Crossover of the weighted mean fragment mass scaling in 2D brittle fragmentation

We performed vertical and horizontal sandwich 2D brittle fragmentation experiments. The weighted mean fragment mass was scaled using the multiplicity $\mu$. The scaling exponent crossed over at $\log \mu_c \simeq -1.4$. In the small $\mu (\ll\mu_c)$ regime, the binomial multiplicative (BM) model was suitable and the fragment mass distribution obeyed log-normal form. However, in the large $\mu (\gg\mu_c)$ regime, in which a clear power-law cumulative fragment mass distribution was observed, it was impossible to describe the scaling exponent using the BM model. We also found that the scaling exponent of the cumulative fragment mass distribution depended on the manner of impact (loading conditions): it was 0.5 in the vertical sandwich experiment, and approximately 1.0 in the horizontal sandwich experiment.