| In this paper, according to the characteristics of fatigue crack propagation of nuclear pressure pipe, a coupled finite element/meshless Galerkin algorithm (FE/EFG) is presented, by which the essential boundary conditions can be imposed directly. In order to take advantage of the merits of FE method and EFG method, the whole numerical model is discretized into two types of sub-domains, FE sub-domain and EFG sub-domain. A discretize scheme which can ruduce computing scale and improve calculation accuracy is taken to determine the two types of sub-domans by which EFG sub-domain is used on the part closed to the crack front, the remain part FE sub-domain.Based on the instrinc relation betwin the FE method and EFG method, the whole computational model is discretized using finite elements which are catigried into three types: A, conventional finite element, B, element linked to interface, C, element in EFG sub-domain, according to their utilize characteristics and location. C elements are only used as background integral grids and can be furtherly divided into several small sub-elements in order to improve computational precise. Using this kind of catigary scheme for elements, the apparentment and convention of computational programme can be improved evidently.In view of the deficiency of current methods to calculate stress intensity factor, a virtual crack closure method based on EFG is proposed by which an auxiliary finite element domain is set up to calculate the stiffness matrix of local area around the crack tip. Nodal force of crack tip is determined by multiplying the matrix and nodal displacement vector of the auxiliary finite element. Finally, strain energy release rate of crack front is determined, which can be eventually changed into stress intensity factor. It is showed by several numerical examples that the current method has high computational precision and is not only suitable for the linear material but also for nolinear material.In the simulation of fatigue crack propogation, in order to take advantage of the merit of EFG method and advoid the calculation increase due to the expand of EFG sub-domain, a kind of dynamic sub-domain partition method is proposed. Using the method, finite element grids are used to discretize the whole domain and the grids closed to crack front are only used as background integral grid for EFG method. EFG sub-domain can dynamically move together with crack front using a certain size parameter controlling the scale of EFG sub-domain near to crack front. Thus, EFG sub-domain and FE sub-domain can be adjusted dynamically, which greatly reduces the computing scale and increase calculation efficiency.Paris law is used to determine the stepinterval of crack growth. According to the leak before break technique (LBB), only mode I crack is considered in the study. Thus, the normal of crack front can be used as the crack propagation direction. The current method is used to simulate the extension of centre through crack and semic-elliptic surface crack. It is showed that the result including stress intensity factor obtained from current method is consistent to those from literature. Before penetration, the crack grow faster in depth than in other direction. After penetration, the shape of the crack front grow toward the shape of centre-penetrate crack, which is consistent to phenomenon observed in experiment.According to the LBB method, after the penetration, the crack opening area (COA) should be determined to estimate whether the medium leakage in pressure pipe is enough to be detected by monitor system of refrigerant. Therefore, crack opening area is a very important parameter for LBB technology. Noting the drawback of engineering algorithm for COA calculation, an numerical method is proposed to determine the COA of cracked pressure pipe and it's efficiency is proved by means of the COA calculation of centre-crack panel and pressure pipe.The method presented in this paper is also used to simulate the propagation of surface crack of pressure pipe including axial surface semic-elliptic crack and circumferential surface semic-elliptic crack. It was found that the growth rate of inner surface semic-elliptic crack is faster than those of outer urface semic-elliptic crack and both two types of crack grow faster in depth direction than the other direction before penetration. After penetration, the shape of the crack front develop toward the shape of centre-penetrate crack, which is consistent to phenomenon observed in experiment.Finally, the basic steps of conventional LBB method are presented and the application of numerical method in the method is introduced by means of a typical example of LBB evaluation. The result from the example indicates that it is feasible to adopt numerical method in this paper to analyse the fracture of nuclear pressure pipe. |
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