A continuum damage model for creep fracture and fatigue analysis - - PowerPoint PPT Presentation

A continuum damage model for creep fracture and fatigue analysis

Petteri Kauppila1, Reijo Kouhia2, Juha Ojanper¨ a1, Timo Saksala2, Timo Sorjonen1

1Valmet Technologies Oy, P.O. Box 109, FI-33101 Tampere, Finland 2Tampere University of Technology Department of Mechanical Engineering and Industrial Systems, P.O. Box 589, FI-33101 Tampere, Finland 21st European Conference on Fracture, June 20-24, 2016

1 Introduction 2 TD formulation 3 Specific models 4 Monkman-Grant 5 T24 parameters 6 Results 7 Conclusions

Outline

1 Introduction 2 Thermodynamic formulation 3 Specific models 4 Monkman-Grant parameter 5 T24 material parameters 6 FE analysis and results 7 Concluding remarks

Creep fracture and fatigue – ECF21, June 20-24, 2016 2/20

1 Introduction 2 TD formulation 3 Specific models 4 Monkman-Grant 5 T24 parameters 6 Results 7 Conclusions

1 Introduction 2 Thermodynamic formulation 3 Specific models 4 Monkman-Grant parameter 5 T24 material parameters 6 FE analysis and results 7 Concluding remarks

Creep fracture and fatigue – ECF21, June 20-24, 2016 3/20

1 Introduction 2 TD formulation 3 Specific models 4 Monkman-Grant 5 T24 parameters 6 Results 7 Conclusions

Introduction

Sustainable energy system is a combination of wide variety

• f energy resources.

Result in flexible power generation. New requirements for boiler creep fatigue design due to intermittent power demand.

Creep fracture and fatigue – ECF21, June 20-24, 2016 4/20

1 Introduction 2 TD formulation 3 Specific models 4 Monkman-Grant 5 T24 parameters 6 Results 7 Conclusions

1 Introduction 2 Thermodynamic formulation 3 Specific models 4 Monkman-Grant parameter 5 T24 material parameters 6 FE analysis and results 7 Concluding remarks

Creep fracture and fatigue – ECF21, June 20-24, 2016 5/20

1 Introduction 2 TD formulation 3 Specific models 4 Monkman-Grant 5 T24 parameters 6 Results 7 Conclusions

Thermodynamic formulation

Developed models are completely defined by two potential functions: the specific Helmholtz free energy ψ = ψ(T, εte, ω), (linear kinematics assumed ε = εe + εc + εth, εte = ε − εc, ω = 1 − D) and the complementary dissipation potential ϕ(Y, q, σ; T, ω) defined as γ = ∂ϕ ∂q ·q + ∂ϕ ∂σ :σ + ∂ϕ ∂Y Y. Together with the Clausius-Duhem inequality γ = −ρ( ˙ ψ + s ˙ T) + σ: ˙ ε − T −1 gradT·q ≥ 0 results the constitutive equations − ρ

• s + ∂ψ

∂T

• ˙

T +

• σ − ρ ∂ψ

∂εte

• : ˙

εte +

• ˙

εc − ∂ϕ ∂σ

• : σ

−

• ˙

ω + ∂ϕ ∂Y

• Y −

gradT T + ∂ϕ ∂q

• ·q = 0.

Creep fracture and fatigue – ECF21, June 20-24, 2016 6/20

1 Introduction 2 TD formulation 3 Specific models 4 Monkman-Grant 5 T24 parameters 6 Results 7 Conclusions

1 Introduction 2 Thermodynamic formulation 3 Specific models 4 Monkman-Grant parameter 5 T24 material parameters 6 FE analysis and results 7 Concluding remarks

Creep fracture and fatigue – ECF21, June 20-24, 2016 7/20

1 Introduction 2 TD formulation 3 Specific models 4 Monkman-Grant 5 T24 parameters 6 Results 7 Conclusions

Specific models

The specific Helmholtz free energy ρψ = ρcε

• T − T ln T

Tr

• + 1

2(εte − εth): ωC e: (εte − εth), εth = α(T − Tr), thermal strain, C e elasticity tensor, α thermal expansion coefficients, Tr stress free reference temperature. The complementary dissipation potential ϕ(Y, q, σ; T, ω) = ϕth(q; T) + ϕd(Y ; T, ω) + ϕc(σ; T, ω), where the thermal part is ϕth(q; T) = 1 2T −1q·λ−1q. For creep the following Norton type potential function is adopted ϕc(σ; T, ω) = hc(T) p + 1 ωσrc tc

• ¯

σ ωσrc p+1 , ¯ σ = √3J2, hc(T) = exp(−Qc/RT).

Creep fracture and fatigue – ECF21, June 20-24, 2016 8/20

1 Introduction 2 TD formulation 3 Specific models 4 Monkman-Grant 5 T24 parameters 6 Results 7 Conclusions

Damage potential

Kachanov-Rabotnov type ϕd(Y ; T, ω) = hd(T) r + 1 Yr td ωk Y Yr r+1 , model 1 ϕd(Y ; T, ω) = hc(T) ( 1

2p + 1)(1 + k + p)

Yr td ωk Y Yr 1

2 p+1

, model 2 td is a characteristic time for damage evolution, hd(T) = exp(−Qd/RT), where Qd is the damage activation energy and R is the universal gas constant. The reference value Yr = σrd2/(2E), where σrd is a reference stress for the damage process.

Creep fracture and fatigue – ECF21, June 20-24, 2016 9/20

1 Introduction 2 TD formulation 3 Specific models 4 Monkman-Grant 5 T24 parameters 6 Results 7 Conclusions

1 Introduction 2 Thermodynamic formulation 3 Specific models 4 Monkman-Grant parameter 5 T24 material parameters 6 FE analysis and results 7 Concluding remarks

Creep fracture and fatigue – ECF21, June 20-24, 2016 10/20

1 Introduction 2 TD formulation 3 Specific models 4 Monkman-Grant 5 T24 parameters 6 Results 7 Conclusions

Monkman-Grant parameter

Experimental relationship CMG = ( ˙ εc

min)mtrup ≈ constant.

For the two models the Monkman-Grant parameter have the values (m = 1) CMG = ˙ εc

mintrup =

1 1 + k + 2r tdhc tchd σ σr p−2r model 1 CMG = td tc model 2. Model 2 can be obtained by imposing the following constrains to the model 1: p = 2r, 1 1 + k + 2r tdhc tchc = constant.

Creep fracture and fatigue – ECF21, June 20-24, 2016 11/20

1 Introduction 2 TD formulation 3 Specific models 4 Monkman-Grant 5 T24 parameters 6 Results 7 Conclusions

1 Introduction 2 Thermodynamic formulation 3 Specific models 4 Monkman-Grant parameter 5 T24 material parameters 6 FE analysis and results 7 Concluding remarks

Creep fracture and fatigue – ECF21, June 20-24, 2016 12/20

1 Introduction 2 TD formulation 3 Specific models 4 Monkman-Grant 5 T24 parameters 6 Results 7 Conclusions

T24 material parameters

The calibrated model parameters for the 7CrMoVTiB10-10 steel (T24), qc = Qc/R and qd = Qd/R, p(T ) = pr(1 + a(T − Tr)/Tr) and r(T ) = rr(1 + b(T − Tr)/Tr), σrc = σrd = sigr = σy0(T ) = σ∗ − cT , with σ∗ = 1123 MPa, c = −1 MPa/K. mod tc [s] pr td [s] a qc [K] rr qd [K] b 1 3039.9 14.77 37.768 −4.804 7137.6 7.545 9350.1 −5.201 2 3414.1 14.59 41.26 −4.891 7137.6

• ˙

εc,min [%/103 h] σ [MPa] 101 100 10−1 10−2 400 300 200 100 50 trup [h] σ [MPa] 105 104 103 102 400 300 200 100 50 Minimum creep strain-rate (lhs) and the creep strengths (rhs). Solid lines = model 1, dashed lines = model 2. Top 500◦C, middle 550◦C bottom 600◦C. Creep fracture and fatigue – ECF21, June 20-24, 2016 13/20

1 Introduction 2 TD formulation 3 Specific models 4 Monkman-Grant 5 T24 parameters 6 Results 7 Conclusions

Monkman-Grant parameter

model 2 300 MPa 200 MPa 100 MPa T[◦C] CMG 600 580 560 540 520 500 0.024 0.022 0.02 0.018 0.016 0.014 0.012 0.01 model 2 model 1, T = 600◦C model 1, T = 550◦C model 1, T = 500◦C ˙ εc,min [s−1] trup [s] 10−6 10−7 10−8 10−9 10−10 10−11 10−12 1012 1011 1010 109 108 107 106 105 Creep fracture and fatigue – ECF21, June 20-24, 2016 14/20

1 Introduction 2 TD formulation 3 Specific models 4 Monkman-Grant 5 T24 parameters 6 Results 7 Conclusions

1 Introduction 2 Thermodynamic formulation 3 Specific models 4 Monkman-Grant parameter 5 T24 material parameters 6 FE analysis and results 7 Concluding remarks

Creep fracture and fatigue – ECF21, June 20-24, 2016 15/20

1 Introduction 2 TD formulation 3 Specific models 4 Monkman-Grant 5 T24 parameters 6 Results 7 Conclusions

FE analysis and results

The models are implemented in ANSYS using the USERMAT subroutine and the mesh consists of mainly 20 node hexahedral ANSYS SOLID186 elements & some 10 node tetrahedal SOLID187 elements. Prescribed displacement history at the end of the tube nozzle. The computed lifetime is roughly 150 cycles. Ramp time 1 hour and hold time 200 hours. Internal pressure 14 MPa.

500 600

Temperature (°C) Displacement Time

Displacement Temperature Creep fracture and fatigue – ECF21, June 20-24, 2016 16/20

1 Introduction 2 TD formulation 3 Specific models 4 Monkman-Grant 5 T24 parameters 6 Results 7 Conclusions

Results

Damage distribution near the most critical location of the header. The accumulated damage and the equivalent creep strain at the most critical location as functions of the prescribed displacement.

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1 Introduction 2 TD formulation 3 Specific models 4 Monkman-Grant 5 T24 parameters 6 Results 7 Conclusions

1 Introduction 2 Thermodynamic formulation 3 Specific models 4 Monkman-Grant parameter 5 T24 material parameters 6 FE analysis and results 7 Concluding remarks

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1 Introduction 2 TD formulation 3 Specific models 4 Monkman-Grant 5 T24 parameters 6 Results 7 Conclusions

Concluding remarks

Thermodynamically consistent model for high-temperature creep fatigue analyses has been developed. A specific model with Norton-Bailey type creep and Kachanov-Rabotnov type damage models are used. Two version of the damage evolution equations. One-version satisfies the Monkman-Grant hypothesis exactly. Materials parameters for the 7CrMoVTiB10-10 steel (T24) have been estimated in the temperature range 500-600 0C. Developed models have been implemented in the ANSYS FE-software by using the USERMAT subroutine.

Acknowledgements This work was carried out in the research program Flexible Energy Systems (FLEXe) and supported by Tekes and the Finnish Funding Agency for Innovation. The programme is coordinated by CLIC Innovation Ltd. www.clicinnovation.fi Creep fracture and fatigue – ECF21, June 20-24, 2016 19/20

1 Introduction 2 TD formulation 3 Specific models 4 Monkman-Grant 5 T24 parameters 6 Results 7 Conclusions

Thank You for Your Attention! Etna the Living Mountain Oil painting on canvas by Gilda Gubiotti 2008.

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