材料的疲勞破壞經常發生於週次循環應力作用下，而大部分的材料疲勞破壞均始於一微小疲勞裂縫之萌生及其成長。本文乃在於研究裂縫之疲勞成長，探討裂縫於不同的材料，不同的纖維方向，不同的初始裂縫長度及不同的應力作用時之成長特性。由於，在異向性材料(Anisotropic Material)中，不同方向上之拉伸強度(Tensile Strength)並不相同，因而對疲勞裂縫之成長影響甚鉅，所以在本文中利用正向應力規則(Normal Stress Criterion)，假設裂縫在不同方向上延伸之機率正比於該方向上的環周應力與拉伸強度之比值，以此作為疲勞裂縫成長方向選取之依據。在本文研究中，假設每一單層板(Lamina)的厚度均相同，並且以上下對稱的方式黏結而成一複合材料疊層板(Laminate)，並將其視為一個整體平板，利用複合材料力學的理論公式，計算出電腦模擬所需之材料常數。為了簡化問題，吾人假設裂縫均以第Ⅰ型（張裂型）的破裂方式朝著幾個離散方向進行延伸，並且根據蒙地卡羅法的理論，藉由亂數產生器所產生的隨機亂數值，來選擇裂縫成長的方向。
接著，藉由他人的實驗數據，經過適當地修正換算及假設後，得到程式模擬所需的材料常數值，並且利用蔣長榮教授所提出的疲勞裂縫成長公式，將其撰寫成電腦程式，開始進行電腦數值模擬。

透過電腦數值的模擬，可以得到疲勞裂縫的成長曲線圖及其疲勞拉伸壽命。由模擬結果可知，疲勞裂縫大致上仍沿著主裂縫方向進行延伸，在裂縫成長初期，疲勞裂縫以非常緩慢的速率穩定地成長，隨著裂縫長度不斷地增長，使得裂縫開始呈現快速且不穩定的成長。

最後吾人以本文所選用的材料為例，將電腦模擬所得之數據結果，經過適當的處理，並且利用統計迴歸分析中的最小平方法(Least-Square Method)，計算得到一近似的疲勞裂縫拉伸壽命預測公式。提供他人一種對於其它複合材料或其它纖維堆疊方向得到該預測公式的方法。

The fatigue failure of materials, which usually occurs on the loading of cyclic stress, almost starts on the initiation and growth of small fatigue crack. This study investigates the growth of fatigue cracks, and analyzes the phenomena of crack growth in different materials, different fiber orientations, different initial crack lengths, and different loadings. Owing to anisotropy of materials, the tensile strengths of different orientations are not equivalent, and this greatly affects the growth of fatigue crack. So the Normal Stress Criterion is assumed in this study. The probabilities of crack growth in different directions are assumed to be proportional to the ratio of the normal tensile stress and tensile strength in the prospect direction. In this study, the thickness of each ply is supposed to be the same and cohere to a composite Laminate symmetrically, and can be taken as an anisotropic plate. Using the formulae of composite material mechanics to calculate the material constants necessary for computer simulations. In order to simplify the problem, it is assumed the cracks may extend in one of several possible directions, and let the random numbers generated by random number producer to select the direction of crack growth.
The experimental data of the material T300/5208 has been used to calculate the material constants that are needed for computer simulation.

In the computer simulation, we can get the da/dN vs. ΔK curve and predict the fatigue life conveniently. The results indicate that fatigue cracks still extend toward the orientation of main crack. In the initial stage of crack growth, the fatigue crack grows very slowly and steady. As the crack length increasing, the growth of the fatigue crack becomes quickly and unsteady.

Finally, the results of computer simulation are summarized through Least-Square Method to find the regression formulae of the life of fatigue cracks.

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