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

A continuum damage model for creep fracture and fatigue analysis Petteri Kauppila 1 , Reijo Kouhia 2 , Juha Ojanper¨ a 1 , Timo Saksala 2 , Timo Sorjonen 1 1 Valmet Technologies Oy, P.O. Box 109, FI-33101 Tampere, Finland 2 Tampere 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 Outline 3 Specific models 4 Monkman-Grant 5 T24 parameters 1 Introduction 6 Results 7 Conclusions 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 1 Introduction 2 TD formulation 3 Specific models 2 Thermodynamic formulation 4 Monkman-Grant 5 T24 parameters 6 Results 3 Specific models 7 Conclusions 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 Introduction 3 Specific models 4 Monkman-Grant 5 T24 parameters 6 Results 7 Conclusions Sustainable energy system is a combination of wide variety of 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 1 Introduction 2 TD formulation 3 Specific models 2 Thermodynamic formulation 4 Monkman-Grant 5 T24 parameters 6 Results 3 Specific models 7 Conclusions 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 Thermodynamic formulation 3 Specific models 4 Monkman-Grant 5 T24 parameters Developed models are completely defined by two potential functions: 6 Results the specific Helmholtz free energy ψ = ψ ( T, ε te , ω ) , 7 Conclusions (linear kinematics assumed ε = ε e + ε c + ε th , ε te = ε − ε c , 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 ε − T − 1 grad T · q ≥ 0 γ = − ρ ( ˙ ψ + s ˙ T ) + σ : ˙ results the constitutive equations � � � � � � s + ∂ψ σ − ρ ∂ψ ε c − ∂ϕ ˙ − ρ T + : ˙ ε te + ˙ : σ ∂T ∂ ε te ∂ σ � grad T � ω + ∂ϕ � + ∂ϕ � ˙ Y − · q = 0 . − ∂Y T ∂ q Creep fracture and fatigue – ECF21, June 20-24, 2016 6/20

1 Introduction 1 Introduction 2 TD formulation 3 Specific models 2 Thermodynamic formulation 4 Monkman-Grant 5 T24 parameters 6 Results 3 Specific models 7 Conclusions 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 Specific models 3 Specific models 4 Monkman-Grant The specific Helmholtz free energy 5 T24 parameters � T − T ln T � + 1 6 Results ρψ = ρc ε 2( ε te − ε th ) : ω C e : ( ε te − ε th ) , T r 7 Conclusions ε th = α ( T − T r ) , thermal strain, C e elasticity tensor, α thermal expansion coefficients, T r stress free reference temperature. The complementary dissipation potential ϕ ( Y, q , σ ; T, ω ) = ϕ th ( q ; T ) + ϕ d ( Y ; T, ω ) + ϕ c ( σ ; T, ω ) , where the thermal part is ϕ th ( q ; T ) = 1 2 T − 1 q · λ − 1 q . For creep the following Norton type potential function is adopted � p +1 ϕ c ( σ ; T, ω ) = h c ( T ) ωσ rc � σ ¯ , p + 1 t c ωσ rc σ = √ 3 J 2 , h c ( T ) = exp( − Q c /RT ) . ¯ Creep fracture and fatigue – ECF21, June 20-24, 2016 8/20

1 Introduction 2 TD formulation Damage potential 3 Specific models 4 Monkman-Grant 5 T24 parameters 6 Results Kachanov-Rabotnov type 7 Conclusions � Y � r +1 h d ( T ) Y r ϕ d ( Y ; T, ω ) = , model 1 r + 1 t d ω k Y r � Y � 1 2 p +1 h c ( T ) Y r ϕ d ( Y ; T, ω ) = , model 2 ( 1 t d ω k 2 p + 1)(1 + k + p ) Y r t d is a characteristic time for damage evolution, h d ( T ) = exp( − Q d /RT ) , where Q d is the damage activation energy and R is the universal gas constant. The reference value Y r = σ rd2 / (2 E ) , where σ rd is a reference stress for the damage process. Creep fracture and fatigue – ECF21, June 20-24, 2016 9/20

1 Introduction 1 Introduction 2 TD formulation 3 Specific models 2 Thermodynamic formulation 4 Monkman-Grant 5 T24 parameters 6 Results 3 Specific models 7 Conclusions 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 Monkman-Grant parameter 3 Specific models 4 Monkman-Grant 5 T24 parameters Experimental relationship 6 Results ε c min ) m t rup ≈ constant . 7 Conclusions C MG = ( ˙ For the two models the Monkman-Grant parameter have the values ( m = 1 ) � σ � p − 2 r 1 t d h c ε c C MG = ˙ min t rup = model 1 1 + k + 2 r t c h d σ r C MG = t d model 2 . t c Model 2 can be obtained by imposing the following constrains to the model 1: 1 t d h c p = 2 r, = constant . 1 + k + 2 r t c h c Creep fracture and fatigue – ECF21, June 20-24, 2016 11/20

1 Introduction 1 Introduction 2 TD formulation 3 Specific models 2 Thermodynamic formulation 4 Monkman-Grant 5 T24 parameters 6 Results 3 Specific models 7 Conclusions 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 T24 material parameters 3 Specific models 4 Monkman-Grant The calibrated model parameters for the 7CrMoVTiB10-10 steel (T24), q c = Q c /R and q d = Q d /R , 5 T24 parameters p ( T ) = p r(1 + a ( T − T r) /T r) and r ( T ) = r r(1 + b ( T − T r) /T r) , σ rc = σ rd = sigr = σ y0( T ) = σ ∗ − cT , with σ ∗ = 1123 MPa, c = − 1 MPa/K. 6 Results 7 Conclusions mod t c [s] p r t d [s] a q c [K] r r q d [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 - - - 400 400 300 300 200 200 σ [ MPa ] σ [ MPa ] 100 100 50 50 10 − 2 10 − 1 10 0 10 1 10 2 10 3 10 4 10 5 ε c , min [ % / 10 3 h ] t rup [ h ] ˙ 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 Monkman-Grant parameter 3 Specific models 4 Monkman-Grant 5 T24 parameters 6 Results 7 Conclusions 10 12 0.024 model 1, T = 500 ◦ C 10 11 0.022 model 1, T = 550 ◦ C 100 MPa model 1, T = 600 ◦ C 200 MPa 10 10 0.02 300 MPa model 2 model 2 10 9 0.018 t rup [ s ] C MG 10 8 0.016 10 7 0.014 10 6 0.012 0.01 10 5 500 520 540 560 580 600 10 − 12 10 − 11 10 − 10 10 − 9 10 − 8 10 − 7 10 − 6 T [ ◦ C ] ε c , min [ s − 1 ] ˙ Creep fracture and fatigue – ECF21, June 20-24, 2016 14/20

1 Introduction 1 Introduction 2 TD formulation 3 Specific models 2 Thermodynamic formulation 4 Monkman-Grant 5 T24 parameters 6 Results 3 Specific models 7 Conclusions 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 FE analysis and results 3 Specific models 4 Monkman-Grant 5 T24 parameters The models are implemented in ANSYS using the USERMAT 6 Results subroutine and the mesh consists of mainly 20 node hexahedral ANSYS 7 Conclusions 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. Displacement Temperature (°C) Temperature Displacement 600 0 500 Time Creep fracture and fatigue – ECF21, June 20-24, 2016 16/20

1 Introduction 2 TD formulation Results 3 Specific models 4 Monkman-Grant 5 T24 parameters 6 Results 7 Conclusions 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. Creep fracture and fatigue – ECF21, June 20-24, 2016 17/20

1 Introduction 1 Introduction 2 TD formulation 3 Specific models 2 Thermodynamic formulation 4 Monkman-Grant 5 T24 parameters 6 Results 3 Specific models 7 Conclusions 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 18/20