Ghiath MONNET EDF - R&D Dep. Materials and Mechanics of Components, Moret-sur-Loing, France

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

2. Objective : Prediction of radiation effects on mechanical properties • 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 Case of void interaction with dislocations

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

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. Atomic simulations S g motion attraction R Bowing-up unpinning h • Size dependent results • Different interaction phases • Analysis of pinning phase • Reversible isothermal regime

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

7. Energetics decomposition at 0K (a) (b) Upot Upot gr gr Eel Energie (eV) Eel Ecurv Ecurv Eint Eint g (%) g (%) 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. Analyses of atomic simulations at 0 K How to define an intrinsic strength of local obstacles ?

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

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

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

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

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

14. Survival probability T = 300 K t(MPa) Survival probability: Po(t) dP(t) = Po(t) w(t) dt g(%) Probability density: p(q) Interaction time Dt The rate function dp = w(t) dt

15. Analyses of thermal activation: activation energy Peierls Mechanism Local obstacles w Case of constant stress t = tc Determination of the attack frequency

16. Analyses of thermal activation: critical stress tc little sensitive to V* For constant strain rate: teffvaries during Dt Can we find a constant stress (tc) providing the same survival probability at qs ? Development of DG = A - V*teff

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

18. Activation energy = f (stress, temperature) DG (eV) C = 8.1 tc(GPa) Activation energy Experimental evidence DG(tc) = CKT DG (eV) T (K) • Dt varies slowly with T • Dt varies with strain rate MD simulations (Dt 1 ns): C = 8 Experiment (Dt 1 s): C = 25

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

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

21. Comparison of dislocation shape Edge dislocation - void interaction

22. Thermal activation simulations in DD teff DD MD Comparison between DD and MD results Edge dislocation - void interaction Activation path in DD • Computation ofteff • Calculation of DG(teff) • Estimation of dp =w(t)dt • Selection of a random number x • jump if x > dp

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

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. 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. 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 teff is small (construct the whole DG(teff)) • 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. Screw dislocation in first principals simulations EAM potential,Ackland et al. 1997 Ab initio simulation EAM potential, Mendelev et al. 2003