由两个相互作用的裂纹形成的通用形状
Universal shapes formed by two interacting cracks
摘要：
我们调查的起源广泛观察到的“恩passant”裂纹图案，通过两个接近的裂纹之间的相互作用形成。在矩形弹性板的每一个长边切口，然后从短边受到准静态单轴应变。这两个裂纹沿着近似直线的路径传播，直到它们彼此通过，之后它们弯曲并释放透镜状碎片。我们发现，对于具有不同的机械性能的材料，该碎片的形状具有2：1的纵横比，长度尺度由初始裂纹偏移量$s$设定，时间尺度由$s$与拉伸速度的比率设定。裂纹具有通用的平方根形状，我们使用裂纹-裂纹相互作用的简单几何模型来理解。
英文摘要：
We investigate the origins of the widely-observed "en passant" crack pattern which forms through interactions between two approaching cracks. A rectangular elastic plate is notched on each long side and then subjected to quasistatic uniaxial strain from the short side. The two cracks propagate along approximately straight paths until they pass each other, after which they curve and release a lenticular fragment. We find that for materials with diverse mechanical properties, the shape of this fragment has an aspect ratio of 2:1, with the length scale set by the initial crack offset $s$ and the time scale set by the ratio of $s$ to the pulling velocity. The cracks have a universal square root shape which we understand using a simple geometric model of the crack-crack interaction.
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