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)

2

• 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.

4

• 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

5

• 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

8

• 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
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• 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
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• 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
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• Let the screw dislocation be dislocation I at
  the origin.
• The stress field for screw dislocation is given
  by
• based on the assumption,
• we have

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• For the other dislocation

18

• (continued)

19
(b)
(a)
Figure 14-6. (a) Diffusion of vacancy to edge
dislocation (b) dislocation climbs up one
lattice spacing