1. The Structures of Metals
Chapters 1
The Structures of Metals

2. Chapter 1 Outline
Figure 1.1 An outline of the topics described in Chapter 1

3. Body-Centered Cubic Crystal Structure
Figure 1.2 The body-centered cubic (bcc) crystal structure: (a) hard-ball model; (b) unit cell; and (c) single crystal with many unit cells
Example: Iron (Fe)
Good strength
Moderate ductivity

4. Face-Centered Cubic Crystal Structure
Figure 1.3 The face-centered cubic (fcc) crystal structure: (a) hard-ball model; (b) unit cell; and (c) single crystal with many unit cells
Example: Aluminum (Al)
Moderate strength
Good ductivity

5. Hexagonal Close-Packed Crystal Structure
Figure 1.4 The hexagonal close-packed (hcp) crystal structure: (a) unit cell; and (b) single crystal with many unit cells
Example: Beryllium, Zinc
Low strength
Low ductivity

6. Slip
Figure 1.5 Permanent deformation (also called plastic deformation) of a single crystal subjected to a shear stress: (a) structure before deformation; and (b) permanent deformation by slip. The size of the b/a ratio influences the magnitude of the shear stress required to cause slip.

7. Slip and Twinning
Figure 1.6 (a) Permanent deformation of a single crystal under a tensile load. Note that the slip planes tend to align themselves in the direction of the pulling force. This behavior can be simulated using a deck of cards with a rubber band around them. (b) Twinning in a single crystal in tension.

8. Defects in a Single-Crystal Lattice (point imperfections)
Figure 1.9 Schematic illustration of types of defects in a single-crystal lattice: self-interstitial, vacancy, interstitial, and substitutional.

9. Movement of Dislocation (line imperfection)
Figure Movement of an edge dislocation across the crystal lattice under a shear stress. Dislocations help explain why the actual strength of metals in much lower than that predicted by theory.

10. Solidification
Nucleation of crystals at random sites in the molten metal; note that the crystallographic orientation of each site is different.
(b) and (c) Growth of crystals as solidification continues.
(d) Solidified metal, showing individual grains and grain boundaries; note the different angles at which neighboring grains meet each other.
Figure Schematic illustration of the stages during solidification of molten metal; each small square represents a unit cell.
Grain boundary
voids
inclusions
Plane imperfection
Volume imperfection

11. Grain sizes Yield strength y Hall-Petch Equation y = y + k d–1/2
Smaller grain size?
Nano scale?
Grain boundary
Plane imperfection

12. Preferred Orientation
before deformation
after deformation.
Note the alignment of grain boundaries along a horizontal direction; this effect is known as preferred orientation.
Figure Plastic deformation of idealized (equiaxed) grains in a specimen subjected to compression (such as occurs in the rolling or forging of metals
Anisotropy induced by crystallographic deformation
because of preferred orientation of the grains

13. Anisotropy
(b)
Figure (a) Schematic illustration of a crack in sheet metal that has been subjected to bulging (caused by, for example, pushing a steel ball against the sheet). Note the orientation of the crack with respect to the rolling direction of the sheet; this sheet is anisotropic.
(b) Aluminum sheet with a crack (vertical dark line at the center) developed in a bulge test; the rolling direction of the sheet was vertical.

14. Deformation of Soft and Hard Inclusions
Figure Schematic illustration of the deformation of soft and hard inclusions and of their effect on void formation in plastic deformation. Note that, because they do not comply with the overall deformation of the ductile matrix, hard inclusions can cause internal voids.
Mechanical fibering induce anisotropy
because of alignment of impurities, inclusion and voids in the material

15. Annealing
Figure Schematic illustration of the effects of recovery, recrystallization, and grain growth on mechanical properties and on the shape and size of grains. Note the formation of small new grains during recrystallization

16. Homologous Temperature Ranges for Various Processes
T: working temperature
Tm: melting point of metal (based on absolute temperature scale)
For lead
Tm = 327 C
At room temperature (20 C), T/Tm = ( )/( ) = 0.5

17. Factors influencing properties and (Manufacturing) Behavior of Metals
Atomic Structures
Crystal structures: bcc, fcc, hcp
Slip, slip planes:b/a ratio, anisotropy
Imperfections
Line: dislocations (strain hardening)
Point: vacancy, interstitial (alloys, e.g. FeC), impurity (alloys, e.g., Al, Cu)
Volume: voids, inclusions (e.g. oxides, carbides, sulfides
Planar: grain boundaries
Grain boundaries
Properties depend on size, large grains are softer (why?) lower strength, hardness, & ductility and produce rough surface after stretching

18. Factors influencing properties and (Manufacturing) Behavior of Metals
Plastic deformation (cold working)
Compression and tension: forging vs. stretching processes
Anisotropy:
Two types: Preferred orientation and mechanical
Often occurs as a result of a mfg process (cold rolling)
Degree of anisotropy depends on uniformity of deformation
Cold, Warm, and hot working
Surface condition
Recrystallization
Size
Environment

19. CHAPTER 2
Mechanical Behavior, Testing, and Manufacturing Properties of Materials

20. Tensile-Test Specimen and Machine
(b)
Figure 2.1
(a) A standard tensile-test specimen before and after pulling, showing original and final gage lengths.
(b) A typical tensile-testing machine.

21. Stress-Strain Curve Engineering stress  = P/A0 Engineering strain
e = (l- l0) / l0
Measures of ductility
% elongation
(lf - l0) / l0 x 100
% Reduction area
(Af - A0) / A0 x 100
Figure 2.2 A typical stress- strain curve obtained from a tension test, showing various features.

22. Loading and Unloading of Tensile-Test Specimen
E = stress / strain
e.g.,
spring back in bending
Figure 2.3 Schematic illustration of the loading and the unloading of a tensile- test specimen. Note that, during unloading, the curve follows a path parallel to the original elastic slope.

23. True Stress-True Strain
True stress,  = P/A
P: load
A: Instantaneous area
True strain,  = ln (l/l0)

24. Construction of True Stress-True Strain Curve
Figure 2.5
Load-elongation curve in tension testing of a stainless steel specimen.
Engineering stress-engineering strain curve, drawn from the data in Fig. 2.5a.
True stress-true strain curve, drawn from the data in Fig. 2.5b. Note that this curve has a positive slope, indicating that the material is becoming stronger as it is strained.
True stress-true strain curve plotted on log-log paper and based on the corrected curve in Fig. 2.5c. The correction is due to the triaxial state of stress that exists in the necked region of a specimen.

25. True Stress-True Strain Curve
 = K n
K: strength coefficient
N: strain-hardening exponent
Higher the slope, stronger when it is strained

26. Toughness Area under the true stress-true strain curve
The amount of energy per unit volume that material dissipates prior to fracture
Involves height and width of the curve
Larger areas in the curve, tougher