The Research Of Some Fracture Mechanics Problems Of Classic, Quasicrystals And Composite Materials With Complex Defects

The core task of fracture mechanics problem is to calculate the stress and strain field and todetermine the stress intensity factor at the crack tip of solid materials or structures with all kinds ofdefects under external load.As two kinds of complex variable function method to solve the planeproblems in fracture mechanics, Westergaard stress function method and Muskhelishvili method arevery practical and effective.The Muskhelishvili method and conformal transformation method by thedevelopment of Muskhelishvili method both transform the area in physical plane to the unit circleinside (outside) or the upper half-plane (lower half-plane) in mathematical plane by a conformaltransformation.Then to solve tne corresponding problems.In the second chapter of this article,by using the complex variable function method andproposing a new conformal mapping,the problems of mode Ⅰ,mode Ⅱ and mode Ⅲ crack in astrip are studied respectively.The analytic solutions of the stress intensity factors at the crack tip arecalculated.When the height of the strip tends to infinite, the present results can be degenerated to thesolutions of a finite Griffith crack in a infinite plane.In the third chapter,the control equations of the anti-plan elasticity problem of point group6ofone-dimensional hexagonal quasicrystals are obtained.By using the complex variable functionmethod,complex representations of the components of stress and boundary conditions of theanti-plane elasticity problem of point group6of one-dimensional hexagonal quasicrystals in thecycle plane are given.The problems of point group6of one-dimensional hexagonal quasicrystalswith an elliptical hole, a semi-infinite crack,two collinear semi-infinite cracks and a power functioncurved crack are studied respectively.The fracture problem of a finite Griffith crack in a point group6of one-dimensional hexagonal quasicrystals strip is also studied.The analytic solutions of the stressintensity factors of mode Ⅲ problem of the corresponding defects of phonon field and phason fieldare obtained.In the limite case,the obtained results of the phonon field are completely consistent withthe classical elasticity results.In the fourth chapter,by using the generalized complex variable function method,complexrepresentations of the components of stress and boundary conditions of the plane elasticity problemof plate of orthotropic composite material are given.By constructing the appropriate generalized conformal mapping,the analytic solutions of the stress field and the stress intensity factor at thecrack tip of the plane elasticity problem of plate of orthotropic composite material with semi-infinitecrack are obtained.