Precipitate shape transitions during coarsening under uniaxial stress

Abstract

Precipitate shape transitions of elastically misfitting inclusions in the presence of a uniaxial stress field are examined for cubic materials using simple bifurcation theory. Both size-induced shape transitions that occur during growth of the precipitate under zero or constant stress and stress-induced shape transitions resulting from changes in the external stress field at constant precipitate volume and misfit are identified. Using elastic fields valid for small differences in elastic constants between precipitate and matrix, a dimensionless stress parameter and precipitate volume are identified from a Landau-type expansion that indicate the type and nature of permissible shape transitions. These dimensionless parameters incorporate the interfacial energy density, difference in elastic constants between precipitate and matrix, precipitate misfit, precipitate volume and external stress field into simple algebraic relationships. They indicate under what combination of material parameters a shape transition might be expected and whether the transition is continuous or discontinuous. Results of the model are applied using material parameters from a nickel-based alloy.