中国物理B ›› 2008, Vol. 17 ›› Issue (5): 1565-1573.doi: 10.1088/1674-1056/17/5/006

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Young's modulus surface and Poisson's ratio curve for tetragonal crystals

张建民1, 张 研1, Ji Vincent2, 徐可为3   

  1. (1)College of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China; (2)ICMMO/LEMHE UMR CNRS 8182, Universit'e Paris-Sud 11, 91405 Orsay Cedex, France; (3)State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, Xi'an 710049, China
  • 收稿日期:2007-07-26 修回日期:2007-09-02 出版日期:2008-05-20 发布日期:2008-05-20
  • 基金资助:
    Project supported by the State Key Development Program for Basic Research of China (Grant No 2004CB619302) and the National Natural Science Foundation of China (Grant No 50271038).

Young's modulus surface and Poisson's ratio curve for tetragonal crystals

Zhang Jian-Min(张建民)a)†, Zhang Yan(张研)a), Xu Ke-Wei(徐可为)b), and Ji Vincentc)   

  1. a College of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China; b State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, Xi'an 710049, China; c ICMMO/LEMHE UMR CNRS 8182, Universit'e Paris-Sud 11, 91405 Orsay Cedex, France
  • Received:2007-07-26 Revised:2007-09-02 Online:2008-05-20 Published:2008-05-20
  • Supported by:
    Project supported by the State Key Development Program for Basic Research of China (Grant No 2004CB619302) and the National Natural Science Foundation of China (Grant No 50271038).

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摘要： This paper gives the general expressions for the compliance s' ijkl , Young's modulus E(hkl) and Poisson's ratio \upsilon (hkl,θ ) along arbitrary loading direction [hkl] for tetragonal crystals. The representation surface for which the length of the radius vector in the [hkl] direction equals E(hkl) and representation curve for which the length of the radius vector with angle θ deviated from the reference directions [00\overline 1 ], [100], [00\overline 1 ], [10\overline 1 ] and [11\overline 2 ] equals \upsilon (100,θ ), \upsilon (001,θ ), \upsilon (110,θ ), \upsilon (101,θ ) and \upsilon (111,θ ) respectively, are constructed for nine tetragonal crystals (ammonium dihydrogen arsenate, ammonium dihydrogen phosphate, barium titanate, indium, nickel sulfate, potassium dihydrogen arsenate, potassium dihydrogen phosphate, tin and zircon). The characteristics of them are analysed in detail.

关键词: tetragonal crystals, elastic properties, representation surfaces, representation curves

Abstract: This paper gives the general expressions for the compliance $s'_{ijkl}$, Young's modulus $E(hkl)$ and Poisson's ratio $\upsilon (hkl, \theta)$ along arbitrary loading direction $[hkl]$ for tetragonal crystals. The representation surface for which the length of the radius vector in the $[hkl]$ direction equals $E(hkl)$ and representation curve for which the length of the radius vector with angle $\theta$ deviated from the reference directions $[00\overline{1}]$, [100], $[00\overline{1}]$, $[10\overline{1}$] and $[11\overline{2}]$ equals $\upsilon (100, \theta), \upsilon (001, \theta), \upsilon (110, \theta), \upsilon (101, \theta)$ and $\upsilon (111, \theta)$ respectively, are constructed for nine tetragonal crystals (ammonium dihydrogen arsenate, ammonium dihydrogen phosphate, barium titanate, indium, nickel sulfate, potassium dihydrogen arsenate, potassium dihydrogen phosphate, tin and zircon). The characteristics of them are analysed in detail.

Key words: tetragonal crystals, elastic properties, representation surfaces, representation curves

中图分类号:  (Elasticity)

  • 62.20.D-
68.35.Gy (Mechanical properties; surface strains) 81.40.Jj (Elasticity and anelasticity, stress-strain relations)