| Since the quasicrystals was first revealed,the physical properties and defects(cracks,holes,particle)of quasicrystals have always been a hot issue for physical,mechanical,and mathematical researchers.The application of quasicrystals is often related to its stable performance,and one of the main causes of quasicrystal instability is the presence of cracks.The work of this paper is first to focus on the dynamic response of two-dimensional octagonal quasicrystals stress intensity factors with mode I cracks in finite large planar,and then to study two-dimensional decagonal quasicrystal with mode II cracks in finite large planar and with round hole crack in infinity planar.The full text structure is as follows.In the first chapter,The research status,preparation knowledge,problems and research methods of this paper on elasto-/hydrodynamic problem of plane quasicrystals are introduced briefly.In the second chapter,the elasto-/hydrodynamic model was used to study the two-dimensional octagonal quasicrystal with mode I cracks.The model is discretized using the finite difference method,that is discrete the control equations which is represented by the displacements and boundary conditions and initial conditions which are determined by mode I cracks,and then the further numerical simulation were performed.Based on the numerical results,the variation of stress intensity factor with time at crack initiation stage was discussed,and the displacement,stress and stress intensity factors were analyzed.The results show that different types of loads have different effects on the model.The difference between them confirms that the peak value of the stress intensity factor is related to the energy contained in the impact loading,indicating that selecting an appropriate load has certain significance in the actual dynamic problem.According to the elastic-hydrodynamic model,the phase subfield is considered to be a diffusion motion,which has little effect on the propagation of the phonon field wave,but due to the phonon field-phase subfield coupling effect,the influence of the phase subfield cannot be ignored.The results corroborate the theoretical conclusion.In the third chapter,the elastic-hydrodynamic model was used to study the two-dimensional decagonal quasicrystal dynamic behavior changes with mode II cracks under different impact loads,different coupling coefficients,different sheet widths,and different loading positions.Changing the coupling coefficient has an effect on the displacement.The phonon field has only slight changes,but it has a great influence on the phase subfield.Loading step load at different time shows the hysteresis of the change of stress loudness factor.And the different width of the plate changes the cycle of the stress intensity factor.Finally,the change of the load loading position has a great influence on the stress intensity factor.Plate-end loading can induce larger stress intensity factors and thus more easily lead to fractures.However,the stress intensity factor loaded on the crack surface only makes slight fluctuations around the static value.The stress intensity factors of these two loading methods are not equal.In the fourth chapter,the problem of two-dimensional decagonal quasicrystal with circular hole cracks in infinite planar is studied.First,the complex function method is used to represent the stress function and stress boundary conditions as complex variable functions.By introducing the conformal mapping function,the circular hole cracks in the infinite planar are mapped into an unit circle,and the infinitely large outer region of the hole becomes the inside of the unit circle.Finally the finite-term truncation method is used to process the conformal mapping,and the stress intensity factor of the two-dimensional decagonal quasicrystal with circular hole cracks in an infinite plate under the remote tension is solved.A semi-analytical semi-numerical method with universal applicability is proposed. |
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