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Applied Mathematics and Mechanics >

2023 , Vol. 44 >Issue 5: 841 - 856

DOI: https://doi.org/10.1007/s10483-023-2989-7

Articles

Thermal-induced interfacial behavior of a thin one-dimensional hexagonal quasicrystal film

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  • 1. School of Mechanics and Safety Engineering, Zhengzhou University, Zhengzhou 450001, China;
    2. School of Mechanical Engineering, Zhengzhou University, Zhengzhou 450001, China;
    3. School of Civil and Mechanical Engineering, Curtin University, Western Australia 6845, Australia

Received date: 2023-01-05

  Revised date: 2023-03-04

  Online published: 2023-04-24

Supported by

the National Natural Science Foundation of China (Nos.11572289, 1171407, 11702252, and 11902293) and the China Postdoctoral Science Foundation (No.2019M652563)

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Abstract

In this paper, we investigate the interfacial behavior of a thin one-dimensional (1D) hexagonal quasicrystal (QC) film bonded on an elastic substrate subjected to a mismatch strain due to thermal variation. The contact interface is assumed to be non-slipping, with both perfectly bonded and debonded boundary conditions. The Fourier transform technique is adopted to establish the integral equations in terms of interfacial shear stress, which are solved as a linear algebraic system by approximating the unknown phonon interfacial shear stress via the series expansion of the Chebyshev polynomials. The expressions are explicitly obtained for the phonon interfacial shear stress, internal normal stress, and stress intensity factors (SIFs). Finally, based on numerical calculations, we briefly discuss the effects of the material mismatch, the geometry of the QC film, and the debonded length and location on stresses and SIFs.

Key words： one-dimensional (1D) hexagonal quasicrystal (QC) film; stress intensity factor (SIF); thermal variation; Chebyshev polynomial; interfacial behavior

Cite this article

Huayang DANG, Dongpei QI, Minghao ZHAO, Cuiying FAN, C.S. LU . Thermal-induced interfacial behavior of a thin one-dimensional hexagonal quasicrystal film[J]. Applied Mathematics and Mechanics, 2023 , 44(5) : 841 -856 . DOI: 10.1007/s10483-023-2989-7

References

[1] FREUND, L. B. and SURESH, S. Thin Film Materials: Stress, Defect Formation and Surface Evolution, Cambridge University Press, Cambridge (2004)
[2] KENZARI, S., BONINA, D., DUBOIS, J. M., and FOURNEE, V. Quasicrystal polymer composites for selective laser sintering technology. Materials & Design, 35, 691-695(2012)
[3] PARSAMEHR, H., CHANG, S. Y., and LAI, C. H. Mechanical and surface properties of aluminum-copper-iron quasicrystal thin films. Journal of Alloys and Compounds, 732, 952-957(2018)
[4] RYABTSEV, S. I., POLONSKYI, V. A., and SUKHOVA, O. V. Structure and corrosion of quasicrystalline cast alloys and Al-Cu-Fe film coatings. Materials Sciences, 56(2), 263-272(2020)
[5] EISENHAMMER, T., HAUGENEDER, A., and MAHR, A. High-temperature optical properties and stability of selective absorbers based on quasicrystalline AlCuFe. Solar Energy Materials and Solar Cells, 54(1-4), 379-386(1998)
[6] BALBYSHEV, V. N., KING, D. J., KHRAMOV, A. N., KASTEN, L. S., and DONLEY, M. S. Investigation of quaternary Al-based quasicrystal thin films for corrosion protection. Thin Solid Films, 447-448, 558-563(2004)
[7] KANJILAL, A., TIWARI, U., and CHATTERJEE, R. Preparation of Al-Cu-Fe thin films by vapor deposition technique from a single source. Materials Research Bulletin, 37(2), 343-351(2002)
[8] YADAV, T. P., SINGH, D., SHAHI, R. R., SHAZ, M. A., TIWARI, R. S., and SRIVASTAVA, O. N. Synthesis of quasicrystalline film of Al-Ga-Pd-Mn alloy. Thin Solid Films, 534, 265-269(2013)
[9] POLISHCHUK, S., USTINOV, A., MERSTALLINGER, A., MOZDZEN, G., and MELNICHENKO, T. Fabrication of thick, crack-free quasicrystalline Al-Cu-Fe coatings by electron-beam deposition. Surface and Coatings Technology, 291, 406-412(2016)
[10] USHAKOV, A. V., KARPOV, I. V., FEDOROV, L. Y., SHAIKHADINOV, A. A., DEMIN, V. G., DEMCHENKO, A. I., GONCHAROVA, E. A., and ZEER, G. M. Synthesis of quasicrysalline powders and coatings by vacuum arc plasma evaporation. Physics of the Solid State, 61, 2547-2552(2019)
[11] USTINOV, A. I., MOVCHAN, B. A., and POLISHCHUK, S. S. Formation of nanoquasicrystalline Al-Cu-Fe coatings at electron beam physical vapour deposition. Scripta Materialia, 50(4), 533-537(2003)
[12] PHILLIPS, B. S. and ZABINSKI, J. S. Frictional characteristics of quasicrystals at high temperatures. Tribology Letters, 15(1), 57-64(2003)
[13] DUBOIS, J. M. Properties and applications of quasicrystals and complex metallic alloys. Chemical Society Reviews, 41(20), 6767-6777(2012)
[14] PARSAMEHR, H., CHANG, S. Y., and LAI, C. H. Mechanical and surface properties of aluminum-copper-iron quasicrystal thin films. Journal of Alloys and Compounds, 732, 952-957(2018)
[15] PARSAMEHR, H., YANG, C. L., LIU, W. T., CHEN, S. W., and LAI, C. H. Direct observation of growth and stability of Al-Cu-Fe quasicrystal thin film. Acta Materialia, 174, 1-8(2019)
[16] FAN, T. Y., XIE, L, Y., FAN, L., and WANG, Q. Z. Interface of quasicrystal and crystal. Chinese Physics B, 20(7), 076102(2011)
[17] YANG, L. Z., GAO, Y., PAN, E., and WAKSMANSKI, N. An exact closed-form solution for a multilayered one-dimensional orthorhombic quasicrystal plate. Acta Mechanica, 226(11), 3611-3621(2015)
[18] GUO, J. H., SUN, T. Y., and PAN, E. Three-dimensional nonlocal buckling of composite nanoplates with coated one-dimensional quasicrystal in an elastic medium. International Journal of Solids and Structures, 185-186, 272-280(2020)
[19] ZHAO, M. H., FAN, C. Y., LU, C. S., and DANG, H. Y. Interfacial fracture analysis for a two-dimensional decagonal quasi-crystal coating layer structure. Applied Mathematics and Mechanics (English Edition), 42(11), 1633-1648(2021) https://doi.org/10.1007/s10483-021-2786-5
[20] 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
[21] TORUN, H. and UREY, H. Thermal deflections in multilayer microstructures and a thermalization. Journal of Applied Physics, 100, 023527(2006)
[22] ARUTIUNIAN, N. K. Contact problem for a half-plane with elastic reinforcement. Prikladnaya Matamatika i Mekhanika, 32, 652-655(1968)
[23] ERDOGAN, F. and GUPTA, G. D. The problem of an elastic stiffener bonded to a half plane. Journal of Applied Mechanics--Transactions of the ASME, 38, 937-941(1971)
[24] ERDOGAN, F. and JOSEPH, P. F. Mechanical modeling of multilayered films on an elastic substrate, part I: analysis. Journal of Electronic Packaging, 112, 309-316(1990)
[25] SHIELD, T. W. and KIM, K. S. Beam theory models for thin film segments cohesively bonded to an elastic half space. International Journal of Solids and Structures, 29, 1085-1103(1992)
[26] AKISANYA, A. R. and FLECK, N. A. The edge cracking and decohesion of thin films. International Journal of Solids and Structures, 31, 3175-3199(1994)
[27] YU, H. H., HE, M. Y., and HUTCHINSON, J. W. Edge effects in thin film delamination. Acta Materialia, 49, 93-107(2001)
[28] ALACA, B. E., SAIF, M. T. A., and SEHITOGLU, H. On the interface debond at the edge of a thin film on a thick substrate. Acta Materialia, 50(5), 1197-1209(2020)
[29] WANG, X. D. and MEGUID, S. A. On the electroelastic behaviour of a thin piezoelectric actuator attached to an infinite host structure. International Journal of Solids and Structures, 37, 3231-3251(2000)
[30] JIN, C. and WANG, X. Analytical modelling of the electromechanical behavior of surface-bonded piezoelectric actuators including the adhesive layer. Engineering Fracture Mechanics, 78, 2547-2562(2011)
[31] 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)
[32] CHEN, P. J., PENG, J., LIU, H., GAO, F., and GUO, W. The electromechanical behavior of a piezoelectric actuator bonded to a graded substrate including an adhesive layer. Mechanics of Materials, 123, 77-87(2018)
[33] LANZONI, L. Analysis of stress singularities in thin coatings bonded to a semi-infinite elastic substrate. International Journal of Solids and Structures, 48, 1915-1926(2011)
[34] LANZONI, L. and RADI, E. A loaded Timoshenko beam bonded to an elastic half plane. International Journal of Solids and Structures, 92-93, 76-90(2016)
[35] ZHAO, Y., HAN, X., LI, G. Y., LU, C. H., CAO, Y. P., FENG, X. Q., and GAO, H. J. Effect of lateral dimensional on the surface wrinkling of a thin film on compliant substrate induced by differential growth/swelling. Journal of the Mechanics and Physics of Solids, 83, 129-145(2015)
[36] DING, D. H., YANG, W. G., HU, C. Z., and WANG, R. H. Generalized elasticity theory of quasicrystals. Physical Review B: Condensed Matter, 48(10), 7003-7010(1993)
[37] LI, X. Y. Fundamental solutions of penny-shaped and half-infinite plane cracks embedded in an infinite space of one-dimensional hexagonal quasi-crystal under thermal loading. Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences, 469, 20130023(2013)
[38] LANZONI, L. and RADI, E. Thermally induced deformations in a partially coated elastic layer. International Journal of Solids and Structures, 46, 1402-1412(2009)
[39] MUSKHELISHVILI, N. I. Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Groningen (1953)
[40] 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
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