中国物理B ›› 2014, Vol. 23 ›› Issue (5): 56102-056102.doi: 10.1088/1674-1056/23/5/056102

• CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES • 上一篇    下一篇

Finite size specimens with cracks of icosahedral Al–Pd–Mn quasicrystals

杨连枝a b, Ricoeur Andreasc, 何蕃民d, 高阳a   

  1. a College of Science, China Agricultural University, Beijing 100083, China;
    b College of Engineering, China Agricultural University, Beijing 100083, China;
    c Institute of Mechanics, University of Kassel, Kassel 34125, Germany;
    d Sichuan Hydropower Investment & Management Group LTD, Chengdu 611130, China
  • 收稿日期:2013-11-07 修回日期:2013-12-17 出版日期:2014-05-15 发布日期:2014-05-15
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 11172319), the Scientific Fund of Chinese Universities (Grant Nos. 2011JS046 and 2013BH008), the Opening Fund of State Key Laboratory of Nonlinear Mechanics, Program for New Century Excellent Talents in University, China (Grant No. NCET-13-0552), and the National Science Foundation for Post-doctoral Scientists of China (Grant No. 2013M541086).

Finite size specimens with cracks of icosahedral Al–Pd–Mn quasicrystals

Yang Lian-Zhi (杨连枝)a b, Ricoeur Andreasc, He Fan-Min (何蕃民)d, Gao Yang (高阳)a   

  1. a College of Science, China Agricultural University, Beijing 100083, China;
    b College of Engineering, China Agricultural University, Beijing 100083, China;
    c Institute of Mechanics, University of Kassel, Kassel 34125, Germany;
    d Sichuan Hydropower Investment & Management Group LTD, Chengdu 611130, China
  • Received:2013-11-07 Revised:2013-12-17 Online:2014-05-15 Published:2014-05-15
  • Contact: Gao Yang E-mail:gaoyangg@gmail.com
  • About author:61.44.Br; 62.20.D-; 62.20.M-; 07.05.Tp
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 11172319), the Scientific Fund of Chinese Universities (Grant Nos. 2011JS046 and 2013BH008), the Opening Fund of State Key Laboratory of Nonlinear Mechanics, Program for New Century Excellent Talents in University, China (Grant No. NCET-13-0552), and the National Science Foundation for Post-doctoral Scientists of China (Grant No. 2013M541086).

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摘要： Icosahedral quasicrystals are the most important and thermodynamically stable in all about 200 kinds of quasicrystals currently observed. Beyond the scope of classical elasticity, apart from a phonon displacement field, there is a phason displacement field in the elasticity of the quasicrystal, which induces an important effect on the mechanical properties of the material and makes an analytical solution difficult to obtain. In this paper, a finite element algorithm for the static elasticity of icosahedral quasicrystals is developed by transforming the elastic boundary value problem of the icosahedral quasicrystals into an equivalent variational problem. Analytical and numerical solutions for an icosahedral Al-Pd-Mn quasicrystal cuboid subjected to a uniaxial tension with different phonon-phason coupling parameters are given to verify the validity of the numerical approach. A comparison between the analytical and numerical solutions of the specimen demonstrates the accuracy and efficiency of the present algorithm. Finally, in order to reveal the fracture behavior of the icosahedral Al-Pd-Mn quasicrystal, a cracked specimen with a finite size of matter is investigated, both with and without phonon-phason coupling. Meanwhile, the geometry factors are calculated, including the stress intensity factor and the crack opening displacement for the finite-size specimen. Computational results reveal the importance of phonon-phason coupling effect on the icosahedral Al-Pd-Mn quasicrystal. Furthermore, the finite element procedure can be used to solve more complicated boundary value problems.

关键词: icosahedral quasicrystals, finite-size crack specimen, finite element method, cuboid

Abstract: Icosahedral quasicrystals are the most important and thermodynamically stable in all about 200 kinds of quasicrystals currently observed. Beyond the scope of classical elasticity, apart from a phonon displacement field, there is a phason displacement field in the elasticity of the quasicrystal, which induces an important effect on the mechanical properties of the material and makes an analytical solution difficult to obtain. In this paper, a finite element algorithm for the static elasticity of icosahedral quasicrystals is developed by transforming the elastic boundary value problem of the icosahedral quasicrystals into an equivalent variational problem. Analytical and numerical solutions for an icosahedral Al-Pd-Mn quasicrystal cuboid subjected to a uniaxial tension with different phonon-phason coupling parameters are given to verify the validity of the numerical approach. A comparison between the analytical and numerical solutions of the specimen demonstrates the accuracy and efficiency of the present algorithm. Finally, in order to reveal the fracture behavior of the icosahedral Al-Pd-Mn quasicrystal, a cracked specimen with a finite size of matter is investigated, both with and without phonon-phason coupling. Meanwhile, the geometry factors are calculated, including the stress intensity factor and the crack opening displacement for the finite-size specimen. Computational results reveal the importance of phonon-phason coupling effect on the icosahedral Al-Pd-Mn quasicrystal. Furthermore, the finite element procedure can be used to solve more complicated boundary value problems.

Key words: icosahedral quasicrystals, finite-size crack specimen, finite element method, cuboid

中图分类号:  (Quasicrystals)

  • 61.44.Br
62.20.D- (Elasticity) 62.20.M- (Structural failure of materials) 07.05.Tp (Computer modeling and simulation)