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• 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, 2nd 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).

bllW 21

21 lflW f

bfWW f M.F. Ashby and D.R.H. Jones, Engineering Materials 1, 2nd ed. (2002)

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).

2max

G

b

aG

b

ff

2exp

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

T

2

2

1GbT

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

T T

R

/2/2

bLT

2sin2

2

GbR

2

2

1GbT

R

L

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 Cu Cu

Cu Cu Cu Cu

Zn Zn

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:

TbL 2

L

Gb

bL

T

2

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

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

YU

YL

Strain hardening×

UTS

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)

• Strength depends on grain size (Hall-Petch).

YY 3

2/10

KdY

Dislocation pile-up at grain boundaries