Hardening in Fe-Cr alloys under neutron irradiation: effects of segregation and defect spatial distribution D. Terentyev1 and X. Xiao2 1Nuclear Materials Science Institute, SCK•CEN, Mol, Belgium 2Department of Mechanics and Engineering Science, Peking University, P.R. China Add here Logos of Kukseko, Bergner, Hernandez 1

Introduction: range of Temp and Dose Mechanical properties of RAFM (see reviews Gaganidze et.al.1): Recovery of DBTT under irradiation above 350 °C Saturation of hardening above 10 dpa at T=300-335 °C 1E. Gaganidze et.al. Fus. Eng. Design 88 (2013) 118

Introduction: tensile properties Mechanical properties at T=300-350 (see E. Gaganidze et.al.1): While hardening saturates above 10 dpa, Loss of ductility below 10% takes place within 0.5-1 dpa 1E. Gaganidze et.al. Fus. Eng. Design 88 (2013) 118

Introduction: plastic flow localization Tensile mechanical properties at T >350C: As irradiation dose (hardening) ↑ plastic flow instability emerges1 Empirical analysis was applied by Aktaa et.al.2 1Z. Tong, Y. Day et.al. J. Nucl. Mater. 398 (2010) 43 2J. Aktaa et.al. J. Nucl. Mater. 417 (2011) 1123

Introduction: plastic flow localization Plastic flow instability in other materials: Fe, Cu, Ni, Cu-Cr-Zr also appear plastic flow instability1 Singh, Ghoniem, Trinkaus, and Zinkle: “clear channels” 2 1B. Singh, et.al.. J. Nucl. Mater. 307-311 (2002) 912/159 2S. Zinkle and et.al. J. Nucl. Mater. 351 (2006) 269

Introduction: revealing role of µ-structure Dedicated grades were irradiated and tested at SCK-CEN 1: Pure Fe: fully ferrite Fe and 2.5Cr were fully ferrite Fe-5Cr; Fe-9Cr: Ferrite + bainite E97, T91: RAFM steels As-received 1.5 dpa 1M. Matijasevic et.al. J. Nucl. Mater. 377 (2008) 147

Introduction: “invisible” hardening damage Correlation between µ-structure and hardening analysed in 1: Loop Density/Size did not change strongly 0.06-0.6-1.5 dpa, but hardening increased visibly Orowan expression does not account for the measured hardening Either “invisible” defects (voids/SIA clusters) contribute strongly or TEM-visible loops changed their strength (segregation/morphology)   (0.06 dpa) (0.6 dpa) (1.5 dpa) 1D. Terentyev, F. Bergner et.al. Acta Mat. 61 (2012) 1444

Results: Atom Probe Tomography APT (SCK-CEN, Idaho NL - USA, ITEP - RF): “Donuts” of Cr-Mn clusters in HT9 410C, 100 dpa Direct EELS and EDX measurements confirm Cr segregation at loops Cr-Mn-Si clusters in Eurofer 97 327 C, 15 dpa S.V. Rogozhkin et.al. Mat. Pow. Eng. 4 (2013) 112 •Cr •Mn D. Terentyev and M. Klimenkov, J. Nucl. Mater. 393 (2009) 30 O. Anderoglu et al. J. Nucl. Mater. 430 (2012) 194

Results: Atom Probe Tomography AP studies Univ. Roen by V. Kuksenko: Revealing Cr-Si-Ni-P clusters, D ≈ 3 nm; C ≈ 1024 m-3 Irregular shape of clusters suggest “preferential growth” The only alloy with Carbon dissolved in matrix Significant excess of Cr, well above solubility limit 10.4±0.9 15.5±1.3 24.2±2.4 6.4 ± 0.7 6.6 ± 0.8 7.9 ± 1.5 1.7 ± 0.4 1.3 ± 0.4 1.2 ± 0.6 2.1 ± 0.4 2.2±0.5 3.3 ± 1.0 1.8 ± 0. 3 0.8 ± 0.2 4.9 5 11.3 ±0. 7 Fe-5%Cr Fe-9%Cr Fe-12%Cr Fe-2.5%Cr Insert here Movie from Slava; get normal pictures from Slava; ask him to exclude Fe-12Cr as it is not discussed here V. Kuksenko et al. J. Nucl. Mater. 432 (2013) 160

Results: Dispersed Barrier Hardening model HZDR (Bergner): Application of DBH Model to link µ-structure and hardening Ask Frank to check the slide; add reference for Bacon Kocks Scattergood (BKS) model F. Bergner et al. J. Nucl. Mater. 448 (2014) 96 Invisible Solute-Rich Clusters (SRC) bring controlling) contribution to hardening

Microstructural Evolution under n-irradiation µ-structure diagram by Golubov and Singh: Presence of 1D-mobile clusters Presence of Immobile loops Given currently available knowledge: Solute/Carbon segregation immobilize Iclusters Formation & Growth of SRC clusters Which role SRC play in strain hardening ? S. Golubov, B. Sing et al. J. Nucl. Mater. 276 (2000) 78

Crystal plasticity assessment Experiment Single crystal model under irradiation Input Evolution of dislocation and defect density Initial µ-structure L D Defect pattern Dislocation-defect interaction Macro mechanical behavior Deformation Output Self-consistent method Ask Xiao to perfm CP calculations treating SRC like loops with respect to asborption Transfer Constitutive equation Grain size Irradiation hardening

Main elements of crystal plasticity Critical resolved shear stress (CRSS) on slip system a is given as:   Four principal contributions are accounted for Intrinsic lattice resistance + solid solution Dislocation network hardening Irradiation induced defect hardening Grain boundary hardening   Here one has to take formula from our recent draft  

Elasto-plastic self-consistent method using CP Macroscopic elasto-plastic model: H. Sabar, M. Berveiller, et.al. Int. Journal Sol. and Struc. 39 (2002) 3257 Self-consistent approach to study macroscopic response RVE The macroscopic strain and stress tensors are obtained according to the classical homogenization progress: fi – volume fraction of each grain; N – number of grains in RVE; εi - ϭi strain-stress tensor

Dislocation – defect interaction tensor Constitutive laws for Dislocation Loops account for: Direct interaction (a) Elastic interaction (b) Interaction Tensor accounts for annihilation1,2 η – defect annihilation probability, defined via Activation Energy and Effective stress     1N. Barton et al., J. Mech. Phys. Solids 61 (2013) 341 2X. Xiao et al., J. Mech. Phys. Solids 78 (2015) 1

Thermally activated absorption of loops Early MD studies by Bacon, Rodney, Osetsky, Soneda: Dislocation loops exhibit dual behaviour: Low temperature: strong Orowan obstacles High temperature: absorbable obstacles with α ≈ 0.5 Interaction mechanism Loop’s strength Check equations as proposed in our recent draft D. Terentyev et.al. Scripta Mat. 62 (2010) 697

Activation energy for loop absorption   Check equations as proposed in our recent draft Time-temperature dependent stress-strain history provides ΔG – τ function for absorption probability G. Monnet et.al. Philos. Mag. 90 (2010) 1001

Transfer to dislocation dynamics Assessment of ½<111> loops as stochastic absorbable obstacles Check equations as proposed in our recent draft Acceptable agreement for critical stress in a wide temperature range D. Terentyev et.al. Scripta Mat. 69 (2013) 578

How to treat Solute-Rich-Clusters ? Thermally activated absorbable defects (e.g. large loop) L D (I) φ ~ 0   Ask Xiao to perfm CP calculations treating SRC like loops with respect to asborption Weak shearable (e.g. small precipitate)1 (II) φ ≥ 45 Defect annihilation area   SRC density and size 1S. Krishna, A. Zamiri, S. De, Phil. Mag. 90 (2010) 4013

CP applied to pure Fe (RT 0.1 dpa1) Model for single crystal Model for poly-crystal Absorption of loops 2 and Thermally activated softening Ask Xiao to perfm CP calculations treating SRC like loops with respect to asborption 1M. Hernandez, D. Gomez-Briceno, J. Nucl. Mater. 399 (2010) 146 2S. Zinkle and B. Singh, J. Nucl. Mater . 351 (2006) 269

CP applied to non-irradiated Fe-Cr alloys Non-irradiated Fe-Cr alloys, important data to account for: Initial dislocation density and Grain size Solid solution hardening: linear expression following Ref. 1 and 2 Temperature dependent GB strengthening (same as for Fe) 1M. Matjiasevic, et.al. J. Nucl. Mater. 377 (2008) 147 2K. Suganuma, et.al. J. Nucl. Mater . 105 (1982) 23

Effect of temperature in non-irradiated alloys Ask Xiao to perfm CP calculations treating SRC like loops with respect to asborption Increasing temperature Lattice friction is vanished GB strengthening is reduced

Irradiated Fe-Cr alloys: 0.6 dpa; 300C Solute-Rich-Clusters: Dislocation-like obstacles absorbed by the same rules as Loops

Irradiated Fe-Cr alloys: 0.6 dpa; 300C Solute-Rich-Clusters: Weak obstacles that shear and reduce their strength as precipitates

Conclusive remarks: contributions to hardening Two major µ-structural contributions: TEM-visible loops : Spatial distribution depends carbon dissolved in matrix Enrichment by Cr-Mn can be important for strengthening TEM-invisible solute-rich clusters: Thermal stability and growth kinetics is unclear Irregular shape points to segregation at cascade-produced loops Computational assessment: Loops and SRC bring comparable contribution to hardening Loops and SRC experience different interaction with dislocations Role of SRC besides hardening source: SRC: centres for defect recombination → explains low swelling SRC: “seeds” for the emergence of non-equilibrium phases → extra hardening and observation of new phases at high DPA ~µm + ~0.05 µm Δσ Fe-Cr Pure Fe Φ1/2