2024 Volume 65 Issue 2 Pages 237-241
Creep lifetimes of polycrystalline nickel (Ni) based superalloys with given chemical compositions were predicted using the Larson–Miller parameter (LMP) and chemical composition, which reflects the effects of solid-solution strengthening and precipitation strengthening. Herein, the former effect is denoted as a δ parameter representing the amount of strengthening by multiple elements; the latter effect is a lattice misfit between γ and γ′ phases: ξ. These parameters respectively generate vertical and parallel translations of an LMP plot. The solid solution affects strengthening, i.e., vertical translation. The precipitate affects heat resistance in the alloys, i.e., parallel translation. After the trends were formulated in the first order, the amount of translation was evaluated quantitatively. The prediction worked well in the solid-solution strengthened Alloy 600 and Alloy 617 and in the solid-solution strengthened and precipitation strengthened γ + γ′ TMP alloy. Creep lifetimes of Ni-based alloys and superalloys can be predicted well using the simple formulae.
Nickel (Ni) based superalloys have been applied for hot sections of jet engines, such as high-pressure compressors, turbine blades, vanes, and discs. Because they are located after the combustion chamber, they are adversely affected by high-temperature, compressed combustion gases. Therefore, their heat resistance and high-temperature mechanical properties have been emphasized to improve engine properties. Although turbine discs are not affected directly by hot gas during operation, they must resist strong centrifugal forces because of their own weight and that of turbine blades. Presumably, that stress reaches about 1000 MPa during the take-off sequence. Temperatures become approximately 973 K.1,2) Therefore, the alloys contain highly dense (volume fraction (Vγ′) of about 50%3)) γ′-Ni3Al type precipitates (L12 structure) in their matrix to inhibit dislocation motion at high temperatures. Recently, the National Institute for Materials Science (NIMS) developed new-generation Ni–Co-based superalloys containing 25–29 mass% of Co and 3.9–6.2 mass% of Ti, which are designated as Tokyo-Meguro/Tsukuba-Material Wrought (TMW) alloys. The alloys were designed using a concept based on a combination between Ni-based and Co-based superalloys that have γ/γ′ two-phase structure, i.e., Co–Co3Ti structure, with the following characteristics: (1) good phase stability, (2) good oxidation resistance, (3) 100 MPa higher ultimate tensile strength, and (4) an approximately 70 K temperature advantage in 0.2%-strain creep performance compared to Udimet 720Li alloy.4)
To improve their heat resistance, powder metallurgy (P/M) has been applied for Ni-based superalloys. Application of P/M products to turbine discs started in the 1970s5) because of their uniformity of microstructure. For example, P/N Rene 95 showed superior low-cycle fatigue data to those of materials that had been conventionally cast and wrought (C&W).6) In addition, ME3,7) Low Solvus High Refractory (LSHR) alloys8) and TMP (Tokyo-Meguro/Tsukuba-Material P/M) alloys,9) which have been developed during the last two decades, show superior creep properties to those of C&W alloys.
Although strengthening mechanisms have come to be a highly attractive topics, creep lifetime is an important parameter to secure safe flight. Usually, the lifetime has been predicted using the Larson–Miller parameter (LMP),10) the Monkman–Grant relation,11) and the Burt–Wilshire equation,12) respectively expressed as shown below.
| \begin{equation} \mathrm{LMP} = T (\log t_{\text{r}} + C) \end{equation} | (1) |
| \begin{equation} K = t_{\text{r}} \dot{\varepsilon}_{\text{m}}{}^{p} \end{equation} | (2) |
| \begin{equation} \sigma/\sigma_{\text{B}} = \exp\{-k[t_{\text{r}} \exp(-Q/\mathit{RT})]^{u}\} \end{equation} | (3) |
In those equations, T stands for temperature, tr denotes the time-to-rupture, $\dot{\varepsilon}_{\text{m}}$ represents the minimum creep rate, σ signifies stress, σB expresses the ultimate tensile strength, Q denotes the activation energy for creep, R is the gas constant, and C, K, p, k, and u are materials’ constants. However, these parameters are not able to predict the lifetime of given materials because the equations include the parameters of the respective materials. Usually, these parameters are obtained from the series of creep tests. Therefore, obtaining the parameters themselves is time-consuming.
For this study, we explore the possibility of predicting the creep lifetime using a parameter depending on the nominal alloy compositions for Ni-based superalloys. For that prediction, the reported creep lifetimes and chemical compositions of Ni-based superalloys7,8) and Ni alloys13–16) were referred from the literature. The superalloys were heat-treated at supersolvus conditions and were assumed to contain γ′ phase with Vγ′ of about 50%.3)
In addition, the creep lifetimes of commercially pure Ni (Alloy 201) and a solid-solution strengthened alloy with the same chemical composition of γ phase in a TMP alloy (hereinafter, γ TMP alloy) were obtained from results of creep tests at 773 K–1073 K in air to produce the prediction equations presented in section 3. The as-received Alloy 201 was annealed at 973 K for 1 h or at 1073 K for 3 h in vacuo to obtain a fine-grained (FG) sample with grain size (d) of about 20 µm or a coarse-grained (CG) sample with d of about 100 µm as presented in Fig. 1. The γ TMP alloy was prepared using a cold crucible melting process in vacuo for making a billet. Then, the billet was forged and rolled to manufacture a 21-mm-diameter round bar. Heat treatments were applied at 1123 K for 5 h in vacuo to remove residual strain, where d was about 10 µm. These chemical compositions of both Ni samples are shown in Table 1. For this study, creep specimens with 30 mm gauge length and 6 mm diameter were manufactured from the round bars by machining.
Microstructure of Alloy 201 with d ∼ (a) 20 µm and (b) 100 µm, (c) the γ TMP alloy and (d) the γ + γ′ TMP alloy, which were taken by EBSD. (e) SEM image showing precipitate morphology in the γ + γ′ TMP alloy.
The TMP alloy (hereinafter, γ + γ′ TMP alloy) was crept to confirm the accuracy of the prediction method described in section 4. The manufacturing process was explained in an earlier report.9) A supersolvus heat treatment was selected to compare creep data in the literature.7,8,13–15) Solution heat treatment was conducted at 1473 K for 4 h; then aging treatments were done at 923 K for 24 h and then at 1033 K for 16 h in vacuo, where d was about 30 µm. The compositions of γ and γ′ phases evaluated using a 3D atom probe are shown in Table 1. Their microstructure was observed using electron back-scattered pattern (EBSD) analyses. Because only γ + γ′ TMP alloy contains γ′ phase, a scanning electron microscope (SEM) image was also taken, where the volume fraction of γ′ phase was inferred as about 55%. Although the value is slightly higher than those of ME3 and LSHR,3) the values were assumed to be of a similar quality to those of the present study.
First, creep lifetimes of the alloys7,8,13–16) are shown as a double logarithmic plot of applied stress and LMP (Fig. 2). As the figure shows, a high-stress region and low-stress region were apparent for all samples. The regression formulae in each region were defined as presented below.
| \begin{equation} \sigma = A \exp(-0.2\,\mathrm{LMP})\ \text{for high-stress region} \end{equation} | (4) |
| \begin{equation} \sigma = B \exp(-0.4\,\mathrm{LMP})\ \text{for low-stress region} \end{equation} | (5) |
In those equations, σ represents the applied stress; A and B are constants. However, Waspaloy were excluded for the analyses because the value of Al/Nb + Ta + Ti is less than 0.85 and because the alloy contains η and/or δ phases, which engender less creep.17) As shown in this figure, creep lifetime of solid-solution strengthened alloys shifts “vertically” in terms of the amount of solid-solution strengthening. “Vertically” means not truly a vertical shift, but with a slightly horizontal component included, as shown schematically in Fig. 3(a). It means that the solid-solution strengthening affects the increase of strength dominantly and increases the LMP collaterally.
Relation between applied stress and LMP (C = 16.6). High stress and low stress regions are divided clearly. Regression formulae for regions are included.
(a) Schematic plot showing how data shift by σt and LMPt, (b) σt vs. δ, (c) LMPt vs. δ, and (d) LMPt vs. ξ for the Ni alloys. Regression lines are shown in panels (b)–(d).
The creep lifetime of Ni-based superalloys with precipitates shifted horizontally in terms of precipitation strengthening. For Ni-based superalloys used for turbine disc applications, γ′ precipitate plays an important role in the strengthening at operating temperatures of around 973 K, showing that the yield stress and 1000 h life increase concomitantly with increasing volume fraction of the precipitate.1) Although the misfit between γ/γ′ phases is small to suppress the precipitate growth,1) the large misfit decreases the minimum creep rate18) and tends to increase creep lifetime.19,20) It is described that the misfit between γ/γ′ phases strongly affects LMP because the parameter includes the time-to-rupture, as shown in eq. (1). Therefore, the misfit tends to shift the creep data horizontally as presented in Fig. 2.
To evaluate the shifts quantitatively, the δ parameter (eq. (6)) and misfit between γ/γ′ phases, ξ, (eq. (8)21)) were applied respectively for solid-solution strengthening and precipitation strengthening as
| \begin{equation} \delta = 100 \times \sqrt{\sum\nolimits_{i = 1}^{N}c_{i}\left(1 - \frac{r_{i}}{\bar{r}} \right)^{2}}, \end{equation} | (6) |
| \begin{equation} \bar{r} = \sum\nolimits_{i = 1}^{N}c_{i}r_{i},\ \text{and} \end{equation} | (7) |
| \begin{equation} \xi = \frac{2(a_{1} - a_{2})}{a_{1} + a_{2}}, \end{equation} | (8) |
where ci and ri respectively represent the atomic concentration and atomic radius of the i-th element. Furthermore, $\bar{r}$ denotes the average atomic radius of the constituent elements as shown in eq. (7):22,23) a1 stands for the lattice parameter of γ′ phase; a2 stands for that of the γ phase. The lattice parameters of both phases were calculated using eq. (7) with chemical compositions reported in each reference. Figure 3 shows the relations among δ, ξ, stress and LMP: (b) stress at the transition point (hereinafter, transition stress, σt) vs. δ, (c) LMP at the point (hereinafter, transition LMP, LMPt) vs. δ, and (d) LMPt vs. ξ. σt and LMPt are defined respectively as the y and x values at the transition point from the high-stress region to the low-stress region (Fig. 3(a)). These parameters were correlated well, as depicted specifically in Fig. 3(b)–(d). That finding indicates clearly that the data simply shift in accordance with the δ parameter and ξ parameter as shown below.
| \begin{equation} \sigma_{\text{t}} = 101.7 \exp(0.6237\,\delta) \end{equation} | (9) |
| \begin{equation} \mathrm{LMP}_{\text{t}} = 15.23 + 0.3915\,\delta \end{equation} | (10) |
| \begin{equation} \mathrm{LMP}_{\text{t}} = 15.30 + 157.2\,\xi \end{equation} | (11) |
The effects of volume fraction of γ′ phase on the prediction are small in this study because the materials in the dataset shows only a small difference of Vγ′. Therefore, the proposed method can predict the creep lifetime of Ni-based superalloys with Vγ′ of about 50% currently.
Using the relations presented above, the creep lifetimes of Alloy 600, Alloy 617 and the γ + γ′ TMP alloys were predicted as portrayed in Fig. 4. First, δ and ξ for each alloy were calculated using the chemical compositions presented in Tables 1 and 2.13,24) Because Alloy 600 and Alloy 617 belong to solid-solution strengthened alloy with ξ = 0, σt and LMPt were evaluated using eqs. (9) and (10). Those of the γ + γ′ TMP alloy were calculated using eqs. (9) and (11) because the alloy contains γ′ phase. Then, the constants A and B for each alloy were obtained by substituting σt and LMPt into eqs. (4) and (5). Finally, the equations of prediction lines in a high-stress region and low-stress region for Alloy 600, Alloy 617, and the γ + γ′ TMP alloy were drawn. As the figure shows, the creep lifetimes of Alloy 600,13) Alloy 61725,26) and the γ + γ′ Ni-based superalloys can be evaluated based on the effects of solid-solution strengthening and precipitation strengthening with high accuracy. Although the data of chemical compositions and creep data of Alloy 617 are referred by different reports,24–26) they can be regarded as the data from the same sample in this study because the grades of the materials are the same.
Reportedly, newly developed alloys contain γ′ phase with Vγ′ of about 55%.3) As shown in Fig. 4, the LMP of the γ + γ′ TMP alloys is well predicted using the data of the materials with Vγ′ of about 50%.3) However, because the predicted data is located just below the experimentally obtained data, the volume fraction of the precipitate might exist. Because the high volume fraction of γ′ phase can suppress creep deformation, it is possible that the predicted data shifts rightward for materials with higher volume fraction of the precipitate, reflecting that the increasing the volume fraction increases the effect of ξ on the creep lifetime. According to the trend, it is implied that the volume fraction affects the amount of ξ in eq. (8) and eq. (11) changes as LMPt = 15.30 + 157.2 × f × ξ, where f is the parameter reflecting the amount of Vγ′. To modify the effect with high accuracy, the data of materials with wide-ranged volume fraction of γ′ phase and chemical compositions of γ and γ′ phases are necessary to ascertain of f in the near future.
In conclusion, this study demonstrated a creep lifetime prediction method in Ni-based alloys and superalloys using LMP plots and their chemical compositions. Chemical compositions were correlated well with the amount of solid-solution strengthening (δ parameter) and precipitation strengthening (ξ parameter), which respectively generate vertical and parallel translation of the LMP plot in the alloys. The trends, which can be formulated simply (eqs. (9)–(11)), show the degree to which the translations occur quantitatively. Therefore, the equations predicted creep lifetimes of the Ni-based alloys with given chemical compositions except for precipitation strengthened alloys with Al/Nb + Ta + Ti of <0.85. This study actually demonstrated that the prediction works well in the solid-solution strengthened Alloy 600 and Alloy 617 and the solid-solution strengthened and precipitation strengthened γ + γ′ TMP alloy, as portrayed in Fig. 4. Therefore, the simple prediction method of creep lifetime can be available to design a new polycrystalline Ni based superalloys. Although the volume fraction of precipitate is currently restricted because of a lack of data, its effect on creep lifetime will be apparent if adequate data are accumulated in the near future.
This work was supported by Cabinet Office, Government of Japan, Cross-ministerial Strategic Innovation Promotion Program (SIP), “Materials Integration for Revolution Design System of Structural Materials” (funding agency: JST). The authors would like to thank Dr. T. Sasaki, Dr. T. Osada, Mr. T. Kohata, and Ms. H. Gao (NIMS) for technical assistance with microstructural observations.
