(creep) 500~ ~ 30 MPa 9Cr-1Mo 100 MPa ( ) 9Cr-1Mo Threshold Stress Larson-Miller Manson-Haferd Ω

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1 9Cr-1Mo Cr-1Mo ( ) 9Cr-1Mo Larson-Miller Manson-Haferd MPC Ω 823K 848K 873K 923K Ω 9Cr-1Mo Ω 9Cr-1Mo Larson-Miller Manson-Haferd 9Cr-1Mo Larson-Miller Manson-Haferd Ω

2 (creep) 500~ ~ 30 MPa 9Cr-1Mo 100 MPa ( ) 9Cr-1Mo Threshold Stress Larson-Miller Manson-Haferd Ω

3 1. 9Cr-1Mo 2. Larson-Miller Manson-Haferd Ω 9Cr-1Mo 3. 9Cr-1Mo 9Cr-1Mo 4.1 Larson-Miller Larson-Miller Arrhenius εss = n Aσ e Q RT. 4.1 A Q J R J/K*mole dε t r dt minimum = (4.1)(4.2) Q At r exp = RT constant Larson-Miller Q P L M = = T( C + log10 t r ) R T K t r hr C 20 Larson-Miller 15~ /T=0 log = C 1 Larson-Miller t r

4 t r 4.2 Manson-Haferd P M H = ( T Ta ) ( log t log t ) a Larson-Miller Manson-Haferd 1953 Larson-Miller - - Larson-Miller Larson-Miller C=20 Manson-Haferd P M-H Manson-Haferd T K T a Manson-Haferd t hr t a Manson-Haferd 4.3 Ω Omega Method MPC The Materials Properties Council 1986 Larson-Miller Kachanov Monkman-Grant Ω m + p + c Monkman-Grant Ω dlnε = m+ p+ c=ω dε m Norton p c Norton 9Cr-1Mo K MPa

5 K MPa 155 MPa 142 MPa 136 MPa Strain, % x x x x10 3 Time, s 823 K - 6.2

6 155 MPa K 848 K 873 K 40 Strain, % x x x x x10 3 Time, s 155 MPa εss = n Aσ e Q RT n (K), n, r log (Minimum Creep Rate, mm/mm/s) K 848 K 873 K 923 K log (Applied Stress, MPa)

7 n ss = ε A ( σ σ ) th n e Q RT 6.2 ε ss (1/s) A σ (MPa) σ th (MPa) n Q (J) R (J/mol/K) T (K) n ε ss 1/ n ε ss 1/ 40 (Minimum Creep rate, mm/mm/s)^1/n K 848 K 873 K 923 K Applied Stress, MPa 9Cr-1Mo 6.5 Larson-Miller Larson-Miller Larson Miller Larson-Miller Larson-Miller

8 /Temperature, K MPa 155 MPa 142 MPa 136 MPa 128 MPa 110 MPa log (Rupture Time, hr) - Larson-Miller Larson-Miller 20 4 L-M (K) (MPa) (hr) % ,874,475 12% 4 83,066, ,474 12% 4 140, ,955 12% 4 3, ,399,749 3% 4 31,368, ,692 3% 4 43, % ,356,506 21% 4 27,029, ,790 15% 4 15, % ,689,853 37% 4 2,697, % % MPa 3 % ~ 17 % 30 MPa 3 %~37 % 923 K, 90 MPa 17 % 40 3 % 823K 30MPa 90

9 Larson-Miller 6.6 Manson-Haferd log (Rupture Time, hrs) log t a =16 hr Ta=449 K 155 MPa 142 MPa 136 MPa 128 MPa 110 MPa Absolute Temperature, K Manson-Haferd t a T a log (Minimum Creep Strain Rate, mm/mm/sec) MPa 155 MPa 142 MPa 136 MPa 128 MPa 110 MPa Absolute Temperature, K Ta=420 K log ra= -23 mm/mm/sec Manson-Haferd r a T a log t a =16 hr T a = 449 K 8 log r a = -23 mm/mm/sec T a = 420 K 4.5 Manson-Haferd Manson-Haferd

10 -24 Manson-Haferd Parameter K 848 K 873 K 923 K -30 P M H ( T 449) = = (logt 15.95) r ( T 420) σ σ PM H = = σ 0.08σ log εss + 23 Applied Stress, MPa Manson-Haferd Manson-Haferd 9Cr-1Mo 6.3 Manson-Haferd Manson-Haferd Manson-Haferd t t a ε ss r a 9 Cr-1 Mo Manson-Haferd Parameter K 848 K 873 K 923 K Applied Stress, MPa Manson-Haferd

11 6.7 Ω Ω Ω Ω K r Ω = 0.427σ Ω = 0.280σ Ω = 0.212σ Ω = 0.179σ Ω 6.5 t t s r ε tsω = ε t Ω + 1 s 6.5 Ω ε 1 = ln 1+ Ω s t s ε Ω Ωεs ts = ( 1 e ) εos Ω t s hr t r hr ε 1/hr ε s (mm/mm) os ε 1/hr 9Cr-1Mo Larson-Miller Manson-Haferd Ω 1. 9Cr-1Mo 2. Larson-Miller ~37% 3. 9Cr-1Mo Larson-Miller Manson-Haferd

12 Larson-Miller 4. Manson-Haferd 5. Manson-Haferd 6. Ω Ω 1. 99, pp , pp , Ennis, P. J. and Czyrska-Filemonowicz, A., Recent advances in creep resistant steels for power plant applications, OMMI, Vol. 1, No. 1, April , Lehigh Energy Update, Project on welding of 9Cr-1Mo steels seeks sponsors, Vol. 21, No. 1, pp. 1, January Annual Book of ASTM Standards: Iron and Steel Products, ASTM, Vol , pp , Dieter, G. E., Mechanical metallurgy (2 nd ed.), McGraw-Hill, pp. 451~489, Spigarelli, S., Creep of aluminum and aluminum alloys, EAA, pp. 3-14, Andrade, E. N. DaC. On the viscousflow of metals and allied phenomena, Proceedings of the Royal Society, Section A, 84, pp. 1-12, Dowling, N. E., Mechanical behavior of materials, Prentice Hall, Englewood Cliffs, New Jersey, Nabarro, F. R. N., Report of a conference on the strength of solids, Physical Society, London, pp. 75, Coble, R. L., A model for boundary diffusion controlled creep in polycrystalline materials, Journal of Applied Physics, Vol. 34, pp , Shi, L. and D. O. Northwood, Recent progress in the modeling of high temperature creep and its application to alloy development, Journal of Materials Engineering and Performance, Vol. 4, No. 2, pp , Thomas H. C., Mechanical behavior of materials, McGraw-Hill, pp , 1990.

13 16.Frost, H. J. and Ashby, M. F., Deformation mechanism map, pp. 1-37, Penny, R. K. and Marriott, D. L., Design for creep, Chapman & Hall, pp , Larson, F. R. and Miller, J., A time-temperature relationship for rupture and creep stresses, Trans. ASME, Vol. 174, No. 5, pp , Manson, S. S. and Haferd, A. M. A linear time-temperature relation for extrapolation of creep and stress-rupture data, NACA TN 2890, Maruyama, K., Nonaka, I., Sawada, K., Sato, H., Koike, J. I., and Umaki, H., Improvement of omega method for creep life prediction, ISIJ International, Vol. 37, No. 4, pp , Perager, M., Development of the MPC omega method for life assessment in the creep range, Journal of Pressure Vessel Technology, Vol. 117, No. 4, pp , May Cheng, L., Liu, P., Zhao, and Northwood, D. O., Room temperature creep of a high strength steel, Material and Design, Vol. 22, pp , CNS Dieter, G. E., Mechanical metallurgy (3 rd ed.), McGraw-Hill, Nardone, V. C., Tien, J. K., On the creep rate stress dependence of particle strengthened alloys, Scripta Metallurgica, Vol. 20, , Lund, R. W., & Nix, W. D., On high creep activation energies for dispersion strengthened metals, Metallurgical Transactions A, 6A, pp , Barth, E. P., Morton, J. T., and Tien, J. K., Threshold for creep resistance in a silicon carbide reinforced aluminum alloy, The Metallurgical Society, pp , Morimoto, T., Taya, M., Yamaoka, T., and Lilholt, H., Second stage creep of SiC whisker/6061 aluminum composite at 573 K, Journal of Engineering Materials and Technology, Vol. 110, pp , 1

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