Simulation of macroscopic solidification with an incorporated one-dimensional microsegregation model coupled to thermodynamic software

Abstract

In this article, a numerical model is presented which predicts phase distributions and dendrite arm spacings for a realistic casting within suitable CPU time. Three software components are coupled to perform calculations: (1) an FEM simulation package for the macroscopic temperature field, (2) an FDM code for the microstructure parameters, and (3) a thermodynamic software package for equilibrium calculations at the interfaces. The macrosoftware provides the micromodule with the present temperature at each node of a finite-element grid. At each such node, the micromodule calculates the dendrite arm spacings, the phase amounts, and the diffusion-controlled segregation profiles for the current time-step using equilibrium information from the thermodynamic software. A change of solid fraction and of the phase concentrations results in the release of latent heat and in the change of the heat capacity. These values are used as input parameters in the macrosoftware for the temperature calculation in the next time-step. Simulations have been performed for the ternary alloy AlCu4Mg1 and the results have been compared to "traditional" temperature calculations and to experimentally determined phase fractions and dendrite arm spacings. Measurements have been done by means of an interactive image analysis system over the entire breadth of an ingot casting at four different heights as well as at three different longitudinal cuts.

Polynomial regression and interpolation of thermodynamic data in Al–Si–Mg–Fe system

“…At each composition of Fe, the liquid fraction data is fitted using functions at different temperatures (T 0 À T i ), of which the degrees are consistent with Eq. (8). As a result, the general regression function for the liquid fractions in the L þα two-phase region can be expressed as [21] f a a w a w a w a w w a w where i is from 0 to i, and j is from 0 to j.…”

“…During recent years, the CALculation of PHAse Diagrams (CALPHAD) method has been proved to be a powerful tool in making accurate predictions of the phase equilibria transition in solidification processes. It is possible to calculate solidification processes in detail by coupling CALPHAD software with different solidification models [5][6][7][8]. However, the large physical memory it takes when performing repetitive calculations for complex phase equilibria makes it less efficient to simulate the solidification processes on multicomponent alloy systems with macroscopic models [9].…”

Methodological Progress for Computer Simulation of Solidification and Casting

“…In this stand point, many other micro segregation models were proposed. [74][75][76][77][78][79][80][81][82][83][84] A summary of major assumptions used in these micosegregation models is given in Table 2.…”

Phase-field simulation of microstructure formation in technical castings – A self-consistent homoenthalpic approach to the micro–macro problem

“…Macroscopic simulation tools for casting typically allow specifying a global relation for the enthalpy or the fraction of solid versus temperature. More advanced approaches include microstructure models into the macroscopic heat flow model which are simple enough to be solved for all nodes of the macroscopic grid, but which are able to predict latent heat formation as a function of the local thermal conditions [3,4,17]. Those models can be regarded as a real solution of the general micro-macro problem, because full coupling between the scales is achieved.…”

“…For industrial applications, in most cases, no exact information on the microstructure formation process is available, and heat flow simulation tools often use simplified latent heat descriptions based on DSC experiments or thermodynamic Scheil modeling. More elaborate microstructure models allow for an improvement of the heat flow prediction and, at the same time, they provide some microstructural information which might be of interest for material processing [1][2][3][4]. But this is only 0021-9991/$ -see front matter Ó 2009 Elsevier Inc. All rights reserved.…”