14 materials science structure of matter
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8/8/2019 14 Materials Science Structure of Matter
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MATERIALS SCIENCE/STRUCTURE OF MATTER
MATERIALS SCIENCE/STRUCTURE OF MATTER
ATOMIC BONDING
Primary Bonds
Ionic (e.g., salts, metal oxides)
Covalent (e.g., within polymer molecules)
Metallic (e.g., metals)
CORROSION
A table listing the standard electromotive potentials of metals
is shown on the previous page.
For corrosion to occur, there must be an anode and a cathode
in electrical contact in the presence of an electrolyte.
Anode Reaction (Oxidation) of a Typical Metal, M
Mo → Mn+
+ ne –
Possible Cathode Reactions (Reduction)
½ O2 + 2 e – + H2O → 2 OH –
½ O2
+ 2 e – + 2 H
3O+
→ 3 H2O
2 e – + 2 H3O
+ → 2 H2O + H2
When dissimilar metals are in contact, the more
electropositive 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
noncoldworked; different oxygen concentrations can cause
oxygen-decient regions 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 Coefcient
D = Do e−Q/ ( RT ), where
D = diffusion coefcient,
Do = proportionality constant,
Q = activation energy,
R = gas constant [8.314 J / (mol•K)], and
T = absolute temperature.
THERMAL AND MECHANICAL PROCESSING
Cold working (plastically deforming) a metal increasesstrength 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). (See Mechanics of Materials section.)
Endurance TestEndurance tests (fatigue tests to nd 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.
The gure below is typical of steel but may not be true for
other metals; i.e., aluminum alloys, etc.
ENDURANCE LIMIT
LOG N (CYCLES)
σ
KNEE
The endurance stress (endurance limit or fatigue limit ) is the
maximum stress which can be repeated indenitely 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 nd 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 ductile to brittle
transition temperature.
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MATERIALS SCIENCE/STRUCTURE OF MATTER
Creep
Creep occurs under load at elevated temperatures. The general
equation describing creep is:
dt d A en Q RT =
fv
- ] g
where:
ε = strain,
t = time,
A = pre-exponential constant,σ = applied stress,
n = stress sensitivity.
For polymers below, the glass transition temperature, T g , n is
typically between 2 and 4, and Q is ≥ 100 kJ/mol. Above T g , n
is typically between 6 and 10, and Q is ~ 30 kJ/mol.
For metals and ceramics, n is typically between 3 and 10, and
Q is between 80 and 200 kJ/mol.
STRESS CONCENTRATION IN BRITTLE
MATERIALSWhen a crack is present in a material loaded in tension,
the stress is intensied in the vicinity of the crack tip. This
phenomenon can cause signicant loss in overall ability of a
member to support a tensile load.
K y aI = v r
K I = the stress intensity in tension, MPa·m1/2,
y = is a geometric parameter,
y = 1 for interior crack
y = 1.1 for exterior crack
σ = is the nominal applied stress, and
a = is crack length as shown in the two diagrams below.
a2a
EXTERIOR CRACK (y = 1.1) INTERIOR CRACK (y = 1)
The critical value of stress intensity at which catastrophic
crack propagation occurs, K Ic, is a material property.
Representative Values of Fracture Toughness
Material K Ic (MPa•m1/2) K Ic (ksi•in1/2)
A1 2014-T651 24.2 22
A1 2024-T3 44 40
52100 Steel 14.3 13
4340 Steel 46 42
Alumina 4.5 4.1
Silicon Carbide 3.5 3.2
HARDENABILITY OF STEELS
Hardenability is the “ease” with which hardness may be
attained. Hardness is a measure of resistance to plastic
deformation.
♦
♦
♦Van Vlack, L., Elements of Materials Science & Engineering , Addison-Wesley,
Boston, 1989.
JOMINY HARDENABILITY CURVES FOR SIX STEELS
(#2) and (#8) indicate grain size
JOMINY HARDENABILITY CURVES FOR SIX STEELS
(#2) and (#8) indicate grain size
COOLING RATES FOR BARS QUENCHED IN AGITATED WATERCOOLING RATES FOR BARS QUENCHED IN AGITATED WATER
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MATERIALS SCIENCE/STRUCTURE OF MATTER
♦
RELATIONSHIP BETWEEN HARDNESS AND
TENSILE STRENGTH
For steels, there is a general relationship between Brinellhardness and tensile strength as follows:
TS psi 500 BHN
TS MPa 3.5 B HN
-
-
_
^
i
h
ASTM GRAIN SIZE
.,
S P
N
N N
2
2
0 0645Actual Area mmwhere
.
V L
n0 0645
1
2
mm
actual
2
=
=
=
-
_
_^
i
ih
S V
= grain-boundary surface per unit volume,
P L = 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 f
C f c
E f
E f E
f
c i i
c i i
i
ic i i
c i i
1
# #
=
=
=
t t
v v
R
R
R R
R
-< F
ρc = density of composite,
C c = heat capacity of composite per unit volume,
E c = Young’s modulus of composite,
f i = volume fraction of individual material,
ci = heat capacity of individual material per unit volume,
and
E i = Young’s modulus of individual material
σc = strength parallel to ber direction.
COOLING RATES FOR BARS QUENCHED IN AGITATED OILCOOLING RATES FOR BARS QUENCHED IN AGITATED OIL
Also, for axially oriented, long, ber-reinforced composites,
the strains of the two components are equal.
(∆ L/ L)1 = (∆ L/ L)2
∆ L = change in length of the composite,
L = original length of the composite.
HALF-LIFE
N = N oe – 0.693t/ τ, where
N o = original number of atoms, N = nal number of atoms,
t = time, and
τ = half-life.
Material ρ
Mg/m3
E
GPa
E/ ρ
N•m/g
Aluminum
Steel
Magnesium
Glass
Polystyrene
Polyvinyl ChlorideAlumina fiber
Aramide fiber
Boron fiber
Beryllium fiber
BeO fiber
Carbon fiber
Silicon Carbide fiber
2.7
7.8
1.7
2.5
1.05
1.33.9
1.3
2.3
1.9
3.0
2.3
3.2
70
205
45
70
2
< 4400
125
400
300
400
700
400
26,000
26,000
26,000
28,000
2,700
< 3,500100,000
100,000
170,000
160,000
130,000
300,000
120,000
Density Young's Modulus
CONCRETE
Portland Cement Concrete
Concrete is a mixture of portland cement, ne aggregate,
coarse aggregate, air, and water. It is a temporarily plasticmaterial, which can be cast or molded, but is later converted
to a solid mass by chemical reaction.
Water-cement (W/C ) ratio is the primary factor affecting
the strength of concrete. The gure below shows how
W/C, expressed as a ratio by weight, affects the compressive
strength for both air-entrained and non-air-entrained concrete.
Strength decreases with an increase in W/C in both cases.
Concrete strength decreases with increases in water-cement
ratio for concrete with and without entrained air.
(From Concrete Manual , 8th ed., U.S. Bureau of Reclamation, 1975.)
♦Van Vlack, L., Elements of Materials Science & Engineering , Addison-Wesley,
Boston, 1989.
8,000
6,000
4,000
2,000
1,000
W/C BY WEIGHT
0.40 0.60 0.80 1.00
RECOMMENDED
PERCENT
ENTRAINED AIR
NO ADDED AIR
A V E R A G E
2 8 - D A Y
C O M P R E S S I V E
S T R E N G T H ,
P S I
8,000
6,000
4,000
2,000
1,000
W/C BY WEIGHT
0.40 0.60 0.80 1.00
RECOMMENDED
PERCENT
ENTRAINED AIR
NO ADDED AIR
A V E R A G E
2 8 - D A Y
C O M P R E S S I V E
S T R E N G T H ,
P S I
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MATERIALS SCIENCE/STRUCTURE OF MATTER
Water Content affects workability. However, an increase
in water without a corresponding increase in cement
reduces the concrete strength. Air entrainment is the
preferred method of increasing workability.
♦
POLYMERS
Classication of Polymers
Polymers are materials consisting of high molecular weight
carbon-based chains, often thousands of atoms long. Two
broad classications of polymers are thermoplastics or
thermosets. Thermoplastic materials can be heated to
high temperature and then reformed. Thermosets, such as
vulcanized rubber or epoxy resins, are cured by chemical
or thermal processes which cross link the polymer chains,
preventing any further re-formation.
Amorphous Materials and Glasses
Silica and some carbon-based polymers can form either
crystalline or amorphous solids, depending on their
composition, structure, and processing conditions. These two
forms exhibit different physical properties. Volume expansion
with increasing temperature is shown schematically in the
following graph, in which Tm is the melting temperature,
and Tg is the glass transition temperature. Below the glass
transition temperature, amorphous materials behave like brittle
solids. For most common polymers, the glass transition occurs
between –40°C and 250°C.
♦ Merritt, Frederick S., Standard Handbook for Civil Engineers, 3rd ed.,
McGraw-Hill, 1983.
6,000
4,000
3,000
2,000
5,000
1,000
C O M P R E S S I V E S
T R E N G T H ,
P S I
AGE, DAYS
081098241730
STORED CONTINUOUSLY IN LABORATORY AIR
IN AIR AFTER 28 DAYS
IN AIR AFTER 14 DAYS
IN AIR AFTER 7 DAYS
IN AIR AFTER 3 DAYS
CONTINUOUSLY MOIST CURED
Concrete compressive strength varies with moist-curing conditions. Mixes tested
had a water-cement ratio of 0.50, a slump of 3.5 in., cement content of 556 lb/yd3,
sand content of 36%, and air content of 4%.
6,000
4,000
3,000
2,000
5,000
1,000
C O M P R E S S I V E S
T R E N G T H ,
P S I
AGE, DAYS
081098241730
STORED CONTINUOUSLY IN LABORATORY AIR
IN AIR AFTER 28 DAYS
IN AIR AFTER 14 DAYS
IN AIR AFTER 7 DAYS
IN AIR AFTER 3 DAYS
CONTINUOUSLY MOIST CURED
Concrete compressive strength varies with moist-curing conditions. Mixes tested
had a water-cement ratio of 0.50, a slump of 3.5 in., cement content of 556 lb/yd3,
sand content of 36%, and air content of 4%.
TEMPERATURE
V O L U M E
Tg Tm
GLASSES OR AMORPHOUS
MATERIALS
CRYSTALLINE
MATERIALS
Thermo-Mechanical Properties of Polymers
The curve for the elastic modulus, E, or strength of polymers,
σ, behaves according to the following pattern:
Tg Tm
L O
G E
o r L O G σ
TEMPERATURE
Polymer Additives
Chemicals and compounds are added to polymers to improve
properties for commercial use. These substances, such as
plasticizers, improve formability during processing, while
others increase strength or durability.
Examples of common additives are:
Plasticizers: vegetable oils, low molecular weight polymers or monomers
Fillers: talc, chopped glass bers
Flame retardants: halogenated parafns, zinc borate,
chlorinated phosphates
Ultraviolet or visible light resistance: carbon black
Oxidation resistance: phenols, aldehydes
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MATERIALS SCIENCE/STRUCTURE OF MATTER
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
%
%
x x
x x
x x
x x
100
100
wt
wt
#
#
=-
-
=-
-
a
b
b a
b
b a
a
Iron-Iron Carbide Phase Diagram
♦
♦ Van Vlack, L., Elements of Materials Science & Engineering , Addison-Wesley, Boston, 1989.
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