Fracture-damage Mechanical Analysis Of One-Dimensional Hexagonal Quasicrystals Finite Plate

With the discovery of the quasicrystals,the mechanical research of quasicrystals has become a new popular topic in recent years.This paper mainly studies the fracture or damage mechanics behavior of one-dimensional hexagonal quasicrystals,including the anti plane fracture problem and micro defect damage problem.The different polarization directions and different crack directions for constitutive specific equations are derived,what's more,the constitutive equation of quasicrystal with micro-damage is established,specifically,the following is the main research contents and main conclusions:1.As a new solid material,which is different from the crystals and the noncrystals.By means of its unique quasi-periodic structure,leading to variations of the physical properties of quasicrystals,such as power,electricity,magnetism and heat,which are essential differences with crystal materials.A lot of scholars have studied the relative problems in the study of the mechanics of quasicrystals,which is based on the transversely isotropic constitution.For further researches of the effects by the polarization direction and the crack through direction on the constitutive equation of quasictystals,we used the coordinate transformation method to study the polarization direction of the piezoelectric quasicrystal transformation and the constitutive equations of different crack propagation direction under one-dimensional quasicrystal six specific forms of expression,macro are characterized as transversely isotropic,orthotropic and anisotropic.2.Multi fields coupling problem is important,which should be considered in the study of fracture mechanics of quasicrystals.It has been proved that the piezoelectric effect is obvious,and the applied electric loading could be transformed into mechanical behavior.Most mechanical researchers are focusing on the the infinite boundary condition,however,it is inevitable that the finite boundary condition sometimes is more available in the engineering.Similar to the classical elastic materials,for quasicrystals,some of the fundamental research of fracture mechanics are about solving the basic structure with different forms of Griffith cracks,such as single crack,multi center crack(non single crack,non center crack etc.)and plate edge crack(single crack,unilateral containing hole and crack etc.).That the basic characteristics of quasicrystal quasicrystal,such as stress intensity factors and the energy release rate.In this paper,the fracture problem of quasicrystals rectangular plate under the coupling of the piezoelectric field and the elastic field is studied.The study found that with the plate height width ratio decreases and the increase of aspect ratio,the crack tip stress will gradually increase,and two kinds of crack electric boundary conditions would have different effects on the piezoelectric effect of quasicrystals.Therefore,in fact it isnecessary to consider not only the influence of the structure size,but also the effects by the different electric boundary conditions.3.Damage mechanics,is similar to the fracture mechanics,which are all belong to the failure mechanics category.Degradation of material properties are often accompanied by the initiation and propagation of micro defects,on the other hand,the initiation and propagation of micro defects are also accompanied by the degradation of material properties.The strength of the material is sensitive to micro or meso defects,and before the macro cracks appearing,micro defects(micro holes,micro crack initiation and development)will accelerate the consumption of the service life of the structure.Therefore,in order to better design and to predict the servicing ages of the structure by the strength and stiffness,so it is necessary to consider the damage.So far,the development of damage mechanics on quasicrystals or functionally graded materials,or other new materials,but not for elastic material or viscoelastic material.The mechanical researches about the damage mechanics theory applied to the new materials is very rare.In this paper,we analyze the one-dimensional hexagonal piezoelectric materials with micro hole damage and the mechanical behavior of functionally graded materials with changing elastic modulus and coefficient of thermal expansion.For the one-dimensional hexagonal quasicrystals,which is established a damage constitutive model,and we solve the anti plane fracture problems of one-dimensional hexagonal piezoelectric quasicrystal,from the results,the effect of the damage on the piezoelectricity of quasicrystal is obvious and elastic field,effects on the phason field also slightly larger than the effects of phonon field.On the other hand,for functionally graded materials,solving thermal buckling problems,the results show that the damage would have an influence in the critical loading that would resist it,and various boundary sizes may cause different effects on damage.When the size reaches a critical value,damage must have an inevitable impact in engineering application which should be considered.