Approximate initial critical projectile-to-target mass ratio (Y_c) for the models considered in Sects. 4.2 and 4.3. Blue and orange lines are for low-excitation (e_max = 0.01) and high-excitation discs (e_max = 0.2). respectively, and the different line styles are for different $Q_{\text{D}}^{*}$ models shown in Table 1; see plot legend. Here for the average impact velocity we adopt υ_imp = υ_Ke_max/2, evaluated at the centre of the belt, at 40 au. The nearly power-law size-dependence is due to only considering sizes up to 100 m, which are all in the strength regime of material strength. Where the mass ratio shown is higher than unity, the exact value of it is unphysical, as the assumptions behind the simple formula break down, as discussed in Sect. 2. Nevertheless, this figure shows for which parameters we expect the disc evolution to be dominated by fragmentation, as opposed to bouncing or cratering.