Roughness of fracture surfaces

We study the fracture surface of three dimensional samples through a model for quasi-static fractures known as Born Model. In particular, we consider the roughness of this fracture surface. We find for the roughness exponent a value ζ = 0.5 expected for “small length scales” in microfracturing experiments. Since this corresponds to a slow evolution for the fracture, our simulations confirm that at small length scales the fracture can be considered as quasi-static. We also show the isotropy of the roughness exponent on the crack surface. Finally, considering the crack front, we compute the roughness exponents for this line for longitudinal and transverse fluctuations (ζ‖ ∼ ζ⊥ ∼ 0.5). It results in agreement with experimental data, and supports the possible application of the model of line depinning in the case of long-range interactions.