Modeling of Cyclic Hardening and Softening in a Viscoplastic ... - IOM3 [PDF]

Constitutive material model with cyclic hardening and softening. •. Verification with cyclic tests. •. Advantages of

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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



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.

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