Stochastic modelling of microstructure formation in solidification processes

Abstract

To relax many of the assumptions used in continuum approaches, a general stochastic model has been developed. The stochastic model can be used not only for an accurate description of the fraction of solid evolution, and therefore accurate cooling curves, but also for simulation of microstructure formation in castings. The advantage of using the stochastic approach is to give a time- and space-dependent description of solidification processes. Time- and space-dependent processes can also be described by partial differential equations. Unlike a differential formulation which, in most cases, has to be transformed into a difference equation and solved numerically, the stochastic approach is essentially a direct numerical algorithm. The stochastic model is comprehensive, since the competition between various phases is considered. Furthermore, grain impingement is directly included through the structure of the model. In the present research, all grain morphologies are simulated with this procedure. The relevance of the stochastic approach is that the simulated microstructures can be directly compared with microstructures obtained from experiments. The computer becomes a `dynamic metallographic microscope'. A comparison between deterministic and stochastic approaches has been performed. An important objective of this research was to answer the following general questions: (1) `Would fully deterministic approaches continue to be useful in solidification modelling?' and (2) `Would stochastic algorithms be capable of entirely replacing purely deterministic models?'

Compactness Degree of Longitudinal Section of Outer Columnar Grain Zone in Continuous Casting Billet Using Cellular Automaton-Finite Element Method

“…6) Cellular Automaton method is one of the stochastic models. Rappaz and Gandin, 7,8) Nastac and Stefanescu 9,10) are the earliest researchers engaged in the this field. 6) Moreover, Rappaz and Gandin simulated the solidification structure and CET (columnar grain to equiaxed grain transition) of metals using the CAFE method (cellular automaton-finite element method) for the first time.…”

Cellular Automaton Simulation For Volume Changes Of Solidifying Nodular Cast Iron

“…In the CA microstructure modeling the outer grain shape is the result of the simulation and is not presupposed beforehand. The model development for a one-phase microstructure evolution is a subject of the numerous researches [18][19][20][21][22][23][24][25]. Model of the eutectic solidification of DI in the uniform temperature field and superimposed cooling rate is known [26].…”

Simulation of 3D-Microstructure in Free-cutting Steel 9SMn28 under Water Cooling Condition with Convection and Porosity

“…This model first calculates heat transfer equation of castings during solidification processes using FE model, and then sets up regulation of nucleation and growth of cells through mechanism of the formation of microstructure, the calculated results of FE model are coupled to CA model to simulate microstructure. In 1990s, Rappaz and Gandin, 8,9) Nastac and Stefanescu, 10) and Zhu 11,12) successively simulated the metal microstructure during solidification processes by this model.…”