Department of Physics and Center for Interdisciplinary Research on Complex Systems, Northeastern University, Boston, Massachusetts 02115, USA.
Nature. 2010 Mar 4;464(7285):85-9. doi: 10.1038/nature08862.
Planar crack propagation under pure tension loading (mode I) is generally stable. However, it becomes universally unstable with the superposition of a shear stress parallel to the crack front (mode III). Under this mixed-mode (I + III) loading configuration, an initially flat parent crack segments into an array of daughter cracks that rotate towards a direction of maximum tensile stress. This segmentation produces stepped fracture surfaces with characteristic 'lance-shaped' markings observed in a wide range of engineering and geological materials. The origin of this instability remains poorly understood and a theory with which to predict the surface roughness scale is lacking. Here we perform large-scale simulations of mixed-mode I + III brittle fracture using a continuum phase-field method that describes the complete three-dimensional crack-front evolution. The simulations reveal that planar crack propagation is linearly unstable against helical deformations of the crack front, which evolve nonlinearly into a segmented array of finger-shaped daughter cracks. Furthermore, during their evolution, facets gradually coarsen owing to the growth competition of daughter cracks in striking analogy with the coarsening of finger patterns observed in nonequilibrium growth phenomena. We show that the dynamically preferred unstable wavelength is governed by the balance of the destabilizing effect of far-field stresses and the stabilizing effect of cohesive forces on the process zone scale, and we derive a theoretical estimate for this scale using a new propagation law for curved cracks in three dimensions. The rotation angles of coarsened facets are also compared to theoretical predictions and available experimental data.
在纯拉伸载荷（模式 I）下，平面裂纹扩展通常是稳定的。然而，当平行于裂纹前缘的剪切应力叠加时（模式 III），它会变得普遍不稳定。在这种混合模式（I+III）加载配置下，最初的平母裂纹会分成一组朝向最大拉伸应力方向旋转的子裂纹。这种分段会产生具有台阶状断裂表面的特征“矛头状”标记，这种标记在广泛的工程和地质材料中都可以观察到。这种不稳定性的起源仍然理解得很差，并且缺乏预测表面粗糙度尺度的理论。在这里，我们使用描述完整三维裂纹前缘演化的连续相场方法对混合模式 I+III 脆性断裂进行了大规模模拟。模拟结果表明，平面裂纹扩展在螺旋变形下对螺旋变形是线性不稳定的，这种螺旋变形会非线性地演变成手指状子裂纹的分段阵列。此外，在它们的演化过程中，由于子裂纹的生长竞争，晶面逐渐粗化，这与在非平衡生长现象中观察到的指状图案的粗化非常相似。我们表明，动态优先不稳定波长由远场应力的失稳效应与过程区尺度上的内聚力的稳定效应之间的平衡来控制，并使用三维弯曲裂纹的新扩展定律来导出该尺度的理论估计。粗化晶面的旋转角度也与理论预测和现有实验数据进行了比较。
