MA Qing, WANG Guixia, LI Lianhe. Dynamic Problems of Mode Ⅱ Cracks in 2D Octagonal Quasicrystals[J]. Applied Mathematics and Mechanics, 2018, 39(10): 1180-1188. doi: 10.21656/1000-0887.380272
Citation: MA Qing, WANG Guixia, LI Lianhe. Dynamic Problems of Mode Ⅱ Cracks in 2D Octagonal Quasicrystals[J]. Applied Mathematics and Mechanics, 2018, 39(10): 1180-1188. doi: 10.21656/1000-0887.380272

Dynamic Problems of Mode Ⅱ Cracks in 2D Octagonal Quasicrystals

doi: 10.21656/1000-0887.380272
Funds:  The National Key R&D Program of China(2017YFC1405600);The National Natural Science Foundation of China(11462020;11361039)
  • Received Date: 2017-10-27
  • Rev Recd Date: 2018-02-26
  • Publish Date: 2018-10-01
  • Based on the elasto-hydrodynamic model, the dynamic problems of mode Ⅱ cracks in octagonal 2D quasicrystals were investigated with the finite difference scheme. The dynamic responses of stress intensity factors to different loading periods and different specimen sizes were analyzed, respectively. Then the influence of different phonon-phason coupling elastic constants on the displacement component of the phason field was demonstrated. The results indicate that, the stress intensity factor increases with the loading period, while the curve approaches the curve under the step load. The wider the specimen size is, the longer the time will be for the stress wave to reach the crack tip, and the smaller the stress intensity factor will be. The crack loading is different from the board loading, for the change of the stress intensity factor under the former is greater than that under the latter. With the increasing phonon-phason coupling constant, the displacement component of the phason field rises. Because of the influence of the phonon and phonon-phason coupling effect, the displacement component of the phason field equals zero when the phonon-phason coupling constant is zero.
  • loading
  • [1]
    SHECHTMAN D, BLECH I, GRATIAS D, et al. Metallic phase with long-range orientational order and no translational symmetry[J]. Physical Review Letters,1984,53(20): 1951-1953.
    [2]
    李联和, 刘官厅. 准晶断裂力学的复变函数方法[M]. 北京: 科学出版社, 2013.(LI Lianhe, LIU Guanting. Quasicrystal Fracture Mechanics of Complex Variable Function Method [M]. Beijing: Science Press, 2013.(in Chinese))
    [3]
    YANG W, FEUERBACHER M, TAMURA N, et al. Atomic model of dislocations in Al-Pd-Mn icosahedral quasicrytals[J]. Philosophical Magazine A, 1998,77(6): 1481-1497.
    [4]
    WANG X. Green functions for a decagonal quasicrystalline material with a parabolice boundary[J]. Acta Mechanica Solida Sinica,2005,18(1): 57-62.
    [5]
    WANG X, ZHANG J Q. A steady line heat source in a decagonal quasicrystalline half-space[J]. Mechanics Research Communications,2005,32(4): 420-428.
    [6]
    CHEN W Q, MA Y L, DING H J. On three-dimensional elastic problems of one-dimensional hexagonal quasicrystal bodies[J]. Mechanics Research Communications, 2004,31(6): 633-641.
    [7]
    GAO Y, XU S P, ZHAO B S. Boundary conditions for plate bending in one-dimensional hexagonal quasicrystals[J]. Journal of Elasticity,2007,86(3): 221-233.
    [8]
    郭俊宏, 刘官厅. 一维六方准晶中具有不对称裂纹的圆形孔口问题的解析解[J]. 应用数学学报, 2007,30(6): 1066-1075.(GUO Junhong, LIU Guanting. Analytic solutions of the one-dimensional hexagonal quasicryst about problem of a circular hole with asymmetry cracks[J]. Acta Mathematicae Applicatae Sinica,2007,30(6): 1066-1075.(in Chinese))
    [9]
    LI X Y. Elastic field in an infinite medium of one-dimensional hexagonal quasicrystal with a planar crack[J]. International Journal of Solids & Structures,2014,51(6): 1442-1455.
    [10]
    BAK P. Phenomenological theory of icosahedral incommensurate (“quasiperiodic”) order in Mn-Al alloys[J]. Physical Review Letters,1985,54(14): 1517-1519.
    [11]
    BAK P. Symmetry, stability, and elastic properties of icosahedral incommensurate crystals[J]. Physical Review B: Condensed Matter,1985,32(9): 5764-5772.
    [12]
    LUBENSKY T C, RAMASWAMY S, TONER J. Hydrodynamics of icosahedral quasicrystals[J]. Physical Review B: Condensed Matter,1985,32(11): 7444-7452.
    [13]
    FAN T Y, WANG X F, LI W, et al. Elasto-hydrodynamics of quasicrystals[J]. Philosophical Magazine,2009,89(6): 501-512.
    [14]
    LI X F. Elastohydrodynamic problems in quasicrystal elasticity theory and wave propagation[J]. Philosophical Magazine,2013,93(13): 1500-1519.
    [15]
    张超华, 李联和, 云国宏. 十次对称二维准晶材料的位错动力学问题[J]. 固体力学学报, 2017,38(2): 165-169.(ZHANG Chaohua, LI Lianhe,YUN Guohong. Study on moving dislocations in decagonal quasicrystals[J]. Chinese Journal of Solid Mechanics, 2017,38(2): 165-169.(in Chinese))
    [16]
    ZHU A Y, FAN T Y. Dynamic crack propagation in decagonal Al-Ni-Co quasicrystal[J]. Journal of Physics Condensed Matter,2008,20(20): 295217.
    [17]
    WANG X F, FAN T Y, ZHU A Y. Dynamic behaviour of the icosahedral Al-Pd-Mn quasicarystal with a Griffith crack[J]. Chinese Physics B,2009,18(2): 709-714.
    [18]
    YIN Z H, FAN T Y, ZHU A Y. Dynanmic crack propagation in five-fold symmetry quasicrystals[J]. Modern Physics Letters B,2009,23(12): 1509-1518.
    [19]
    尹姝媛, 周旺民, 范天佑. 八次对称准晶中的Ⅱ型裂纹[J]. 应用数学和力学, 2002,23(4): 376-380.(YIN Shuyuan, ZHOU Wangmin, FAN Tianyou. A model Ⅱ crack in a two-dimensional octagonal quasicrystals[J]. Applied Mathematics and Mechanics,2002,23(4): 376-380.(in Chinese))
    [20]
    ZHU A Y, FAN T Y. Elastic analysis of a mode Ⅱ crack in an icosahedral quasicrystal[J]. Chinese Physics,2007,16(4): 1111-1118.
    [21]
    郭玉翠, 范天佑. 平面十次对称准晶中Ⅱ型中Griffith裂纹的求解[J]. 应用数学和力学, 2001,22(11): 1181-1186.(GUO Yucui, FAN Tianyou. A model-Ⅱ Griffith crack in decagonal quasicrytals[J]. Applied Mathematics and Mechanics,2001,22(11): 1181-1186.(in Chinese))
    [22]
    郝莉. Ⅱ型动态裂纹的动态应力强度因子的数值分析[J]. 北京建筑工程学院学报, 1998,14(3): 72-84.(HAO Li. The numerical analysis about dynamic stress intensity factor of Ⅱ dynamic crack[J]. Journal of Beijing Institute of Civil Engineering and Architecture,1989,14(13): 72-84.(in Chinese))
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (1047) PDF downloads(619) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return