Multiscale 2D Extended Finite Element Method For The Interaction Between The Macro Crack And Micro Defects In Metal Material

Under cyclic loading during service time,the metal structures in civil and marine engineering suffer varying stress,the fatigue failure problem become the vital main issue of the structure design.During the propagating process of the main crack in the structure,multiple micro defects(cracks,voids,inclusions)accumulate around the main crack tip.The interaction between the macro crack and micro defects may accelerate the propagation of the main crack.Taking the fatigue and fracture problem in the metal structures as engineering background,the present thesis developed elastic-plastic e Xtended finite element method(XFEM),and improved multiscale XFEM.The law of stable crack propagation in elastic-plastic material is studied,as well as the mechanism of the interaction between the macro crack and micro defects during the propagation of the macro crack.The main innovations and contributions are summed as follows:1.The XFEM is extended in the domain of elastic-plastic nonlinearity to numerically simulate the stable crack propagation in ductile materials.In the elastic-plastic XFEM,plastic enrichment functions are adopted for modelling the displacement field in the vicinity of the crack tip,Newton-Raphson iterative technique is employed to solve the nonlinear equation.It can be applied in numerical simulation of the stable fatigue growth in ductile materials.The feasibility of the method is verified through comparison with experimental data and ANSYS simulation.2.The multiscale mechanical model is established by combining multiscale projection technique and XFEM.In this method,computational models at different scales can be solved by XFEM independently,and the micro discontinuities can be ignored in the macroscale model.The algorithm is implemented in the platform Matlab,for simulation of discontinuities at different scales.Through case study,the influences of key parameters(density of macroscale mesh,density of microscale mesh,size of the microscale domain)on the accuracy of the algorithm are investigated.3.With special treatment on the blending elements,the multiscale XFEM is improved.With such modification,the accuracy of displacement solution around the crack tip on the macroscale level is improved.Therefore,the necessary microscale domain size can be reduced,meanwhile,the convergence of the algorithm is enhanced,which lead to computational cost saving.4.Based on application backgrounds of the fatigue and fracture problem of the metal structure in civil and marine engineering,the mechanism of interaction between the macro crack and micro defects is studied.By using the multiscale XFEM established in the present thesis for numerical simulation,the relation between the location of the micro defect and its effect on the macro crack is analyzed thoroughly.Suggestion for initiative control of the fatigue life is made.5.Based on application backgrounds of the fatigue life prediction problem of the metal structure in civil and marine engineering,the effect of the micro initial defects on the propagation of the macro crack and fatigue life is studied,the effect of presence of micro defects on the macro crack path,propagation speed and fatigue life is revealed,as well as the stress concentration of micro defects.The results of the present study can be provided as reference for fatigue design of metal structures.The elastic-plastic XFEM,multiscale XFEM developed in the present thesis,can simulate the macro crack propagation in presence of multiple micro defects accurately and efficiently.The detailed conclusions and suggestion on the specific research issues which are refined from particular engineering applications can be provided as design reference and theoretical basis for fatigue and fracture problem civil and marine engineering.In addition,it is also of substantial academic importance to extend the knowledge of intrinsic mechanism of the issue.