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)
u
b=n1xn2= (111)x(1 1 1 ) = [101]
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
a
a
a
Motio
n of
partial
s
Separation of
partials
2

1 01 6 211 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
b1p 1u
 
n=(001)
n

bp2

a
2

110


u  110



u2  1 1 0

b2 
a
01 1
2
b1 
a
 

 
b1 
 
b2 
101
n1  11 1
2

a
n2  111
b2  01 1
2



a
a
a
b1  b2  101  01 1  b  110
2  2
2

 
   
 



u  110

a

b2p 2u

111


b2p 1


u1  1 1 0
 1
u1  1 1 0
b

111

a
a
101 b1p 1  b1p 2  112  2 1 1

2
6
6
a
a
a
01 1 b2p 1  b2p 2  1 2 1 112

2
6
6
b1p 2  b2p 1 
a
a
a
2 1 1 1 2 1 b  110 

6
6
6
n  b  u  [001]
 dislocation on same plane cannot move past.
Unless lock (sessile dislocation) is removed,
Sessile dislocation in bcc
[001] is not a close-packed direction -> brittle fracture
Edge dislocation stress field
y=x
y=–x
– Gbx2 3 x12  x22
 Gbx2 x12 – x22
 11 
 22 
2 (1  ) ( x12  x22 ) 2
2 (1  ) ( x12  x22 ) 2
 33   ( 11   22 ) 
– Gbx2
1
2 (1  ) ( x12  x22 ) 2
 Gbx1 x12 – x22
 12   21 
2 (1  ) ( x12  x22 ) 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)
0 0

 0 0
0 
z

b(1)= (001)b = –b(2)
0   0  0
    
Gb  b
 z    0 X 0   rˆ 1 2  rˆ(b z )
2r





0    b 1
radial force
r ... ....z
0
0

 (1)  0 0
0 
z

z 
Gb1
2r
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