Application of a new porosity model for predicting shrinkage defects in castings

INTRODUCTION

In modern foundry production, issues related to the implementation of new castings, increasing yield, reducing labor, and material costs are addressed through the use of software designed to simulate casting processes. This allows for a reduction in the costs of designing and adjusting foundry technology, as the development of the feeding system and the time-temperature variables of the technological process are carried out not in real and costly melts, but in the virtual space of a mathematical simulation.

The low cost and short timelines of computer experiments, as well as the large volume and clarity of the information obtained regarding the influence of the technological process and the quality of the future casting, make computational simulation an essential tool in experimental production.

Years of experience using commercial foundry software shows that the most demanded procedure is the prediction of macro and micro shrinkage porosity in castings.

The adequacy of the mathematical simulations implemented in foundry software can be easily evaluated by the results of their application in numerous foundry plants. There is convincing evidence that the simulation results quite accurately predict the location and size of the areas affected by shrinkage defects.

In practice, a qualitative level porosity prediction is generally sufficient. However, foundry software developers, in response to the increasing demands of modern production, aim to improve the simulations to achieve not only a qualitative image but also a fairly accurate quantitative picture of porosity.

The porosity simulation used to solve practical problems in foundry production is always a simplified simulation model. In this simulation, the process of shrinkage defect formation is divided into two relatively independent processes: the process of shrinkage cavity formation and the process of microporosity formation.

The objective of this study is the first part of the porosity simulation: the process of shrinkage cavity formation at different crystallization rates. The paper presents the results of shrinkage defect simulation using two different modules. Calculations were performed in the standard porosity module of "PoligonSoft" [1] and in the new porosity simulation, included in the software as an alternative model.

Porosity models in PoligonSoft

The macroscopic theory of alloy crystallization in its most general form was formulated by V.A. Zhuravlev [2]. His work presents a complete system of equations that describes thermal, diffusion, and hydrodynamic processes in the two-phase region of the casting.

The PoligonSoft system is one of the most well-known Russian commercial programs for the simulation of casting processes, with its porosity model developed based on the macroscopic theory of alloy crystallization.

In the standard porosity model of the PoligonSoft program, the formation of shrinkage cavities occurs due to the drop in the free surface of the liquid metal, caused by contraction during solidification. The flow of liquid metal occurs under the action of gravitational forces. The scenario for the formation of a shrinkage cavity depends on the fraction of solid phase in the liquid metal near the free surface. From the moment a stationary solid structure forms, the flow of liquid metal begins to be influenced by surface tension forces. When the capillary effect surpasses the gravitational forces, the flow of liquid metal and the formation of the shrinkage cavity stop.

The magnitude of the drop in the free surface of the casting is calculated at each time step of the simulation, based on the condition of mass conservation of the solidifying metal.

In the new porosity model of the PoligonSoft casting simulation system, the mechanism of formation for internal shrinkage cavities and macroporosity has been refined, where porosity's volumetric fraction is comparable to the contraction coefficient during solidification. It is assumed that pore formation requires work to create a new interface surface. The process of pore formation is a form of stress relaxation that arises in the liquid metal due to its deformation during solidification. The viability of the formed pores is determined by the balance between the negative pressure in the liquid metal and the surface tension force that tends to close the pore. The location of pore formation, in addition to pressure, depends on the dispersion of the dendritic structure, which limits the pore size. It is also important to determine which of the two possible porosity development processes is energetically more favorable: the formation of a new pore or the growth of an existing one [3, 4].

The formation of internal shrinkage cavities in a closed thermal node begins with the appearance of a free surface of the liquid metal. According to the new concept of the porosity model, the free surface of the liquid metal is the interface boundary "liquid metal-environment," whose formation is possible when the pressure in the thermal node drops to a certain critical value P_crit​. Until this critical pressure is reached, there is an increase in the thickness of the solid metal surrounding the liquid metal, that is, an increase in the thickness of the layer over the future shrinkage cavity.

The free surface of the liquid metal forms only if there is no continuous dendritic structure of solid phase in the liquid metal. If such a structure has already formed, it is not possible for a free surface of the liquid metal to move freely. In this case, metal contraction will not lead to the formation of a shrinkage cavity but to the formation of dispersed macroporosity. The size and shape of the pores formed will be determined by the configuration of the interdendritic space.

Another feature of the new porosity model is the consideration of the capillary effect. It is assumed that the movement of liquid metal under the action of gravitational forces is impossible. Surface tension forces prevent the drainage of the interdendritic space when the free surface of the liquid metal descends.

Casting Technology

The evaluation of the adequacy of the porosity models in SKM LP «PoligonSoft» was conducted on 14X17N2L steel castings. The metal was poured into ceramic molds with a wall thickness of 10-12 mm, placed inside a steel box. Crushed chamotte from ceramic molds was used as support filler. The molds were preheated to a temperature of 950°C for 14-16 hours. The metal was poured into the molds within 5 minutes after the mold was removed from the furnace. The pouring temperature was 1580°C. All operations were conducted outdoors.

Two types of castings were produced using this technology. The first was a simple casting, for which a cylinder with a diameter of 40 mm and a length of 335 mm, including the riser, was used as a model. The weight of the casting was 3.7 kg.

The second casting was a serial casting block with a rectangular section model of 45x55 mm and a total length of 370 mm, with a weight of 9.5 kg.

Two identical castings were placed in the mold. After filling the mold, the surface of the metal in one of the molds was insulated with a layer of thermal insulating powder. The surface of the metal in the other mold remained uninsulated.

Casting Test Results

The obtained castings were milled along their entire length. The metal was removed up to the plane of symmetry of the sprue. Figure 1 shows the shrinkage cavities formed in the castings with the free surface of the metal insulated and in the castings without such insulation.

Figure 1. Shrinkage cavities in 14X17N2L steel castings with the free surface of the metal insulated (a, c) and uninsulated (b, d). (a, b) – rectangular section; (c, d) – cylindrical section.

In castings with the free surface of the metal insulated, the shrinkage cavity forms due to the growth of the solid phase on the walls of the casting cup and the descent of the free surface of the metal caused by the contraction of the solidifying metal. As a result, a classically shaped conical shrinkage cavity is obtained, as observed in Figure 1a.

The formation of the shrinkage cone stops when the solid phase growing from the opposite walls of the casting cup meets at the center. In the thermal node formed, a series of closed shrinkage cavities arise within the body of the casting.

In the castings shown in Figures 1b and 1d, the intense cooling of the liquid metal surface leads to the early formation of a closed thermal node within the casting cup. As a result, there is a significantly larger amount of liquid metal at a higher temperature in the thermal node. At the moment of formation of the free surface of the metal, a gas layer arises between the liquid metal and the solid phase above, drastically reducing the intensity of cooling of the liquid metal. Additionally, it is important that the free surface of the metal occupies an insignificant part of the casting's cross-section. This means that the rate of descent of the free surface of the metal is greater than in the case of the insulated casting cup (Figures 1a and 1c). All of this creates conditions for the formation of an extended shrinkage cavity instead of a series of small cavities.

It is interesting to note that the depth of penetration of the shrinkage cavities in the body depends little on the heat transfer conditions on the metal surface. Quantitative analysis showed that the area of the shrinkage cavity section in Figure 1a is 18.6%, while in Figure 1b it is 13.8% of the casting area, meaning the volume occupied by the voids is approximately the same. Therefore, it can be assumed that the shrinkage volume, compensated by the liquid metal from the shrinkage cavities, is approximately the same in both cases.

It should be noted that open shrinkage cavities maintain the circular symmetry of the cup in which they form (Figure 1a). In closed shrinkage cavities, only the solid metal layer beneath which the cavity is located exhibits signs of symmetry. The initial point of formation of this cavity is the point of minimum pressure in the closed thermal node. With a strictly vertical arrangement of the casting and an ideal circular symmetry of the cup and inward-curved metal layer, as in Figures 1b and 1d, the area of minimum pressure should be at the center of symmetry and circular in shape. If these conditions are not met, when the shape is not strictly vertical and the metal layer is unevenly curved due to fluctuations in heat transfer, the pressure minimum is located at a point whose location is random. The free surface of the metal formed in the vicinity of this point will not immediately occupy the entire cross-section of the thermal node. This determines the asymmetry of the shrinkage cavity, which we observe in Figures 1b and 1d.

Simulation Methodology

The simulation of the crystallization process of the aforementioned castings was carried out using the PoligonSoft casting process simulation system and then repeated under similar conditions in the ProCAST system.

The calculations were performed in two stages. In the first stage, the cooling process of the ceramic molds, located in the workshop awaiting casting, was simulated. The results of this calculation provide the initial temperature distribution in the mold, necessary for the second stage of calculation. In the second stage, the crystallization process of the metal was simulated from the moment it was poured into the mold until complete solidification.

The thermophysical properties of the metal, necessary for the calculations, were computed based on the chemical composition of the alloy in the thermodynamic database included in the ProCAST system. The calculations were performed using the Scheil non-equilibrium crystallization model, which assumes limited diffusion in the solid phase [5, 6]. The chemical composition of 14X17N2L steel is presented in Table 1. The thermophysical properties of the ceramic shell and support material are presented in Table 2.

Table 1. Chemical Composition of 14X17N2L Steel

Table 2. Thermophysical Properties of the Mold and Support Material

The crystallization conditions of the casting significantly depend on the heat transfer conditions at the contact between the casting and the mold, as well as at the interfaces of all solid bodies: the mold, the support material, and the mold box.

It was assumed that the heat transfer coefficient at the metal-mold interface decreases significantly from the moment a solid layer forms on the surface of the casting (Table 3).

However, in the calculations, it was considered that thermal energy is transferred in two ways at the contact between the support material and the solid bodies. One part of the thermal energy is transferred through direct contact of the granular material particles with the surfaces of the bodies, and the other part is transferred by thermal radiation [7]. It was assumed that 50% of the direct contact surface of the support material particles with other bodies participates in thermal exchange by contact, while the rest of the surface of the solid bodies (mold and mold box) participates in thermal exchange by radiation. The heat transfer coefficient at the contact was set at 100 W/(m²·K), and the emissivity factor of the surfaces participating in thermal exchange by radiation was set at 0.8.

Table 3. Heat Transfer Coefficient at the Metal-Mold Interface

Porosity Model Configurations

In this work, all calculations in PoligonSoft were performed using the standard porosity model and then repeated with the new porosity model. The calculations in the ProCAST system were conducted using the standard porosity model, which is very similar to the standard porosity model of PoligonSoft with respect to shrinkage cavity formation.

In all calculations in PoligonSoft, the default configurations of the porosity models were used. It is noteworthy that, for the new porosity model, the part of the standard model configurations related to the flow of liquid metal in the two-phase zone and microporosity formation is relevant. The specific configurations of the new model related to shrinkage cavity and macroporosity formation include the compressibility modulus of the liquid metal E, the surface tension coefficient σ, and the distance between the secondary dendrite arms λII. An important parameter of the porosity model is the critical pressure P_crit​, which determines the formation of a new interface surface, i.e., the free surface of the liquid metal or a pore. As mentioned earlier, in the new porosity model, P_crit​ is a crucial variable. In the standard porosity model, P_crit​ always has a positive value that is only significant for microporosity formation. The values set for the calculations approximately correspond to the physical representation of shrinkage defect formation in the standard model. The values of these configurations used in the calculations are: E=2000Mpa, σ= 1*10^-6N/m,  λ_II=30μm,  P_crit=-0.1Mpa.

The configuration values for the standard porosity model of PoligonSoft responsible for shrinkage cavity formation were: Pl₁=0.7, Pl₂=0.4, Pl₃=0.3. . The equivalent parameters in the standard porosity model of ProCAST were MACROFS=0.7 and PIPEFS=0.3.

Simulation Results

The simulation results for shrinkage defects in castings with rectangular and cylindrical sections are presented in Figures 2, 3, and 4, 5, respectively. Figures 2a-5a show the results obtained with the standard porosity model, while Figures 2b-5b present the simulation results using the new porosity model of PoligonSoft. For a complete comparison, Figures 2c-5c show the results obtained with the standard porosity model of the ProCAST system. All figures display a longitudinal section of the casting, as seen in Figure 1.

For the calculations performed in PoligonSoft, the shrinkage defects are shown in two ways. The images on the left display only the shrinkage cavities, while the images on the right show the fields of all the macro- and microporosity present in the casting.

Casting with the Insulated Free Surface of the Metal

In the case of the insulated free surface of the metal (Figures 2, 3), the simulation results for the shrinkage cavity generally correspond to the real experiment (Figures 1a, 1c). Calculations performed with the standard porosity model of PoligonSoft show a conical shrinkage cavity, at the bottom of which there is a zone of macro- and microporosity. The overall dimensions of the shrinkage defect zone in the casting cup correspond to the real experiment. However, the shrinkage cavity obtained in the calculation is more shallow than in the actual casting. The calculations in ProCAST show a small shrinkage cavity in the casting cup, practically identical to that in Figure 2a.

Figure 2. Shrinkage cavities in a casting with a rectangular section and an insulated free surface of the metal.
‍a) – standard porosity model; b) – new porosity model; c) – ProCAST porosity model.
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Below the shrinkage cavity, in the body of the casting, the calculations show the presence of shrinkage defects. The standard porosity model of PoligonSoft (Figure 2a) shows an extensive zone of shrinkage defects, with an area larger than in Figure 1a, but its extent and location in the casting correspond well to the actual piece. The volumetric fraction of porosity in this zone is only 5-10% and does not constitute a shrinkage cavity, but in terms of shrinkage volume, it could provide a value close to the experiment.

Figure 3. Shrinkage cavities in a cylindrical casting with an insulated free surface of the metal.
‍a) – standard porosity model; b) – new porosity model E=2000Mpa, P_crit=-0.1Mpa.; c) – modelo de porosidad ProCAST.

The new porosity model of PoligonSoft and the calculations in the ProCAST system show a similar representation of shrinkage defects in the cylindrical casting (Figures 3b and 3c). The porosity in the body of this piece is presented as a series of local zones with a volumetric porosity fraction of approximately 40-50% (Figures 3b and 3c), which reasonably corresponds to the actual casting (Figure 1c)

In the case of the rectangular section piece, the new porosity model of PoligonSoft and the standard model of ProCAST confidently predict the presence of an internal cavity at the center of the cylinder (Figures 2b and 2c), although its dimensions are smaller than in Figure 1a. Additionally, some smaller shrinkage cavities that are present in the actual casting are missing.

Casting with the Non-Insulated Free Surface of the Metal

When the liquid metal comes into direct contact with the environment, there is more intense cooling of the liquid metal surface. This leads to the formation of a metal layer and, consequently, a closed shrinkage cavity (Figures 1b, 1d). The simulation results for the formation of the shrinkage cavity in the case of direct contact between the liquid metal and the environment differ significantly from the real experiment (Figures 1b and 1d). In the standard porosity model of PoligonSoft, an open shrinkage cavity forms in both types of castings, which contradicts the real experiment. A thin layer of solid metal (porosity of 10-70%) appears only in the new porosity model for rectangular section castings. The standard ProCAST porosity model predicts the appearance of a metal layer whose thickness corresponds to the actual casting.

In the body of the casting, all models predict the appearance of shrinkage defects. However, the new porosity model of PoligonSoft and ProCAST are considerably closer to reality, although these predictions do not show a continuous shrinkage cavity, as in the center of the piece shown in Figure 1b.

Figure 4. Shrinkage cavities in a casting with a rectangular section and a non-insulated free surface of the metal.
a) – standard porosity model; b) – new porosity model E=2000Mpa, P_crit=-0.1Mpa.;  c) – ProCAST porosity model.

Figure 5. Shrinkage cavities in a cylindrical casting with a non-insulated free surface of the metal.
a) – standard porosity model; b) – new porosity model; c) – ProCAST porosity model.

Discussion of Results

As can be seen from the results obtained, the porosity models considered successfully solve the practical task of determining the size and location of shrinkage defects in the casting. The discrepancies between the simulation results and the defects in the real castings have several causes. The main reason is that all porosity models are deterministic, meaning the simulation outcome is completely determined by the algorithm, the values of the input variables, and the initial state of the system.

The formation of a shrinkage cavity is related to the pressure drop in the two-phase zone of the casting or in a closed thermal node and occurs in all nodes of the computational mesh where the pressure reaches a critical value. The symmetry of the casting and, consequently, the symmetry of the boundary conditions of the thermal problem inevitably lead to the symmetry of the shrinkage defect zone. The only source of randomness in the simulation is the asymmetry of the finite element mesh.

In reality, there are many random factors that cannot be accounted for. These include the non-vertical arrangement of the casting, uneven mold thickness, and non-uniform composition of the support material. The deviation from the vertical axis is clearly visible in all the castings shown in Figure 1. The deviation from the vertical leads to the formation of a metal layer with an asymmetric bulge (Figures 1b, 1d). The formation of a closed shrinkage cavity begins with the formation of the free surface of the metal in the area of minimum pressure, i.e., at the highest point where the liquid metal exists. If the solid layer is not symmetrical and the casting is not arranged vertically, the minimum pressure area is reduced to a point. This leads to the formation of an elongated and narrow shrinkage cavity.

In Figure 1b, it is clearly observed how the shrinkage cavity extends to the side wall of the casting cup. It is natural to assume that the uneven thickness of the metal layer indicates fluctuations in heat transfer at the "metal-mold" interface. These fluctuations may arise due to the presence of combustible material particles in the support material or due to the spillage of liquid metal outside the cup.

Another reason for the discrepancy between the simulation results and the experiment is the design of the porosity model algorithm. Porosity models in commercial programs include simplifications that drastically reduce computation time, which is important for engineering calculations. One of the techniques to simplify the problem concerns the flow of liquid metal during the formation of the shrinkage cavity. Since in each time step, a certain amount of liquid metal solidifies, the weight of the casting formally increases, as its volume, defined by the unchanged finite element mesh, remains constant. One way to adjust the casting volume to normalize the weight is to lower the metal level in the mold. Lowering the metal level in the mold is formally represented as "deactivating" the calculation mesh nodes above the free surface of the metal. This algorithm easily ensures mass constancy; however, as the comparison with the experiment shows, it introduces errors in determining the volume of the casting that is crystallizing. One of the visible consequences of this error is that the metal layer over the shrinkage cavity is too thin (Figure 4) or absent (Figure 5), which does not match the appearance of the actual castings (Figure 1b, 1d).

Conclusion

The porosity models of PoligonSoft allow for a highly probable and reliable determination of the location and size of shrinkage porosity zones in castings. Generally, this qualitative assessment of defects is sufficient to solve engineering problems.

The prediction of defects at a quantitative level, where not only the location of shrinkage defect zones can be compared with the actual casting, but also the volumetric fraction of the defect at a given point in the casting, requires improvements in simulation algorithms. Achieving this level of prediction is an important task with significant practical implications.

Within this task, the new porosity model of PoligonSoft has refined the mechanisms for the formation of closed shrinkage cavities and the appearance of shrinkage macropores. The results presented show that the prediction of shrinkage defects in the new model more closely resembles real castings.

When evaluating these results, it should be noted that the random factors inherent in industrial casting technology can have a strong impact on the shape and type of shrinkage defects. The results presented in this work allow for an evaluation of the applicability of these models to real production conditions. However, the true verification of the adequacy of the porosity models should be conducted on laboratory castings obtained under controlled experimental conditions.

REFERENCES

[1] Trademark of OAO "CSoft Development," Moscow, http://csdev.ru.
[2] Zhuravlev V.A. On the Macroscopic Theory of Alloy Crystallization // Proceedings of the Academy of Sciences of the USSR. Metals, 5. 1975. pp. 93-99.
[3] Monastyrskiy V.P., Ershov M.Yu. Simulation Model of Shrinkage Cavity and Macroporosity Formation // Russian Foundryman, No. 8, 2014, pp. 41-45.
[4] Monastyrskiy V.P. Modeling of Microporosity in Castings Solidifying under Directed Heat Transfer Conditions // Thermal Processes in Engineering, vol. 3, No. 1, 2011, pp. 20-27.
[5] Thermodynamic Database for Nickel-Based Superalloys: PanNickel 5.0, CompuTerm, LLC, USA.
[6] ProCAST, trademark of ESI Group, France, www.esi-group.com.
[7] Monastyrskiy V.P., Monastyrskaya E.V., and Zuev A.V. Thermophysical Features of Directed Crystallization Using Support Material // FKHOM. 2004. No. 5. pp. 79–87.

Translated by A.J. Camejo Severinov.
Original text in Russian.