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研究生: 洪偉宸
Hung, Wei-Chen
論文名稱: 含缺口平板之脆性破壞分析
Brittle Fracture Analysis of Notched Plates
指導教授: 褚晴暉
Chue, Ching-Hwei
學位類別: 碩士
Master
系所名稱: 工學院 - 機械工程學系
Department of Mechanical Engineering
論文出版年: 2003
畢業學年度: 91
語文別: 中文
論文頁數: 89
中文關鍵詞: 缺口平板脆性破壞分析壓克力
外文關鍵詞: PMMA, brittle fracture analysis, notch
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  • 對於裂縫(crack)在受力破壞時的理論與分析,已發展多時,而楔形(wedge)結構,在現今工程有很多的應用實例,但作為楔形結構破壞規範的應力強度因子K,目前並沒有可靠之理論來預測,也沒有固定的規範提供工程上的應用。本文藉由含缺口平板之簡易幾何外型,在缺口尖端附近可視為一楔形結構,對不同缺口角度,不同缺口深度,以實驗方式配合現有理論對其作破壞分析,並觀察應力強度因子能否作為楔形結構的破壞準則。
    分析結果在有限元素法部分,對於應力奇異性階數為一個實數楔形,應力強度因子在各角度的分布相當穩定;對於兩個實數的楔形,本文只在缺口尖端局部之對稱軸求得應力強度因子。在實驗部分,單純第一型實驗中,同一缺口角度不同深度比a/w的平板其臨界應力強度因子(KIC)pure不會隨深度比的不同而改變,故(KIC)pure可以作為破壞準則。且不同缺口角度的(KIC)pure,隨著缺口角度遞增而增加,也就是隨著應力奇異性階數的遞減而增加,如此可為考慮含缺口平板破壞一重要依據;對於混合型實驗,同一缺口角度型一臨界應力強度因子(KIC)mix會隨著深度比(a/w)的遞增而遞減,反之型二(KIIC)mix則會隨之遞增,且不同缺口角度與深度比(a/w)在混合型實驗中之臨界應力強度因子(KIC)mix, (KIIC)mix與型一之臨界應力強度因子(KIC)pure,在(KIIC)mix相對(KIC)mix值較小時之情況下,有((KIIC)mix/(KIC)pure)^2+((KIC)mix/(KIC)pure)^2=1的關係存在。

    The objective of this paper is to propose a fracture criterion for predicting the fracture behavior of a notched plate under arbitrary loads. We performed three-point bending test on PMMA specimen contains an edge-notch with different wedge angle and depth. The concentrated load is applied directly at the central line to form a pure fracture mode I or at a small distance to the central line to form a mixed fracture mode. Firstly, the stress singularity orders are computed by solving eigenvalues of a matrix [M] theoretically. With these values, the correct finite element mesh can be obtained. From the numerical stress field, the generalized stress intensity factors will be computed by using the least square method. Secondly, the critical load, which is needed to fracture the specimen, is recorded experimentally. Finally, combining with previously obtained generalized stress intensity factors, we get the critical stress intensity factors (i.e. (KIC)pure for pure mode I, (KIC)mix and (KIIC)mix for mixed mode).
    For pure mode I, the results show that the critical stress intensity factor (KIC)pure depends only on the stress singularity order. It can be used as a material property for a certain singularity order. It is similar to the fracture mechanics concept in which the fracture toughness is defined for the case of square root singularity. Larger (KIC)pure is needed to fracture a notched plate with larger wedge angle, which has a smaller stress singularity order.
    For mixed mode, the critical stress intensity factors (KIC)mix and (KIIC)mix are in not in the same magnitude order. It presents that the specimen is not a good one to perform the mixed mode test. However, under the assumption of small (KIIC)mix, the relation((KIIC)mix/(KIC)pure)^2+
    ((KIC)mix/(KIC)pure)^2=1 can be considered as a fracture criterion.

    摘要Ⅰ AbstractⅡ 誌謝Ⅲ 目錄Ⅳ 表目錄Ⅶ 圖目錄Ⅸ 符號說明XIII 第一章 緒論1 1.1 前言1 1.2 文獻回顧2 1.3 研究方法3 1.4 本文架構4 第二章 理論基礎5 2.1 單一材料楔形結構及其應力奇異性參數5 2.2 應力奇異性階數之特徵值7 2.2.1 特徵函數展開法7 2.2.2 複變函數展開法10 第三章 問題描述與分析方法14 3.1 有限元素法數值分析14 3.1.1 三點彎曲單純第一型,僅有一個實數λ15 3.1.2 三點彎曲混合型,兩個實數λ18 3.2 有限元素網格的建立22 3.2.1 奇異點附近有限元素網格的建立22 3.2.2 範例說明23 3.2.2.1 三點彎曲單純第一型23 3.2.2.2 三點彎曲混合型26 第四章 實驗設計與規劃28 4.1 實驗儀器28 4.2 實驗平板規格29 4.3 實驗步驟31 4.3.1 實驗基本流程31 4.3.2 問題的發生與解決32 4.3.3 問題改善後的實驗流程33 4.3.3.1 三點彎曲單純第一型實驗步驟33 4.3.3.2 三點彎曲混合型實驗步驟35 4.4 實驗過程記錄36 第五章 結論與討論38 5.1 實驗結果及誤差分析比較38 5.1.1 三點彎曲單純第一型38 5.1.2 混合型(型一與型二) 47 5.2 單純第一型實驗所得臨界應力強度因子(KIC)pure50 5.2.1 (KIC)pure在相同缺口角度r,不同角度下的關係50 5.2.2 單純第一型臨界應力強度因子(KIC)pure在相同缺口 角度r,不同深度比(a/w)下之關係55 5.2.3 (KIC)pure在不同缺口角度r下的關係65 5.2.4 缺口角度r=0度之臨界應力強度因子(KIC)pure值69 5.2.5 缺口角度r=60度的實驗誤差探討71 5.3 混合型(型一和型二)實驗所得臨界應力強度因子 (KIC)mix與(KIIC)mix 72 5.3.1 (KIC)mix和(KIIC)mix在不同缺口角度r,不同深度 比(a/w)下的關係72 5.3.2 混合型實驗中(KIIC)mix相對於(KIC)mix值之探討80 第六章 結論與建議81 參考文獻83 附錄A 88

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