Phase-field modeling of micropore formation in a solidifying alloy

This thesis is focused on the study of the morphology of micropores formed during solidification of metallic alloys. Micropores constrained to form in well-developed dendritic solid network adopt complex non-spherical shapes. Previous studies using X-ray tomography (XRT) have shown that the local mean curvature of micropores can be as large as 0.2μm−1. Such a high curvature induces an overpressure of 400 kPa in the pore with respect to the surrounding liquid and thus highly affects its volume fraction. While trying to predict pore formation at the macro-scale using average equations, the effect of this curvature is usually introduced using simple mathematical relationships, i.e., pinching model, describing the pore curvature as a function of the volume fraction and a typical length scale (e.g., the secondary dendrite arm spacing or DAS) of the primary phase. Such relationships, however, are based on simplifications of the pore morphology that are not generally backed up with an extensive study of the pore shape and its evolution during solidification. On the other hand, direct observations using XRT offer valuable information about micropore morphologies after solidification, but unfortunately their limited spatial resolution does not allow yet for a detailed study of the curvature of micropores during their formation. In this work, a multiphase-field model has been developed in order to study and better understand the formation of micropores constrained to grow in a solid network (i.e., pinching effect). The model accounts for the pressure difference due to capillarity forces between liquid and gas and the mechanical equilibrium condition at triple (solid-liquid-pore) lines. The partitioning and diffusion of dissolved gases such as hydrogen in aluminum alloys are also incorporated into the model by solving together Sievert’s law, the perfect gas law and Fick’s equation. The model was first implemented in 2-D, and then was extended to 3-D by developing a program for parallel Distributed Memory Processor (DMP) machines. The model was used to study the influence of the DAS, primary phase solid fraction and gas content on the morphology of micropores. After validating the multiphase-field approach for a spherical micropore growing freely in a supersaturated liquid, the calculations show that a pore constrained to grow in a narrow liquid channel exhibits a substantially higher mean curvature, a larger pressure and a smaller volume than an unconstrained pore. The morphology of pores at steady state, obtained with the model for different solid morphologies and initial gas concentrations, was also analyzed. From their predicted 3-D morphologies, entities such as the Interfacial Shape Distribution (ISD) were plotted and analyzed. As expected, it was verified that the mean curvature of the pore-liquid interface, and thus also the pressure inside the pore, is uniform. The local morphology of the pore, however, varies depending on the position of the pore-l