The Reanalysis Based Control And Multi-scale Computational Method For Crack Propagation

The existence of micro defects and macro cracks is inevitable for most mechanical components.Usually,it is difficult to predict the crack path accurately because the crack propagation is related to many factors.Therefore,the numerical computation of the crack propagation has been a challenging work for a long time.As for the numerical studies on crack propagation,there are many numerical methods have been proposed to study the crack propagation.However,it still can be improved in the following aspects:(1)The computational efficiency can be further improved: Although the Extended Finite Element Method(XFEM)improved the computational efficiency without mesh reconstruction,but the high-precision simulation often requires a high-density mesh,which decreases the computational efficiency obviously.(2)Research on crack control methods is not complete: It is significant for manufacturing industry to guide and prevent crack propagation after crack initiation.However,there are few studies on crack control methods at domestic and overseas,and the theory is not complete yet.(3)The location of the initial crack still needs to be specified: At present,most numerical methods still need to specify the location and number of the initial crack before analyzing the crack growth.However,the crack initiation is usually related to the microscopic defects and the crystal structure of the material,and the influence of the microscopic structure cannot be ignored.In view of the main problems of the numerical methods for crack propagation,a novel multi-scale computational method which calculated both the microscopic crack initiation and macroscopic crack propagation is proposed in this dissertation.Moreover,a macroscopic crack path control method is proposed to protect the critical area of the component,extend the life of the component and reduce the economic loss in production.The main content of this dissertation is as follows:(1)According to the characteristics of XFEM,only local change of the stiffness matrix happened during the computational process,the decomposition update reanalysis algorithm is proposed to improve the efficiency of the XFEM.The mechanical response after crack propagation can be obtained by solving the equilibrium and un-equilibrium equations which are separated from the residual equilibrium equation.Numerical examples show that the accuracy of the proposed algorithm is high for the problems of single,double crack and crack with holes or inclusions.In terms of efficiency,the efficiency of the proposed algorithm is obviously higher than the full analysis algorithm,and the advantage is more obvious for large-scale problems.(2)An optimization algorithm based crack path control method is proposed in this dissertation.In this method,the BP neural network(BPNN)assisted particle swarm optimization(PSO)algorithm is used to optimize the design variables including the position,size and number of holes to drive the crack extended along the specified path that is away from the key working area of the component.Numerical examples show that the optimization efficiency of the BPNN assisted PSO algorithm is higher than the classic PSO algorithm,but its result is slightly worse than that of the classic PSO algorithm.However,it can be seen that the result fully meets the requirement of the crack controllable propagation from the final path.In addition,the result shows that the reanalysis algorithm saves a lot of time for calculating the crack path,which verifies that the reanalysis is a highly efficient algorithm,especially in optimization iterative problems.(3)The evolution of the crystal defects is systematically analyzed according to the mechanism of the microscopic crack initiation in this dissertation.The point,line and face defects are studied to understand the process of crystal crack initiation.Moreover,the models of inter-granular and trans-granular cracks are constructed to fully investigate the rule of crystal crack propagation.It can be found that the evolution of crystal defects obeys a certain law.Usually,the point defects will collapse into dislocations under certain conditions.Then the dislocations will spread,grow and gather at the grain boundaries.Subsequently,the crack initiation will appear at the grain boundaries and then grow along the grain boundaries.Finally the poly-crystal structure will fracture.It can be also found that both the inter-granular and trans-granular cracks are usually growing along grain boundaries.(4)A multi-scale computational method which combines with the Finite Element Method(FEM),XFEM,and Molecular Dynamics(MD)method is proposed in this dissertation.This method can be used to calculate both the microscopic crack initiation and macroscopic crack propagation under the multi-scale framework.The numerical example shows that the microscopic crack initiation has been successfully calculated by the Latin hypercube sampling method and the microscopic crack initiation has been successfully transferred to the macro-crack model.Finally,the analysis of crack initiation and propagation of the plate which is under the loading of mode I is completed.