14 materials science structure of matter

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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.




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




♦

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




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 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 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




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.

14 materials science structure of matter

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