Atomic-scale modeling of Clear Band formation in FCC metals

1. Atomic-scale modeling of Clear Band formation in FCC metals David Rodney GPM2/ENSPG INP Grenoble, France Special thanks to Y. Bréchet, M. Fivel and C. Pokor

2. Irradiation microstructures depend on the material and the irrad. conditions (temperature, flux and spectrum) In Copper: In austenitic steels: (0.1dpa,100°C+anneal 300°C)[Singh,'01] 316 steel (10dpa,375°C)[Pokor,'02] Interstitial defects black dots (f~ 2 nm), Frank loops (f~ 10 nm) Vacancy-type defects stacking fault tetrahedra (f~ 2 nm) + Defects not visible in TEM: glissile interstitial loops (f < 1 nm)

3. In all materials, irradiations induce a degradation of the mechanical properties: • hardening (increase in yield stress) • decrease in ductility • plastic instability (upper yield point + softening) Polycrystal FCC steel BCC Mo Polycrystal FCC Cu Single crystal FCC Cu

4. The plastic instability corresponds to the localization of the deformation in clear bands (or defect free zones) Correlation between steps and clear bands in neutron irradiated copper [Sharp,'68,'72] Clear bands in Cu [Robach,'03] • The band width saturates with the deformation, ~ 0.15 mm • Shear in the bands is high, ~ 0.5 mm ≡ several thousand dislocations • There are traces of cross-slip events • There are pile-ups at the head of the channels

5. To understand clear band formation, atomistic input is needed, because: • Interactions involve core contacts between dislocations and defects • (+absorption/shear of the defects) • Cross-slip traces are systematically observed in TEM • Irradiation defects have sizes and separations in the nanometer range Up to now, MD studies have focused onedge dislocationsinteracting with: Glissile interstitial loops in Ni [Rodney&Martin,'99] Stacking fault tetrahedra in Cu [Wirth et al,'02 Osetsky&Bacon,'03] Voids and precipitates in Cu & Fe [Osetsky&Bacon,'03]

6. Our aim: • Understand the dynamics of formation of clear bands in austenitic steels • Systematic study of edge and screw dislocations interacting • with interstitial Frank loops (austenitic) • Study interaction mechanisms •  Role of cross-slip, defect shape, temperature, chemistry • Evaluate critical unpinning stresses •  Use in larger scale simulations (DDD) • and models (internal variable models) Since no potential for austenitic steels is available YET, we use Nickel as a prototypical FCC crystal

7. Outline: • Simulation technique and boundary conditions • Interaction Edge dislocation / Glissile loops • Interaction Screw dislocation / Frank loops

8. Simulation technique

9. EAM Nickelpotential[Angelo, Moody, Baskes, 1995] • MolecularStatics(Conjugate Gradient) or • MolecularDynamics(Verlet Algorithm) • Boundary conditions that constructinfinite periodic glide planes Boundary conditions for screw dislocation: 2D dynamics in Z s Z=[111] Y=[110] 17 nm X=[112] Periodic condition in X (+Shift b/2 in Y dir.) and Y s 20, 37, 60 nm 21.5 nm

10. Edge dislocation in interaction with glissile interstitial loops [Rodney & Martin, PRL 82 3272 (1999), PRB 61 8714 (2000)]

11. Are clusters of <110> dumbbells • Are very mobile along their glide cylinder (Brownian motion) • When in contact with core of edge dislocations: • Collective flip of the dumbbells such that the final Burgers vector lies in the glide plane of the dislocation • Absorption and drag by the moving dislocations b MD simulation at T = 100 K ,s= 150 MPa, 4-SIA loops "The vacuum cleaner effect" → removes all loops within a capture distance (~2 nm) → the dislocation climbs and broadens the band. Provides a mechanism for clear band formation but not for hardening

12. Screw dislocation in interaction with interstitial Frank loops [Rodney, Acta Mater. 52 607 (2004)]

13. Frank loops have a {111} habit plane and a a/3<111> Burgers vector. • For a screw dislocation, there are 2 non planar contact configurations: B D C A bA Cb

14. Frank loops have a {111} habit plane and a a/3<111> Burgers vector. • For a screw dislocation, there are 2 non planar contact configurations: B • Loop in a cross-slip plane of the dislocation D C A bA Cb

15. Frank loops have a {111} habit plane and a a/3<111> Burgers vector. • For a screw dislocation, there are 2 non planar contact configurations: B • Loop in a cross-slip plane of the dislocation • Loop not in a cross-slip plane of the dislocation D C A bA Cb • We consider hexagonal loops with edges in <121> (austenitic steels and Nickel) or <110> directions (Gold and Copper), with or without jogs on their border • Diameter : 6 to 10 nm ; Density ~ 80 1022 m-3 • → realistic values close to saturation values

16. Loop with perfect hexagonal shape and <110> edges • Initial configuration : Relaxed (CG) with no applied stress • MD simulation at T = 100 K, s = 150 MPa • What do we see? • Athermal cross-slip driven by the core interaction between disl./loop • Disl. recombines with the loop edges • Helical turn is sessile Burgers vector

17. Unpinning Mechanism from the helical turn • Simulation at 425 MPa • Unpinning involves an • Orowan process • Net result: • transformation of • the Frank loop into a • perfect prismatic loop

18. Influence of the shape: Loop with <121> edges Case of Austenitic steels and Nickel • What do we see? • Configuration not favorable • to recombination • Emission of a • constricted node • The loop is not unfaulted • but sheared + step

19. Loops with Jogs • Loops often contain jogs on their border, with a flower-like structure • Can the jogs block the unfaulting reaction by impeding the cross-slips? • We produced jogged loops by removing interstitials contained in smaller hexagons at the periphery of hexagonal loops CG simulation: Screw dislocation Loop diameter 7 nm Jog height 2 nm Applied stress 150 MPa Burgers vector direction

20. What do we see? • The jogs do not impede the cross-slips • The helical turn has the complicated structure of the initial loop • Vacancy clusters are produced (containing ~ 10 vacancies) Burgers vector direction Vacancy clusters Full structure of the helical turn Helical turn seen in the direction of the Burgers vector

21. Evaluation of the Unpinning Stress • Simulations with increasing applied stress with • dislocation lengths ~ 20, 40, 60 nm • Compare unpinning stress with Orowan stress[Scattergood & Bacon,'82] for screw dislocation (L=Ly-D) with impenetrable obstacles (D) <110> loops • <121>: D = 3.2 nm • <110>: D = 5.3 nm • Effective size D close to real size • Unpinning controlled by bowing out • of the screw dislocation <121> loops

22. Summary • Reactions involve athermal cross-slips promoted by the • short-range interactions btwn dislocation/Frank loops and the applied stress • The cross-slipped segments emitted from the loops can serve as dislocation sources in cross-slip planes The short-range core interactions may be directly responsible for the high number of cross-slip events observed in clear bands Cross-slipped segment emitted from a <121> loop

23. Summary • Importance of the shape of the loops <110>: systematically unfaulted • <121>: sheared in 2 out of 3 cases • Can the dislocation recombine with the loop edges? • Suzuki et al. ('92) identified <121> loops in proton-irradiated austenitic steels ; the loops were sheared in bands containing many debris

24. Can shear be at the origin of the clear bands? • Shear of Frank loops is more frequent than assumed in the literature • The same is observed with Stacking Fault Tetrahedra(Wirth, Osetsky, Bacon) • Defect shearing also leads to the localization of the deformation, as in alloys hardened by coherent shearable precipitates • A possible scenario, not considered up to now, could be that clear bands form by shearing the irradiation defects until they become unstable and/or are absorbed in dislocation cores, as in the case of glissile loops • But this requires confirmation! Al-Li alloy SFT interacting with a screw dislocation

25. Perspectives PERFECT program • At the atomic scale • Complete study with edge dislocations • Consider solid-solutions to investigate alloying effects Ni-Al solid-solution (L. Proville, D. Rodney, Y. Bréchet, G. Martin) • At the micron scale (with Marc Fivel, GPM2) • Import information in Dislocation Dynamics • Account for non trivial effects : • - Role of grain boundaries as sources • - Role of pile-ups • Obtain : • - Clear band formation dynamics • - Stress-Strain curve during clear band formation Dislocation gliding through glissile interstitial loops (M. Fivel, C. Lemaignan)