Origin of the universal roughness exponent of brittle fracture surfaces: Stress-weighted percolation in the damage zone

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 approximate to 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 = 2nu/(1+2nu) = 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 +/- 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.