Elsevier

Acta Materialia

Volume 48, Issue 2, 24 January 2000, Pages 405-417
Acta Materialia

Diffusion-controlled growth of hydrogen pores in aluminium–silicon castings: in situ observation and modelling

https://doi.org/10.1016/S1359-6454(99)00363-8Get rights and content

Abstract

In situ observations were made of the nucleation and growth kinetics of hydrogen porosity during the directional solidification of aluminium–7 wt% silicon (Al7Si) with TiB2 grain refiner added, using an X-ray temperature gradient stage (XTGS). The effect of altering the solidification velocity on the growth rate and morphology of the porosity formed was characterized by tracking individual pores with digital analysis of the micro-focal video images. It was found that increasing the solidification velocity caused the pore radius to decrease and pore density to increase. Insight gained from the experimental results was used to develop a computational model of the evolution of hydrogen pores during solidification of aluminium–silicon cast alloys. The model solves for the diffusion-limited growth of the pores in spherical coordinates, using a deterministic solution of the grain nucleation and growth as a sub-model to calculate the parameters that depend upon the fraction solid. Sensitivity analysis was carried out to assess the effects of equiaxed grain density, pore density, initial hydrogen content and cooling rate. The model agrees with the experimental results within the resolution limits of the XTGS experiments performed.

Introduction

Increasing demands for reduced pollution and improved fuel efficiency are drawing the automotive and aerospace industries towards using increasingly lighter materials. This trend has led to a move to convert safety-critical parts from heavy wrought ferrous products to high quality Al–Si castings. Shape casting also offers an economically advantageous method of producing parts because complex shapes can be formed directly from the molten metal, reducing the number of production steps required. The major obstacle to increasing the use of shape cast parts vs those produced through wrought techniques is the difficulty in reducing casting defects due to the complex shapes of many of the parts.

With the recent application of mathematical modelling to casting design, it is now possible to evaluate ever more involved correlations between processing parameters and final properties in a complex geometry. These mathematical models have been shown to be very capable of simulating macroscopic phenomena such as mould filling and heat transfer, allowing the prediction of hot spots or macroshrinkage. Mathematical models are now being used to simulate the evolution of the solidifying microstructure [1], including the grain size [2] and the dendrite arm spacing [3]. However, the prediction of the occurrence, magnitude and shape of defects, such as porosity and inclusions, is not as well advanced, even though such defects constitute two of the major casting defects for Al–Si alloys and are both detrimental to the final mechanical properties. In particular the formation of porosity during the solidification of metals is a major concern for the casting industry since it reduces fatigue performance and reduces total elongation 4, 5, 6. In spite of recommended guidelines for process optimization during casting 7, 8, porosity remains a costly problem for both the foundry industry and end users.

The main causes of pore formation during casting are insoluble gas evolution and inadequate feeding of the volumetric shrinkage due to solidification. The defects resulting from these causes are referred to as gas porosity (or microporosity) and shrinkage porosity (or macroporosity), respectively. The classification of observed pores is often based upon their shape, i.e. rounded pores are classified as gas pores whereas irregular pores are classified as shrinkage pores. This classification embodies the assumption that, gas pores form exclusively by the growth of bubbles in the liquid, whereas shrinkage pores form by removal of liquid from around solidified dendrites. Whittenberger and Rhines [9], however, showed that the content of potential gas forming species such as hydrogen is a key factor in the formation of both types of porosity, indicating that the evolution of gas from solution also occurs during the formation of irregular pores.

Prior work on the modelling of porosity formation during the solidification of aluminium (both shrinkage and gas) can be divided into four main approaches:

  • 1.

    analytic pipe flow solutions combined with constant solidification shrinkage;

  • 2.

    gas partitioning and diffusion-controlled models;

  • 3.

    combined analytic and semi-empirical models; and

  • 4.

    numerical solutions of Darcy's law, the energy, continuity, and hydrogen conservation equations.

While considerable success has been made in the prediction of the evolution of shrinkage (macroporosity) 10, 11, 12 through heat transfer and fluid flow simulations, little progress has been made in the prediction of microporosity formation.

The use of analytic solutions for shrinkage porosity was prevalent for several decades 13, 14 until numerical solutions of Darcy's law incorporating the heat transfer became feasible in the 1980s as per the work of Kubo and Pehlke [15]. The Darcy flow models were then extended to include hydrogen conservation by Poirier et al. [16], but their model did not include diffusion limited growth. During the same period many criteria functions were developed from combined analytic and semi-empirical models to try and predict the amount of porosity, most notably the work of Niyama et al. [17]. These criteria functions offer the benefit of simple incorporation into macromodels of the heat transfer and fluid flow. One limitation shared by many of the criteria functions and Darcy flow models is that they only predict the percentage porosity, and not its size and distribution. The latter strongly affects the mechanical properties, especially as fatigue life.

At the same time as the Darcy flow models started to develop, Fang and Granger [18] combined the original analytic solution to the pressure drop due to shrinkage with an experimentally justified isolated liquid pocket approach. In the solution presented, they assumed the shrinkage was negligible, and found that pore size was a function of the partitioning of hydrogen in each liquid pocket. The model results correlated reasonably with their experimental observations.

In this paper, a model based upon the diffusion limited growth of pores will be presented. The model assumes, similar to Fang and Granger [18], that the pores draw hydrogen from a limited area, although here the assumption is based upon competitive growth, rather than isolation of pockets of liquid. This model is based upon the insight gained from in situ observations of porosity formation in a directionally solidified aluminium silicon alloy that will be presented first. The in situ observations were made using a technique which one of the authors [19] used previously to observe the interaction of gas pores with the developing microstructure in Al–Cu–H alloys, an X-ray temperature gradient stage (XTGS). The Al–Cu–H system allowed greater resolution of both the pores formed, and the developing columnar dendrites due to the larger X-ray attenuation of copper. In the previous work, the pores were seen to be restricted by the growing columnar dendrites, forming irregular shapes while applied conditions limited the effect of restricted interdendritic flow. This experimental technique has been extended for application to equiaxed Al–Si–H alloys, and the results are presented herein. In addition the theory, assumptions and results of the new model based on diffusion limited growth of pores will be presented. In this model, hydrogen pores were assumed to nucleate in the interdendritic liquid between equiaxed grains. An average pore radius was calculated based on the thermodynamics and kinetics of hydrogen rejection from the solidifying metal and diffusion into the pores. Impingement with evolving grains was assumed to occur when the size of a spherical pore reached the size of the interdendritic region between grains. The validity of the model was then investigated with respect to initial hydrogen content, grain density, pore density and solidification rate, and assessed with respect to the experiments.

Section snippets

Experimental methods

Real time micro-focal radiography was used to observe the solidification of Al7Si alloys in a conventional temperature gradient stage which allows the independent control of solidification velocity and thermal gradient [20]. A schematic diagram of the XTGS is shown in Fig. 1. Molten aluminium was poured into a thin boron nitride specimen container with a cavity size of 180×25mm2 and a thickness of 2.0 mm. This container was moved at a constant speed from the hot to the cold zone, producing a

Computational model

The experimental results, as will be discussed later, illustrated a correlation between pore size and local solidification time that is indicative of a hydrogen diffusion limited process rather than one governed by shrinkage or restricted interdendritic feeding. To simulate porosity formation during solidification as a diffusion-controlled process, one must solve for the diffusion of hydrogen into the pores. To do this, the source of excess hydrogen generating the supersaturation must also be

Results and discussion

The in situ observations are discussed first to illustrate that the predominant driving force for pore growth is diffusion. The model results are then presented together with its sensitivity to the critical parameters, followed by a comparison between the model and experiment.

Conclusions

An X-ray temperature gradient stage (or XTGS) was used to observe porosity formation in a TiB2 grain refined Al7Si alloy. Increasing the solidification velocity was found to cause a decrease in pore radius whilst increasing pore density. This supports the hypothesis that the pore growth under the conditions studied is primarily governed by diffusion of hydrogen.

The results from observations using the XTGS were used as input for a newly developed model to predict the evolution of hydrogen

Acknowledgements

This work was funded in part by the EPSRC in collaboration with BAe, Federal-Mogul and Aeromet under grants GR/L88351 and GR/L70042 and using computer facilities provided in part under grant GR/L86821. One of the authors would also like to thank John Hunt at the University of Oxford and Alcan International's Kingston Research and Development Centre for their assistance and sponsorship of the experimental work. The authors would also like to thank their colleagues in the Materials Processing

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