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Heterogeneous deformation and dislocation dynamics in Cu single crystal micropillars under compression Sreekanth Akarapu, Hussein Zbib and David Bahr The support from the Division of Materials Science and Engineering, Office of Basic Energy Science at the DOE under grant number DE-FG02-07ER46435 is gratefully acknowledged.
Background ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Storage  of geometrically necessary dislocations (GNDs) SIZE EFFECTS
Greer et al, Physical Review B, 73, 245410,2006 Constant strain rate Experimental Observations
Background ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Objectives Multi-Scale approach FE-DD Tang et.al Acta Materialia 55 (2007) 1607–1616  (3D DD only) Benzerga et.al Scripta Materialia 54 (2006) 1937–1941  (2D)
Hooke’s Law:   Momentum : Continuum Discrete Dislocation Dynamics Equation of Motion  Discrete systems Multi-scale Dislocation Dynamics Plasticity (MDDP) Image stress effects: Superposition principle (FEM) Zbib et. al, IJP, V.18, 1133 (2002)
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Problem Setup Junctions 6  (green) Jogs 5  (cyan) (1,1,1) plane 4  (red) (-1,-1,1) plane 3  (yellow) (-1,1,1) plane 2  (orange) (1,-1,1) plane 1  (black) Denotation Color label
Stress-Strain response  and size dependence ,[object Object]
 
Dislocation burst:  Dislocation mechanisms Spiral Source A B B B C E G G D G D F A B A’ B’ Pinned Traction free boundary Traction free boundary A C B
[object Object],[object Object],[object Object]
Hardening:  Dislocation Configurations Effective Mean Free Path is reduced Increase in stress to mobilize (111) A B B B C D q p s r s q Pinned Traction free Pinned
Deformed Contour plots % Effective Plastic Strain σ zz Magnified 10 times A B C D E F Pinned Stress concentration due to ledge at the surface
Effect of boundary conditions With friction between indenter and the specimen top surface Without friction between indenter and the specimen top surface The thickness of the specimen is 0.5 microns Double slip deformation
Sensitivity of dislocation distribution
Effect of image stresses  Dislocation  density: 10 14   1/m 2
Conclusions ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Thank you
 
Multi-Scale Discrete Dislocation Plasticity (MDDP) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

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Fall 2008 MRS presentation (Boston)

  • 1. Heterogeneous deformation and dislocation dynamics in Cu single crystal micropillars under compression Sreekanth Akarapu, Hussein Zbib and David Bahr The support from the Division of Materials Science and Engineering, Office of Basic Energy Science at the DOE under grant number DE-FG02-07ER46435 is gratefully acknowledged.
  • 2.
  • 3. Greer et al, Physical Review B, 73, 245410,2006 Constant strain rate Experimental Observations
  • 4.
  • 5. Hooke’s Law: Momentum : Continuum Discrete Dislocation Dynamics Equation of Motion Discrete systems Multi-scale Dislocation Dynamics Plasticity (MDDP) Image stress effects: Superposition principle (FEM) Zbib et. al, IJP, V.18, 1133 (2002)
  • 6.
  • 7.
  • 8.  
  • 9. Dislocation burst: Dislocation mechanisms Spiral Source A B B B C E G G D G D F A B A’ B’ Pinned Traction free boundary Traction free boundary A C B
  • 10.
  • 11. Hardening: Dislocation Configurations Effective Mean Free Path is reduced Increase in stress to mobilize (111) A B B B C D q p s r s q Pinned Traction free Pinned
  • 12. Deformed Contour plots % Effective Plastic Strain σ zz Magnified 10 times A B C D E F Pinned Stress concentration due to ledge at the surface
  • 13. Effect of boundary conditions With friction between indenter and the specimen top surface Without friction between indenter and the specimen top surface The thickness of the specimen is 0.5 microns Double slip deformation
  • 15. Effect of image stresses Dislocation density: 10 14 1/m 2
  • 16.
  • 18.  
  • 19.

Editor's Notes

  1. Title of my talk is “Heterogeneous..” and this work is supported by “Division of Materials science…” Lot of cosmetic work is to be done!!!!