Instructor: Yuntian Zhu. Lecture 5

Transcription

1 MSE 791: Mechanical Properties of Nanostructured Materials Module 3: Fundamental Physics and Materials Design Instructor: Yuntian Zhu Office: 308 RBII Ph: Lecture 5 Grain size effect on deformation twinning and detwinning in CG and NC fcc metals. Optimal grain size Department of Materials Science and Engineering 1

2 Grain Size effect on twining in CG samples Smaller grains are harder to deform by twining Hall-Petch relationship: Dislocation slip: σ S = σ 0 +κ S d 1/2 Twinning: σ t = σ 0 +κ t d 1/2 Department of Materials Science and Engineering 2

3 Grain Size effect on twining in CG samples Smaller grains are harder to deform by twining Hall-Petch relationship: κ t κ S Dislocation slip: σ S = σ 0 +κ S d 1/2 Twinning: σ t = σ 0 +κ t d 1/2 Department of Materials Science and Engineering 3

4 Grain size effect on deformation twinning To twin or not to twin? A controversy on twinning MD simulations by Dr. Van Swygenhoven s group In nc Al, Ni and Cu, twins are rarely observed (Nature Mater. 3 (2004) 399; Adv. Eng. Mater. 7 (2005) 16) MD simulations by Dr. Wolf s group In nc Al, twins are frequently observed (Nature Mater. 1 (2002) 45; 2 (2004) 43) Experimental Observations In nc Al, Cu and Ni, twins were observed Who is right? No One is Wrong!!!

5 Grain size effect on deformation twinning Statistical grain-size effect on the formations of stacking faults and deformation twins in NC Ni. Physical Review Letters, 101 (2008)

6 Grain size effect Optimum grain size for twinning Coarse-grained fcc metal: Smaller grains are harder to twin nc fcc metal: larger grains: Smaller grains are easier to twin Normal grain size effect nc fcc metal: smaller grains Smaller grains are harder to twin Maximum grain size for stacking fault Inverse grain size effect Twinning difficulty Grain Size

7 Similar results also observed in Cu Zhang, Lu, Wang, Li, Sun, Ma, PRB, 81, (2010)

8 What s the reason for the observed inverse grain size effect and optimum grain size for twinning?

9 Theory #1: Smaller grain size favors partial activation continuously from the CG to nano grain range (Chen et al, Science, 300 (2003) 1275; Liao et al, Phil. Mag. 83 (2003) 3065/our work) The stress for activating partial dislocation is (Venables, Phil Mag. 6 (1961) 379): τ P = γ b 1 + Gb d 1 τ τ P = γ b 1 + Gb d 1 The stress for activating lattice dislocation is (Johari&Thomas, Acta Met. 2 (1964) 1152): τ L = Gb d τp increases at a slower rate with decreasing d than τl τ L = Gb d 1/dc 1/d Emission of partials = twin formation

10 Our model extends beyond the previous models Zhu et al, APL, 85 (2004) 5049.(LANL+UCD) 3 systems: Screw 60 I 60 II d τ α b1 (111) Assumption: Dislocation emission from grain boundaries Simplification: Square grain Straight dislocation line Non-relaxed dislocation line on GB Stress for emitting a 30 partial needs to overcome: 1) The lengthening of partial dislocation line on the GB 2) The increase of total stacking fault energy τ p = 1 & $ sinα % 6γ a + 2 Ga 6πd ln 2d a #! "

11 Critical Stresses vs Grain Sizes at Two angles 2 α=90 d 1 A B' τ p τ α b (111) d B B τ shrink τ twin τ L τ trail Grain Size (nm) Driving force = τ b d, Dragging force is independent of d More difficult for dislocation slip with smaller grain size

12 Our Analytical Model on Twinning Stresses vs Grain Sizes (Al) o I Screw Twin nucleation o I Screw Twin growth Grain Size d (nm) After considering all α values (stress orientations) Appl. Phys. Lett. 85, 5049 (2004).

13 Minimum Shear Stresses for deformation twinning: Critical stress for deformation twinning: τ m = ( ν )γ 2a Optimum grain sizes for deformation twinning: d m ln 2 d m a ( ) = 9.69 ν ( ) ν Ga 2 γ Prog. Mater. Sci. 57 (2012) 1-62.

14 Compare with Experimental Observations Critical stresses and optimum grain size range for twin nucleation Ag Al Au Cu Ni G (GPa) ν γ (mjm -2 ) A (Å) τ m (GPa) d m (nm)

15 Generalized planar fault energy effect b1 b2 Generalized Planar Fault Energy for Ni b Conventional wisdom: nc-ni should deform by full dislocation, with no stacking fault or twin Recent MD simulations: Nano-Ni should deform by partial dislocation emission from grain boundaries, creating stacking fault, but not twins (Van Swygenhoven, Nature Mater. 3 (2004) 399 ). The observed inverse grain size effect explains/reconciles the controversy

16 Detwinning is also affected by grain size Physical Review B, 84, (2011).

17 Mechanism for the grain size effect on detwinning Schematics of the grain size effect on the twinning and de-twinning tendency Physical Review B, 84, (2011).

18 Homework, due in one week Lecture 5: 2 Department of Materials Science and Engineering 18