Forces%20B/w%20Dislocations - PowerPoint PPT Presentation

About This Presentation

Title:

Forces%20B/w%20Dislocations

Description:

When the two dislocations are separated by large distance: The total elastic ... opposite signs will prefer to come together and annihilate (cancel) each other. ... – PowerPoint PPT presentation

Number of Views:108

Avg rating:3.0/5.0

Slides: 20

Provided by: drpete

Learn more at: https://eng.fsu.edu

Category:

more less

Transcript and Presenter's Notes

Title: Forces%20B/w%20Dislocations

1
Forces B/w Dislocations

Consider two parallel (//) edge dislocations
lying in the same slip plane.
The two dislocations can be of same sign or
different signs
(a) Same Sign (on same slip plane)

When the two dislocations are separated by large
distance The total elastic energy per unit
length of the dislocation is given by
When dislocations are very close together The
arrangement can be considered approximately a
single dislocation with Burgers vector 2b
In order to reduce the total elastic energy,
same sign dislocations will repel each other
(i.e., prefer large distance separation).

(14.34)
(14.35)
3

Dislocations of opposite sign (on same slip
plane)
If the dislocations are separated by large
distance
If dislocations are close together Burgers
vector b - b 0
Hence, in order to reduce their total energy,
dislocations of opposite signs will prefer to
come together and annihilate (cancel) each other.

The same conclusions are obtained for dislocation
of mixed orientations
(a) and (b) above can be summarized as
Like dislocations repel and
unlike dislocations attract

Dislocations Not on the Same Slip Plane
Consider two dislocations lying parallel to the z
(x3) -axis
In order to solve this
(a) We assume that dislocation I is at the
origin
(b) We then find the interaction force on
dislocation II due to dislocation I

II
I
6

Recall Eqn. 14.29
Note that the dislocation at the origin
(dislocation I) provides the stress field, while
the Burgers vector and the dislocation length
belongs to dislocation II
Since is edge
Also bII is parallel to x1 Therefore,
This means that b2 b3 0 and b1 b

14.29
7

Since tII is parallel to x3, then
This means that t1 t2 0 and t3 1
From Eqn. 14.31, we can write
Therefore

But
Therefore, F along the x1 Direction is given as
?21b
This component of force is responsible for
dislocation glide motion - i.e., for dislocation
II to move along x1 axis.

14.30
9

F along the x2 Direction is given as - ?11b
This component of force is responsible for climb
(along x2).
At ambient (low) temperature, Fx2 is not
important (because, no climb).
For edge dislocation, movement is by slip slip
occurs only in the plane contained by the
dislocation line its Burgers vector.

14.31
10

Consider only component Fx1
For x1gt0 Fx1 is negative (attractive)
when x1ltx2 for
same sign, or
x1gtx2 for
opposite sign.
For x1lt0 Fx1 is positive (repulsive)
when x1gt-x2 same sign disl. or x1lt-x2 for
opposite sign disl.
Fx10 when x1 0, ? ? ? x2,

Usually for edge dislocations of same sign
For edge dislocations of opposite signs
11

Hence
Stable positions for two edge dislocations.

900
450
12

Equations 14-30 and 14-31 can also be obtained by
considering both the radial and tangential
components. The force per unit length is given
by
Because edge dislocations are mainly confined to
the plane, the force component along the the x
direction, which is the slip direction, is of
most interest, and is given by

14.32
14.33
13

Eqn. 14-34 is same as 14-30. Figure 14-5 is a
plot of the variation of Fx with distance x,
using equation 14-34. Where x is expressed in
units of y. Curve A is for dislocations of the
same sign curve B is for dislocations of
opposite sign. Note that dislocations of the
same sign repel each other when x gt y, and
attract each other when x lt y.

14.34
14
Figure 14-5. Graphical representation of Eq.
(14-21). Solid curve A is for two edge
dislocations of same sign. Dashed curve B is for
two unlike two dislocations.
15

Example A dislocations lies parallel to 100
with Burgers vector blt110gt. Compute the force
acting on the dislocation due to the stress field
of a neighboring screw dislocation lying parallel
to 001.
Assume that for the
screw dislocations

Solution
16