Abstract: 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.

Key words: surface crack, fatigue propagation, highly efficient and accurate analysis, hybrid boundary element method, stress intensity factor