EFFECT OF ALLOYING ELEMENTS ON CREEP AND FATIGUE DAMAGE OF NI- BASE SUPERALLOY CAUSED BY STRAIN-INDUCED ANISOTROPIC DIFFUSION

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1 Proceedings of the ASME 13 International Mechanical Engineering Congress and Exposition IMECE13 November 15-1, 13, San Diego, California, USA IMECE EFFECT OF ALLOYING ELEMENTS ON CREEP AND FATIGUE DAMAGE OF NI- BASE SUPERALLOY CAUSED BY STRAIN-INDUCED ANISOTROPIC DIFFUSION Ken Suzuki Fracture & Reliability Research Institute, Tohoku University, Sendai, Miyagi, Japan Tomohiro Sano Department of Nanomechanics, Tohoku University Sendai, Miyagi, Japan Hideo Miura Fracture & Reliability Research Institute, Tohoku University Sendai, Miyagi, Japan ABSTRACT In order to make clear the mechanism of the directional coarsening (rafting) of γ' phases in Ni-base superalloys under uni-axial tensile strain, molecular dynamics (MD) analysis was applied to investigate effects of alloying elements on diffusion characteristics around the interface between the γ phase and the γ' phase. In this study, a simple interface structure model corresponding to the / ' interface, which consisted of Ni as and Ni 3 Al as ' structure, was used to analyze the diffusion properties of Ni and Al atoms under tensile strain. The straininduced anisotropic diffusion of Al atoms perpendicular to the interface between the Ni(1) layer and the Ni 3 Al(1) layer was observed in the MD simulation, suggesting that the straininduced anisotropic diffusion of Al atoms in γ phase is one of the dominant factors of the kinetics of the rafting during creep damage. The effect of alloying elements in the Ni-base superalloy on the strain-induced anisotropic diffusion of Al atoms was also analyzed. Both the atomic radius and the binding energy with Al and Ni of the alloying element are the dominant factors that change the strain-induced diffusion of Al atoms in the Ni-base super-alloy. INTRODUCTION Since creep is a dominant failure mechanism of structural materials which are exposed to high temperature and pressure for long periods, improvement of creep resistance of high temperature materials is one of the most important issues for assuring the long life reliability in actual operation. Ni-base superalloys have been widely applied to gas turbine blades in combustion power plants and aircraft engines. Directionally solidified or single crystal Ni-base superalloys are employed for the blade material used at high temperatures because they show the superior stress-rupture resistance, higher thermal fatigue resistance, and higher incipient melting temperatures comparing with polycrystalline Ni-base superalloys. High temperature mechanical properties of the Ni-base superalloys are improved by the fine cuboidal γ (Ni 3 Al) precipitates orderly-dispersed in the γ matrix (Ni-rich matrix) because the dispersed texture in a grain inhibits dislocation motion. However, directional coarsening of the ' phase perpendicular to a principal stress, which is called rafting, occurs when an uni-axial external stress is applied to the superalloys at high temperatures (~1 o C). The γ' precipitates start to grow perpendicularly to the direction of the externally applied load, and the initial finely-dispersed cuboidal texture changes to large layered texture. Since the formation of the raft causes softening of the alloys, strength of the alloys at high temperature decreases drastically and cracks starts to propagate rapidly along the layered interface between the newly grown γ' phase and the γ phase. As a result, creep fracture is accelerated seriously once the layered texture appears. Therefore, it is very important to suppress the rafting for improving the strength of the Ni-base super-alloy at high temperatures under the applied load and thus, assuring the reliability of the turbine systems. Similar micro texture change was observed in this alloy near crack tips after fatigue loading [1, ]. This means that the rafting occurs not only during creep loading but also during cyclic loading. Therefore, it is very important to understand mechanisms of the rafting for improving both creep and fatigue resistance of the Ni-base superalloys at high temperatures. Though, not a few 1 Copyright 13 by ASME

2 research activities have been continued, the mechanism of the micro texture change has not been clarified fully yet [3-9]. The rafting tends to occur when the Ni-base superalloys are subjected to a small tensile stress at elevated temperatures and thus, the rafting process is basically considered as hightemperature diffusion-controlled process. Conventionally, the atomic diffusion is expressed by the gradients of temperature and concentration. In addition to these gradients, stress (strain) acts as the driving force of the atomic diffusion in solids because strain can alter chemical potentials of component atoms. Since the combination of the externally applied load and the lattice mismatch between the phase and the phase produces the anisotropic strain field in the Ni-base superalloy, atoms and vacancies diffuse anisotropically depending on the local strain state. In the past study, diffusion properties of component elements near the Ni/Al interface structure was analyzed quantitatively by using molecular dynamics (MD) simulation [1]. The anisotropic diffusion of Al atoms perpendicular to the interface occurred when uni-axial tensile strain was parallel to the interface. This diffusion behavior corresponds well to the fact that the finely-dispersed γ phase starts to grow and form thin layered structures perpendicular to the direction of the applied uni-axial strain. We have considered, therefore, that the strain-induced anisotropic diffusion in the Ni-base superalloys is one of the most important factors that dominate the rafting phenomenon. Thus, the suppression of the anisotropic diffusion of Al atoms should decrease the evolution of the rafting and improve both the creep and fatigue resistance of the Ni-base superalloy. The addition of different alloying elements is an effective method for controlling the kinetics of the rafting. In this study, the effect of alloying elements in the Ni-base superalloys on the strain-induced anisotropic diffusion of Al atoms was analyzed by MD simulations. In particular, co-doping effects on the diffusion were investigated by considering the interaction between alloying elements. Dopant atoms γ phase Ni (FCC) [4 atoms] [1] [1] Ni3Al (FCC) [4 atoms] z y x γ phase (a) (b) Fig. 1 MD simulation models of the interface between γ and γ phases; (a) Ni(1)/Ni3Al(1) and (b) single-element-doped Ni(1)/Ni3Al(1) interfaces. dopant atoms in the single-element-doped Ni/Ni3Al interface model was changed from.1 at% (1 atoms) to.5 at% ( atoms). In the case of co-doped Ni/Ni3Al interfaces, two kinds of dopant elements were added to the Ni layer at the same time. The atomic concentration of both dopant elements was.6 at% (5 atoms). The MD simulations were carried out using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) code [11]. Since normal strain exists parallel to the interface due to the lattice mismatch between Ni and Ni3Alcrystal, the structural relaxation calculation at 1573 K was performed by changing the volume for 5 ps in order to obtain the equilibrium lattice parameters of the Ni/Ni3Al interface model. It was assumed that obtained Ni/Ni3Al interface structure was under stress (strain) free condition at 1573 K. The uni-axial tensile strain was applied to the equilibrium interface structure by increasing the length of the lattice parameters from the equilibrium value. For example, in the case of the Ni/Ni3Al interface model with uni-axial % tensile strain parallel to the interface, only the lattice parameter along the x-axis of the interface model was expanded. When uni-axial tensile strain was applied to the interface structure, the structure tended to shrink in the other two directions (y- and z-directions) perpendicular to the direction of tensile strain. Thus, in order to obtain the equilibrium lattice parameters along y- and z-axis of the Ni/Ni3Al interface structure under tensile strain along xdirection, the Ni/Ni3Al interface structure was relaxed by ps MD calculation. After the relaxation, the MD simulations were carried out for 5 ps under the fixed volume condition (no fluctuation of lattice constants during the simulation) for evaluating the change of the diffusion constants of Ni and Al atoms around the strained Ni/Ni3Al interface. The analytical condition used in this analysis is summarized in Table 1.The diffusion constants of atoms were evaluated from the slope of the mean square displacement (MSD) of each element. The MSD values were calculated according to Eq. (1), and the selfdiffusion coefficient (D) was obtained from the slope of MSD versus time [1] based on Einstein s equation: ANALYTICAL METHOD A simple interface structure model corresponding to the / ' interface, which consisted of Ni as and Ni3Al as ' structure, was used to analyze the diffusion properties around the interface under tensile strain at elevated temperature of 1573 K. Figure 1 shows the supercell model of Ni/Ni3Al interface. In the Ni/Ni3Al interface model, interfacial crystallographic plane was (1) plane, which is mainly observed in the actual / ' coherent interface. The supercell model was composed of 8 atoms, and three-dimensional periodic boundary conditions were applied. To examine the effects of alloying elements on the diffusion properties of Ni and Al atoms in the Ni/Ni3Al interface, W, Mo, Ta, Cu, Pd, Pt, Zr and Ti were individually placed into the Ni layer as the dopant. In the case of singleelement-doped Ni/Ni3Al interfaces, some Ni atoms in the Ni layer were replaced by dopant atoms (one alloying element) randomly as shown in Fig. 1 (b). The atomic concentration of Copyright 13 by ASME

3 MSD(t ) 1 N 6Dt, N Table 1 Analytical condition r t r i Structure Relaxation NTP* 1. fs, steps % GEAM 1573K i i 1 Ensemble Time Step Number of Steps Applied strain Potential Function Temperature (1) where N is the total number of atoms, ri is the position of the i-th atom and t is time. The generalized embedded atom method (GEAM) interatomic potential was used for all simulations. The potential parameters defined by Zhou et al., [13] were used for all alloying elements except aluminum. Because melting temperature of bulk aluminum evaluated from the MD simulation using the original parameters was lower than experimental value, the parameters for two-body potential part of aluminum were modified to reproduce lattice constants as well as melting temperature. The modified parameters of aluminum are listed in Table. Figure shows the total energy per atom and the lattice constants of aluminum as a function of temperature. The total energy and the lattice constant in this figure are average values calculated from the 1-step MD simulation using the modified parameters for each temperature. As can be seen in this figure, calculated lattice constant at 3 K (4.5 Å) and melting temperature (around 93 K) are good agreement with experimental values of 4.5 Å and 933 K, respectively. Main Analysis NTV** 1. fs 5, steps ~% GEAM 1573K *NTP; Number of atoms, temperature, pressure are fixed. **NTV; Number of atoms, temperature, volume are fixed. Table Potential parameters of aluminum for two-body terms re fe A B Energy (ev) Lattice constant (Å) -3.4 STRAIN-INDUCED ANISOTROPIC DIFFUSION OF AL ATOMS Figure 3 shows the atomic configuration of the Ni/Ni3Al interface structure under % strain along x-direction (parallel to the interface). Both Ni and Al atoms around the interface diffused significantly, and the mixing of Al and Ni atoms around the interface was found to occur at 5 ps. Figure 4 shows the MSD values of Al atoms in the Ni/Ni3Al interface under % strain (no strain) and % tensile strain along x-direction. The MSD value of Al atoms perpendicular to the interface (zdirection) was increased when the tensile strain of % was applied parallel to the interface. The calculated diffusion constants of Al atoms are summarized in Table 3. It was found that the tensile strain accelerated the atomic diffusion in all directions. In particular, the atomic diffusion perpendicular to the interface was accelerated remarkably. This anisotropic diffusion of Al atoms in the Ni/Ni3Al interface under tensile strain corresponds well to the fact that the finely-dispersed γ phase starts to grow and form thin layered structures perpendicular to the direction of the applied uni-axial stress. Figure 5 shows the strain dependence of diffusion constants of Al atoms in the Ni/Ni3Al interface. Diffusion constants perpendicular to the interface increased with increasing tensile strain. The diffusion coefficient perpendicular to the interface with 4% tensile strain was increased by about times. This result clearly indicates that the high local strain accelerated the atomic diffusion. When stress or strain was applied to the crystal structure, Temperature (K) Fig. Total energy and lattice constant of aluminum as a function of temperature 5 ps 5 ps Fig.3 Snapshots of Ni/Ni3Al interface structure under % tensile strain parallel to the interface the structure deforms to relieve the applied stress or the high strain energy. The relaxation of strain energy by the diffusion of component elements has often been found in metal thin films used for interconnections and the contact (bond) interface between metal wires used in electronic devices [14]. In the Ni/Ni3Al interface structure, the anisotropic diffusion of Al 3 Copyright 13 by ASME

4 Diffusion constants ( 1-9cm/s) MSD(Å ) (a).17 x y z Time (ps) at%.6 at% 1.3 at%.5 at% Strain (%) Fig. 5 Strain dependence of diffusion constants of Al atoms perpendicular to the interface of Ni/Ni3Al x y z Diffusion constant [1 cm /s] MSD(Å ) (b) Time (ps) Fig. 4 Mean square displacement (MSD) of Al atoms in Ni/Ni3Al interface with (a) no strain and (b) % tensile strain parallel to the interface Table 3 Calculated diffusion constants of Al atoms in each direction of Ni/Ni3Al interface with % and % tensile strain parallel to the interface Diffusion constants ( 1-9 cm/s) strain x-direction y-direction z-direction % % Mo W Ta Cu Pd Pt Zr Ti Fig. 6 Effect of dopant elements on the strain-induced anisotropic diffusion of Al atoms in the single-element-doped Ni/Ni3Al interface. The red line indicates the value of diffusion constant of Al atoms in the non-doped Ni/Ni3Al interface. and phases, and consequently to modify the coherency stress between the two phases. Naturally, the thermodynamic stability of both phases can also be improved by the alloying elements. The effect of alloying elements in the Ni-base superalloy on the strain-induced anisotropic diffusion of Al atoms was, therefore, analyzed by replacing some Ni atoms in the Ni layer of Ni/Ni3Al interface system. Figure 6 summarizes the effect of the alloying element (dopant element) on the diffusion constant of Al atoms perpendicular to the interface of single-element-doped Ni/Ni3Al under % tensile strain. It was found that the diffusion constant of Al atoms was changed drastically by the dopant elements and their atomic concentration. Compared with the diffusion constant in the non-doped Ni/Ni3Al interface, Zr and Ta accelerated the diffusion at all concentrations of the dopant considered in this analysis. On the other hand, the addition of small amount (.1 at%) of Mo, W, Cu, Pd and Pt decreased the diffusion of Al atoms. However, Mo, W and Cu accelerated the diffusion with increasing the concentration of the dopant, while Pt and Pd decreased the diffusion at all concentrations. The addition of Ti showed no significant change in the diffusion atoms perpendicular to the interface resulted in the mixing of Al and Ni atoms around the interface as shown in Fig. 3. As a result, the lattice mismatch at the interface decreased and the high strain field was relaxed substantially. This means that the strain-induced anisotropic diffusion in the Ni/Ni3Al interface occurs for relaxing the elastic strain energy. Therefore, the rafting phenomenon is attributed to the process for relaxing the elastic strain energy by the atomic diffusion under creep condition at high temperatures. EFFECT OF ALLOYING ELEMENTS ON STRAININDUCED ANISOTROPIC DIFFUSION OF AL ATOMS Since the anisotropic diffusion of Al atoms plays a key role in the rafting phenomenon of phase, the reduction of the mobility of Al atoms perpendicular to the interface between Ni and Ni3Al should decrease the evolution of the rafting and thus, improve both the creep and fatigue resistance of the Ni-base superalloy. The addition of different alloying elements is an effective method for controlling the kinetics of the rafting because it is generally possible to change the lattice constant of 4 Copyright 13 by ASME

5 constant. From this analysis, Pd is one of the most effective elements that restrain Al atoms from moving around the interface. Both the atomic radius and the binding energy of the dopant elements are the dominant factors that change the diffusion of Al atoms in the Ni-base super-alloy. Since the lattice constant of Ni crystal (3.5 Å) is smaller than that of Ni 3 Al crystal (3.57 Å), the Ni and Ni 3 Al layers are expanded and shrunk in the equilibrium coherent Ni/Ni 3 Al interface, respectively. Therefore, the doping into the Ni layer decreased the lattice mismatch between Ni and Ni 3 Al layers and, consequently, the residual strain due to the lattice mismatch in each layer of the Ni/Ni 3 Al interface became small. The decreasing diffusivity of Al atoms by the addition of small amount of Mo, W and Cu was mainly due to the decreasing the lattice mismatch. However, when the lattice constant of the Ni layer became larger than that of the Ni 3 Al layer by the addition of the dopant elements, the tensile strain was induced in the Ni 3 Al layer of the coherent Ni-dopant/Ni 3 Al interface. In addition to the external tensile strain, the residual tensile strain in the Ni 3 Al layer enhanced the diffusion of Al atoms and thus, the diffusion of Al atoms was accelerated by increasing the concentration of Mo, W and Cu, and by the addition of Zr and Ta. On the other hand, in the case of Pt and Pd, the binding energy with Al is the dominant factor controlling the diffusivity of Al atoms. Figure 7 shows the binding energies of the dopant elements with Ni and Al. These values were calculated from the pair interaction of the GEAM potential and large positive value of the binding energy in this figure indicates that atomic bonds are strong and energetically stable. The binding energies of Pt and Pd with Al are small compared with the other dopant elements. This small binding energy indicates that that the attractive interactions between Pt or Pd and Al are weak and thus, the bond formation of Al with Ni is more energetically favorable than that with Pt or Pd. Therefore, since Al atoms tended to keep away from Pt or Pd atoms in the system, these elements were effective for reducing the diffusion of Al atoms perpendicular to the Ni-dopant/Ni 3 Al interface. Since actual Ni-base superalloy consists of multi elements, it is necessary to clarify the presence of the interaction between the different dopant elements. Therefore, two kinds of dopant elements were added to the Ni layer and the diffusion property of Al was also analyzed. In this analysis, four dopant pairs, W- Pd, W-Mo, Pd-Pt and Pd-Mo were considered. Figure 8 summarizes the analytical results. Though both Pd and Pt atoms are effective dopant elements for decreasing the diffusion of Al atoms as shown in Fig. 6, the diffusion of Al atoms was accelerated when both Pd and Pt atoms were doped in the Ni layer simultaneously. On the other hand, W-Mo co-doping suppressed the diffusion of Al atoms significantly though single doping of W and Mo in the Ni layer showed little effect on decreasing the diffusion of Al atoms. These results indicated the presence of the interaction between the dopant elements. Figure 9 shows the binding energy between dopant elements. The binding energy of W-Mo is more than twice that of Ni-Ni, while Fig. 7 Binding energies of dopant element with Ni and Al calculated from the pair potential interaction of GEAM. Diffusion constant [1-8 cm /s] W-Pd W-Mo Pd-Pt Pd-Mo Fig. 8 Diffusion constant of Al atoms in the co-doped Ni/Ni 3 Al interface under %-strain Fig. 9 Binding energy between dopant elements the binding energy of Pd-Pt is much smaller than that of Ni-Ni. This means that co-doping of W-Mo makes the Ni-base superalloy more energetically stable, but the superalloy becomes unstable by co-doping of Pd-Pt. Therefore, the diffusion of Al atoms was decreased by co-doping of W-Mo because of the stabilization of the Ni-base superalloy. The magnitude of the binding energy between dopant elements is also dominant factor controlling the strain-induced anisotropic diffusion of Al atoms. 5 Copyright 13 by ASME

6 CONCLUSION In this study, molecular dynamics (MD) simulations were applied to explicate the mechanism of creep damage of Ni-base superalloy, i.e., the mechanism of the change of the micro texture of the alloy from the initial finely-dispersed ' phase to the coarse layered ' phase. The strain-induced anisotropic diffusion of Al atoms in the Ni/Ni 3 Al interface structures was found to occur under the tensile strain applied parallel to the interface. The effect of alloying elements (dopant elements) on diffusion characteristics of Al atoms around the Nidopant/Ni 3 Al interface was investigated. The diffusion constant of Al atoms was changed drastically by the dopant elements and their atomic concentration. Both the atomic radius and the binding energy of the dopant elements with Al are the dominant factors that change the diffusion of Al atoms in the Ni-base super-alloy. It was found that Zr and Ta accelerated the straininduced anisotropic diffusion of Al atoms. On the other hand, Pd and Pt decreased the diffusion significantly. In the case of the addition of Mo, W and Cu, the diffusion of Al atoms was decreased by small amount of the dopants although the diffusion was accelerated with increasing the concentration of the dopant elements. When two kinds of dopant elements were added to the Ni layer of the Ni/Ni 3 Al interface, there was the presence of the interaction between the dopant elements. Although W and Mo atoms accelerated the diffusion of Al atoms when they were doped separately, the diffusion of Al atoms was decreased when W and Mo were added simultaneously. From the analysis, the magnitude of the binding energy between dopant elements is also dominant factor controlling the strain-induced anisotropic diffusion of Al atoms. Since the strain-induced change of the micro texture causes abrupt fracture of the alloy, it is very important to develop the countermeasure which minimizes the strain-induced anisotropic diffusion of Al atoms in order to assure the long life reliability of the alloy in actual operation. ACKNOWLEDGMENTS This research was partly supported by the Grants-in-Aid for Scientific Research and the Japanese special coordination funds for promoting science and technology. REFERENCES (1) Miura, H., Akahoshi, K., and Suzuki, K., 9, Nondestructive evaluation of creep and fatigue damages in nickel base super-alloys using a scanning blue laser microscope, J. of NDT and E International, 4, pp () Okazaki, M., and Yamazaki, Y., 1999, Creep-fatigue small crack propagation in a single crystal Ni-base superalloy, CMSX- Microstructural influences and environmental effects, INTERNATIONAL JOURNAL OF FATIGUE, 1, pp. S79-S86. (3) Ratel, N., Calderon, H. A., Mori, T., and Withers, P.J., 1, Predicting the onset of rafting of gamma ' precipitates by channel deformation in a Ni superalloy, PHILOSOPHICAL MAGAZINE, 9, pp (4) Zhou, N., Shen, C., Mills, M., and Wang, Y. Z., 1, Large-scale three-dimensional phase field simulation of gamma'-rafting and creep deformation, PHILOSOPHICAL MAGAZINE, 9, pp (5) Fedelich, B., Kunecke, G., Epishin, A., Link, T., and Portella, P., 9, Constitutive modeling of creep degradation due to rafting in single-crystalline Ni-base superalloys, MATERIALS SCIENCE AND ENGINEERING A-STRUCTURAL MATERIALS PROPERTIES MICROSTRUCTURE AND PROCESSING, 51-11, pp (6) Zhou, N., Shen, C., Mills, M. J., and Wang, Y., 9, Contributions from elastic inhomogeneity and from plasticity to gamma ' rafting in single-crystal Ni-Al, ACTA MATERIALIA, 56, pp (7) Yeh, A. C., Sato, A., Kobayashi, T., and Harada, H., 8, On the creep and phase stability of advanced Ni-base single crystal superalloys, MATERIALS SCIENCE AND ENGINEERING A-STRUCTURAL MATERIALS PROPERTIES MICROSTRUCTURE AND PROCESSING, 49, pp (8) Sakaguchi, M. and Okazaki, M., 7, Fatigue life evaluation of a single crystal Ni-base superalloy, accompanying with change of microstructural morphology, INTERNATIONAL JOURNAL OF FATIGUE, 9, pp (9) Yu, J. J., Sun, X. F., Jin, T., Zhao, N. R., Guan, H. R., and Hu, Z. Q., 7, Effect of Re on deformation and slip systems of a Ni base single-crystal superalloy, MATERIALS SCIENCE AND ENGINEERING A- STRUCTURAL MATERIALS PROPERTIES MICROSTRUCTURE AND PROCESSING, 458, pp (1) Suzuki, K., Ito, H., Inoue, T., and Miura, H., 9, Creep Damage Process of Ni-Base Superalloy Caused by Stress- Induced Anisotropic Atomic Diffusion, Journal of Solid Mechanics and Materials Engineering, 3, pp (11) LAMMPS Molecular Dynamics Simulator, (1) W. Sekkal et al., Computational Mater. Sci., 9 (1998) 95. (13) Zhou, X. W., Wadley, H. N. G., Johnson, R. A., Larson, D. J., Tabat, N., Cerezo, A., Petford-Long, A. K., Smith, G. D. W., Clifton, P. H., Martens, R. L., and Kelly, T. F., 1, Atomic scale structure of sputtered metal multilayers, Acta mater., 49, pp (14) A.Tezaki et al., 199, Measurement of Three Dimentional Stress and Modeling of stress Induced Migration Failure in Aluminium Interconnects, IRPS 9. P1. 6 Copyright 13 by ASME