Phase field modeling of precipitation in Zr-1%Nb-1%Sn alloy: a study of statistical properties and mechanical response

We develop the phase field model to simulate precipitation of secondary phase in ternary alloys with extra-small content of doping. This approach is applied to study beta-phase precipitation in the model system of commercial alloy Zr-Nb-Sn at thermal treatment. An analysis of local rearrangement of doping and equilibrium vacancies during precipitation has shown that the dissolved Tin is mostly segregated around phase interface by trapping vacancies. Kinetics of precipitation, size and distribution of the precipitates, concentration of the species in precipitates and matrix are studied where it is revealed that Lifshits-Slyozov-Wagner distribution can be used to predicate statistical properties of precipitates. Mechanical response including the plastic deformations in precipitated solid is discussed. It is shown that yield strength change increases during precipitation. Yield and ultimate stresses are studied at different shear rates for the annealed alloy. A transition to plastic flow is described by means of dislocation structure evolution. Formation and growth of slip planes and dislocation loop-precipitate interaction governed by elastic moduli difference is analyzed. It is shown that emergence of dislocation loops around precipitates follows the Orowan mechanism.