臺灣博碩士論文加值系統

鎳鈦形狀記憶合金(SMAs，Shape Memory Alloys)擁有傑出的機械性質、電耦合性質以及抗腐蝕性，在接受到外在環境刺激時，能感測並表現出獨特的現象。例如：形狀記憶效應(shape memory effect)，材料在加熱到相變化溫度以上後，可以恢復在低溫時受到的形變；超彈性(superelasticity) 現象，使材料在常溫下有比一般金屬更良好的延展性，兩者都是非常重要的特性。其中奈米壓印應力誘發形狀記憶效應，因其同時牽涉應力、溫度誘發之麻田散體相轉變、特殊微結構排列、差排等塑性機制，使得其仍難以在一般實驗方法觀察微結構演變的細節，因此分子動力學模擬計算便扮演了微結構動力學過程研究的重要工具。然而在分子動力學領域中，過往在其他材料模型的研究上，已被發現到具有尺寸效應的問題，也就是過小的分子動力學模型，就算使用已經被驗證且廣泛被使用的原子間勢能函數進行計算，也有機會產生偏差的計算結果。例如在差排滑移受到限制，進而影響到力學性質的評估。因此本研究將採用多個大型模型與過往小型模型比較，探討鎳鈦形狀記憶合金的在微結構與力學性質上的尺寸效應。另一方面，過去常用的微結構分析方法，common neighbor analysis (CNA) 或是polyhedral template matching (PTM)，儘管能夠區分出沃斯田體相和麻田散體相之間的轉變，卻尚不足以分辨出麻田散體兄弟晶，因此需要使用已開發的辨認方法 Martensite variants identification method (MVIM)來觀察麻田散體兄弟晶。除此之外，本研究也引入了平行化計算架構來改編MVIM，降低其在分析計算大型模型時的時間成本。
在目前的研究成果中，已經發現到微結構演進具有獨特的路徑，同時演進路徑中也發現到了兄弟晶分佈區域具有特定的臨界大小。在抵達臨界值後，模型會藉由新的麻田散體相變化區域生成，來適應壓印產生之應變。除此之外，模型中的各兄弟晶種類比例也與微結構演進路徑息息相關，相同的壓印深度比例下，尺寸越大的模型會生成更加細緻且具備高對稱性的微結構分佈，並有更少的過渡相兄弟晶比例，與實驗結果吻合。我們也針對模型週期性邊界對相變化演進的影響進行了探討。期望能透過這些結果，為形狀記憶合金的分子動力學模擬研究，提出模型尺寸設計的建議與方向，進而使計算結果更加貼近實驗結果，達到對實際設計材料提出創見的可能性。

Nickel-titanium shape memory alloys (SMAs) have outstanding mechanical properties, electrical coupling properties, and corrosion resistance. They can sense the external environmental stimuli and exhibit unique phenomena. For example, the shape memory effect, where the material can recover from the deformation at low temperatures when heated above the transformation temperature; the superelasticity phenomenon, which gives the material better ductility than conventional metals at room temperature. Nanoscale indentation stress-induced shape memory effect is difficult to observe the details of microstructure evolution using the conventional experimental methods due to the involvement of stress- and temperature-induced martensitic transformation, special microstructure arrangement, and plastic mechanisms such as dislocation movement. Therefore, molecular dynamics simulations play an important role in the study of microstructure dynamics. However, it has been found that there are size effects in the previous molecular dynamics studies of other material models. This means that, even using validated and widely used interatomic potential functions, there is still a chance of deviation in the calculation results for small molecular dynamics models. For example, dislocation slip is restricted, which affects the evaluation of mechanical properties. Therefore, this study compared multiple large models with the small models to investigate the size effects of nickel-titanium shape memory alloys on microstructure and mechanical properties. On the other hand, the commonly used microstructure analysis methods in the past, e.g. Common Neighbor Analysis (CNA) or Polyhedral Template Matching (PTM), can distinguish the transition between the austenite and martensite phases, but they failed to distinguish the martensite variants. Thus, the developed identification method, Martensite Variants Identification Method (MVIM), is needed to observe the martensite variants. In addition, a parallel computing architecture for MVIM is developed and reduce the time cost of analyzing large models.
In the current research results, a unique path of microstructure evolution has been discovered；the critical size of the region of the certain martensite variant patterns has also been found in the evolution path. After reaching the critical size, the model generates a new martensitic transformation region to adapt to the increasing strain generated by indentation. In addition, the proportions of various crystal variant types in the model are closely related to the microstructure evolution path. Under the similar indentation depth ratio, larger models generate finer and more symmetrical microstructure distributions with fewer transitional phases, which are consistent with the experimental results. We also investigated the effect of periodic boundaries of the model on phase transformation. It is hoped that through these results, suggestions and design guideline for model size can be proposed for the molecular dynamics simulations for shape memory alloys. The calculation results can be closer to experimental results and the possibility for the new design of materials can be achieved.

摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
誌謝. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
圖目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
表目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii
一、緒論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 前言. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 研究動機. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 論文架構. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
二、文獻回顧. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1 形狀記憶合金具備之特性. . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 熱彈性麻田散體相變化. . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.2 形狀記憶效應. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.3 超彈性效應. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 鎳鈦形狀記憶合金. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.1 微結構研究. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.2 晶格理論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3 分子動力學模擬應用於鎳鈦形狀記憶合金. . . . . . . . . . . . . . . . . . 17
2.4 超大型分子動力學模擬與尺寸效應. . . . . . . . . . . . . . . . . . . . . . 19
三、理論與研究方法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.1 原子間交互作用力勢能. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.1.1 2NN-MEAM 勢能. . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.1.2 Tersoff 勢能. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.1.3 Lennard-Jones 勢能. . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2 結晶固體的連續理論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2.1 變形梯度與轉變矩陣. . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2.2 Cauchy-Born 法則: 連體與晶格間的關係. . . . . . . . . . . . . . . 27
3.3 Martensite Variants Identification Method (MVIM) . . . . . . . . . . . . . . . 28
3.3.1 麻田散體相兄弟晶之理論轉變矩陣. . . . . . . . . . . . . . . . . . 28
3.3.2 單位晶胞選擇與判別兄弟晶種類的條件判斷式. . . . . . . . . . . 31
3.3.3 區域投票法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.3.4 平行化處理架構之MVIM . . . . . . . . . . . . . . . . . . . . . . . 38
3.4 分子動力學模型與模擬條件設置. . . . . . . . . . . . . . . . . . . . . . . . 40
3.4.1 物理模型設定. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.4.2 球狀壓印頭模型設定. . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.4.3 能量最小化與溫度平衡流程設定. . . . . . . . . . . . . . . . . . . 43
3.4.4 以奈米壓印產生應力誘發流程設定. . . . . . . . . . . . . . . . . . 45
3.5 計算核心負載之動態平衡. . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
四、結果與討論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.1 微結構分布與邊界影響. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.2 奈米壓印試驗之微結構演進階段. . . . . . . . . . . . . . . . . . . . . . . . 49
4.3 微結構之臨界值. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.3.1 微結構演變範圍之臨界值. . . . . . . . . . . . . . . . . . . . . . . 51
4.3.2 雙晶面間距之臨界值. . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.4 應力應變曲線. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.5 微結構生成之比例統計. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.5.1 不同尺寸下兄弟晶組成比例統計. . . . . . . . . . . . . . . . . . . 59
4.5.2 持續下壓之兄弟晶比例變化. . . . . . . . . . . . . . . . . . . . . . 61
五、結論與未來展望. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.1 結論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.2 未來展望. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
參考文獻. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

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