ASE324: Aerospace Materials Laboratory

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ASE324 Aerospace Materials Laboratory

• Instructor Rui Huang
• Dept of Aerospace Engineering and Engineering
  Mechanics
• The University of Texas at Austin
• Fall 2003

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Lecture 4

• September 9, 2003

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Plastic deformation

• Material remains intact
• Original crystal structure is not destroyed
• Crystal distortion is extremely localized
• Possible mechanisms
• Translational glide (slipping)
• Twin glide (twinning)

4
Translational glide

• The principle mode of plastic deformation
• Slip planes preferred planes with greatest
  interplanar distance, e.g., (111) in fcc crystals
• Slip directions with lowest resistance, e.g.,
  closed packed direction
• Slip lines intersection of a slip plane with a
  free surface
• Slip band many parallel slip lines very closely
  spaced together

Slip plane
Slip line
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Existence of defects

• Theoretical yield strength predicted for perfect
  crystals is much greater than the measured
  strength.
• The large discrepancy puzzled many scientists
  until Orowan, Polanyi, and Taylor (1934).
• The existence of defects (specifically,
  dislocations) explains the discrepancy.

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Defects

• Point defects vacancies, interstitial atoms,
  substitional atoms, etc.
• Line defects dislocations (edge, screw, mixed)
• Most important for plastic deformation
• Surface defects grain boundaries, phase
  boundaries, free surfaces, etc.

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Edge dislocations

• Burgers vector characterizes the strength of
  dislocations
• Edge dislocations b ?? dislocation line

D.R. Askeland and P.P. Phule, The Science and
Engineering of Materials, Brooks/Cole (2003).
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Screw dislocations

• Burgers vector b // dislocation line

D.R. Askeland and P.P. Phule, The Science and
Engineering of Materials, Brooks/Cole (2003).
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Mixed dislocation

• Have both edge and screw components.

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Observation of dislocations

• Transmission Electron microscopy (TEM)
  diffraction images of dislocations appear as dark
  lines.

M.F. Ashby and D.R.H. Jones, Engineering
Materials 1, 2nd ed. (2002)
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Glide of an edge dislocation

• Break one bond at a time, much easier than
  breaking all the bonds along the slip plane
  simultaneously, and thus lower yield stress.

D.R. Askeland and P.P. Phule, The Science and
Engineering of Materials, Brooks/Cole (2003).
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Motion of dislocations
William D. Callister, Jr., Materials Science and
Engineering, An Introduction, John Wiley Sons,
Inc. (2003)
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Force acting on dislocations

• Applied shear stress (?) exerts a force on a
  dislocation
• Motion of dislocation is resisted by a frictional
  force (f, per unit length)
• Work done by the shear stress (W?) equals the
  work done by the frictional force (Wf).

M.F. Ashby and D.R.H. Jones, Engineering
Materials 1, 2nd ed. (2002)
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Lattice friction stress

• Theoretical shear strength
• Lattice friction stress for dislocation motion
• Lattice friction stress is much less than the
  theoretical shear strength
• Dislocation motion most likely occurs on closed
  packed planes (large a, interplanar spacing) in
  closed packed directions (small b, in-plane
  atomic spacing).

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Interactions of dislocations

• Two dislocations may repel or attract each other,
  depending on their directions.

Repulsion
Attraction
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Line tension of a dislocation

• Atoms near the core of a dislocation have a
  higher energy due to distortion.
• Dislocation line tends to shorten to minimize
  energy, as if it had a line tension.
• Line tension strain energy per unit length

T
T
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Dislocation bowing

• Dislocations may be pinned by solutes,
  interstitials, and precipitates
• Pinned dislocations can bow when subjected to
  shear stress, analogous to the bowing of a string.

?bL
?/2
?/2
L
T
T
R
R
?
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Dislocation multiplication

• Some dislocations form during the process of
  crystallization.
• More dislocations are created during plastic
  deformation.
• Frank-Read Sources a dislocation breeding
  mechanism.

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Frank-Read sources in Si
Dash, Dislocation and Mechanical Properties of
Crystals, Wiley (1957).
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Strengthening mechanisms

• Pure metals have low resistance to dislocation
  motion, thus low yield strength.
• Increase the resistance by strengthening
• Solution strengthening
• Precipitate strengthening
• Work hardening

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Solution strengthening

• Add impurities to form solid solution (alloy)
• Example add Zn in Cu to form brass, strength
  increased by up to 10 times.

Bigger Zn atoms make the slip plane rougher,
thus increase the resistance to dislocation
motion.
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Precipitate strengthening

• Precipitates (small particles) can promote
  strengthening by impeding dislocation motion.

Dislocation bowing and looping. Critical
condition at semicircular configuration
M.F. Ashby and D.R.H. Jones, Engineering
Materials 1, 2nd ed. (2002)
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Work-hardening

• Dislocations interact and obstruct each other.
• Accounts for higher strength of cold rolled
  steels.

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Polycrystalline materials

• Different crystal orientations in different
  grains.
• Crystal structure is disturbed at grain
  boundaries.

D.R. Askeland and P.P. Phule, The Science and
Engineering of Materials, Brooks/Cole (2003).
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Plastic deformation in polycrystals

• Slip in each grain is constrained
• Dislocations pile up at grain boundaries
• Gross yield-strength is higher than single
  crystals (Taylor factor)
• Strength depends on grain size (Hall-Petch).

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Dislocation pile-up at grain boundaries