Solute effect on twinning deformation in Mg alloys

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Solute effect on twinning deformation in Mg alloys A.

Curtin1 1 Institute of Mechanical Engineering, École

Department of Materials Science and Engineering, Ohio

Predictive Computational Metallurgy, EPFL & NSF-GOALI

1 Solute effect on twinning deformation in Mg alloys A. Luque1, M. Ghazisaeidi2, W.A. Curtin1 1 Institute of Mechanical Engineering, École Polytechnique Fédérale de Lausanne, Switzerland 2 Department of Materials Science and Engineering, Ohio State University, USA Supported by ERC grant # Predictive Computational Metallurgy, EPFL & NSF-GOALI grant # International Workshop on Computational Micromechanics of Materials, 1-3 October Madrid (Spain)

2 INTRODUCTION Mg & Mg Alloys Magnesium: Excellent candidate for low-weight structural applications Limited ductility due to strong plastic anisotropy Twinning is one of e main deformation mechanisms Magnesium alloys: Substitutional elements (Al, Zn...; rare-ears: Gd, Y...) CRSS modification & optimization of processing route & texture Improved ductility & formability Lack of understanding of e effect of solutes on Interface structures & energies Solute-dislocation interactions Twinning: What is e intervening mechanism? What is e activation stress? What is e role of solute fluctuations? What is e effect of segregation? What are e implications in real materials? 24 International Workshop on Computational Micromechanics of Materials, 1-3 October Madrid (Spain) 2

INTRODUCTION The {10-12}<-1011> (Tension) Twin Twin boundary: symmetrical tilt boundary wi a misorientation of ~87º Twinning: creation of a twinning dislocation (btw ~ 0.

86 Å): mechanism of nucleation & grow not well-established Twin #1 Twin dislocation (0001) <10-12> h No diffusion (0001) Twin #2 Symmetry conservation Initial state Nucleated

3 INTRODUCTION The {10-12}<-1011> (Tension) Twin Twin boundary: symmetrical tilt boundary wi a misorientation of ~87º Twinning: creation of a twinning dislocation (btw ~ Å) wi step character (h ~ 3.86 Å): mechanism of nucleation & grow not well-established Twin #1 Twin dislocation (0001) <10-12> h No diffusion (0001) Twin #2 Symmetry conservation Initial state Nucleated state We propose: A stress-driven, ermally-activated mechanism for nucleation & grow Pure Mg & Mg solid-solution alloys Material parameters: Twin dislocation line energy (MD) Solute/twin-boundary interaction energies (DFT) 24 International Workshop on Computational Micromechanics of Materials, 1-3 October Madrid (Spain) 3

4 THE MODEL MD simulations Material: Mg-Al: a reliable EAM potential exists Geometry: x // <-1011>, y // <-1210> & z // <10-12> Lx = 12.1 nm, Ly = 6.4 nm, Lz = 50.0 nm Size effects on nucleation energetics are accounted for: Interactions wi periodic images Limited fluctuations Boundary conditions: Periodic boundary conditions along x, y & z Control of σ x, σ y, σ z & τ xz Elastic anisotropy of e material Intrinsic interface stress Individual events, long quiescent periods Simulation conditions: T = 300 K Pure Mg & Random Mg alloy (1, 3, 5 at.% Al) Constant shear stress tests: migration rates τ Grain 1 Twin boundary Grain 2 Twin boundary y Grain 1 z τ x 24 International Workshop on Computational Micromechanics of Materials, 1-3 October Madrid (Spain) 4

5 Critical-size (L*) loop τ Initial (flat) twin boundary Nucleation τ Thermal vibrations Embryos (L<L*: disappear) Grow Grow Grow Final twin boundary (color code: z coordinate; only atoms belonging to e twin boundary are showed)

THE MODEL Pure Mg Energy analysis (nucleation of loop of size L): NO interface energy change Mechanical driving force ~ τ Dislocation line energy ~ Γ τ L1 Γ L* τ L2 L3 * Critical condition: *

6 THE MODEL Pure Mg Energy analysis (nucleation of loop of size L): NO interface energy change Mechanical driving force ~ τ Dislocation line energy ~ Γ τ L1 Γ L* τ L2 L3 * Critical condition: * Critical loop size: * Stability condition: * Migration rate (Arrhenius model): * Energy barrier: Σ/L*2: atoms involved in nucleation; D2/L*2: possible nucleation sites 24 International Workshop on Computational Micromechanics of Materials, 1-3 October Madrid (Spain) 6

7 ATOMISTIC RESPONSE Pure Mg MD results (1 m/s) Fit Γ = 4.23 mev/å ν0 = 17 THz The model works in pure Mg (1 mm/s) 24 International Workshop on Computational Micromechanics of Materials, 1-3 October Madrid (Spain) 7

8 ATOMISTIC RESPONSE Randomly-distributed solutes MD results (Just eye-guiding lines) Randomly-distributed solutes enhance e migration rate Experimentally-relevant stresses & concentrations Fit Γ = 4.23 mev/å ν0 = 17 THz 24 International Workshop on Computational Micromechanics of Materials, 1-3 October Madrid (Spain) 8

9 THE MODEL Solute/twin-boundary interaction energies 'Structural' symmetry conservation (NO diffusion!): 8 unique sites: 1 5, 2 6, 3 7 & 4 8 Solutes interact wi e twin boundary: Attractive (binding) & Repulsive interaction energies Solutes breaks e energetic symmetry Solutes provide a driving or retarding force for migration Site (ev) International Workshop on Computational Micromechanics of Materials, 1-3 October Madrid (Spain) 9

10 THE MODEL Effect of solutes Additional energy term associated to e interface Consider one Al solute laying on site 1; after twin migration (no diffusion) it occupies a site 5: The associated energy is E5 E1 If positive, nucleation is hindered If negative, nucleation is facilitated Mg-Al 24 International Workshop on Computational Micromechanics of Materials, 1-3 October Madrid (Spain) 10

11 THE MODEL Effect of solutes How does is relates to concentration/segregation ci & concentration fluctuations? Average number of occupied sites i is Standard deviation in e number of occupied sites i is Current number of occupied sites i is ci αi αi1 L1 L* αi2 L2 Magnitude of fluctuations associated wi site i (if N large, αi Gaussian) Therefore, energy change associated wi sites 1 and 5: Segregation Statistical fluctuations 24 International Workshop on Computational Micromechanics of Materials, 1-3 October Madrid (Spain) 11

12 THE MODEL Effect of solutes When it comes to energy maximization & determination of L*: Concentration/segregation, related to e state of e entire twin area Fluctuations vary from place to place (favorable fluctuations) The critical condition yields, for τ > τpin (stability condition): * Critical loop size: * Energy barrier: where and 24 International Workshop on Computational Micromechanics of Materials, 1-3 October Madrid (Spain) 12

THE MODEL Effect of solutes Statistical analysis provides fluctuations accurately: α i gets e largest probable value so Γ is maximum * Migration rate: wi If ci = c: τpin = 0 αi = α ~ 2-2.

13 THE MODEL Effect of solutes Statistical analysis provides fluctuations accurately: α i gets e largest probable value so Γ is maximum * Migration rate: wi If ci = c: τpin = 0 αi = α ~ {α1,α2,α5,α6}(a) {α1,α2,α5,α6}(b) {α1,α2,α5,α6}(f) {α1,α2,α5,α6}(c) {α1,α2,α5,α6}(d) {α1,α2,α5,α6}(e) {α1,α2,α5,α6}(g) {α1,α2,α5,α6}(h) {α1,α2,α5,α6}(i) {α1,α2,α5,α6}(l) {α1,α2,α5,α6}(m) {α1,α2,α5,α6}(n) {α1,α2,α5,α6}(*) Nucleation occurs where e largest favorable fluctuations can be found {α1,α2,α5,α6}(j) {α1,α2,α5,α6}(k) L* 24 International Workshop on Computational Micromechanics of Materials, 1-3 October Madrid (Spain) 13

14 VALIDATION OF THE MODEL Random solutes MD results NO extra adjustable parameters Fit Γ = 4.23 mev/å ν0 = 17 THz Predictions 24 International Workshop on Computational Micromechanics of Materials, 1-3 October Madrid (Spain) 14

15 IMPLICATIONS FOR REAL MATERIALS Segregation Segregation: Nie et al Science 340: polycrystalline Mg-0.2%at. Gd samples Annealing conditions (150 ºC, 3h): c2=0.76, c6=0.01, c1=c5=0 τpin = 2.1 GPa As-cast, recompressed (4.5%): grow of e existing twins & nucleation of new twins As-cast, compressed (2.5%): nucleation of twins (τ ~ 25 MPa) Annealed & recompressed (4.5%): nucleation of new twins (τ ~ 40 MPa) 24 International Workshop on Computational Micromechanics of Materials, 1-3 October Madrid (Spain) 15

16 CONCLUSIONS We propose a new mechanism for e ickening of an existing twin Energetic model based on: Solute/twin interactions & dislocation line energy Segregation & concentration fluctuations (statistical analysis) Validated by means of carefully-controlled MD simulations We successfully apply it to evaluate several observations in Mg alloys: Randomly-distributed solutes enhance e migration process (detwinning) Segregation of solutes inhibits e migration process Nie et al Science International Workshop on Computational Micromechanics of Materials, 1-3 October Madrid (Spain) 16

17 Solute effect on twinning deformation in Mg alloys A. Luque1, M. Ghazisaeidi2, W.A. Curtin1 1 Institute of Mechanical Engineering, École Polytechnique Fédérale de Lausanne, Switzerland 2 Department of Materials Science and Engineering, Ohio State University, USA Supported by ERC grant # Predictive Computational Metallurgy, EPFL & NSF-GOALI grant # International Workshop on Computational Micromechanics of Materials, 1-3 October Madrid (Spain)

Chapter Outline Dislocations and Strengthening Mechanisms. Introduction

Chapter Outline Dislocations and Strengthening Mechanisms What is happening in material during plastic deformation? Dislocations and Plastic Deformation Motion of dislocations in response to stress Slip