八次对称二维准晶中的Ⅱ型裂纹

基金项目: 国家自然科学基金资助项目(19972011)

A Mode Ⅱ Crack in a Two-Dimensional Octagonal Quasicrystals

1.
Department of Basic Courses, Hebei Institute of Architectural Science & Technology, Handan, Hebei 056038, P. R. China;
2.
Research Center of Materials Science, Beijing Institute of Technology, Beijing 100081, P. R. China

摘要: 发展了八次对称二维准晶材料的断裂理论.应用Fourier变换与对偶积分方程理论,得到了八次对称二维准晶材料Ⅱ型Griffith裂纹的精确解析解,并由此确定了应力强度因子和应变能释放率,讨论了与相位子场有关结果的物理意义以及晶体与准晶体裂纹问题力学行为的差别,这些为研究此新固体材料的变形和断裂提供了重要的信息.
- Ⅱ型裂纹 /
- 八次对称二维准晶 /
- 应力强度因子
Abstract: The present study develops the fracture theory for a two-dimensional octagonal quasicrystals. The exact analytic solution of a Mode Ⅱ Griffith crack in the material was obtained by using the Fourier transform and dual integral equations theory, then the displacement and stress fields, stress intensity factor and strain energy release rate were determined, the physical sense of the results relative to phason and the difference between mechanical behaviors of the crack problem in crystal and quasicrystal were figured out. These provide important information for studying the deformation and fracture of the new solid phase.
- mode Ⅱ crack /
- two-dimensional octagonal quasicrystal /
- stress intensity factor

[1]	Shechtman D,Blech I,Gratias D,et al.Metallic phase with long-range orientational order and no translational symmetry[J].Phys Rev Lett,1984,53(20):1951-1953.
[2]	Levine D,Steinhardt P J.Quasicrystals:a new class of ordered structure[J].Phys Rev Lett,1984,53(26):2477-2480.
[3]	Ye H Q,Wang D N,Kuo K H.Five-fold symmetry in real and reciprocal spaces[J].Ultramicroscopy,1985,16(2):273-278.
[4]	Zhang Z,Urban K.Transmission electron microscope observation of dislocation and stackling faults in a decagonal Al-Cu-Co alloy[J].Phil Mag Lett,1989,60(1):97-102.
[5]	孟祥敏,佟百运,吴玉琨.Al65Cu20Co15准晶体的力学性能[J].金属学报,1994,30(1):60-64.
[6]	LI Xian-fang,FAN Tian-you,SUN Ying-fei.A decagonal quasicrystal with a Griffith crack[J].Phil Mag A,1999,79(8):1943-1952.
[7]	HU Cheng-zheng,DING Di-hua,YANG Wen-ge,et al.Possible two-dimensional quasicrystal structures with a six-dimensional embedding soace[J].Phys Rev B,1994,49(14):9423-9427.
[8]	HU Cheng-zheng,WANG Ren-hui,YANG Wen-ge,et al.Point groups and elastic properties of two-dimensional quasicrystals[J].Acta Cryst A,1996,52(2):251-256.
[9]	范天佑.准晶数学弹性力学与缺陷力学[J].力学进展,2000,30(2):161-172.
[10]	范天佑.断裂力学基础[M].南京:江苏科学技术出版社,1978.
[11]	吴祥法.准晶弹性与缺陷的有限元方法[D].博士学位论文.北京:北京理工大学,1998.
[12]	ZHOU Wang-min,FAN Tian-you.Axisymmetric elasticity problem of cubic quasicrystal[J].Chinese Physics,2000,9(4):294-303.