Transcript Document

ASE324: Aerospace Materials Laboratory
Instructor: Rui Huang
Dept of Aerospace Engineering and Engineering Mechanics
The University of Texas at Austin
Fall 2003
Lecture 4
September 9, 2003
Plastic deformation
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Material remains intact
Original crystal structure is not destroyed
Crystal distortion is extremely localized
Possible mechanisms:
– Translational glide (slipping)
– Twin glide (twinning)
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
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.
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.
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).
Screw dislocations
• Burgers vector b // dislocation line
D.R. Askeland and P.P. Phule, The Science and Engineering of Materials, Brooks/Cole (2003).
Mixed dislocation
• Have both edge and screw components.
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, 2 nd ed. (2002)
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).
Motion of dislocations
William D. Callister, Jr., Materials Science and Engineering, An Introduction, John Wiley & Sons, Inc. (2003)
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).
W  l1l2  b
Wf   fl1  l2
W  Wf  f  b
M.F. Ashby and D.R.H. Jones, Engineering Materials 1, 2 nd ed. (2002)
Lattice friction stress
• Theoretical shear strength:
 max
G

2
• Lattice friction stress for dislocation motion:
f
 2a 
 f   G exp 

b
 b 
• 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).
Interactions of dislocations
• Two dislocations may repel or attract each other,
depending on their directions.
Repulsion
Attraction
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
1 2
T  Gb
2
T
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

 
2T sin   bL
 2
1 2
T  Gb
2
R
Gb
R
2
Dislocation multiplication
• Some dislocations form during the process of crystallization.
• More dislocations are created during plastic deformation.
• Frank-Read Sources: a dislocation breeding mechanism.
Frank-Read sources in Si
Dash, Dislocation and Mechanical Properties of Crystals, Wiley (1957).
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
Solution strengthening
• Add impurities to form solid solution (alloy)
• Example: add Zn in Cu to form brass, strength
increased by up to 10 times.
Cu Cu Cu Cu Cu Cu
Cu
Zn Cu
Zn Cu
Cu Cu Cu Cu
Bigger Zn atoms make the
slip plane “rougher”, thus
increase the resistance to
dislocation motion.
Precipitate strengthening
• Precipitates (small particles) can promote strengthening
by impeding dislocation motion.
Dislocation bowing and looping.
Critical condition at semicircular
configuration:
bL  2T
2T Gb


bL
L
M.F. Ashby and D.R.H. Jones, Engineering Materials 1, 2 nd ed. (2002)
Work-hardening
• Dislocations interact and obstruct each other.
• Accounts for higher strength of cold rolled steels.

UTS
YU
YL
×
Strain hardening
f

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).
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)
 Y  3 Y
• Strength depends on grain size (Hall-Petch).
 Y   0  Kd
1/ 2
Dislocation pile-up at grain boundaries