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The modeling of Ostwald-Ripening during non-isothermal heat treatments resulting in temperature dependent matrix solubility of the precipitate forming elements: A furhter development of the LSW-theory
In order to improve the mechanical properties of cast single crystal nickel-base superalloy turbine blades, heat treatments are performed after Bridgman casting. The excellent high temperature strength of these alloys is almost entirely due to precipitation of the ordered coherent gamma prime (γ′) precipitates in the gamma (γ) matrix. The precipitate size distribution (PSD) of the polydispersed γ′ changes at elevated temperatures by Ostwald ripening during the post-cast heat treatment, which is used to remove the interdendritic cast segregation and to control the γ′ PSD evolution. The aim of this work is to develop a method to predict the γ′ PSD evolution in a real turbine blade geometry under industrial vacuum heat treatment conditions. Competitive isothermal growth (Ostwald-ripening) of precipitates is described by the classical LSW-theory (Lifshitz, Slyozov, Wagner 1961), which has been extended for non-isothermal conditions. The changing matrix solubility has been taken into account by adding a source term to the growth rate and assuming that no new precipitates are formed and instantaneous precipitation. The continuity equation is solved using a finite difference method, thus allowing the simulation of the transient PSD.