基于弹性力学理论，建立了三维裂纹应力强度因子计算的混合边界元法基本理论和数值求解技术；针对表面裂纹疲劳扩展过程中，需要计算每个裂纹扩展步下的应力强度因子，从而需要重复计算大型非对称系数矩阵问题，提出了仅在初始裂纹状态下一次计算主控矩阵，对于随后的疲劳裂纹扩展，只需做非常小规模矩阵的计算，且以显式形式给出应力强度因子解而无需求解大型线性代数方程组的方法，大大提高了计算效率；针对疲劳裂纹扩展过程中，单元需要不断重新划分问题，由于混合边界元法中的主控矩阵与裂纹无关，故只需对裂纹表面单元进行重新划分，对半椭圆表面裂纹，由于将其映射到单位半圆上划分单元，而单位半圆上的单元在疲劳扩展过程中不变，从而通过映射关系自动重新划分裂纹表面单元。最后，通过若干算例和试验，考核了本文方法的精度和可靠性。本文的研究为工程结构表面裂纹疲劳扩展和寿命计算的高效高精度数值分析建立了理论基础和实现方法。
The basic theory and numerical solving technique of the hybrid boundary element method for the calculation of the stress intensity factors of three-dimensional crack is established based on the theory of elastic mechanics. In analyzing the fatigue propagation of the surface crack, the stress intensity factor at each crack propagating step needs to be calculated, and accordingly the large non-symmetric coefficient matrix should be computed repeatedly. A method is proposed that the master matrix is calculated only once in the initial crack state, and then a very small-scale matrix is calculated during the subsequent fatigue crack propagation.The solution for the stress intensity factor is also given in an explicit form without solving large-scale linear algebraic equations so that the calculation efficiency is improved greatly. To address the problem of continuous division and remeshing of elements during the fatigue crack propagating, the hybrid boundary element method is applied as the master matrix is independent of the crack, and therefore only remeshing of elements on the crack surface is required. For the semielliptical surface crack, the elements on the crack surface are remeshed according to the mapping relationship as the crack is mapped into the semicircle in meshing and the elements in the unit semicircle have no change during the fatigue propagation. The accuracy and reliability of the proposed method are verified by several examples and experiments. The research efforts may provide the theoretical foundation and the realization method for highly efficient and accurate numerical analysis of the surface crack fatigue propagation and the life prediction of engineering structures.
[1] 胡博, 于润桥, 徐伟津. 人工槽模拟GH4169涡轮盘表面裂纹缺陷的微磁检测[J]. 航空学报, 2015, 36(10):3450-3456. HU B, YU R Q, XU W J. Micro-magnetic NDT for surface crack defect in a GH4169 turbine disc simulated by artificial groove[J]. Acta Aeronautica et Astronautica Sinica, 2015, 36(10):3450-3456(in Chinese).[2] RAJU I S, NEWMAN J C, Jr. Stress-intensity factors for a wide range of semi-elliptical surface cracks in a finite-thickness plate[J]. Engineering Fracture Mechanics, 1979, 11(4):817-829.[3] 国家标准化管理委员会. 在用含缺陷压力容器安全评定:GB/T 19624-2004[S]. 北京:中国标准出版社, 2004. Standardization Administration of China. Safety assessment for in-service pressure vessels containing defects:GB/T 19624-2004[S]. Beijing:China Standard Press, 2004(in Chinese).[4] LIN X B, SMITH R A. Finite element modelling of fatigue crack growth of surface cracked plates:Part I:The numerical technique[J]. Engineering Fracture Mechanics, 1999, 63(5):503-522.[5] LIN X B, SMITH R A. Finite element modelling of fatigue crack growth of surface cracked plates:Part Ⅱ:Crack shape change[J]. Engineering Fracture Mechanics, 1999, 63(5):523-540.[6] LIU C H, CHU S K. Prediction of shape change of corner crack by fatigue crack growth circles[J]. International Journal of Fatigue, 2015, 75:80-88.[7] YU P S, GUO W L. An equivalent thickness conception for prediction of surface fatigue crack growth life and shape evolution[J]. Engineering Fracture Mechanics, 2012, 93:65-74.[8] GUCHINSKY R, PETINOV S. Numerical modeling of the surface fatigue crack propagation including the closure effect[J]. International Journal for Computational Methods in Engineering Science and Mechanics, 2016, 17(1):1-6.[9] 李有堂, 张洋洋. 压力容器中表面裂纹在高周疲劳下的扩展规律[J]. 兰州理工大学学报, 2015, 41(6):168-172. LI Y T, ZHANG Y Y. Surface crack growth pattern of pressure vessel with high-cycle fatigue[J]. Journal of Lanzhou University of Technology, 2015, 41(6):168-172(in Chinese).[10] CHAI G Z, FANG Z M, JIANG X F, et al. Hybrid boundary element analysis for surface cracks[J]. Computer Methods in Applied Mechanics and Engineering, 2004, 193(23-26):2069-2086.[11] WATSON J O. Advanced implementation of the boundary element method for two and three-dimensional elastostatics[J]. Developments in Boundary Element Methods, 1979, 61:31-63.[12] IOAKIMIDIS N I. Application of finite-part integrals to the singular integral equations of crack problems in plane and three-dimensional elasticity[J]. Acta Mechanica, 1982, 45(1-2):31-47.
CJA