High strain-rate crack growth in rate-dependent plastic solids

At high crack velocities in metallic materials nearly all plastic strain accumulates at very high strain-rates, typically in the range 10³ s^?1 to 10⁵ s^?1. At these rates, dislocation motion is limited by dynamic lattice effects and the plastic strain-rate increases approximately linearly with stress. The problem for a crack growing at high velocity is posed for steady-state, small scale yielding in elastic/rate-dependent plastic solids. A general expression is derived for the near-tip stress intensity factor in terms of the remote intensity factor, or equivalently for the near-tip energy release-rate in terms of the overall release-rate. An approximate calculation of the plastic strain-rates provides this relation in analytical form. Imposition of the condition that the near-tip energy release-rate be maintained at a critical value provides a propagation equation for the growing crack. A single, nondimensional combination of material constants emerges as the controlling parameter. Implications for dynamic crack propagation are discussed.