随机扰动晶格中I型断裂的微分支
Micro-branching in mode-I fracture in a randomly perturbed lattice
摘要：
我们研究了具有噪声键的晶格中的I型断裂。与以前的尝试相比，通过使用一个小参数，在完美的晶格中的原子之间的力定律和使用三体力定律的扰动，模拟再现的定性行为的超稳态裂纹在高速政权，包括合理的微分支。就诸如结构因子$g(r)$、径向或角分布的物理性质而言，这些晶格共享完美晶格的物理性质，而不是非晶材料的物理性质（例如，连续随机网络模型）。可以看到一个明确的过渡之间的稳定状态的裂纹，其中一个单一的裂纹在中线的样品和政权的不稳定裂纹，其中微分支开始出现在主裂纹附近，与以前的实验结果。这在蜂窝晶格和完全六边形晶格中都可以看到。该模型再现了脆性材料中裂纹扩展的主要物理特征，包括速度作为驱动位移的函数的行为和电阻振荡幅度的增加。此外，可以看到微分支形状的幂律行为的初步迹象，潜在地再现脆性断裂的最有趣的实验结果之一。
英文摘要：
We study mode-I fracture in lattices with noisy bonds. In contrast to previous attempts, by using a small parameter that perturbs the force-law between the atoms in perfect lattices and using a 3-body force law, simulations reproduce the qualitative behavior of the beyond steady-state cracks in the high velocity regime, including reasonable micro-branching. As far as the physical properties such as the structure factor $g(r)$, the radial or angular distributions, these lattices share the physical properties of perfect lattices rather than that of an amorphous material (e.g., the continuous random network model). A clear transition can be seen between steady-state cracks, where a single crack propagates in the midline of the sample and the regime of unstable cracks, where micro-branches start to appear near the main crack, in line with previous experimental results. This is seen both in a honeycomb lattice and a fully hexagonal lattice. This model reproduces the main physical features of propagating cracks in brittle materials, including the behavior of velocity as a function of driving displacement and the increasing amplitude of oscillations of the electrical resistance. In addition, preliminary indications of power-law behavior of the micro-branch shapes can be seen, potentially reproducing one of the most intriguing experimental results of brittle fracture.
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