Numerical Simulation Of Fatigue Crack Propagation Of Brittle Fracture Based On Phase Field Method

As the main form of mechanical damage in the actual structure of engineering,fatigue damage has seriously affected the actual development of the project,and also brought serious harm and great damage to people.Therefore,it is necessary to conduct a detailed study on fatigue damage.At present,with the continuous development and advancement of computer technology,the method of studying fatigue cracks has been further developed,gradually transitioning from traditional experimental methods and analytical methods to numerical methods.As far as the current numerical research methods are concerned,mainly including the finite element method,the extended finite element method and the meshless method,these methods have their own advantages and are frequently used for the study of fatigue cracks.Recently,researchers have developed a new method for simulating crack propagation: Phase Field Method.The phase field method is mainly used to simulate the crack propagation of brittle materials or quasi-brittle materials.It has the characteristics of simple implementation,grid insensitivity and easy handling of crack initiation,but there are few studies on fatigue crack growth,especially for the study of fatigue crack growth rate.Therefore,this paper will try to use this new method to carry out the research on the rate of fatigue crack growth.In order to demonstrate the feasibility of the phase field method for fatigue crack propagation research and to verify the accuracy of the proposed new projection operator algorithm,this paper has carried out the following research:(1)According to the relevant theory of phase field method,we established a crack topology model,and established the differential equation of the fracture phase field from the perspective of energy and fracture mechanics,and carried out finite element discretization.Then we combine the fatigue crack propagation theory to carry out the finite element discretization of the calculation equations of stress intensity factor,strain energy and fatigue crack growth rate,and finally compile the corresponding finite element program with MATLAB.(2)For the shifted strain split algorithm used in the calculation of displacement in the general phase field method,the calculation method of the projection operator is improved in this paper,which makes it more concise in expression and easier in calculation.In addition,it is verified whether it is correct or not.(3)The effects of regularization length and grid number on crack propagation under isotropic homogeneous materials are discussed.And the improved algorithm and the original algorithm are compared and analyzed.In addition,the effects of pre-crack length,load ratio(or average load),fracture toughness,pre-crack location and pre-crack angle on the fatigue crack growth rate were investigated based on phase field theory and Paris formula.