Quenched disorder and instability control dynamic fracture in three dimensions
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arXiv
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| Natura: | Preprint |
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2023
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| _version_ | 1866912007710572544 |
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| author | Lubomirsky, Yuri Bouchbinder, Eran |
| author_facet | Lubomirsky, Yuri Bouchbinder, Eran |
| contents | 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 to 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_11692 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quenched disorder and instability control dynamic fracture in three dimensions Lubomirsky, Yuri Bouchbinder, Eran Materials Science Disordered Systems and Neural Networks Soft Condensed Matter Pattern Formation and Solitons 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 to 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. |
| title | Quenched disorder and instability control dynamic fracture in three dimensions |
| topic | Materials Science Disordered Systems and Neural Networks Soft Condensed Matter Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2311.11692 |