Study On The Elastic Defects And Crack In ID Hexagonal Quasicrystals

Due to special arrangement of atoms, quasicrystals have special mechanicalproperties and broad application prospects. Therefore, investment on elastic defects ofquasicrystal is of great significance. The problem of defects, fracture andnano-interface layer in one-dimensional hexagonal quasicrystals elastic material wasstudied in this thesis.First, the interaction of the circular inhomogeneity with the screw dislocation inthe interfacial layer is studied. By using the complex potential method, the closed an-alytical solutions are obtained. The explicit expressions of the displacement fields andimage forces acting on screw dislocations in the annular interfacial layer are derived.The numerical analyses clearly reveal that the elastic constants of material have agreat impact on the image force and the dislocation motion. With the increasing ofelastic constant of the phason or the phonon field, the repulsion force on the disloc a-tion due to the inhomogeneity or matrix increases. However, with the increasing ofcoupling elastic constant of the phonon-phason field, the attraction force acting on thedislocation due to the inhomogeneity or matrix increases. The attraction force actingon the dislocation due to the inhomogeneity or matrix increases with the increasingthe phason field elastic constant and phonon-phason coupling elastic constant, whenthe dislocation is close to the inhomogeneity or the matrix.Second, many researchers have less work involving nano-effect models on thequascicrystals mechanical behavior. Hence, the interaction of the circular inhomog e-neity with a screw dislocation in the nanoscale interfacial layer is investigated. Byusing the complex potential method, the closed analytical solutions are obtained whena screw dislocation is located in the nanoscale interfacial layer. Additional, the e x-plicit expression of the image forces acting on the screw dislocation are given byPeach-Koehler formula. The results show that the interface stress effect on the dislo-cation motion is significant. Due to the interfacial stress, there are more the equili b-rium points of a screw dislocation in the interfacial layer. Considering the interfacialstresses of the positive (negative) phonon field and phason field, there will be an ad-ditional repulsion (attraction) force acting on the dislocations. Considering the co u-pling interfacial stresses of the positive (negative) phonon field-phason field, therewill be additional attraction (repulsion) acting on the dislocations. The smaller radius of the inhomogeneity results in more obvious the dislocation motion due to interfacestress.Finally, the interaction between the circular interfacial cracks and a screw di s-location is investigated in one-dimensional hexagonal quasicrystals. By using theRiemann-Schwarz’s symmetry principle and the complex potential method, the e x-pressions of the displacement function and the stress intensity factor at the crack tipare obtained. The results show that the effects of quasicrystals elastic constants andthe distance between the dislocation and the crack tip play strongly role on the stressintensity factor at the crack tip. The stress intensity factor reduces with the increase ofthe distance between the dislocations and the crack tip. There is a critical openingangle which makes the value of the stress intensity factor reaching to the maximum.When the elastic constants of the phonon field and the phason field are greater, thestress intensity factor becomes larger. However, when the coupling elastic constantsof the phonon-phason field are greater, the stress intensity factor becomes smaller.