残余应力固体的动态碎裂：从微观不稳定性到通用缩放
Dynamic fragmentation of residually stressed solids: From microscopic instabilities to universal scaling
AI总结：
研究通过高速冲击实验和微机械模型揭示残余应力固体动态碎裂的通用缩放规律，发现碎片尺寸分布遵循指数衰减并可归一化为单一主曲线。
摘要：
残余应力固体的动态碎裂涉及存储的弹性能量、应力波传播和裂纹不稳定性之间的复杂相互作用。在本研究中，我们通过高速弹体冲击实验和一种新颖的微机械网络模型，探讨了化学增强玻璃的断裂力学。我们通过规定非弹性应变（特征应变）分布，严格地将残余应力纳入离散晶格框架中，该分布被公式化为等效体和表面力，以确保断裂路径的网格无关性。我们的实验和模拟表明，尽管随着冲击能量的增加，断裂拓扑结构从粗到细变化，但累积碎片尺寸分布始终遵循指数衰减。关键的是，我们揭示了一个通用缩放定律：当碎片尺寸分布被归一化为平均碎片面积时，来自不同加载条件和应力剖面的碎片尺寸分布可以坍缩到一条主曲线上。此外，该模型阐明了碎片化的决定因素，表明所形成的碎片尺寸不仅由残余应力的大小决定，还由应力梯度的陡峭程度决定。在微观尺度上，我们识别出一种动态不稳定性机制，非顺序的裂纹尖端前的键断裂导致局部裂纹速度明显超过瑞利波速（c_r）。这些被抑制的微观分支，类似于布里奇-安德鲁斯机制，为断裂后显微镜观察中观察到的“舌状”特征和hackle区提供了物理解释。
英文摘要：
The dynamic fragmentation of residually stressed solids involves a complex interplay between stored elastic energy, stress wave propagation, and crack instabilities. In this work, we investigate the fracture mechanics of chemically toughened glass through high-velocity projectile impact experiments and a novel micromechanical network model. We rigorously incorporate residual stress into the discrete lattice framework via a prescribed inelastic strain (eigenstrain) distribution, formulated as equivalent body and surface forces to ensure mesh-independent fracture paths. Our experiments and simulations demonstrate that while the fracture topology shifts from coarse to fine with increasing impact energy, the cumulative fragment size distribution consistently follows an exponential decay. Crucially, we reveal a universal scaling law: fragment size distributions from diverse loading conditions and stress profiles collapse onto a single master curve when normalized by the mean fragment area. Furthermore, the model elucidates the determinants of fragmentation, showing that the resulting fragment size is governed not only by the magnitude of residual stress but also by the steepness of the stress gradient. At the microscopic scale, we identify a mechanism for dynamic instability where non-sequential bond breaking ahead of the crack tip leads to apparent local crack speeds exceeding the Rayleigh wave speed ($c_r$). These arrested micro-branches, analogous to the Burridge-Andrews mechanism, provide a physical explanation for the "tongue-like" features and hackle zones observed in post-mortem fractography.
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