含對稱翼型和對稱唇型裂紋平板承受機械和熱流負載下之應力強度因子分析與破裂角度預測

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研究生：	潘睿澤 Ruei-Ze Pan
論文名稱：	含對稱翼型和對稱唇型裂紋平板承受機械和熱流負載下之應力強度因子分析與破裂角度預測 Stress Intensity Factors and Failure Initiation for an Infinite Plate with a Symmetric Airfoil Crack or a Symmetric Lip Crack under Mechanical and Thermal Loading
指導教授：	趙振綱 Ching-Kong Chao
口試委員:	沈明河 Ming-He Shen 張瑞慶 Rwei-Ching Chang 黃榮芳 Rong-Fung Huang
學位類別：	碩士 Master
系所名稱：	工程學院 - 機械工程系 Department of Mechanical Engineering
論文出版年：	2022
畢業學年度：	110
語文別：	英文
論文頁數：	80
中文關鍵詞：	平面、應力強度因子、保角映射法、解析連續、熱流、機械力、應變能理論
外文關鍵詞：	In-plane, Stress intensity factors, Conformal mapping, Analytical continuation, Heat flow, Mechanical loads, Strain energy density criterion
相關次數：	點閱：298 下載：0
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基於二維平面彈性理論和複變理論的概念下，本文主要研究在遠端均勻機械力和熱流負載下對稱翼型裂紋和對稱唇形裂紋之應力強度因子及破裂角度分析。透過保角應射法，將對稱翼型及對稱唇形裂紋轉換成同心圓孔洞，並利用溫度函數和應力函數求解相關的邊界條件問題。透過引入輔助函數和解析連續的概念，可以求得對稱翼型和對稱唇形裂紋尖端的應力強度因子。求得應力強度因子後，便可透過應變能理論計算出裂紋的破裂角度。應力強度因子和破裂角度的大小取決於機械力和熱流組合的不同，其中某些組合會導致應力強度因子和破裂角度變大。本文提供了不同負載下的應力強度因子以及破壞角度並以圖表表示之。

Based on the two-dimensional isotropic elasticity and complex variable theory, a general analytical solution for a symmetric airfoil crack and a symmetric lip crack embedded in an infinite plate under a remote uniform mechanical loading and heat flow is provided in this article. According to the method of conformal mapping, a symmetric airfoil crack and a symmetric lip crack are mapped onto a unit circle and both the temperature and stress potentials are used to solve the relevant boundary value problems. Based on the auxiliary function and the analytical continuation theorem, the stress intensity factors (SIFs) at the symmetric airfoil crack tip and symmetric lip crack tip can be obtained analytically. After the SIFs are obtained, the fracture angle of the crack can be determined by using the strain energy density criterion. The obtained results of SIFs and fracture angle are found to be dependent of the magnitude of mechanical and thermal load. For some combinations of mechanical and thermal load, the SIFs will take a maximum value representing the most dangerous situation and the corresponding fracture angle will also be obtained and discussed in detail.

中文摘要 I
ABSTRACT II
致謝 III
Table of Contents IV
List of figures  VI
Explanation of Symbols XII
Chapter 1 Introduction 1
1 Research motivation 1
2 Literature review 1
3 Research method 3
Chapter 2 Problem formulation 5
1 Two-dimensional isotropic thermoelasticity theory 5
2 Temperature potential energy function 5
3 Auxiliary stress function 6
4 Mapping function 6
5 Analytic functions 7
6 Analytic continuation theorem 7
7 Stress intensity factors 8
8 Strain energy density criterion 8
Chapter 3 Temperature field solution 13
1 Problem Description 13
2 Derivation of temperature field 13
2.1 Symmetric airfoil crack 13
2.2 Symmetric lip crack 14
Chapter 4 Stress field solution 16
1 Problem Description 16
2 Derivation of stress field 16
2.1 Symmetric airfoil crack 16
2.2 Symmetric lip crack 19
3 Numerical solution 24
Chapter 5 Strain energy density criterion 25
1 Preliminary Remarks 25
2 Fracture mechanics discipline 26
Chapter 6 Finite Element Method 31
1 Modeling 31
2 Material parameters and grid 31
3 Boundary conditions 31
4 Method 32
Chapter 7 Result and Discussion 37
1 Result of temperature field 37
1.1 Analytical solution of temperature field for the symmetric airfoil crack 37
1.2 Verification of temperature field by finite element analysis for the symmetric airfoil crack 37
1.3 Analytical solution of temperature field for the symmetric lip crack 37
1.4 Verification of temperature field by finite element analysis for the symmetric lip crack 38
2 The SIFs with different conditions 38
2.1  Analytical solution of SIFs for the symmetric airfoil crack and the symmetric lip crack 38
2.2 Finite element solution of SIFs for the symmetric airfoil crack and the symmetric lip crack 40
3 The fracture angle of symmetric airfoil crack and symmetric lip crack 40
3.1 Fracture angle for the symmetric airfoil crack 41
3.2 Fracture angle for the symmetric lip crack 42
4 Discussion of the result 43
4.1 Discussion of temperature field 43
4.2 Discussion of SIFs 43
4.3 Discussion of fracture angle 43
Chapter 8 Conclusion and future prospects 76
1 Conclusion 76
2 Future prospects 77
References 78
Appendix 80

                                

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全文公開日期 2025/06/27 (校內網路)
全文公開日期 2027/06/27 (校外網路)
全文公開日期 2027/06/27 (國家圖書館：臺灣博碩士論文系統)

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