Two-dimensional materials (2DMs) are prone to brittle failure under load but a recent experiment has demonstrated intrinsic toughening in hexagonal boron nitride (-BN), which calls for a general understanding of fracture toughness in 2DMs. Using atomistic calculations combined with a developed size-dependent extrapolation method, we show that 2DMs with strong anisotropy of edge energy favor bifurcated cracks for intrinsic toughening as in -BN, while those with weak edge energy anisotropy exhibit split cracks for brittle failure as in graphene. The interplay between chemical bond strength and fracture energy of bifurcated crack tips leads to alternate deflections and, thus, rough crack edges as observed in the previous experiment. We further develop a robust descriptor for identifying 2DMs exhibiting similar fracture behavior to that in -BN. More interestingly, we reach a physically interpretable formula capable of quantitatively determining the toughness of 2DMs based on easily accessible intrinsic features of elements. These findings lay a solid foundation for nanodevice applications where controlled toughness is required.

中文翻译：

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边缘能量各向异性主导的二维材料断裂韧性

二维材料 (2DM) 在负载下容易发生脆性破坏，但最近的一项实验证明了六方氮化硼 (-BN) 具有内在增韧作用，这需要对 2DM 的断裂韧性有一个总体的了解。使用原子计算结合开发的尺寸相关外推法，我们发现具有强边缘能量各向异性的 2DM 有利于分叉裂纹以实现本征增韧（如 -BN），而具有弱边缘能量各向异性的 2DM 则表现出分裂裂纹以实现脆性破坏（如石墨烯） 。分叉裂纹尖端的化学键强度和断裂能之间的相互作用导致交替偏转，从而导致先前实验中观察到的粗糙裂纹边缘。我们进一步开发了一个强大的描述符，用于识别表现出与-BN 相似的断裂行为的 2DM。更有趣的是，我们得出了一个物理上可解释的公式，能够根据易于获取的元素固有特征定量确定 2DM 的韧性。这些发现为需要控制韧性的纳米器件应用奠定了坚实的基础。