Idea Transcript
Modeling of Cyclic Hardening and Softening in a Viscoplastic Material Model of Chaboche-Type 8th International Charles Parson Conference Andreas Simon Portsmouth, 06.09.2011
Contents •
TMF loading of large steam turbine components
•
Constitutive material model with cyclic hardening and softening
•
Verification with cyclic tests
•
Advantages of constitutive material models
•
Conclusion
•
Acknowledgement
8th international Charles Parson Conference - 05 September 2011 - P 2 © ALSTOM 2010. All rights reserved. Information contained in this document is indicative only. No representation or warranty is given or should be relied on that it is complete or correct or will apply to any particular project. This will depend on the technical and commercial circumstances. It is provided without liability and is subject to change without notice. Reproduction, use or disclosure to third parties, without express written authority, is strictly prohibited.
Possible field of application TMF Loading TMF loading of large steam turbine components due to transient temperature 600
Primary Load
a)
T / °C Ta
400
Secondary Load
Tm
200
temperature at surface Ta average core temperature Tm
0 15
thermal stress at blade notches
0,15
20
25
30
t/h
35
b)
εT / % 0,00 εT -0,15
thermal introduced strain εT = αK α (Tm-Ta)
Stress response σ(t) = σ(MATERIAL, T, ε, t) -0,30 8th international Charles Parson Conference - 05 September 2011 - P 3
15
20
25
30
t/h
35
© ALSTOM 2010. All rights reserved. Information contained in this document is indicative only. No representation or warranty is given or should be relied on that it is complete or correct or will apply to any particular project. This will depend on the technical and commercial circumstances. It is provided without liability and is subject to change without notice. Reproduction, use or disclosure to third parties, without express written authority, is strictly prohibited.
Deformation and life time assessment „Conventional“
Constitutive Material Model
600
600
σ / MPa
σ / MPa
400
Exponential
400
σmax
200
σmax
Linear cyclic softening
200
σmean
0
σmean
0
-200
-200
-400
-400
σmin
-600
σmin
-600
NA = 167 -800
NA = 167 -800
0
20
40
60
80
100
120
140
N160 /-
180
200
0
20
40
60
80
100
120
140
N160 /-
Description of the Ni / 2 Cycle:
N = 1 to Ni:
e.g with Ramberg-Osgood and Creep laws
System of algebro-differential equations
180
200
Figure shows maximum and minimum stresses of a non isothermal TMF tests on X12CrMoWVNbN10-1-1 8th international Charles Parson Conference - 05 September 2011 - P 4 © ALSTOM 2010. All rights reserved. Information contained in this document is indicative only. No representation or warranty is given or should be relied on that it is complete or correct or will apply to any particular project. This will depend on the technical and commercial circumstances. It is provided without liability and is subject to change without notice. Reproduction, use or disclosure to third parties, without express written authority, is strictly prohibited.
Material Model of Chaboche-Type Viscoplastic material model of type Chaboche
E = Ee + Ep
T := ρ
∂ψ e = C [E e ] ∂E e
ξ i = C ⋅ c i Yi
Y& i = E& p − B ⋅ b i Yi s& − p i c i Yi
w i −1
Tsakmakis and Reckwerth 2003, Haupt, Kamlah and Tsakmakis 1995
Yi New
ξ = ξ1 + ξ 2
f = f ( T, ξ ) =
3 ( T − ξ )D ⋅ ( T − ξ )D 2
F = F ( T, ξ, R ) = f ( T, ξ ) − k = f − k s& =
F
m
stress
resistance
Hm ⋅ η
∂f 3 ( T − ξ )D & & Ep = Λ= s ∂T 2 f
Modified parameters as result of the cyclic loading history
1 ci ξ = i,11,max 1 + abqξ B ⋅ bi s& q& ξ = ξ − qξ s0
B=
(
)
1 F = H ⋅ ( η ⋅ s& )1 / m 1 + a H qF & &q F = s (F − q F ) s0 H=
8th international Charles Parson Conference - 05 September 2011 - P 5 © ALSTOM 2010. All rights reserved. Information contained in this document is indicative only. No representation or warranty is given or should be relied on that it is complete or correct or will apply to any particular project. This will depend on the technical and commercial circumstances. It is provided without liability and is subject to change without notice. Reproduction, use or disclosure to third parties, without express written authority, is strictly prohibited.
Material Investigated material One heat of a modern 10%Cr-steel of type X12CrMoWVNbN10-1-1 Steam turbine rotors Maximum application temperature 600°C Main testing temperature 600°C
Test database Tensile tests Creep tests Standard LCF tests Special LCF and TMF tests 8th international Charles Parson Conference - 05 September 2011 - P 6 © ALSTOM 2010. All rights reserved. Information contained in this document is indicative only. No representation or warranty is given or should be relied on that it is complete or correct or will apply to any particular project. This will depend on the technical and commercial circumstances. It is provided without liability and is subject to change without notice. Reproduction, use or disclosure to third parties, without express written authority, is strictly prohibited.
Short and long term quasi static material behavior Tensile tests and LCF tests Creep tests with test durations between 100h and 80,000h Tensile and 1st loop of LCF tests
Creep tests 100
σ / MPa
a)
qξ = 0
. ε = 6%/min
σ438 p02 . ε = 0.06%/min
qF = 0
% εp /10
viscous effect
1
b)
0,1
0,01
0 0,0
0,2
0,4
0,6
ε0,8 /%
1,0
0,1 0
1 1
10 10
2 3 5 t / h 1000 10 1000 10 1000 10 100 0 00
8th international Charles Parson Conference - 05 September 2011 - P 7 © ALSTOM 2010. All rights reserved. Information contained in this document is indicative only. No representation or warranty is given or should be relied on that it is complete or correct or will apply to any particular project. This will depend on the technical and commercial circumstances. It is provided without liability and is subject to change without notice. Reproduction, use or disclosure to third parties, without express written authority, is strictly prohibited.
Description of the cyclic softening Standard LCF test, εa = 1·εaN=1685, 6%/min, 600°C
LCF test, 600°C, 6%/min
-1
Simulation, 600°C, 6%/min
Saturation
1.5 x ξ 11 and F / σ p02
Stress / σ p02
1
Max and min stresses per cycle
0.5
a)
Simulation, 600°C, 6%/min LCF test, 600°C, 6%/min
F ξ
Simulation, 600°C, maximum and minimum kinematic back-stress -0.5
-0,69
-1 -0,46
-0,23
0
0,23
1 0,46
0,69
Strain / ε a, Ni = 1685
0
500
1000
1500
2000
2500
0
500
Number of cycles
1000
1500
2000
2500
Number of cycles
1
1
qξ and qF / σ p02
Stress / σ p02
Simulation, 600°C, inner variable qxi and qF
F
qF
1.5 x ξ 11
qξ
0
0
0
0,23 Strain / ε
0,46 1
a, NiConference = 1685 8th international Charles Parson - 05 September 2011 - P 8
0
500
1000
1500
2000
Number of cycles
© ALSTOM 2010. All rights reserved. Information contained in this document is indicative only. No representation or warranty is given or should be relied on that it is complete or correct or will apply to any particular project. This will depend on the technical and commercial circumstances. It is provided without liability and is subject to change without notice. Reproduction, use or disclosure to third parties, without express written authority, is strictly prohibited.
2500
Cyclic softening at different strain amplitudes
Stress / σ p02
0.70·εa,N=1685
Simulation, 600°C, 6%/min -1 -0,46
-0,23
0
0,23
Max and min stress per cycle
1
Simulation, 600°C, 6%/min LCF test, 600°C, 6%/min
0
0,46 1
1000
2000
3000
4000
Number of cycles
Strain / ε a, Ni = 1685
1
Stress / σ p02
Max and min stress per cycle
0.55·εa,N=1685
Simulation, 600°C, 6%/min
Simulation, 600°, 6%/min LCF test, 600°, 6%/min
-1 -1 -0,46 -0,23 Conference 0 8th international Charles Parson - 05 September0,23 2011 - P 9
1 0,46
0
2000
4000
6000
8000
10000
© ALSTOM 2010. All rights reserved. Information contained in this document is indicative only. No representation or warranty is given or should be relied on that it is complete or correct or will apply to any particular project. This will ofexpress cycles depend on the technical and commercial circumstances. without liability and is subject to change without notice. Reproduction, use or disclosure to thirdNumber parties, without written authority, is strictly prohibited. Strain / a, NiIt is= provided 1685
ε
Non-symmetric loading Cyclic mean stress relaxation Non-symmetric LCF test, Rε = 0, ·εa = 0.87·εa,N=1685, 6%/min, 600°C
LCF test, 600°C, 6%/min
-1
Simulation, 600°C, 6%/min -0,23
0
0,23
0,46 1
0,69
2 0,92
Max and min stresses per cycle
Stress / σ p02
1
LCF test, 600°C, 6%/min Simulation, 600°C, 6%/min
1
10
Strain / ε a, Ni = 1685
100
1000
10000
Number of cycles
Cyclic mean stress relaxation
ξ = ξ1 + ξ 2 8th international Charles Parson Conference - 05 September 2011 - P 10 © ALSTOM 2010. All rights reserved. Information contained in this document is indicative only. No representation or warranty is given or should be relied on that it is complete or correct or will apply to any particular project. This will depend on the technical and commercial circumstances. It is provided without liability and is subject to change without notice. Reproduction, use or disclosure to third parties, without express written authority, is strictly prohibited.
Cyclic softening at low strain rates
Max and min stresses per cycle
LCF test with low strain rate, 1.40·εaN=1685, 0.06%/min, 600°C
6%/min 0.06%/min
Stress / σ p02
1
LCF test, 600°C, 0,06%/min
-1
Simulation, 600°C, 0,06%/min -1
-10
0
0
0
Strain / ε a, Ni = 1685
0 1
1
LCF test, 600°, 0.06%/min Simulation, 600°, 0.06%/min
1
10
100
1000
Number of cycles
Loading speed during start ups of steam turbines is much lower than 6%/min 8th international Charles Parson Conference - 05 September 2011 - P 11 © ALSTOM 2010. All rights reserved. Information contained in this document is indicative only. No representation or warranty is given or should be relied on that it is complete or correct or will apply to any particular project. This will depend on the technical and commercial circumstances. It is provided without liability and is subject to change without notice. Reproduction, use or disclosure to third parties, without express written authority, is strictly prohibited.
Cyclic softening during LCF tests with dwell Max and minm stresses per cycle
1
Stress / σ p02
a)
-1 -1 0
0
0
0
Strain / ε a, Ni = 1685
10
b)
1
10
100
1000
10000
Number of cycles
1 c)
Stress / σ p02
LCF test with tension and compression dwells, εa = 0.70·εaN=1685, 6%/min, tHzd = 3min, 600°C Simulation, 600°C, 6%/min, 3min LCF test, 600°C, 6%/min, 3min, N = 2
Dwell times occur also during stationary operation of steam turbines
-1 8th international - P 12 0,09Charles Parson Conference 0,14 - 05 September 20110,19 © ALSTOM 2010. All rights reserved. Information contained in this document is indicative only. No representation or warranty is given or should be relied on that it is complete or correct or will apply to any particular project. This will depend on the technical and commercial circumstances. t / Ithis provided without liability and is subject to change without notice. Reproduction, use or disclosure to third parties, without express written authority, is strictly prohibited.
Half lifetime cycles Ni / 2
Ni / 2
1
Stress / σ p02
Stress / σ p02
1
LCF test, 600°C, 6%/min
-1
LCF test, 600°C, 0,06%/min
-1
Simulation, 600°C, 6%/min -0,69
-1 -0,46
-0,23
0
0,23
1 0,46
Simulation, 600°C, 0,06%/min
0,69
-1
Strain / ε a, Ni = 1685
-10
0
0
0
0 1
1
Strain / ε a, Ni = 1685
1 Ni / 2
Stress / σ p02
Good description of the half lifetime cycles
Simulation, 600°C, 6%/min, 3min LCF test, 600°C, 6%/min, 3min, N = 2 -1 -1 0 0 0 - 05 September02011 - P 13 8th international Charles Parson Conference
10
© ALSTOM 2010. All rights reserved. Information contained in this document is indicative only. No representation or warranty is given or should be relied on that it is complete or correct or will apply to any particular project. This will depend on the technical and commercial circumstances. It is provided without liability and is subject to change without notice. Reproduction, use or disclosure to third parties, without express written authority, is strictly prohibited. Strain /
ε a, Ni = 1685
Viscous effects at the beginning of load reversals in LCF tests
Stress / σ p02
Stress
1
E-Modulus
1
2
1
1
Strain
Simulation, 600°C, 0,06%/min -1
-10
0
0
0
0 1
1
2
Plastic Strain
LCF test, 600°C, 0,06%/min
-1
Strain / ε a, Ni = 1685 1
1
1
Strain
Viscous effects still occur at the beginning of load reversals when pure elastic behaviour is expected 8th international Charles Parson Conference - 05 September 2011 - P 14 © ALSTOM 2010. All rights reserved. Information contained in this document is indicative only. No representation or warranty is given or should be relied on that it is complete or correct or will apply to any particular project. This will depend on the technical and commercial circumstances. It is provided without liability and is subject to change without notice. Reproduction, use or disclosure to third parties, without express written authority, is strictly prohibited.
Conclusion • •
The simulation of the cyclic softening correlates with cyclic tests on a 10%Crsteel (standard LCF tests, LCF tests with low strain rate and with dwell times) Physically based constitutive material models allow an improved description of the mechanical material behaviour
Open issues • Parameter identification at lower temperatures to enable non-isothermal simulations • Further improvement e.g. of the fatigue and creep damage evolution • Implementation of the presented features in a user subroutine for FEM calculations (UMAT) • Description of the mean and minimum mechanical behaviour of a material type?
8th international Charles Parson Conference - 05 September 2011 - P 15 © ALSTOM 2010. All rights reserved. Information contained in this document is indicative only. No representation or warranty is given or should be relied on that it is complete or correct or will apply to any particular project. This will depend on the technical and commercial circumstances. It is provided without liability and is subject to change without notice. Reproduction, use or disclosure to third parties, without express written authority, is strictly prohibited.
Acknowledgement Thank you for your attention
Thanks are due to IfW, TU-Darmstadt Experiments in this work are published in [1] Haase, H.: Betriebsähnliches Langzeitdehnwechselverhalten moderner martensitischer 9 bis 10%Cr-Stähle. Dr.-Ing. Diss., TU-Darmstadt, D17, Shaker Verlag, 2004. [2] Schwienheer, M.: Statisches und zyklisches Hochtemperaturverhalten der 600°C Dampfturbinenstähle (G)X12CrMoWVNbN10-1-1. Dr.-Ing. Diss., TU-Darmstadt, D17, VDI Verlag, 2005.
Research groups of the German power plant industry
8th international Charles Parson Conference - 05 September 2011 - P 16 © ALSTOM 2010. All rights reserved. Information contained in this document is indicative only. No representation or warranty is given or should be relied on that it is complete or correct or will apply to any particular project. This will depend on the technical and commercial circumstances. It is provided without liability and is subject to change without notice. Reproduction, use or disclosure to third parties, without express written authority, is strictly prohibited.