Lubomirsky Yuri, Bouchbinder Eran
Chemical and Biological Physics Department, Weizmann Institute of Science, Rehovot, 7610001, Israel.
Nat Commun. 2024 Aug 29;15(1):7494. doi: 10.1038/s41467-024-51573-6.
Materials failure in 3D still poses basic challenges. We study 3D brittle crack dynamics using a phase-field approach, where Gaussian quenched disorder in the fracture energy is incorporated. Disorder is characterized by a correlation length R and strength σ. We find that the mean crack velocity v is bounded by a limiting velocity, which is smaller than the homogeneous material's prediction and decreases with σ. It emerges from a dynamic renormalization of the fracture energy with increasing crack driving force G, resembling a critical point, due to an interplay between a 2D branching instability and disorder. At small G, the probability of localized branching on a scale R is super-exponentially small. With increasing G, this probability quickly increases, leading to misty fracture surfaces, yet the associated extra dissipation remains small. As G is further increased, branching-related lengthscales become dynamic and persistently increase, leading to hackle-like structures and a macroscopic contribution to the fracture surface. The latter dynamically renormalizes the actual fracture energy until, eventually, any increase in G is balanced by extra fracture surface, with no accompanying increase in v. Finally, branching width reaches the system's thickness such that 2D symmetry is statistically restored. Our findings are consistent with a broad range of experimental observations.
三维材料失效仍然面临着基本挑战。我们使用相场方法研究三维脆性裂纹动力学，其中引入了断裂能中的高斯淬火无序。无序由相关长度R和强度σ表征。我们发现平均裂纹速度v受限于一个极限速度，该极限速度小于均匀材料的预测值，且随σ减小。它源于随着裂纹驱动力G增加，断裂能的动态重整化，类似于一个临界点，这是由于二维分支不稳定性和无序之间的相互作用。在小G时，尺度为R的局部分支概率超指数级小。随着G增加，该概率迅速增大，导致断裂表面模糊，但相关的额外耗散仍然很小。随着G进一步增加，与分支相关的长度尺度变得动态且持续增加，导致出现类似毛边的结构，并对断裂表面有宏观贡献。后者动态重整实际断裂能，直到最终，G的任何增加都由额外的断裂表面平衡，而v没有随之增加。最后，分支宽度达到系统厚度，使得二维对称性在统计上得以恢复。我们的发现与广泛的实验观察结果一致。
