CRYSTALLOGRAPHY
Common Metallic Crystal Structures
body-centered cubic, face-centered cubic, and hexagonal close-packed.
♦ Body- Centered Cubic (BCC)
Face- Centered Cubic (FCC)
Hexagonal Close-Packed (HCP)
Number of Atoms in a Cell BCC: 2
FCC: 4 HCP: 6 Packing Factor
The packing factor is the volume of the atoms in a cell (assuming touching, hard spheres) divided by the total cell volume.
BCC: 0.68 FCC: 0.74 HCP: 0.74
Coordination Number
The coordination number is the number of closest neigh-boring (touching) atoms in a given lattice.
Miller Indices
The rationalized reciprocal intercepts of the intersections of the plane with the crystallographic axes:
•
(111) plane. (axis intercepts at x = y = z)
(112) plane. (axis intercepts at x = 1, y = 1, z = 1/2)
•
(010) planes in cubic structures. (a) Simple cubic. (b) BCC.
(axis intercepts at x = ∞, y = 1, z = ∞)
•
(110) planes in cubic structures. (a) Simple cubic. (b) BCC.
(axis intercepts at x = 1, y = 1, z = ∞) ATOMIC BONDING
Primary Bonds
Ionic (e.g., salts, metal oxides)
Covalent (e.g., within polymer molecules) Metallic (e.g., metals)
♦Flinn, Richard A. & Paul K. Trojan, Engineering Materials & Their Application, 4th Ed. Copyright © 1990 by Houghton Mifflin Co. Figure used with permission.
•Van Vlack, L., Elements of Materials Science & Engineering, Copyright 1989 by Addison-Wesley Publishing Co., Inc. Diagram reprinted with permission of the publisher.
69 CORROSION
A table listing the standard electromotive potentials of metals is shown on page 67.
For corrosion to occur, there must be an anode and a cathode in electrical contact in the presence of an electrolyte.
Anode Reaction (oxidation) Mo → Mn+ + ne–
Possible Cathode Reactions (reduction)
½ O2 + 2 e– + H2O → 2 OH–
½ O2 + 2 e– + 2 H3O+→ 3 H2O 2 e– + 2 H3O+ → 2 H2O + H2
When dissimilar metals are in contact, the more electroposi-tive one becomes the anode in a corrosion cell. Different regions of carbon steel can also result in a corrosion reaction:
e.g., cold-worked regions are anodic to non-cold-worked;
different oxygen concentrations can cause oxygen-deficient region to become cathodic to oxygen-rich regions; grain boundary regions are anodic to bulk grain; in multiphase alloys, various phases may not have the same galvanic potential.
DIFFUSION
Diffusion coefficient D = Do e–Q/(RT), where D = the diffusion coefficient, Do = the proportionality constant, Q = the activation energy,
R = the gas constant [1.987 cal/(g mol⋅K)], and T = the absolute temperature.
BINARY PHASE DIAGRAMS
Allows determination of (1) what phases are present at equilibrium at any temperature and average composition, (2) the compositions of those phases, and (3) the fractions of those phases.
Eutectic reaction (liquid → two solid phases) Eutectoid reaction (solid → two solid phases) Peritectic reaction (liquid + solid → solid) Pertectoid reaction (two solid phases → solid) Lever Rule
The following phase diagram and equations illustrate how the weight of each phase in a two-phase system can be determined:
(In diagram, L = liquid) If x = the average composition at temperature T, then
Iron-Iron Carbide Phase Diagram
•
Gibbs Phase Rule
P + F = C + 2, where
P = the number of phases that can coexist in equilibrium, F = the number of degrees of freedom, and
C = the number of components involved.
•Van Vlack, L., Elements of Materials Science & Engineering, Copyright 1989 by Addison-Wesley Publishing Co., Inc. Diagram reprinted with permission of the publisher.
100 wt
100 wt
− ×
= − β
− ×
= − α
α β
α α β
β
x x
x
% x
x x
x
% x
70 THERMAL PROCESSING
Cold working (plastically deforming) a metal increases strength and lowers ductility.
Raising temperature causes (1) recovery (stress relief), (2) recrystallization, and (3) grain growth. Hot working allows these processes to occur simultaneously with deformation.
Quenching is rapid cooling from elevated temperature, preventing the formation of equilibrium phases.
In steels, quenching austenite [FCC (γ) iron] can result in martensite instead of equilibrium phases—ferrite [BCC (α) iron] and cementite (iron carbide).
TESTING METHODS Standard Tensile Test
Using the standard tensile test, one can determine elastic modulus, yield strength, ultimate tensile strength, and ductility (% elongation).
Endurance Test
Endurance tests (fatigue tests to find endurance limit) apply a cyclical loading of constant maximum amplitude. The plot (usually semi-log or log-log) of the maximum stress (σ) and the number (N) of cycles to failure is known as an S-N plot.
(Typical of steel, may not be true for other metals; i.e., aluminum alloys, etc.)
The endurance stress (endurance limit or fatigue limit) is the maximum stress which can be repeated indefinitely without causing failure. The fatigue life is the number of cycles required to cause failure for a given stress level.
Impact Test
The Charpy Impact Test is used to find energy required to fracture and to identify ductile to brittle transition.
Impact tests determine the amount of energy required to cause failure in standardized test samples. The tests are repeated over a range of temperatures to determine the transition temperature.
HARDENABILITY
Hardenability is the "ease" with which hardness may be attained. Hardness is a measure of resistance to plastic deformation.
•
Hardenability Curves for Six Steels
•
• Van Vlack, L., Elements of Materials Science & Engineering, Copyright 1989 by Addison-Wesley Pub.
Co., Inc. Diagrams reprinted with permission of the publisher.
in (#2) and (#8) indicated ASTM grain size
71 ASTM GRAIN SIZE
SV = 2PL
where
SV = grain-boundary surface per unit volume,
PL = number of points of intersection per unit length between the line and the boundaries,
N = number of grains observed in a area of 0.0645 mm2, and n = grain size (nearest integer > 1).
COMPOSITE MATERIALS ρc = Σ fiρi
Cc = Σ fici
Ec = Σ fiEi
where
ρc = density of composite,
Cc = heat capacity of composite per unit volume, Ec = Young's modulus of composite,
fi = volume fraction of individual material,
ci = heat capacity of individual material per unit volume, and Ei = Young's modulus of individual material.
Also
(∆L/L)1 = (∆L/L)2
(α∆T + e)1 = (α∆T + e)2
[α∆T + (F/A)/E]1 = [α∆T + (F/A)/E]2
where
∆L = change in length of a material, L = original length of the material,
α = coefficient of expansion for a material,
∆T = change in temperature for the material, e = elongation of the material,
F = force in a material,
A = cross-sectional area of the material, and E = Young's modulus for the material.
HALF-LIFE
N = Noe –0.693t/τ, where No = original number of atoms, N = final number of atoms, t = time, and
τ = half-life.
Material
Density ρρρρ Mg/m3
Young's Modulus
E GPa
E/ρρρρ N⋅⋅⋅⋅m/g Aluminum
Steel Magnesium Glass Polystyrene Polyvinyl Chloride Alumina fiber Aramide fiber Boron fiber Beryllium fiber BeO fiber Carbon fiber Silicon Carbide fiber
2.7 7.8 1.7 2.5 1.05 1.3 3.9 1.3 2.3 1.9 3.0 2.3 3.2
70 205 45 70 2
< 4 400 125 400 300 400 700 400
26,000 26,000 26,000 28,000 2,700
< 3,500 100,000 100,000 170,000 160,000 130,000 300,000 120,000
( )
(
2)
actual mm
mm 0645 Area 0
Actual
1 2
. N N
n N0.0645 2
=
−
=
72