石墨烯是當今最有潛力的奈米材料之一，其優異的物理性質使其得以被應用在如電子、生醫與奈米工程等多種領域上。然而現實中完美的石墨烯幾乎不存在，因此許多研究必須將材料缺陷納入材料設計的分析中。隨著研究的發展科學家也逐漸了解到「缺陷」在材料中所扮演的腳色。不同於宏觀的缺陷，微觀缺陷的本質是晶格不完美的排列，而這些不完美的排列會造成材料性質的改變。在石墨烯的研究中，科學家已能透過微結構的缺陷來改變石墨烯的性質，包括降低熱傳導、誘發磁性或是提高韌性等。然而石墨烯在這些缺陷下的力學性質和破壞行為仍缺乏更深入的研究，尤其石墨烯抵禦裂紋擴張的能力不佳，所以探討其破壞的行為就變成相當重要的議題。
一直以來預測裂紋如何擴展是破壞力學中一項重要的任務，雖然目前為止已經發展出許多方法模擬材料的破壞例如擴展型有限元素法、有限離散元素法或 分子動力學等，但這些方法需要倚靠龐大的計算資源才能得到精確的結果。隨著深度學習強勢地崛起，越來越多的研究將深度學習應用在複雜的物理系統上，例如蛋白質摺疊的預測或是複合材料的設計。因此在本研究中我們也期望能夠將深度學習的模型應用到破壞領域的研究上，能夠更有效地預測石墨烯在複雜的缺陷結構下的破壞。
在本論文中我們引入深度學習模型預測石墨烯的裂紋發展。此模型以具有卷積結構的特殊長短期記憶模型—ConvLSTM為核心，再結合池化層、卷積層和全連接層，能夠學習裂紋在擴張中空間與時間的相依性。在研究的一開始，為了產生訓練資料我們建置了多組具有不同晶格方向或是孔洞結構的石墨烯作為訓練資料。接著以分子動力學進行石墨烯的單軸拉伸試驗的模擬以獲得石墨烯在奈米尺度下真實的斷鍵現象。我們再將模擬結果轉換成灰階圖像並進行數值轉換整理成訓練資料。在深度學習的預測流程上，我們將裂紋圖像切割成多段有序的圖像，並透過ConvLSTM學習序列之間的影響以及幾何特徵。模型會預測出下一個時刻的裂紋位置並更新到下一個時刻的裂紋圖上。最終透過不斷的迭代能得到完整的裂紋狀態。
在分子動力學模擬的結果中，我們觀察到裂紋的走向與石墨烯的角度高度相關，這很大一部份與石墨烯在鋸齒方向的碳-碳鍵比較容易斷有關。我們也觀察到孔洞會影響應力的分布，使得裂紋容易被引導至孔洞所在處。這其中產生較為特別的案例，可以發現裂紋被引導至孔洞後，消除了應力集中而延緩材料的失效。深度學習預測的結果在不同角度下裂紋發展的精確度高達99.45%，也能預測雙晶石墨烯以及多晶石墨烯的裂紋。另一方面模型在預測不同缺陷配置下裂紋發展精確度達94.50%。以300組分子動力學的結果作為訓練資料所建立的模型能夠預測任意缺陷配置的石墨烯，足見ConvLSTM模型在裂縫發展的預測力。總體來說，本研究提出了一種有效的方式預測石墨烯的裂紋，展現ConvLSTM在裂縫預測的可行性，未來能以注意力機制加以修正模型並更進一步預測裂紋下的應力狀態。

Fracture behaviors of brittle materials have been a crucial problem when it comes to safety and reliability. With deep learning (DL) recently drawing attention in material field, several studies have applied deep learning techniques on predicting crack growth of brittle materials. In this study, we aim to use deep sequential model to predict the fracture path of graphene under two systems of defective configuration. One involves graphene with different crystalline and the other involves graphene with different porous defects. First, we perform uniaxial tensile test simulation on graphene using molecular dynamics. The fracture results are then transformed into gray scale image-based data for the deep learning model. Finally, we construct two ConvLSTM-based models to learn the spatiotemporal information about the sequential crack growth images of each graphene system, respectively. Results show that our ConvLSTM-based models can predict the fracture path of graphene with 99 percent pixel-wise accuracy on system of different crystalline and pixel-wise 94 percent accuracy on system of different defects. It takes a few second to get reasonable simulation results, which is much more efficient way than conventional atomic simulation method.

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