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Stress rupture characteristics of Inconel 718 alloy for ramjet combustor Duck-Hoi Kim a , Jae-Hoon Kim b,∗ , Jeong-Woo Sa a , Young-Shin Lee b , Chul-Kyu Park b , Soon-Il Moon c b

a National Fusion Research Center, 52 Yeoeun-dong, Yuseong-gu, Daejeon 305-333, Republic of Korea Department of Mechanical Design Engineering, Chungnam National University, 220 Gung-dong, Yuseong-gu, Daejeon 305-764, Republic of Korea c Agency for Defense Development, Daejeon Yuseong P.O. Box 35, Yuseong-gu, Daejeon 305-600, Republic of Korea

Received 6 June 2006; received in revised form 5 November 2006; accepted 21 December 2006

Abstract To evaluate the accelerated creep phenomena for ramjet combustor, the stress rupture tests for Inconel 718 alloy were performed at a temperature range of 649–760 ◦ C and a stress range of 381–1093 MPa. The stress exponent, n, under the given conditions was obtained. Also, the activation energy, H, was calculated from the experimental results. An empirical formula of accelerated creep rate for Inconel 718 alloy was calculated by computer simulation. The accelerated creep life of Inconel 718 alloy was evaluated by using Larson–Miller parameter. © 2007 Elsevier B.V. All rights reserved. Keywords: Accelerated creep; Stress rupture; Inconel 718 alloy; Creep life; Stress exponent; Activation energy

1. Introduction In the design of components operating at elevated temperatures, creep behavior needs to be considered primarily. In general, creep involves the time dependent deformation and fracture of materials. Creep is accelerated by an increase in stress or temperature. Creep is the slow deformation of a material under constant stress leading to a permanent change in shape. Creep fracture is normally related to the tertiary creep and characterized mainly by the nucleation, growth, and coalescence of microscopic internal cavities [1–3]. Inconel 718, a precipitation-strengthened nickel-iron-base super alloy, is one of the most widely used super alloys that exhibit adequate creep strength, ductility, and fatigue resistance up to 650 ◦ C. Applications of this alloy expanded from disk alloys in gas turbine engines to the components used in nuclear and cryogenic structures, high-strength bolts and fasteners, and components in space craft, owing to its excellent fabricability and weldability. Up to now, the creep characteristics of Inconel 718 alloy have been focused on conditions within maximum service temperature. On the contrary, studies related to accelerated ∗

Corresponding author. Tel.: +82 42 821 6645. E-mail address: [email protected] (J.-H. Kim).

0921-5093/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2006.12.159

creep rupture at a very high temperature environment have been progressed a little. However, accelerated creep rupture behavior of Inconel 718 alloy is one of major considerations in the application in the aerospace structures. In this study, the accelerated creep behavior of Inconel 718 alloy was investigated to be used in the combustor design of ramjet propulsion system. The stress exponent, n, under a given condition was obtained. Also, the activation energy, H, was calculated from the experimental results. An empirical formula of accelerated creep rate was obtained from the experimental results. The accelerated creep life was finally evaluated by using the Larson–Miller parameter (LMP). 2. Experimental procedures The test material was Inconel 718 alloy, and its chemical composition is shown in Table 1. The material was heat-treated in accordance with AMS 5596. Table 2 shows the mechanical properties, which were measured at RT and high temperatures of 649 ◦ C (1200 ◦ F), 704 ◦ C (1300 ◦ F) and 760 ◦ C (1400 ◦ F). In general, the recommended service temperature of Inconel 718 alloy is within 650 ◦ C. As can be seen in Table 2, the mechanical strengths at 649 ◦ C decreased about 20% compared with those at room temperature (RT).

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Table 1 Chemical compositions Element

Composition (mass%)

Ni Cr Fe Mo Ti Co Nb + Ta

55.0–55.5 17.0–21.0 18.5 3.0 0.65–1.15 1.00 5.1

The accelerated creep rupture tests were controlled by constant loading conditions based on ASTM E139. Stress rupture tests were performed using MTS 810 and test temperatures were 649 ◦ C, 704 ◦ C and 760 ◦ C on equal terms of tensile test. Initial stress level was selected from 45% to 95% of the ultimate strength. 3. Results and discussions 3.1. Creep curves Fig. 1 shows the strain–time curves for accelerated creep rupture tests of Inconel 718 alloy at various temperatures and stresses. As the temperature increases, tertiary creep behavior becomes dominant. Fig. 2 shows the dependence of stress on the accelerated creep rupture life of Inconel 718 alloy. As can be seen in Fig. 2, the stress dependence increases with increasing test temperature. 3.2. Stress exponent due to creep deformation Creep rupture is usually caused by thermally activated timedependent plastic deformation. The dependence of creep rate on the applied stress, called stress exponent n, can be calculated using the following Eq. (1) [4,5]: n=

dln ε dln σ

(1)

Fig. 3 shows the dependence of creep rate on the applied stress. The stress exponent decreased with increasing test temperature. This behavior can be explained that with decreasing temperature, dislocation diffusion is dominant due to the increase in the dislocation density under increasing stress. However, with increasing temperature, lattice diffusion is dominant [6]. From Fig. 3, the stress exponent, n, can be expressed as a linear function of temperature. Fig. 4 shows the stress exponent as a function of the temperature for accelerated creep rupture test.

Fig. 1. Strain–time curves obtained from the stress rupture tests. (a) 649 ◦ C, (b) 704 ◦ C and (c) 760 ◦ C.

Table 2 Mechanical properties Temperature (◦ C)

Yield strength (MPa)

Ultimate strength (MPa)

Young’s modulus (GPa)

Reduction of area (%)

Room temperature 649 704 760

1227 1023 936 814

1423 1150 997 848

209 163 161 151

15.54 8.18 3.17 1.06

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Fig. 2. Dependence of stress on the accelerated creep rupture.

Fig. 5. Dependence of creep rate on temperature.

obtained by [6]: H = −R

dln ε d(1/T )

(2)

where T is absolute temperature and R is the gas constant. Fig. 5 shows the dependence of creep rate on temperature. It is seen that the activation energy decreased with increasing stress. Also, the activation energy can be expressed as a linear function of stress, and the fitting result is presented in Fig. 6. 3.4. Empirical formula of creep rate ε˙

Fig. 3. Dependence of creep rate on the applied stress.

3.3. Activation energy of creep deformation

The creep behavior is a function of temperature (T), stress (σ), structural factor (SF) and chemical compositions, etc. It can be expressed using the following empirical equation [6]: −HA(σ, T, SF) ε˙ = A(σ, T, SF)σ(ε)n(σ,T,ST) exp (3) RT

Creep deformation is also progressed by thermally activated process, and activation enthalpy, H, can be

where stress exponent (n) and activation enthalpy (H) were already obtained as a function of temperature and stress in Figs. 4 and 6.

Fig. 4. Stress exponents vs. temperatures curve for accelerated creep rupture tests.

Fig. 6. Relation between the activation enthalpy and stress.

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Fig. 8. Correlation of Larson–Miller parameter for Inconel 718 alloy from accelerated stress rupture tests.

accelerated creep rupture life can be easily predicted by using this result.

Fig. 7. Dependence of ln A on stress.

The relations between ln A and stress under a certain temperature using computer simulation are shown in Fig. 7. As can be seen in Fig. 7, ln A under constant temperature conditions can be expressed as a linear function of stress. (i.e. Eq. (4)): ln A = gσ + h

(4)

Coefficients g and h in Eq. (4) were calculated using computer simulation, and then used in Eq. (4). Thus, ln A can be expressed as ln A = (4.61 × 10−6 σ − 2.7 × 10−2 )σ +(0.3952σ − 234.296)

(5)

Therefore, the empirical equation of creep rate ε˙ can written: ε˙ = exp[(4.61 × 10−6 σ − 2.7 × 10−2 )σ +(0.3952σ − 234.296)] ×σ

(−6.66×10−2 T +62.84)

(−0.23σ + 209.64) × 103 exp RT

4. Conclusions (i) Accelerated creep tests of Inconel 718 alloys showed a good creep resistance up to 704 ◦ C. (ii) The stress exponents, n, were evaluated as 9.6, 6.2 and 2.2 at 649, 704 and 760 ◦ C, respectively. The stress exponent decreased with increasing test temperature. (iii) The activation energies, H, were calculated as 515.8, 196.7, 55.6 kcal/mol K under 700, 800 and 900 MPa, respectively. (iv) An empirical formula of accelerated creep rate of Inconel 718 alloy was obtained by computer simulation. The accelerated creep life for Inconel 718 alloy can be expressed as follows, (LMP = (T + 273.15)(log tr + 625) × 10−3 ). Acknowledgments

(6) 3.5. Accelerated creep life prediction To predict the accelerated creep rupture life, the well-known Larson–Miller parameter was used. Fig. 8 shows the correlation of Larson–Miller parameter for Inconel 718 alloy. The data in Fig. 8 is comparable to the data given in the specification. The

This work was partially supported by the Agency for Defense Development project (ADD-03-04-02). References [1] J.T. Yeom, J.Y. Kim, Y.S. Na, N.K. Park, Metall. Mater. Int. 9 (2003) 555–560. [2] R. Viswanathan, J. Foulds, J. Press. Vess.-Trans. ASME 120 (1998) 105–115. [3] S. Srinivas, K.S. Prasad, D. Gopikrishna, M.C. Pandey, Mater. Charact. 35 (1995) 93–98. [4] F. Garofulo, Trans. TMS-AIME 229 (1963) 351. [5] L.J. Cuddy, Metall. Trans. 1 (1970) 395. [6] Y.G. Park, B.J. Yoon, J.H. Choi, J. Ksht. 13 (2000) 383–390 (in Korean).