Dislocation precipitate bypass through elastically mismatched precipitates

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The Orowan bypass mechanism for elastically homogeneous precipitates has been thoroughly studied. In engineering materials, alternate phased precipitates exhibit elastic moduli differing from the host matrix. To further our understanding of realistic dislocation precipitate interactions, we employ a three dimensional coupled discrete dislocation dynamics and finite element computational scheme to compute the Orowan bypass stress (τ Orowan) required for a dislocation to bypass a row of elastically stiff precipitates. Specifically, we examine the influence of elastic mismatch between precipitates and the host matrix on τ Orowan. Unique to our computational study, our simulations span a range of precipitate diameters (D), inner precipitate spacings (L), and an order of magnitude in precipitate-matrix elastic mismatch ratio. We partition observed increases in τ Orowan into dislocation image stress interactions and additional stress concentrations due to the interaction of the applied stress with the elastically stiff precipitates. Finally, we incorporate the dependence of τ Orowan on precipitate-matrix elastic mismatch into our derived model for τ Orowan by introducing an effective D which depends explicitly on the elastic mismatch. Both our simulations and analyses suggest that strengthening due to relative increases in precipitate stiffness is modest compared to strengthening with precipitate width.