Anti-plane Fracture Problems Of Nano Defects In Multi-Field Coupling Materials

In practical engineering,the application of multi-field coupling materials(magnetoelectroelastic materials,Quasicrystal materials and piezoelectric materials)is more and more extensive.However,various defects,such as cracks,holes and dislocations,are inevitable in production and using.The discontinuity of defects leads to stress concentration and even damage of material structure.Therefore,the fracture problem of multi-field coupling materials is widely concerned by researchers.In the classical elasticity theory,the influence of surface effect on analytical solution can be ignored,but when the defect size is nano-scale,the influence of surface effect must be considered.In this paper,the anti-plane fracture problems of nano-scale defects in magnetoelectroelastic materials,one-dimensional hexagonal quasicrystals and one-dimensional hexagonal piezoelectric quasicrystals are studied,which has a good reference value for analyzing that the stress intensity factors and the energy release rate of multi-field coupling materials change with the size of material defects.Firstly,based on the Gurtin–Murdoch surface/interface model and the theory of complex potential,the anti-plane fracture problem of two nano-cracks emanating from a regular 2(n+1)-polygon nano-hole in one-dimensional hexagonal quasicrystals is studied by constructing a new conformal mapping.The analytical solutions of the phonon field and the phason field are obtained,the solutions of the stress intensity factors and the energy release rate are also obtained.In the numerical examples,the surface effect on the stress intensity factors of phonon field and phason field,the dimensionless stress intensity factor and the energy release rate is analyzed.It is found that the stress intensity factors of dimensionless phonon field and phason field are affected by the mechanical loads of phonon field and phason field when considering the surface effect,which is obviously different from the conclusion of classical elasticity theory.Secondly,by constructing a new conformal mapping and using the analytic function theory,the fracture problem of six cracks emanating from a hexagonal hole in one-dimensional hexagonal piezoelectric quasicrystals is studied for the first time at nanoscale.In the case of electric impermeability,the analytical solutions of the stress intensity factor and energy release rate of the complex defect problem of quasicrystals,a new material,is obtained.In the numerical examples,the stress intensity factor,the electric displacement intensity factor and the energy release rate are discussed.In addition,the effects of mechanical and electrical loads on fracture parameters are discussed.The results show that when the surface effect is considered,the phonon field,phason field and electric field are coupled,and when the defect size increases to a certain extent,the values of fracture parameters tend to the results of classical elasticity theory.Finally,the anti-plane fracture of four nano-cracks emanating from a regular 4n-polygon nano-hole in magnetoelectroelastic materials is studied.The analytical solutions of the stress intensity factor,the electric displacement intensity factor,magnetic induction intensity factor and energy release rate are obtained under the boundary conditions of magnetoelectric impermeability with surface effect.The numerical examples show the influence of surface effect and the size of defect on the stress intensity factor,electric displacement intensity factor,magnetic induction intensity factor and energy release rate.It can be seen that the stress intensity factor,electric displacement intensity factor,and magnetic induction intensity factor are significantly size-dependent when considering the surface effects of the nanoscale defects.And when the size of defect increases to a certain extent,the influence of surface effect begins to decrease and finally tends to follow the classical elasticity theory.