Finite Difference Analysis Of Dynamic Fracture In Decagonal And Icosahedral Quasicrystals

Based on the elasto-hydro-dynamic model and the Bak’s model,a novel finite difference method is proposed to investigate the dynamic response of a plate made of decagonal and icosahedral quasicrystals respectively.The dynamic crack problem of decagonal quasicrystals is investigated first via a novel type of explicit finite difference method based on the elasto-hydro-dynamic model. The accuracy and convergence of the finite difference scheme is analyzed, the validity and applicability of the scheme is also verified through a special case of vanishing coupling parameter. In addition, numerical simulations are performed to illustrate the interplay of crack and wave, which demonstrate that the proposed method is appropriate to solving dynamic problems in quasicrystals with high efficiency. The effectiveness is due to that the combination of the least square fitting with extrapolations first introduced to compute dynamical stress intensity factor for quasicrystals, and the high efficiency lies in that it is an explicit scheme.Based on the elasto-hydro-dynamic model and the Bak’s model, a centered-cracked plate of icosahedral quasicrystal is then investigated via finite difference method. Through comparing the stress intensity factors of the two models, similarities are observed between the temporal variation of stress intensity factors, and the peak value of the Bak’s model is larger than that of the elasto-hydro-dynamic model but with some delay, in which Bak’s model is first utilized when studying the dynamic crack problems in icosahedral quasicrystals. Moreover, the influences of different friction coefficients and different coupling parameters on the stress intensity factors are studied. According to the elasto-hydro-dynamic model, a single-edge cracked plate is analysed, we obtain the numerical results of several important fracture parameters, which are well consistent with that of the classic results of crystals under the condition of vanishing coupling parameters.Finally, based on the elasto-hydro-dynamic model, a mode II crack in decagonal quasicrystal is first considered by using finite difference scheme. The dynamic initiation is analyzed in detail and the temporal variation of the normalized dynamical stress intensity factor is obtained, on the basis of which fast crack propagation is also discussed,and the problems to overcome related to fast crack propagation of mode II crack as well as their possible solutions are both given.