9Cr-1Mo 1 2 2 9Cr-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 1. 2. 3.
(creep) 500~600 15 ~ 30 MPa 9Cr-1Mo 100 MPa ( ) 9Cr-1Mo Threshold Stress Larson-Miller Manson-Haferd Ω
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 =...... 4.2 (4.1)(4.2) Q At r exp = RT constant. 4.3 4.3 Larson-Miller Q P L M = = T( C + log10 t r ). 4.4 2.3R T K t r hr C 20 Larson-Miller 15~25 20 1/T=0 log = C 1 Larson-Miller t r
3 2 1 1 2 3 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.. 4.5 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.... 4.6 dε m Norton p c Norton 9Cr-1Mo K MPa 1 823 177
2 155 3 142 4 136 5 162 6 155 7 848 142 8 136 9 128 10 177 11 155 12 142 873 13 136 14 128 15 110 16 142 17 110 923 18 104 19 97 6.1 823 K 60 177 MPa 155 MPa 142 MPa 136 MPa 50 40 Strain, % 30 20 10 0 0 100x10 3 200x10 3 300x10 3 400x10 3 Time, s 823 K - 6.2
155 MPa 60 50 823 K 848 K 873 K 40 Strain, % 30 20 10 0 0 20x10 3 40x10 3 60x10 3 80x10 3 100x10 3 Time, s 155 MPa - 6.3 εss = n Aσ e Q RT 6.1 6.1 n (K), n, r 2 823 8.41 0.97 4 848 8.79 0.95 5 873 10.45 0.95 6 923 12.00 0.96 4 log (Minimum Creep Rate, mm/mm/s) -2-3 -4-5 -6 823 K 848 K 873 K 923 K -7 1.95 2.00 2.05 2.10 2.15 2.20 2.25 2.30 log (Applied Stress, MPa)
6.4 6.1 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 0.8 823 K 848 K 873 K 923 K 0.6 0.4 0.2 0.0 0 50 100 150 200 Applied Stress, MPa 9Cr-1Mo 6.5 Larson-Miller Larson-Miller Larson Miller Larson-Miller Larson-Miller
0.00125 1/Temperature, K 0.00120 0.00115 0.00110 0.00105 0.00100 177 MPa 155 MPa 142 MPa 136 MPa 128 MPa 110 MPa 0.00095 0.00090-6 -4-2 0 2 4 log (Rupture Time, hr) - Larson-Miller Larson-Miller 20 4 L-M (K) (MPa) (hr) % 823 30 20 72,874,475 12% 4 83,066,485 60 20 123,474 12% 4 140,743 90 20 2,955 12% 4 3,368 848 30 20 30,399,749 3% 4 31,368,111 60 20 41,692 3% 4 43,020 90 20 881 3% 4 910 873 30 20 21,356,506 21% 4 27,029,042 60 20 12,790 15% 4 15,093 90 20 166 12% 4 188 923 30 20 3,689,853 37% 4 2,697,995 60 20 725 24% 4 584 90 20 4.93 17% 4 4.20 90 MPa 3 % ~ 17 % 30 MPa 3 %~37 % 923 K, 90 MPa 17 % 40 3 % 823K 30MPa 90
Larson-Miller 6.6 Manson-Haferd log (Rupture Time, hrs) 15 10 5 0 log t a =16 hr Ta=449 K 155 MPa 142 MPa 136 MPa 128 MPa 110 MPa -5 300 400 500 600 700 800 900 1000 Absolute Temperature, K Manson-Haferd t a T a log (Minimum Creep Strain Rate, mm/mm/sec) 0-5 -10-15 -20-25 177 MPa 155 MPa 142 MPa 136 MPa 128 MPa 110 MPa -30 200 400 600 800 1000 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
-24 Manson-Haferd Parameter -25-26 -27-28 -29 823 K 848 K 873 K 923 K -30 P M H ( T 449) = = 1.86 10 (logt 15.95) r ( T 420) -31 80 100 120 140 160 180 200 220 5 σ 2 + 0.11σ 38.91 4 2 PM H = = 1.34 10 σ 0.08σ + 34.89 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 6.4 29 Manson-Haferd Parameter 28 27 26 25 24 823 K 848 K 873 K 923 K 23 22 80 100 120 140 160 180 200 220 Applied Stress, MPa Manson-Haferd
6.7 Ω Ω Ω Ω K r 2 823 Ω = 0.427σ + 100. 195 0.97 848 Ω = 0.280σ + 60. 296 0.83 873 Ω = 0.212σ + 45. 482 0.87 923 Ω = 0.179σ + 32. 182 0.95 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.... 6.6 1 Ωεs ts = ( 1 e )... 6.7 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 4 20 3~37% 3. 9Cr-1Mo Larson-Miller Manson-Haferd
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