臺灣博碩士論文加值系統

缺陷對於金屬材料力學行為一直扮演重要的角色，其中差排對於材料塑性，阻尼，應變硬化與潛變均具有關鍵地位，自 Volterra 提出空心圓柱差排變形模型以來，差排研究一直是一門重要的課題。然而，差排運算受限於複雜運算公式與材料內部大量生成差排數量，在實際運算上有其困難度，因此差排計算與實際巨觀物理現象存在著差距。離散化差排動力 (discrete dislocation dynamic) 模擬是一種數值模擬研究方法，首先以較簡單幾何模型 (如直線段) 離散分割複雜的差排幾何形狀，藉由直線段較易處理的力學公式求得應力場或與移動等相關方程式，再利用電腦大量快速運算能力處理龐大運算量。本論文將建立差排離散化模型將差排以節點與線段模擬，利用直線段差排應力場公式計算各線段所受交互作用應力，並與外部施加應力疊加，再利用 Peach-Koehler formula 計算差排線段受力，考慮差排運動時所受黏滯 (viscous drag) 阻力與作用力平衡，藉以一階微分運動方程式，利用數值積分 (Euler-trapezoidal method) 求解後即可使用程式 (Matlab) 模擬差排動態行為；在 Frank-Read source 模擬中可得知形成一個差排迴圈的時間是線性正比於黏滯阻尼係數與障礙物 (obstacle) 距離，且隨著驅動應力增加而快速減少，在 0.75Gpa 應力下，形成時間與障礙物距離比值為 9.3 ns/nm，在在 2.0Gpa 應力下，比值為 3.0 ns/nm。


關鍵字: 離散化差排動力分析, Granato-Lücke 阻尼, Frank-Read 差排源

Defects play an important role in metal mechanics behavior. Dislocation (line defect) relate to metal plastic deformation, damping, strain hardening and creep phenomenon. Since Volterra provide cut cylinder deformed model, dislocation study is an essential material science subject always. However, computation of dislocation is still difficult due to complicated formula and large dislocation numbers in material. The relationships between dislocations calculate results and macroscopic mechanical properties didn’t connect perfectly. Discrete dislocation dynamic (DDD) simulation is a numerically simulation approach. Firstly, one adopts simple components (ex. straight segments) which replaces complex geometry with piece-wise line. And take advantage of computer operation ability to handle large computation work. This thesis represents dislocation by node and line segment to set up geometry model. Apply straight segment dislocation stress equations to calculate each segment interaction stresses then overlap external stresses. By Peach-Koehler formula, one obtains dislocation line force. Consider force balance between driven force and viscous drag resistant force during dislocation moving. Finally, one derives a first-order differential equation which be solved by numerical integrator (Euler trapezoidal method). In practices, a Matlab code program simulates dislocation mobility behavior. In Frank-Read (FR) source simulation, the time which forms a dislocation loop is proportional to viscous drag coefficient and obstacle distance linearly. And the FR formation time decreases rapidly as applied stress increases. In 0.75 GPa stress level, the formation time versus obstacle distance ratio is 9.3 ns/nm. In 2.0 GPa stress level, the formation time versus obstacle distance ratio is 3.0 ns/nm.

Keyword: Discrete dislocation dynamics, Granato-Lücke damping, Frank-Read source

Abstract I
摘要 II
Acknowledgements III
Table of Contents IV
List of Tables VI
List of Figures VII
Nomenclature X

Chapter 1 Introduction 1
1.1 Motivation and Goals 1
1.2 Literature survey 2
1.3 Outline 5

Chapter 2 Theoretical development 6
2.1 Introduction dislocation 6
2.1.1 Burgers vector and line vector 6
2.1.2 Dislocation type 7
2.1.3 Dislocation motion 9
2.2 Stress field about a straight dislocation segment 12
2.3 Introduction dislocation simulation 17
2.4 Representation of dislocation 19
2.5 Driving force and distribution 21
2.6 Mobility equation 23
2.7 Time integrator 25
2.8 Topological Change 28
2.8.1 Re-mesh 28
2.8.2 Merge and split 30

Chapter 3 Simulation results and discussion 32
3.1 Dislocation stress fields 33
3.1.1 Segment dislocation stress field comparison
with infinite dislocation 33
3.1.2 Dislocation array 38
3.2 Dislocation interactions 40
3.2.1 Two parallel dislocations attraction and
repulsion 41
3.2.2 Two perpendicular dislocations repulsion 52
3.3 Frank-Read sources 57
3.4 Relationship between dislocation and mechanics
properties of materials 67
3.4.1 Strength of metal crystals and dislocation
density 67
3.4.2 Deformation-Mechanism map 68
3.4.3 Mechanical damping due to dislocations 70
Chapter 4 Conclusions and future works 76
References 78
Appendix A Matlab program framework 83
自述 87

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