Direct Simulation of a Solidification Benchmark Experiment

Abstract

A solidification benchmark experiment is simulated using a three-dimensional cellular automaton-finite element solidification model. The experiment consists of a rectangular cavity containing a Sn-3 wt pct Pb alloy. The alloy is first melted and then solidified in the cavity. A dense array of thermocouples permits monitoring of temperatures in the cavity and in the heat exchangers surrounding the cavity. After solidification, the grain structure is revealed by metallography. X-ray radiography and inductively coupled plasma spectrometry are also conducted to access a distribution map of Pb, or macrosegregation map. The solidification model consists of solutions for heat, solute mass, and momentum conservations using the finite element method. It is coupled with a description of the development of grain structure using the cellular automaton method. A careful and direct comparison with experimental results is possible thanks to boundary conditions deduced from the temperature measurements, as well as a careful choice of the values of the material properties for simulation. Results show that the temperature maps and the macrosegregation map can only be approached with a three-dimensional simulation that includes the description of the grain structure.

Modeling and characterization of grain structures and defects in solidification

“…An interesting benchmark for the simulation of macrosegregation and freckling in columnar grain structures (no grain movement) has been reported in [15]. Besides comparison with carefully calibrated experiments [16,17], such benchmarks of complex codes are really necessary. Indeed, very small differences in the resolution scheme, method or mesh size can lead to slightly different results, especially for freckles.…”

“…A very good example of such a CAFE calculation combining grain growth, thermosolutal convection and macrosegregation is given in [17]. These authors have simulated the solidification of a Sn -3 wt% Pb alloy in a rectangular cavity having the dimensions of Hebditch and Hunt's experiment [29].…”

“…1. Grain structure and velocity field at two instants in a Sn-3 wt.% Pb alloy solidified in a rectangular cavity 10 Â 6 Â 1 cm 3 which has temperature-controlled external surfaces [17]. Since the beginning of 2000, one has seen the emergence of so-called ''modified CAFE'' models.…”

3D Coupled Cellular Automaton (CA)–Finite Element (FE) Modeling for Solidification Grain Structures in Gas Tungsten Arc Welding (GTAW)

“…The other advantage is the possibility to handle independent partitioning as already explained elsewhere. 9) However, communication between the two meshes then needs to be organized: following the CAFE coupling scheme, 8) the temperature field computed on the FE mesh must be projected onto the CA mesh for performing the algorithms of remelting and grain growth in later solidification on the CA grid. Oppositely, the fraction of liquid, growing and solid cells in the volume associated to the triangles defined for a given node of the CA mesh should be made available on the FE mesh to solve the heat flow problem.…”

“…It was followed by a first dynamic allocation strategy 4) capable of handling large volume casting. 6) These algorithms have been recently improved by Carozzani and co-workers [8][9][10][11] to reach predictions for even larger casting size thanks to the use of parallel computing facilities and special dynamic allocation strategies.…”