2020 年 61 巻 4 号 p. 632-640
The high temperature deformation and microstructure evolution of Ni–Co base superalloy TMW-4M3 during the isothermal forging process were studied. A uniform compression test of TMW-4M3 where both the strain rate and compression temperature were controlled showed dynamic recrystallization flow stress. The peak stress and steady stress of the deformation resistance curve were characterized with the Zener-Hollomon parameter. The average grain size after dynamic recrystallization was also correlated with the Zener-Hollomon parameter, but this relationship changed with compression temperature. We found that this temperature dependency was related to the pinning effect of the γ′ precipitates in the γ matrix and proposed a new prediction model for dynamic recrystallization grain size considering not only the Zener-Hollomon parameter but also the volume fraction of the γ′ precipitates. This enables us to calculate the average grain size after isothermal forging within an error of 12%.
Fig. 14 Prediction accuracy of developed numerical model for dynamic recrystallization grain size considering pinning effect.
The turbine disks used in the jet engines or power generators are mainly made of cast and wrought Ni-base superalloys because of their high heat resistance and high strength properties. The temperature in a combustion chamber determines the performance of the gas turbines. Therefore, a lot of novel superalloys are constantly being developed to improve the service temperature. The high temperature strength property of the Ni-base superalloy is caused by the γ′ precipitates, which prevent dislocation migration during deformation. In the case of turbine blades, single crystal Ni-base superalloys are used, and the volume fraction of the γ′ phase is about 70%. On the other hand, the microstructure of the turbine disks is usually designed as fine grain structure to obtain a good low cycle fatigue property. This fine grain structure was achieved by dynamic recrystallization during the hot processing. If the alloy has a much larger amount of γ′ precipitates, the workability decreases although the high temperature strength property is improved. The turbine disks usually have complex shapes and are manufactured by forging process. Therefore, we need to take into account both the required material properties and good manufacturability.
TMW-4M3 is a superalloy that was developed by the National Institute for Material Science in Japan.^{1}^{,}^{2}^{)} This Ni–Co base superalloy was designed to have good phase stability and thermal resistance by adding Co and Ti to Alloy 720Li. The nominal compositions of TMW-4M3 and Alloy 720Li are shown in Table 1. Since the Ti composition is higher than that of Alloy 720Li, the amount of γ′ phase increases, which has a precipitation strengthening effect. The maximum volume fraction of the γ′ phase is about 50% for TMW-4M3 and 45% for Alloy 720Li.
To apply TMW-4M3 to turbine disks, we have to design the forging process. Generally, the hot forging process is applied to these high strength superalloys which have a large amount of γ′ precipitates. In this process, the material is preliminarily heated to decrease its deformation resistance. However, during the forging process, the material temperature decreases due to the material being in contact with the forging dies. The temperature drop during the forging process causes γ′ precipitation, which leads to an increase of deformation resistance. One solution to this is isothermal forging, where the forging dies are kept at the same temperature as the forging material, and we can forge the target material with relatively low deformation resistance compared to the conventional hot forging process. On the other hand, both an active grain boundary migration and a smaller volume fraction of γ′ precipitates are led by too high temperature processing. This situation often causes grain coarsening, which results in lower tensile strength and low cycle fatigue properties.
Prior to the trial and error approach of prototype production, numerical modeling and simulation was used as a very strong tool to find the optimum forging conditions because the prototype production of large forged parts such as turbine disks cost too much. For example, dynamic recrystallization behavior during the hot deformation process and the resulting microstructure has usually been studied by the relationship with the Zener-Hollomon parameter in many Ni-base superalloys.^{3}^{–}^{5}^{)} On the other hand, the effect of γ′ precipitates on recrystallization are only considered qualitatively.^{5}^{,}^{6}^{)}
The objective of this work is to investigate the high temperature deformation property and the dynamic recrystallization behavior of TMW-4M3 using isothermal compression tests and to reveal the relationship between the forging parameters and the microstructures under the effect of γ′ precipitates.
The chemical composition of TMW-4M3 used in this study is listed in Table 2. The as-received alloy was a wrought billet, and cylindrical specimens were cut from the middle part of the billet, along the longitudinal direction. They are 12 mm in height and 8 mm in diameter. Microstructures observed by optical microscope are shown in Fig. 1. The shapes of the γ′ particles were clearly indicated by etching in Kalling’s solution. We found that the effect of solute segregation in the casting process was sufficiently small because of the uniform distribution of the γ′ precipitates. The average grain size of the matrix γ phase was about 18–20 µm.
Optical micrographs of TMW-4M3 specimen with (a) low magnification and (b) high magnification. The γ′ particles are uniformly distributed.
Compression tests were conducted to reproduce isothermal forging conditions using a THERMECMASTOR-Z thermo-mechanical simulator.^{7}^{,}^{8}^{)} We inserted dummy metallic dies between the specimen and the SiC anvils and heated the specimen with a surrounding induction heating coil to control the material temperature. Although the ceramic anvils were not heated, the dummy dies were heated together with the specimen. Therefore, the heat transfer from the specimen to the anvils was extremely reduced, and the isothermal compression test could be performed. In this experiment, we used Nimowal alloy as the dummy dies’ material.^{9}^{,}^{10}^{)} In addition, we inserted glass sheets between the dummy dies and the specimen and moreover made concentric grooves on the upper and lower surfaces of the cylindrical specimens. When the dummy dies and specimens are heated, melted glass enters the grooves and acts as a lubricant during compression. Then, we can evaluate the exact loading data of the material due to the reduced friction at the upper and lower surfaces of the compression specimen.
As for the compression conditions, the deformation temperature ranged from 1223 to 1433 K, and the strain rate ranged from 0.0005 to 0.05 s^{−1}. All specimens were heated to the deformation temperature and soaked for 10 min to achieve uniform temperature distributions and equlibrium state of the temperature. Just after the specimens were compressed at the target temperature and strain rate, they were quenched by N_{2} gas to keep the deformed microstructure. During the whole of the compression process, we monitored the temperature history of the specimens with thermocouples connected to their surfaces and controlled the power of the induction heating coil so as to maintain the isothermal conditions.
The flow stress curve of TMW-4M3 was calculated from the load curve measured during the compression test. Moreover, we cut the compressed specimens parallel to the compression axis through the center. The surfaces of the cut samples were polished with colloidal silica and etched in Kalling’s solution. Micrographs of the samples were taken at around the center of the etched surface using an optical microscope. These observation points were decided by finite element analysis, which enables us to select points whose temperature and strain rate history were relatively stable through compression. The matrix grain size was evaluated by planimetric method. The volume fraction of γ′ precipitates of the SEM image was quantitatively analyzed using Image-Pro Plus software.^{11}^{)}
We calculated the true stress-strain curves of TMW-4M3 from actual load-stroke data obtained from compression tests. The flow stress curves in Fig. 2 show dynamic recrystallization behavior, which has peak stress σ_{p} and steady stress σ_{s}. Peak stress σ_{p} is the maximum point of flow stress and originates from the balance between work hardening by accumulation of dislocation and softening by dynamic recovery and recrystallization. After the peak stress point, dynamic recrystallization becomes predominant relative to work hardening, and flow stress decreases. Steady stress σ_{s} is the stable value of the flow stress curve in the larger strain range. In this region, the whole of the matrix phase is composed of recrystallized grains, and introduced dislocation by deformation is constantly balanced with dislocation annihilation by dynamic recrystallization. The relationship between these characteristic stresses and compression conditions in the precipitation strengthening type Ni-base superalloys is given as the following numerical modeling,
\begin{equation} Z = \dot{\varepsilon}\exp (Q/RT) = A\sigma^{n'}, \end{equation} | (1) |
Flow stress curve of TMW-4M3 at 1223 K.
First, the temperature dependency of σ_{p} and σ_{s} were investigated. We took the natural log of eq. (1) and obtained the following expression,
\begin{equation} \ln \dot{\varepsilon} + (Q/R)(1/T) = \ln A + n'\ln \sigma. \end{equation} | (2) |
Temperature dependency of flow stress with (a) peak stress and (b) steady stress.
Secondly, stress index n′ was investigated from the relationship between $\ln \dot{\varepsilon }$ and ln σ for each compression temperature shown in Fig. 4. As with Fig. 3, the slope of the approximate straight line in this relationship denotes stress index n′. The calculated values of index n′ for all compression conditions are also written in Fig. 4. Stress index for pure metal and alloys usually ranged from 3 to 7 in previous research, and that for TMW-4M3 was generally consistent with this tendency.^{7}^{)}
Relationship between strain rate and flow stress with (a) peak stress and (b) steady stress.
From the slopes shown in Fig. 3 and Fig. 4, we found that the activation energies in different compression conditions differ. Calculation results of activation energies based on the peak stress and stready stress for all conditions are summarized in Table 3 and Table 4, respectively. These variations in activation energies are thought to be due to the γ′ state change with time and temperature. For example, at a lower temperature, the higher volume fraction of γ′ precipitates increase deformation resistance, which will lead to a large activation energy of deformation. In fact, it has been reported that the activation energy of high temperature deformation in Alloy 720Li also differs according to compression conditions.^{14}^{)} As shown here, in the case of dual phase structure, the microstructure evolution of the matrix phase is affected by the other phase, and the influence rate differs according to the process conditions. In this study, the best fit value of activation energy for the ranges of compression conditions was derived from the average value of the slope in both Fig. 3 and Fig. 4. As for the strain rate of 0.0005 s^{−1} in Fig. 3, the slopes Q/n′R defined from whole temperature range were used: 20050 K·mol for the peak stress, and 13275 K·mol for the steady stress. Then, we obtained 18843 K·mol and 13552 K·mol as the the average values of Q/n′R for the peak stress and the steady stress, respectively. Moreover, the average values of n′ derived from Fig. 4 were 3.92 and 3.64 for the peak stress and the steady stress respectively. Finally, we found the activation energies Q as 613.6 kJ for the peak stress and 410.3 kJ for the steady stress. As a result, we developed the following prediction model of σ_{p} and σ_{s} using the Zenner-Hollomon parameter on the basis of eq. (1).
\begin{equation} [\sigma_{\text{p}}]\quad Z = \dot{\varepsilon}\exp \left(\frac{613.6 \times 10^{3}}{RT} \right) = 1.07 \times 10^{14} \times \sigma_{\text{p}}^{3.92}, \end{equation} | (3) |
\begin{equation} [\sigma_{\text{s}}]\quad Z = \dot{\varepsilon}\exp \left(\frac{410.3 \times 10^{3}}{RT} \right) = 2.19 \times 10^{7} \times \sigma_{\text{s}}^{3.64}. \end{equation} | (4) |
Relationship between Zener-Hollomon parameter and flow stress of TMW-4M3 with (a) peak stress and (b) steady stress.
Typical microstructures after isothermal compression tests are shown in Fig. 6. The true strains of all test pieces were about 1.4, which showed steady flow stress, and then all the matrix grains were dynamically recrystallized ones. The average grain size after dynamic recrystallization D_{DRX} increased with higher compression temperature. At the same time, the amount of γ′ particles decreased. Moreover, the strain rate dependency of D_{DRX} is indicated in Fig. 7. A faster strain rate resulted in a fine microstructure, and a slower strain rate resulted in a coarse one. Then, the compression temperature dependency of D_{DRX} evaluated by an Arrhenius plot and the strain rate dependency of D_{DRX} are shown in Fig. 8 and Fig. 9, respectively. For the temperature dependency, the slope of the Arrhenius plot changes with temperature. For the strain rate dependency, the slopes of the double logarithmic chart also change and are clarified to be in three temperature range groups: lower temperature range below 1373 K, middle temperature range from 1383 to 1413 K, and higher temperature range around 1433 K.
Optical micrographs of compressed TMW-4M3 under the compression strain of 1.4, strain rate of 0.005 s^{−1}, and compression temperature of (a) 1223 K, (b) 1373 K, (c) 1383 K, (d) 1398 K, (e) 1413 K, and (f) 1433 K.
Optical micrographs of compressed TMW-4M3 under the compression strain of 1.4, compression temperature of 1383 K, and strain rate of (a) 0.0005 s^{−1}, (b) 0.005 s^{−1}, and (c) 0.05 s^{−1}.
Compression temperature dependency of dynamic recrystallization grain size.
Strain rate dependency of dynamic recrystallization grain size.
Here, it is known that the Zener-Hollomon parameter, characteristic value of isothermal forging process, and D_{DRX} have the following relationship,
\begin{equation} D_{\text{DRX}} = A_{\text{DRX}}Z^{- n_{\text{DRX}}}, \end{equation} | (5) |
Relationship between Z and D_{DRX} for all compression conditions. Error bar denotes the standard error.
Measured fraction and average radius of γ′ precipitates after compression test. Error bar denotes the range of values.
We analyzed the grain growth behavior affected by γ′ particles using the following Smith-Zener relationship,^{21}^{)}
\begin{equation} \skew3\bar{R} = a\frac{\bar{r}}{f^{b}}, \end{equation} | (6) |
Relationship between $\skew3\bar{R}/\bar{r}$ and f.
We thought that the pinning effect in region 1 was large enough in any temperature conditions, and the difference in grain size for each temperature was quite small. The volume fraction in this region was almost same. However, the contribution of Z was obvously confirmed in Fig. 10. To include the effect of strain rate conditions, one certain D_{DRX} − Z relationship was applied to this region, which enables us to predict the relationship between forging conditions and resulting grain sizes. Using the method of least squares, we derived the following prediction formulae,
\begin{equation} \text{Region 1}\quad D_{\text{DRX}} = 51.4 \times Z^{- 0.0577}. \end{equation} | (7) |
\begin{equation} \text{Region 3}\quad D_{\text{DRX}} = 72403 \times Z^{- 0.227}. \end{equation} | (8) |
\begin{equation} \ln D_{\text{DRX}} = \ln A_{\text{DRX}} - n_{\text{DRX}}\ln Z. \end{equation} | (9) |
\begin{equation} \ln A_{\text{DRX}} = 590.4 \times f^{2} - 247.3 \times f + 30.8, \end{equation} | (10) |
\begin{equation} n_{\text{DRX}} = - 0.219 \times f + 0.131. \end{equation} | (11) |
The γ′ fraction, f, dependency of material constants of (a) ln A_{DRX} and (b) n_{DRX}.
Prediction accuracy of developed numerical model for dynamic recrystallization grain size considering pinning effect.
Finally, we summarize our D_{DRX} prediction model. In the dynamically crystallized microstructure system where the pinning effect is significant, the relationship between D_{DRX} and the Zener-Hollomon parameter of the isothermal forging condition is shown as
\begin{equation} D_{\text{DRX}} = A_{\text{DRX}}(f)Z^{- n_{\text{DRX}}(f)}. \end{equation} | (12) |
\begin{equation} A_{\text{DRX}} = A_{1},\quad n_{\text{DRX}} = n_{1}. \end{equation} | (13) |
\begin{equation} \ln A_{\text{DRX}} = A_{2}f^{2} + A_{2}'f + A_{2}'',\quad n_{\text{DRX}} = n_{2}f + n_{2}'. \end{equation} | (14) |
\begin{equation} A_{\text{DRX}} = A_{3},\quad n_{\text{DRX}} = n_{3}. \end{equation} | (15) |
In this paper, the high temperature deformation behavior and the microstructure evolution of Ni–Co base superalloy TMW-4M3 during the isothermal forging process were experimentally and numerically analyzed. Based on the results, the following findings can be summarized:
\begin{equation*} Z = \dot{\varepsilon}\exp (613600/RT) = 1.07 \times 10^{14} \times \sigma_{\text{p}}^{3.92}, \end{equation*} |
\begin{equation*} Z = \dot{\varepsilon}\exp (410300/RT) = 2.19 \times 10^{7} \times \sigma_{\text{s}}^{3.64}. \end{equation*} |