Concerns with stress intensity factors for cracks emanating from an elliptical hole in a rectangular plate under biaxial loads by means of a boundary element method which consists of non-singular displacement discontinuity element presented by Crouch and Starfied [6] and crack-tip displacement discontinuity elements proposed by the author. In the boundary element implementation the left or the right crack-tip displacement discontinuity element is placed locally at the corresponding left or right crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and other boundaries. The present numerical results further illustrate that the present numerical approach is very effective and accurate for calculating stress intensity factors of complex cracks in a finite plate and can reveal the effect of the biaxial load and the cracked body geometry on stress intensity factors.
This paper presents an extension of a displacement discontinuity method with crack-tip elements (a boundary element method) proposed by the author for fatigue crack growth analy-sis in plane elastic media under mixed-mode conditions. The boundary element method consistsof the non-singular displacement discontinuity elements presented by Crouch and Starfield andthe crack-tip displacement discontinuity elements due to the author. In the boundary elementimplementation the left or right crack-tip element is placed locally at the corresponding left orright crack tip on top of the non-singular displacement discontinuity elements that cover the en-tire crack surface and the other boundaries. Crack growth is simulated with an incremental crackextension analysis based on the maximum circumferential stress criterion. In the numerical sim-ulation, for each increment of crack extension, remeshing of existing boundaries is not requiredbecause of an intrinsic feature of the numerical approach. Crack growth is modeled by addingnew boundary elements on the incremental crack extension to the previous crack boundaries. Atthe same time, the element characteristics of some related elements are adjusted according tothe manner in which the boundary element method is implemented. As an example, the fatiguegrowth process of cracks emanating from a circular hole in a plane elastic plate is simulated usingthe numerical simulation approach.
A simple and effective boundary element method for stress intensity factor calculation for crack problems in a plane elastic plate is presented. The boundary element method consists of the constant displacement discontinuity element presented by Crouch and Starfield and the crack-tip displacement discontinuity elements proposed by YAN Xiangqiao. In the boundary element implementation the left or the right crack-tip displacement discontinuity element was placed locally at the corresponding left or right each crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. Test examples ( i. e. , a center crack in an infinite plate under tension, a circular hole and a crack in an infinite plate under tension) are included to illustrate that the numerical approach is very simple and accurate for stress intensity factor calculation of plane elasticity crack problems. In addition, specifically, the stress intensity factors of branching cracks emanating from a square hole in a rectangular plate under biaxial loads were analysed. These numerical results indicate the present numerical approach is very effective for calculating stress intensity factors of complex cracks in a 2-D finite body, and are used to reveal the effect of the biaxial loads and the cracked body geometry on stress intensity factors.
