2.dislocations - 1.pdf

7/30/2019 2.Dislocations - 1.pdf

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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

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