Numerical Analysis Of Elastodynamic Problems Of Several Kinds Of Quasicrystal Materials With Different Cracks

Since the discovery quasicrystals,scholars are very interested in it,including mathematics,physics,materials and other researchers.Because there are both phonon field and phason field in quasicrystals.So the equations are very complex.As a result,scholars can not the analytical solution.Now,if we want to analyze the physical properties and movement mechanism of quasicrystals.we are realize by numerical method.The work of this paper is mainly based on the dynamic model from S.B.Rochal and V.L.Lorman,that is,the initial boundary value problem of wave-telegraph equations.The dynamic problems and cracks propagation of decadal symmetric two-dimensional quasicrystal materials of point group 10 mm with mode ? and ? Griffith cracks are studied by finite difference method.Secondly,we discuss the influence of the crack length of different directions on stress intensity factor at the crack tip of the right end for four cracks with arbitrary length emanating from an elliptional hole in an infinite plate.The structure of the full text is as follows:In the first chapter,we describe the study background and significance of quasicrystal dynamics,the research status at home and abroad in the past decade and the basic knowledge and the numerical method involved in the article.In the second chapter,based on the dynamic model proposed by S.B.Rochal and V.L.Lorman,we have studied the dynamic problems of the decadal symmetric two-dimensional quasicrystals with mode ? Griffith cracks by the finite difference method.Firstly,through the normalized dynamic stress intensity factor at the crack tip,we analyze significances of the loading position of the step load and width of the specimen in the material.Secondly,through the displacement component in the x direction of the phason field,we analyze the role of the phonon-phason field coupling elastic constant,friction coefficient and effective phason mass density in the phason field.There are fluctuation characteristics in the phason field.But it is mainly the diffusion characteristics.As the value of the friction coefficient decreases gradually,the displacement component in the x direction of the phason field changes from diffusions to fluctuations.In the third chapter,we study the decadal symmetric two-dimensional quasicrystals with mode ? Griffith cracks.The dynamic stress intensity factor of phonon field is related to the loading time of pulse load,loading position of step load and specimen width.The phonon-phase coupling elastic constant affects the displacement component of phason field.The propagation characteristics of the phason field waves are related to the selection of the value of the friction coefficient and the effective phason mass density.There is fluctuation characteristic in the phason field.But it is mainly the diffusion characteristic.As the value of the friction coefficient decreases gradually,the displacement component in the y direction of the phason field changes from the diffusion characteristic to the fluctuation.In the fourth chapter,we have solved the dimensionless stress,the dimensionless dynamic stress intensity factor,the crack propagation velocity and the y-direction displacement of the phonon field at near the crack tip of the mode ? Griffith cracks by stress criterion and stress intensity factor criterion.At the same time,the dimensionless dynamic stress intensity factor and crack propagation velocity of mode ? Griffith cracks at near the crack tip are solved by stress criterion.At the position close to the break of the plate,the dimensionless dynamic stress intensity factor and dimensionless stress suddenly become very large,and the crack propagation velocity has a downward trend.The size of critical value of fracture affects the state of crack propagation.With the increase of the critical value of fracture,the variation range of dimensionless stress and dimensionless dynamic stress intensity factor increases.There are two stages of acceleration and uniform velocity in the crack propagation process.At the crack tip,the phase and phonon-phase coupling is evident.Under the same material constants,crack propagation occurs only when mode ? Griffith cracks is subjected to a greater external loading than mode ?.In the fifth chapter,by using the finite section method,combined with the conformal mapping function,we solve the stress intensity factor at the crack tip of the right crack,and analyze the effect of the crack length of different directions on it.When the angle between the tensile stress direction and the leveal direction is 90 degrees,the effect of the vertical cracks on the stress intensity factor at the right crack tip is related to the length of leveal cracks,and the change finally tends to be stable.With the increase of leveal cracks at both ends,the stress intensity factor increases.