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Publication# Liquid metal infiltration of silicon based alloys into porous carbonaceous materials. Part II: Experimental verification of modelling approaches by infiltration of Si-Zr alloy into idealized microchannels

Giovanni Bianchi, Caroline Hain, Manoj Kondibhau Naikade, Alberto Ortona, Ludger Weber

*ELSEVIER SCI LTD, *2022

Article

Article

Résumé

In this work, the mechanisms leading to the pore closure in reactive melt infiltration (RMI) of carbon by pure silicon and a near eutectic Si-8 at-pct Zr alloy at 1500 and 1700 degrees C under vacuum were studied. Various geometrical configurations of microchannels were fabricated via laser ablation of glassy carbon plates. The micron size capillary channels allowed simplifying the complicated porosity distribution in the infiltration of powder or fibres based porous preform while keeping the physical dimensions in the range of where the physical phenomenon of pore closure takes place. The extent of infiltration was analysed by means of X-ray radiography. For RMI of pure Si, the widely accepted decrease in capillary radius by the formation of a solid state SiC layer by the reaction of liquid Si and C was observed, but did not lead to closure and it is hence not the infiltration limiting step in channels as small as 10 mu m. However, in the case of the Si-Zr alloy infiltration, another mechanism of pore closure was observed, namely the precipitation of zirconium silicides at the infiltration front, due to Zr enrichment in the alloy by the continuous consumption of Si for the formation of SiC.

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Porosity is one of the major defects in castings because it reduces the mechanical properties of a cast piece [1]. Porosity formation results from the effect of two concomitant mechanisms, namely solidification shrinkage and segregation/precipitation of gases [1]. A model for the prediction of microporosity, macroporosity and pipe shrinkage during the solidification of alloys has been developed at the Computational Materials Laboratory (LSMX-EPFL) [2]. This model has then been improved by taking into account the effect of various alloying elements and gases on porosity formation [3, 4, 5]. However, the modeling of two physical phenomena still needed to be improved: (i) the curvature influence and (ii) the hydrogen diffusion influence on the growth of pores. The effect of pinching, i.e. the pores are forced by the growing solid network to adopt a complex non spherical shape, induces curvature restriction to the pores. This pinching effect can be a limiting factor for the growth of pores and is too simply modeled in the model of Péquet et al. [2]. Several other pinching models exist, but a rigorous experimental study to validate either one of these models is needed. Additionally, Carlson et al. [6] have recently shown that hydrogen diffusion might also be a limiting factor for the growth of pores. In the model of Péquet et al. [2], this effect was not taken into account. This thesis is mainly aimed to (i) provide experimental results that specifically validate the pinching model developed by Couturier et al. [4], (ii) investigate the influence of hydrogen diffusion on the growth of pores and (iii) provide a new model that takes into account the pinching effect and the hydrogen diffusion influence on the growth of pores. At first, pores formed in aluminum-copper (Al-Cu) samples (cast under controlled conditions) have been analyzed using high resolution X-ray tomography. The influence of the alloy inoculant, copper content, cooling rate and initial hydrogen content on the morphology of pores has been investigated. The results show that the curvature of micropores pinched in either non-inoculated or inoculated Al-4.5wt%Cu alloys can be fairly well approximated to that of cylinders. The results also show that the pinching model must be function of (i) the volume fraction of the primary phase gα and (ii) the secondary dendrite arm spacing λ2. However, the influence of the initial hydrogen content appears to be negligible. The pinching model developed by Couturier et al. [4] accounts for these observations and their relation fits fairly well the average mean curvature value of our experimental data. A new model has been developed to calculate an effective hydrogen diffusion coefficient De(gs), that is a function of the volume fraction of solid only. For that purpose, in-situ X-ray tomography has been performed on Al-Cu alloys. For each volume fraction of solid 0.6 ≤ gs ≤ 0.9, a representative volume element of the microstructure has been obtained from the tomography data. Solid and liquid voxels being assimilated to solid and liquid nodes respectively, a hydrogen diffusion equation has then been solved numerically. Calculations have been run until steady-state was reached in order to deduce De(gs) and the simulation results were successfully compared with a new theory based on effective-medium approximations. Both approaches lead to the main conclusion that hydrogen diffusion through the solid phase cannot be neglected, unlike it is assumed in the model of Carlson et al. [6]. Next, using the pinching model of Couturier et al. [4] and the obtained De(gs), a new volume-averaged model has been developed in order to simulate the growth of pores limited by (i) the curvature of the pore phase and (ii) the diffusion of hydrogen. The results show that, although hydrogen diffusion can be a limiting factor for the growth of pores, the pinching effect has a much larger influence. Accordingly, any model for porosity prediction should carefully take into account the influence of curvature and hydrogen diffusion on the growth of pores. In order to ripen this study at a refined scale, a 2D phase-field model has been developed to describe the complex shape of a pore formed within interdendritic liquid channels [7]. The influence of the solid, which can force the pore to adopt a non-spherical shape, is taken into account through the geometry of the domain and appropriate boundary conditions. This model accounts for curvature influence and hydrogen diffusion in the liquid, two of the main aspects governing the growth kinetics of a pore. However, the model still needs to be combined with a description of the liquid flow induced by the pore growth. Basically, this model should serve as a sound basis for further developments that might lead to more sophisticated pinching models. Finally, an experimental study has been conducted in order to track the inoculant influence on the shape of pipe shrinkage. Simultaneously, pipe shrinkage calculations (using the model of Péquet et al. [2]) were performed in order to track the influence of the gs,c parameter on the shape of the pipe shrinkage. This gs,c parameter corresponds to the critical volume fraction of solid at which mass feeding stops. Comparisons between experimental and simulation results show that the gs,c parameter should be set equal to 0.6 or 0.1 for a casting simulation of an inoculated or non-inoculated alloy, respectively.

Concepts associés (17)

thumb|Du bronze liquide versé dans des moules.
En métallurgie, un alliage est un mélange de plusieurs éléments chimiques, dont le principal constituant est un métal, et dont les caractéristiques sont

Le carbone est l'élément chimique de et de Il possède trois isotopes naturels :

- C et C qui sont stables ;
- C qui est radioactif de demi-vie ce qui permet de dater des éléments utilisant du car

An aluminium alloy (or aluminum alloy; see spelling differences) is an alloy in which aluminium (Al) is the predominant metal. The typical alloying elements are copper, magnesium, manganese, silicon

Hot tearing is one of the most severe defects observed in castings, e.g. in billets or sheet ingots of aluminum alloys produced by DC casting. It is due to both tensile strains and a lack of interdendritic feeding in the mushy zone. In order to predict this phenomenon at the scale of an entire casting, the two-phase averaged conservation equations for mass and momentum must be solved in the mushy (i.e. mixed solid and liquid) region of the material. In recent contributions, M'Hamdi et al [1] proposed a strongly coupled resolution scheme for this set of equations. The solution of the problem was obtained using a rheological model established by Ludwig et al [2] and that captures the partially cohesive nature of the mushy alloy. In the present contribution, the problem is addressed using a slightly different approach. The same rheological model (i.e. saturated porous media treatment) is used, but the influence of the liquid pressure is neglected at this stage. This assumption allows for a weakly coupled resolution scheme in which the mechanical problem is first solved alone using ABAQUS™ and user subroutines. Then the pressure in the liquid phase is calculated separately accounting for the viscoplastic deformation of the porous solid skeleton and solidification shrinkage. This is done with a code previously developed for porosity calculations, and that uses a refined mesh in the mushy zone [3]. This semi-coupled method was implemented and its numerical convergence studied from the point of view of both time step and mesh size. Guidelines for selecting these numerical parameters as well as the conditions under which the semi-coupled method may be applied are provided. The model was then applied to three cases, i.e. two tensile tests conducted on mushy alloys [4, 5] and the casting of an entire billet [6]. Experimental data was indeed available concerning these problems prior to the present work. This information was used for the validation of the thermal and mechanical models that were setup to describe these different cases. The results of the semi-coupled approach were also used to describe in more details these different castings. First of all, the numerical study of the mushy zone tearing test [5] proved helpful for distinguishing different fracture modes. The role of the high strain rate applied to the mushy alloy in this case was also outlined. Another tensile test, referred to as the rig test [4], was successfully modeled in the present framework. The numerical results could be used to quantify the redistribution of strain in the mushy sample. As a consequence, intrinsic properties of the material, such as its ductility, could be extracted from the results. This study also gave further insight about the conditions under which tearing occurs in the samples. Finally, the semi-coupled method was used to study the DC casting process. In this case, a real process performed under realistic conditions for the production of an industrial scale billet was modeled. As it is more complex and difficult to characterize experimentally, the conditions for hot tearing formation are less accessible. However, the isotherm velocity, the strain, the strain rate and the liquid pressure could be described reasonably accurately. It was thus possible to correlate experimental observations of the hot tear with various calculated indicators of hot tearing susceptibility. Even with this information, it remains difficult to formulate new hot tearing criteria because all the indicators follow a similar trend during the casting and their respective contributions can thus not be distinguished. The present work showed that the level of accuracy and detail that can be reached using two-phase models with appropriate materials properties and boundary conditions is satisfactory. It is indeed possible to model the relevant phenomena (heat flow, solid deformation and liquid feeding) at the scale of an entire casting. The variation of the different simulated fields can be described down to a scale of the order of a few millimeters. In that sense, this approach is one important aspect required to build a multiscale model for the problem of hot tearing. It is expected that coupling such a method with granular models (which cover length scales from a few microns to a few centimeters [7]) will allow for a more complete description of the phenomena at hand. In the future, the development of such a multiscale numerical tool may prove to be the most efficient way towards quantitative predictions of hot tearing formation in real solidification processes.

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-liquid interface with respect to the primary solid: In between two parallel dendrite arms, the pore adopts a cylindrical-type shape with one principal curvature being almost nil and the other being about twice the mean curvature of the pore-liquid interface growing with a spherical-type tip in between four parallel dendrite arms. The results were then compared with analytical pinching models. While predicting a similar trend, analytical models tend to underestimate the pore curvature at high solid fraction and gas concentration. For pores spanning over distances larger than the average DAS, the simulations showed that the mean curvature varies between two limits: a minimum curvature given by the largest sphere that can be fitted in the interdendritic liquid, and a maximum curvature given by the size of the narrowest section that the pore needs to pass in order to expand. The pore curvature is therefore a complex non-monotonic function of the DAS, solid fraction, gas content and statistical variations of the liquid channel widths. Based on this and considering the complex morphology of pores reconstructed using high-resolution XRT, the present phase-field results suggest that a simple pinching model based on a spherical tip growing in between remaining liquid channels is a fairly good approximation. This model was further validated by performing phase-field calculations for a pore growing in a representative volume element taken from XRT. For such condition, it was observed that as the pore grows and penetrates thin liquid channels, the fraction of cylindrical-type pore-liquid interfaces increases and becomes dominant over spherical-type ones, a feature already observed in XRT observations of as-solidified micropores. Finally, in-situ XRT observations were also performed on Al-Cu samples directionally viii solidified in a Bridgman furnace and then quenched. Macroscopic calculations of porosity formation using the software ProCast showed that a high fraction of pores can form during the quench itself, and not so much during directional solidification. After solidification, small specimens were analyzed by XRT on the TomCat beamline of the Paul Scherrer Institute in Villigen, during isothermal holding at a temperature slightly above the eutectic temperature. It was shown that the volume fraction of primary solid increases during holding time, as a result of solid state diffusion of copper, while coalescence of secondary dendrite arms simultaneously modifies the topology of the remaining liquid from continuous films to isolated droplets. This topology change is shown to modify substantially the average hydrogen diffusion coefficient in the mushy zone. In parallel to the evolution of the solid-liquid interface, the number of micropores and their volume fraction change over time. This evolution is analyzed in terms of a local mass balance of hydrogen and of diffusion of hydrogen toward the ambient atmosphere.