Recent development of modelling techniques in nano- and meso-scale simulations of dislocation dynamics

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1 Recent development of modelling techniques in nano- and meso-scale simulations of dislocation dynamics Department for Microstructure Physics and Alloy Design, Düsseldorf, Germany S.M. Hafez Haghighat, D. Raabe J. von Pezold, C.P. Race, F. Körmann, M. Friák, R. Schäublin, J. Neugebauer, G. Eggeler ICME workshop, June 24-27, 2014, Aachen/Rolduc

2 Dislocation plasticity Dislocation-assisted plastic deformation of crystalline materials: Mobility and multiplication of dislocations Interaction with other dislocations Interaction with nano-sized voids, secondary phase precipitates and dislocation loops Interaction with grain boundaries Plastic deformation Dislocation mobility and Interactions Dislocation density increases Strain hardening through forest hardening 1

3 Dislocation mechanisms in reality In situ TEM study of the interaction between moving ½ <111> dislocation and obstacles of dislocation character in pure bcc-fe. Orowan mechanism governs the interactions: strength of ~Gb/L, highest possible strength for an obstacle S.M. Hafez Haghighat, R. Schaeublin, Phil. Mag. Lett. 03 (2013)

4 Multiscale simulation approach Molecular dynamics (MD) is used to obtain information on the mobility of dislocations and dislocation-obstacle interaction at nanoscale. Discrete dislocation dynamics (DDD) is used to study dislocation mechanisms and their resulting macroscopic strength at mesoscale. 3

5 Atomistic simulation using embedded atom method 4

6 Glide of ½<111> edge dislocation in bcc-fe The embedded atom method (EAM) is the method of choice to study the kinetics and mechanisms of dislocations at atomic scale. Four commonly used EAM potentials for bcc-fe are evaluated with respect to their description of the dislocation dynamic and ist core structure. Simulation codes: MDCASK, LAMMPS 5

7 Dislocation core structure Distribution of the edge component of the Nye tensor in the core of the ½[11-1](-110) edge dislocation in bcc-fe 6

8 Dislocation core structure The glide stress predicted by the different EAM potentials qualitatively relates to the edge dislocation core structure. The GSF energy determined by the different interatomic potentials is reflected in the predicted core structure of the edge dislocation. 7

9 Dislocation reactions; the [100] junction Interaction between a ½[-111] edge and a ½[111] screw dislocation Edge dislocation speed: 440 m s 1 Crystal: bcc-fe T = 10 K 8

10 Junction characteristics F. Louchet, L.P. Kubin, Acta Metallurgica 23 (1975) 17. The [100] binary junction, 2-4 nm, is zipped in the glide plane of the edge dislocation. Kinks are emitted along the screw dislocation line in either of its glide planes. Thus the zipping is not constrained by the screw dislocation three-fold glide planes. 9

11 Junction mechanism in some DDD codes Interaction between dislocations leads to junction formation (b j = b i ) provided; E j < E i (b j 2 < b i2 ) In bcc metals the reaction between the ½<111> dislocations leads to binary junction formation; ½[-111] + ½[111] = [100] This junction is believed to lay at the intersection of the two dislocation glide planes. Three types of junction form due to the interaction of a dislocation in (101) glide plane with another dislocation in 3 different glide planes: Second dislocation glide plane Junction line direction Junction character Junction mobility (-110) [11-1] Mixed Sessile (10-1) [010] Edge Sessile (01-1) [-111] Mixed Glissile 10

12 Hardening due to the [100] junction The interaction steps: 1. Attraction of dislocations and formation of the junction with a drop in stress 2. Junction unzipping with a rise in stress to the critical release stress Temperature : Critical stress Dislocation speed (strain rate) : Critical stress S. M. Hafez Haghighat, R. Schaeublin, D. Raabe, Acta Materialia (2013). 11

13 Nano-sized defects (void) Edge dislocation interaction with copper precipitate and void in bcc-fe Y.N. Osetsky, D.J. Bacon, Journal of Nuclear Materials 323 (2003) 268. S. M. Hafez Haghighat, J. Fikar, R. Schaeublin, Journal of Nuclear Materials 382 (2008)

14 Nano-sized defects (Cr precipitate) Interaction of the edge dislocation with a 2 nm coherent Cr precipitate. Interaction between the edge dislocation and precipitate is repulsive. Softening in the Cr precipitate shearing by temperature although clear screw segments are not observed. S. M. Hafez Haghighat, D. Terentyev, R. Schaeublin, Journal of Nuclear Materials 417 (2011)

15 Comparison to nano-sized defects Low temperatures: the [100] binary junction strength is comparable to the coherent Cr precipitate and softer than void, and ½<111> and <100> dislocation loops (with similar sizes). At the highest temperature (300 K): all defects induce a similar hardening, within ~ 0.1(Gb/L). 14

16 DDD modeling of obstacle hardening DDD simulation of dislocation plasticity in the presence of 2 nm spherical defects in bcc-fe Obstacles strength from molecular dynamics input for DDD Presence of obstacles Flow stress and dislocation density 15

17 DDD simulation of creep in Ni base superalloys CMSX-4 16

18 Discrete dislocation dynamics method Defining a simulation box with periodic boundary conditions (PBC). Dislocations are randomly located in the simulation box and decomposed into straight segments having character from pure edge to pure screw depending on their orientation to the Burgers vector. Stress on the dislocation segments is calculated through Peach-Koehler force from applied stress, stress field of other dislocations and misfit stress; F pk t ( b) u a t mf d The position of segments is defined by calculating the speed of the segments (F=B V) and local events occurring during the displacement, such as direct annihilation, junction formation, cross-slip, climb and interaction with particles. 17

19 Hybrid mobility law To investigate the specific effect of climb: o o ParaDiS code Glide-climb dislocation mobility law Proposed glide-climb mobility of a dislocation in Ni base superalloys: S.M. Hafez Haghighat, G. Eggeler, D. Raabe, Acta Materialia 61(2013) Hybrid mobility law: B B B B gc oc g c B g B [ B B c 2 eg ec ( m m) B ( n n) ( n n) b t b t 2 B 2 sg c m n t ( b t) 2 ] 1/ 2 b, n and t are unity vectors of Burgers vector, glide plane normal and dislocation line direction. Z. Zhu et al., Acta Materialia 60 (2012)

20 Dislocation-precipitate interaction Cubic slip of a mixed 60 degree ½ a 0 [011](1-11) dislocation along the γ/γ interface at 150 MPa loading along y = [010]. Three stages of the interaction in the graph; A. Easy glide of dislocation before approaching the particle B. Dislocation slip along the γ/γ interface by the glide-climb mobility C. Release of the dislocation from the particle 19

21 Microstructure at low stress creep Microstructure of the single crystal Ni base superalloy with loading conditions of 150 MPa with Mg/Mc = 10 at ~0.0, 0.3 and 0.5 % creep strains. Experimental microstructure of Ni base superalloy in primary creep stage at 85 MPa shear loading condition. M. Kolbe, A. Dlouhy, G. Eggeler, Materials Science and Engineering A, 246 (1998)

22 Microstructure at high stress regime S.M. Hafez Haghighat, G. Eggeler, D. Raabe, Acta Materialia (2013) Simulated (at 350 MPa along [100]) and experimental (at 552 MPa along [001]) creep microstructures Deposited straight dislocations and bent dislocations on the γ/γ interfaces parallel and perpendicular to the loading directions T.M. Pollock, A.S. Argon, Acta Metall Mater, 40 (1992)

23 Simulated creep rate Variation of strain rate as a function of simulation time at different applied stresses with Mg/Mc = 10 At initial deformation stage the strain rate is dropped by about one order of magnitude. Strain rate then increases depending on the magnitude of applied stress similar to the experimental creep tests. This minimum and its later increase are more pronounced by increasing the applied stress. M. Kolbe, A. Dlouhy, G. Eggeler, Materials Science and Engineering A,

24 Summary Multiscale modeling approach is used to; 1. Investigate the transferability of Fe-EAM potentials using experimental and ab initio results for the study of dislocation dynamics. 2. Provide information at atomistic scale on dislocation-dislocation and dislocation-obstacle interactions in bcc-fe for DDD simulations. 3. Introduce proper hybrid glide-climb mobility in DDD simulations for the modeling of dislocation-interface interaction at high temperatures. 23