Analyticla formulas for a 2-D crack tip singular boundary element for rectilinear cracks and crack growth analysis

摘要

Simple analytical formulas for the displacement, traction, and stress intensity factor for a 2-D crack tip singular boundary element are developed using the continuous distribution of dislocation dipoles and Chebyshev polynomials. The known (sq root r) crack tip opening displacement and the (1/sq root r) stress singularity at the crack tip is mathematically built into the formulas. In the boundary element implementation the crack tip singular element is placed locally at each crack tip on top of the ordinary non-singular crack elements that cover the entire crack surface. Within the constraint of the rectilinear approximation, any curvilinear cracks can be modeled,including center and edge cracks. Although the quarter-point element is accurate and easy to use, it does not provide the analytical formula for the stress intensity factor which is the key feature of the proposed method. The performance of the crack tip singular element is compared against other crack elements that incorporate the creak tip singularity analytically. A numerical result is given for a crack growth problem where repeated update of the crack shape and calculation of the stress intensity factor are required as the crack grows in a curvilinear path.