Figure 11

(a) Advancement fluctuation \(\sigma\) along the crack fronts, as per Eq. (15), for the simulation (plain points) and an experimental data set from Santucci et al.²⁷ (see their Fig. 4). Different self-affine behaviours are observed above and below the \(\delta x^*\) cut-off, with comparable Hurst exponents \(\zeta\). The dashed lines mark the slopes fitted on the simulation data for the two cases. The experimental points are from an experiment different from those of Tallakstad et al.²⁸ to which the model was calibrated. (b) Power spectra of the simulated crack advancement, averaged over 10,000 consecutive fronts. It is shown both before (raw) and after (binned) binning the fronts to the experimental camera pixel size. The difference between these two plots shows an influence of the observation scale on the small-scale study of the crack morphology. The plain line is the approximation⁸ from Eq. (18), which is valid between \(l_c\) and \(R_c\), where the morphology is dominated by the material quenched disorder. Note that the scaling regime for scales above \(l_c\) was already studied by Cochard et al.⁸, while the model match to the experiment below this cut-off scale, shown in (a), is a new result, as already discussed in the “Local velocity distribution and fracture energy standard deviation” section.