# Crack Surface Roughness in Three-Dimensional Random Fuse Networks

## Abstract

Using large system sizes with extensive statistical sampling, we analyze the scaling properties of crack roughness and damage profiles in the three-dimensional random fuse model. The analysis of damage profiles indicates that damage accumulates in a diffusive manner up to the peak load, and localization sets in abruptly at the peak load starting from a uniform damage landscape. The global crack width scales as $$W \sim L^{0.5}$$ and is consistent with the scaling of localization length $$\xi \sim L^{0.5}$$ used in the data collapse of damage profiles in the post-peak regime. This consistency between the global crack roughness exponent and the post-peak damage profile localization length supports the idea that the post-peak damage profile is predominantly due to the localization produced by the catastrophic failure, which at the same time results in the formation of the final crack. Finally, the crack width distributions can be collapsed for different system sizes and follow a log-normal distribution.

- Authors:

- ORNL
- University of La Sapienza, Rome

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1003700

- DOE Contract Number:
- DE-AC05-00OR22725

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review E; Journal Volume: 74; Journal Issue: 2

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DISTRIBUTION; PEAK LOAD; ROUGHNESS; SAMPLING

### Citation Formats

```
Nukala, Phani K, Zapperi, Stefano, and Simunovic, Srdjan.
```*Crack Surface Roughness in Three-Dimensional Random Fuse Networks*. United States: N. p., 2006.
Web. doi:10.1103/PhysRevE.74.026105.

```
Nukala, Phani K, Zapperi, Stefano, & Simunovic, Srdjan.
```*Crack Surface Roughness in Three-Dimensional Random Fuse Networks*. United States. doi:10.1103/PhysRevE.74.026105.

```
Nukala, Phani K, Zapperi, Stefano, and Simunovic, Srdjan. Sun .
"Crack Surface Roughness in Three-Dimensional Random Fuse Networks". United States.
doi:10.1103/PhysRevE.74.026105.
```

```
@article{osti_1003700,
```

title = {Crack Surface Roughness in Three-Dimensional Random Fuse Networks},

author = {Nukala, Phani K and Zapperi, Stefano and Simunovic, Srdjan},

abstractNote = {Using large system sizes with extensive statistical sampling, we analyze the scaling properties of crack roughness and damage profiles in the three-dimensional random fuse model. The analysis of damage profiles indicates that damage accumulates in a diffusive manner up to the peak load, and localization sets in abruptly at the peak load starting from a uniform damage landscape. The global crack width scales as $W \sim L^{0.5}$ and is consistent with the scaling of localization length $\xi \sim L^{0.5}$ used in the data collapse of damage profiles in the post-peak regime. This consistency between the global crack roughness exponent and the post-peak damage profile localization length supports the idea that the post-peak damage profile is predominantly due to the localization produced by the catastrophic failure, which at the same time results in the formation of the final crack. Finally, the crack width distributions can be collapsed for different system sizes and follow a log-normal distribution.},

doi = {10.1103/PhysRevE.74.026105},

journal = {Physical Review E},

number = 2,

volume = 74,

place = {United States},

year = {Sun Jan 01 00:00:00 EST 2006},

month = {Sun Jan 01 00:00:00 EST 2006}

}