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研究生： 蔡尚武
Tsai, Shang-Wu
論文名稱： 含任意方向裂縫之功能梯度熱彈性破壞力學問題
The Thermoelastic Problem of a Functionally Graded Infinite Medium Containing an Arbitrarily Oriented Crack
指導教授： 褚晴暉
Chue, Ching-Hwei
屈子正
Chiu, Tz-Cheng
學位類別： 博士
Doctor
系所名稱： 工學院 - 機械工程學系
Department of Mechanical Engineering
論文出版年： 2013
畢業學年度： 102
語文別： 英文
論文頁數： 182
中文關鍵詞： 功能梯度材料 、熱負載 、應力強度因子 、任意方向裂縫 、高斯-切比雪夫數值積分法。
外文關鍵詞： Graded material, Heat conduction, Stress intensity factor, Arbitrarily oriented crack, Gauss-Chebyshev integration technique.
相關次數： 點閱：164  下載：12 
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    • 本論文探討含有單一嵌入式任意方向裂縫之功能梯度材料無窮平面受到遠端均勻熱通量作用下之面內破壞力學問題。文中所考慮之熱通量與材料梯度方向一致，且裂縫面假設為部份絕熱條件。本文依據熱彈性力學相關之理論基礎，運用傅立葉積分轉換，將此混合邊界值問題化解成奇異積分方程組，再藉由高斯-切比雪(Gauss-Chebyshev)多項式技術化簡為代數聯立方程組，以求得裂縫表面附近之溫度場、裂縫尖端熱通量強度因子與應力強度因子之數值解。接著從數值結果分別討論裂縫部份絕熱參數、材料非均質參數以及裂縫方向對溫度場、熱通量與應力強度因子之影響。相較於先前發表的文獻，本論文之裂縫方向不再侷限於垂直熱通量方向，因而能夠分析探討在任意裂縫方向與材料非均質參數的交互影響下，裂縫表面附近之溫度場、裂縫附近的熱通量強度因子與應力強度因子的變化。

    In this dissertation, the problem of an arbitrarily-oriented partially-insulated crack in an infinite FGM plane subjected to uniform remote heat flux along the direction of material gradient is considered. The material gradient is assumed to be in the exponential form. By using Fourier transform, the field equations with mixed boundary conditions are reduced into a system of singular integral equations and then solved numerically by using the Gauss-Chebyshev polynomials. Results are shown graphically to illustrate the effects of crack insulating capability, material inhomogeneity, and crack orientation on the temperature fields, the heat flux intensity factors and stress intensity factors at both crack tips. The crack closure algorithm is also applied to evaluate crack surface contact induced stress intensity factor changes at both crack tips. Compared to the thermo-mechanical problem discussed in literatures, the orientation of the cracking defect considered in this thesis is not restricted to be perpendicular to the direction of material grading. Consequently, the thermo-elastic solutions can be and are used to evaluate the effect of crack orientation and its interaction with the influence of grading inhomogeneity on the temperature gradient, heat intensification around the cracking defect and crack-tip stress intensity factor.

    Abstract i 摘 要 ii 誌 謝 iii List of Contents iv List of Tables viii List of Figures xiii Nomenclature xvi Chapter 1 Introduction 1 1.1 Introduction 1 1.2 Functionally graded materials 2 1.2.1 Concept 2 1.2.2 History 4 1.2.3 Types of manufacturing process techniques 5 1.2.4 Gradient forms 6 1.2.5 Application 8 1.3 Literature survey 9 1.4 Statement of the crack problem 12 1.4.1 Geometry of the problem 12 1.4.2 Superposition technique 13 1.5 Overview 16 Chapter 2 Temperature formulation 17 2.1 Basic theory of heat conduction and thermoelasticity 17 2.1.1 Heat conduction 17 2.1.2 Thermoelasticity 18 2.2 Governing equation 20 2.3 Boundary conditions 22 2.4 The integral equation 23 2.5 Formulation of temperature field 27 Chapter 3 Displacement formulation 29 3.1 Governing equations 29 3.2 Boundary conditions 32 3.3 Formulation of displacement field 32 3.3.1 Homogeneous solution 32 3.3.2 Particular solution 36 3.3.3 The integral equations 38 Chapter 4 Thermal stress analysis 45 4.1 Introduction 45 4.2 Thermal stress for stress free condition 46 4.3 Thermal stress for fully constrained condition 46 Chapter 5 Solution of singular integral equations and numerical procedures 50 5.1 Solution of integral equations 50 5.1.1 Heat conduction problem 50 5.1.2 Temperature field 53 5.1.3 Thermoelastic problem 55 5.2 Integrals involving the Chebyshev polynomials 58 5.3 Convergence of the approximation 59 Chapter 6 Intensity factors and crack-closure algorithm 61 6.1 Intensity factors 61 6.1.1 Nature of heat flux and stress singularity 61 6.1.2 Heat flux intensity factor 63 6.1.3 Stress intensity factor 65 6.2 Crack opening shape 66 6.3 Crack closure algorithm 67 Chapter 7 Results and discussion 72 7.1 Heat conduction problem 72 7.1.1 Temperature field along the crack surface planes 72 7.1.2 Temperature distribution around the crack 81 7.1.3 Heat flux intensity factor 89 7.2 Thermoelastic problem 94 7.2.1 Thermal crack surface stress 94 7.2.2 Crack opening shape for closure-closure algorithm 105 7.2.3 Stress intensity factor 109 Chapter 8 Conclusion 121 References 123 Appendix A Expressions of various functions 134 A.1 Expressions in particular displacement field 134 A.2 Expressions of Kij in the integral equations (3.91) and (3.92) 135 A.3 Expressions of fi and hi in the equations (3.95) and (3.96) 136 Appendix B Asymptotic expressions for the integrands in the kernels 138 Appendix C Formula for evaluating the asymptotic kernels 140 Appendix D Gauss-Legendre quadratures 142 Appendix E Closed-form expressions for the infinite homogeneous medium 144 E.1 Closed-form expressions for the crack surface temperature field 144 E.2 Closed-form expressions for thermal crack surface stresses 144 E.3 Closed-form expressions for stress intensity factors 145 Appendix F Tables for crack-closure algorithm 146 Appendix G Tables for heat conduction problem 153 G.1 Tables for temperature field 153 G.2 Tables for heat flux intensity factor 166 Appendix H Tables for thermoelastic problem 168 H.1 Tables for equivalent thermal crack surface stresses 168 H.2 Tables for crack surface displacement 175 H.3 Tables for stress intensity factors 177 Vita 182

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