Research On Crack Propagation And Fatigue Life Based On Smooth-extended Finite Element Method

The smooth finite element method is a new type of numerical simulation method,which has advantages over the traditional finite element method.The unremitting efforts of many scholars over the past decades have made it more and more extensive.However,for the crack propagation problem,both the traditional finite element method and the smooth finite element method need to encrypt the mesh near the crack,and the crack can only expand along the boundary of the divided mesh.This paper introduces the extended finite element method theory,and combines the smooth finite element method with the extended finite element method to form a smooth-extended finite element method(S-XFEM).The specific research content is as follows:1)This paper introduces the basic theory of the smooth finite element method,analyzes the reconstructed strain field of the smooth finite element method,compares its advantages with the traditional finite element method,and discusses its shortcomings in the analysis of cracked models.The extended finite element method is introduced to deal with cracked models,and the smooth finite element method is combined with the extended finite element method to derive a new algorithm that has both the advantages of the smooth finite element method and the extended finite element method.2)Based on the smooth-extended finite element method theory,a finite element analysis program suitable for general problems is written in the Matlab software platform.The main program flow chart and main sub program flow chart are given,as well as the main parameter expressions.The program is used to analyze the unidirectional tensile force of an infinite slab with a central oblique crack.The analysis results show that the smooth-expanded finite element method can avoid local mesh encryption of the stress field near the crack.At the same time,the theory and algorithm have excellent performance in numerically solving the stress intensity factors of mode I cracks,mode II cracks,and mode I and II compound cracks.3)The crack propagation criterion is introduced,and the smooth-expanding finite element method is used to study the dynamic crack growth problem.A crack propagation judgment algorithm and crack propagation are added to the source code of static crack problem analysis.The numerical simulation results of the crack propagation trajectory tracking of the side crack plate model and the four-point bending test model show that the smooth-expanding finite element method has the advantage of the extended finite element method,and the crack can freely expand in the problem domain without being restricted by the stress field grid,and there is no need to encrypt local mesh near the crack.4)Fatigue theory was introduced to extend the use of the smooth-expanded finite element method to crack fatigue life prediction under cyclic loading.An analytical program for predicting crack fatigue life based on various crack growth rate models is designed.Numerical simulations show that the algorithm can obtain a very accurate prediction of crack fatigue life.