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Thermo-mechanical effects and microstructural evolution-coupled numerical simulation on the hot forming processes of superalloy turbine disk

  • Zhang Haoqiang EMAIL logo , Cai Liu , Peng Dongli , Ronaldo Juanatas , Jasmin Niguidula and Jonathan M. Caballero
Published/Copyright: May 21, 2024
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High Temperature Materials and Processes
From the journal High Temperature Materials and Processes Volume 43 Issue 1

Abstract

Macroscopic deformation and microstructural evolution simultaneously exist in the hot forming processes of superalloy. In order to effectively and accurately study the hot forming processes of superalloy turbine disk with the numerical simulation method, a multi-scale finite element model of GH4065 superalloy turbine disk involving macroscopic and microscopic aspects was established by defining macro- and micromaterial model of superalloy, hot forming processing parameters, and boundary conditions. Via the numerical simulations of superalloy turbine disk, the macroscopic material flow and microstructural evolution behaviors in the hot forming processes of superalloy turbine disk were studied. Besides, the macroscopic deformation and microstructure distribution states after the hot forming processes were revealed and analyzed. A corresponding hot forming physical test of superalloy turbine disk was conducted to verify the results of the numerical simulation. Via the qualitative and quantitative analyses, it was concluded that the macroscopic deformation and microstructural evolution in the hot forming processes of superalloy turbine disk can be accurately predicted by the numerical simulation method.

Keywords: turbine disk; multi-scale finite element model; GH4065 superalloy; numerical simulation

1 Introduction

Turbine disk is a hot section component of aircraft engine and works under harsh conditions [1]. Wear and fracture are prone to occur in turbine disk due to thermal fatigue, corrosion fatigue, and mechanical stress fatigue in the working conditions [2]. Therefore, turbine disk has high requirements for mechanical properties. Considering the strength, toughness, heat resistance, and corrosion resistance of the material, GH4065 nickel-based superalloy has become an optimal material of turbine disk. GH4065 superalloy is a novel superalloy, which has outstanding processabilities and mechanical properties and has advantages in oxidation, corrosion, and radiation resistance [3]. GH4065 superalloy is a hard processing material at room temperature and often deformed at the elevated temperature [4,5,6]. Under high-temperature environment, not only macroscopic deformation but also microstructural evolution simultaneously occurs in the hot deformation processes of GH4065 superalloy [7]. As the compositions of the material are fixed, the microstructure could determine the performance of the material [8]. Therefore, the macroscopic deformation and microstructural evolution of GH4065 superalloy are both worth being emphatically analyzed and controlled in the forming processes of turbine disk.

Numerical simulation is a simple and effective method to study the hot forming processes of materials, which can avoid repeated trial and error as well as considerable waste of human and material resources [9]. At present, the numerical simulation method was mainly used to determine or optimize the macroscopic process parameters and solve the macroscopic forming problems of material during the hot forming processes. For example, Sun investigated the relationships between technological factors and the temperature rise, extrusion force during tube hot extrusion of IN718 superalloy via a numerical model [10]. In recent years, the analysis on microstructural evolution of superalloys was realized via the numerical simulation method. For example, Tian simulated the grain growth behaviors of P/M nickel-based superalloy during the heat treatment process [11]; Poelt conducted the simulations on the dynamic recrystallization of Ni-based superalloy [12]. On the one hand, most of the current numerical simulation studies on the macroscopic deformation and microstructural evolution of superalloys only considered the direct or critical forming processes, while ignoring the heating, temperature holding, transferring, and cooling processes. In these processes, there are also different degrees of microstructural evolution, which would ultimately affect the microstructure and performance of parts. Therefore, systematic analysis based on the numerical simulation method involving the whole processes should be carried out to study the microstructural evolution of superalloy and ensure the effectiveness and precision of numerical simulation. On the other hand, the current studies on the microstructural evolution of superalloy mainly focus on the single microstructural evolution mechanism, such as dynamic recrystallization or grain growth. In the actual hot forming processes of superalloy parts, dynamic recrystallization and grain growth often simultaneously occur and influence each other [13]. Therefore, dynamic recrystallization, grain growth, and their interactions should be considered in the finite element model.

In order to reveal the macroscopic deformation and microstructural evolution behaviors of superalloy turbine disk in the whole hot forming processes, in this research, a finite element model was established to conduct the thermo-mechanical–microstructural-coupled numerical simulation. The core of the finite element model mainly includes two parts. One part is the material models and parameters of GH4065 superalloy, the most important points of which are the constitutive model describing the macroscopic deformation and microstructural evolution models describing the microstructural evolutions including dynamic recrystallization and grain growth. These material models and parameters originate from physical tests and theoretical calculation. The macroscopic and microscopic models of GH4065 superalloy were coupled by the numerical simulation software DEFORM. The other crucial part is the process parameters and boundary conditions of the hot forming processes. Accurate definitions of process parameters and boundary conditions are the prerequisite for the effective numerical simulation. Based on the thermo-mechanical–microstructural-coupled finite element model, the macroscopic deformation and microstructural evolution in the whole hot forming processes of the superalloy turbine disk were simulated and analyzed. And the physical experiments involving heating, transferring, hot forming, and cooling processes and in accordance with the designed ones were conducted to verify the reliabilities of the numerical simulation results. This research provides a feasible path for the macroscopic and microscopic multi-scale numerical simulation of the hot forming processes and lays the foundation for the macroscopic deformation and microstructural evolution controls of superalloy forgings.

2 Finite element model establishment

2.1 Material model of GH4065 superalloy

Reliable material data and model are the premises of accurate numerical simulation. The chemical compositions of the turbine disk material, GH4065 superalloy with forged state, were 16.12% Cr, 13.09% Co, 4.14% Mo, 3.97% W, 3.65% Ti, 2.24% Al, 0.74% Nb, 1.25% Fe, and balanced Ni, which was evaluated by percentage of weight. Its initial average grain size was measured as 28 μm. The thermo-physical material parameters will change with the change of temperature, and the accuracy of numerical simulation can be guaranteed and improved using material parameters that change with temperature [14]. The thermal conductivity, Young’s modulus, thermal expansion coefficient, and heat capacity of GH4065 superalloy are shown in Tables 1–4. These material data were tested via a series of thermo-physical tests. Besides, the Poisson’s ratio of GH4065 superalloy was set as the constant of 0.28.

Table 1

Thermal conductivities of GH4065 superalloy under different temperatures

Temperature (°C) 20 100 300 500 700 800 900 1,000 1,100
Conductivity (t·mm·s−3·K−1) 10.31 11.88 15.17 18.46 24.14 25.09 25.71 26.31 29.01
Table 2

Young’s modulus of GH4065 superalloy under different temperatures

Temperature (°C) 20 100 300 500 700 800 900 1,000 1,100
Young’s modulus (GPa) 219 216 204 191 175 165 153 141 131
Table 3

Thermal expansion coefficient of GH4065 superalloy under different temperatures

Temperature (°C) 20 100 400 500 700 900 1,100
Thermal expansion coefficient 1.3 × 10−5 1.31 × 10−5 1.41 × 10−5 1.43 × 10−5 1.58 × 10−5 1.65 × 10−5 1.75 × 10−5
Table 4

Heat capacity of GH4065 superalloy under different temperatures

Temperature (°C) 20 100 300 500 700 800 900 1,000 1,100
Heat capacity (N·mm−2·°C−1) 3.62 3.77 4.01 4.28 5.02 5.44 5.35 5.53 5.68

To accurately describe the flow behaviors under high-temperature environment, the true stress–strain data shown in Figure 1 were employed as the constitutive model of GH4065 superalloy, which is the basis for accurately predicting the macroscopic deformation of GH4065 superalloy [15]. These true stress–strain data were obtained from isothermal compression tests conducted by Gleeble-3500 thermo-mechanical physical simulator. In the isothermal compression tests, specimens with a diameter of Φ8 mm and a height of 12 mm were, respectively, first heated to 1,100, 1,200, 1,300, or 1,400 K with a constant heating rate of 5 K·s−1, then held for 300 s to obtain uniform temperature, and subsequently compressed to 5.4 mm with a strain rate of 0.001, 0.01, 0.1, or 1 s−1, and eventually oil-quenched as soon as the compression process was completed. The range of the employed true stress–strain data covers the range of hot forming deformation parameters of GH4065 superalloy.

Figure 1 True stress–strain data of GH4065 superalloy corresponding to the strain rates of (a) 0.001 s−1, (b) 0.01 s−1, (c) 0.1 s−1 and (d) 1 s−1.
Figure 1

True stress–strain data of GH4065 superalloy corresponding to the strain rates of (a) 0.001 s−1, (b) 0.01 s−1, (c) 0.1 s−1 and (d) 1 s−1.

Aside from macroscopic deformation, microstructural evolution also occurs in GH4065 superalloy during hot forming processes. The main forms of microstructural evolution are dynamic recrystallization during hot deformation and grain growth in high-temperature environment.

Equations (1)–(5) are the employed dynamic recrystallization mathematical models of GH4065 superalloy [16]. Equations (1) and (2) define the critical condition to trigger the dynamic recrystallization at high temperature. Equations (3) and (4) describe the dynamic recrystallization volume fraction during hot deformation process. And equation (5) describes the grain sizes of the generated dynamic recrystallization grains.

(1) ε c = 0.383 ε p ,

(2) ε p = 0.108 ε ̇ 0.01778 exp ( 7 , 167 / R T ) ,

(3) X drx = 1 − exp − 1.023 ε − ε c ε 0.5 1.864 ,

(4) ε 0.5 = 0.02769 ε ̇ 0.03776 exp ( 30 , 321 / R T ) ,

(5) d drx = 75.91 ε ̇ − 0.09372 exp ( − 26 , 173 / R T ) ,

where ε c and ε p represent the critical strain and peak strain, respectively; X drx stands for the volume fraction of dynamic recrystallized grains; ε 0.5 is the corresponding true strain as dynamic recrystallized volume fraction is 50%; d drx represents the dynamic recrystallized grain size (unit: μm); T and ε ̇ represent the temperature (unit: K) and strain rate (unit: s−1), respectively; R = 8.31 J·mol−1·K−1 is the universal gas constant.

High-temperature condition is conducive to the grain growth of GH4065 superalloy. And the ultimate grain size is mainly affected by holding time, holding temperature, and original grain size [17]. Here, the grain growth behaviors of GH4065 alloy were described by the grain growth model shown in the following equation [18]:

(6) d A 2.61 = d 0 2.61 + 1.7159 × 10 9 t 0.7759 exp − 193 , 528 RT , T ≤ 1,250 K d A 9.22 = d 0 9.22 + 1.0505 × 10 44 t 1.6819 exp − 830 , 905 RT , T > 1,250 K

in which d A, d 0, t, and T stand for the grain size in high-temperature condition (unit: μm), original grain size (unit: μm), holding time (unit: s), and holding temperature (unit: K), respectively.

2.2 Hot forming finite element model of GH4065 superalloy

2.2.1 Hot forming processes of superalloy turbine disk

The workpiece of the superalloy turbine disk is a cylinder with a total height of 240 mm, a diameter of φ270 mm, and a bevel angle of 10 × 10 mm. The hot forming processes of GH4065 superalloy turbine disk are shown in Figure 2, which mainly include four stages such as heating, transferring, hot forming, and cooling.

Figure 2 Hot forming processes of superalloy turbine disk.
Figure 2

Hot forming processes of superalloy turbine disk.

The main processes of each stage were shown as follows.

The heating stage of the workpiece was divided into two procedures as shown in Figure 3. In the first stage, the environment temperature was slowly elevated to 920°C and held to obtain evenly distributed temperature of the workpiece. In the second stage, the workpiece was rapidly heated to the initial forging temperature of 990°C and held at 990°C to homogenize the workpiece temperature. Since the grain growth rate of GH4065 superalloy is slow below 920°C, and the grain may grow rapidly above 920°C [18], the ways of gradient heating and temperature holding were carried out to reduce the time staying in the high-temperature environment and reduce the grain growth degree.

Figure 3 Heating curve of the turbine disk.
Figure 3

Heating curve of the turbine disk.

When the heating stage was completed, the workpiece was first wrapped with a covering made up of glass fibers to reduce the heat loss, and then, the workpiece was transferred from the heating furnace (XSL-25-12TC box-type furnace in the real physical experiments) to the bottom die installed on the press. The preheating temperature of the dies was 400°C, and the transfer time was about 40 s. After the transferring of the workpiece, the top die would start to deform the workpiece on a press (YR27-8000 hot die forging press in the real physical experiments) in one stroke with a speed of gradient descent, as shown in Figure 4. Adopting high forming speed in the early stage of hot forming process is beneficial for reducing heat loss and temperature decrease to ensure forming temperature. Gradually decreasing speeds were employed to reduce forming load and promote dynamic recrystallization in the later stage of hot forming process and simultaneously reduce the maximum forming load. Subsequently, a pressure holding process was schemed. After all the forming processes, the forging would be air-cooled to room temperature.

Figure 4 Forging speeds during hot forming processes.
Figure 4

Forging speeds during hot forming processes.

2.2.2 Hot forming finite element model

Thermo-mechanical effects and microstructural evolution synchronously exist in the hot forming processes of GH4065 superalloy turbine disk. Correspondingly, in the finite element model, not only the microstructural evolution, heat transfer, and mechanical behaviors, but also their interactions should be considered [19].

The constructed finite element model is represented in Figure 5. The grids of the workpiece and dies were chosen as tetrahedral grids. The workpiece was set as plastic body. The initial temperature and grain size were defined as 20°C and 28 μm, respectively. The cylindrical surface and the end faces were set as the thermal convection surfaces with the air during heating, transfer, and cooling, and the cylindrical surface was set as the thermal convection surface with the air during hot forming. The dies were set as rigid bodies with an initial temperature of 400°C. All surfaces of the die were defined as thermal convection surfaces with air during the hot forming processes.

Figure 5 Finite element model of superalloy turbine disk.
Figure 5

Finite element model of superalloy turbine disk.

2.2.3 Finite element process parameters

According to the proposed hot forming processes of GH4065 superalloy turbine disk, the finite element process parameters were defined as follows.

In the heating and holding stage, the environmental temperature that changes with the time is shown in Figure 3. The emissivity of GH4065 superalloy was set as 0.48, and the heat transfer coefficient between the workpiece and the environment was defined as 0.025 N·s−1·mm−1·°C−1.

The transferring process was assumed being completed in 40 s. Due to the heat insulation effect of glass fiber covering, the emissivity of GH4065 superalloy was set to 0.06, and the heat transfer coefficient between the workpiece and the environment was defined as 0.005 N·s−1·mm−1·°C−1.

In the hot forming stage, the initial distance between the top and bottom dies is 247 mm. The initial distance between the bottom surface of the top die and the top surface of the workpiece is 20 mm. And after the workpiece transferring is completed, the top die started to move and deform the workpiece. The hot forming process can be subdivided as empty stroke, forging, and pressure holding. The movement speed of the top die during hot deformation is displayed in Figure 4. The top die stops moving as the distance between the top and bottom dies reaches 25 mm. The friction type between the die and the workpiece was assumed as shear friction, and the friction coefficient was 0.25. The heat transfer coefficient of the contact surface between the dies and the workpiece was 0.6 N·s−1·mm−1·°C−1. The work-to-heat conversion coefficient was set to 0.95. The die material is H13 hot-working die steel, the material parameters of which were chosen as the available ones in the material library of DEFORM software. The heat transfer coefficients between the dies and the environment were defined as 0.025 N·s−1·mm−1·°C−1. After forging process, the top die stopped moving and the pressure was held for 20 s.

Based on the previous practical engineering experience, the simulation of air cooling process for 14,400 s was carried out. And in the cooling process, the glass fiber covering was removed. The emissivity of GH4065 superalloy was set to 0.48, and the heat transfer coefficients were defined as 0.025 N·s−1·mm−1·°C−1.

3 Thermo-mechanical–microstructural-coupled numerical simulation of superalloy turbine disk

The thermo-mechanical–microstructural-coupled numerical simulation was carried out based on the constructed finite element model of the superalloy turbine disk. In order to conduct in-depth and detailed analysis on the macroscopic deformation and microstructural evolution of the turbine disk, points P1 and P2 in the wheel core region, points P3 and P4 in the wheel hub region, point P5 in the wheel spoke region, and point P6 in the wheel flange region were selected as tracking points, as shown in Figure 6.

Figure 6 Schematic locations of the selected tracking points: (a) workpiece and (b) forging.
Figure 6

Schematic locations of the selected tracking points: (a) workpiece and (b) forging.

3.1 Numerical simulation of heating process

3.1.1 Temperature evolution during heating stage

The temperature distributions of the workpiece in heating stage are shown in Figure 7. It is easy to find that the temperature of the workpiece increases from the initial temperature of 20 to 632–764°C when the furnace temperature (environment temperature) reaches 920°C. At this time, the temperatures of the edges on the workpiece are the highest; the temperatures of the end surfaces and the cylindrical surface are next to the ones of the edges; the temperature of the core is the lowest. This is due to the fact that the edges of the workpiece are the juncture areas of the cylindrical surface and end faces, where the effects of thermal convection and thermal radiation are the most significant; thus, the temperatures rise fastest. The cylindrical surface and the end faces are also in direct contact with the environment; therefore, thermal convection and thermal radiation with the environment can occur synchronously. The core of the workpiece is not in direct contact with the environment; thus, the temperature rise relies on the heat conduction among the heat region, the cylinder, and the end faces, so its temperature rise is the slowest. After holding at 920°C for 7,200 s, the temperature distribution is uniform and tends to the furnace temperature of 920°C. When the furnace temperature rises to 990°C, the billet temperature rises to 923–951°C, and the temperature distribution is consistent with that when heated to 920°C. After holding at 990°C for 4,800 s, the temperature distribution is homogeneous and close to the furnace temperature of 990°C.

Figure 7 Temperature distributions of the workpiece in the heating stage: (a) heating to 920°C, (b) holding at 920°C, (c) heating to 990°C, and (d) holding at 990°C.
Figure 7

Temperature distributions of the workpiece in the heating stage: (a) heating to 920°C, (b) holding at 920°C, (c) heating to 990°C, and (d) holding at 990°C.

The temperature evolutions of the tracking points are shown in Figure 8. Obviously, the points P2 and P4 near the edges of the workpiece exhibit the fastest heating response speed and temperature rise, followed by the point P6 near the cylindrical surface, and the points P1, P3, and P5 in the center of the workpiece show the slowest heating response speed. With the increase of the environment temperature, the temperature rise rate of each point increases first and then decreases, which is related to the temperature gap between the environment and the workpiece. The temperature gap is positively correlated with the heating rate of the workpiece. Therefore, minor temperature gap between the environment and the workpiece results in a low temperature rise rate at the beginning of heating stage. With the increase of the environment temperature, the temperature gap between the environment and the workpiece increases gradually, and the workpiece temperature increases rapidly. When the temperature rise rate of the workpiece is greater than the environment temperature rising rate, the temperature gap decreases and the temperature of the workpiece accordingly decreases. In the holding stage, the environment temperature keeps constant, so the temperature gap decreases significantly, and the rise rate of the workpiece temperature also decreases significantly.

Figure 8 Temperature evolution of the tracking points in the heating stage.
Figure 8

Temperature evolution of the tracking points in the heating stage.

3.1.2 Microstructural evolution during heating stage

The average grain size distributions of the workpiece during heating and holding stages are presented in Figure 9. It is apparent that when the environment temperature reaches 920°C, the temperature of the workpiece still keeps in a low level; thus, no grain growth occurs and the average grain size of the workpiece keeps the initial state. After holding at 920°C for 7,200 s, a small degree of grain growth occurred, and the average grain sizes of the workpiece increase to 33.8–35.8 μm. After holding, the average grain sizes of the edges are the largest, then the ones of the end faces and the cylindrical surfaces are the middle, and the average grain size of the core is the smallest. This corresponds to the temperature distributions of the workpiece in the heating stage. That is to say, higher heating rate and local temperature will promote the grain growth during the heating stage. When the furnace temperature reaches 990°C, the average grain sizes of the workpiece slightly increase to 34.9–37.5 μm in the rapid heating process. After holding at 990°C for 4,800 s, the average grain sizes of the workpiece further increase to 66.8–74.9 μm, which is a significantly higher level in contrast to the one at 920°C, indicating the grain grows rapidly at high temperature. It can be inferred from the simulation results that the segmented heating strategy can significantly reduce the residence time of the workpiece under high-temperature environment and greatly limit the grain growth of the workpiece.

Figure 9 Average grain size distributions of the workpiece in the heating stage of (a) heating to 920°C, (b) holding for 7200s at 920°C, (c) heating to 990°C and (d) holding for 4800s at 990°C.
Figure 9

Average grain size distributions of the workpiece in the heating stage of (a) heating to 920°C, (b) holding for 7200s at 920°C, (c) heating to 990°C and (d) holding for 4800s at 990°C.

The average grain size evolution of the tracking points on the workpiece during the heating stage is shown in Figure 10. Figure 10 shows that the temperature of the workpiece is low and no grain growth occurs in the preliminary heating stage, and the grains begin to grow in the holding process at 920°C. With the rise of the environment temperature, the grain growth rates gradually increase. Corresponding to the temperature evolution of the workpiece, the average grain sizes of P2 and P4 increase fastest, followed by P6, and grain growth also occurs in P1, P3, and P5, but grain growth rates are the slowest.

Figure 10 Average grain size evolution of the tracking points in the heating stage.
Figure 10

Average grain size evolution of the tracking points in the heating stage.

3.2 Numerical simulation of transferring process

3.2.1 Temperature evolution during transferring stage

The temperature distribution of the workpiece after transferring to the forming station is shown in Figure 11. It shows that the temperature change amplitudes of the different regions in the transferring stage are similar to those in the heating stage. For the temperature reduction values of the edges, the end and cylindrical surfaces, the core descends orderly. This is also affected by the heat exchange area and heat exchange approach.

Figure 11 Temperature distribution of the workpiece after transferring to the forming station.
Figure 11

Temperature distribution of the workpiece after transferring to the forming station.

The temperature evolution of the tracking points during the transferring stage is shown in Figure 12. The temperature range of the workpiece at the end of transferring stage is 962–989°C. During the transfer stage, the temperatures of P2 and P4 near the edges of the workpiece show the fastest decrease. The temperature of P6, which is near the cylindrical surface, also decreases, but the temperature decrease rate is slower than those of P2 and P4. The temperatures of P1, P3, and P5 points in the core are rarely affected by the external temperature and only decrease slightly.

Figure 12 Temperature evolution of the workpiece during the transferring stage.
Figure 12

Temperature evolution of the workpiece during the transferring stage.

3.2.2 Microstructural evolution during transferring stage

The average grain size distribution after the workpiece is transferred to the forming station, as shown in Figure 13. At the end of the transferring process, the average grain size of the workpiece increases slightly from 66.8–74.9 to 67.1–75 μm. Due to the short transferring time and the small temperature gap at each position of the billet, the overall distribution of the average grain size is consistent with the one before transferring.

Figure 13 Average grain size distribution of the workpiece after transferring to forming station.
Figure 13

Average grain size distribution of the workpiece after transferring to forming station.

The average grain size evolutions of the tracking points during the transferring stage are shown in Figure 14. From the curves in Figure 14, it is known that the average grain sizes of the tracking points increase almost linearly during the transferring stage with growth amplitudes of 0.2–0.4 μm. The average grain sizes of the tracking points still retain the inhomogeneity and relative size relationship as the heating process.

Figure 14 Average grain size evolution of the workpiece during transferring stage.
Figure 14

Average grain size evolution of the workpiece during transferring stage.

3.3 Numerical simulation of hot forming process

3.3.1 Deformation characteristics during hot forming stage

The effective strain distributions of the workpiece during the deformation processes are shown in Figure 15. It can be seen that the workpiece was compressed and deformed with the movement of the top die. The convex platform of the wheel hub first completes the filling, and then, the convex platform of the wheel core gradually completes the filling. The material continues to flow to the wheel spoke and flange, and finally, the flash was generated. During the forming process, the material flows from the center to the periphery, and the effective strain correspondingly increases from the center to the periphery. After forming, large deformation occurred in the workpiece. The effective strains of wheel core, hub core, spoke, and flange are considerable, but the effective strains of the convex platforms of the wheel core and hub are minor.

Figure 15 Effective strain distributions at the strokes of (a) 72 mm, (b) 123.6 mm, (c) 189 mm, and (d) 222 mm in the deformation process.
Figure 15

Effective strain distributions at the strokes of (a) 72 mm, (b) 123.6 mm, (c) 189 mm, and (d) 222 mm in the deformation process.

3.3.2 Temperature evolution during hot forming stage

The temperature distributions in the hot forming processes are shown in Figure 16. Two types of temperature evolution manners can be concluded, and the corresponding areas are the contact surfaces with dies and the inner deformed regions. The temperatures of the contact surfaces with dies on the workpiece decrease rapidly due to the major contact heat transfer with the dies and secondary heat radiation, convection in the hot forming process. At the final stage of hot forming, the minimum temperature of the forging reaches 917°C. As for the inner of the workpiece, the temperatures of some deformed regions are elevated. This is due to the fact that the press does work on the workpiece during hot forming process, and the work done is converted into heat and stored inside the workpiece. The inner deformed regions accumulate abundant heat by doing work, and the temperature increases significantly. As the hot forming is completed, the maximum temperature of the forging core reaches 1,035°C. In summary, the final temperatures of different regions in the hot deformation process are determined by the interactions of the heat accumulation by work–heat conversion and heat dissipation by the heat conduction. And the heat accumulation depends on the deformation degree or effective strain, as more work is required to generate greater deformation and work would be converted into heat. Therefore, the central region of the workpiece, which is severe deformed area and is isolated from the outside environment, keeps the highest temperature due to the most heat accumulation and the least heat dissipation; in contrast, the contact surfaces with dies, which belong to small deformation area or no deformation area and directly contact with the dies, keep the lowest temperature.

Figure 16 Temperature distributions of the workpiece in the hot forming process: (a) stroke 20 mm, (b) stroke 123.6 mm, (c) stroke 222 mm, and (d) after pressure holding.
Figure 16

Temperature distributions of the workpiece in the hot forming process: (a) stroke 20 mm, (b) stroke 123.6 mm, (c) stroke 222 mm, and (d) after pressure holding.

During the pressure holding process, the top die stops moving and the work–heat conversion is severed, so the forging temperature no longer rises. At this time, the contact area between the forging surface and the dies reaches the maximum, and the contact heat transfer becomes more intense. Therefore, the forging temperature decreases rapidly during the pressure holding process. As the pressure holding is completed, the forging temperature has been reduced from 917–1,035 to 887–1,010°C.

3.3.3 Microstructural evolution during hot forming stage

The dynamic recrystallization volume fraction distributions of the workpiece during the hot forming process are shown in Figure 17. As known, the necessary prerequisites for dynamic recrystallization to occur are reaching sufficient temperature and critical strain. Under the hot forming conditions, temperature satisfies the environment requirement for dynamic recrystallization, so effective strain or deformation degree becomes the most critical condition that triggers dynamic recrystallization. With the movement of the top die, the effective strain of the deformed regions gradually reaches the critical strain, and then, dynamic recrystallization occurs in these regions. As the hot deformation process finishes, complete dynamic recrystallization occurs at the center of the wheel core, the center of the wheel hub, the wheel spoke, and the wheel flange. Due to the large rigid displacement instead of plastic deformation in the convex platforms of wheel core and hub, incomplete dynamic recrystallization occurs in these regions due to low-level strain. The dynamic recrystallization levels in different regions coincide well with the corresponding effective strain levels, which is consistent with theoretical logic.

Figure 17 Dynamic recrystallization volume fraction distributions at the strokes of (a) 72 mm, (b) 123.6 mm, (c) 189 mm, and (d) 222 mm in the deformation process.
Figure 17

Dynamic recrystallization volume fraction distributions at the strokes of (a) 72 mm, (b) 123.6 mm, (c) 189 mm, and (d) 222 mm in the deformation process.

The dynamic recrystallization volume fraction evolutions of the tracking points during the hot forming stage are shown in Figure 18. It is apparent that deformation and dynamic recrystallization first occur in the wheel hub, and the dynamic recrystallization fraction of P3 preemptively rapidly increases to a high level. Then, P1, P5, and P6, respectively, located in wheel core, wheel spoke, and wheel flange also repeat the same changes as P3 in order. At the end of hot deformation process, the dynamic recrystallization volume fractions of P1, P3, P5, and P6 are 100%. Although the material flow occurs earlier at P4, the effective strain was small, and the critical strain was not reached at the beginning of deformation; therefore, no large-scale dynamic recrystallization occurred. At the final stage of the hot deformation process, the ultimate dynamic recrystallization fraction of P4 reached about 30 %. P2 has the latest dynamic recrystallization opportunity and minimum deformation degree, so the final dynamic recrystallization fraction is only about 15 %.

Figure 18 Dynamic recrystallization volume fraction evolutions of the tracking points in the hot deformation processes.
Figure 18

Dynamic recrystallization volume fraction evolutions of the tracking points in the hot deformation processes.

The average grain size distributions during the hot forming stage are shown in Figure 19. With the increase of the distance of the top die and the effective strain of the workpiece, dynamic recrystallization occurs in the workpiece, which significantly promotes the significant decrease of the grain sizes. At the final stage of the deformation process, dynamic recrystallization occurs in wheel core, hub core, spoke, and flange with severe deformation; thus, fresh fine and uniform grains are generated and the grain sizes sharply decrease in these regions, and the minimum grain size is merely 1.79 μm. The dynamic recrystallization volume fractions of the convex platforms in the wheel core and hub regions, which are small deformation area or no deformation area, are relatively low due to the fact that the critical strain are not reached; thus, the grain sizes are relatively large and the maximum reaches 72.1 μm. After the pressure holding for 20 s, the fine dynamic recrystallization grains grow slightly in a short time, and the minimum grain size increases to 2.09 μm.

Figure 19 Average grain size distributions at the strokes of (a) 20 mm, (b) 72 mm, (c) 222 mm and (d) after pressure holding in the deformation processes.
Figure 19

Average grain size distributions at the strokes of (a) 20 mm, (b) 72 mm, (c) 222 mm and (d) after pressure holding in the deformation processes.

The average grain size evolutions of the tracking points during the hot forming processes are shown in Figure 20. During the hot forming processes, P3 located in wheel hub, P1 located in the wheel core, P5 located in the wheel spoke, P6 located in the wheel flange, P4 and P2, respectively, located in the convex platform of the wheel hub and core regions are successively deformed, and correspondingly, the grains are successively fined. Finally, the average grain sizes of P1, P3, P5, and P6 with dynamic recrystallization volume fractions of 100% decreased to a low level. However, the dynamic recrystallization volume fractions of P2 and P4 are relatively low, and the average grain size remained at relatively high level.

Figure 20 Average grain size evolutions of the tracking points in the deformation processes.
Figure 20

Average grain size evolutions of the tracking points in the deformation processes.

During the hot deformation stage, no significant grain growth in workpiece occurs under high temperature due to short duration of hot forming process. However, as shown in Figure 20, the increase in grain size caused by grain growth can offset the decrease in grain size caused by dynamic recrystallization, resulting in fluctuations within a narrow range of the evolution curve of average grain size.

During the pressure holding process, the temperatures of P2 and P4 located wheel hub and core regions of the forging are below 900°C. Such environment cannot provide enough energy for grain growth of the superalloy, so the grain sizes of P2 and P4 maintain stable. P1, P3, P5, and P6, which are located inside the forging, still keep high temperatures during the pressure holding process, and their average grain sizes exhibit small-amplitude linear increase.

3.4 Numerical simulation of cooling process

3.4.1 Temperature evolution during cooling stage

The temperature distribution of the forging during air cooling stage is shown in Figure 21. It is obvious that the temperature of the forging gradually decreases to room temperature the air cooling process. Via the air cooling for 14,400 s, the forging temperature drops to 28.8–35.8°C. During the air cooling stage, the forging temperature gradually decreases from the center of the superalloy turbine disk to the periphery, and the inner temperature of the forging is higher than the surface temperature.

Figure 21 Temperature distribution at the final stage of the cooling process.
Figure 21

Temperature distribution at the final stage of the cooling process.

The temperature evolutions of the tracking points during the air cooling stage of forgings are shown in Figure 22. It was implied by Figure 22 that the cooling rate of the forgings gradually decreases with the decreases of the forging.

Figure 22 Temperature evolutions of the tracking points in the cooling process.
Figure 22

Temperature evolutions of the tracking points in the cooling process.

3.4.2 Microstructural evolution during cooling stage

The ultimate average grain size distribution of the forging is presented in Figure 23. The overall average grain size distribution of the forging during air cooling stage is consistent with that after hot forming stage.

Figure 23 Average grain size distributions of the forging in the cooling process.
Figure 23

Average grain size distributions of the forging in the cooling process.

The evolutions of the average grain size during the air cooling stage are shown in Figure 24. As shown in Figure 24, in the early stage of air cooling, except for P2 and P4, the average grain sizes still slightly increase due to high temperature in these points. As air cooling continues, the temperature further decreases and the average grain size remains stable. At the end of air cooling, the average grain sizes of P2 and P4 stay in a high level, while the grains corresponding to the other positions are fine, less than 15 μm. The average grain sizes of the tracking points are closely related to the dynamic recrystallization volume fraction. The higher the dynamic recrystallization volume fraction, the smaller the final average grain size. The dynamic recrystallization volume fractions of the final wheel core convex and wheel hub convex regions are relatively low, and both large and fine dynamic recrystallization grains exist in these regions, presenting as mixed crystal state.

Figure 24 Average grain size evolutions of the tracking points in the cooling process.
Figure 24

Average grain size evolutions of the tracking points in the cooling process.

4 Verification of numerical simulation results

The hot forming test of GH4065 superalloy turbine disk was conducted according to the hot forming processes. In the hot forming test, a cylindrical workpiece was first heated to 990°C with segmented heating and holding procedures in XSL-25-12TC box-type furnace, then transferred to the bottom die, and forged on YR27-8000 hot die forging press; finally, the forging was air-cooled to room temperature. The whole processes are in conformity with the procedures in Figure 2. The obtained superalloy turbine disk forging was cut and its cross-section is shown in Figure 25. It is obvious that the shape of the forging obtained from numerical simulation and the one obtained from actual physical experiment have a high degree of similarity via the comparison between Figures 21 and 25, indicating that the previous numerical simulation can accurately predict the macroscopic deformation of the superalloy turbine disk during the hot forming processes. The samples were prepared according to the positions of P1-P6 as shown in Figure 25, and metallographic tests were conducted to verify the microstructure of the superalloy turbine disk. P1–P6 in Figure 25 correspond to the ones in Figure 6.

Figure 25 Schematic sampling positions of the superalloy turbine disk.
Figure 25

Schematic sampling positions of the superalloy turbine disk.

The metallographic photographs obtained from metallographic testing of superalloy turbine disk forging are shown in Figure 26. As shown in Figure 26, the grains at the P1, P3, P5, and P6 of the forging were fine and uniform with high dynamic recrystallization degrees, and there are almost no deformation large grains that have not undergone dynamic recrystallization. The microstructures at P2 and P4 exhibit as mixed crystal structure [20], and the grain sizes are relatively inhomogeneous. The large grains in Figure 26b and d are the ones that have not undergone dynamic recrystallization but grown during hot forming processes, and the fine grains are dynamic recrystallized grains.

Figure 26 Microstructures of the tracking points on superalloy turbine disk forging: (a) P1, (b) P2, (c) P3, (d) P4, (e) P5, and (f) P6.
Figure 26

Microstructures of the tracking points on superalloy turbine disk forging: (a) P1, (b) P2, (c) P3, (d) P4, (e) P5, and (f) P6.

The simulated and measured average grain sizes of the tracking points are shown in Table 5. It shows that the grain sizes of P1, P3, P5, and P6 are in the range of 11.48–16.41 μm, which is significantly smaller than the initial grain size. Such fine grains can be identified as 100 % dynamic recrystallization grains. However, full-scale dynamic recrystallization does not occur in P2 and P4. Some deformed large grains without dynamic recrystallization can be clearly observed, around which the fine and uniform dynamic recrystallization grains generate. Such coarse deformed grains and fine dynamic recrystallization grains form a type of mixed crystal structure [21]. The average grain sizes of P2 and P4 are 65.48 and 55.64 μm, respectively, which were significantly higher than the initial grain size.

Table 5

Comparisons between the measured and simulated grain sizes

P1 P2 P3 P4 P5 P6
Measured grain size (μm) 11.66 65.48 16.41 55.64 15.87 11.48
Simulated grain size (μm) 12.65 61.97 14.95 52.93 14.03 12.01
Relative error 8.49% −5.36% −8.89% −4.87% −11.59% 4.61%

It can be known from Table 5 that the simulated average grain sizes of the tracking points are close to the ones of the actual forging manufactured by the hot forming processes. The maximum relative error of the simulated average grain sizes is only −11.59% (P5), and the average error is only 7.30%. This magnitude of the maximum relative error and average relative error shows that the numerical simulation of the hot forming processes can not only fully reflect the microstructural evolution law of the turbine disk in the actual hot forming processes, but also has high accuracy.

5 Conclusions

The main conclusions were drawn as follows:

  1. A macro–micro multi-scale finite element model for the hot forming processes of the GH4065 superalloy turbine disk was constructed by establishing macro–micro material model, and setting process parameters and boundary conditions.

  2. Via the thermo-mechanical–microstructural-coupled numerical simulation of the superalloy turbine disk, the macroscopic deformation and microstructural evolution of superalloy turbine disk during the hot forming processes were studied, and the ultimate macroscopic shape and grain sizes were predicted.

  3. A physical hot forming test of the superalloy turbine disk was conducted to verify the numerical simulation results. The results indicate that numerical simulation can accurately predict the macroscopic deformation and microstructural evolution laws of the actual processes.

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Acknowledgments

The authors are grateful for the reviewer's valuable comments that improved the manuscript.

  1. Funding information: This work was supported by The doctoral research start-up funding project for Guangdong University of Science and Technology (GKY-2024BSQDK-1) and the Guangdong University of Science and Technology In-novative Research Team Project (GKY-2022CQTD-1).

  2. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and consented to its submission to the journal, reviewed all the results and approved the final version of the manuscript. Zhang Haoqiang established the multi-scale finite element model and carried out the numerical simulation. Peng Dongli prepared the fundamental data of the finite element model. Cai Liu conducted the hot forming experiment of turbine disk and prepared the manuscript. Ronaldo Juanatas, Jasmin Niguidula and Jonathan M. Caballero provided important contribution and guidance in the preparations and modifications the manuscript.

  3. Conflict of interest: Authors state no conflict of interest.

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Received: 2023-10-29
Revised: 2024-03-28
Accepted: 2024-04-27
Published Online: 2024-05-21

© 2024 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/htmp-2024-0013
Keywords for this article
turbine disk; multi-scale finite element model; GH4065 superalloy; numerical simulation
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