由於優秀的機械性質、導電性及導熱性等特性，石墨烯及奈米碳管是近年研究的熱門材料。兩者應用的一大重點，是添加進複合材料內，提升整體的機械性質。為了瞭解添加之後抗破壞效果如何，首先得測定石墨烯及奈米碳管的破壞韌度，但由於兩者尺寸、製造成本、成品良率等問題，進行實體實驗比較困難，難度較低的代替方案為電腦模擬。目前大部分的做法，是建立石墨烯及奈米碳管的分子模型，運用分子動力學來求出兩者的破壞韌度；本文則使用有限元素軟體ANSYS，先建立以節點代表碳原子、非線性樑元素代表鍵結，以模擬兩者真實分子結構的非連體模型，求出非連體模型的機械性質；之後將石墨烯視為平板、奈米碳管視為薄殼，建立兩者的連體模型，並套入從非連體模型求得的機械性質，接著使用破壞力學理論，求出石墨烯及奈米碳管的破壞韌度皆為3.37MPa√m。

Because of their excellent mechanical, electrical, thermal and other properties, graphene and carbon nanotube are popular materials for research in recent years. One of the important applications is adding them into composite materials to enhance the material’s mechanical properties. To understand their ability to resist the failure, we have to acquire their fracture toughness first. Because of the small scale, cost and quality of manufacture, etc, conducting experiments on them physically is rather rare; instead, computer simulation is widely used. Most of the popular methods are building up molecular models of graphene and carbon nanotube and applying molecular dynamics to determine their fracture toughness. This article tries a different way: by using finite element software ANSYS, first build up molecular models of graphene and carbon nanotube and find out their mechanical properties; second, build up a plane and a cylindrical shell model, each for graphene and carbon nanotube (both are continuum model), then apply the properties we found from molecular models previously; third, apply fracture mechanics on the continuum models. In the end, the fracture toughness of graphene and carbon nanotube determined by this method are both 3.37MPa√m.

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