Context:
The figure below gives an illustration of (left) the solid structures and (right) the chemical segregations formed during casting of a metallic alloy. A zone with an elongated structure, called columnar, is located at the periphery of the ingot. A zone with more isotropic dendritic structures, called equiaxed, is located at the centre of the ingot. To each zone are associated a fraction of the dendritic phase and a fraction of the interdendritic phases. The composition of the alloying elements varies at the centre of the ingot, from 0.16 wt% C in the lower part to 0.7 wt% C in the upper part, for a nominal composition of 0.22 wt% C approximately retrieved in the columnar zone.
Solidification is the scientific domain of physical metallurgy that studies the formation of these structural and chemical heterogeneities. It heavily relies on numerical modelling of the exchanges of mass, energy and momentum. A consortium of French industries using solidification processes has formed to study these phenomena. The objective is to better understand and control the structural and chemical variations through the development of numerical tools.
The Center for Materials Forming (www.cemef.mines-paristech.fr) and the company TRANSVALOR (www.transvalor.com) develop and commercialize the software THERCAST used by the consortium of industries. As detailed below, the Ph. D. thesis aims to improve the metallurgical module of the software THERCAST.
Objective:
The work will consist of modelling nucleation and growth of columnar and equiaxed grains, their competition, and their interaction with the movement of the liquid phase that leads to macrosegregations. The difficulty lies in the need to add the presence of a moving solid phase to the usual formalism of the partial differential equations, thus taking into account not only the convective transport of the liquid and solid phases but also the sedimentation of the equiaxed structure. The numerical solution of the problem requires the coexistence of a solid mechanics formulation to describe the themomechanical deformation of the columnar structure with a fluid mechanics formulation for the transport of the equiaxed structure.
The modelling work will be lead by the thesis directors and will benefit a co-direction by the Ecole des Mines de Nancy, already experienced in this field. More precisely, the developments of the metallurgical module will be conducted in the software library CimLib that already includes finite element solvers, advanced remeshing techniques and parallel calculations. TRANSVALOR will be in charge of the implementation of the metallurgical module in the commercial version of THERCAST.
