Dislocation: dynamics, interactions and plasticity
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Transcript 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
radial force
.... 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