The Crack Speed Limit: Terminal Crack Velocity as a Fixed Fraction of the Rayleigh Wave Speed

A mode-I crack in a homogeneous brittle solid cannot outrun its energy supply: the dynamic energy release rate falls toward zero as crack speed approaches the Rayleigh wave speed cR, making cR a hard ceiling. Rayleigh speeds are computed from standard elastic constants for glass, PMMA, steel, aluminium, ice, silicon and granite (exact Rayleigh solution and standard approximation agree within 0.25%). Measured speeds: glass 1500 m/s = 0.48 cR (inside the 0.38-0.60 band); PMMA 550 m/s = 0.61 cR and steel about 1000 m/s = 0.34 cR straddle the band; fast freshwater ice 1100 m/s = 0.61 cR, with a documented double-cantilever outlier at about 20 m/s. Any claim of a homogeneous mode-I crack faster than its material's Rayleigh speed is excluded by energy supply. AI use is disclosed: drafting and computation assistance was provided by Dave, an AI system built and operated under the author's direction. The author, William Alexander Aldred, directed the work and is sole author of record.