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研究生：	江承諭 Chiang, Cheng-Yu
論文名稱：	負普松材料應力腐蝕開裂之相場模擬研究 Phase field modeling of stress corrosion cracking in auxetic composites
指導教授：	王雲哲 Wang, Yun-Che
學位類別：	碩士 Master
系所名稱：	工學院 - 土木工程學系 Department of Civil Engineering
論文出版年：	2018
畢業學年度：	106
語文別：	英文
論文頁數：	114
中文關鍵詞：	應力腐蝕破裂、有限元素法、相場模擬、負普松、複合材料
外文關鍵詞：	stress corrosion cracking, finite element method, phase field modeling, auxetic, composites
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應力腐蝕破裂是導致金屬脆性斷裂的主要破壞機制之一，特別是氫脆效應，故本論文藉由相場模擬方法探討二維的應力腐蝕破裂，並討論了拉脹性（即負普松比）對裂紋擴展的影響。在我們的建模中，材料的楊氏模數會因為腐蝕和裂紋的生長而降低，且材料的表面包含腐蝕的起始孔洞，所有隨之而來的腐蝕和開裂都可能從此開始。我們研究了單向拉伸和剪切加載模式，使用描述濃度場（c場）的擴散方程來模擬腐蝕，以描述孔洞附近的固 - 液相轉變。然後濃度場與敘參數場（p場）耦合以描述裂紋擴展。我們通過引入局部損傷來穿透材料表面上的鈍化膜，然後腐蝕進行，形成半圓腐蝕坑，從而對孔蝕進行建模。

以不銹鋼為基材，改變其普松比為變數以探討應力腐蝕破裂，並觀察應力腐蝕破裂發生時所產生的變化。應力腐蝕破裂會受到不同的普松比的材料影響腐蝕破裂的速度。當整體材料為負普松時，在應力控制下，負普松比會減緩裂紋發展;而在位移控制下，負普松比反而會增加裂紋生長速度。當只有內含物為負普松，可以觀察到腐蝕破裂的速率受到複合材料的影響變慢，並且誘導腐蝕破裂沿著負普松材料的邊緣改變腐蝕路徑。負普松材料在被拉昇的時候會膨脹，進而阻止裂縫前進。

Stress corrosion cracking (SCC) is one of major damage mechanisms to cause brittle fracture in metal, in particular the hydrogen embrittlement effects. In this work, we adopt the phase field modeling technique to study SCC in two dimensions, and discuss the effects of auxeticity, i.e. negative Poisson's ratio, on the crack propagation. In our modeling, Young's modulus of the material is reduced due to corrosion and crack, and the surface of the material initially contains a corrosion pit, where all consequent corrosion and cracking may start from. Both uniaxial tension and shear loading modes are studied. The corrosion is modeled by using a diffusion equation describe the concentration field (c-field) to describe the solid-liquid transition near the pit. The concentration field, then, couples with the order parameter field (p-field) to describe the crack propagation. We model pitting corrosion by introducing a local damage to penetrate the passive film on the surface of material, and then corrosion progresses to form a semi-circle corroded pit.

Using material parameters for stainless steel, SCC is studied in conjecture with the effects of Poisson's ratio. SCC is strongly affected by loading rates, and may be slow or arrested by negative Poisson's ratio.
Negative Poisson ratio may reduce crack advancement under load control. But, it increase crack propagation speed under displacement control. When inclusions (auxetic or not) are present, the advancement of SCC may be deflected, so that crack path increases. Auxeticity may locally increase deformation volume, hence reduce the crack propagation speed and reduce corrosion rates.

CHINESE ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1 Goals and motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.1 Forms of corrosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.2 Corrosion Prevention . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.3 Phase field modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3 Outline of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Theoretical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1 Electrochemical considerations . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.1 Oxidation reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2 Nernst Planck equation . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3 Current boundary conditions at electrodes . . . . . . . . . . . . . . . . 7
1.4 Orange Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 Stress cracking corrosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3 Kim-Kim-Suzuki phase field model . . . . . . . . . . . . . . . . . . . . . . . 11
Numerical considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1 Finite element solver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2 Model description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.1 Elasticity analysis for matrix of two-dimensional composite model . . . 18
2.2 A phase field model of stress corrosion cracking . . . . . . . . . . . . 20
2.3 Nondimensionalization . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
1 Crack growth under tension (p+u) . . . . . . . . . . . . . . . . . . . . . . . . 27
2 Crack growth under shear (p+u) . . . . . . . . . . . . . . . . . . . . . . . . . 33
3 Destruction of the passive film induces pitting corrosion (c+p) . . . . . . . . . 37
4 Stress corrosion cracking (c+p+u) . . . . . . . . . . . . . . . . . . . . . . . . 41
4.1 Stress corrosion cracking model . . . . . . . . . . . . . . . . . . . . . 41
4.2 Shear stress model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.3 Effects of diffusion coefficient . . . . . . . . . . . . . . . . . . . . . . 54
5 Effects of auxeticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.1 Effects of auxeticity by displacement control . . . . . . . . . . . . . . 56
5.2 Effects of auxeticity by load control . . . . . . . . . . . . . . . . . . . 62
6 Effects of inclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.1 Different Poisson’s ratio inclusions . . . . . . . . . . . . . . . . . . . 70
6.2 Different Young’s modulus inclusions . . . . . . . . . . . . . . . . . . 76
6.3 Different size inclusions . . . . . . . . . . . . . . . . . . . . . . . . . 81
7 Effects of anisotropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
Conclusions and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
LIST OF REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
APPENDICES
Appendix A: Presentation slides . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

                                    

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校內：2023-08-31公開
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