Phase-field modeling of microstructure evolution during solidification in presence of gas bubble

https://doi.org/10.1016/j.commatsci.2015.12.018Get rights and content

Highlights

  • A phase-field model for gas bubble growth in pure melts is proposed.

  • Gas bubble growth from pre-existing pores is simulated and discussed.

  • Pressure effect on the gas bubble formation is investigated and discussed.

  • Gas bubble nucleation and growth in pure melts is simulated.

Abstract

The microstructure evolution during solidification of pure Aluminum metal with gas bubble nucleation and growth is modeled and simulated by the phase-field method. Interface microstructure formation in the presence of gas bubble is simulated to investigate the interaction between gas bubble and microstructural evolution, and also a pressure correction equation is implemented to study the effect of pressure difference between the bubbles and melts. Results indicate that pressure difference between gas bubble and the liquid melt can significantly affect the gas atoms diffusion near the gas–liquid interface, which will lead to the bubble growth velocity change. These simulation results are in agreement with experimental observations.

Introduction

There has been an increasing use of aluminum castings in transportation vehicles to save weight, improve fuel economy, and reduce emissions. Despite the maturity of the aluminum casting industry, to achieve the mechanical integrity required for automobile components of the future requires innovative approaches to the design of alloys [1], [2], [3], [4], [5]. One of the critical factors that limit the mechanical properties is the formation of porosity in Al-castings. Two types of porosity are common: gas and shrinkage-driven pores. Hydrogen is always present in foundries, being easily formed from the reduction of atmospheric moisture and other products of combustion. Liquid aluminum readily dissolves hydrogen and, even if the melt is degassed, porosity can occur as the result of the large difference in hydrogen solubility between the liquid and solid states. Gas-driven pores are prototypically spherical, and the roundness of the pores depends on the hydrogen gas pressure when they form and also the impingement of phases that are already solid. Porosity related defects are a major cause of casting rejection and rework in the casting industry [6], [7], [8]. The porosity formation and its influence upon the subsequent microstructure development during solidification of an Al–6 wt.% Sn alloy was investigated by using X-ray imagining and directional solidification and X-ray computed tomography techniques [9], the growing porosity induces abnormal macro-segregation of Sn above the pores, which is attributed to mass transportation caused by local variations in thermal and solution concentration. The evolution of porosity during re-melting of near-eutectic casting Al alloys has been investigated in-situ using X-ray micro-focus radiography [10]. During re-melting process, gas bubbles float out of the melt quickly when the liquid melt interface passes through them. The presence of microporosity and oxides is very detrimental to the mechanical properties, in particular to the fatigue resistance to crack initiation and growth. Therefore, there is a need to understand the phenomena and to predict the porosity present in the castings to avoid defects. Despite experimental investigations [9], [10], [11], [12], [13], several models have been developed in the past to determine the pore size and the pore volume fraction both deterministically and stochastically [6], [7], [8], [14], [15]. Important ones among these are Darcy’s law coupled with conservation laws, diffusion controlled growth models, Cellular Automata models with stochastic approach to nucleation, First-principle calculations, molecular dynamics simulations and finite element method. These models essentially aim at predicting the porosity fraction and the maximum size of the pore in an averaged manner. Recently, phase-field method has been employed to study the porosity formation problem [16], [17], [18], [19], but these attempts are mainly dealing with the microporosity shape change under different conditions, the interaction between gas bubble growth and solidifying still need further modeled and investigated. In this paper, a phase-field model for gas bubble growth during solidification in pure metal is proposed, and a pressure correction term is introduced into the model to study the pressure effect on gas bubble growth, and finally the gas bubble nucleation and growth during columnar dendrite formation is simulated and discussed.

Section snippets

Phase-field model and simulation method

The total free energy density of the system with gas bubble nucleation and growth during pure metal solidifying can be expressed as:ftotal=fϕ(ϕ,T)+fc(η,Cgas)+κϕ2(ϕ)2+κη2(η)2+κc2(Cgas)2+finterwhere η is the phase parameter introduced to identify the gas phase and liquid phase and ϕ is the phase parameter to identify the solid phase and liquid melt. Cgas represents the concentration the gas.

The chemical free energy for solid phase fϕ is assumed [20] to befϕ(ϕ,T)=14ϕ2(1-ϕ)2-16ϕ2(3-2ϕ)m(T)and

Directional solidification with a fixed gas bubble

First we consider the solidifying process with a fixed volume gas bubble in presence to investigate the effect of pre-existing gas bubble on the dendrite formation. As shown in Fig. 1, when the evaluating dendrite tip encounters with the gas bubble, the microstructural formation process is very different comparing with the free dendrite evolution as shown in the right part of the simulation zone. The tip of the primary dendrite is split by the gas bubble and leads to the further progression of

Conclusion

A phase-field model is proposed to study the gas bubble growth during solidification in pure Aluminum metal, and a pressure correction term is introduced to study the effect of the pressure inside bubbles on the gas atoms diffusion as well as the bubble formation rate. The gas bubble nucleation and evolution, as well as the interaction between gas bubbles and the solid–liquid interface are simulated and discussed. Based on these simulations, we find that the gas bubble in presence of

Acknowledgements

This work was supported by the Natural Science Foundation of China (51501146, 21503165), the PhD research startup foundation of Xi’an University of Science and Technology (2015QDJ017), the Key Innovation Team of Shaanxi Province (2014KCT-04), and the Major International Joint Research Program of Shaanxi Province (2012KW-10).

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