Université de Lorraine

PhD thesis: Motion and packing of dendrites during solidification – modeling and scale bridging

Nancy, France

2024-05-31 (Europe/Paris)

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Background

Metallic materials are composed of crystal microstructures and their mechanical properties depend on the size, morphology, and chemical composition of these microstructures. In manufacturing of virtually all metal products, solidification processes, such as casting, welding, or additive manufacturing, are a decisive step for the formation of the microstructure. Understanding the link between process parameters and the microstructure of the product is particularly important for the improvement of properties of high- performance components with high added value, e.g., the impact toughness of steel nuclear reactor pressure vessels or the fatigue strength of turbine blades in an aircraft engine.

During the solidification of a metal alloy, the solid crystal structure often forms in the shape of dendritic grains. The dendrites, a few millimeters in size, first grow freely in the liquid and can move during their growth. They are carried by the flow and are spread across the whole solidifying piece, which can be several meters in size. They sediment, pack, and continue to grow until complete solidification. The structure of the solidified piece depends strongly on these transport phenomena.

Our work on the dynamics of motion of dendritic grains has shown that the transition between the zone of free-floating grains and the packed layer of stationary grains occurs across a narrow zone, with the thickness of about 5 times the grain size. In this packing zone, the distance between the grains decreases rater abruptly and the coupling between the flow of the liquid, the motion of the grains and their growth leads to high variations of chemical composition and temperature. Today, a theory to describe the packing zone does not exist. The phenomena in this zone are one of the key factors for the formation of the nonuniform structure and chemical composition in castings.

Objectives and Methods

The objective of the PhD thesis is to answer the following questions:

What are the principal phenomena that control the formation of the structure in the grain packing zone?
How can we describe the packing zone at a macroscopic scale of the solidifying part in order to incorporate the description into a model for the simulation of the industrial process?

Experimental characterization of the phenomena in the packing zone is extremely difficult. However, recently developed mesoscopic models of solidification can provide detailed quantitative information on the evolution of the shape and size of the grains, concentration and thermal fields, etc. They can simulate ensembles of up to a hundred grains; it is therefore possible to carry out numerical experiments and characterize all these aspects.

The Grain Envelope Model (GEM) will be employed to investigate the growth and motion of the grains, as well as the relevant couplings in the packing zone. The GEM describes the growth of individual grains, coupled with a CFD finite-volume modeling of flow, diffusion and heat transfer and with a DEM (Discrete Element Method) model of contact between grains. The code is developed on the OpenFOAM platform. The project will consist of the following steps:

An extension of the GEM will be developed to incorporate the phenomena in the packing zone into the model.
Simulations of solidification in the packing zone will be performed for prototype configurations, relevant for the conditions encountered in metallurgical processes.
The simulations will be upscaled to formulate constitutive laws that describe the solidification in the packing zone in macroscopic process models.