Velocity Behavior of a Growing Crack

Abstract

An expression for the velocity behavior of a growing crack in a plate of brittle material is obtained by a mathematical refinement of the Mott energy balance around a moving crack. Crack velocity ċ is given by $${\mathrm{ċ=V}}_T{\text{(1−c}}_0\mathrm{/c)}$$ , where V_T is terminal crack velocity, c is instantaneous half‐crack length, and c₀ is initial half‐crack length. This predicts that velocity makes a hyperbolic asymtotic approach to terminal velocity. Growing cracks in large sheets of polymethyl methacrylate approach terminal velocity over three‐quarters of their length as predicted by this theory but as though from an initial crack larger than the actual initiating crack. This is interpreted as due to energy losses at the very beginning of crack growth not included in the Mott energy balance.