### Dislocation: dynamics, interactions and plasticity

```Dislocation: dynamics,
interactions and plasticity
• Slip systems in bcc/fcc/hcp metals
• Dislocation dynamics: cross-slip, climb
• Interaction of dislocations
• Intersection of dislocations
Edge/screw/mixed dislocations?
• Screw: Burgers vector parallel to the dislocation line.
• Edge: Burgers vector normal to the dislocation line.
Dislocation dynamics
Edge
Screw
Slip Direction
|| to b
|| to b
n=(111)
 between
line and b

||
b
Line movement
rel. to b
||

How can disloc.
leave slip plane
climb
n=( 1 1 1)
n=(111)
b=n1xn2= (111)x(1 1 1 ) =
u
[10 1 ]
cross-slip

Climb: diffusion controlled.
Important mechanism in creep.
Slip systems in crystals
{110}
{211}
{321}
Fe, Mo,
W, Na
Fe, K
• BCC
<111>
Fe, Mo,
W,  brass
• FCC
<110>
{111}
• HCP
<11-20>{0001}
<11-20>(10-10)
<11-20>(10-11)
Superdislocation and partial dislocations
Superdislocations in ordered material are connected by APB
b
b
Partial Dislocations b = b1 + b2
Motio
n of
partial
s
Separation of
partials
a
2



1 01 
a
6


2 11 
a
6
1 1 2 
If energy is favorable, Gb2 > Gb12 + Gb22
then partial dislocation form.
( Ga2/2 > Ga2/3)

Sessile dislocation in fcc
Lormer lock
Lormer-Cottrell lock
11 1 
11 1 
b
a
b1 
101
2


n=(001)
a
2
n


u2  1 1 0
110 


u  110



b2 

a
b1 
b2 
2
a
2

101 

n 1  11 1

a
01 1 
2
n 2  111
b1  b2 
a
2


101 

a
2


a
01 1 
2


b2 




u  110

b
p2
2
b
111 
a
a
p1
p2
101   b
b
 112  2 1 1

1
1
2
6
6
a
p2
1
u


a

p1
2

b1 
110 


p1
u
1
u1  1 1 0
b

01 1  b 

 b 1
111 


p2





u1  1 1 0
b
b
a
a
p1
p2
01 1   b
b
 1 2 1  11 2 

2
2
2
6
6
b
p1
2

a
a
a
2 1 1 6 1 2 1   b  6 110 
6
n  b  u  [00 1 ]

Unless lock (sessile dislocation) is removed,
dislocation on same plane cannot move past.
Sessile dislocation in bcc
[001] is not a close-packed direction -> brittle fracture
Edge dislocation stress field
y=x
y=–x
 11 
– Gbx
3 x1  x 2
2
2
2
2  (1   ) ( x1  x 2 )
2
 33   ( 11   22 ) 
 12   21 
 Gbx 1
2
2
 22 
– Gbx
 Gbx
2
2
2  (1   ) ( x1  x 2 )
2
1
2
2  (1   ) ( x1  x 2 )
2
2
2
x1 – x 2
2  (1   ) ( x1  x 2 )
2
2
2
2
x1 – x 2
2
2
2
2
Edge dislocations interaction
edges dislocations with
identical b
attractive
X=Y
repulsive
Stable at X=0
for identical b;
Stable at X=Y
for opposite b.
Edge dislocations interaction (general case)
For an edge dislocations
Screw dislocations interaction
Example: two attracting screws u(1)= (001) =u(2)
F
( 2 1 )
r
0
(1) 

 0
0

 z 
0

 0
0

... 
0
0
 z
G b1
2 r
0
0
 z
b(1)= (001)b = –b(2)
0   0  0
 
  
Gb 1  b 2
  z    0  X  0   rˆ
 rˆ (  b   z )
2 r





0   b 1
.... z
b1
0 r

  z 
0 
z
b1
2
1
r
Edge-Edge Interactions: creates edge jogs
**Dislocations each acquire a jog equal to the component of the other
dislocation’s Burger’s vector that is normal to its own slip plane.
after
before
This dislocation got a jog
in direction of b1e.
b1e
b2e
b2e
Dislocation 1 got a “jog” in
direction of b2e of the other
dislocation; thus, it got longer.
Extra atoms in half-plane
increases length.
b1e
Dislocation intersection
Interaction of two
edges with
parallel b
Two screw kinks
(screw)
Edge jog on the
edge
Edge kink on the
screw
Edge jogs on screws
```