D. Terentyev 1 and X. Xiao 2 1 Nuclear Materials Science Institute, SCK•CEN, Mol, Belgium

1. 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

2. 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

3. 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

4. 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

5. 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

6. 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 1.5 dpa As-received 1M. Matijasevic et.al. J. Nucl. Mater. 377 (2008) 147

7. 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) (1.5 dpa) (0.06 dpa) (0.6 dpa) 1D. Terentyev, F. Bergner et.al. Acta Mat. 61 (2012) 1444

8. 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

9. 24.2±2.4 15.5±1.3 10.4±0.9 11.3 ±0. 7 1.2 ± 0.6 1.3 ± 0.4 1.7 ± 0.4 0.8 ± 0.2 7.9 ± 1.5 1.8 ± 0. 3 6.4 ± 0.7 6.6 ± 0.8 4.9 ± 0. 5 3.3 ± 1.0 0.8 ± 0.2 2.2±0.5 2.1 ± 0.4 Fe-2.5%Cr Fe-5%Cr Fe-9%Cr Fe-12%Cr 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 V. Kuksenko et al. J. Nucl. Mater. 432 (2013) 160

10. Results: Dispersed Barrier Hardening model • HZDR (Bergner): Application of DBH Model to link µ-structure and hardening F. Bergner et al. J. Nucl. Mater. 448 (2014) 96 Invisible Solute-Rich Clusters (SRC) bring controlling) contribution to hardening

11. 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

12. L D Crystal plasticity assessment Evolution of dislocation and defect density Experiment Single crystal model under irradiation Input Initial µ-structure Defect pattern Dislocation-defect interaction Macro mechanical behavior Deformation Output Self-consistent method Transfer Constitutive equation Grain size Irradiation hardening

13. Main elements of crystal plasticity Critical resolved shear stress (CRSS) on slip system a is given as: Four principal contributions are accounted for

14. 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

15. 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

16. 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 Loop’s strength Interaction mechanism D. Terentyev et.al. Scripta Mat. 62 (2010) 697

17. Activation energy for loop absorption Time-temperature dependent stress-strain history provides ΔG – τ function for absorption probability G. Monnet et.al. Philos. Mag. 90 (2010) 1001

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

19. L D How to treat Solute-Rich-Clusters ? Thermally activated absorbable defects (e.g. large loop) (I) φ ~ 0 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

20. 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 1M. Hernandez, D. Gomez-Briceno, J. Nucl. Mater. 399 (2010) 146 2S. Zinkle and B. Singh, J. Nucl. Mater . 351 (2006) 269

21. 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

22. Effect of temperature in non-irradiated alloys Increasing temperature • Lattice friction is vanished • GB strengthening is reduced

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

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

25. Conclusive remarks: contributions to hardening ~µm • 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 + ~0.05 µm Δσ Fe-Cr Pure Fe Φ1/2