZHANG, W. K., LU, C. S., ZHAO, M. H., FAN, C. Y., and DANG, H. Y. On the interfacial behavior of a one-dimensional hexagonal piezoelectric quasicrystal film based on the beam theory. Applied Mathematics and Mechanics (English Edition), 46(2), 289–304 (2025) https://doi.org/10.1007/s10483-025-3214-9 |
| [11] | LI, D. K., CHEN, P. J., LIU, H., PENG, Z. L., GULER, M. A., and CHEN, S. H. The interfacial behavior of an axisymmetric film bonded to a graded inhomogeneous substrate. Mechanics of Materials, 193, 104983 (2024) |
| [12] | ALINIA, Y. and GüLER, M. A. On the problem of an axisymmetric thin film bonded to a transversely isotropic substrate. International Journal of Solids and Structures, 248, 111636 (2022) |
| [13] | GAO, S. J., NIE, G. Q., LIU, J. X., and CHEN, W. Q. Spherical indentation on a piezoelectric semiconductor film/elastic substrate system. Acta Mechanica Solida Sinica, 38(5), 872–883 (2025) |
| [14] | HOU, P. F., CHEN, B. J., and ZHANG, Y. An accurate and efficient analytical method for 1D hexagonal quasicrystal coating under the tangential force based on the Green’s function. International Journal of Mechanical Sciences, 131, 982–1000 (2017) |
| [15] | DUBOIS, J. M. Properties and applications of quasicrystals and complex metallic alloys. Chemical Society Reviews, 41(20), 6760–6777 (2012) |
| [16] | KAMIYA, K., TAKEUCHI, T., KABEYA, N., WADA, N., ISHIMASA, T., OCHIAI, A., DEGUCHI, K., IMURA, K., and SATO, N. K. Discovery of superconductivity in quasicrystal. Nature Communications, 9(1), 154 (2018) |
| [17] | HU, C. Z., WANG, R. H., and DING, D. H. Symmetry groups, physical property tensors, elasticity and dislocations in quasicrystals. Reports on Progress in Physics, 63(1), 1–39 (2000) |
| [18] | RAMA MOHANA RAO, K., HEMAGIRI RAO, P., and CHAITANYA, B. S. K. Piezoelectricity in quasicrystals: a group-theoretical study. Pramana Journal of Physics, 68(3), 481–487 (2007) |
| [19] | AABID, A., RAHEMAN, M. A., IBRAHIM, Y. E., ANJUM, A., HRAIRI, M., PARVEEZ, B., PARVEEN, N., and ZAYAN, J. M. A systematic review of piezoelectric materials and energy harvesters for industrial applications. Sensors, 21(12), 4145 (2021) |
| [20] | GAO, X. Y., YANG, J. K., WU, J. G., XIN, X. D., LI, Z. M., YUAN, X. T., SHEN, X. Y., and DONG, S. X. Piezoelectric actuators and motors: materials, designs, and applications. Advanced Materials Technologies, 5(1), 1900716 (2020) |
| [21] | ZHANG, L. Y., ZHANG, H. L., LI, Y., WANG, J. B., and LU, C. G. Static electro-mechanical response of axisymmetric one-dimensional piezoelectric quasicrystal circular actuator. Materials, 15(9), 3157 (2022) |
| [22] | SU, M. Y. and XIAO, J. H. Model III fracture analysis of a nanoscale elliptical hole with four cracks in one-dimensional hexagonal piezoelectric quasicrystals. Engineering Fracture Mechanics, 274, 108776 (2022) |
| [23] | MU, X., HU, Z. M., ZHU, Z. W., ZHANG, J. M., LI, Y., ZHANG, L. L., and GAO, Y. Analytical solutions for two-dimensional piezoelectric quasicrystal composite wedges and spaces. Mechanics of Advanced Materials and Structures, 30(21), 4303–4316 (2023) |
| [24] | LI, Y. and GAO, Y. Three-dimensional axisymmetric analysis of annular one-dimensional hexagonal piezoelectric quasicrystal actuator/sensor with different configurations. Crystals, 14(11), 964 (2024) |
| [25] | LI, P. D., LI, W. D., FAN, H. D., WANG, Q. Y., and ZHOU, K. A phase-field framework for brittle fracture in quasi-crystals. International Journal of Solids and Structures, 279, 112385 (2023) |
| [26] | ZHAO, S. M., LI, P. D., ZHENG, R. F., FAN, H. D., and WANG, Q. Y. Phase-field fracture modelling of piezoelectric quasicrystals. Engineering Fracture Mechanics, 305, 110176 (2024) |
| [27] | FARHADIAN, A. and ALINIA, Y. Thermal stress analysis in a graded thermoelectric film bonded to a homogeneous substrate. Mechanics of Materials, 203, 105256 (2025) |
| [28] | LI, Y., YANG, L. Z., and GAO, Y. Thermo-elastic analysis of functionally graded multilayered two-dimensional decagonal quasicrystal plates. ZAMM Journal of Applied Mathematics and Mechanics, 98(9), 1585–1602 (2018) |
| [29] | LI, Y., YANG, L. Z., and GAO, Y. An exact solution for a functionally graded multilayered one-dimensional orthorhombic quasicrystal plate. Acta Mechanica, 230(4), 1257–1273 (2019) |
| [30] | MU, X., XU, W. S., ZHU, Z. W., ZHANG, L. L., and GAO, Y. Multi-field coupling solutions of functionally graded two-dimensional piezoelectric quasicrystal wedges and spaces. Applied Mathematical Modelling, 109, 251–264 (2022) |
| [31] | LI, Y., LI, Y., QIN, Q. H., YANG, L. Z., ZHANG, L. L., and GAO, Y. Axisymmetric bending analysis of functionally graded one-dimensional hexagonal piezoelectric quasi-crystal circular plate. Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, 476(2241), 20200301 (2020) |
| [32] | LI, Y., YANG, L. Z., and GAO, Y. Bending analysis of laminated two-dimensional piezoelectric quasicrystal plates with functionally graded material properties. Acta Physica Polonica A, 135(3), 426–433 (2019) |
| [33] | WANG, Y. X., LIU, C., ZHANG, L. L., PAN, E. N., and GAO, Y. Mechanical analysis of functionally graded multilayered two-dimensional decagonal piezoelectric quasicrystal laminates with imperfect interfaces. Crystals, 14(2), 170 (2024) |
| [34] | ZHANG, L., GUO, J. H., and XING, Y. M. Nonlocal analytical solution of functionally graded multilayered one-dimensional hexagonal piezoelectric quasicrystal nanoplates. Acta Mechanica, 230(5), 1781–1810 (2019) |
| [35] | LANZONI, L. and RADI, E. Thermally induced deformations in a partially coated elastic layer. International Journal of Solids and Structures, 46(6), 1402–1412 (2009) |
| [36] | LIU, D. L., MU, R. D., HE, L. M., LI, S., and YANG, W. H. Failure behaviour of EB-PVD YSZ thermal barrier coatings under simulated aero-engine operating conditions. Surface and Coating Technology, 474, 130027 (2023) |
| [37] | CUI, Y. J., WANG, K. F., WANG, B. L., and WANG, P. Analysis of thermally induced delamination of thermoelectric thin film/substrate system. International Journal of Fracture, 214(2), 201–208 (2018) |
| [38] | WANG, J. F., LI, P. H., TIAN, X. B., SHI, S. Q., and TAM, L. H. Molecular investigation on temperature-dependent mechanical properties of PMMA/CNT nanocomposite. Engineering Fracture Mechanics, 293, 109705 (2023) |
| [39] | YAO, Q. Y., DONG, P., ZHAO, Z. Y., LI, Z. Y., WEI, T. Q., WU, J. L., QIU, J., and LI, W. G. Temperature dependent tensile fracture strength model of rubber materials based on Mooney-Rivlin model. Engineering Fracture Mechanics, 292, 109646 (2023) |
| [40] | ZHANG, H. L., KIM, S., CHOI, G., XIE, D. M., and CHO, H. H. Effect of temperature dependent material properties on thermoelastic damping in thin beams. Internal Journal of Heat and Mass Transfer, 139, 1031–1036 (2019) |
| [41] | LI, X. Y., LI, P. D., WU, T. H., SHI, M. X., and ZHU, Z. W. Three-dimensional fundamental solutions for one-dimensional hexagonal quasicrystal with piezoelectric effect. Physics Letters A, 378(10), 826–834 (2014) |
| [42] | LI, X. Y., WANG, T., ZHENG, R. F., and KANG, G. Z. Fundamental thermo-electro-elastic solutions for 1D hexagonal QC. Journal of Applied Mathematics and Mechanics, 95(5), 457–468 (2015) |
| [43] | FAN, T. Y., XIE, L. Y., FAN, L., and WANG, Q. Z. Interface of quasicrystal and crystal. Chinese Physics B, 20(7), 076102 (2011) |
| [44] | HOU, P. F., JIANG, H. Y., and LI, Q. H. Three-dimensional steady-state general solution for isotropic thermoelastic materials with applications I: general solutions. Journal of Thermal Stresses, 36(7), 727–747 (2013) |
| [45] | TANIGAWA, Y., MATSUMOTO, M., and AKAI, T. Optimization of material composition to minimize thermal stresses in nonhomogeneous plate subjected to unsteady heat supply. JSME International Journal Series A, Mechanics and Material Engineering, 40(1), 84–93 (1997) |
| [46] | LI, X. Y., LI, P. D., and KANG, G. Z. Crack tip plasticity of a thermally loaded penny-shaped crack in an infinite space of 1D QC. Acta Mechanica Solida Sinica, 28(5), 471–483 (2015) |
| [47] | OZTURK, M. and ERDOGAN, F. Axisymmetric crack problem in bonded materials with a graded interfacial region. International Journal of Solids and Structures, 33(2), 193–219 (1996) |
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