The Williams Element With Generalized Degrees Of Freedom For Fracture Parameter Analysis Of Interface Crack

The two kinds of materials combined by a certain way are usually complicated in forces bearing and prone to interface crack.In this paper,the interface crack can be divided into two types,that is,material property continuous interface crack and material property discontinuous interface crack,according to the relationship between the properties of the materials on the upper and lower surfaces of the crack.There is an essential difference in the stress field at the crack tip between the two.The stress field at the crack tip of the material property continuous interface crack has the traditional square root singularity.However,in addition to the square root singularity,the stress field at the crack tip of the material discontinuous interface crack also has oscillatory singularity.During fracture analysis,the Williams element with generalized degrees of freedom based on the Generalized Parameter finite element method,can directly calculate the stress intensity factors of crack tip by solving the generalized parameters related to stress intensity factors,which has been well applied in uniform material crack problem,though,the continuous and discontinuous changes of material properties at the interface crack have not been considered.In this paper,to take advantage of the Williams element with generalized degrees of freedom to solve the stress intensity factors of crack tip,the following research work has been carried out around the problem of continuous and discontinuous change of stress intensity factors of crack tip at the interface crack:Firstly,the Williams element with generalized degrees of freedom has realized the fast solution of the stress intensity factors of the single crack tip and the independent multi-crack tip in uniform materials under different fracture modes.However,the interaction of crack tips after crack propagation has not taken into account.In this paper,the scheme of the Williams element with generalized degrees of freedom for each crack stress intensity factors analysis of multi-crack intersecting is established.Further research shows that the method is insensitive to the size of singular zone and has high calculation accuracy and efficiency,which lays a theoretical foundation for the interface crack analysis of continuous material properties in this paper.Secondly,with the material property continuous interface crack problem simplified into the functional gradient material crack problem,the Williams element with generalized degrees of freedom of the functional gradient material plane fracture analysis is established.According to the change of types and directions of material elastic modulus,the calculation models are divided into 8 cases,combined with non-uniform element to characterize the non-uniformity of the properties of functional gradient material.In this case,the crack SIFs of functional gradient material can be obtained by solve the relative generalized parameters of SIFs,which,in the meantime,verifies that it is feasible to manage the material property discontinuous interface crack,that has been equivalently transformed,with the solution in this paper.Thirdly,when characterizing the stress intensity factors of the material property discontinuous interface crack,the Williams stress function has oscillatory singularity.As a result,the Williams element with generalized degrees of freedom based on generalized parameter finite element method and Williams series can not directly solve the stress intensity factors of the material property discontinuous interface crack.Combined with the research results in chapter 3,the interface crack in the material property discontinuous interface crack model is equivalent to a functional gradient material interface layer,which translates the material property discontinuous interface crack into a material property continuous interface crack problem.At the same time,the parameter sensitivity analysis of the stress intensity factor of the material property continuous interface crack after equivalent transformation is carried out.The calculated results of this method are compared with the solution of ANSYS finite element software,and the suggested values of important parameters are given.By changing the relative parameters,such as the thickness of the interface layer and the relative position of the crack,the range of the parameters when the material property discontinuous interface crack and the material property continuous interface crack after equivalent transformation is approximately equivalent is given.