Fracture Roughness Scaling: a case study on planar cracks

Using a multi-resolution technique, we analyze large in-plane fracture fronts moving slowly between two sintered Plexiglas plates. We find that the roughness of the front exhibits two distinct regimes separated by a crossover length scale ${\delta }^{\ast }$. Below ${\delta }^{\ast }$, we observe a multi-affine regime and the measured roughness exponent ${\zeta }_{\parallel }^{-}=0.60\pm 0.05$ is in agreement with the coalescence model. Above ${\delta }^{\ast }$, the fronts are mono-affine, characterized by a roughness exponent $\zeta_{\parallel}^{+} = 0.35\pm0.05$, consistent with the fluctuating line model. We relate the crossover length scale to fluctuations in fracture toughness and the stress intensity factor.