Extended Displacement Discontinuity Method For Internal And Interface Cracks In Materials Under Multi-field Environment

In this dissertation,the interface crack problems in thermoelastic,piezothermoelastic,magneoelectrothermoelastic and 1D hexagonal quasicrystal bi-materials and the crack problems in thermoporoelastic material are studied.With the aid of extended displacement discontinuity method(EDDM),the fracture behaviors of thermoelastic bi-material and homogeneous material are analyzed theoretically and numerically.The interface crack problems in piezothermoelastic and magneoelectrothermoelastic bi-materials are studied by extending the EDDM,and the effects of different electric and thermal boundary conditions on the fracture behaviors are discussed in the study of interface cracks in piezothermoelastic bi-material.Utilizing the analogy method,the solution for interface crack problem in 1D hexagonal quasicrystal bi-material is directly obtained according to the solution for magneoelectrothermoelastic bi-material.Furthermore,the EDDM is applied in the study of fracture mechanics in thermoporoelastic material,and the calculation for the extended stress intensity factors is conducted.The main work is listed as follows:(1)With the aid of general solution and Hankel transform technique,the fundamental solutions for unit-point displacement discontinuity and temperature discontinuity are obtained for isotropic thermoelastic bi-material.The boundary integral-differential equations are constructed for an arbitrarily shaped planar interface crack.By analyzing the singularity of the stress and temperature fields in the vicinity of crack front,the stress intensity factors with oscillatory singularity and the energy release rate are obtained.The fundamental solutions for a constant triangular element under uniform displacement discontinuity and temperature discontinuity are obtained based on the fundamental solutions for unit-point displacement discontinuity and temperature discontinuity.The oscillatory singularity is removed by replacing the Delta function with Gaussian distribution function.Afterwards,based on the obtained fundamental solutions for triangular elements,the boundary element method is proposed to numerically study an elliptical interface crack as an example.When reducing the bi-material to homogeneous one,the solution for homogeneous material is obtained,and the corresponding boundary integral equations for arbitrarily shaped planar cracks are presented.The expressions for stress intensity factors and energy release rate for homogeneous one are obtained as well.(2)Extending the analysis method for interface cracks in thermoelastic bi-material,the interface crack problems in three-dimensional transversely isotropic piezothermoelastic and mangeoelectrothermoelastic bi-materials are studied.In the study of interface crack problems in piezothermoelastic bi-material,the effects of different electric and thermal boundary conditions are discussed,and the iteration method is proposed to determine the electric displacement and heat flux in the cack cavity for electric and thermal semi-permeable boundary condition.Using the analogy method,the interface crack problem in three-dimensional transversely isotropic 1D hexagonal quasicrytal bi-material is analyzed,and the extended stress intensity factors and energy release rate are obtained.In the numerical methods,the fundamental solutions for a constant triangular element under uniform extended displacement discontinuities are presented.Adopting the same mathematical treatment,the oscillatory singularity in the intensity factors is removed.In the results and discussion,an elliptical crack is chosen as an example,the reliability of the proposed method is validated at first.Then the influence of ellipticity ratio,boundary conditions,material mismatch and applied loadings on the fracture behaviors is discussed.(3)Utilizing the extended displacement discontinuity method,the fracture problems in three-dimensional transversely isotropic thermoporoelastic media is studied,and the extended stress intensity factors in terms of the extended displacement discontinuities are obtained.In the numerical simulation,the coplanar elliptical cracks are chosen as an example,and the effects of ellipticity ratio,distance between cracks and the size of cracks on the fracture behaviors are discussed.