Stress intensity factors for asymmetric branched cracks in plane extension by using crack-tip displacement discontinuity elements

Stress intensity factors are important in the analysis of cracked materials. They are directly related to the fracture propagation and fatigue crack growth criteria. Based on the analytical solution (Crouch, S.L., 1976. Solution of plane elasticity problems by displacement discontinuity method, Int. J. Numer. Methods Eng. 10, pp. 301-343; Crouch, S.L., Starfield, A.M., 1983. Boundary Element Method in Solid Mechanics, with Application in Rock Mechanics and Geological Mechanics, London, Geore Allon and Unwin, Bonton, Sydney) to the problem of a constant discontinuity in displacement over a finite line segment in the x, y plane of an infinite elastic solid, recently, the crack-tip displacement discontinuity element which can be classified as the left and right crack-tip displacement discontinuity elements are developed by the author Yan, X., (in press. A special crack-tip displacement discontinuity element, Mechanics Research Communications) to model the crack-tip fields to more accurately compute the stress intensity factors of cracks in general plane elasticity. 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 ordinary non-singular displacement discontinuity elements that cover the entire crack surface and the other boundaries. To prove further the efficiency of the suggested approach and provide more results of the stress intensity factors, in this study, analysis of an asymmetric branched crack bifurcated from a main crack in plane extension is carried out.