7International Journal of Metalcasting/Spring 2013

CRACK FORMATION DURING FOAM PATTERN FIRING IN THE INVESTMENT CASTING PROCESS

W. Everhart, S. Lekakh, V. Richards, J. Chen and K. ChandrashekharaMissouri University of Science and Technology, Rolla, MO, USA

Copyright 2013 American Foundry Society

Abstract

were obtained from experimental tests. A 3D nonlinear fi-nite element model was developed to predict possible crack formation in the shells during pattern removal. The effects of the thermo-mechanical properties of the foam and the shell, as well as the firing process parameters were mod-eled, and extreme cases were experimentally validated. Recommendations for firing process parameters and pat-tern design to decrease stress and eliminate crack forma-tion in the shell were formulated.

Keywords: ceramic shell, investment casting, crack, stress modeling, molding, foam pattern

Large patterns made from wax often do not have the strength necessary to hold their shape due to their higher weight, especially in situations where the pattern has un-supported extensions, which can lead to creep as dem-onstrated by Cannell and Sabau.4 These are reasons for the use of polymeric foam as a pattern material in invest-ment casting. Kline et al.5 showed that some of the first foams used were expanded polystyrene (EPS) foams. This material has a much lower density than wax and, despite its lower strength, can support its own weight much better in larger patterns. This becomes especially important for the dimensional stability of the pattern when stored. However, EPS foams are also very buoy-ant which causes problems when the pattern is initially dipped in the slurry. The forces on the pattern when sub-merged can be high enough to distort or even break the pattern. Because of this issue, stronger, higher density polymeric foams are needed. Polyurethane foams fit these requirements well and can be made in complicated shapes with high surface quality and dimensional accu-racy. However, polyurethane foams have higher ther-mal expansion and higher decomposition temperatures which can cause the pattern to expand and break the shell during the pattern removal process.

The objective of this research was to prevent crack formation in the green ceramic shell during polyurethane foam pattern removal. To achieve this goal, the thermo-mechanical prop-

The application of rigid polymeric foam for large invest-ment casting patterns with complex geometries can im-prove the dimensional tolerances and the surface quality of the casting. However, these pattern materials have a tendency to promote crack formation in investment casting shells during pattern removal by firing. Experimental meth-ods were combined with finite element modeling to predict stress in the shell. The model takes into consideration the thermal and mechanical properties of the pattern and the shell materials to determine the heat transfer and thermal expansion stresses developed in the shell during firing. The thermal and mechanical properties of the pattern and shell

Introduction

The investment casting process is generally used to pro-duce small, thin walled castings with high detail. The pro-cess starts with the manufacture of a pattern. The most common material for patterns is wax but different types of polymeric patterns are also used as demonstrated by Foster’s1 work with rapid prototyping patterns as well as Yao and Leu’s2 work with stereolithography patterns. Ca-padona described the shell making process and the impact of process controls.3 The pattern is dipped in slurry made of ceramic binder and flour usually containing some com-bination of fused silica, zircon, alumina, or other ceramic materials. Refractory granules referred to as stucco are then applied to the wet slurry coating. The combination of slurry and stucco makes a single coat which is allowed to dry before the next coat is applied. The shell building process generally consists of one or two prime coats, de-signed to provide a better surface finish for the casting, four to ten back up coats, designed to add strength to the shell, and a seal coat, designed to seal the stucco in the final backup coat. The pattern is then removed from the “green” shell by melting or decomposition in an autoclave or furnace. Whether done as a part of pattern removal, or as an additional firing process, the ceramic is sintered to increase the strength of the shell enough to hold the pres-sure of liquid metal. Liquid metal is then poured into the shell, which is usually preheated.

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erties of the polyurethane foam and ceramic shell were ex-perimentally determined. These data were used in a finite element model that predicts crack formation during pattern removal. The modeling results were validated by experi-ments and recommendations were made on the investment casting process to minimize the chances of shell cracking during pattern removal.

Procedures

Experimental

Polyurethane foam with a density of 170 kg/m3 (10.6 pcf) was tested. The properties of the polyurethane foam were also compared to EPS foam with 26 kg/m3 (1.6 pcf) density. All foamed pattern materials (Polyurethane foam and EPS) have some degree of non-uniform internal structure and sur-face layer. In this study, the tested articles were produced from foamed patterns with less cuts or machining to repre-sent the real foam pattern structure. Samples were cut from the foam blocks with a cross-section of 7000 mm2 (10.8 in.2) Compression testing of the foam was done to determine the elastic modulus with varying pattern dimensions. Samples had a cross-section of 2580 mm2 (4 in.2) and a thickness of 25.4 mm (1 in.) or 50.8 mm (2 in.). Tests were run accord-ing to ASTM D1621.6 Thermal gravimetric analysis (TGA) was carried out using a 2950 Thermo-gravimetric analyzer. Samples were tested in air from 30C (86F) to 600C (1112F) using a constant heating rate of 10°C/min (18°F/min). The air flow rate was set to 100 ml/min. The thermal expansion of the foam was measured using a laser assisted dilatometer. Foam samples were cut into 50 mm long (1.97 in.) 18 mm (0.7 in.) diameter cylinders. Two thin aluminum disks were placed on both ends of the foam and inserted into a quartz glass tube (19 mm (0.75 in.) diameter) and then submerged in an oil bath. A small hole was present in the end of the tube to allow oil flow inside for improved heating of the sample. Another quartz tube was placed on the upper aluminum disk. The expansion of the foam sample was monitored through the linear movement of the upper tube using a laser prox-imity probe with 1 µm precision. The average temperature of the foam samples was collected by averaging the read-ings from two thermocouples inserted in the oil bath, one of which was inserted in a spare foam sample and the other thermocouple was left exposed to the oil. The heating rate of the foam was approximately 1°C/min (1.8°F/min.).

A simple pattern was used to test shell cracking during burnout (Figure 1). Tests were performed on patterns with dimensions of 50.8 x 63.5 x 63.5 mm (2 x 2.5 x 2.5 in.). The slurry was made of colloidal silica binder (Megasol BI) and fused silica flour (-200 mesh). The slurry viscosity was measured by a Brookfield DVII+ Pro Viscometer. All coat-ings were applied at 800 ± 100 cP viscosity which is equiva-lent to 19-22 seconds on a #5 Zahn cup. The patterns were submerged in the slurry until completely covered and then removed and suspended over the slurry for approximately

50 seconds. During this time, the pattern was rotated and al-lowed to drip from different points to promote an even coat-ing. A uniform distribution of stucco was then applied using the rainfall method. This was done by continuously rotating the pattern so that all surfaces were directly impacted by the falling stucco until no more stucco would adhere to the sur-face. The stucco for the prime coat was granular zircon (-100 +200 mesh) and the stucco for the back-up coats was fused silica (-30 +50 mesh). The seal coat used no stucco. The samples were dried for at least four hours between coats.

To increase sensitivity to shell cracking, shells were devel-oped with one prime coat, either three backup coats (3.8 mm (0.15 in.) average thickness) or five backup coats (6.4 mm (0.25 in.) average thickness), and one seal coat. After the seal coat was applied the samples dried for another 24 hours. All experimental specimens were tested the week after shell de-velopment. Shells were fired in an electric box furnace using two different procedures: continuous heating from room tem-perature to 600C (1112F) at 3°C/min (5.4°F/min.) and flash firing in a furnace preheated to 600C (1112F). The maximum stress at rupture and elastic modulus of the shells were deter-mined using three-point bend testing of “green” shells per-formed at room temperature according to ASTM C1161.7 The tip of the testing fixture had a radius of 3.0 mm (0.12’’). Five samples of shells with five and seven layers were tested. The density and open porosity of the shells was measured using the Archimedes method in distilled water according ASTM C208 using approximately 10 g (.022 lb) samples.

Modeling

A nonlinear coupled finite element model was developed to study crack formation in the shell during pattern removal. The model accounts for both mechanical and thermal load-ings. It is capable of performing complete and detailed pat-tern and shell behavior during the firing process. For saving computational time, one quarter of the pattern surrounded by shell has been modeled and symmetric boundary conditions

Figure 1. This shell was built around a foam pattern that was 50.8 x 63.5 x 63.5 mm (2 x 2.5 x 2.5 in.) in size.

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are applied. An eight-node brick element is used to mesh the model. The mesh of the finite element model for both the shell and foam pattern is shown in Figure 2. Finer mesh is used near the corner of ceramic shell. 19,683 brick elements were used for the model.

The formulation for the transient mechanical analysis can be written as:

Eqn. 1

Where:

[Me] is the mass matrix, [Ke] is the stiffness matrix, [Fe] and are mechanical and thermal loadings, N is the shape function, B is the strain-displacement function, C is the elas-ticity matrix, ρ is the density, and {u, v, w}T are displacement components in a rectangular Cartesian coordinate system.

The formulation for heat transfer can be expressed as:

Eqn. 2

Where:

is the heat capacitance matrix, is the conductivity matrix, and {Qe} is the external flux vector. Cp is the specific heat of the material, k is the thermal conductivity, q is the surface heat flux, and r is the body heat flux generated by plastic deformation.

A smeared crack model was used to describe the response of the ceramic material when a crack initiates. The crack model does not track individual “macro” cracks. Cracking

is assumed to occur when the stress reaches a crack detec-tion criterion surface. This failure surface is a mathemati-cal construction which is a linear relationship between the equivalent pressure stress and the von Mises equivalent deviatoric stress. When a crack has been detected its ori-entation is stored for subsequent calculations. Subsequent cracking at the same point is restricted to being orthogo-nal to this direction since stress components associated with an open crack are not included in the definition of the failure surface used for detecting additional cracks. All models were formulated using ABAQUS software. A more detailed discussion in terms of numerical derivation and applications with respect to the smeared crack model can be found in literature.9-11

Results

The elastic modulus is an important property of foam pat-terns used in the investment casting process. When a low density pattern sinks into the slurry, the buoyancy of the pattern causes it to bend and hence produce distortion or possibly cracks in the thin prime coat. The elastic modulus of the foam is required to accurately simulate the possible pattern distortion during the shell building process as well as any stress in the shell during pattern removal. Compres-sion testing of the foam was done to determine the elastic modulus. The average measured elastic modulus was 53 MPa (7687 psi).

This data was used to predict foam pattern distortion when it is dipped into the slurry. The deflection of the foam is denot-ed by “∆”. The density of slurry used in the model was 1.5 g/cm3. A simple plain-strain finite element model (Figure 3) was developed in ABAQUS9 to estimate the distortion of the pattern in the slurry. The dimensions of the foam plate are 127 mm (5 in.) [length] × 6.35 mm (0.25 in.) [thickness] × 25.4 mm (1 in.) [width]. Table 1 lists the material properties of polyurethane and EPS patterns and the calculated pattern deflection. Polyurethane foam has an order of magnitude less deflection during dipping when compared to less rigid EPS foam.

Figure 2. Mesh of the finite element model for the foam pattern and ceramic shell. Figure 3. A schematic of the foam deflection model.

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While a higher modulus prevents deflection during shell con-struction, polyurethane foam may create larger pressures on the shell during foam removal. To understand these effects it is important to know the thermal behavior of the foam. The results of thermal gravimetric analysis (TGA) are shown in Figure 4. These test results show that the foam begins to decompose at approximately 260C (500F) regardless of the density, and full decomposition occurred at 600C (1112F).

The results from thermal expansion tests are shown in Fig-ure 5. Over the temperature range tested, two distinct regions of differing thermal expansion coefficients can be noticed. At temperatures below 90C (194F) the thermal expansion coefficient is approximately 80 x10-6 °C-1 while above that temperature the value of the thermal expansion coefficient increases to 400 x10-6 °C-1. At approximately 155C (311F), the foam stops expanding and begins to soften. At this point coefficient of thermal expansion becomes slightly negative. The thermal expansion coefficient does not change signifi-cantly with changes in density. The maximal dimensional increase of the studied polyurethane foams was approxi-mately 2%. An additional thermal expansion test of loaded polyurethane foam was performed for more precise mea-

surement of the effect of temperature on elastic modulus. In this case the elastic modulus at elevated temperatures was estimated from a ratio of applied load to the difference in thermal expansion of the specimens. The results show that above approximately 80C (176F) the elastic modulus of the foam decreases from 53 MPa (7687 psi) at a steady rate until it reaches a very low value at the foam softening temperature (155C / 311F).

The maximum stress and elastic modulus of the shell was ex-perimentally determined for shells with five and seven layers using three point bend testing performed at room tempera-ture. Five samples for both types of shells were tested (Table 2). The failure stress for the five layer shells was lower than the seven layer shells but had a larger elastic modulus. These differences in mechanical properties were related to differ-ent sizes of stucco particles applied in coatings.

These thermo-mechanical properties for the pattern and the shell were used as input into the model (Table 3). The ap-plied generalized model has capabilities to take into consid-eration temperature dependence of all thermo-mechanical properties of the shell and pattern, however in this study

Table 1. Foam Properties Used in Model and Model Results

Figure 4. TGA results for three densities of foam in air.Figure 5. Thermal expansion of polyurethane foam at different densities.

Table 2. Strength, Density and Porosity of Shells

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only experimentally obtained pattern CTE (Coefficient of Thermal Expansion) versus temperature was used because this property has a dominant effect on shell cracking. In addition to the experimental data from above, thermal con-ductivity and specific heat capacity of the shell material was taken from work done by Mahimkar et al.12 Niknejad et al.13 demonstrated the specific heat capacity and thermal conduc-tivity of the polyurethane. Two types of heating methods (flash fire and continuous heating) were used to remove the foam pattern. The foam was assumed to decompose when its temperature reached 155C (311F). The thermal boundary conditions used in the simulation are shown in Table 4. The modeling was done for pattern dimensions of 50.8 x 63.5 x 63.5 mm (2 x 2.5 x 2.5 in.).

In the model a linear temperature profile was monitored along the path shown in Figure 6a. The temperature values

along the path for different heating methods at the time of firing are shown in Figure 6b. Compared to flash firing, the difference between the internal and surface temperatures of the pattern is not significant in continuous heating. The aver-age temperature of the pattern for flash firing is significantly lower than the average temperature for continuous heating. A lower average temperature means there is less thermal ex-pansion and therefore less pressure on the shell during flash firing. An example of the modeling results for both flash fire and continuous heating of a pattern with dimensions, 50.8 x 63.5 x 63.5 mm (2 x 2.5 x 2.5 in.), and shell of 6.4 mm thick-ness is given in Figure 7.

The maximum stress in the shell occurs when the bound-ary temperature between shell and pattern reaches the foam softening temperature. After that, the applied pressure will decrease as a result of foam softening. This critical temper-

Table 4. Thermal Boundary Conditions

Table 3. Material Properties for Modeling

Figure 6. Path (a) and temperature distribution along the path for flash firing and continuous heating (b) at the moment when surface temperature of the pattern increased to the foam decomposition temperature.

(a) (b)

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less likely to cause shell cracking and increasing shell thick-ness decreased the maximal principal stress below critical

Figure 7. Temperature distribution, unit: °C (a), maximum principal stress, unit: Pa (b), and strain distribution (c) of the shell and pattern at the end of flash firing and continuous heating for 170 kg/m³ (10.6 pcf) foam.

(a)

(b)

(c)

ature was experimentally defined from the thermal expan-sion test. The distribution of temperature, stress and strain at that moment for the two firing processes is illustrated in Figure 8. The maximum stress occurs at the internal edges of the shell. The strain distribution results also indicate the internal edges are the most vulnerable place to failure. Com-pared to flash firing, continuous heating produces a much higher stress concentra-tion at the internal corner of the shell.

DiscussionCrack formation in the shell during rigid foam pattern removal by firing depends on multiple parameters which could be divid-ed into these groups:

• Group 1—Foam Properties, most important of which in-clude elastic modulus, ther-mal expansion and softening temperature

• Group 2—Shell Properties, most important of which include failure stress, elas-tic modulus, and shell wall thickness

• Group 3—Firing Regime, continuous heating versus flash firing in a high tem-perature preheated furnace.

In this article, the factors from Group 1 to Group 3 were computationally analyzed. In Group 1 most of the factors are di-rectly affected by the density of the foam. Two extreme cases of foam density, EPS foam (26 kg/m³ or 1.6 pcf) and high den-sity polyurethane foam (170 kg/m³ or 10.6 pcf), were modeled (Figure 8). The low value of elastic modulus in the EPS foam prevents shell cracking for both burnout methods. However, low elas-tic modulus in the EPS foam causes much more deflec-tion during shell making (Table 1). At the same time, the more rigid polyurethane foam creates significantly larger pressure on the shell during pattern removal.

In Group 2, the failure stress, elastic modulus, and thick-ness of the shell are dependent on variables in the shell making process such as slurry viscosity, stucco size and number of coats. It was assumed in a one variable model-ing analysis on the effect of shell thickness on cracking tendency that the modulus of the shell does not depend on shell thickness. Results show that thicker shells are

Figure 8. The effects of foam properties on maximum principal stress/strain in the shell during pattern flash firing are shown graphically (pattern size: 50.8 x 63.5 x 63.5 mm (2 x 2.5 x 2.5 in.)

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values (shown by the arrow in Figure 9 for “not cracked” samples). In low thickness shells, the high stress generates cracks. The maximum principal stress was close to critical for all thicknesses.

In Group 3, the heating rate can affect the amount of material that is expanded, and therefore the amount of stress on the shell (Figure 10). The results show that patterns removed dur-ing flash fire were less likely to crack the shell than patterns removed using continuous heating at 3°C/min. (5.4°F/min.).

Some critical situations were modeled according to the properties of experimentally built shells. These cases were experimentally verified using two firing procedures. The comparison of predicted crack formation and experimentally observed cracks (Figure 11) are given in Table 5. The simu-lation results match well with the experimental results and show that flash firing reduces the chances of shell cracking during pattern removal.

Figure 9. The effect of the firing process and shell thickness on maximum principal stress (a) and strain (b) in the shell (50.8 x 63.5 x 63.5 mm (2 x 2.5 x 2.5 in.). Hollow markers designate cases where there was no shell cracking.

Figure 10. The effect of the firing process on the maximal principal stress at the point of crack initiation (50.8 x 63.5 x 63.5 mm (2 x 2.5 x 2.5 in.).

(a) (b)

Table 5. Comparison of Simulation and Experimental Results

Figure 11. An example of a crack formed in the shell during pattern removal.

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Conclusions

The mechanism of crack formation in investment casting ce-ramic shells during rigid polymeric foam pattern removal was analyzed. A model was developed for predicting crack forma-tion in investment casting shells due to pattern expansion. The model takes into consideration the thermal and mechanical properties of the pattern and shell materials to determine the heat transfer and thermal expansion stresses developed in the shell during firing. The model shows that increasing foam den-sity, elastic modulus, and foam softening temperature increase the chance of shell cracking. Increasing the shell strength and thickness decrease the chance of shell cracking. The model accurately predicts the presence of cracking during pattern removal. The results of the model and the experiments dem-onstrate that patterns should be made with the lower density polyurethane foam in order to prevent shell cracking during pattern removal. It is also recommended that the pattern should be removed using flash firing at 600C (1112F) or higher.

Acknowledgements

The authors would like to thank U.S. Army Armaments Re-search, Development and Engineering Centers (ARDEC)-Benet Labs (BL) for funding this research. The authors wish to recognize the assistance of Darryl Kline for the thermal expansion tests, Hongfang Zhao for TGA analysis, and Tom Towey and Katherine Ramsey for sample preparation. The results and opinions expressed in this paper are those of the authors and not necessarily those of U.S. Army-Benet Labs.

REFERENCES

1. Foster, G. “Flashfire Dewax for Today’s Investment Casting Foundry,” Investment Casting Institute 42nd Annual Meeting, pp. 2:1-2:11, Atlanta, Georgia; USA; 25-28 (Sept 1994).

2. Yao, W.L. and Leu, M.C., “Analysis of Shell Cracking in Investment Casting with Laser Stereolithography Patterns,” Rapid Prototyping Journal, vol. 5, no. 1 (March 1999).

3. Capadona, J.A., “Slurry Process Control in Production can Crack Down on Shell Cracking,” Incast, vol. 4, no. 4 pp. 10-12 (April 1991).

4. Cannell, N. and Sabau, A.S., “Predicting Pattern Tooling and Casting Dimensions for Investment Casting, Phase II,” Final Technical Report (September 2005).

5. Kline, D., Lekakh, S., Mahimkar, C. and Richards, V., “Crack Formation in Ceramic Shell during Foam Pattern Firing,” Technical and Operating Conference, Chicago, Illinois; USA (December 2009).

6. ASTM D1621, “Standard Test Method for Compressive Properties of Rigid Cellular Plastics,” ASTM International (2010).

7. ASTM C1161, “Standard Test Method for Flexural Strength of Advanced Ceramics at Ambient Temperature,” ASTM International (2002).

8. ASTM C20, “Standard Test Methods for Apparent Porosity, Water Absorption, Apparent Specific Gravity, and Bulk Density of Burned Refractory Brick and Shapes by Boiling Water,” ASTM International (2000).

9. ABAQUS Version 6.9. Manual, Dassault Systèmes (2009).

10. DeBorst, R., “Smeared Cracking, Plasticity, Creep, and Thermal Loading-A Unified Approach,” Computer Methods in Applied Mechanics and Engineering, vol. 62, pp. 89-110 (1987).

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13. Niknejad, A., Liaghat, G.H., Moslemi, N.H. and Behravesh, A.H., “Theoretical and Experimental Studies of the Instantaneous Folding Force of the Polyurethane Foam-Filled Square Honeycombs,” Materials and Design, vol. 32, no. 1, pp. 69-75 (January 2011).

Technical Review & Discussion

Crack Formation During Foam Pattern Firing in the Investment Casting ProcessW. Everhart, S. Lekakh, V. Richards, J. Chen and K. ChandrashekharaMissouri University of Science and Technology, Rolla, MO, USA

Reviewer: The authors say that they are comparing foam density by using EPS and PU foams at different densities. Are both variables changing (density and material)? This should be made clearer. Many of the properties change with

differences in density, so it is unclear that a computational approach would work without developing more data for the PU at the lower temperatures.

Authors: The effect of foam density on thermo-mechanical properties were investigated in our previously published ar-ticles. In this paper, the general comparison was done for two different types of foaming pattern (Polyurethane foam and EPS). These materials have large differences in densi-ties and modulus which affect the stress in the shell. The variations on these properties of each class of foam pattern material have significantly less effect.