1. Dislocation Modelling: Linking Atomic-scale to the Continuum Dislocation Modelling: Linking Atomic-scale to the Continuum David Bacon and Yuri Osetsky* Department of Engineering The University of Liverpool * Oak Ridge National Laboratory David Bacon and Yuri Osetsky* Department of Engineering The University of Liverpool * Oak Ridge National Laboratory The University of Liverpool Cambridge June 2004

2. dislocations under stress move through field of irradiation-induced obstacles - dislocation loops, SFTs, point defect clusters, voids, precipitates, etc. Irradiation microstructure - effect on mechanical properties Channelling: Pd [p + ; 0.12dpa] - Victoria et al. (2000) Decoration & rafts: Mo [n] - Singh & Evans (1997) - Yamakawa & Shimomura (1998) (a) Single xtal Cu [p + ] (b) Polycrystal Fe [n] - Victoria et al. (2000) Issue: how to model strengthening effects, yield phenomena, defect absorption, defect motion, etc.?

3. Issues: models able to give quantitative information? models able to describe candidate materials? periodic boundary conditions? dislocation density? statics or dynamics? is high strain rate unavoidable in dynamics? - is it realistic? how good is simulation based on elasticity theory? - dislocation shape, critical stress, core effects,... incorporation of atomic-scale information from statics and/or dynamics into models based on elasticity theory? - obstacle forces, mechanisms,... Issues: models able to give quantitative information? models able to describe candidate materials? periodic boundary conditions? dislocation density? statics or dynamics? is high strain rate unavoidable in dynamics? - is it realistic? how good is simulation based on elasticity theory? - dislocation shape, critical stress, core effects,... incorporation of atomic-scale information from statics and/or dynamics into models based on elasticity theory? - obstacle forces, mechanisms,...

4. Multiscale modelling approach is necessary - continuum scale for strength, stress-strain characteristics, obstacle statistics effects, etc. - atomic scale for dislocation-obstacle interaction mechanisms, strength parameters, etc. (not obvious a priori) - nano-  micro-  meso-mechanics Multiscale modelling approach is necessary - continuum scale for strength, stress-strain characteristics, obstacle statistics effects, etc. - atomic scale for dislocation-obstacle interaction mechanisms, strength parameters, etc. (not obvious a priori) - nano-  micro-  meso-mechanics

5. Atomic-scale Requirements - long-distance motion of dislocation - extraction of stress/strain and stress/strain-rate characteristics - T = 0K and T > 0K - atomic structure of obstacle and dislocation after interaction Atomic-scale Requirements - long-distance motion of dislocation - extraction of stress/strain and stress/strain-rate characteristics - T = 0K and T > 0K - atomic structure of obstacle and dislocation after interaction - ~1-10M atoms - simple, short-range potentials Issue: models able to give quantitative information? Issue: models able to describe candidate materials?

6. Fixed Periodic Moveable LbLb H L Issue: statics or dynamics? T=0K (statics) simulations - apply shear strain T>0K (dynamics) simulations - apply shear stress or strain rate Issue: statics or dynamics? T=0K (statics) simulations - apply shear strain T>0K (dynamics) simulations - apply shear stress or strain rate  appl = F ext /(L b L) F ext F int  gen = F int /(L b L) Issue: dislocation density? e.g. L b = 120b H = 80b L = 120b N atoms ~ 1.5M  D = 1/(L b x H) ~ 1/(10 4 b 2 ) ~ 1.6 x 10 15 m -2 Issue: dislocation density? e.g. L b = 120b H = 80b L = 120b N atoms ~ 1.5M  D = 1/(L b x H) ~ 1/(10 4 b 2 ) ~ 1.6 x 10 15 m -2

7. Static simulation (T = 0K) Ex. edge dislocation  row of voids in  -Fe at T = 0K Static simulation (T = 0K) Ex. edge dislocation  row of voids in  -Fe at T = 0K void spacing L void size D increasing strain 2nm (339v) void in Fe L=42nm, T=0K. C1 xtal

8. Bacon, Scattergood, Kocks (1973-) - the effect of self-interaction on the critical stress  c (L,D,b) Issue: how good is simulation based on elasticity theory?

9. edge  s =0  s ≠0  D/L  void = [ln(D -1 +L -1 )+1.52] Gb 2  L  Orowan = [ln(D -1 +L -1 )+0.7] Gb 2  L the atomic simulation stress values are similar so are the line shapes the atomic simulation stress values are similar so are the line shapes data fits where B depends on  s - energy (tension) of dipole  ln[D] - D and L are in units of core radius r 0 data fits where B depends on  s - energy (tension) of dipole  ln[D] - D and L are in units of core radius r 0   c c     b b 2 2   L L ln 1 1 1 1 / / D D   1 1 / / L L   B B ( ( ) ) [ [ ] ]

10. Issue: incorporation of atomic-scale mechanisms into models based on elasticity theory? Ex 1 - Dislocation climb due to vacancy absorption from voids

11. critical shape: Cu precipitates Ex 2 - Dislocation-induced transformation of Cu precipitates in Fe

12. Dynamics simulation (T > 0K) - dislocation dynamics at the atomic scale - motion under applied strain-rate ~ (10 6 -10 8 )s -1 Dynamics simulation (T > 0K) - dislocation dynamics at the atomic scale - motion under applied strain-rate ~ (10 6 -10 8 )s -1 Issue: is high strain rate unavoidable? - is it realistic? e.g. SR = 5 x 10 6 s -1, L b = 120b,  D = 1.6 x 10 15 m -2 : v = 12ms -1, t = 2.4ns If  t = 2fs, N atom = 1.5M, computational speed = 10 -5 s/atom/  t: time = 170 days e.g. SR = 5 x 10 6 s -1, L b = 120b,  D = 1.6 x 10 15 m -2 : v = 12ms -1, t = 2.4ns If  t = 2fs, N atom = 1.5M, computational speed = 10 -5 s/atom/  t: time = 170 days

13. Ex 1. 2nm voids in Fe - strain rate 5 x 10 6 s -1 - mechanisms of T-dependence?

14. 136-VAC SFT (T=10K) – different h 0.00.10.20.30.40.50.60.70.80.9 -25 0 25 50 75 100 125 150 175 SFT 4.1nm 136 VAC at T=10K 7 6 5 4 3 3 2 1 - h=-0.48nm 2 - h= 0 3 - h= 0.48nm 4 - h= 0.96nm 5 - h= 1.44nm 6 - h= 1.92nm 7 - h= 2.40nm stress, MPa strain, % 1 -0.50.00.51.01.52.02.53.03.5 0 50 100 150 200 4.1nm SFT, T=10K critical stress, MPa h, nm No SFT damage -  c depends on h - effect on structure of SFT depends on h h

15. Conditions in cleared channels in n-irradiated Cu: high density of small SFTs (<6nm, maximum at ~2.5nm) high velocity of dislocations many dislocations glide in the same and/or neighbouring slip planes  channels may be cleared due to damage of SFTs by dislocations and dissolution due to instability of damaged clusters Conditions in cleared channels in n-irradiated Cu: high density of small SFTs (<6nm, maximum at ~2.5nm) high velocity of dislocations many dislocations glide in the same and/or neighbouring slip planes  channels may be cleared due to damage of SFTs by dislocations and dissolution due to instability of damaged clusters Dislocation-SFT interactions are complex: -  c depends on weakly on D -  c depends on h - effect on structure of SFT depends on h - effect on structure of SFT depends on D - SFTs can be destroyed by multiple interactions A. 3nm (78-vac) SFT in Cu L=35nm T=50K SR=5x10 6 B. 3nm (78-vac) SFT in Cu L=35nm T=50K SR=5x10 6 2.5nm (45-vac) SFT in Cu L=35nm T=300K 300MPa - multiple 8nm (496-vac) SFT in Cu L=35nm T=300K SR=2x10 7 9nm (630-vac) SFT in Cu L=35nm T=100K SR=2x10 7 - screw (B) 9nm (630-vac) SFT in Cu L=35nm T=100K SR=2x10 7 - screw (A,C)

16. 0100200300400500 0 25 50 75 100 125 150 critical stress, MPa temperature, K Void: D=2nm ( 369-VACs) SFTs: D=2.5nm ( 45-VACs) D=3.0nm ( 78-VACs) D=4.1nm ( 136-VACs) Effect of T on  c for SFTs and voids in Cu: - glide plane through obstacle centre - 45-vac SFT  369-vac void - 45-vac SFT stronger than 78-vac SFT

17. - obstacle forces - dislocation dynamics - obstacle dynamics - obstacle forces - dislocation dynamics - obstacle dynamics General Issue: incorporation of information from atomic-scale simulations into models based on elasticity theory?

18. Issues: models able to give quantitative information? models able to describe candidate materials? periodic boundary conditions? dislocation density? statics or dynamics? is high strain rate unavoidable in dynamics? - is it realistic? how good is simulation based on elasticity theory? - dislocation shape, critical stress, core effects,... incorporation of atomic-scale information from statics and/or dynamics into models based on elasticity theory? - obstacle forces, mechanisms,... Issues: models able to give quantitative information? models able to describe candidate materials? periodic boundary conditions? dislocation density? statics or dynamics? is high strain rate unavoidable in dynamics? - is it realistic? how good is simulation based on elasticity theory? - dislocation shape, critical stress, core effects,... incorporation of atomic-scale information from statics and/or dynamics into models based on elasticity theory? - obstacle forces, mechanisms,...