應力強度因子(Stress Intensity Factor)K為一評估材料強度的重要指標，在本文中我們假定在巨觀下正交性複合材料(Orthotropic Composite Materials)的應力強度因子為1來求相對微觀尺度下鈍化型裂縫前端位於基材與纖維各分析點處的無因次應力強度因子K。我們以工程分析軟體ANSYS與Matlab來輔助我們模擬分析非均質性材料的破裂問題，並由已知結果的正確解先確定有限元素模型的合理性，然後再以兩種不同的數值步驟來求得K值。我們發現裂縫位於彈性係數較大的纖維內將比位於彈性係數較小的基材內有較大的K值，也由此可知複合材料大部分的應力均由纖維所承受。

The stress intensity factor (S.I.F) has widely been used in the evaluation of material strength in the presence of a crack. When a crack in a composite material is treated as a crack in a homogeneous anisotropic material, the derived S.I.F can only be used in characterizing the material properties at macroscopic scales. To characterize the material behavior at microscopic scales, the presence of the inhomogeneities around the crack tip must be taken into consideration. In this thesis, an idealized case for a fibrous composite is studied. The crack is assumed to be normal to the fiber direction and subjected to Mode-I loading. To avoid numerical difficulty, the crack tip is taken to be rounded with a finite radius of curvature. The near-tip stress distribution at the microscopic scale is determined by ANSYS and Matlab, then the associated microscopic S.I.Fs are extracted by two different numerical approaches. We have found that the larger modulus of elasticity in the fiber has higher S.I.Fs than the smaller one in the matrix. Clearly, most of stress is supported by fibers in a composite material. It is concluded that for the same macro-S.I.Fs, the micro-S.I.Fs may be significantly different depending on the crack tip position and the elastic properties of the constituent phases of the composite.

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