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Atomistic and multiscale analyses of brittle fracture in crystal lattices

机译：晶格脆性断裂的原子和多尺度分析

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Applicability of the Griffith criterion [A. A. Griffith, Philos. Trans. R. Soc. London, Ser. 221, 163 (1920); S. Zhang, S. L. Meilke, R. Khare, D. Troya, R. S. Ruoff, G. C. Schatz, and T. Belytschko, Phys. Rev. B 71, 115403 (2005)] for predicting the onset of crack extension in crystal lattices is systematically evaluated using atomistic and multiscale simulations with a focus on the effects of crack size and lattice discreteness. An atomistic scheme is developed to determine the true Griffith load defined by the thermodynamic energy balance of crack extension for both finite-sized and semi-infinite crack models. For a model monolayer lattice, we identify a characteristic crack length (about ten lattice spacings) below which the Griffith fracture stress markedly overestimates the true Griffith load. Through a stability analysis of crack-tip bond separation, the athermal (nonthermally activated) loads of instantaneous fracture are determined, thereby yielding the estimated lattice trapping range. Our simulations show that the strength of lattice trapping depends on the interaction range of the interatomic force fields. Using the reaction pathway exploration method, we determine the minimum energy paths of bond breaking and healing at a crack tip, giving a more precise estimate of the lattice trapping range. The activation energy barriers governing the rate of kinetic crack extension are extracted from the minimum energy paths. Implications concerning the distinction between the athermal and Griffith fracture loads are discussed. Based on these results, a general criterion is established to predict the onset of crack growth in crystal lattices. In addition to taking into account the lattice trapping effect, this criterion is applicable to a large spectrum of crack sizes.
机译：格里菲斯准则的适用性[A.格里菲斯（A. ​​Griffith），菲洛斯（Philos）。反式R. Soc。伦敦，序列221，163（1920）; S. Zhang，S. L. Meil​​ke，R. Khare，D.Troya，R.S. Ruoff，G.C. Schatz和T.Belytschko，物理学Rev.B 71，115403（2005）]使用原子和多尺度模拟系统地评估了预测晶格中裂纹扩展的开始，重点是裂纹尺寸和晶格离散性的影响。开发了一种原子方案来确定由有限尺寸和半无限裂纹模型的裂纹扩展的热力学能量平衡定义的真实格里菲斯负荷。对于模型单层晶格，我们确定特征裂纹长度（大约十个晶格间距），在该长度以下，格里菲斯断裂应力明显高估了真实的格里菲斯载荷。通过裂纹尖端粘结分离的稳定性分析，确定了瞬时断裂的非热（非热活化）载荷，从而得出了估计的晶格俘获范围。我们的模拟表明，晶格俘获的强度取决于原子间力场的相互作用范围。使用反应路径探索方法，我们确定了裂纹尖端处键断裂和修复的最小能量路径，从而给出了对晶格俘获范围的更精确估计。从最小的能量路径中提取控制动态裂纹扩展速率的活化能垒。讨论了有关无热和格里菲斯断裂载荷之间区别的含义。基于这些结果，建立了一个通用准则来预测晶格中裂纹扩展的开始。除了考虑晶格捕获效应之外，该标准还适用于大范围的裂纹尺寸。

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