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Simulation-based prediction of micro-shrinkage porosity in aluminum casting: Fully-coupled

numerical calculation vs. criteria functions

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2012 IOP Conf. Ser.: Mater. Sci. Eng. 27 012066

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Simulation-based prediction of micro-shrinkage porosity in aluminum casting: Fully-coupled numerical calculation vs. criteria functions

J Jakumeit1, S Jana1, B Böttger1, R Laqua1, M Y Jouani2 and A Bührig-Polaczek2 1Access e.V., Intzestr. 5, 52072 Aachen, Germany 2Foundry Institute, Intzestr. 5, 52072 Aachen, Germany

E-mail: [email protected]

Abstract. Micro-shrinkage porosity in aluminum casting is analysed by computer simulation using three criteria functions and a fully-coupled shrinkage porosity model. Three process simulations of different precision were executed as basis for the porosity prediction for investigation of the impact of simulation precision on porosity prediction. To validate the simulation predictions, three identical blocks were cast in a special experimental setup. Chill plates enforce shrinkage porosity, which was analyzed using computer tomography. The results demonstrate that both precise numerical simulations and precise porosity models are needed for reliable porosity prediction.

1. Introduction Currently, numerical simulation for the prediction of porosity can include complex models describing fluid flow through the dendrite network, segregation, pore nucleation, pore growth and related phenomena on different length scales [1-3]. Such simulations often need high amounts of computation time and their predictive capability is limited by the quality of the material parameters available. Nevertheless, in industrial practice, simple criteria functions, such as the well-known Niyama criterion [4], based on fast, purely thermal simulations, are still widely used. They are easy to apply and simulation results can be obtained within hours [5]. This work investigates if well-calibrated, fast models are sufficient, or whether more complex and computationally expensive simulations are necessary for reliable porosity prediction.

Predictions of three criteria functions, namely the Niyama criterion [4], the dimensionless Niyama criterion [6] and the newly-developed Böttger, Laqua, Jakumeit (BLJ) criterion were compared with results from a fully-coupled porosity model and measurement results. The BLJ criterion combines pressure estimation with a geometrical factor. Basis for the porosity prediction were three process simulations of different precision. A fast, purely thermal simulation without flow, a solidification simulation with convection, and a fully-coupled mold filling and solidification simulation were executed, and the impact on porosity prediction analysed.

The simulation results are compared with experimental findings for a simple test geometry, consisting of three symmetrical blocks fed by a single runner system. Chill plates are used to enforce a columnar solidification with regions likely to show shrinkage porosity.

The 3rd International Conference on Advances in Solidification Processes IOP PublishingIOP Conf. Series: Materials Science and Engineering 27 (2011) 012066 doi:10.1088/1757-899X/27/1/012066

Published under licence by IOP Publishing Ltd 1

2. Theory Basis for the porosity prediction is the fully-coupled, three-phase simulation program STAR-Cast, which enables realistic, fully-coupled mould filling and solidification simulation for the test geometry [7]. The code is based on a fixed grid volume-of-fluid approach in order to allow simulation of the gas, melt and solidified phase evolution during filling and solidification. Based on this code, three simulation approaches with different model precision and computational expenditures were executed:

• Purely thermal: a fast, purely thermal simulation. Only the energy equation is solved for a filling cavity - filling and convection are neglected.

• Convection: a solidification simulation with convection. The simulation starts with a cavity filled by a melt of zero velocity, but convection is included. Thus, only the flow from the filling process is neglected.

• Filling: a fully-coupled mold-filling and solidification simulation which simulates filling, convection and solidification simultaneously.

By comparison of the porosity predicted by these three simulation approaches of different complexity, the effort on the simulation side needed to get a reliable porosity prediction is investigated. The computational effort for the three simulation approaches is remarkably different (see table 1).

Table 1. Simulation time for the three different simulation approaches

Simulation model Simulation time CPU number * time [h] Purely thermal 40 min. on 4 CPUs 2.7

Convection 8 hours on 7 CPUs 56 Filling 39 hours on 8 CPUs 312

To obtain the porosity data, the simulated time-dependent temperature field during solidification is post-processed using the Niyama criterion, the dimensionless Niyama criterion and the newly developed BLJ criterion (see below). In each cell, the criteria are calculated using the values of the temperature gradient G=dT/dx, cooling rate dT/dt, and local solidification time ts at the moment when this cell reaches the critical temperature Tcrit at which porosity formation is assumed. In this analysis, a critical temperature of 565.8 °C is applied, where the fraction solid is 90 %.

Using the Darcy equation for porous media, and assuming a columnar solidification, the fluid flow through the dendrite network can be analysed and an equation for the pressure drop deduced. Using simplifying assumptions (see [4] for details) the Niyama criterion value Ny for each cell is then given by:

For the deduction of the dimensionless Niyama criterion, Carlson et al. [6] used the Kozeny-

Carman relation K=K0 (1-gl)2/gl3 where K0 = λ2

2/180, λ2 is the secondary dendrite arm spacing and gl the volume fraction of liquid. The dimensionless Niyama criterion value Ny

* is given by:

ΔPcrit is the critical pressure drop, where shrinkage pores begin to form and used as a free parameter. Throughout this analysis, ΔPcrit = Patm was applied (Patm = atmospheric pressure = 105).

One interesting aspect of the dimensionless Niyama criterion is the possibility of estimating pore volume fraction as: gp = ß’ * gl,cr. (ß’ = (ρs – ρl)/ ρs is the total solidification shrinkage, ρs is the density at the solidus temperature, and ρl is the density at the liquidus temperature). gl,cr is the fraction liquid, where the integral I(gl,cr) is equal Ny

*2 [6]. (gl,cr is not necessarily the fraction liquid value at Tcrit.)

TGNy/=

)( ,2*

crlfl

crity gI

TPG

N =Δ

Δ=

βµ

λl

lg l

lcrl dg

dgd

gggI

crl

θ∫

−=

1

2

2

,

,

)1(180)(


2

The third used criterion is the BLJ criterion, developed by some of the present authors (Böttger, Laqua, Jakumeit). It takes account of pressure drop in the mushy zone in a way similar to the other two criteria

with an additional geometrical factor fgeo, which is the ratio between the consuming volume Vconsuming and the feeding volume Vfeeding. Vconsuming is the volume of the region, which is in the critical stage of solidification and needs an additional melt volume to compensate for the volume deficit. Vfeeding is the volume of the surrounding area, which can supply the necessary melt. The temperature range of the critical stage of solidification is given by Tcrit and a small arbitrary temperature interval dTconsuming. To calculate this ratio for each cell of the mesh, the cells within a radius of 10 times the average cell diameter are analysed. If the temperature in these cells is between the critical temperature Tcrit and Tcrit + dTconsuming, the cell volume is added to Vconsuming. If the temperature is above Tcrit + dTconsuming, the cell volume is added to Vfeeding. dTconsuming = 1 K was used for the analysis. The geometrical factor is normalized so that fgeo = 1 holds for a planar solidification front and is given by:

Figure 1 shows the geometrical factor. If the solidification front is convex, or solidification starts in

a corner of the cavity, Vconsuming is much smaller than Vfeeding and fgeo<1. This geometrical configuration simplifies feeding and the pressure drop is smaller (figure1, left). In contrast, if the solidification front is concave or, in the extreme case, melt is surrounded by solid, Vconsuming is larger then Vfeeding, and the pressure drop is enhanced (figure 1, right). In this way, the geometrical factor ensures that the BLJ criterion indicates hot spots, which is not always the case with the other two criteria. The BLJ criterion predicts porosity in regions where the total pressure in the melt Ptotal = Patm + Phydro - Pmushy is less than the capillary pressure Ppore = -2σ/rpore , where Phydro the hydrostatic pressure, rpore is the pore radius and σ the surface tension. Since the model does not provide data on the pore radius, Ppore and rpore are handled as free parameters. For the comparison, Ppore was assumed to be the critical pressure used in the dimensionless Niyama criterion: Ppore = Pcrit = 105 (rpore = 2 * 0.8 / 105 = 16 µm).

Unlike the criterion functions, the fully-coupled model for shrinkage porosity applies the pressure and phase fields provided by the fully-coupled simulation to estimate pore volume. Pliq = Patm + Phydro. G, dT/dt, gl are derived directly from the calculation. The pressure drop in the dendrite network cannot be modeled on the macroscopic scale of the simulation and is, therefore, calculated using similar considerations as in the BLJ criterion:

Shrinkage pores are assumed to nucleate if the total pressure Ptotal = Patm + Phydro - Pmushy is below the capillary pressure Ppore = 2σ/rpore. As for the BLJ criterion, Ppore = Pcrit = 105 (rpore = 2 * 0.8 / 105 = 16

Figure 1. Schematic diagram of the geometrical factor fgeo. A geometrical configuration, which enhances feeding (fgeo<1, left) and a configuration, which hinders feeding (fgeo>1, right) are displayed.

dTgg

GTfP liq

crit

T

Tl

llgeomushy ∫

−⋅=Δ 2

2

222

)1(180

λβµ

)/( min feedinggconsunormgeo VVFf =

dTgg

GTP liq

crit

T

Tl

llmushy ∫

−=Δ 2

2

222

)1(180

λβµ


3

µm) is applied. Pore volume was estimated using the same approximation as in the dimensionless Niyama criterion: the pore volume fraction is given by gp = ß’ gl,crit.

3. Experiment The test geometry consists of three symmetrical blocks (20 x 30 x 4cm) in a Furan sand mold fed by one runner system (see figure 2) Chill plates are arranged to enforce shrinkage porosity. Liquid AlSi7Mg0.3 is poured into the cavity within 18 s, and complete solidification is achieved after 6 min. Porosity in the blocks is measured using computer tomography (CT). Figure 3 shows the direct CT scan (left) and the average scan over all three samples as well as block thickness (centre) and the position of the CT scan in the block (right).

In the experiments, most pores show a complex, structured surface formed by the dendrite network, which is typical for shrinkage-induced pores, while round gas pores are hardly present (see inset of the left micrograph). The conclusion is that a shrinkage-induced pressure drop was the main source of porosity in this case and shrinkage porosity models and criterion functions can be applied for predicting porosity.

Two regions of high porosity were found, one at the center of the block between the chilled area, and a second beneath the chilled area towards the runner. Having only three samples, statistics remain poor. A series of pores found at the centre of one block between the chilled areas is the reason for the strong average porosity indication in this region.

Figure 3. CT analysis of porosity. A direct CT scan (left) and the averaged porosity over 3 blocks are displayed together with the location of the scanned area. The inset left shows the pore beneath enlarged. The complex shape of the pores is typical for shrinkage porosity.

4. Results Figure 4 shows the porosity level predicted by the BLJ criterion, based on the temperature field from a convection simulation (left: 3D distribution of regions with a high risk of pore formation (Ptotal < 0), centre: porosity distribution on the centre section of the block, right: porosity distribution in the area

Figure 2. Sketch of the test geometry


4

analyzed by the CT scan). Results shown in the centre and right of figure 4 are the mean values of all three blocks, averaged over a thickness of 2 cm. The volume deficit at the top of the block, indicated

in the simulation results by the low pressure region at the top centre of the block, is in reality compensated by a sinking melt level and not by porosity. Since a sinking melt level as a consequence of a volume deficit is not included in the model assumptions, all porosity criteria mark this region erroneously. At the same time, the low pressure region below the chill plate and the pressure reductions in-between the chilled region are real indications of porosity. The latter appears to have a pressure level above zero in the averaged plot. This is clearly a result of the averaging process, since the 3D plot on the left shows a region of negative pressure. In addition, small quantities of resolved gas may increase the critical pressure where pore nucleation starts to positive values. In general, the

Figure 4. Porosity predicted using the BLJ criterion. The 3D distribution (left), the averaged distribution in the centre section of the blocks (center), and the scanned area (right) are displayed. The blue rectangle indicates the position of the chill plates.

Figure 5. Comparison of porosity predicted by the Niyama criterion (top left), the dimensionless Niyama criterion (left, right), the BLJ criterion (left bottom) and the fully-coupled model (bottom right). Experimental results of the same area are in figure 3.


5

pressure levels are merely indications of regions likely to show pores. The simulation predicts a higher

likelihood of porosity below the chilled region than between the chill plates. Figure 5 compares the results of the three criterion functions and the fully-coupled porosity model with the averaged CT scan. All porosity predictions are based on the “convection” simulation. The Niyama and the dimensionless Niyama criterion do not mark the correct regions, whereas the porosity volume fraction estimated by the dimensionless Niyama criterion is in agreement with the experiment.

The BLJ criterion identifies the lower porosity region correctly, but only a slight pressure drop is visible at the position between the chill plates. The fully-coupled model shows the best agreement: both porosity regions are marked although the relative magnitude of porosity does not correspond with the experimental findings.

The same results can be found when com-paring the 3D distribution of porosity (figure 6). The Niyama and dimension-less Niyama criterion nicely mark the volume deficit at the top of the block, but the position of the porosity is not correct. Of the three criteria, only the BLJ criterion marks both porosity positions. The fully-coupled model provides closest agreement with the experimental findings.

Figure 6. Comparison of porosity predicted by the Niyama criterion (top left, Ny<300 (Ks)1/2/m), the dimensionless Niyama criterion (top right, Ny

* < 50), the BLJ criterion ( bottom left, P < 0 Pa) and the fully-coupled model ( bottom right, P < 0 Pa) showing the 3D distribution of regions likely to have micro shrinkage.

Figure 7. Effect of the geometrical factor. Regions with enhanced feeding conditions (fgeo < 0.1, left) and difficult feeding conditions (fgeo > 1, right) are shown


6

Figure 7 shows the effect of the geometrical factor in the BLJ criterion, based on the convection simulation. In the left plot, regions with enhanced feeding (fgeo<0.1) are shown, while the right plot displays regions with hindered feeding (fgeo>1). As expected, the regions near the chill plates and the corner of the block (which solidify first) have good feeding conditions and porosity is unlikely. Poor feeding conditions (fgeo>1) are predicted for the top and the runner side of the block just beneath the chilled area. These are areas where all criteria functions predict porosity.

Finally, figure 8 compares the porosity predicted by the three different simulation approaches, “purely thermal”, “convection”, and “filling”, using the best prediction model available for each respective simulation approach. For the purely thermal simulation, the fully coupled model cannot be applied, since a self-consistent calculation of temperature, pressure, and phase distribution is not available. Interestingly, the BLJ criterion, when applied to the temperature field of the purely thermal simulation, indicates only slightly the porosity region at the centre between the chill plates by a pressure, which is only slightly reduced.

Consequently, a clear prediction of both regions of porosity is not possible based on the “purely thermal” simulation. For the “convection” and “filling” simulation, the fully-coupled model is the best option, indicating both porosity positions nicely. When flow and solidification are calculated in a fully-coupled approach, as in the “convection” and “filling” approach, the fully-coupled shrinkage porosity model can be applied without any extra costs. The prediction based on the “filling” simulation provides slightly better agreement with the measurement than that based on the “convection” simulation. However, the advantage is small and the calculation needs about 6 times more CPU hours (see table 1).

Figure 8. Comparison of the porosity predicted using the three different simulation approaches, pure thermal (top left), convection (top right), and filling (bottom left), using the best prediction model found, with the experimental findings (bottom right).


7

5. Conclusion Porosity in an aluminum (AlSi7Mg0.3) sand casting was analyzed using three different simulation approaches (purely thermal, convection and filling), three porosity criteria (Niyama, dimensionless Niyama and BLJ criterion) and a fully-coupled shrinkage porosity model. The results were compared to CT scans of an experimental model casting. The best agreement was found with the filling and solidification simulation and the fully-coupled porosity model. Similar results could be found when applying the fully-coupled model to the convection simulation. Thus, for a sand-casting process as in this test case, where solidification starts after filling is completed, buoyancy-driven convection dominates the solidification process over remaining flow from the filling.

Of the three criteria, only the BLJ criterion was able to indicate both regions of porosity when applied to the time-dependent temperature field data from convection or filling and solidification simulation. However, with this criterion a prediction of the pore volume fraction is not possible, unlike in the case of the dimensionless Niyama criterion, where the volume fraction of porosity predicted agrees well with the experimental value. Based on the purely thermal simulation, only one of the two regions of porosity could be identified, and a purely thermal simulation was, therefore, found to be insufficient for reliable porosity prediction.

In future, a better statistical experimental basis (more samples) and a more precise measurement of the porosity volume would be desirable. In addition, the negligence of gas porosity in the aluminum casting may be an over-simplification.

Acknowledgement This research work is supported by German Science Foundation (DFG) project 194 /JA 853/2-1.

References [1] Stefanescu D M, Int. J. of Cast Metals Research, Vol. 18, 129-143, (2005) [2] Carlson K D , Lin Z, Beckermann C, Metall. Mater Trans. B Vol. 38B, 541-555, 2007 [3] Péquet C, Gremaud M, Rappaz M, Metall. and Mat. Trans. A, Vol 33a, 2095-2106, 2002 [4] Niyama E, Uchida, Morikawa T M, Saito S, AFS Cast Met. Res. J.,Vol. 7, 52, 1982 [5] Lotti E, Previtali B, Alluminio e leghe, 2006 [6] Carlson K D, Beckermann C, Metall. and Mat. Trans. A, Vol. 40a, 163-175, 2009 [7] Jana S, Jakumeit J, Jouani M Y, Proceedings of MCWASP XII ,Vancouver, 377-384, 2009


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