Fig. 3. Minimal lengths exist for supershear crack propagation under uniform loading.

(A) Crack simulations for nonuniform τ₀/τ_p profiles (see Fig. 2A, top), where the size of the weak patch is varied. Dashed and solid curves indicate propagation within the weak and strong regions, respectively. τ₀/τ_p values in the figure correspond to the strong region (in the weak region, τ₀/τ_p = 0.8). Supershear propagation in the strong region cannot be sustained for l < l_m (l_m is indicated by stars), where the supershear–to–sub-Rayleigh transition occurs. (B) l_m obtained numerically (green line) from Eq. 1 shows that no minimal length exists for τ₀/τ_p ≳ 0.45 (for fixed C_S/C_L). Normalization by l₀ and τ_p is applied for convenient comparison to (A). Stars correspond to the values denoted in (A). The dashed line is the analytic approximation based on Eq. 2.