La plasticité cristalline au service de la compréhension de la Corrosion sous Contrainte

Transcription

1 La platicité critalline au ervice de la compréhenion de la Corroion ou Contrainte T. Couvant, P. Roy, J.M. Proix, N. Sellenet, G. Nicola Vi cloion-renfort de interne de cuve (circuit primaire REP) Cloion de GV (circuit primaire REP) Canne chauffante de preurieur (circuit primaire REP)

2 Stre corroion cracking (SCC) reulted in the local interaction between microtructure, oxidation and loading 2 nm nm 1 min h Oxidation Loading 1 µm 200 µm < 1 µm Irradiation Microtructure 50 µm 1 cm

3 Phenomenology of SCC Maximal crack depth Water Microtructure under tenion Detectable crack in component Incubation period Initiation tage Propagation tage Time

4 Need to predict the time to initiation of SCC Time to initiation = i Material i i Stre Temperature Calibrated on laboratory reult i Stre = σ 4 i Temperature = exp T Example: Alloy 600 (heat WF675) i m = 2 when calibrated on RUB pecimen (after few thouand of h) i m = 0.16 when calibrated on tenile pecimen (after 18,000 h of teting) Prediction of the time to initiation (h) at 325 C: i Material RUB pecimen Applied tre (MPa) h 877 h h h Tenile pecimen Need of undertanding for a realitic prediction

5 Origin of the effect of a complex loading on SCC? Prior deformation in ambient air Load in primary water at 360 C Load in primary water at 360 C Need of undertanding Intergranular SCC in tainle teel Trangranular SCC in tainle teel

6 Apparent correlation between train gradient and preferential ite of intergranular SCC initiation Prior E xx 316L teted 720 h in primary water at 360 C Mean(prior-E xx ) = 0.06 Mean(econd-E YY ) = 0.02 ö YY = Second train axi Y (in primary water) Prior train axi X (in air) Second E yy Rolled Alloy 600 teted 2014 h in primary water at 360 C Mean(prior-E xx ) = Mean(econd-E YY )= 0.182

7 Toward a phyical modeling of SCC Objective To improve our undertanding of SCC To improve the predictibility of exiting model To improve our ability to extrapolate exiting knowledge Approach To quantify and model individual mechanim and their coupling To improve the exiting model baed on fundamental conideration Development of appropriate and flexible tool to imulate the IGSCC at the cale of the mechanim

8 Quantification and modeling of individual mechanim and their coupling INPUTS: Microtructure T, ph T, fluence Load Time Microtructural evolution: RIS Matrix damage OUTPUTS: Time to initiation Crack growth rate Cracking criteria: True initiation? Crack extenion? Platicity law evolution: Interaction matrix Critical reolved hear tre Stre & train evaluation: Local value Strain localization (clear band) Stre concentration on GB Oxidation: Mean & max oxide penetration Metal-oxide interface

9 Modeling microtructure 172 grain, node, TET10, 210 TET10/grain 111 V3 = 0 (unloaded) V3 = 1 (loaded) NE TG EN V3 = 2 (cracked) Non oxidized element Oxidized element σ C 500 grain σ C κ 0 Κ 2Gc σ c

10 Network of triple junction: preferred diffuion path for oxygen

11 Quantification and modeling of individual mechanim and their coupling INPUTS: Microtructure T, ph T, fluence Load Time Microtructural evolution: RIS Matrix damage OUTPUTS: Time to initiation Crack growth rate Cracking criteria: True initiation? Crack extenion? Platicity law evolution: Interaction matrix Critical reolved hear tre Stre & train evaluation: Local value Strain localization (clear band) Stre concentration on GB Oxidation: Mean & max oxide penetration Metal-oxide interface

12 Crytal platicity law & cracking behavior Crytal platicity law ~ ~ ~ p ~ p ε ɺ ε ɺ ε e ɺ = ɺ ε + = ɺ γ m n ɺ γ = τ x K τ c n ( τ τ x x ) τ = ~σ : m ~ Kinematic hardening x = c α ɺ = ɺ γ α dα ɺ γ τ Iotropic hardening γ c = τ 0 + Q r r cum ɺ γ = t r h dt r r ( 1 exp( bγ )) cum Temperature E τ ν 0 K Q b ( C) (MPa) (MPa) (MPa. 1/n ) n c d , , Muienko (Mine Pari-Tech) Cracking behavior σ C σ C corr Parameter et (MPa) (MPa) κ 0 κ corr 0 κ M κ corr M PENA_ADHE PENA_CONT E E E E

13 Overview on reult on non-cracked aggregate Mean equivalent tre Second load Mean number of activated lip ytem before a change of train path Mean number of activated lip ytem after a change of train path Prior load

14 Comparion between numerical & experimental 0,08 evaluation of train heterogeneitie (304L) 0,07 y = 0,3538x 0,06 R 2 = 0,9253 0,05 STD 0,04 0,03 0,02 0,01 0,00 0,00 0,05 0,10 0,15 0,20 Mean prior equivalent train Experimental evaluation FEM analyi

15 Experimental correlation between local train and local microtructure (crytal orientation, grain boundarie) Higher level of train are oberved on grain boundarie Axi of loading and correponding train (E eq ) reported in tandard triangle Axi of loading and correponding train (E eq ) reported in tandard triangle Conidering the total urface Conidering 2 µm max. from grain boundarie

16 Stre on grain boundarie, where SCC occur Code_ASTER Ditance from the grain boundarie (arbitrary unit)

17 Change of axi of loading promote tre concentration on grain boundarie Future model calibrated with intergranular parameter? i 2 σ [ k ( ε, β, ε ) mean( )] 4 11 Stre = GB 1 2 Second train at 90 from the prior train Prior train

18 Quantification and modeling of individual mechanim and their coupling INPUTS: Microtructure T, ph T, fluence Load Time Microtructural evolution: RIS Matrix damage OUTPUTS: Time to initiation Crack growth rate Cracking criteria: True initiation? Crack extenion? Platicity law evolution: Interaction matrix Critical reolved hear tre Stre & train evaluation: Local value Strain localization (clear band) Stre concentration on GB Oxidation: Mean & max oxide penetration Metal-oxide interface

19 Oxide formed in primary water at the urface of 304L Anionic growth of the inner Cr-rich rich oxide layer 304L, prior-e xx = 0.10, 700 h in primary water at 360 C, E YY = 0.02 STEM, bright field STEM, bright field 350 nm Magnetite Gold (µgrid) Metal/µgrid interface poition before teting Inner oxide layer Oxide penetration along hear band Shear band Metal

20 Oxide penetration law Statitical analyi baed on 3996 meaure on EFTEM Cr map, covering 12.4 µm (304L/316L expoed to primary water at 360 C, tranmiion ele ctron microcopy) Cr-rich oxide penetration (nm) Strain promote oxide penetration (p) Max Mean Min SD y = 264,6x + 54,6 R 2 = 0,5 y = 161,5x + 20,2 R 2 = 0, ,02 0,04 0,06 0,08 0,1 0,12 0,14 0,16 0,18 0,2 Local cumulated axial train Thickne (nm) Increae of alkalinity promote oxide penetration (p) Time (h) ph = 9,1 ph = 7,2 Max( p) = Max( p 2 ( 0,01t e ) ) 1 ph T ph m Max( p ) = 38.6e ε for 240 h < t < h 7.2 < ph 325 C < < ε < 0.12

21 Quantification and modeling of individual mechanim and their coupling INPUTS: Microtructure T, ph T, fluence Load Time Microtructural evolution: RIS Matrix damage OUTPUTS: Time to initiation Crack growth rate Cracking criteria: True initiation? Crack extenion? Platicity law evolution: Interaction matrix Critical reolved hear tre Stre & train evaluation: Local value Strain localization (clear band) Stre concentration on GB Oxidation: Mean & max oxide penetration Metal-oxide interface

22 Which fracture criterion ahead of a crack tip? Oxygen Iron Crack extenion? 200 nm Chromium Nickel Crack extenion? 200 nm

23 Calibration of the intergranular tre to fail grain boundarie affected by oxidation Forged Alloy 600 expoed 2000 h in PWR primary water Tenile tet in SEM up to failure of the oxidized GB: Mean final tre on GB = 438 MPa Fraction of cracked GB: f CGB = 0.8% FEM on polycrytalline aggregate gave the correponding tre ditribution Aumption: higher treed oxidized GB failed Threhold of IG tre to fail oxidized GB = 625 MPa Frequency Oxidized & higher treed GB (0.8%) Stre on grain boundarie (MPa)

24 Quantification and modeling of individual mechanim and their coupling INPUTS: Microtructure T, ph T, fluence Load Time Microtructural evolution: RIS Matrix damage OUTPUTS: Time to initiation Crack growth rate Cracking criteria: True initiation? Crack extenion? Platicity law evolution: Interaction matrix Critical reolved hear tre Stre & train evaluation: Local value Strain localization (clear band) Stre concentration on GB Oxidation: Mean & max oxide penetration Metal-oxide interface

25 Simulation of intergranular cracking, combining an oxide penetration law with a fracture criterion Diplacement field

26 Concluion Need to predict the time to initiation and the crack growth rate of tre corroion cracking The undertanding of cracking mechanim can improve our confidence in model prediction The imulation of SCC can help to validate aumed mechanim Fundamental tudie, combining experiment, microcopy & imulation, are ueful to improve actual engineering model (at hort and long term)

27 Limitation Future work Corroionit have a poor undertanding of the coupling: need to oberve (electronic microcopy) Mehing realitic microtructure (X-ray tomography) Platicity law: h r, no internal length for the platicity law Aniotropic elatic behavior to be conidered Non-ufficient intelligent & dynamic mehing refinement (ahead of crack) No crytal network tilt Size of the model Young moduli (MPa) Interaction matrix effect on tre concentration Synthetic v. realitic grain morphologie Gerard (Intitut Galilée)

28 Appendix

29 Mechanic calculation (0) Damage : V3= 0 : unloaded point V3= 1 : loaded point V3= 2 : broken point Mechanic calculation(1) Mechanic calculation (2) At thee different tage, the oxide propagation doe not affect any element. Mechanic calculation (3) Mater propertie : Non-oxidized element Oxidized element

30 Mechanic calculation (3) Damage : V3= 0 : unloaded point V3= 1 : loaded point V3= 2 : broken point Local oxidation time : 1 1 Determining the local oxidation time (3) 1 τ = 1 2 τ = 2 Oxidation depth : Pox(τ = 1) Pox(τ = 2) Pox(τ = 3) Determining the oxidation depth (3) 1 1 Mater propertie : Non-oxidized element Oxidized element

31 Determining the oxidation depth (3) Determining the oxidation tate (3) Damage : V3= 0 : unloaded point V3= 1 : loaded point V3= 2 : broken point Local oxidation time : 1 2 τ = 1 τ = 2 Oxidation depth : Pox(τ = 1) Pox(τ = 2) Pox(τ = 3) Oxidation tate : Ind = 0 (non oxidized) Ind = 1 (oxidized) Mater propertie : Non-oxidized element Oxidized element

32 Determining the oxidation tate (3) Mechanic calculation (4) Oxide Propagation (4) Damage : Local oxidation time : 1 2 V3= 0 : unloaded point V3= 1 : loaded point V3= 2 : broken point τ = 1 τ = 2 Oxidation depth : Pox(τ = 1) Pox(τ = 2) Pox(τ = 3) Oxidation tate : Ind = 0 (non oxidized) Ind = 1 (oxidized) Mater propertie : Non-oxidized element Oxidized element

33 2 2 Mechanic calculation and oxide propagation (4) Mechanic calculation (5) Oxide Propagation (5) Damage : V3= 0 : unloaded point V3= 1 : loaded point V3= 2 : broken point Local oxidation time : 1 2 τ = 1 τ = 2 Oxidation depth : Pox(τ = 1) Pox(τ = 2) Pox(τ = 3) Oxidation tate : Ind = 0 (non oxidized) Ind = 1 (oxidized) Mater propertie : Non-oxidized element Oxidized element

34 3 3 Mechanic calculation and oxide propagation (5) Mechanic calculation (5) Oxide Propagation (5) Damage : V3= 0 : unloaded point V3= 1 : loaded point V3= 2 : broken point Local oxidation time : 1 2 τ = 1 τ = 2 Oxidation depth : Pox(τ = 1) Pox(τ = 2) Pox(τ = 3) Oxidation tate : Ind = 0 (non oxidized) Ind = 1 (oxidized) Mater propertie : Non-oxidized element Oxidized element