Calculations Of SIFs For Linear Elastic V-Shaped Notches And Angular Distribution Functions For HRR Field

Initial defects such as cracks and notches are widespread in components of engineering structures,and these defects will greatly reduce the mechanical properties of the components.The stress field near the crack or notch tip is singular and this singularity may lead to the failure of the components under low stress state,so it is very necessary to define a crack initiation criterion.The stress intensity factor(SIF)is used as the initiation criterion in linear elastic fracture mechanics and the J-integral is the initiation criterion in elastoplastic fracture mechanics.Computing the SIF or J-integral of the crack or notch accurately is of great significance to safety analysis of structural components.This thesis uses improved Müller method to calculate the eigenvalues for V-shaped notches,which lays the foundation for the calculation of SIFs of linear elastic V-shaped notches.In this thesis,the weak form quadrature element method combined with the subregion generalized variational principle is used to calculate the SIF of linear elastic Vshaped notches under mode I cracking.The idea is to divide the region to be solved into two parts,known as the complementary energy area and potential energy area,and stresses and displacements are independent variables in the complementary energy area and potential energy area,respectively.The complementary energy is a function of stress and the potential energy is a function of displacement.Then the numerical discrete expression of the complementary energy,potential energy and mixed boundary work can be carried out by numerical integration and numerical differentiation.After taking variation on the mixed energy functional equation consisting of the complementary energy,potential energy and mixed boundary work,algebraic equations containing the coefficients of the stress field and the displacements can be obtained.These unknown quantities can be obtained by solving the equations.For the linear elastic V-shaped notch,the SIF can be obtained by the direct relation between the SIF and the first stress field coefficient.This thesis calculates the SIF of linear elastic V-shaped notches under mode I cracking and it proves that the weak form quadrature element method has high accuracy in calculating the SIF of the notch.And this method is more flexible than traditional finite element method in mesh generation.Meanwhile,the definition and properties of the J-integral are introduced,and the relation between the J-integral and the stress at the elastoplastic crack tip is explained in this thesis.The angular distribution functions of the HRR field for a power hardening material is calculated by the differential quadrature method,which lays a foundation for calculating the J-integral.