Phase-Field Modeling of the Coarsening in Multi-component Systems
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THE prediction of the secondary dendrite arm spacing (SDAS) in alloy systems is very important because it influences the mechanical properties and the homogenization heat treatment of the products. The knowledge of this quantity can also be used to investigate the influence of the diffusion effects on the solidification process at various process parameters, e.g., solidification rates and fluid flow conditions. The microstructure prediction and particularly the definition of the SDAS is a very difficult task which requires computationally intensive modeling methods such as phase-field models[1] and cellular automata (CA),[2–6] dendrite lattice models,[7] or averaged concentration methods.[8] The solidification at various cooling rates proceeds often far from the equilibrium and the obtained microstructure is generally not homogeneous and has variations in the composition known as segregation. CA models can simulate the macro- and meso-scale grain structures, but they have difficulties in resolving the microstructure. In contrary, the phase-field method is able to reproduce the microstructure of the dendritic grains on a very small scale. JULIA KUNDIN, Academische Rat and HEIKE EMMERICH, Professor, are with the Material and Process Simulation (MPS), University Bayreuth, 95448 Bayreuth, Germany. Contact e-mail: [email protected] JOAO LUIZ LOPES REZENDE, Post Doctorate, Department of Ferrous Metallurgy IEHK, RWTH Aachen, Aachen, Germany. Manuscript submitted January 25, 2013. Article published online September 25, 2013 1068—VOLUME 45A, FEBRUARY 2014
In the last 10 years the phase-field modeling has undergone a number of significant improvements and became a very popular technique for the investigation of the microstructure formation during solidification.[9–12,21] Phase-field models have been applied to the simulation of equiaxed growth by solving both the solute and heat diffusion equations as well as to directional solidification. This method has been used extensively to predict dendritic, eutectic, and peritectic structures in alloys. Further phase-field models were extended to multicomponent and multi-phase systems.[13–18] A phase-field model proposed by Kim et al.[14] for binary alloys was applied by Suzuki et al.[1] for binary iron and aluminium alloys to investigate in principle the qualitative possibility of the simulation of the growth and the selection of the SDAS. The effect of the dendritic morphology on the mechanical strength of low carbon steels has been investigated for the first time by Seol et al.[19] by a prediction of the dendritic morphology as well as by the estimation of the SDAS by the phase-field approach for binary alloys.[14] An increasingly complication of the multi-component models in recent years requires a rethinking of their applicability and effectivity to predict the microstructure parameters. The theoretical prediction by means of thermodynamic and kinetic analyses is an alternative technique for the investigation of the microstructure. Analytical expressions of the SDAS for binary alloys wer
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