本論文利用有限元素分析法與實驗方法研究在一個有限平板的三維效應，並且本研究也探討三維裂縫問題的柏松比效應。本研究之試體材料為鋼材, 並且有兩種厚度為9毫米的均質平板，其中一種是中央水平裂縫，另一種是中央傾斜裂縫。對於實驗部分的主要目的是從對試體進行拉伸實驗中得到位移場。對於有限元素分析方法來說，其主要目的是模擬出在不同柏松比下的位移場以及應力強度因子，並且將模擬出的位移場結果與實驗的位移場結果作比較。比較結果顯示，有限元素與實驗兩者模擬出的位移等高線圖形相似，並且位移等高線在裂縫尖端排列緊密且有很大的變化。此外，有限元素分析也展示了Mode-I、Mode-II以及Mode-III三種不同負載類型下應力強度因子的結果，對於研究應力強度因子而言，假如柏松比增加，應力強度因子會隨著最大半徑的改變而有明顯的變化，而當最大半徑增加，則每一層的應力強度因子將會逐漸的趨近於中間層應力強度因子值。因此結果證明柏松比效應對於應力強度因子的影響是清晰可見的，並且裂縫問題具有明顯的三維效應。

This thesis researched the three dimensional (3D) effect of crack problems in a finite plate by using finite element and experimental methods, and the study also observed the Poisson’s ratio effect for the 3D crack problems. The material of specimens is steel, and there are two homogeneous specimens for the 9-mm thickness plates with a central horizontal crack and a central slant crack, respectively. For the experiment, the aim is to obtain the displacement field from the experiment, which the specimen is subjected by the tension forces. For the finite element method (FEM), the aim is to simulate the displacement field and the stress intensity factors (SIFs) with different Poisson’s ratio, and the results of the displacement are used to compare with the experimental results. The comparisons indicated that displacement contours graphics are similar between the finite element and experimental simulations, and the displacement contour has a great variation and tightly packed in the vicinity of the crack tip. Moreover, the finite element analyses also show the results of SIFs under different load types, which are Mode-I, Mode-II and Mode-III. For the investigation of the SIFs, if the Poisson’s ratio increases, the variations of the SIFs are more obvious changing with the maximum radius (Rmax). When the Rmax increases, the SIFs of all layers approach gradually to the SIFs of the middle layer. Thus, the results proved that the Poisson’s ratio effect affects the SIFs visibly, and the crack problem has the obvious 3D effect.

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