Low self-affine exponents of fractured glass ceramics surfaces

The morphology of fracture surfaces encodes the various complex damage and fracture processes occurring at the microstructure scale during crack propagation. It is now well established that fracture surfaces are self-affine characterized by a roughness exponent usually found close to $\zeta \quad \approx $ 0.75 for a wide range of materials. Recently, fracture surfaces of sandstone were found to be also self-affine but with a lower roughness exponent $\zeta \quad \approx $ 0.4-0.5. To investigate its origin, we studied fracture surfaces of glassy ceramics which are obtained by sintering glass beads. Such a material mimics the structure of sandstone with the advantage that their porosity may be tuned. They are also found to be self-affine, characterized by a roughness exponent $\zeta \quad \approx $ 0.40 $\pm $ 0.04 significantly lower than the ``universal'' roughness exponent $\zeta \quad \approx $ 0.75 widely reported in the literature. Its value is found to depend very slightly on the crack growth velocity and the microstructure (grain diameter, porosity) in the range studied. This suggests the existence of a second universality class in failure problems. Its physical origin is then discussed and a model proposed.