Analytic model of the remobilization of pinned glide dislocations from quasi-static to high strain rates

• A kinetic equation describing mobile-immobile dislocation interactions is derived.
• Relates plastic strain rate to applied stress, dislocation densities, and temperature.
• Kinetic equation applies to high strain rate, pressure, and temperature regimes.
• Kinetic equation does not rely on standard activation theory.
• Mean-first-passage-time theory specific to dislocation intersections is developed.

In this paper, we construct an analytic model describing mobile-immobile dislocation intersections using a mean-first-passage-time (MFPT) framework. By applying MFPT theory to dislocation intersection, the deformation mechanics at high strain rates is more reliably described than in traditional models based on Van't Hoff-Arrhenius thermal activation. The plastic strain rate is expressed as a function of the applied stress, mobile and immobile dislocation densities, material density, and temperature. This kinetic equation is applicable at strain rates from quasi-static to rates in excess of 1012 s−1, pressures from ambient to about 1000 GPa, and temperatures ranging from zero to the melt temperature.