重新抽樣法於分析金屬疲勞裂縫成長行為之應用

Abstract

由於金屬疲勞裂縫成長行為具有隨機性，因此我們可以配合統計學上的方法來描述金屬材料的特性，例如利用各種機率函數來嵌合疲勞裂縫成長參數的分佈。通常我們可以使用各種測試方法來判斷這些嵌合函數的優劣，繼而從中選取一個最接近的函數，將之視為裂縫成長參數的近似分佈，然而所得的參數分佈偶爾會發生以下兩個問題：（一）、使用最佳嵌合函數所得到的分析結果仍然無法充分描述實驗試片行為；（二）、不同的實驗數據可能會得到不同的最佳嵌合函數。為了避免這些缺憾，本研究採用兩種重新抽樣方法來求得裂縫成長參數的機率分佈，據以應用於隨機疲勞裂縫成長之模擬與可靠度之評估。由於本研究中假設裂縫成長的隨機性來自於各試片間的差異，因此所求得的裂縫成長參數分佈被視為所有試片的裂縫成長參數分佈，而在分析某特定試片的裂縫成長行為時，另得以特殊的方法先求出此試片獨特的參數值，再藉以獲得較精確的裂縫成長與可靠度評估結果。

Considering the randomness of fatigue crack growth of metals, some researchers proposed to describe the crack growth curves by statistical methods. For example, one can fit parameters describing the fatigue crack growth rate by certain kinds of probability distributions. The best-fitted distribution functions can be determined through statistical tests. However, the following two problems remained. Firstly, even the best-fitted function is not enough to describe the real fatigue crack growth result. Secondly, different best-fitted functions may be derived for different experiment data sets. To resolve these problems, two kinds of statistical resampling methods are employed in this thesis in order to find more exact probability distributions of these random parameters. It is assumed that the randomness of fatigue crack growth curves is due to the uniqueness of each individual specimen. Thus, the derived parametric distributions reflect the mother property of all specimens under the same loading. For a certain specimen having a certain crack size observed, a method is proposed to narrow-down the finding of more appropriate parametric distributions that can describe the unique specimen more exactly. The result can accordingly provides us more exact fatigue crack growth prediction as well as its reliability assessment.