Crack Propagation Control And Performance Optimization Of Brittle Materials Based On Phase Field Method

With the rapid development of materials engineering technology,a large number of new materials,structures,and process technologies have been widely used in actual engineering.Although the use of new technologies largely meets the ever-changing material structure design requirements,the uncertain factors brought about by new technologies also indirectly lead to higher suddenness of accidents in actual applications.The problem of fracture failure caused by passing through the critical area of the material structure is particularly prominent.Therefore,the relevant research on the crack propagation law is of great engineering significance for effectively avoiding the fracture failure of the material structure and improving the overall mechanical properties of the structure.However,when the traditional discrete numerical calculation method is used to analyze the crack propagation,it is often necessary to prefabricate the crack and select the fracture criterion in advance.At the same time,it is also necessary to track and describe the topological path of the complex crack surface,which greatly limits its analysis and application in two-dimensional multi-crack interaction and three-dimensional complex structure cracks.In recent years,the fracture phase field method developed based on damage mechanics perfectly overcomes the above shortcomings and can accurately simulate the entire process of crack initiation,propagation,crossover and fracture failure.Therefore,this paper will study and analyze the crack growth behavior of brittle materials based on the fracture phase field method.The specific research contents are as follows:(1)Based on the theory of fracture damage mechanics,a fracture phase field model is constructed,and the governing equation of the fracture phase field and its corresponding finite element discretization scheme are derived.Subsequently,the multi-field coupling problem of the fracture phase field is decoupled into two subproblems of displacement field and phase field,and the staggered solution algorithm is used to solve the problem numerically.In order to simulate the crack propagation behavior of the material structure,through the user subroutine interface(UMAT and UEL)provided by the commercial software ABAQUS,the fracture phase field model of the unilateral notched plate was established,and the mesh element size,length dimension parameters,and displacement increment of the model were established.The iterative step and other parameters have been verified for convergence.The results show that in order to obtain the true crack growth behavior of the material structure,the smaller mesh element size,length size parameter,and displacement increment iteration step should be used as much as possible.In addition,by comparing its numerical simulation results with literature and experimental data,the accuracy of the fracture phase field model established in this paper is verified.(2)Based on the above-mentioned brittle fracture phase field model,the influence of factors such as different initial crack parameters,pore structure parameters and material structure composition on the initial crack propagation behavior of the material structure is explored.The study found that the holes and inclusions introduced in the material structure have a greater impact on the crack propagation path,the overall loadbearing capacity of the material structure and the fracture toughness.In addition,based on the ABAQUS internal script file and subroutine interface combined with MATLAB parameterized modeling,and combined with multi-objective optimization algorithms,this paper transforms the crack growth control problem into a material structure optimization problem.By rationally arranging the positions of the holes,the crack propagation behavior can be effectively controlled to improve the overall bearing capacity(fracture resistance)and displacement strain capacity of the damaged material structure.(3)Based on the above-mentioned fracture phase field crack growth control closed-loop optimization framework,a crack propagation path prediction method based on the variational autoencoder generation model is proposed,which effectively solves the high cost and time-consuming calculation of the fracture phase field numerical simulation during the closed-loop optimization process.And other issues.The method first encodes the numerical simulation cloud image of the fracture phase field through the coding structure part of the variational autoencoder,and obtains the lowdimensional hidden vector that characterizes the cloud image of the crack propagation path.Then,the mapping relationship between it and the design parameters is constructed through the proxy model.Finally,the low-dimensional latent vector is restored to the corresponding numerical simulation cloud image of the fracture phase field through the variational autoencoder decoder part,thereby effectively constructing the mapping relationship between the design parameters and the numerical simulation cloud image of the fracture phase field.The crack propagation path prediction method based on the variational autoencoder generation model proposed in this paper greatly reduces the computational cost of the numerical simulation of the fracture phase field,and can quickly predict the damage of the crack propagation to the related material structure.