M.A. Tschopp 1,2, D.L. McDowell 3,4

Transcription

1 1 KEYNOTE LECTURE Atomistic Simulations of Dislocation Nucleation M.A. Tschopp 1,2, D.L. McDowell 3,4 1 Center for Advanced Vehicular Systems (CAVS), Mississippi State University 2 UTC, Air Force Research Laboratory RXLMN, WPAFB 3 School of Materials Science and Engineering 4 GWW School of Mechanical Engineering Georgia Institute of Technology 12 th International Conference on Fracture 2009 Atomistic Fracture & Deformation T03-S5 Thursday, July 16, 2009, 13:50-14:30

2 2 Outline Introduction Simulation Methodology Bicrystal Atomistic Simulations Results Grain Boundary Characterization Grain Boundary Dislocation Nucleation Single Crystal Atomistic Simulations Orientation dependence of dislocation nucleation Influence of resolved stresses on dislocation nucleation Temperature dependence of dislocation nucleation Conclusions

3 Introduction Enhanced functional properties in materials with nanoscale dimensions Nanocrystalline materials! Experiments regarding inelastic mechanisms are often difficult to perform Plasticity at the nanoscale is dominated by grain boundary behavior, i.e., grain boundary sliding, grain rotation, and dislocation nucleation Khan et al Shan et al

4 4 Introduction Enhanced functional properties in materials with nanoscale dimensions Nanocrystalline materials! Experiments regarding inelastic mechanisms are often difficult to perform Plasticity at the nanoscale is dominated by grain boundary behavior, i.e., grain boundary sliding, grain rotation, and dislocation nucleation In situ TEM observations of grain-boundary motion in stressed nanocrystalline aluminum films Legros, Gianola, Hemker 2008

5 5 Introduction Enhanced functional properties in materials with nanoscale dimensions Nanocrystalline materials! Experiments regarding inelastic mechanisms are often difficult to perform Plasticity Effective at tool the nanoscale for analyzing is dominated dislocation by grain nucleation boundary and behavior, grain boundary i.e., grain sliding boundary in sliding, nanocrystalline grain rotation, materials and dislocation nucleation Provides insight into mechanisms and quantitative data that can be used in higher scale models to predict bulk properties of nanomaterials Nanocrystalline Atomistic Simulations of Inelasticity at the Nanoscale Deformation mechanisms agree with limited experimental results Van Swygenhoven et al. 2006

6 6 Introduction Enhanced functional properties in materials with nanoscale dimensions Nanocrystalline materials! Experiments regarding inelastic mechanisms are often difficult to perform Plasticity Effective at tool the nanoscale for analyzing is dominated dislocation by Bicrystal grain nucleation boundary and Atomistic behavior, grain boundary Simulations i.e., grain sliding boundary in of sliding, Inelasticity nanocrystalline grain rotation, at materials the and Nanoscale dislocation nucleation Provides Grain boundaries insight into in mechanisms nanocrystalline and quantitative materials are data very that complex, can be used though in higher scale models to predict bulk properties of Bicrystal simulations can manipulate grain nanomaterials boundary degrees of freedom to assess their impact Deformation on inelastic mechanisms mechanisms agree with limited experimental results Primarily performed on symmetric tilt grain boundaries Nanocrystalline Atomistic Simulations of Inelasticity at the Nanoscale Sansoz & Molinari 2005; Warner et al. 2006

7 Introduction Enhanced functional properties in materials with nanoscale dimensions Nanocrystalline materials! Experiments regarding inelastic mechanisms are often difficult to perform Plasticity Effective at tool the nanoscale for analyzing is dominated dislocation by Bicrystal grain nucleation boundary and Atomistic behavior, grain boundary Simulations i.e., grain sliding boundary in of sliding, Inelasticity nanocrystalline grain rotation, at materials the and Nanoscale dislocation nucleation Provides Grain boundaries insight into in mechanisms nanocrystalline and quantitative materials are data very that complex, can be used though in higher scale models to predict bulk properties of Bicrystal simulations can manipulate grain nanomaterials boundary degrees of freedom to assess their impact Deformation on inelastic mechanisms mechanisms agree with limited experimental results Primarily performed on symmetric tilt grain boundaries Nanocrystalline Atomistic Simulations of Inelasticity at the Nanoscale Spearot et al Spearot et al

8 8 Present research The present research investigates the influence of grain boundary degrees of freedom on heterogeneous dislocation nucleation using BICRYSTAL SIMULATIONS Energy Boundary Structure Dislocation Nucleation SITB CTB e.g., σ bc max Φ=0 ο D C D D D D D D D D D D D D C Stress (GPa) Increasing Inclination Angle, Φ Φ=10.02 ο Φ=19.47 ο Φ=29.50 ο Φ=35.26 ο 2 Φ=43.31 ο Strain (%) Tschopp, Spearot, McDowell, Influence of Grain Boundary Structure on Dislocation Nucleation in FCC Metals," Dislocations in Solids, Vol. 14, pp (2008)

9 9 Present research The present research also investigates homogeneous dislocation nucleation for improved understanding of lattice orientation using SINGLE CRYSTAL SIMULATIONS Resolved Stress Lattice Stress Effect Dislocation Nucleation resolved normal stress σ NF = NF σ uniaxial tensile stress 11 σ 11 resolved shear stress τ = SF σ SF 11 [ 112 Active slip system { } loading axis orientation resolved shear stress τ = PF σ PF 11 [ 110 loading axis ( ) 11 1 Slip Plane 9 ε =10 Tschopp, McDowell, Influence of single crystal orientation on homogeneous dislocation nucleation under uniaxial loading JMPS 56 (2008)

10 10 Simulation Methodology 12 th International Conference on Fracture 2009 Atomistic Fracture & Deformation T03-S5 Thursday, July 16, 2009, 13:50-14:30

11 Simulation Methodology FCC EAM Potentials Copper (and Aluminum) Mishin and coworkers (1999, 2001) EAM potentials provide a relatively accurate description of unstable and stable stacking fault energy Minimum Energy Grain Boundary Starting Configuration 3D periodic simulation cell Specify appropriate lattice directions Use a nonlinear conjugate gradient energy minimization w/ starting configurations M θ H Expand dimensions to minimize sensitivity to simulation cell dimensions Spearot, Tschopp, McDowell, Jacob, Acta Mat (2007) 705; Tschopp, McDowell, IJP (2008) 191. W B 11

12 Simulation Methodology Single Crystal Configurations 49 loading axis orientations used for starting configurations with minimum edge dimension of 16 nm Uniaxial Tensile/Compressive Deformation Equilibrate at temperature Uniaxial strain of 10 9 s -1 in the loading direction (e.g., perpendicular to GB) Modified NPT equations of motion (Spearot et al. 2005) are used for the lateral boundaries Strain until dislocation nucleation Tschopp, Spearot, McDowell, MSMSE (2007) 693; Tschopp, McDowell JMPS (2008); Tschopp, McDowell APL (2007) ε 9 =10 σ = 0 Stereographic triangle showing the 49 uniaxial loading axis orientations investigated in the single crystal deformation simulations. 12

13 Strain Rate Dependence of Dislocation Nucleation Stress Orientation and Rate Dependence of Dislocation Nucleation Stress Computed using Molecular Dynamics Stress, σ YY (GPa) [ s -1 strain rate [ s -1 strain rate [ s -1 strain rate Normalized Tensile Stress Required for Dislocation Nucleation, σ YY,max / σ YY,10^ [100 [110 [111 [210 [221 [311 [ Strain, ε YY e+6 1e+7 1e+8 1e+9 Strain Rate (s -1 ) As the strain rate is reduced from 10 9 to 10 7 s -1, the tensile stress required for dislocation nucleation is reduced by at most 4%. Spearot, Tschopp, McDowell, Scripta Materialia (2009) 13

14 14 Bicrystal Simulations 12 th International Conference on Fracture 2009 Atomistic Fracture & Deformation T03-S5 Thursday, July 16, 2009, 13:50-14:30

15 Grain Boundary Degrees of Freedom Asymmetric tilt grain boundaries are the most experimentally observed boundaries in polycrystals (Rohrer, Rollett, et al.). ( ) Σ=3/ 111 / STGB [ 111 [ 110 [ [ 111 Rotate (a) by , (a) STGB Rotated about tilt direction, <110> here Lattices ARE symmetric about GB plane Slip planes of MRSS ARE of the same geometric relationship with the GB plane, i.e., Schmid factor is equal in both lattices ( ) ( ) Σ=3/ 110 / 114 ATGB 1 2 [ 110 [ [ 114 Rotate (b) by (b) Symmetric (a) and asymmetric (b) tilt grain boundaries in the Σ3 system. Tschopp, McDowell, Phil Mag (2007)

16 Grain Boundary Degrees of Freedom Asymmetric tilt grain boundaries are the most experimentally observed boundaries in polycrystals (Rohrer, Rollett, et al.). ( ) Σ=3/ 111 / STGB [ 111 [ 110 [ [ 111 Rotate (a) by , (a) ATGB Lattices ARE NOT symmetric about GB plane Slip planes of MRSS ARE NOT of the same geometric relationship with the GB plane, i.e., Schmid factor is not equal in both lattices ( ) ( ) Σ=3/ 110 / 114 ATGB 1 2 [ 110 [ [ 114 Rotate (b) by (b) Symmetric (a) and asymmetric (b) tilt grain boundaries in the Σ3 system. Tschopp, McDowell, Phil Mag (2007)

17 Grain Boundary Characterization The structure, energy and free volume of symmetric and asymmetric tilt grain boundaries can provide insight into interfacial properties, such as dislocation nucleation. [ 558 [ 445 SITB CTB 4, 4,11 11,11, 8 SITB CTB D C D D D D D D D D D D D D C C C D C C C D D D D D D [ 774 [ 223 [ 227 [ 334 Grain boundary structures of a few Σ3 asymmetric boundaries in Cu compared to HRTEM images in Ag (Ernst et al. 1992). Tschopp, McDowell, Phil Mag, 87 (2007) 3147; Tschopp, McDowell, J. Materials Science (2007) 17

18 Grain Boundary Characterization The structure, energy and free volume of symmetric and asymmetric tilt grain boundaries can provide insight into interfacial properties, such as dislocation nucleation. CSL ATGB systems investigated: Σ3, Σ5, Σ9, Σ11, Σ13 * Most extensive atomistic work on ATGB energy and structure in Cu & Al Tschopp and McDowell, Phil Mag, 87 (2007) 3147; Tschopp and McDowell, Phil Mag, 87 (2007) Ni/Al grain boundaries, see Olmsted, Foiles, Holm, Acta Materialia (2009). 18

19 Grain Boundary Dislocation Nucleation Uniaxial Tension Virial Stress without microkinetic component over all atoms e.g., σ bc max Φ=0 ο Σ3 ATGBs Stress (GPa) Increasing Inclination Angle, Φ Φ=10.02 ο Φ=19.47 ο Φ=29.50 ο Φ=35.26 ο 2 Φ=43.31 ο Strain (%) 10 K Strain measured over entire length of simulation cell Spearot, Tschopp, McDowell, Jacob, Acta Mat (2007) 705; Tschopp, McDowell, IJP (2008) 191. The maximum tensile stress corresponds to dislocation nucleation and emission from the Σ3 asymmetric tilt GBs. 19

20 Grain Boundary Dislocation Nucleation Mechanisms Dislocations initially dissociate from the boundary and then are emitted into the lattice. LOW Dislocation Nucleation Stress Tschopp, McDowell, Scripta Materialia 58 (2008) 299. Highlighted recently in, Derlet, Gumbsch, Hoagland, J. Li, McDowell, Van Swygenhoven, and J. Wang, March 2009 MRS Bulletin 20

21 Grain Boundary Dislocation Nucleation Mechanisms Dislocation loops nucleate homogeneously in the lattice. (a) before nucleation, (b) after nucleation, (c) 3D image rendered with centrosymmetry parameter, (d) a schematic of dislocation nucleation, and (e) Slices showing various stages of dislocation loop nucleation on the {111} slip HIGH plane. Dislocation Nucleation Stress Tschopp, McDowell, Scripta Materialia 58 (2008) 299. Highlighted recently in, Derlet, Gumbsch, Hoagland, J. Li, McDowell, Van Swygenhoven, and J. Wang, March 2009 MRS Bulletin 21

22 Dislocation Nucleation Stress No apparent correlation with GB ENERGY MISORIENTATION ANGLE SIGMA VALUE FREE VOLUME Can we predict the dislocation nucleation stress using grain boundary metrics, e.g., the grain boundary energy or the grain boundary misorientation angle? 22

23 Dislocation Nucleation Stress Maximum Tensile Strength (GPa) <100> Symmetric Tilt Grain Boundaries {100} {110} Cu <100> Misorientations Cu <100> Single Crystals Model for Int. Strength Model for SC Strength MRSS <100> Interfaces MRSS <100> SCs Maximum {111}<112> Resolved Shear Stress (GPa) Single Crystal Difference Accounted for w/ GB Free Volume Interface Misorientation Angle (degrees) Bicrystal Can we predict the grain boundary dislocation nucleation stress from single crystal dislocation nucleation stresses? (Later, this will be calculated from resolved stress components) Spearot, Tschopp, Jacob, McDowell, Acta Materialia, (2007) 23

24 Tension-Compression Asymmetry Tension Compression 1/3<111> Disconnection Medlin, Carter, Angelo, Mills (1997) Medlin (1999, Advances in Twinning) Foiles and Medlin (2001) Marquis and Medlin (2005) Marquis, Medlin and Léonard (2007) Tschopp, Tucker, McDowell, Acta Mat (2007) 3959; Tschopp, Tucker, McDowell, Comp Mat Sci (2008). Σ171 Vicinal Twin <110> Symmetric Tilt Boundary 24

25 25 Heterogeneous dislocation nucleation findings Grain boundary structure plays an important role in dislocation nucleation mechanism Heterogeneous nucleation stress in grain boundaries is related to the homogeneous nucleation stress of the crystal lattice Nucleation stress IS NOT correlated with energy, Σ content, disorientation angle, or excess free volume (LATER) Single crystal nucleation stress IS related to resolved stresses (Schmid stress, normal stress) Tension-compression asymmetry in dislocation nucleation Partial dislocations nucleate in tension, full dislocations in compression (LATER) Normal stress! Shear stress in opposite directions.

26 26 Single Crystal Simulations 12 th International Conference on Fracture 2009 Atomistic Fracture & Deformation T03-S5 Thursday, July 16, 2009, 13:50-14:30

27 Orientation Dependence of Dislocation Nucleation Stress Tension Compression Tension-Compression ~ 200 simulations in tension and compression Dislocation nucleation is highly orientation-dependent, with different dependences in tension and compression. Dislocation nucleation stresses should be related to the resolved stress components in FCC Copper, i.e., the Schmid resolved shear stress? Tschopp, McDowell, APL 90 (2007)

28 Resolved Stress Components resolved normal stress σ NF = NF σ uniaxial tensile stress 11 σ 11 resolved shear stress τ SF = SF σ 11 Schmid factor (SF) Schmid Factor [ 111 Active slip system { } loading axis orientation resolved shear stress τ = PF σ PF 11 [ 100 Normal factor (NF) Normal Factor [ 110 [ Dislocation nucleation tends to follow both the Schmid resolved shear stress and the non-schmid resolved normal stress. Spearot, Tschopp, Jacob, McDowell, Acta Materialia (2007) 705; Tschopp, Spearot, McDowell, MSMSE (2007) 693 [ [

29 Resolved stress components and the dislocation nucleation stress Tension τ σ nucl = SF ideal For dislocation nucleation in tension, the following trends emerge: the higher the Schmid factor, the lower the dislocation nucleation stress the higher the normal factor, the lower the dislocation nucleation stress τ ideal σ nucl = NF Tschopp, McDowell, JMPS (2008)

30 Resolved stresses and tension-compression asymmetry in dislocation nucleation stress Tension-Compression Uniaxial Tension σ NF τ SF Uniaxial Compression σ NF τ SF For dislocation nucleation, the following trends emerge: High normal factor orientations have a higher tension-compression asymmetry in dislocation nucleation stress Tension-Compression Asymmetry Cu 10 K Cu 300 K [111 [ [ Tschopp, McDowell, APL 90 (2007) ; Tschopp, McDowell, JMPS (2008) 1806 Normal Factor (NF) 30

31 Dislocation nucleation stress model Classical Schmid Law w/ non-schmid normal stress component τ σ motion = SF σ nucl = α SF ideal Calculated Stress Required for Dislocation Nucleation (GPa) τ ideal SF + α Cu Single 10 K Cu Single 300 K 4 [ NF NF Predicted Stress Required for Dislocation Nucleation (GPa) NF dislocation nucleation region SF dislocation nucleation region SF NF In single crystal FCC Cu, the non-schmid normal stress plays an important role in the dislocation nucleation stress. [ 111 [ 110 Spearot, Tschopp, McDowell, Acta Materialia (2007) 705; Tschopp, Spearot, McDowell, MSMSE (2007)

32 Activation energy, activation volume Stress Required for Dislocation Nucleation (GPa) at 300 K Uniaxial Tension Uniaxial Compression Linear Regression σ(300k)=0.79*σ(10k) R 2 =0.96 σ(300k)=0.72*σ(10k) R 2 = σ Motivated by Zhu, Li et al. (2008) nucl σ ( T 0 K) nucl τ Q* α SF + α NF Ω ideal = = = s n [ σ ( T) = f( T) ( T = 0 K) nucl kt B kbtnv f( T) = 1 ln Q* ΩE ε 0 Stress Required for Dislocation Nucleation (GPa) at 10 K Ω Activation volume b Q* Activation energy ( σ = 0) ev Q Activation energy 0.3 ev 3 Tschopp, McDowell, JMPS (2008)

33 Activation energy, activation volume Stress Required for Dislocation Nucleation (GPa) at 300 K Uniaxial Tension Uniaxial Compression Linear Regression σ(300k)=0.79*σ(10k) R 2 =0.96 σ(300k)=0.72*σ(10k) R 2 = Ω Stress Required for Dislocation Nucleation (GPa) at 10 K Activation volume σ nucl σ ( T 0 K) nucl b Q* Activation energy ( σ = 0) ev Q Activation energy 0.3 ev Motivated by Zhu, Li et al. (2008) τ Q* α SF + α NF Ω ideal = = = s n [ σ ( T) = f( T) ( T = 0 K) nucl kt B kbtnv f( T) = 1 ln Q* ΩE ε 3 Homogeneous dislocation nucleation has activation volumes & energies on the order of heterogeneous dislocation nucleation 0 Tschopp, McDowell, JMPS (2008)

34 Activation energy, activation volume Stress Required for Dislocation Nucleation (GPa) at 300 K Uniaxial Tension Uniaxial Compression Linear Regression σ(300k)=0.79*σ(10k) R 2 =0.96 σ(300k)=0.72*σ(10k) R 2 =0.95 Schuh, Mason, et al., (2005) Nanoindentation on Pt Ω Q expt expt 0.5 b ev Ω Stress Required for Dislocation Nucleation (GPa) at 10 K Activation volume b Q* Activation energy ( σ = 0) ev Q Activation energy 0.3 ev T. Zhu, J. Li, et al., (2007, 2008) CINEB on nanopillars & boundaries 3 Q Q Q Q side surface corner disl absorption disl transmission 0.64 ev 0.1eV 0.49 ev 0.67 ev Tschopp, McDowell, JMPS (2008)

35 Dislocation mechanisms TENSION [ 112 [ 112 [ 112 ( ) 111 Slip Plane 9 ε =10 ( ) 111 Slip Plane ε =10 9 ( ) 111 Slip Plane ε =10 9 [ 110 loading axis COMPRESSION [ 111 loading axis [ 221 loading axis 9 ε =10 9 ε =10 9 ε =10 [ 211 loading axis [ 210 loading axis [ 321 loading axis Tschopp, McDowell, JMPS (2008)

36 Generalized Stacking Fault Energy Curve Motivated by Zimmerman et al. (2000) Compressive Normal Stress <112 > [ 112 Energy/Area (mj/m 3 ) % 0.5% 1% 2% 2% 1% 0.5% Tensile Normal Stress Similar to results found by Xu, Yip, et al for BCC Mo ( ) 111 Slip Plane Unstable SFE Stable SFE Shear Displacement (Angstroms) <112 > The ratio of stable to unstable stacking fault energy, γ sf /γ usf, has been used to describe the partial/full dislocation behavior between FCC metals, where γ sf /γ usf of approximately 1 (i.e., Al) exhibits full dislocation loops (Van Swygenhoven et al., 2004). Tension -Compression behavior shown here does not follow this trend for Cu. 36

37 37 Homogeneous dislocation nucleation findings Resolved normal stress plays an important role in homogeneous dislocation nucleation (unlike dislocation motion) Also important for explaining tension-compression asymmetry in dislocation nucleation Activation energies (~0.30 ev) and activation volumes (~1 b 3 ) are on the order of those calculated for heterogeneous dislocation nucleation Mechanisms - Partial dislocations nucleate in tension, full dislocations in compression Unstable stacking fault energy on GSF curve Influence of normal stress

38 38 Conclusion Bicrystal Simulations of Dislocation Nucleation NORMAL STRESS Single Crystal Simulations of Dislocation Nucleation

39 Thank you! Questions? Dissertation (free online): Tschopp, M.A., Atomistic simulations of dislocation nucleation in single crystals and grain boundaries GOOGLE: tschopp and ETD 39