Investment casting of nozzle guide vanes from nickel-based superalloys: part II – grain structure prediction
© Torroba et al.; licensee Springer. 2014
Received: 24 July 2014
Accepted: 3 October 2014
Published: 20 November 2014
The control of grain structure, which develops during solidification processes in investment casting of nozzle guide vanes (NGVs), is a key issue for optimization of their mechanical properties. The main objective of this part of the work was to develop a simulation tool for predicting grain structure in the new generation NGVs made from MAR-M247 Ni-based superalloy. A cellular automata - finite element (CAFE) module is employed to predict the three-dimensional (3D) grain structure in the as-cast NGV. The grain structure in the critical sections of the experimentally cast NGV is carefully analyzed, the experimental results are compared with the modeling outcomes, and the model is calibrated via tuning parameters which govern grain nucleation and growth. The grain structures predicted by the calibrated model show a very good accordance with the real ones observed in the critical sections of the as-cast NGV. It is demonstrated that the calibrated CAFE model is a reliable tool for the foundry industry to predict grain structure of the as-cast NGVs with very high accuracy.
KeywordsNi-based superalloys Investment casting Nozzle guide vanes Modeling Cellular automata finite element (CAFE) module Grain structure
Solidification microstructure is of great importance for controlling the properties and the quality of the nozzle guide vanes (NGVs) produced via investment casting. In the last decades, emergence of accurate simulation capabilities and development of rigorous analytical models have contributed to a better understanding of solidification process and enabled prediction of solidification grain structure.
Phase-field models have attracted considerable interest since the early 90s to describe phase transitions for a wide range of systems . Phase-field models based on the rigorous framework of reversible thermodynamics , have been developed to describe both the solidification of pure materials  and binary alloys ,. They also have been used extensively to simulate numerically dendritic growth into an undercooled liquid -. These computations provide realistic simulations of dendritic growth, including side arm production and coarsening. Systems with three phases as well as grain structures with an ensemble of grains of different crystallographic orientations have also been modeled by the phase-field method using a vector-valued phase field -. The shortcoming of phase-field method is the very fine grid size (<1 μm) required to capture the solid–liquid boundary layer, limiting the size of domains which can be simulated (e.g., <1 mm2 in 2D) .
Cellular automata (CA) is another technique widely applied in modeling of solidification. The CA technique was originally developed by Hesselbarth and Göbel . It is based on the division of the simulation domain into cells, which contain all the necessary information to represent a given solidification process. Each cell is assigned information regarding the state (solid, liquid, interface, grain orientation, etc.) and the value of the calculated fields (temperature, composition, solid fraction, etc.). In addition, a neighborhood configuration is selected, which includes the cells that can have a direct influence on a given cell. The fields of the cells are calculated by analytical or numerical solutions of the transport and transformation equations. The change of the cell states is calculated through transition rules, which can be analytical or probabilistic. When these rules are probabilistic, the technique is called stochastic. The important feature of the method is that all cells are considered at the same time to define the state of the system in the following time step. Thus, the computational time step can be directly related to the physical time step.
The CA technique is often coupled with finite difference (FD) or finite element (FE) methods that makes it possible to obtain more accurate results. The modeling technique based on combining the CA method for tracking the solid–liquid front location with a FD solution of solute diffusion is referred to as CAFD model. This model was successfully used to simulate dendritic growth in a range of alloys ,. The CAFD model solves the solute conservation equation subjected to equilibrium conditions at the solid–liquid interface. The model simulates the solutal interaction within the developing dendritic network, predicting when overgrowth or branching will occur. The model was applied to investigate the effect of changing the pulling velocity on directionally solidified dendritic structures in Ni-based superalloys .
Rappaz and Gandin  started to explore the possibility of coupling FE heat flow computations with two-dimensional (2D) CA calculations describing the mechanisms of nucleation and growth of dendritic grains. The first model was applied only to small specimens of uniform temperature, i.e., it was an isothermal model. One year later, Gandin and Rappaz  extended the model to non-uniform temperature situations, and the modeling tool was referred to as cellular automata - finite element (CAFE) module. In 1997, Gandin and Rappaz  proposed a three-dimensional (3D) CA algorithm to model the growth of octahedral dendritic grains from the liquid phase. The 3D CAFE module was able to account for different cooling conditions, crystallographic orientations, and growth kinetics parameters. The CAFE model is based on the concept of marginal stability to uniquely define the dendrite tip radius, allowing the analytical solution of Kurz, Giovanola, and Trivedi (KGT) to be applied . CAFE models do not incorporate details of dendritic growth, but they are very useful for simulating grain structures on orders of magnitude larger simulation domains than is possible using the phase-field method. Another advantage of CAFE models is a clear prediction of grain size and shape.
The developed 3D CAFE module found a wide application for simulation of solidification grain structure in casting of complex shape parts. Gandin et al.  were first to apply it for grain structure prediction in directionally solidified blades. In particular, the growth competition occurring among columnar grains was directly reproduced, taking into account the crystallographic orientation of the grains and the temperature evolution in representative 3D investment cast parts. Seo et al.  successfully applied the model to predict grain structure in turbine blades produced via investment casting of CM247LC Ni-based superalloy. The overall appearance of grain structure in the cast blades was very well reproduced by the CAFE module at various investment casting conditions. Wang et al.  applied the CAFE module for simulation of grain selection during single crystal casting of a DD403 Ni-based superalloy with spiral grain selector, and the model was validated experimentally via investment casting using different spiral geometries. It was demonstrated that the CAFE module was a reliable tool for optimization of crystal orientation via manipulation with mold geometry.
The second part of our work aims to develop the CAFE module for grain structure prediction in the new generation NGVs to be produced via investment casting in a real plant process. Along with the thermal model and ProCast model for porosity prediction, it will form a modeling tool for further optimization of the NGV design at industrial scale.
Description of the modeling tool
The CAFE module is a software tool which allows the prediction of structures of castings in which columnar and equiaxed crystals are formed. CAFE is based on a stochastic model which combines grain nucleation and grain growth algorithms with the calculation of the heat transfer by FE as described by Gandin et al. . These algorithms and their parameters are considered below.
Grain nucleation algorithm
Initial values of the parameters for the surface and volume nucleation algorithms
1 · 106
1 · 109
Grain growth algorithm
Chemical composition of Mar-M247 Ni-based superalloy
Values of parameters for the growth kinetics function of Mar-M247 Ni-based superalloy (CAFE database)
6.3 · 10−7
3.33 · 10−6
All parameters defined above are considered by the software to calculate the transition from equiaxed to columnar grains. No specific parameter is used to determine this transition, being described by the grain growth competition, which depends on the mean undercooling in each location of the mushy zone .
It is seen that the most important data to perform correct calculations with the CAFE module are provided by the thermal model, so a reliable thermal model well describing the real solidification process is required. A detailed description of the thermal model used in our work can be found in the first part of this manuscript.
Domain selection: the model includes not only the cast part but also other elements such as the mold, insulation layer, etc. Therefore, the domain of interest is to be selected. The areas of no interest, such as the feeding system, the pouring cap, etc. can be ignored.
General parameters: the cell size and the number of cells per block are defined at this point. In our case, the selected values are 60 μm for the cell size, and each block is composed of a cube of 10 × 10 × 10 cells.
Window definition: the zones for calculations are to be defined. In our case, only critical sections of the NGV are investigated. Modeling results for these sections will be compared with results from experimental analyses of real grain structure. Otherwise, analysis of a whole part would lead to very time-consuming calculations.
Surface nucleation (nucleation algorithm): values that describe Gaussian distribution for surface nucleation (Equation 1) must be defined (Table 1). Since these values depend on the alloy, cast shape and casting procedure, they are calibrated by comparison of modeling and experimental results.
Calibrated values of parameters for the surface and volume nucleation algorithms
5.5 · 106
Results: after definition of zones for modeling (window definition), the CAFE module may request to store additional information such as cuts/planes of interest.
Once the CAFE pre-processor is settled, the CAFE solver is run. The obtained grain structure is demonstrated by Visual-Viewer (CALCOM Software).
Material and experimental procedures
The MAR-M247 Ni-based superalloy was chosen as the material for this investigation. The chemical composition of the material is presented in Table 2. Preparation of the ceramic molds and investment casting process was described in detail in the first part of the manuscript. The as-cast NGV was cut into smaller specimens for analysis of grain structure. The selected areas for grain structure evaluation are shown below in the ‘Conclusions’ section. The specimens were ground and polished to a mirror-like surface using standard metallographic technique. The polished specimens were etched using a chemical solution consisting of 25 g FeCl3, 60 ml HCl, and 25 ml H2O to reveal grain structure.
The optical microscope OLYMPUS BX51 (Olympus Corporation, Shinjuku-ku, Japan) was used for characterization of grain structure. At least three images were taken from each area of interest. Quantitative analysis of grain structure (grain size, standard deviation of grain size, and aspect ratio) was performed using ANALYSIS software. The grain size was measured as an equivalent circle diameter due to complex shape of some grains. Aspect ratio was calculated as a ratio of grain length to its width, as specified in the ANALYSIS software.
Results and discussion
Modeling vs. experimental
After first comparison between experimental and calculated results, the parameters governing the nucleation algorithm in the CAFE module were calibrated. The final grain structure predicted by the CAFE module for four critical NGV sections (transversal section of a hollow vane, transversal and longitudinal sections of a solid vane, and longitudinal section of the bottom platform) is compared with the real grain structure of the as-cast NGV. The comparison is based on (1) visual comparison of grain structure for critical sections of the NGV and (2) comparison of average grain size, standard deviation of the grain size, and aspect ratio of grains for these NGV sections.
The final calibrated values for the surface and volume nucleation algorithms are presented in Table 4. As calibrated values will remain the same for the full cast part, the prediction of the grain structure at any location of the piece will be possible. It should be noted that the final values of parameters for surface nucleation are close to the original ones proposed by Precicast Bilbao (Table 1). Nevertheless, even such a small difference can significantly affect the final modeling result.
Grain structure on transversal section of a hollow vane
Average grain size (μm)
Standard deviation (μm)
Grain structure on transversal section of a solid vane
Average grain size (μm)
Standard deviation (μm)
Grain structure on longitudinal section of a solid vane
Comparison of grain structure predicted by CAFE model with experimental results for longitudinal section of solid vane (Figure 7 )
Average grain size (μm)
Standard deviation (μm)
Grain structure on longitudinal section of a bottom platform
Average grain size (μm)
Standard deviation (μm)
The comparison of the modeled grain structure with the real one formed in the critical sections of the as-cast NGV clearly shows that the CAFE module is a very useful tool for prediction of grain structure in the complex shape parts manufactured from Ni-based superalloys via investment casting. It is able to predict with high accuracy the size, shape, and orientation of grains throughout the complex shape part. The thermal model and models for porosity and grain structure prediction constitute a tool for further improvement of NGV design. This tool can provide the optimum parameters for investment casting at low cost in a quick manner. It should be also noted that thus obtained modeling results on porosity and grain structure could potentially be used for modeling of mechanical and functional properties of various sections of NGVs. So the integrated modeling tools could be developed in the future, which will dramatically minimize or even eliminate the number of experimental casting trials.
A CAFE module was employed to predict the 3D grain structure in NGVs manufactured from Ni-based superalloys via investment casting. The grain structure of the critical sections in the experimentally cast NGV was carefully analyzed, the experimental results were compared with preliminary grain structure prediction, and the model was calibrated via tuning parameters in the algorithms describing grain nucleation and growth.
It is demonstrated that the calibrated CAFE model is a reliable tool for the foundry industry to predict grain structure in the new design NGVs with high accuracy. Microstructure consisting of small equiaxed grains is predicted in the trailing edge and thin walls of the vanes, where fast solidification occurs. Grain growth follows the heat flux directions described by the thermal model, so larger grains appear in the thicker sections. The predicted grain size is always in the range of grain sizes measured in the real as-cast NGV, though the CAFE module provides smaller standard deviation. Transition from equiaxed to columnar grains is correctly predicted in the bottom platform of the NGV.
It is outlined that the calibrated CAFE module is a useful and reliable tool for the foundry industry to predict grain structure of the as-cast NGVs.
This investigation was carried out in frame of the VANCAST project (EU, FP7, ERA-NET MATERA+). SM and IS acknowledge gratefully the Spanish Ministry of Economy and Competitiveness for financial support through the Ramon y Cajal fellowships.
- Janssens KGF, Raabe D, Miodownik Y, Kozeschnik MA, Nestler B: Computational Materials Engineering. Elsevier Academic Press, Burlington, MA, USA; 2007.Google Scholar
- Penrose O, Fife PC: Thermodynamically consistent models of phase-field type for the kinetic of phase transitions. Phys D 1990, 43: 44–62. doi:10.1016/0167–27890167–2789(90)90015-HView ArticleGoogle Scholar
- Wang SL, Sekerka RF, Wheeler AA, Coriell SR, Murray BT, Braun RJ, McFadden GB: Thermodynamically-consistent phase-field models for solidification. Phys D 1993, 69: 189–200. doi:10.1016/0167–27890167–2789(93)90189–8View ArticleGoogle Scholar
- Caginalp G, Fife PC: Phase field methods of interfacial boundaries. Phys Rev B 1986, 33: 7792–7794. doi:10.1103/PhysRevB.33.7792View ArticleGoogle Scholar
- Lowen H, Bechoefer J, Tuckerman LS: Crystal growth at long times: critical behavior at the crossover from diffusion to kinetics-limited regimes. Phys Rev A 1992, 45: 2399–2415. doi:10.1103/PhysRevA.45.2399View ArticleGoogle Scholar
- Warren JA, Boettinger WJ: Prediction of dendritic growth and microsegregation patterns in a binary alloy using the phase-field method. Acta Metall Mater 1994, 43: 689–703. doi:10.1016/0956–7151(94)00285-PView ArticleGoogle Scholar
- Kobayashi R: Modeling and numerical simulations of dendritic crystal-growth. Phys D 1993, 63: 410–423. doi:10.1016/0167–2789(93)90120-PView ArticleGoogle Scholar
- Wheeler AA, Murray BT, Schaefer RJ: Computation of dendrites using a phase field model. Phys D 1993, 66: 243–262. doi:10.1016/0167–27890167–2789(93)90242-SView ArticleGoogle Scholar
- Wang SL, Sekerka RF: Algorithms for phase eld computations of the dendritic operating state at large su-. percoolings. J Comp Phys 1996, 127: 110–117. 10.1006/jcph.1996.0161View ArticleGoogle Scholar
- Provatas N, Goldenfeld N, Dantzig J: Efficient computation of dendritic microstructures using adaptive mesh refinement. Phys Rev Lett 1998, 80: 3308–3311. doi:10.1103/PhysRevLett.80.3308View ArticleGoogle Scholar
- Chen LQ, Young W: Computer simulation of the domain dynamics of a quenched system with a large number of nonconserved order parameters: the grain-growth kinetics. Phys Rev B 1994, 50: 15752–15756. doi:10.1103/PhysRevB.50.15752View ArticleGoogle Scholar
- Chen LQ: A novel computer simulation technique for modeling grain growth. Scr Metall Mater 1995, 32: 115–120. doi:10.1016/S0956–716X(99)80022–3View ArticleGoogle Scholar
- Steinbach I, Pezzolla F, Nestler B, Seesselberg M, Schmitz GJ, Rezende J: A phase field concept for multiphase systems. Phys D 1996, 94: 135–147. doi:10.1016/0167–27890167–2789(95)00298–7View ArticleGoogle Scholar
- Nestler B, Wheeler AA: Anisotropic multi-phase-field model: interfaces and junctions. Phys Rev E 1998, 57: 2602–2609. doi:10.1103/PhysRevE.57.2602View ArticleGoogle Scholar
- Kobayashi R, Warren JA, Carter WC: Vector-valued phase field model for crystallization and grain boundary formation. Phys D 1998, 119: 415–423. doi:10.1016/S0167–2789(98)00026–8View ArticleGoogle Scholar
- Garcke H, Nestler B, Stoth B: On anisotropic order parameter models for multi-phase systems and their sharp interface limits. Phys D 1998, 115: 87–108. doi:10.1016/S0167–2789(97)00227–3View ArticleGoogle Scholar
- Boettinger WJ, Warren JA: The phase-field method: simulation of alloy dendritic solidification during recalescence. Metall Mater Trans A 1996, 27: 657–669. doi:10.1007/BF02648953View ArticleGoogle Scholar
- Hesselbarth HW, Göbel IR: Simulation of recrystallization by cellular automata. Acta Metall 1991, 39: 2135–2143. 10.1016/0956-7151(91)90183-2View ArticleGoogle Scholar
- Wang W, Kermanpur A, Lee PD, McLean M: Simulation of dendritic growth in the platform region of single crystal superalloy turbine blades. J Mater Sci 2003, 38: 4385–4391. doi:10.1023/A:1026303720544View ArticleGoogle Scholar
- Wang W, Lee PD, McLean M: A model of solidification microstructures in nickel based superalloys: predicting primary dendrite spacing selection. Acta Mater 2003, 51: 2971–2987. doi:10.1016/S1359–6454(03)00110–1View ArticleGoogle Scholar
- Rappaz M, Gandin CA: Probabilistic modelling of microstructure formation in solidification processes. Acta Metall Mater 1993, 41: 345–360. doi:10.1016/0956–7151(93)90065-ZView ArticleGoogle Scholar
- Gandin CA, Rappaz M: A coupled finite element-cellular automaton model for the prediction of dendritic grain structures in solidification processes. Acta Metall Mater 1994, 42: 2233–2246. doi:10.1016/0956–7151(94)90302–6View ArticleGoogle Scholar
- Gandin CA, Rappaz M: A 3D cellular automaton algorithm for the prediction of dendritic grain growth. Acta Mater 1997, 45: 2187–2195. doi:10.1016/S1359–6454(96)00303–5View ArticleGoogle Scholar
- Kurz W, Giovanola B, Trivedi R: Theory of microstructural development during rapid solidification. Acta Metall 1986, 34: 823–830. doi:10.1016/0001–6160(86)90056–8View ArticleGoogle Scholar
- Gandin CA, Rappaz M, Desbiolles JL, Lopez R, Swierkosz M, Thevoz PH (1997) 3D modeling of dendritic grain structures in turbine blade investment cast parts. In: Loria EA (ed) Proceedings of the TMS Meeting. TMS, p 121
- Seo SM, Kim IS, Jo CY, Ogi K: Grain structure prediction of Ni-base superalloy castings using the cellular automaton-finite element method. Mater Sci Eng A 2007, 449–451: 713–716. doi:10.1016/j.msea.2006.02.400View ArticleGoogle Scholar
- Wang N, Liu L, Gao S, Zhao X, Huang T, Zhang J, Fu H: Simulation of grain selection during single crystal casting of a Ni-base superalloy. J Alloys Compd 2014, 586: 220–229. doi:10.1016/j.jallcom.2013.10.036View ArticleGoogle Scholar
- Gandin CA, Desbiolles JL, Rappaz M, Thevoz P: A three-dimensional cellular automation-finite element model for the prediction of solidification grain structures. Metall Mater Trans A 1999, 30: 3153–3165. doi:10.1007/s11661–999–0226–2View ArticleGoogle Scholar
- Lipton J, Glicksman ME, Kurz W: Equiaxed dendrite growth in alloys at small supercooling. Metall Trans A 1987, 18: 341–345. doi:10.1007/BF02825716View ArticleGoogle Scholar
- ProCast user Manual & Technical Reference:Technical Reference (2007). Version 6.1. ESI software, France; 2007.Google Scholar
- Qingyan X, Baicheng L, Dong P, Jing Y: Progress on modeling and simulation of directional solidification of superalloy turbine blade casting. Res Develop 2012, 2: 69–77.Google Scholar
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