1. Instructor: Yuntian Zhu
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
Text book,
Office hour, by appointment
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:
Twinning:
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:
Dislocation slip:
Twinning:
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
This is caused by the grain size effect on twinning
Who is right?
No One is Wrong!!!

5. Grain size effect on deformation twinning
Strain rate and strain effect
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
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. t 1/d tp increases at a slower rate with decreasing d than tL
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): t
1/d
1/dc
The stress for activating lattice dislocation is
(Johari&Thomas, Acta Met. 2 (1964) 1152):
tp increases at a slower rate with decreasing d than tL
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 °I ° II
Assumption:
Dislocation emission from grain boundaries
Simplification:
Square grain
Straight dislocation line
Non-relaxed dislocation line on GB d
(111) a t
Stress for emitting a 30° partial needs to overcome:
The lengthening of partial dislocation line on the GB
The increase of total stacking fault energy b1
Stress increases with decreasing d

11. Critical Stresses vs Grain Sizes at Two angles
(111) d b a t
Driving force = t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)
After considering all a values (stress orientations)
Appl. Phys. Lett. 85, 5049 (2004).

13. Minimum Shear Stresses for deformation twinning:
Critical stress for deformation twinning:
Optimum grain sizes for deformation twinning:
Prog. Mater. Sci. 57 (2012) 1-62.

14. Compare with Experimental Observations
Critical stresses and optimum grain size range for twin nucleation

15. Generalized planar fault energy effect
Generalized Planar Fault Energy for Ni b1 b2 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