An Orowan precipitate strengthening equation for mechanical twinning in Mg

This study develops an Orowan precipitate hardening equation applicable to twin propagation. It is derived from a series of two dimensional dislocation dynamics simulations of a twin tip impinging upon a line of obstacles. When the number of twinning dislocations present is low, the Orowan stress increases with the number of twinning dislocations in the twin. When the number of twinning dislocations is high, the trailing dislocations do not partake in the critical initial bypass event, instead, they multiply the stress on those leading dislocations that do. The result is that bypass takes place at lower stresses when more twinning dislocations are present. A double super dislocation model provides a good description of the phenomenon. It is seen that particle size exerts a stronger role than in the conventional Orowan hardening equation and that there exists a number of twinning dislocations for which the Orowan stress is greatest. For alloy design using non-shearable precipitates, the basic objective of decreasing the inter-particle spacing on the twin plane remains most efficacious.