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Article Dans Une Revue Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences Année : 1995

Process Modelling and Microstructure


Among the many routes which are used for the processing of high-temperature materials, solidification plays a key role. Several modelling tools are now available for the simulation of the interconnected macroscopic phenomena associated with any casting process (heat exchange, mould filling, convection, stress development, etc.). Based upon finite-difference (FD) or finite-element (FE) techniques, these models solve the continuity equations of mass, energy, momentum, solute species, averaged over the liquid and solid phases. As such, macroscopic models do not account for the detailed phenomena occurring at the scale of the microstructure. For that reason, a stochastic cellular automaton (CA) model has been developed recently for the prediction of the grain structure formation in solidification processes, in particular during the investment casting of superalloys. Such a microscopic model considers the heterogeneous nucleation of grains at the surface of the mould and in the bulk of the liquid, the growth kinetics and preferential growth directions of the dendrites and the microsegregation. The microscopic CA model has been coupled to FE heat flow computations in order to predict the grain structure at the scale of a casting. It is shown that microstructural features and crystallographic textures can be simulated as a function of the casting conditions and alloy composition.

Dates et versions

hal-01564443 , version 1 (18-07-2017)



Michel Rappaz, Charles-André Gandin. Process Modelling and Microstructure. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1995, 351 (1697), pp.563 - 577. ⟨10.1098/rsta.1995.0053⟩. ⟨hal-01564443⟩


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