Abstract
We suggest that the observed large-scale universal roughness of brittle fracture surfaces is due to the fracture propagation being a damage coalescence process described by a stress-weighted percolation phenomenon in a self-generated quadratic damage gradient. We use the quasistatic 2D fuse model as a paradigm of a mode I fracture model. We measure for this model, which exhibits a correlated percolation process, the correlation length exponent and conjecture it to be equal to that of classical percolation, . We then show that the roughness exponent in the 2D fuse model is . This is in accordance with the numerical value . Using the value for 3D percolation, , we predict the roughness exponent in the 3D fuse model to be , in close agreement with the previously published value of . We furthermore predict for 3D brittle fractures, based on a recent calculation giving . This is in full accordance with the value found experimentally.
- Received 15 July 2002
DOI:https://doi.org/10.1103/PhysRevLett.90.045504
©2003 American Physical Society