The following article appears in the journal JOM,
47 (10) (1995), pp. 64-68.

JOM is a publication of The Minerals, Metals & Materials Society


An Integrated Procedure for Modeling Investment Castings

John S. Tu, R. Kelly Foran, Albert M. Hines, and Paul R. Aimone

Editor's Note: The results presented here are based on research funded by the U.S. Advanced Research Projects Agency (ARPA) through the Investment Casting Cooperative Arrangement (ICCA). The ICCA is a consortium of five companies: General Electric Aircraft Engines, Pratt & Whitney, Howmet Corporation, PCC, and UES. In addition to these five member companies, a number of research institutes are participating members of the program. For more information on the ICCA, refer to Reference 5.

A major roadblock preventing the widespread use of casting simulation technology is the intensive effort required by a highly skilled professional to construct a finite-element model. To address this situation, this article proposes an integrated-model construction procedure that reduces model construction time for a typical aeropropulsion component from two weeks to two days. It also describes another step toward the accurate and practical prediction of the coating process through coupled heat transfer, fluid flow, and stress calculation.


The application of computer technology offers the potential to reduce product cycle time through computer-aided design (CAD) applications. As indicated in Figure 1, a master CAD model can be used in various design stages and provides greater flexibility for design iteration. In this way, product cycle time can be effectively reduced through streamlining operations.

Figure 1

Figure 1. CAD model utilization.

Casting simulation was first applied to produce equiaxed investment castings in the early 1980s. At that time, only heat-transfer calculation was considered. It was then employed to simulate directionally solidified and single-crystal castings by integrating radiative viewfactor calculation with thermal analysis.1,2 In the early 1990s, commercial codes with a coupled thermal, radiative viewfactor and fluid-flow calculation became available. Successful cases were reported.3,4

A typical investment-casting process involves the following operations. Core and wax toolings are made from product definitions provided by the engine manufacturer; the tooling may include gating information contributed by the casting house. Wax patterns and ceramic cores are produced by dies. The wax patterns are assembled with other features of the gating system such as the pour cup, downfeed, ring gates, and runners. The resulting wax assembly is dipped into a ceramic slurry and sprinkled with ceramic powder repetitively to form a shell that envelopes the wax assembly. Wax is removed in an autoclave and/or burnout furnace. This produces a ceramic mold, the cavity of which takes on the shape of the original wax assembly. The mold is preheated, and the liquid metal is cast into it. To a certain degree, the proposed model-construction procedure mimics the process of manufacturing a ceramic mold.

Until now, only a portion of the physical phenomena associated with these procedures were analyzed. With only a portion of the physical laws being considered, a complete picture of the resulting casting cannot be accurately obtained. This situation is, however, changing by use of an integrated CAD/finite-element analysis (FEA) approach.5 It consists of seven steps: electronic data transfer; gating library; automatic mesh generation; automatic mold generation; finite-element preprocessing; coupled thermal, fluid flow, and stress analysis; and finite-element post-processing.


Since more original equipment manufacturers (OEMs) are replacing blueprints with CAD models, the FEA procedure should take full advantage of these data to reduce model construction time and become an integral part of the product-design cycle. That is, a finite-element mesh should be generated from the CAD model directly. This will not only reduce the redundancy of building the geometric model, but it will also improve the geometric accuracy utilized in the analysis. However, generating a mesh from a CAD model is not easy; a common standard on data format must be developed between OEM and the supplier.

From experience, it is always desirable to reduce the number of data translations; therefore, the same CAD software should be used whenever possible by the OEM and supplier. However, if different software packages are already well established in each company, a robust translation protocol should be adopted. Currently, international graphics exchange standard (IGES) protocol is used with only limited success. Due to variations and limitations of IGES, a next-generation intersoftware protocol is being developed called standard for exchange of product model data (STEP), which includes not only enhanced geometric information but also nongeometric information such as assembly, materials, and tolerances.

An example of a solid model is shown in Figure 2. The solid model in this case is a stationary part in the auxiliary power unit of an aircraft engine and is composed of axisymmetric inner and outer shrouds joined by six airfoil struts.

Figure 2

Figure 2. A Unigraphics solid model.

Whether CAD data should be represented by a solid model or a surface model depends on considerations such as preference of the automeshing algorithm and ease of the gating attachment. Depending on methodology, some meshers prefer a surface model; others prefer solids. Most CAD software is heading toward solid modeling. One can always extract surface information from a solid model, and it is much easier to use a solid for Boolean operations such as attaching gating onto the casting part.


In order to cast the part, gating is used to deliver molten metal and to feed shrinkage. Since it affects the mold filling, heat transfer, and stress-field patterns, the gate must be included in the FEA model. In the wax department of an investment-casting foundry, premanufactured wax-gating pieces of various sizes and shapes are available. These gating pieces are joined to the component wax patterns during the wax-assembly operation.

The concept of a gating library is derived from the same operation. Parameterized solid models (primitives) of gating geometries are preconstructed and stored in a directory (gating library). When the CAD model of the component is received from the OEM, the gating primitives are selected and retrieved from the gating library, specifying desired dimensions and locations. These gating pieces are then joined to the solid model of the component using a Boolean operation. This procedure can effectively reduce the solid-model construction time required to modify the OEM model into a casting model when standard gating features are used. Figure 3 shows the final solid model with gating pieces and component booleaned together.

Figure 3

Figure 3. A final solid model.


FEA requires the construction of a congruent finite-element mesh (i.e., every element corner must join to the corners of its neighbor, never to an edge between two nodes). This poses a strenuous prerequisite on its application to complex three-dimensional (3-D) geometry. Traditionally, a geometry is divided into simply shaped regions (hyperpatches in Patran or mesh volumes in Ideas) that would be further subdivided into elements. The difficulty lies in the definition of congruent regions. It would typically take several weeks to prepare hyperpatches for meshing. This long lead time is unacceptable in a production environment.

There are several commercial software packages for automatic mesh generation from a CAD model. When these packages are applied to a complicated geometry, their robustness becomes an issue. Each has strengths and weaknesses, and none consistently succeeds.

In this study, several automatic meshing software packages were evaluated for their ability to produce meshes on Unigraphics solid models—MeshCAST of UES, Finite Octree of Rensselaer Polytechnic Insitute, and P3 of the MacNeal-Schwendler Corporation. MeshCAST uses a combination of Delaunay and the advancing-front method, which requires the generation of a surface mesh before meshing the enclosed region with tetrahedra. Finite Octree uses the octree method to generate linear- or higher-order tetrahedra given a parasolids file. P3 uses a paving/plastering method to generate linear- or higher-order tetrahedra and has direct Unigraphics access. It also requires the generation of surface mesh either explicitly or implicitly before meshing the region with tetrahedra. All three meshers successfully meshed the test model. Figure 4 shows a finite-element mesh of the test geometry generated by MeshCAST. Note that this is the mesh for metal only.

Figure 4

Figure 4. A finite-element mesh of a structural casting.


The ceramic mold is a shell, approximately one centimeter thick, that surrounds the casting geometry. Since it is manufactured by dipping a wax assembly into a viscous slurry, its thickness varies. At interior corners, the mold thickens; at exterior corners, it thins. Between two closely adjacent blades, the mold might completely bridge the gap. Other than these locations, shell thickness should be generally uniform.

There are several possible approaches for creating a finite-element mesh of the mold. One is to create a solid of the shell by offsetting surfaces of the CAD solid and then mesh this shell solid using an automesher. The second approach is to create the finite-element mesh of the mold from the surface of the finite-element mesh of the metal, thus eliminating the extra effort of creating a CAD geometry of the shell.

For this study, the second approach was taken. Automatic-mold-generation software was developed, which extracts the triangular surface elements from the 3-D mesh of the metal and creates multiple layers of wedge elements representing the mold. Certain difficulties were encountered, such as how to deal with the issues of element interference at inner corners, the shell bridging problem between adjacent blades, and variable shell thickness. Hence, it tends to generate many elements with shapes too distorted to be used in the analysis, and the resulting mesh must be repaired. Several codes are available with this feature of automatic mold generation (e.g., MeshCAST, Patran, and Hypermesh) and there are in-house codes at casting houses.

Figure 5 shows a finite-element mesh of a mold created using the automatic mold generator. In many cases, radiation-viewfactor calculation is necessary. Consequently, the model should include the environment or furnace geometry. Once the finite-element meshes of the metal, mold, mold wrap, and furnace are created, they are assembled into a final model as shown in Figure 6. It is then ready for the application of boundary conditions, initial conditions, assignment of material properties, numerical parameters, and other conditions.

Figure 5

Figure 5. A finite-element mesh of a ceramic mold.

Figure 6

Figure 6. A final finite-element model.


During the preheat cycle, the ceramic mold reaches an equilibrium temperature, as verified by thermocouple data that show indistinguishable differences at various locations in the mold. This uniform temperature becomes the initial condition for the mold in the model.

Next, the ceramic mold is transported from the preheat furnace to the casting furnace. At this stage, radiative, convective, and conductive heat exchange starts to occur with the environment. Because of the elevated temperature of the mold relative to its surroundings, radiation is the dominant mode of heat transfer. Since each location on the mold surface sees a different view of its environment, each will have a different rate of heat loss. For example, faces around the outer perimeter of the mold are exposed mostly to the environment, while the view space of those facing the mold centerline see mostly other hot portions of the casting. Consequently, radiative viewfactor calculation is required to accurately account for the heat exchange. The initial mold temperature and heat loss to the environment prior to casting dictate the thermal profiles that exist at the time of pour.

Molten metal is, therefore, poured into the non-uniform temperature mold. It has been found that the pouring profile has a significant impact on the filling sequence and casting defects. The cross-sectional area of the pouring stream, the angle of pour, and the speed of pour all impact the final product. Mathematically, this information serves as an inlet-velocity-boundary condition. This velocity profile, which changes from pour to pour, is a process variable that is difficult to model numerically. Although the mass-flow-rate profile is obtainable, other variables, such as the location where the metal hits the pour cup, remain unknown. Inlet velocity is assumed for the fluid flow calculation.

During and after mold filling, solidification starts to take place. The energy content of the metal continually decreases by heat conduction with the cooler mold and by radiation from the mold surface and exposed metal in the pour cup. Depending on part geometry, solid metal starts to pull away from the mold or press against the mold. This changes the heat-transfer mechanism across the metal/mold interface. Therefore, heat-transfer coefficients (HTCs) between the metal and the mold are not constant and must be calculated from either first principles or an empirical approach.

In the later stage of solidification, the majority of metal in the product component is solidified, while some portion of the gates are still in liquid or mushy states. This solid/liquid interaction creates a significant technical challenge for a stress analysis of the casting. In the present case, certain simplifications were made. For example, the mold is assumed to be rigid and only metal nodes on the interface can freely move away from the interface since the ceramic mold is relatively brittle compared to the high-temperature metals. This becomes the boundary condition for the stress calculation of metal.

Material properties of the metal, IN718, and the ceramic mold were generated2 and applied to the model. After the preprocessing, the finite-element model was solved using the software ProCAST, which is tailored to casting simulation.


There are various degrees of coupling thermal, fluid flow, and stress calculation. A loosely coupled analysis will be to calculate thermal and fluid-flow solution until the end of filling and then apply thermal and stress analysis to the cool-down cycle of the casting. On the other hand, a tightly coupled calculation will involve an HTC between molten metal and the mold based on the flow characteristics, the effect of the solidifying metal on the flow field, an HTC between the solid metal and the mold based on the gap formation that results from thermal characteristics of the system, and the contribution of the total fluid pressure to the stress calculation. In this study, a loosely coupled approach was used to reduced the calculation time.


Figure 7 presents the filling sequence from the fluid-flow simulation. The prediction shows the molten metal to flow down from the pour cup and branch into the downfeed and two upper runners. While metal flows through the upper runners, it fills the inner shroud on its way to reach the outer shroud. The metal temperature starts to drop due to contact with the cooler mold. By the time the mold is filled, the metal temperature has dropped substantially (150-200deg.C) and is by no means uniform. This justifies coupling fluid flow with heat transfer.

Figure 7A

Figure 7B

Figure 7. Mold-filling sequences at (a) 5.23 seconds after pouring and (b) 6.13 seconds after pouring.

Since aeropropulsion components are generally made of relatively expensive superalloys, metal is not usually filled to the brim of the pour cup. Also, the end of the pour does not coincide with the end of fill, since metal continues to fill the part after the pour. It can be seen in Figure 7a that the metal level starts to drop as it continues to fill the part. Figure 7b predicts that there are no nonfill defects, since only the pour cup is not filled out with metal. Otherwise, the simulation will show isolated void regions where metal was not present.

Figure 8 presents the prediction of shrinkage hot spots. By making the solidified metal transparent, users can easily see the remaining liquid pool. An isolated region of liquid thus suggests a potential hot spot and macroshrinkage indication. No hot spot was predicted other than that in the gates.

Figure 8

Figure 8. Prediction of a hot spot.

Figure 9 shows the predicted effective-stress distribution on the casting. An elasto-plastic constitutive equation was used for the metal. Since this is a nonlinear case, the stress distribution is a function of its history. Eleven minutes after pour, higher stress has developed in the part. It can be seen that the outer-shroud metal between the leading-edge ring gate and trailing-edge ring gate is subjected to a high tensile stress because its contraction due to cool down is being prevented by the locking mechanism provided by the ceramic mold surrounding the ring gates, as if it is going through tensile testing. Furthermore, the deformation is exaggerated in Figure 9, allowing the user to evaluate the deformation pattern that shows distorted runners and blades. The runners are shrinking inward, radially exerting tension onto the junction between runner and ring gate. Large stress was also observed on the junctions at blades and walls that are prone to hot tears or cracks.

Figure 9

Figure 9. Effective stress and deformation at 645 seconds after pouring.

An improved stress model would incorporate an interactive mold stress solution. This would deform in tandem with the metal to relieve stress or possibly break. Such a model would have to be capable of creep and fracture predictions, as well as handling the slip conditions between the metal and mold.


While significant technical accomplishments have been achieved, much work needs to be accomplished. These raw results must be translated into defect predictions for intuitive interpretation by the foundry engineer. With such a tool in place, the quality of aerospace components can be increased and delivery cycle time decreased. A logical next step is to incorporate microstructure modeling into casting simulation to predict latent heat release and grain growth. For a product designer, the biggest interest is in the strength of product, which is a function of the microstructure. Consequently, empirical and/or theoretical correlation between microstructure and strength must be determined.


The support of ARPA (MDA972-93-2-0001 and F33615-94-2-4439), the other ICCA members, and Howmet Corporation is gratefully acknowledged.


1. K.O. Yu et al., "Solidification Modeling of Single Crystal Investment Casting," AFS Transactions (1990).
2. J.S. Tu and R.K. Foran, "The Application of Defect Maps in the Process Modeling of Single-Crystal Investment Casting," JOM, 44 (6) (1992), p. 26.
3. A.M. Hines and J.S. Tu, "Modeling of Fluid Flow and Heat Transfer in the Solidification of Superalloy Investment Castings," Modeling of Casting, Welding, and Advanced Solidification Processes VI (Warrendale, PA, TMS, 1993), p. 461.
4. J.S. Tu, D.M. Olinger, and A.M. Hines, "Computer-Aided Development of an Investment Casting Process," JOM, 45 (10) (1993), p. 29.
5. B.A. Mueller and P. Monaghan, "Overview of the Investment Casting Cooperative Arrangement," JOM (September 1994), p. 17.
6. M. McLean, Directionally Solidified Materials for High Temperature Service,(London: The Metals Society, 1983), p. 26.


John S. Tu earned his Ph.D. in mechanical engineering at Michigan State University in 1988. He is presently the leader of the process modeling group at Howmet Corporation. Dr. Tu is also a member of TMS.

R. Kelly Foran earned his M.S. in mechanical engineering at Texas Technology University in 1984. He is currently a project engineer in the process modeling group at Howmet Corporation.

Albert M. Hines earned his M.S. in engineering science and mechanics at the University of Tennessee in 1990. He is currently a project engineer in the process modeling group at Howmet Corporation.

Paul R. Aimone earned his M.S. in materials science and engineering at Drexel University in 1986. He is currently a project engineer in the process modeling group at Howmet Corporation.

For more information, contact J.S. Tu, Howmet Corporation, 1500 S. Warner Street, Whitehall, Michigan 49461; (616) 894-7829; fax (616) 894-7826; e-mail jtu@howmet.com.


Production Applications for the Integrated Model Procedure

The integrated procedure outlined here was applied to three production components for validation. In each case, significant reductions in model construction time were achieved.


The first application is an aircraft engine structural casting (Figure A). It is a fairly complicated production geometry. It has double inner shrouds and one outer shroud joined by airfoil struts. A series of bosses on the outer shroud and extensive gating are required to reduce porosity. A solid model was received from the OEM and booleaned together with gating pieces. Automatic mesh generators were employed to produce finite-element meshes. At first, all three meshers failed to mesh the solid model; eventually, a mesh was able to be generated in four hours and drastically reduced the overall model construction time from three months to two weeks.

Figure A

Figure A. A finite-element mesh of an equiaxed structural casting.


The second example is a single-crystal airfoil casting (Figure B). Single-crystal airfoils are cast in a circular-symmetric arrangement. A single-crystal furnace is composed of an active heating chamber and a room-temperature chamber separated by a baffle serving as a radiation shield. During casting, the mold is gradually withdrawn from the upper chamber of the active-heating compartment and placed in the lower room-temperature chamber to establish a unidirectional solidification pattern.

Figure B

Figure B. A mushy-zone profile of single-crystal airfoil casting.

Taking advantage of circular symmetry, only a portion of the mold and furnace needs to be included in the model. The finite-element model was successfully constructed from a solid model in seven days compared to approximately 20 days without the solid model. In Figure B, the mushy zone is the white region.

It is interesting to note that the solidus isotherm located next to the baffle shows a relatively flat profile, and the liquidus isotherm in the upper chamber slants toward the center of the casting mold. This is because in the upper chamber the mold exterior is hotter than the mold center due to the induction heating, while in the lower chamber, the mold exterior is cooler than the mold center because of the room-temperature environment. A flat isotherm indicates that its temperature gradient is in the vertical direction and is aligned with the stacking axis of the airfoil.

At each location, the temperature gradient varies with time; however, what is important to a solidification process is the temperature gradient at solidification. McLean6 has shown that a high-temperature gradient provides favorable casting conditions for single-crystal growth. This is also supported by the empirical defect map,1,2 which suggests that as the temperature gradient becomes higher, the casting window grows wider, or the process becomes more robust. In fact, this is exactly what happens to the actual casting; the process produces high-yield castings. Note that the temperature gradient is a vector quantity that possesses both direction and magnitude. The direction of interest should be in the intended growth direction (i.e., stacking axis). Otherwise, a high gradient on the lateral direction will encourage growth along the secondary dendrite direction and produce scrap castings.

One criticism of casting simulation is its accuracy. Often, an inaccurate model will mislead the user and produce costly results. Therefore, a model should be validated to establish its credibility. By comparing the calculated temperatures and thermocouple measurements, we found the calculated temperatures to be close to the experimental data and within the tolerance of thermocouple measurements.


This integrated procedure was also applied to an equiaxed generic casting (Figure C). It looks like three boxes of different sizes joined together. The pour cup and downfeed (not shown) were placed to the left of the part, and runners fed metal into the casting component from left and bottom. Starting from a solid model, the finite-element model was completed in two days, compared to ten days with manual meshing. Coupled thermal and fluid-flow analysis were employed until the end of filling. A thermal-stress calculation was applied to the cool-down cycle for deformation prediction. The figure shows its effective stress as well as deformation prediction. The deformation has been exaggerated for ease of visualization.

Figure C

Figure C. Effective stress and deformation of a tri-box casting.

During solidification, the casting component is subjected to two phases of thermal stress. The first phase occurs at the early stage of solidification when the part is solidifying and the gating is still in a molten state. At this time, the right side of the boxes starts to shrink, while the left-hand side is kept warmer by the gating. As a result, the boxes are bent toward the right side. Phase two occurs when the gating starts to solidify, and the part is deformed by the shrinking runners. Consequently, high stress develops at the locations of gating attachment, such as the high-stress area at the center of the large box where a runner feeds into its bottom. This stage demonstrates a strong interaction between gating and cast part of the stress/strain distribution. Changing the gating design will certainly affect the load distribution of the system.

Copyright held by The Minerals, Metals & Materials Society, 1995

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