Analytic model for the Orowan dislocation-precipitate bypass mechanism

Abstract

The interaction between glissile dislocations and precipitates within a continuum is responsible for marked increases in material strength. Due to their desirable engineering features, dislocation-precipitate interactions have been the subject of study for decades. Towards enhancing our mechanistic understanding of the Orowan dislocation-precipitate bypass process, we present an analytic model of the Orowan bypass stress (τOrowan) required for a dislocation to bypass a planar array of precipitates. We initially consider spherical precipitates described by a diameter (D) and inner precipitate spacing (L). Our model suggests a τOrowan scaling logarithmically with the precipitate diameter, τOrowan∼lnDe−D/L, which we validate against a well established, yet empirical model. We also examine the influence of precipitate aspect ratio on τOrowan. We find that the precipitate width along the dislocation line is the dominant length scale governing τOrowan. Finally, we demonstrate the application of our model towards predicting the scaling of τOrowan for an array of plate-shaped θ″ precipitates within an Al-Cu molecular statics materials system. Our analyses provide insight into relationships between precipitate size, shape, density, orientation and metallic strengthening mechanisms.