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Coupling of multicomponent thermodynamic databases to a phase ﬁeld model: application to solidiﬁcation and solid state transformations of superalloys
The phase field method has successfully been applied to predict microstructure evolution in metallic alloys such as dendritic solidification as well as the precipitation of coherent ordered phases from a disordered matrix taking into account the effect of elastic strain on the morphology of the precipitates [4, 5 and 6]. Recently, phase field methods employing multiple phase field parameters have been applied to eutectic and peritectic systems in dilute model systems as well as to evaluate the kinetics of solid state grain growth. In order to apply the method quantitatively to these phenomena occurring in technical alloys the method needs to be able to treat multicomponent multi-phase systems. Recently a simplified multicomponent approach using linearized phase diagrams has been applied to steels. The ternary system Fe-Al-Co has been addressed by who use real thermodynamic data within a phase field model. The main target of this work is to simulate solidification and heat treatment of technical single crystal superalloys.
The present paper proposes a multicomponent extension to a multi-phase-field model (PFM) described in employing a general method of obtaining thermodynamic data from databases being assessed according to the CALPHAD method. This method provides realistic thermodynamic descriptions for all phases present in a given material. The present model can be applied to any system if a thermodynamic database is available and is not restricted to a special formulation of the Gibbs energy. To evaluate thermodynamic quantities the FORTRAN interface of the software Thermo-Calc is used for the calculation of molar Gibbs energies and chemical potentials to calculate the driving force at the diffuse interface. Furthermore, a subroutine of the software Dictra, which is also interfaced to Thermo-Calc in order to calculate thermodynamic factors of diffusion, has been coupled to the phase field code. The subroutine calculates the diffusion matrix for given multicomponent phase from a standardized kinetic database containing data on atomic mobilities.
In order to validate the growth kinetics of this model 1D benchmark tests have been performed by comparison with a sharp interface calculation by Dictra using the same thermodynamic and kinetic database [A. Engström and J. Ågren. Z. Metallkunde. 87 2 (1996), p. 92]. of the ternary Ni-Al-Cr system. Moreover, a 2D simulation of Ostwald-ripening of spherical γ′ precipitates in a ternary Ni-Al-Cr alloy with a small γ-γ′ lattice mismatch is presented. The results are compared to experimental data by M. Doi, who determined the coarsening rate of the γ′ precipitates in a Ni-6.2 at.-% Al-18.2 at.-% Cr alloy.