Dislocations

1
Dislocations Plastic Deformation

• Phenomenon
• For ductile materials, plastic deformation will
  result when the applied stress is greater than
  its yield strength
• in tension, specimen becomes longer and thinner
  with deformation
• Tensile stress vs strain curves
• Quantitative description
• yield strength
• tensile strength
• elongation
• equation
• sT K eTn

• What is the mechanism?
• dislocation movement
• Structure of this topic
• revisit concepts of crystals and dislocations
• how dislocation movement causes plastic
  deformation
• slip systems in crystalline materials
• shear vs tensile stresses

Reading 4.5, 7.1-7.6 (6th ed)
2
Dislocations Plastic deformation

• Line defects - dislocations
• edge
• extra half plane
• displaced atoms along disln line
• Associated elastic energy
• screw
• displaced atoms along disln line
• Associated elastic energy
• mixed

• Dislocation (revisit)
• Crystalline materials
• Perfect crystals
• Defects in crystals

IMSE Dislocation-Edge
3
Dislocations Plastic deformation

• Movement of dislocations
• edge dislocations

• dislocation moving on slip plane from position A
  to B to C to D, creating a step on the surface of
  b (burgurs vector)

IMSE Motion-Edge
4
Dislocations Plastic deformation

• Animation (2)

• Animation (1)

Atomic view of edge dislocation motion from left
to right as a crystal is sheared.
Simulation of dislocation motion from left to
right as a crystal is sheared.
(Courtesy P.M. Anderson)
(Courtesy P.M. Anderson)
5
Dislocations Plastic deformation

• Plastic deformation (micro)
• millions of dislocations moving in this way cause
  plastic deformation

• process slip
• plane on which dislocation moves slip plane
• dislocation density
• 105-106 cm/cm3 in annealed state
• 109-1010 cm/cm3 when heavily deformed
• the magnitude and direction of deformation is
  determined by b
• dislocations can move in any way they like on the
  slip plane
• dislocations can be of any type
• Stress field self reading 7.3

Edge
IMSE Motion-Screw/Mixed
Screw
6
Dislocations Plastic deformation

• Slip systems
• Can slip take place on any plane and in any
  direction in a crystalline material?
• Not really. Often, slip takes place on the close
  packed planes and along the close packed
  directions since these are easier (i.e. smallest
  stress required to cause the slip)

• FCC crystals
• slip planes 111
• slip directions lt110gt
• one slip plane plus one slip direction a slip
  system
• 12 slip systems in a FCC structure 4 x 111
  planes 3 lt110gt directions on each plane

7
Dislocations Plastic deformation

• Plastic deformation (macro)
• How can macro-plastic deformation be realised by
  micro-dislocation movement (slip) in a single
  crystal?

• assuming there is only one slip system in
  operation one slip plane and one slip direction
  only
• many parallel planes slip slip lines can be seen
  on the surface
• crystal is elongated under a tensile stress
• Question about the illustration?
• crystal rotation has to happen to keep the
  loading forces in line
• where is the shear stress needed to cause slip?

Zn single crystal
8
Dislocations Plastic deformation

• Slip in single crystals
• Where is the shear stress?

• at a plane (the slip plane) whose normal is at f
  to the tensile force F
• if the slip direction on the slip plane is at l
  to F, the resolved shear stress in this direction
  is
• tR Fs/As s cos f cos l
• cos f cos l is called the Schmid factor
• the maximum resolved shear stress on the slip
  plane is when l p/2 - f (i.e. when the normal,
  the slip direction and the loading direction are
  on the same plan)
• tR (max) s cos f sin f

s F/A
Fs (max) F sin f
Fs F cos l
As A /cos f
Note that the maximum tR direction may not be a
slip direction, i.e. slip may not be allowed in
this direction
9
Dislocations Plastic deformation

• when f  45 and l 45
• cos f cos l 0.5
• which is the maximum, and thus the minimum yield
  stress is
• sy 2 tcrss
• sy changes with f and l (in single crystals)
• tcrss is the fundamental resistance force to
  slip/plastic deformation, i.e. it is a materials
  property.

• Slip in single crystals (2)
• Yielding tR reaches a critical value tcrss (the
  critical resolved shear stress) to cause slip
• tR tcrss
• or
• s cos f cos l tcrss
• that is
• s tcrss / (cos f cos l)

sy
10
Dislocations Plastic deformation

• Solution
• to find out the Schmid factor
• f 45, tan l a (2)0.5/a
• cos f cos l cos 45 cos 54.7 0.409
• (a) tR s cos f cos l 52 x 0.409 21.3 MPa
• (b) sy tcrss/cos f cos l 30/0.409 73.3 MPa

• Slip in single crystals - Example 7.1
• BCC slip plane (110), slip direction 111
• stress direction 010
• (a) tR ? when s 52 MPa
• (b) sy ? when tcrss 30 MPa

11
Dislocations Plastic deformation

• millions of small crystals (grains) form upon
  solidification, separated by grain boundaries
• each grain has its own (normally random)
  orientation
• Schmid factor?
• varies from grain to grain
• those with the greatest Schmid factors deform
  first
• when the grains are randomly oriented, there is
  no dependence of sy on orientation
• Yield strength is grain size dependent

• Plastic deformation of polycrystalline materials
• Revisit
• polycrystalline material

grain
12
Dislocations Plastic deformation

• Slip lines on different grains

• Plastic deformation of polycrystalline materials
  (2)
• Grains are elongated

before deformation
after deformation
300 mm