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Publication# Porosity in Aluminum Alloys

Résumé

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.

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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.

Mario Alberto Salgado Ordorica

The formation of feathery grains during semi-continuous casting of Al-alloys [1, 2] is an interesting problem from both practical and theoretical points of view. These structures are formed by a lamellar sequence of twinned and untwinned regions separated by straight and wavy-like boundaries. Each pair of lamellae contains twinned dendrites split in their trunk center by a coherent {111} twin plane, while lateral arms meet at an incoherent {111} boundary. In practice, feathery grains are considered as defects which reduce the mechanical properties of a solidified ingot. In theory, an understanding of twinned dendrite growth includes different solidification phenomena, e.g., interfacial energy anisotropy, crystallographic growth directions, twinning, growth competition mechanisms, etc. Although several studies have been performed in order to understand the physics leading to the nucleation and growth of twinned dendrites, various questions remain unanswered. In this work, a comprehensive study of twinned dendrite growth has been undertaken, with the main objectives being: i) to study the effect of different alloying elements and solidification conditions on twin formation in binary Al-alloys; ii) to establish a better understanding on the stability of twinned dendrites and the growth kinetic advantage that they exhibit over regular ones; and iii) to elucidate the stable shape of the twinned dendrite tip. In order to study alloying-element effects, binary Al-X alloys (where X = Zn, Mg, Cu and Ni), were produced under Directional Solidification (DS) conditions in the presence of a slight natural convection in the melt. Analysis of these castings has shown that feathery grains can form for all solute elements of interest, but not for all compositions. The probability of forming feathery grains is relatively high when the alloying elements are hcp (Zn or Mg), but decreases for fcc solute elements (Cu or Ni). A study on the effect of forced convection in the melt, performed using different experimental set-ups, confirms previous observations suggesting that it is the shearing components of the liquid slow which induce twin nucleation [3, 4]. However, the poor reproducibility of these experiments and the variable rate of feathery grains formation indicate that twin nucleation is governed by a highly stochastic behavior. The probability of such an event decreases as the melt slow is less complex and the associated Stacking Fault Energy (SFE) of the alloying element is increased. In terms of growth kinetics advantage, a characterization using various metallography techniques and X-ray synchroton tomography has shown that this is in part due to the complex morphology of twinned dendrites. Indeed, it has been confirmed that these dendrites grow along ‹110› directions with ‹110›, and also sometimes ‹100› secondary arms, the primary trunk spacing of these dendrites being much less anisotropic than previously thought [5, 6]. It has been shown that twinned dendrites grow in a stable manner at a lower undercooling than regular ones. In addition, the distribution and orientation of their side arms favors their growth at the expense of less developed regular dendrites. A mechanism to explain the lateral multiplication of twin planes is also proposed in this work. In terms of stability, observations after partial remelting of twinned DS specimens, then re-solidification in a Bridgman furnace, have shown that even if twin planes remain stable during partial remelting, independent regular non-twinned dendrites issued from the twinned and untwinned parts of the seed grow during solidification. This implies that the formation of twinned dendrites is not only related to the ability to nucleate a stacking fault, but also to the imposed solidification conditions. The favorable growth kinetics of twinned dendrites is also explained by their tip morphology. Three hypotheses have been evaluated in this work: i) the grooved tip [7], stabilized by the Young-Laplace equilibrium condition; ii) the doublon [5], i.e., a double tip dendrite that grows with a narrow liquid channel in its center that solidifies at a composition close to C0; and iii) the pointed (or edgy) tip [8], equilibrated by torque terms of γsl when it is too anisotropic. Observations performed at the twinned dendrite tip have revealed the presence of a small groove, which eliminates definitively the hypothesis of the edgy tip. Further examination of the stable growth morphology of twinned dendrites has been done by using a phase field model that reproduces the presence of a twin plane through an appropriate boundary condition. The results of these simulations show that twinned dendrites are doublons that grow with a narrow liquid channel (0.2 to 3 µm width) whose depth depends strongly on the alloy composition and the solidification conditions. In order to validate these simulations, Focused Ion Beam (FIB)-microtomography and X-ray chemical analysis (EDS) in a Scanning Transmission Electron Microscope (STEM) were performed on small specimens extracted from twinned dendrite trunks. These have shown the existence of a positive solute gradient in a region localized within 2 µm around the twin plane, i.e., as expected for a doublon morphology. Additionally, the presence of small particles aligned within the twin plane is in agreement with the formation of small liquid pockets below the doublon root as predicted by the numerical model, but further work is required to explain this remarkable feature. Finally, composition measurements performed after quenching a partially remelted specimen also seem to confirm the existence of a doublon. This work contributes to the understanding on twinned dendrite growth kinetics in several aspects, principally the effect of alloying elements on twin formation, their growth kinetic advantage, their stability and their stable tip morphology. However, further work must be carried out to overcome the limited knowledge on the mechanisms leading to twinned dendrite nucleation. In the same manner, the growth mechanisms of the doublon morphology should also be further investigated in future works.

Vincent Mathier, Michel Rappaz, Stéphane Vernède

Hot tearing formation in both a classical tensile test and during direct chill (DC) casting of aluminum alloys has been modeled using a semicoupled, two-phase approach. Following a thermal calculation, the deformation of the mushy solid is computed using a compressive rheological model that neglects the pressure of the intergranular liquid. The nonzero expansion/compression of the solid and the solidification shrinkage are then introduced as source terms for the calculation of the pressure drop and pore formation in the liquid phase. A comparison between the simulation results and experimental data permits a detailed understanding of the specific conditions under which hot tears form under given conditions. It is shown that the failure modes can be quite different for these two experiments and that, as a consequence, the appropriate hot tearing criterion may differ. It is foreseen that a fully predictive theoretical tool could be obtained by coupling such a model with a granular approach. These two techniques do, indeed, permit coverage of the range of the length scales and the physical phenomena involved in hot tearing.

2009