1. 1 Ghiath MONNET EDF - R&D Dep. Materials and Mechanics of Components, Moret-sur-Loing, France Bridging atomic to mesoscopic scale: multiscale simulation of plastic deformation of iron PERFECT (PERFORM): integrated European project for simulations of irradiation effects on materials

2. 2 Objective : Case of void interaction with dislocations Irradiation leads to material damages production of point defects acceleration of aging formation of clusters, diffuse precipitates Consequences: modification of mechanical behavior strong strengthening deformation localization and embrittlement Prediction of radiation effects on mechanical properties

3. 3 Atomic and mesoscopic approaches Interaction nature: atomic (atomic vibration, neighborhood) Smoothing atomic features into a continuum model No adjustable parameter !! Strengthening scale: microstructure (temperature, disl. density, concentration)

4. 4 In this talk... Molecular Dynamics simulation of dislocation-void interactions Analysis of MD results on the mesoscopic scale Dislocation Dynamics prediction of void strengthening

5. 5 S h  motionattractionR Bowing-upunpinning Atomic simulations Size dependent results Different interaction phases Analysis of pinning phase Reversible isothermal regime

6. 6 Elastic work Dissipated work Curvature work  Mechanical analysis at 0K

7. 7 Energetics decomposition at 0K Energie (eV) (a) E curv U pot E el E int rr  (%) E curv U pot E el E int rr  (%) (b) 20 nm Edge dislocation, 1 nm void 40 nm edge dislocation, 2 nm void Analyses provide interaction energy and estimate of the line tension

8. 8 Analyses of atomic simulations at 0 K How to define an intrinsic strength of local obstacles ?

9. 9 The maximum stress depends on void size dislocation length simulation box dimensions Intrinsic strength of voids at 0K

10. 10 Case of all local obstacles Can be obtained from MD No approximation l w is  c a characteristic quantity ? Intrinsic strength of voids at 0K [Monnet, Acta Mat, 2007]

11. 11 The intrinsic “strength” depends on obstacle nature, not size Strength of voids > strength of Cu precipitates Intrinsic strength of voids at 0K

12. 12 Identification of thermal activation parameters Analyses of atomic simulations at finite temperature

13. 13 Temperature effect on interaction  (MPa)  (%) Decrease of the lattice friction stress Decrease of the interaction strength Decrease of the pinning time Stochastic behavior (time, strength) [Monnet et al., PhiMag, 2010] MD simulation, Iron, 0K, 20 nm edge dislocation - 1 nm void

14. 14 Survival probability The rate function  (MPa)  (%) T = 300 K Interaction time  t Survival probability: P o ( t ) dP(t) = P o (t)  (t) dt Probability density: p (  ) dp =  (t) dt

15. 15 Analyses of thermal activation: activation energy Case of constant stress  =  c Determination of the attack frequency w Peierls MechanismLocal obstacles

16. 16 For constant strain rate:  eff varies during  t Can we find a constant stress (  c ) providing the same survival probability at  s ? Development of  G = A - V *  eff  c little sensitive to V* Analyses of thermal activation: critical stress

17. 17 The critical and the maximum stresses Always  c <  max When T tends to 0K,  c tends to  max At high T,  c is 30% lower than  max Critical stress for voids  max (GPa) cc T (K)

18. 18  G (eV) T (K) C = 8.1  t varies slowly with T  t varies with strain rate MD simulations (  t  1 ns): C = 8 Experiment (  t  1 s): C = 25 Activation energy = f (stress, temperature) Experimental evidence  G(  c ) = CKT  c (GPa)  G (eV) Activation energy

19. 19 Dislocation Dynamics simulations of void strengthening Using of atomic simulation results in DD validation of DD simulations determination of void strengthening

20. 20 Validation of dislocation dynamics code Example of the Orowan mechanism [Bacon et al. PhilMag 1973] Screw Edge Simulation of the Orowan mechanism

21. 21 Comparison of dislocation shape Edge dislocation - void interaction

22. 22 Thermal activation simulations in DD Edge dislocation - void interaction DD MD Comparison between DD and MD results  eff Activation path in DD Computation of  eff Calculation of  G(  eff ) Estimation of dp =  (t)dt Selection of a random number x jump if x > dp

23. 23 DD prediction of void strengthening Average dislocation velocity : 5 m/s Number of voids : 12500 Prediction of the critical stress

24. 24 Conclusions Atomic simulations are necessary when elasticity is invalid Obstacle resistance must be expressed in stress and not in force Void resistance = 4.2 GPa to be compared to Cu prct of 4.3 GPa Despite the high rate: MD are in good agreement with experiment Activation path in DD simulations is coherent with MD results DD simulations are necessary to predict strengthening of realistic microstructures

25. 25 Collaborators Christophe Domain, MMC, EDF-R&D, 77818 Moret sur loing, France Dmitry Terentyev, SCK-CEN, Boeretang 200, B-2400, Mol, Belgium Benoit Devincre, Laboratoire d’Etude des Microstructures, CNRS-ONERA, 92430 Chatillons, France Yuri Osetsky, Computer Sciences and Mathematics Division, ORNL David Bacon, Department of Engineering, The University of Liverpool Patrick Franciosi, LMPTM, University Paris 13, France

26. 26 Any problem? Segment configuration (in DD) influence the critical stress Given MD conditions, thermal activation can not be large How to “explore” phase space where  eff is small (construct the whole  G (  eff )) Accounting for obstacle modification after shearing Develop transition methods for obstacles with large interaction range Give a direct estimation for the attack frequency What elastic modulus should be considered in DD How to model interaction with thermally activated raondomly distributed obstacles?

27. 27 Screw dislocation in first principals simulations Ab initio simulation EAM potential, Mendelev et al. 2003 EAM potential,Ackland et al. 1997