Phase field model for multiphase alloys under arbitrary thermal history: An application to IN718 super-alloy

•Phase field framework to simulate precipitate evolution for alloys during arbitrary thermal history.•Nucleation model parametrized such that calculated and experimental TTT diagrams are quantitatively consistent.•For demonstration we employ super-alloy IN718, and predict precipitate evolution of super-alloy IN718 during fast thermal cycling resembling additive manufacturing process.•Faster thermal cycling promotes the formation of γ′′ and suppresses the formation of γ′ and δ.