Atomic-scale

modeling of Clear

Band formation in FCC

metalsDavid Rodney

GPM2/ENSPGINP Grenoble, France

Special thanks to Y. Bréchet, M. Fivel and C. Pokor

Irradiation microstructures depend on the material and the irrad. conditions

(temperature, flux and spectrum)In Copper:

+ Defects not visible in TEM: glissile interstitial loops (< 1 nm)

Vacancy-type defects

stacking fault tetrahedra ( ~ 2 nm)

(0.1dpa,100°C+anneal 300°C)[Singh,'01]

316 steel (10dpa,375°C)[Pokor,'02]Interstitial defects

black dots ( ~ 2 nm),Frank loops ( ~ 10 nm)

In austenitic steels:

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)

PolycrystalFCC steel BCC Mo

PolycrystalFCC Cu

Single crystalFCC Cu

Correlation between steps and clear bandsin neutron irradiated copper [Sharp,'68,'72]

The plastic instability corresponds to the localization of the deformation in clear bands (or defect free zones)

Clear bandsin Cu [Robach,'03]

• The band width saturates with the deformation, ~ 0.15 m

• Shear in the bands is high, ~ 0.5 m ≡ several thousand dislocations

• There are traces of cross-slip events

• There are pile-ups at the head of the channels

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

Glissile interstitial loopsin Ni [Rodney&Martin,'99]

Stacking fault tetrahedrain Cu [Wirth et al,'02Osetsky&Bacon,'03]

Voids and precipitates inCu & Fe [Osetsky&Bacon,'03]

Up to now, MD studies have focused on edge dislocations interacting with:

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

Outline:

• Simulation technique and boundary conditions

• Interaction Edge dislocation / Glissile loops

• Interaction Screw dislocation / Frank loops

Simulation technique

• EAM Nickel potential [Angelo, Moody, Baskes, 1995]

• Molecular Statics (Conjugate Gradient) or

Molecular Dynamics (Verlet Algorithm)

• Boundary conditions that construct infinite periodic glide planes

Y=[110]

Z=[111]

X=[112]

Periodiccondition in X

(+Shift b/2 in Y dir.)and Y

2D dynamicsin Z

20, 37, 60 nm

21.5 nm

17 nm

Boundary conditions for screw dislocation:

Edge dislocationin interaction with

glissile interstitial loops

[Rodney & Martin, PRL 82 3272 (1999), PRB 61 8714 (2000)]

MD simulation at T = 100 K , = 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

• 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

Screw dislocation

in interaction with

interstitial Frank loops

[Rodney, Acta Mater. 52 607 (2004)]

A

D

C

B

C

A

• 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:

A

D

C

B

C

A

• Loop in a cross-slip plane of the dislocation

• 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:

A

D

C

B

C

•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

A

• Loop in a cross-slip plane of the dislocation

• Loop not in a cross-slip plane of the dislocation

• 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:

• Initial configuration : Relaxed (CG) with no applied stress• MD simulation at T = 100 K, = 150 MPa

Loop with perfect hexagonal shape and <110> edges

Burgersvector

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

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

What do we see?

•Configuration not favorableto recombination

•Emission of a constricted node

•The loop is not unfaultedbut sheared + step

Influence of the shape: Loop with <121> edges

Case of Austenitic steelsand Nickel

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

Burgers vectordirection

CG simulation:

Screw dislocationLoop diameter 7 nmJog height 2 nmApplied stress 150 MPa

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)

Helical turn seen in the directionof the Burgers vector

Full structure of the helical turn

Vacancy clusters

Burgers vectordirection

• Simulations with increasing applied stress with dislocation lengths ~ 20, 40, 60 nm

• Compare unpinning stress with Orowan stress [Scattergood & Bacon,'82]

<110> loops

<121> 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

615.0ln

12

1

L

b

D

b

L

b

for screw dislocation (L=Ly-D)

with impenetrable obstacles (D)

Evaluation of the Unpinning Stress

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

segmentemitted from a

<121> loop

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

•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!

Can shear be at the origin of the clear bands?

Al-Li alloy SFT interacting with a screw dislocation

PerspectivesPERFECT program

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

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)

Dislocation gliding throughglissile interstitial loops

(M. Fivel, C. Lemaignan)