Chapter 5Imperfections: Interfacial and

Volumetric Defects

Grains in a crystalline metal or ceramic; the cube depicted in each grain indicates the crystallographic orientation of the grain in a schematic fashion.

Grains in a Polycrystal

Polycrystalline (a) tantalum and (b) TiC.

Grain Structure of Tantalum and TiC

Low-angle grain boundary observed by high-resolution transmission electron microscopy. Positions ofindividual dislocations are marked by Burgers circuits. (Courtesy of R. Gronsky.)

Low Angle Grain Boudnary

Mean Lineal Intercept

Low-Angle Tilt Boundary

Low-Angle Twist Boundary

Variation of grain-boundary energy with misorientation θ. (Adapted withpermission from A. G. Guy,Introduction to Materials Science (New York: McGraw-Hill, 1972), p. 212.)

Grain-Boundary Energy as a Function of Misorientation

Coincidence lattice boundary made by every seventh atom in the two grains, misoriented 22◦ by a rotation around the <111> axis. (Adapted from M. L. Kronberg and H. F. Wilson, Trans. AIME, 85 (1949), 501.)

Coincidence Lattice Boundary

Coincidence Site Boundaries

Interface between alumina and NiAl2O4 (spinel). (a) High-resolution TEM. (b) Representation of individual atomic positions. (Courtesy of C. B. Carter.)

Interface between Alumina and NiAl2O4

The effect of grain size on calculated volume fractions of intercrystal regions and triple junctions, assuming a grainboundary thickness of 1 nm. (Adapted from B. Palumbo, S. J. Thorpe, and K. T. Aust, Scripta Met., 24 (1990) 1347.)

Grain Size vs. Volume Fraction of Intercrystal Regions

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.)

Ledge Formation in Grain Boundary

Grain boundary ledges as observed by TEM. (Courtesy of L. E. Murr.)

Grain Boundary Ledges

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.)

Tilt Boundary

Twinning

Twinning in FCC Metals

Deformation twins in (a) iron-silicon.(Courtesy of O. Vöhringer.)

Deformation Twins

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.)

Deformation Twins in Silicon Nitride

Serrated stress–strain curve due to twinning in a Cd single crystal. (Adapted with permission from W. Boas and E. Schmid, Z. Phys., 54 (1929) 16.)

Serrated Stress-Strain Curve Due to Twinning

Twinning in HCP Metals

Effect of temperature on the stress required for twinning and slip (at low and high strain rates). (Courtesy of G. Thomas.)

Stress Required for Twinning and Slip

(a) Stress–strain curves for copper (which deforms by slip) and 70% Cu–30% Zn brass (which deforms by slip and twinning). (b) Work-hardening slope dσ/dε 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.)

Mechanical Effects of Slip and Twinning

Effect of temperature on twinning stress for a number of metals. (From M. A. Meyers, O.Voehringer, and V. A. Lubarda, ActaMater., 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.)

Effect of Temperature and Stacking-Fault Energy on Twinning Stress

Temperature–strain rate plots with slip and twinning domains; (a) effect of grain size in titanium; (b) effect of stacking-fault energy in copper–zinc alloys. (From M. A. Meyers, O. Voehringer, and V. A. Lubarda, Acta Mater., 49 (2001) 4025.)

Temperature-Strain Rate Plots

Hall–Petch plot for a number of metals and alloys. Y.S. indicates yield strength.

Grain-Size Strengthening

Hall–Petch plot for iron and low-carbon steelextending 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.)

Hall-Petch Plot

Frank–Read source operating in center of grain 1 and producing two pileups at grain boundaries; the Frank–Read source in grain 2 is activated by stress concentration.

Frank-Read Source

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.)

Dislocation Activity at Grain Boundaries in Stainless Steel

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.

Meyers-Ashworth Theory

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.)

Deformation Twins

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.)

Strength of Drawn Wire

Representation of atomic structure of a nanocrystalline material; white circles indicate grain-boundary regions. (Courtesy of H. Gleiter.)

Nanocrystalline Material: Structure

Stress–strain 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.)

Hall–Petch relationship for nanocrystalline copper. (After G. W. Nieman, J. R. Weertman, and R. W. Siegel, Nanostructured Matls., 1 (1992) 185)

Hall-Petch Relationship

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.)

Dependence of Yield Strength on Grain Size

Voids (dark regions indicated by arrows) in titanium carbide. The intergranular phase (light) is nickel, which was added to increase the toughness of TiC.

Voids in Titanium Carbide

(a) Faceted grain-interior voids in alumina and (b) voids in titanium carbide; dislocations are pinned by voids. TEM.

Voids