Study On Multi-Field Coupled Fracture Mechanics Of An Arbitrary Position Crack Emanating From A Nano-Scale Hole

Based on the Gurtin-Murdoch(G-M)theory of surface elasticity and the complex elasticity,this paper studies the mode III fracture mechanics performance of an arbitrary position crack emanating from a nano-scale hole in one-dimensional hexagonal piezoelectric quasicrystal materials and magnetoelectroelastic materials under the multiphysics field loading.The main contents of this paper are as follows:Based on the piezoelectric quasicrystal theory and the boundary value theory,analysis of the mode III fracture problem of an arbitrary position crack emanating from a nano-scale hole in one-dimensional hexagonal piezoelectric quasicrystal under the condition that the nano-defect surface is electrically impassable is.Based on the theory of complex elasticity,the non-classical boundary conditions of displacement and stress on the surface of nano defects(nano round holes,nano cracks)are established.Based on the conformal mapping theory,the analytical expression of the electroelastic field in the matrix material under the condition that the surface of the nano defect is electrically impassable is given.Based on the definition of fracture parameters of the piezoelectric quasicrystal materials,the analytical solution of the electroelastic field intensity factor at the tip of nano-cracks is given.The effects of nano-defect size,nano-crack location,nanocrack length/aperture ratio,relative size between nano-cracks,phonon field load,phason field load,electrical load and piezoelectric quasicrystal coupling coefficient on the electroelastic field intensity factor are discussed.Based on the magnetoelectroelastic theory,analysis of the mode III fracture problem of an arbitrary position crack emanating from a nano-hole in magnetoelectroelastic material with surface effect containing is.Based on the complex variable elasticity theory,the conformal mapping theory and the non-classical boundary conditions of the nanodefect surface,the analytical expression of the magnetoelectroelastic field the magnetoelectroelastic material under the condition that the nano-defect surface is magnetoelectric impermeable under the action of multiple physical field loads(mechanical load,electric displacement load,magnetic load)is given.Based on the definition of fracture parameters of the magnetoelectroelastic materials,the analytical solution of magnetoelectroelastic field intensity factor at the tip of nano-cracks is given.The change trend of the magnetoelectroelastic field intensity factor at the crack tip with the nano-crack position,nano-defect related parameters and multi-physical field load is analyzed numerically.