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系統識別號 U0026-0901201915173200
論文名稱(中文) 以四點彎曲試驗決定I+II型斷裂韌度之有限元素數值模擬
論文名稱(英文) A Finite Element Numerical Simulation of Mode I+II Fracture Toughness Determination Using A Four-Point Bending Test
校院名稱 成功大學
系所名稱(中) 資源工程學系
系所名稱(英) Department of Resources Engineering
學年度 107
學期 1
出版年 107
研究生(中文) 李權仁
研究生(英文) Chuan-Jen Lee
電子信箱 leechuanjen59@gmail.com
學號 N46064044
學位類別 碩士
語文別 中文
論文頁數 79頁
口試委員 指導教授-王建力
口試委員-徐國錦
口試委員-余騰鐸
口試委員-葉信富
中文關鍵字 斷裂韌度  彎曲試驗  ABAQUS  有限元素分析 
英文關鍵字 Fracture toughness  Bending test  ABAQUS  Finite element analysis (FEA) 
學科別分類
中文摘要 在工程環境中,結構物的破壞多源自材料內部微小裂隙發展。在線彈性條件下,當應力場強度增大到某一臨界值,裂紋便失穩擴展而導致材料斷裂,這個臨界或失穩擴展的應力強度因子即斷裂韌度。前人針對不同材料與形狀之試體進行不同形式之斷裂力學試驗決定斷裂韌度,研究含裂縫之材料在受力變形作用下抵抗斷裂之能力。
本研究根據賴俊仁(2001)以花崗岩與張育源(2017)以砂岩所製作之單裂縫矩型與圓柱試體進行四點彎曲試驗所得之材料參數(楊氏模數、泊松比、破壞負載與邊界條件),建立一套ABAQUS有限元素模型,計算裂縫尖端鄰近處應力及其距離,再換算試體之I與II型斷裂韌度。
本研究分別對純I型、純II型與I+II複合型斷裂韌度之試驗模型選取之不同跨距,進行ABAQUS有限元素分析。針對不同元素選取、網格劃分(全域和局部撒點方式)、節點密度大小、實縫及虛縫缺口之繪製方式,進行數值模擬並比較相關結果。將本研究所得結果與Wang et al.(1977)比較,當裂隙比例介於0.25與0.45之間,I與II型無因次校正因子絕對偏差率均小於5 %。
英文摘要 In the engineering environment, the destruction of structures is mostly due to the growth of tiny cracks inside the material. The fracture criteria can be established by several methods of mechanical tests, and the fracture toughness can be measured.
In this study, the models were established by ABAQUS. The simulation was based on the single edge-cracked four-point bending tests of granite specimens from the study of Lai (2001) and sandstone specimens from the study of Zhang (2017). The material parameters including Young's modulus and Poisson's ratio in ABAQUS models of this study were adopted from their studies. The stress at the fracture and the distance from the crack tip were evaluated. Then, the mode I and the mode II fracture toughness can be obtained.
Comparing the experimental results with simulation results of ABAQUS, the applications of the finite element analysis under different scenarios of element selection, meshing, nodal density and notch drawing method were discussed. The simulated values of the mode I and the mode II fracture toughness were compared with the experimental data, and the values of correlation factors were assessed.
論文目次 摘要 I
Extended Abstract II
誌謝 VII
目錄 VIII
表目錄 XII
圖目錄 XIV
第一章 緒論 1
1.1 研究背景與動機 1
1.2 研究內容與目的 2
第二章 基本理論與文獻回顧 5
2.1 斷裂力學發展 5
2.2 斷裂力學基本理論 5
2.2.1 斷裂型態 5
2.2.2 應力強度因子理論與公式 6
2.2.3 I型與II型斷裂韌度公式 9
2.3 數值模擬相關研究 11
2.5 本研究室歷屆斷裂力學相關研究 17
2.5.1 I型斷裂 17
2.5.2 II型斷裂 18
2.5.3 III型斷裂 23
2.5.4 複合型斷裂 27
2.6 各型斷裂韌度試驗文獻綜合比較 33
第三章 以數值模擬程式ABAQUS分析四點彎曲試驗 37
3.1 數值分析軟體ABAQUS 37
3.2 模擬環境之設定 40
3.2.1 試體尺寸 40
3.2.2 材料參數 41
3.2.3 施加負載 42
3.2.4 邊界條件 42
3.2.5 網格劃分 44
3.3 本研究規劃之模擬樣態 46
第四章 模擬分析之結果與討論 48
4.1 圓柱試體純I型斷裂韌度(賴俊仁試驗之模型) 48
4.2 矩形試體純I型斷裂韌度(賴俊仁試驗之模型) 48
4.3 矩形試體純I、I+II複合與純II型斷裂韌度(張育源試驗之模型) 49
4.4 實縫與虛縫模擬方法效果比較 51
4.5 模擬分析之小結 52
4.6 運算時間 53
4.6.1 網格運算時間 53
4.6.2 節點運算時間 55
4.6.3 網格數與節點數對運算時間影響之分析 57
4.7 其他分析 58
4.7.1 應力外差法 58
4.7.2 能量釋放率 59
4.7.3 求斷裂韌度無因次校正因子 60
4.7.4 隨節點數增加之收斂效果 62
第五章 結論與建議 66
5.1 結論 66
5.2 建議 68
參考文獻 69
附錄A 四點彎曲試驗I+II型斷裂韌度結果參考表 78
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