Crack path selection in 2D crystals

Even though fracture in solids can be rationalized in continuum mechanics, local processes such as the path selection and the formation of facets and kinks along the crack edges cannot be resolved in this framework. The problem is addressed by developing a high-fidelity neural network-based force field NN-F3. An active-learning approach is taken to capture the high strain and non-equilibrium nature of the crack tips in 2D crystals such as graphene and h-BN, which has not been satisfactorily addressed by existing empirical and machine-learning force fields. Atomistic simulations using NN-F3 resolve spatial complexities from lattice-scale kinks to sample-scale crack patterns, which are discussed directly with continuum mechanics predictions and experimental observation. The results show that kinking or deflection of the cracks defines the roughness of cleaved edges and is explained by the alternation of the stress intensity factors. We also find that the selection of crack paths cannot be determined by the anisotropy in the energies of relaxed edges as widely referred to in the literature. The distortion and undercoordination of the cleaved edges play critical roles in the fracture process, which have to be incorporated into the models to predict the crack paths. Measures of fracture toughness are extracted from the fracture patterns, the critical stress intensity factors, or the energies of edges in the intermediate, unrelaxed states.

尽管在连续介质力学中可以对固体中的断裂进行理论解释，但诸如裂纹边缘的路径选择以及沿着裂纹边缘的台阶和曲折的形成等局部过程，却无法在该框架下得到解决。为此，研究者通过开发一种基于高保真神经网络的高精度力场NN-F3来解决这个问题。采用主动学习策略以捕捉二维晶体（如石墨烯和h-BN）裂纹尖端的高应变和非平衡特性，这一特性是现有经验力场和机器学习力场所未能充分解决的。利用NN-F3进行的原子级模拟，从晶格尺度的曲折到样本尺度的裂纹模式，都能解析空间复杂性，并与连续介质力学的预测和实验观察直接对比。结果表明，裂纹的曲折或偏转定义了劈裂边缘的粗糙度，并可通过应力强度因子的交替变化来解释。此外，我们发现，裂纹路径的选择不能由文献中广泛引用的松弛边缘能量各向异性来确定。劈裂边缘的畸变和次配位在断裂过程中起着至关重要的作用，必须将这些因素纳入模型中，以预测裂纹路径。断裂韧性的度量是从断裂模式、临界应力强度因子或中间未松弛状态的边缘能量中提取的。