Stress Singularity Analysis For Three-Dimensional Notched Plates

The notched components are widely used in various engineering structures.The stress singularity at the notch tip has seriously threatened the safety of the structures.In this paper,based on the theoretical and numerical contributions in recent years,investigations about the singularity of the coupled stress field in the root region of three-dimensional notch are carried out according to the finite element method.The influences of different factors on the singularity of out-of-plane coupled mode are studied in detail,such as loading mode,notch form,scale effect and the Poisson's ratio,etc.The main contents and conclusions in this thesis are given as follows:1)The out-of-plane singular mode of V-notched plate under in-plane shear loading is studied by the finite element method.Because of the Poisson's effect,when a 3D V-notched plate is subjected to remote loading,a coupled out-of-plane singular mode is generated near the notch tip,which has a violent variation in the region close to the free surface.An increase of the opening angle leads to the decrease of the singular behavior of mode II,whereas mode O stays singular.The importance of the coupled out-of-plane singular mode increases with the size of V-notched plate,because of their different degrees of singularities.2)In order to obtain the stress fields in the plate weakened by a blunt notch,a series of plate models with different kinds of blunt notches are investigated,such as blunt V-notch,circular notch and elliptical notch.The influence of Poisson's ratio on the intensity of out-of-plane mode is also considered.As a result,the increasing of the ratio between the notch radius and the plate thickness,the intensity of the coupled mode can be decreased significantly.It is clear that lateral contraction caused by the Poisson' ratio is the main factor leading to the induced coupled out-of-plane singular mode.There is a relative deviation between the theoretical stress concentration factor from 2D and 3D analyses.The deviation trends to increase with the increasing of Poisson's ratio.3)The coupled singular mode of a V-notched plate subjected to anti-plane loading is studied.The results show that,along the thickness direction,the stress field of mode II is symmetric with respect to the mid-plane and the stress distribution of mode III is anti-symmetric with respect to the mid-plane.The strength of modeIII decreases with the increase of Poisson's ratio,while mode II is almost unaffected by Poisson's ratio.4)3D stress field ahead of a notch tip in thick plate weakened by a central square hole is analyzed.The results show that the singularity characteristic of the notch in each plane perpendicular to the thickness direction follows the classical plane theory and doesn't change according to different loading mode.On the contrary,the variation of through-thickness stress intensity factors is influenced by the loading mode.