Evaluation Of Stress Intensity Factor And Heat Flow Intensity Factor Of V-notch

Due to material or geometric discontinuities in engineering structures,the stress singularity or stress concentration will occur at the tip of the V-notch,which have a great impact on the strength of the structure and even seriously threaten the safety of the structure.Therefore,the study of the singularity of at the tip of the V-notch is of great importance to the safety of engineering structures.In this paper,the boundary element method is used to study the stress intensity factor and the heat flux intensity factor of the V-notch.The main research contents are as follows:Firstly,the stress intensity factor of the single-material notch is calculated using the point-taking method.The displacement field near the tip of the single material notch is calculated by the elasticity boundary element method.Then,the singularity characteristic equation of the single material notch is established and solved by the numerical method to obtain the singularity index and characteristic angle function.The displacement near the notch tip is expanded asymptotically according to Williams theory.The calculated displacement value,singularity index and characteristic angle function are substituted into the Williams series asymptotic expression to solve the expansion coefficient.The quantitative relationship between the stress intensity factor and the expansion coefficient is used to determine the stress intensity factor for single material notch.Secondly,the point-taking method is used to calculate the stress intensity factor of the bi-material notch.The multi-domain elasticity boundary element method is applied to calculate the displacement field near the bi-material notch.The singular characteristic equation of the bi-material notch is constructed and solved to obtain the singularity index and characteristic angle function.The displacement field near the tip of the bi-material notch is expressed as a linear combination of a finite number of singularity indices and characteristic angle functions.The calculated displacement values of the selected points,the singularity index,and characteristic angle function are substituted into the above mentioned linear combination,from which the stress intensity factor of the bi-material notch can be calculated.Thirdly,the point-taking method is used to calculate the heat flux intensity factor of the notches in isotropic material,orthotropic material and anisotropic material.The potential boundary element method is used to calculate the temperature of the internal point near the notch tip.The heat flux in the small fan-shaped domain near the notch tip is expanded asymptotically.The singularity characteristic equation with respect to the heat flux singularity is derived and solved to provide the heat flux singularity index and characteristic angle function.From the temperature field from the notch tip,the singularity index,and the characteristic angle function,the expansion coefficient of the temperature asymptotic expansion near the notch tip can be calculated.Finally,the heat flux intensity factors of five kinds of bi-material bonding notches such as isotropic-orthotropic,isotropic-anisotropic,orthotropic-anisotropic,orthotropic-anisotropic,are determined by the point-taking method.The multi-domain potential boundary element method is used to calculate the temperature field at the tip of the bonded notch.The heat flux singularity characteristic equation of the bonded notch is established,from which the heat flux singularity index and characteristic angle can be obtained by the numerical method.The temperature values of the selected points and the singularity characteristic analysis result are combined to obtain the heat flux intensity factors of the bi-material notch.