The effect of dislocation self-interaction on the orowan stress

Abstract

The effect of dislocation self-interaction on the Orowan stress was determined for collinear, impenetrable circular obstacles. The line tension approximation was dropped and an appropriate integro-differential equation governing static equilibrium was solved by an algorithm based on curvature adjustments. When the interactions are taken into account, the Orowan stress varies as In where is the harmonic mean of the obstacle size and spacing. In addition, the configuration of a bowing dislocation at the Orowan stress is strongly influenced by the interactions: as the interactions increase in strength, i.e. as the ratio of obstacle size to spacing decreases, the bow-out and area swept are suppressed. The essential features of the interaction can be incorporated into a line tension framework by treating the impenetrable obstacles as if they were penetrable. Based on this line tension analogue, an approximate form for the flow stress of a random distribution of impenetrable obstacles was developed.