Elastic analysis of a circumferential crack in an isotropic curved beam using the modified mapping–collocation method

The modified mapping-collocation (MMC) method was applied to the boundary value problem (BVP) of a circumferential crack in an isotropic elastic curved beam subjected to pure bending moment loading. The stress correlation technique is then used to determine opening and sliding mode stress intensity factor (SIF) values based on the computed stress field near the crack tip. The MMC method aims at solving two-dimensional BVP of linear elastic fracture mechanics (LEFM) circumventing the need for direct treatment of the biharmonic equation by combining the power of analytic tools of complex analysis (Muskhelishvili formulation, conformal mapping, and continuation arguments) with simplicity of applying the boundary collocation method as a numerical solution approach. A good qualitative agreement between the computed stress contours and the fringe shapes obtained from the photoelastic experiment on a plexiglass specimen is observed. A quantitative comparison with FEM results is also made using ANSYS. The effect of crack size, crack position and beam thickness variation on SIF values and mode-mixity is investigated.