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 $\nu \approx 1.35$ and conjecture it to be equal to that of classical percolation, $4/3$. We then show that the roughness exponent in the 2D fuse model is $\zeta =2\nu /(1+2\nu )=8/11$. This is in accordance with the numerical value $\zeta =0.75$. Using the value for 3D percolation, $\nu =0.88$, we predict the roughness exponent in the 3D fuse model to be $\zeta =0.64$, in close agreement with the previously published value of $0.62\pm 0.05$. We furthermore predict $\zeta =4/5$ for 3D brittle fractures, based on a recent calculation giving $\nu =2$. This is in full accordance with the value $\zeta =0.80$ found experimentally.

• Received 15 July 2002

DOI:https://doi.org/10.1103/PhysRevLett.90.045504