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研究生： 許人文
Shiu, Ren-Wen
論文名稱： 混合型裂縫成長方向的統計預測
Statistical Prediction for Mixed-Mode Crack Growth Direction
指導教授： 蔣長榮
Chiang, Chun-Ron
口試委員:
學位類別： 碩士
Master
系所名稱： 工學院 - 動力機械工程學系
Department of Power Mechanical Engineering
論文出版年： 2009
畢業學年度： 97
語文別： 中文
論文頁數： 112
中文關鍵詞： 破裂力學 、混合型 、塑性力學 、統計學
外文關鍵詞： Fracture Mechanics, Mixed-Mode, Plasticity, Statistics
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    • 本研究乃是針對一不□鋼材，在材料未破壞前推估受混合型負載下之裂縫成長的相對概率，由ANSYS模擬所得考慮裂縫前端塑性區內的應變量及塑性區發展範圍，並假設材料內缺陷分佈的機率皆相同的情形下，分析統計其結果，據此計算各角度裂縫成長的相對頻率，並比較其可能發生破壞的概率，進而推估其裂紋可能成長之方向。結果可以發現在不同外力混合比例下時，其最大裂縫成長相對概率所發生的位置皆有所不同。當考慮裂縫成長風險正比於塑性應變時，即m=1時，發現mode 1與mode 2的應力強度因子比例為一比一時，此時最大概率發生在15度角度上；mode 2應力強度因子比例遠大於mode 1應力強度因子時，最大概率發生在5度角度上。由上述可觀察到，當mode 2比例逐漸增加時，其裂縫成長會朝裂縫尖端水平方向而發展。另外一方面，當mode 1應力強度因子比例遠大於mode 2應力強度因子，隨塑性應變著重放大因子(m > 1)的增大，發現裂縫成長會從兩翼方向逐漸變為-20度角度方向，由此可知，畸變能、塑性應變較高的角度方向，其相對概率會隨 值增加而相對提高。

    The statistical prediction of crack growth direction under mixed-mode conditions is studied. By assuming that the probability of finding flaws within the material is uniform, and that the growth risk is related to the plastic strain around the crack tip, using the results of finite element analysis(provided by ANSYS), we determine the most probable direction of crack growth. When the growth risk is proportional to plastic strain (i.e.m=1), it is found that the crack growth direction is at about 15 degree from the crack line with stress intensity factor of mode 1 and mode 2 is 1:1. When stress intensity factor of mode 2 is much larger than mode 1, it occurs at about 5 degree. It is concluded that the crack tend to propagate along the crack line when mode 2 loading is increasingly dominant. On the other hand, when stress intensity factor of mode 1 is much larger than mode 2, for higher value of m(m > 1 ), the crack growth direction is about -20 degree.

    摘要.....................................................I 英文摘要.................................................II 目錄.....................................................III 圖表目錄.................................................VI 第一章 緒論...........................................01 1.1前言..................................................01 1.2研究動機與目的........................................03 1.3文獻回顧..............................................03 第二章 基本理論.......................................06 2.1破裂力學..............................................06 2.1-1裂縫發生的形式......................................06 2.1-2裂縫尖端的應力場..............................07 2.1-3應力強度因子..................................08 2.1-4線彈性破裂力學................................09 2.1-5彈塑性破裂力學................................10 2.1-6 混合型態下負載的裂縫成長角度.................11 2.2材料的硬化規則........................................12 2.2-1等向性硬化規則......................................12 2.2-2隨動性硬化規則......................................13 2.3破壞準則..............................................13 2.3-1 von Mises 降伏準則.................................14 2.4彈塑性力學常用的簡化力學模型..........................14 第三章 有限單元法及工程模擬分析軟體『ANSYS』..........16 3.1有限單元法............................................16 3.1-1有限單元法基本理論..................................16 3.1-2等□數單元..........................................17 3.1-3高斯積分法..........................................18 3.2工程模擬分析軟體『ANSYS』.............................19 3.2-1『ANSYS』軟體簡介...................................19 3.2-2『ANSYS』的非線性分析...............................20 第四章 模型的建立與分析...............................21 4.1問題描述..............................................21 4.2模型建立..............................................21 4.3模型收斂性分析........................................22 4.4模型合理性驗證........................................23 4.5不同混合比例型態下的塑性區分佈........................24 4.6應變硬化率對裂縫尖端附近應力的影響....................26 4.7裂縫成長角度的觀測....................................27 第五章 概率推導.......................................29 第六章 結果與討論.....................................32 第七章 結論...........................................39 □考文獻.................................................41

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