Chapter 5 Imperfections: Interfacial and Volumetric Defects

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Chapter 5Imperfections Interfacial
andVolumetric Defects
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Grains in a Polycrystal
Grains in a crystalline metal or ceramic the
cube depicted in each grain indicates the
crystallographic orientation of the grain in a
schematic fashion.
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Grain Structure of Tantalum and TiC
Polycrystalline (a) tantalum and (b) TiC.
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Low Angle Grain Boudnary
Low-angle grain boundary observed by
high-resolution transmission electron
microscopy. Positions of individual dislocations
are marked by Burgers circuits. (Courtesy of R.
Gronsky.)
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Mean Lineal Intercept
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Low-Angle Tilt Boundary
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Low-Angle Twist Boundary
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Grain-Boundary Energy as a Function of
Misorientation
Variation of grain-boundary energy with
misorientation ?. (Adapted with permission from
A. G. Guy,Introduction to Materials Science (New
York McGraw-Hill, 1972), p. 212.)
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Coincidence Lattice Boundary
Coincidence lattice boundary made by every
seventh atom in the two grains, misoriented 22?
by a rotation around the lt111gt axis. (Adapted
from M. L. Kronberg and H. F. Wilson, Trans.
AIME, 85 (1949), 501.)
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Coincidence Site Boundaries
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Interface between Alumina and NiAl2O4
Interface between alumina and NiAl2O4 (spinel).
(a) High-resolution TEM. (b) Representation of
individual atomic positions. (Courtesy of C. B.
Carter.)
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Grain Size vs. Volume Fraction of Intercrystal
Regions
The effect of grain size on calculated volume
fractions of intercrystal regions and triple
junctions, assuming a grain boundary thickness
of 1 nm. (Adapted from B. Palumbo, S. J. Thorpe,
and K. T. Aust, Scripta Met., 24 (1990) 1347.)
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Ledge Formation in Grain Boundary
Models of ledge formation in a grain boundary.
(Reprinted with permission from L. E. Murr,
Interfacial Phenomena in Metals and Alloys
(Reading, MA Addison Wesley, 1975), p. 255.)
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Grain Boundary Ledges
Grain boundary ledges as observed by TEM.
(Courtesy of L. E. Murr.)
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Tilt Boundary
Image and atomic position model of an
approximately 32? 110 tilt boundary in gold
note the arrangement of polygons representing the
boundary. (From W. Krakow and D. A. Smith, J.
Mater. Res. 22 (1986) 54.)
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Twinning
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Twinning in FCC Metals
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Deformation Twins
Deformation twins in (a) iron-silicon.(Courtesy
of O. Vöhringer.)
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Deformation Twins in Silicon Nitride
Deformation twins in silicon nitride observed by
TEM. (a) Bright field. (b) Dark field. (c)
Electron diffraction pattern showing spots from
two twin variants. (Courtesy of K. S. Vecchio.)
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Serrated Stress-Strain Curve Due to Twinning
Serrated stressstrain curve due to twinning in a
Cd single crystal. (Adapted with permission from
W. Boas and E. Schmid, Z. Phys., 54 (1929) 16.)
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Twinning in HCP Metals
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Stress Required for Twinning and Slip
Effect of temperature on the stress required for
twinning and slip (at low and high strain rates).
(Courtesy of G. Thomas.)
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Mechanical Effects of Slip and Twinning
(a) Stressstrain curves for copper (which
deforms by slip) and 70 Cu30 Zn brass (which
deforms by slip and twinning). (b) Work-hardening
slope ds/de as a function of plastic strain a
plateau occurs for brass at the onset of
twinning. (After S. Asgari, E. El-Danaf, S. R.
Kalidindi,and R. D. Doherty, Met. and Mater.
Trans., 28A (1997) 1781.)
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Effect of Temperature and Stacking-Fault Energy
on Twinning Stress
Effect of temperature on twinning stress for a
number of metals. (From M. A. Meyers,
O. Voehringer, and V. A. Lubarda, Acta Mater., 49
(2001) 4025.)
Effect of stacking-fault energy on the twinning
stress for several copper alloys. (From M. A.
Meyers, O. Voehringer, and V. A. Lubarda, Acta
Mater., 49 (2001) 4025.)
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Temperature-Strain Rate Plots
Temperaturestrain rate plots with slip and
twinning domains (a) effect of grain size in
titanium (b) effect of stacking-fault energy in
copperzinc alloys. (From M. A. Meyers, O.
Voehringer, and V. A. Lubarda, Acta Mater., 49
(2001) 4025.)
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Grain-Size Strengthening
HallPetch plot for a number of metals and
alloys. Y.S. indicates yield strength.
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Hall-Petch Plot
HallPetch plot for iron and low-carbon
steel extending from monocrystal to nanocrystal
notice the change in slope. (After T. R. Smith,
R. W. Armstrong, P. M. Hazzledine, R. A.
Masumura, and C. S. Pande, Matls. Res. Soc. Symp.
Proc., 362 (1995) 31.)
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Frank-Read Source
FrankRead source operating in center of grain 1
and producing two pileups at grain boundaries
the FrankRead source in grain 2 is activated by
stress concentration.
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Dislocation Activity at Grain Boundaries in
Stainless Steel
Dislocation activity at grain boundaries in AISI
304 stainless steel deformed at a strain rate of
10-3 s-1. (a) Typical dislocation profiles after
a strain of 0.15 . (b) Same after a strain of
1.5 . (Courtesy of L. E. Murr.)
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Meyers-Ashworth Theory
Deformation stages in a polycrystal (a) start of
deformation (b) localized plastic flow in the
grain-boundary regions (microyielding) (c) a
work-hardened grain-boundary layer that
effectively reinforces the microstructure.
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Deformation Twins
Deformation twins in shock-loaded nickel (45 GPa
peak pressure 2 µs pulse duration). Plane of
foil (100) twinning planes (111) making 90?.
(Courtesy of L. E. Murr.)
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Strength of Drawn Wire
Strength of drawn wire after recovery treatment
as a function of transverse lineal-intercept cell
size. Recovery temperatures (in ?C) are indicated
on the curves. (Adapted with permission from H.
J. Rack and M. Cohen, in Frontiers in Materials
Science Distinguished Lectures, L. E. Murr, ed.
(New York M. Dekker, 1976), p. 365.)
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Nanocrystalline Material Structure
Representation of atomic structure of a
nanocrystalline material white circles indicate
grain-boundary regions. (Courtesy of H. Gleiter.)
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Hall-Petch Relationship
Stressstrain curves for conventional (D 50 µm)
and nanocrystalline (D 25 µm) copper. (Adapted
from G. W. Nieman, J. R. Weertman, and R. W.
Siegel, Nanostructured Materials, 1 (1992) 185.)
HallPetch relationship for nanocrystalline
copper. (After G. W. Nieman, J. R. Weertman, and
R. W. Siegel, Nanostructured Matls., 1 (1992) 185)
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Dependence of Yield Strength on Grain Size
Yield strength as a function of D-0.5 for two
different equations and computational results
assuming a grain-boundary region and grain
interior with different work-hardening curves. As
grain size decreases, grain-boundary region
gradually dominates the deformation process.
(From H.-H. Fu, D. J. Benson, and M. A. Meyers,
Acta Mater., 49 (2001) 2567.)
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Voids in Titanium Carbide
Voids (dark regions indicated by arrows) in
titanium carbide. The intergranular phase (light)
is nickel, which was added to increase the
toughness of TiC.
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Voids
(a) Faceted grain-interior voids in alumina and
(b) voids in titanium carbide dislocations are
pinned by voids. TEM.