Cracks develop intricate patterns on the surfaces that they create. As faceted^1,2 fracture surfaces are commonly formed by slow tensile cracks in both crystalline and amorphous materials^3,4,5, facet formation and structure cannot reflect microscopic order. Although fracture mechanics predict that slow crack fronts should be straight and form mirror-like surfaces^6,7,8,9, facet-forming fronts propagate simultaneously within different planes separated by steps. Here we show that these steps are topological defects of crack fronts and that crack front separation into disconnected overlapping segments provides the condition for step stability. Real-time imaging of propagating crack fronts combined with surface measurements shows that crack dynamics are governed by localized steps that drift at a constant angle to the local front propagation direction while their increased dissipation couples to long-ranged elasticity to determine front shapes. We study how three-dimensional topology couples to two-dimensional fracture dynamics to provide a fundamental picture of how patterned surfaces are generated.

裂纹在其产生的表面上形成复杂的图案。由于多晶面^1,2断裂表面通常是由晶体和无定形材料^3,4,5中的缓慢拉伸裂纹形成的，因此，小面的形成和结构无法反映微观顺序。尽管断裂力学预测缓慢的裂纹前沿应是笔直的，并形成类似镜面的表面^6,7,8,9，形成刻面的前沿在由台阶分隔的不同平面内同时传播。在这里，我们表明这些台阶是裂纹前沿的拓扑缺陷，并且裂纹前沿分离成不连续的重叠段为台阶的稳定性提供了条件。传播的裂纹前沿与表面测量结果的实时成像显示，裂纹动力学受局部台阶控制，该台阶以与本地前沿传播方向成恒定角度漂移，而增大的耗散则与长程弹性耦合，从而确定了前沿形状。我们研究了三维拓扑如何耦合到二维断裂动力学，以提供有关如何生成图案化表面的基本图片。