Analysis Of The Singular Intensity For The Crack Initiating From The Notch Root

The notch problem is widespread in engineering structures.The stress field at the root of the notch has a strong singularity,which makes it easy for the initiation of crack,and the initiated crack has a new stress singularity.The stress singularity of the notch and the crack at the tip of the notch will superimpose and affect each other,which makes the stress state of the crack at the tip of the notch is very complicated.The existed research mainly focuses on the stress singular field of the notch or crack separately,and the influence on the both is rarely studied.The research of the singular strength of the crack at the tip of the notch has certain theoretical significance and strong engineering application value.This paper mainly uses numerical methods to model the crack at the tip of the notch.The stress intensity factors of the crack at the tip of the notch are calculated,and the influences of the geometry shape,geometric parameters,and material ratio on the stress intensity factor of the crack initiating from the notch tip are evaluated.The main work of this paper is as follows:Firstly,the boundary element method is used to calculate the stress intensity factor of the crack at the tip of the plane bi-material notch.The two-material plane notch structure is divided into four parts.The singularity analysis is carried out in the two parts near the notch tip to obtain the singularity index and the characteristic angle functions.The non-singular region is simulated by the boundary element method.The combination of the linear expansion and the boundary integral equation is used to solve the stress intensity factor of the crack at the tip of the notch.The stress intensity factors for the cracks from the V-shaped notches and semi-circular notches are calculated respectively,and the effects of the factors such as the notch depth,the notch opening angle,the radius of the circular notch,and the elastic modulus ratio on the crack stress intensity for the crack initiating from the notch tip are studied.Secondly,the stress intensity factors of the crack initiating from the bi material anti-plane notch are studied by the finite element method.By the analysis of singularity characteristics,the singularity index of the bi-material anti-planar notch is calculated.The stress field of the crack from the root of the notch is calculated by the finite element method.The stresses of a certain number of internal points are selected,and the logarithmic logarithm is linearly fitted to determine the stress intensity factor.The effects of the shape of the notch,location of the notch,shear modulus ratio and other factors on the stress intensity factor for the crack from the tip of the notch are considered.Thirdly,the stress intensity factor of the crack initiating from the tip of a plate is studied by the finite element method.By substituting the asymptotic expansion of the displacement near the plate notch tip into the Reissner plate controlling equation,the singular characteristic equation of a plate notch is obtained,from which the singularity index can be obtained.The Shell43 element in ANSYS is used to analyze the cracks in the plate notch.It is found that there are three stress intensity factors in the plate notch,and the influences of the geometric parameters of the notch on these stress intensity factors are investigated.Finally,the effect of the non-singular stress on the crack growth and fatigue life is considered.According to the Williams asymptotic expansion theory,the complete elastic stress field at the crack tip region can be expressed by the sum of the singular stress and several non-singular stress terms.A method which combines the boundary element method and singularity analysis is proposed for calculating the complete stress field at the crack tip region.All the non-singular stress term in the expansion of Williams series can be obtained according to the requirements of calculation accuracy.The modified Paris law is introduced to predict the fatigue life of the mixed mode crack,and the effect of the non-singular stress on the fatigue life of the crack is investigated.