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Dislocations (Contd )
Be IV/IV metal forming
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Motion of
Edge
dislocation
Conservative
(Glide)
Non-conservative
(Climb)
For edge dislocation: as bt they define a plane theslip plane
Climb involves addition or subtraction of a row of atoms below the
half plane
+ve climb = climb up removal of a plane of atoms
ve climb = climb down addition of a plane of atoms
Motion of dislocations
On the slip plane
Motion of dislocation
to the slip plane
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Edge Dislocation Glide
Shear stress
Surface
step
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Edge Climb
Positive climb
Removal of a row of atoms
Negative climb
Addition of a row of atoms
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S crew Dislocation The motion of a screw dislocation is also a result of shear
stress
Motion is perpendicular to direction of stress, rather than
parallel (edge)
However, the net plastic deformation of both edge and
screw dislocations is the same
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Ref: Bryan Baker
chemed.chem.purdue.edu/genchem/ topicreview/bp/materials/defects3.html -
[1]
Screw dislocation
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Fig A and B Two views of a model
of a right handed screw dislocation.
The blue line indicates approximate
location of the dislocation line
Ref: Journal of Matl. Education
Fig A
Fig B
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PropertyType of Screw dislocation
Positive negative
Symbol
t and b direction 0180
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Screw dislocation cross-slip
Slip plane 1
Slip plane 2
b
The dislocation is shown cross-slipping from the blue plane to the green plane
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The dislocation line ends on:
The free surface of the crystal
Internal surface or interface
Closes on itself to form a loop
Ends in a node
A node is the intersection point of more than two
dislocations
The vectoral sum of the Burgers vectors of dislocations
meeting at a
node = 0
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Geometric properties of dislocations
Dislocation PropertyType of dislocation
Edge Screw
Relation between dislocation
line (t) and b ||
Slip direction || to b || to b
Direction of dislocation line
movement (t) relative to b||
Process by which dislocation
may leave slip planeclimb Cross-slip
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Mixed Dislocations
In many materials, dislocations are foundwhere the line direction and Burgersvector are neither only perpendicular nor
only parallel and these dislocations arecalled mixed dislocations, consisting ofboth screw and edge character
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Mixed dislocations
b
tb
Pure EdgePure screw
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The same model but viewed frombehind. The same letter correspondsto identical locations in three figures
The schematic model
Ref: Journal of Materials Education
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Ref: http://www.tf.uni-kiel.de/matwis/amat/def_en/kap_5/backbone/r5_1_2.html
Motion of a mixed dislocation
[1]
We are looking at the plane of the cut (sort of a semicircle centered in the lower left
corner). Blue circles denote atoms just below, red circles atoms just above the cut. Up
on the right the dislocation is a pure edge dislocation on the lower left it is pure screw.
In between it is mixed. In the link this dislocation is shown moving in an
animated illustration.
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Energy of dislocations
Dislocations have distortion energy associated with them
E per unit length
Edge Compressive and tensile stress fields
Screw Shear strains
Energy of dislocationElastic
Non-elastic (Core)
E
~E/10
2
2
1GbE Energy of a dislocation / unit length
G () shear modulus
b |b|
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2
2
1GbE Dislocations will have as small a b as possible
Dislocations
(in terms of lattice translation)
Full
Partial
b Full lattice translation
b Fraction of latticetranslation
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Dissociationof dislocations
Consider the reaction:
2b b + bChange in energy:
G(2b)2/2 2[G(b)2/2]
G(b)2
The reaction would be favorable
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Density of dislocations in a crystal
Total length of the dislocation line per unit
volume of the crystal (m.m^-3) or m^-2
Well annealed crystal has a dislocation density
of ~ 10^8-10^10
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Next class topics
Dislocations in FCC Lattice
Stacking faults
Frank partial dislocations
Dislocations in HCP lattice Dislocations in BCC cubic lattice
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References
Dieter, G.E.,Mechanical metallurgy, 1988, SI metric edition, McGraw-
Hill
W.D. Callister,Fundamental of materials science and engineering/ an
interactive e. text., 2001, John Willey & Sons, Inc.
Sanford, R.J.,Principles of fracture mechanics, 2003, Prentice Hall Tapany Udomphol, Dislocation theory, Suranaree University of
Technology
R. Prasad,Models of Dislocations for Classroom , Department of Applied
Mechanics, Indian Institute of Technology, Hauz Khas, New Delhi