Analysis of crack in two-dimensional anisotropic bodies with various shaped boundaries

Abstract

In this thesis, crack problems in two-dimensional anisotropic bodies with various shaped boundaries are treated. Analytical approach is based on the modified mapping-collocation method. Theoretically developing this analysis, traction-free conditions on the crack surface are exactly satisfied. Then, applying the least square collocation procedure on the remaining boundaries, we can approximately obtain the stress intensity factors. First of all, we proposed the general expression for the stress functions which can be applied to the analysis of cracks emanating from, or in the vicinity of areas of stress concentrations in two-dimensional anisotropic bodies. Then we applied these stress functions to the problems, which have not been solved yet, and obtained the stress intensity factors for each problem by using computer codes developed in this analysis. Four types of configurations were treated such as the case of cracks emanating from a circular hole in an orthotropic infinite plate, the case of cracks emanating from a circular hole in an orthotropic finite plate, the case of cracks emanating from an elliptical hole in an orthotropic infinite plate, and the cause of a crack approaching two circular holes in an orthotropic infinite plate. In the analysis of cracks emanating from a circular hole in an orthotropic infinite plate, the model I and mode II are induced for the case of off-axis laminate under shear and tension, respectively, due to inplane normal-shear coupling and in the range of small crack length the mode I stress intensity factors are greatly different according to fiber orientations. In the analysis of cracks emanating from a circular hole in cross-ply laminates with finite size, the stress intensity factors for uniform stress decrease as the aspect ratio increases. But the results for uniform displacement without shear show the reverse trends. The stress intensity factors for clamped ends are almost the same as those for uniform displacement witho...