Fracture theory of quasicrystals

Abstract

Quasicrystals are brittle, study on fracture behaviour of the material is significant. In the previous chapters many crack problems are investigated, and the exact analytic, approximate and numerical solutions are constructed. This provides a basis for discussing the fracture theory. The exact solutions of crack problem of quasicrystals present particular importance, which reveal the essential nature describing fracture behaviour of this kind material. The exact analytic solution on a Griffith crack in decagonal quasicrystals was given by Li and Fan[1] in 1999. Afterward Fan[2], Fan and Mai[3] developed the idea of linear elastic fracture mechanics of quasicrystals based on the common feature of crack solutions obtained in that date. Rudhart et al[4] discussed the relevant topic from other point of view. Recently Fan and Guo[5], Zhu and Fan[6], Li and Fan[7] observed the analytic methods and solutions of cracks in three-dimensional icosahedral quasicrystals, Fan and Fan[8];[9], Li and Fan[15] found the plastic analytic solutions of cracks, Zhu and Fan[10];[11] carried out the numerical analysis on dynamic crack of quasicrystals, respectively. And the measurement of fracture toughness of the material is also reported[12]. The quite fruitful information mentioned above suggests the need to give a summary on the fracture study of quasicrystals. This chapter undertakes such a task and may put forward some pointers for the fracture mechanics of quasicrystals.