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An accurate and efficient analytical method for 1D hexagonal quasicrystal coating based on Green’s function

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Abstract

As a solid material between the crystal and the amorphous, the study on quasicrystals has become an important branch of condensed matter physics. Due to the special arrangement of atoms, quasicrystals own some desirable properties, such as low friction coefficient, low adhesion, high wear resistance and low porosity. Thus, quasicrystals are expected to be applied to the coating surfaces for engines, solar cells, nuclear fuel containers and heat converters. However, when the quasicrystals are used as coating material, it is very hard to simulate the coupling fields by the finite elements numerical methods because of its thin thickness and extreme stress gradient. This is the main reason why the structure of quasicrystal coating cannot be calculated accurately and stably by various numerical platform. A general solution method which can be used to solve this contact problem for a 1D hexagonal quasicrystal coating perfectly bonded to a transversely isotropic semi-infinite substrate under the point force is presented in this paper. The solutions of the Green’s function under the distributed load can be obtained through the superposition principle. The simulation results show that this method is correct and effective, which has high calculation accuracy and fast convergence speed. The phonon–phason coupling field and elastic field in the coating and semi-infinite substrate will be derived based on the axisymmetric general solution, and the complicated coupling field of quasicrystals in coating contact space is explicitly presented in terms of elementary functions. In addition, the relationship between the coating thickness or external force and the stress component is also obtained to solve practical problems in engineering applications. The solutions presented not only bear theoretical merits, but also can serve as benchmarks to clarify various approximate methods.

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Funding

Funding was provided by National Natural Science Foundation of China (Grant No. 11572119).

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Authors and Affiliations

  1. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, 410082, People’s Republic of China

    Peng-Fei Hou, Bing-Jie Chen & Yang Zhang

  2. Department of Engineering Mechanics, Hunan University, Changsha, 410082, People’s Republic of China

    Peng-Fei Hou, Bing-Jie Chen & Yang Zhang

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  1. Peng-Fei Hou
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  2. Bing-Jie Chen
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Correspondence to Bing-Jie Chen.

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Hou, PF., Chen, BJ. & Zhang, Y. An accurate and efficient analytical method for 1D hexagonal quasicrystal coating based on Green’s function. Z. Angew. Math. Phys. 68, 95 (2017). https://doi.org/10.1007/s00033-017-0842-4

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