Paper 10-087.pdf, Page 1 of 7 AFS Proceedings 2010 © American Foundry Society, Schaumburg, IL USA
Improving Investment Casting Mold Permeability Using Graphite Particles D.M. Kline, S.N. Lekakh, V.L. Richards Missouri S&T, Rolla, MO
Copyright 2010 American Foundry Society ABSTRACT Experiments and calculations were performed to increase the permeability of an investment casting mold through the use of sacrificial pore formers. Graphite particles were added to the fused-silica-based slurry and they were incorporated throughout the shell. The resulting shells were fired to remove the graphite and produce pores within the shell. Tests were performed to measure increases in permeability using a digital permmeter. Possible reduction in strength was evaluated through flexural testing. The formation of tunnels in threedimensional layers by connection of randomly distributed spherical pores was modeled by Monte Carlo simulation. The permeability of layers formed was modeled using Fluent CFD. The experimental data was compared to the theoretical model and practical recommendations for increasing investment shell permeability were proposed. INTRODUCTION The permeability of a molding material is of high importance to the metal casting process. The mold must be capable of allowing gases to pass through with at least the same rate as molten metal enters the mold. If gases cannot exit the mold faster than it is filled, then air pressure increases within the mold. This build-up of pressure can result in incomplete mold filling, shell cracking and gas defects in castings. The key reason for low permeability is the use of fine particle-size material with high packing density. While the dense structure gives high strength at low thicknesses, it also restricts the flow of gases. In industry, the issue of low permeability of investment shell molds is generally handled by adding vents to risers. Another, though less exact, method used by a few is to rely on imperfections and micro-cracks forming during mold processing to act as vents. The experiment presented in this paper took generic silica slurry and added graphite particles as a sacrificial fugitive. By using graphite, sample molds were generated with controlled and repeatable levels of permeability throughout all areas. The effect of ceramic porosity on permeability and mechanical properties has been studied intensively1-3 .The majority of previous investigations were done for filters and compacted ceramics. These studies have limited comparison to investment casting molds, since the level
of permeability is not as high in the ceramic mold as for most filters and the method of creation is different. A compaction and sintering method creates a purely monolithic structure, whereas investment casting molds are created through a stucco layering process. When lower viscosity slurries are used for coatings, a near monolithic structure is formed, but it still has some layered structure characteristics. The remainder of this paper will focus on the simulation of thin layer ceramic coatings with relatively large-scale pores, and their experimental results from laboratory testing. Since the corresponding simulations assume a monolithic structure and random particle dispersion, it was limited to single mold layers. This is because the use of stucco between coating layers disrupts the assumption of random graphite dispersion. To make up for this and to correlate the simulated results with complete molds, multiple layer test samples were created and tested for comparison. DESIGN OF EXPERIMENTS MATERIALS AND SAMPLE DESIGN Experimental Test Factors For this experiment, percentage of sacrificial graphite within an investment slurry, layer thickness to graphite particles size ratio, and coating number were investigated. Unless stated otherwise, weight percent graphite is in reference to the weight of graphite particles in the slurry compared to the weight of all solids in the slurry. Material Selection The ceramic slurry used to produce the test samples constituting +325mesh fused silica flour suspended in a colloidal silica binder. High-purity carbon particles were added to the slurry and kept in suspension with the fused silica. The graphite particles used were angular in shape and ranged in size from 0.007-0.031in (180-800um). The size of the graphite particles was selected such that only two to three graphite particles would be required to align to for a complete channel through the roughly 0.039in (1mm) thick coating layers. The stucco applied to the test samples following each dip coating consisted of 0.0120.024in (300-600 μm) fused silica particles. Sample Building To reduce the number of confounding variables in the samples, all coating parameters were targeted to be the
Paper 10-087.pdf, Page 2 of 7 AFS Proceedings 2010 © American Foundry Society, Schaumburg, IL USA
same for all coatings. The dynamic slurry viscosity was maintained at 300cP with an allowed variation of 25cP (roughly equivalent to 7-8sec with a #5 Zahn cup). The size of stucco was -30+50 mesh (300-600um) for all coatings. Commonly the first (prime) coat of an investment mold has a different slurry and stucco than the subsequent (back-up) coats. For this study, the first coating used the same materials and parameters as the other coatings. This created a more uniform structure within the sample and eliminated the presence of a smooth, dense packed internal surface, which could limit permeability. In addition, a seal coat (which does not contain stucco) was omitted since it would impede airflow out of the test samples and limit permeability4. All of the test samples used 0.91x0.39x6.9in (23x10x175mm) foam strips as coating patterns. The foam strips were lightly abraded using 320-grit sandpaper to remove surface texture differences between cut and uncut surfaces. The abrading of the foam surface also created thicker and less smooth first coats, which assisted in making it more like a back-up coat instead of a prime coat. The dipping process used for this experiment followed the same steps as previous experiments by the author5. Following firing at 1650ºF (900ºC), approximately 1.5in (38mm) of the closed end of the shell was cut off for use in permeability testing, while the remaining shell had the sides cut off to produce two samples for flexural testing. TESTING EQUIPMENT AND PROCESSES Porosity The percentage of open porosity within the test samples and sample density were tested using ASTM standard C20. The process involved suspending strips of the test samples in water and comparing suspended, wet, and dried weights following water removal by heating to 300°F (150°C) using Archimedes equation to calculate weight and outer and internal volumes. Permeability Permeability tests were done following the same process as in previous experiments by the author5. Measurements were taken using a digital permmeter and hose attachment shown in Fig.1a. Modulus of Rupture Flexural testing was performed using a ceramic, large radius, 3-point bend fixture shown in Fig.1b. The lower support radii were 0.64in (16.25mm) and the upper loading radius was 1.24in (31.5mm). Samples were loading in compression at a rate of 0.12in of central displacement per minute.
(a)
(b)
Fig. 1. (a) Sample connected to a permmeter for permeability measurement. (b) Sample located between upper and lower supports for 3-pt bend testing.
SIMULATION DESIGN Model Generation Three-dimensional Monte Carlo simulations were generated using physical properties taken from the mold samples created for this experiment. This simulation was used to determine the average number of through channels in each layer. A pseudo-random number generator utilizing the Mersenne Twister algorithm6 was incorporated into the simulation model. The simulated porous structure was modeled as a cuboid with dimensions of H×L×L, where the L×L faces were defined as being open to air and the H×L faces had closed airflow boundary conditions. The parameters H and L were set in relation to the mean pore diameter, D, where H was varied between 1.5 to 5 times D for different simulation runs. For the simulation, L was arbitrary, but to ease simulation, L was adjusted so only 100 porous spheres would be generated within the cuboid for each pore density value. Pores with diameters within the range of D±dD were randomly assigned coordinates within the cuboid, with D being the mean diameter of the pores and dD being half the range of possible pore diameters. The number of pores generated within the cuboid was governed by the fractional density, ρ. The three-dimensional coordinates for the pore centers were randomly generated under the condition that two pore centers must be at least a distance of D-dD apart and can not be within a distance of (DdD)/2 of the outer edges of the cuboid. In the event that the coordinates of a pore center would violate one of
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those two conditions, and the two centers in conflict could not be shifted to fit the center in, such a center would be rejected and a new set of coordinates would be generated instead.
MODELING PREDICTIONS Channel Formation The Monte Carlo generated cuboid models were evaluated to determine the number of channels connecting the base to the top. The simulations were run 1-10 million times for each value of the height and pore density parameters. The mean number of through channels formed for each thickness is displayed in Fig.2 as a function of pore density. As the relative thickness of the modeled volume increased, the number of through channels randomly formed decreased exponentially. As the number of pores within the sample volumes increased, the number of channels that connected through the volume also increased exponentially. For volume thicknesses, three or more times the pore diameters, it was necessary to have a minimum of 5% of the modeled volume being pores. Single Channel Air Flow The predicted geometry on channels created by 3, 4 or 6 interconnected spheres was used for CFD modeling of airflow in individual channel. The inlet conditions for each model were changed to get results over a range of superficial air velocities. The calculated Darcy permeability7 is shown in relation to the superficial air velocity in Fig.3 for all three models. The viscous permeability for the models selected ranged from 50-60 darcy for superficial air velocities below 3cm/s. As the superficial air velocity became faster than 3cm/s, the airflow became increasingly less linear and more turbulent because of fluctuating channel widths. These changes in the airflow cause an increase in the inertia energy losses and creation of gas vortices within the pores. The numbers of pores making up a channel were determined to have little effect on the resulting permeability.
1000 100
4 2
Number of formed channels, n/10 D
RESULTS
(a)
10 1 H=1.5D H=2D H=3D H=5D
0.1 0.01 0.001
0.0001 0.00001 0.01
0.10 Pore Density
1.00
(b) Fig. 2. (a) Example of formed interconnected channel and (b) number of channels (100Dx100D area) versus pore density in layers with different H/D ratios 70 60 50
Permeability, darcy
Air Flow Simulation Models consisting of only 3, 4 and 6 pore channels were generated for use with CFD to calculate individual channel permeability. The pores for these models were based on the average graphite particle diameter, 0.014in (0.36mm), and were to connect two surfaces 0.039in (1mm) apart, which was the average distance between stucco layers of the test samples.. The structure of the pore channels were randomly generated through the same process as described above, but only single channels were evaluated. The airflow through the channels was varied for this portion of the experiment. A steady state solver was applied to calculate the pressure drop across the channel.
3 spheres 4 spheres
40
6 spheres
30 20 10 0 0.0001
0.001
0.01 0.1 Superficial velocity, m/sec
1
10
Fig. 3. Permeability through the generated channels for different superficial air velocities. The constant values at low velocities are the Darcy permeability of the channel.
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Combined Channel Permeability The results of the Monte Carlo and CFD simulations were used to estimate the overall permeability of a layer. The number of pores predicted through the Monte Carlo simulations was multiplied by the airflow rates through the CFD models to determine an average airflow rate through the entire cuboid. The results from these calculations were used to determine curves relating permeability to pore density and layer height. These results are compared with the experimental results later in this paper. EXPERIMENTAL TESTS Shell Thickness The thickness of the test samples, as shown in Fig. 4a, had a near linear relationship to the number of coatings applied. It is also seen that there was a significant difference in thickness between the samples with 5.8 and 10.9wt% graphite. The rate of sample thickening per coating in Fig. 4b shows that the use of 10.9wt% graphite or more gave the samples on average an additional 0.0030.007in (10-20um) per layer. The downward trend displayed in Fig. 4b for all graphite concentrations leads to the conclusion that at least one of the first three layers was larger than the remaining layers. Since only the first layer’s coating surface was different, it is inferred that the first layer was thicker and made more so by higher graphite concentrations. Since the pattern surface was relatively smooth in comparison with the later stucco covered surfaces, the graphite particles at the bottom of the layer all rested on the same plane instead of possibly ending up in the stucco portion of a previous layer. This causes an increase in the average slurry height for that first layer making the stucco applied to it sit higher. The increase from 5.8 to 10.9wt% , but not from 10.9 to 15.5wt% can be explained by there being a limit to how many graphite particles can rest on the pattern surface, and that limit being reached for a concentration between 5.8 and 10.9wt%.
(a)
(b) Fig. 4. (a)Average thickness with error bars of test samples following different numbers of dip coatings and (b) the average thickness for each layer.
Graphite Pick-up Table 1 shows the calculated weight percent of graphite in 0.5oz (14g) test samples assuming that all weight loss during firing was because of graphite removal. Although steps were taken to maintain a uniform distribution of graphite particles within the slurry, the concentration of graphite in the samples did not match that of the slurry. A
Table 1. Experimental weight and calculated volume data for test samples
wt% Graphite of # of Coating wt% Graphite of vol% Graphite in Δ Open Graphite Slurry Solids Layers Samples Samples Porosity (%) Effectiveness (%) 0.00 3 0.00 0.00 -2.43 --0.00 4 0.00 0.00 -0.63 --0.00 5 0.00 0.00 -0.11 --5.77 3 2.92 7.42 2.66 35.81 5.77 4 3.48 8.75 3.16 36.06 5.77 5 2.62 6.68 1.46 21.87 10.91 3 4.81 11.85 5.13 43.26 10.91 4 5.02 12.33 4.17 33.80 10.91 5 4.25 10.56 3.40 32.20 15.52 3 6.28 15.14 6.12 40.41 15.52 4 5.51 13.43 5.64 41.97 15.52 5 5.29 12.95 5.60 43.21
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(a) (b) Fig. 5. The calculated volume percent of open porosity within the test samples shown before (a) and after (b) graphite removal by firing.
possible reason for this occurrence would be differences in surface tension between the graphite and the liquid slurry, pattern, previous mold layer, and air. Since the study of this occurrence is outside the scope of this paper, no formal investigation into this was done at the current time. Although the amount of graphite in the test samples increased with higher graphite concentrations in the slurry, the ratio between the two dropped. This difference in the ratio presents the possibility that there is a limit to the amount of graphite particles, which can adhere per dip coating. Porosity and Permeability Improvements The amount of open porosity in the tested samples is shown in Fig.5 for both the unfired and fired conditions. Prior to graphite removal during firing, the samples showed only a slight difference in porosity ranging from 17 to 26%. As the number of coating layers increased, the porosity lowered because not all pore channels through the newest layers aligned with those of previous layers. The drop in unfired open porosity with the addition of 5.8wt% graphite to the base slurry is caused by the presence of large graphite particles. Possible explanations for this are that the presence of graphite changed the normal surface tension, wetting behavior, and deterred the retention of air bubbles within the samples. The slight increase in unfired open porosity with increasing graphite levels can be accredited to lower density of the purely silica portion of the slurry. The decrease in open porosity for the baseline samples after firing is assumed to be from small pores and channel necks sintering shut during firing. This same occurrence would be present in the other samples, but is counteracted by the large pores generated by the removed graphite. Following graphite removal by firing the test samples, a noticeable increase in open porosity was recorded and is shown in Table 1. The drop in open porosity with increasing coating layers became slightly more
pronounced. As expected, the amount of porosity in the samples increased with the addition of more graphite in the slurry. Ideally, the volume increase in open porosity would have equaled the volume of graphite removed, but this was not the case. The effectiveness of the graphite at creating open porosity is shown in Table 1 where the percentage given is the amount of resulting pores, which were open to the surfaces. As the percentage of graphite within the samples increased, the percentage of resulting pores that were open to the surfaces also increased. For the lower two tested levels of graphite concentration, a drop in effectiveness was seen as layers increased. This was not the case though for test samples made from the 15.52wt% slurry. Test samples created from that source showed nearly the same percentage of graphite created pores being open for all test sample thicknesses.
Fig. 6. Specific permeability for the different parameters tested.
The specific permeability of the samples showed a large improvement with the addition of higher concentrations of graphite as shown in Fig.6. There was an only slight difference in permeability for samples made from the 5.77wt% graphite slurry, but the differences in permeability became greater as more graphite was
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included in the slurry. The permeability of the test samples was divided by their respective thicknesses to determine the air flux through them and is displayed in Fig.7. As the concentration of graphite increased, the allowable air flux through the test samples also increased. At five coating layers, the 5.77% and 10.91% graphite samples appear to converge to the same air flux.
Another parameter of interest for flexural testing of ceramics is adjusted fracture load (AFL)8, which is presented below:
AFL = f * MOR * t 2
Equation 1
where: f is constant factor, t is thickness. Since the thickness (t) of an investment casting mold is a product of slurry and pattern parameters, number of coatings, and how the stucco was randomly orientated, the thickness is not a convenient parameter for strength calculations. By multiplying the flexural stress of the test samples by their thickness squared, the load capacity for a standardized width and length is calculated. The averages of the measured AFL values were adjusted using the constant factor f to set the lowest value to 1. The adjusted data presented in Fig. 9 shows that the samples with graphite additions were able to support 1.3-1.6 times as much load as the baseline samples when only 3 layers were present.
Fig. 7. Air flux through the test samples during permeability testing.
Mechanical Testing While the addition of graphite was beneficial to the gas permeability of the test samples, it was not beneficial for the strength. In Fig.8, a drop in the maximum flexural stress was experienced whenever graphite concentration rose above 5.8wt%. It was noticed that for the range of coating layers tested, the flexural stress of failure generally had a linear correlation with the number of dip coats. Although all the samples showed more strength with more layers, the rate of strengthening was not the same for all. As the percentage of graphite caused pores increased, the strength benefit of additional coatings decreased. The presence of more porosity in the baseline samples compared to the 5.8wt% samples is noticed here still by the consistently higher strength of the low graphite samples.
The calculated AFL values for the samples showed results similar to flexural stress but with less difference between graphite concentrations.
Fig. 9. Adjusted fracture load of test samples standardized so that the lowest value is 1lb.
COMPARISON OF RESULTS
Fig. 8. Flexural stress of the test samples upon failure.
A comparison of specific permeability values derived through simulation and laboratory testing is presented in Fig.10. The predicted trend curves were generated through the CFD simulations and represent ideal results using uniform pore sizes. The experimental data points were determined by combining Table 1 and Fig.6 and adjusted for the molds natural permeability without graphite additions. The experimental data with 4 % open porosity or more all resided between the 2*D and 3*D curves generated through simulation. Since the size range for the graphite particles was originally calculated to require 2-3 particles to form a one layer high channel, this result matches the simulation. Test samples with less than 4 % open porosity all had nearly the same permeability as for the base slurry.
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shell permeability with controlled consideration of decreasing mold load bearing capacity. ACKNOWLEDGMENTS We would like to thank U.S. Army Benet Labs for the funding of this research. The conclusions and opinions expressed are those of the authors and not of Benet Laboratories under contract number W15QKN-07-20004.
Fig. 10. Data points from experimental testing are compared to predicted trend curves generated through simulation.
Since the addition of graphite particles to an investment casting mold has opposing effects for permeability and flexural strength, there is a limit to its benefit. Fig.11 gives a comparison of air flux to adjusted fracture load, both of which are independent of thickness. If graphite particles are to be used, one should first determine the minimum requirement for shell strength to guarantee safe mold handling, pattern removal, and mold filling. The strength requirements of the mold will dictate the maximum concentration of graphite particles allowable in the slurry and the resulting maximum air flux attainable through this method alone.
We would like to thank Dr. Oleg Neroslavsky for development of the three-dimensional Monte Carlo simulations program used for this research. We would like to thank Asbury Carbon for donating the graphite used for this research. The conclusions and opinions expressed are those of the authors and not of Asbury Carbon. REFERENCES 1.
2.
3.
4.
5.
Fig. 11. Comparison of trade between gas removal and strength for the tested graphite concentrations.
6.
CONCLUSION The computer simulation methods generated a good representation of the experimental results. The permeability of an investment casting mold increases exponentially when the concentration of pores increases. As more pores are generated within a mold the probability of them contributing to open porosity greatly increases. The addition of relatively large particles to a slurry can affect its coating behavior and how smaller particles align during drying. The proposed process allows developing
7. 8.
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