Chapters 1

The Structures of Metals

Chapter 1 Outline

Figure 1.1 An outline of the topics described in Chapter 1

Body-Centered Cubic Crystal Structure

• Example: Iron (Fe)• Good strength

• Moderate ductivity

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

Face-Centered Cubic Crystal Structure

• Example: Aluminum (Al)• Moderate strength

• Good ductivity

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

Hexagonal Close-Packed Crystal Structure

• Example: Beryllium, Zinc• Low strength• Low ductivity

Figure 1.4 The hexagonal close-packed (hcp) crystal structure: (a) unit cell; and (b) single crystal with many unit cells

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.

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.

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.

Movement of Dislocation(line imperfection)

Figure 1.10 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.

Solidification(a) 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 1.11 Schematic illustration of the stages during solidification of

molten metal; each small square represents a unit cell.

Grain boundary

Volume imperfection

voids inclusions

Plane imperfection

Grain sizes

Grain boundary

Plane imperfection

• Yield strength y

• Hall-Petch Equation y = y + k d–1/2

• Smaller grain size?• Nano scale?

Preferred Orientation

Figure 1.12 Plastic deformation of idealized (equiaxed) grains in a specimen subjected to compression (such as occurs in the rolling or forging of metals

(a) before deformation

(b) after deformation.

Note the alignment of grain boundaries along a horizontal direction; this effect is known as preferred orientation.

Anisotropy induced by crystallographic deformation– because of preferred orientation of the grains

Anisotropy

Figure 1.13 (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.

(b)

Deformation of Soft and Hard Inclusions

• Mechanical fibering induce anisotropy– because of alignment of impurities, inclusion and voids in the

material

Figure 2.23 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.

Annealing

Figure 1.14 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

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 = (20 +273)/(327 + 273) = 0.5

TABLE 1.2Process T/TmCold workingWarm workingHot working

< 0.30.3 to 0.5> 0.6

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

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

CHAPTER 2

Mechanical Behavior, Testing, and Manufacturing Properties of Materials

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.

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.

Loading and Unloading of Tensile-Test Specimen

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.

E = stress / strain e.g.,

spring back in bending

True Stress-True Strain

• True stress, = P/A– P: load– A: Instantaneous area

• True strain, = ln (l/l0)

Construction of True Stress-True Strain Curve

Figure 2.5

(a) Load-elongation curve in tension testing of a stainless steel specimen.

(b) Engineering stress-engineering strain curve, drawn from the data in Fig. 2.5a.

(c) 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.

(d) 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.

True Stress-True Strain Curve = K n

– K: strength coefficient– N: strain-hardening exponent

• Higher the slope, stronger when it is strained

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