ENGR 151: Materials of Engineering FINAL REVIEW · PDF fileFRACTURE Stable crack: resists...

$: ENGR 151: Materials of Engineering FINAL REVIEW · PDF fileFRACTURE Stable crack: resists further extension unless there is increase in applied stress Brittle fracture: cracks spread$
FINAL REVIEW MATERIAL

ENGR 151: Materials of Engineering

Miller indices - A shorthand notation to describe certain crystallographic directions and planes in a material. Denoted by [ ], <>, ( ) brackets. A negative number is represented by a bar over the number.

Points, Directions and Planes in the Unit Cell

• Coordinates of selected points in the unit cell.

• The number refers to the distance from the origin in terms

of lattice parameters.

Point Coordinates

• Each unit cell is a reference or basis.

• The length of an edge is normalized as a unit of

measurement.

• E.g. if the length of the edge of the unit cell along the

X-axis is a, then ALL measurements in the X-direction

are referenced to a (e.g. a/2).

Point Coordinates – Contd.

Point coordinates for unit cell center are

a/2, b/2, c/2 ½ ½ ½

Point coordinates for unit cell corner are 111

Translation: integer multiple of lattice constants identical position in another unit cell

5

z

x

y a b

c

000

111

y

z

2c

b

b

Point Coordinates

Determine the Miller indices of directions A, B, and C.

Miller Indices, Directions

(c) 2003 Brooks/Cole Publishing /

Thomson Learning™

GENERAL APPROACH FOR MILLER INDICES

7

SOLUTION

Direction A

1. Two points are 1, 0, 0, and 0, 0, 0

2. 1, 0, 0, -0, 0, 0 = 1, 0, 0

3. No fractions to clear or integers to reduce

4. [100]

Direction B

1. Two points are 1, 1, 1 and 0, 0, 0

2. 1, 1, 1, -0, 0, 0 = 1, 1, 1

3. No fractions to clear or integers to reduce

4. [111]

Direction C

1. Two points are 0, 0, 1 and 1/2, 1, 0

2. 0, 0, 1 -1/2, 1, 0 = -1/2, -1, 1

3. 2(-1/2, -1, 1) = -1, -2, 2

2]21[ .4

(c) 2003 Brooks/Cole Publishing

/ Thomson Learning™

CRYSTALLOGRAPHIC DIRECTIONS

9

1. Vector repositioned (if necessary) to pass

through origin.

2. Read off projections in terms of

unit cell dimensions a, b, and c

3. Adjust to smallest integer values

4. Enclose in square brackets, no commas

[uvw]

ex: 1, 0, ½ => 2, 0, 1 => [ 201 ]

-1, 1, 1

z

x

Algorithm

where overbar represents a

negative index

[ 111 ] =>

y

Problem 3.6, pg. 58

10

HCP CRYSTALLOGRAPHIC DIRECTIONS

Hexagonal Crystals

4 parameter Miller-Bravais lattice coordinates are

related to the direction indices (i.e., u'v'w') as follows.

=

=

=

' w w

t

v

u

) v u ( + -

) ' u ' v 2 ( 3

1 -

) ' v ' u 2 ( 3

1 - =

] uvtw [ ] ' w ' v ' u [

Fig. 3.8(a), Callister & Rethwisch 8e.

- a3

a1

a2

z

11


Fig. 3.8(a), Callister & Rethwisch 8e.

- a3

a1

a2

z

12


1. Vector repositioned (if necessary) to pass

through origin.

2. Read off projections in terms of unit

cell dimensions a1, a2, a3, or c

3. Adjust to smallest integer values

4. Enclose in square brackets, no commas

[uvtw]

[ 1120 ] ex: ½, ½, -1, 0 =>

Adapted from Fig. 3.8(a),

Callister & Rethwisch 8e.

dashed red lines indicate

projections onto a1 and a2 axes a1

a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm

13

REDUCED-SCALE COORDINATE AXIS

14

PROBLEM 3.8

FAMILIES OF DIRECTIONS <UVW>

For some crystal structures, several

nonparallel directions with different

indices are crystallographically equivalent;

this means that atom spacing along each

direction is the same.

15

16

CRYSTALLOGRAPHIC PLANES

Adapted from Fig. 3.10,

Callister & Rethwisch 8e.

17

CRYSTALLOGRAPHIC PLANES

Miller Indices: Reciprocals of the (three) axial intercepts for a plane, cleared of fractions & common multiples. All parallel planes have same Miller indices.

Algorithm 1. Read off intercepts of plane with axes in terms of a, b, c 2. Take reciprocals of intercepts 3. Reduce to smallest integer values 4. Enclose in parentheses, no commas i.e., (hkl)

18

CRYSTALLOGRAPHIC PLANES z

x

y a b

c

4. Miller Indices (110)

example a b c z

x

y a b

c


1. Intercepts 1 1

2. Reciprocals 1/1 1/1 1/

1 1 0 3. Reduction 1 1 0

1. Intercepts 1/2

2. Reciprocals 1/½ 1/ 1/

2 0 0 3. Reduction 1 0 0

example a b c

19

CRYSTALLOGRAPHIC PLANES z

x

y a b

c


example 1. Intercepts 1/2 1 3/4

a b c

2. Reciprocals 1/½ 1/1 1/¾

2 1 4/3

3. Reduction 6 3 4

(001) (010),

Family of Planes {hkl}

(100), (010), (001), Ex: {100} = (100),

FAMILY OF PLANES

Planes that are crystallographically equivalent

have the same atomic packing.

Also, in cubic systems only, planes having the

same indices, regardless of order and sign,

are equivalent.

Ex: {111}

= (111), (111), (111), (111), (111), (111), (111), (111)

20

(001) (010), (100), (010), (001), Ex: {100} = (100),

_ _ _ _ _ _ _ _ _ _ _ _

MECHANICAL PROPERTIES OF METALS

TENSION TESTS

Specimen is deformed, to fracture, with load applied

uniaxially on long axis of specimen

Elongate specimen at a constant rate:

Measure the instantaneous applied load

Measure the resulting elongations

Destructive test: specimen is permanently deformed

and usually fractured

TENSION TESTS

Output is recorded as load or force versus

elongation

Engineering stress:

TENSION TESTS

Engineering Strain:

ELASTIC DEFORMATION

The degree to which a structure deforms or

strains depends on the magnitude of stress (in

proportion):

EXAMPLE PROBLEM 6.1

EXAMPLE PROBLEM 6.1 CONTD.

ELASTIC DEFORMATION

Deformation in which stress and

strain are proportional (plot of

stress v. strain is linear, slope is

modulus of elasticity)

The greater the modulus of

elasticity, the stiffer the material

(less strain resulting from stress)

Elastic Deformation is not

permanent (piece returns to

original shape after loads are

released)

ELASTIC DEFORMATION

Application of load corresponds to moving up

the graph, release of the load follows graph in

opposite direction

There are some materials in which the elastic

portion of curve is not linear (cannot find

modulus)

ELASTIC DEFORMATION

Take either the tangent

or secant modulus

Tangent is slope

(derivative) of stress-

strain curve at a

specified level of

stress

Secant is slope of

secant taken from

origin to a point on

the curve

ELASTIC DEFORMATION

At the atomic scale, strain is a result of small changes in interatomic spacing and stretching of atomic bonds.

Therefore, magnitude of modulus elasticity is a measure of the resistance to separation of bonded atoms (interatomic bonding)

Modulus is proportional to slope of interatomic force-separation curve

Increasing temperature, decreases modulus of elasticity

ELASTIC DEFORMATION

ELASTIC PROPERTIES OF MATERIALS

Strain exists along all three axes:


For uniaxial loads and isotropic materials

Poisson’s ratio:

Metals range from .25-.35

Maximum value is .5


Shear and Elastic moduli, and Poisson’s Ratio

are related:

For metals,

PLASTIC DEFORMATION

Most metals have elastic deformation only to

strains of about 0.005

After this amount of strain, plastic deformation

occurs (non-recoverable)

Curvature will occur at the onset of plastic

deformation

PLASTIC DEFORMATION

From atomic perspective, plastic deformation corresponds to the breaking of atomic bonds and the reforming of bonds with neighbors

Yielding: stress level at which plastic deformation occurs

Mark point P (proportional limit) at initial departure from linearity

Yield Strength:

0.002 offset intersection with curve (σy)

PLASTIC DEFORMATION

From atomic perspective, plastic deformation corresponds to the breaking of atomic bonds and the reforming of bonds with neighbors

Yielding: stress level at which

plastic deformation occurs

Mark point P (proportional limit) at initial departure from linearity

Yield Strength:

0.002 offset intersection with curve (σy)

PLASTIC DEFORMATION

Sometimes the plastic

transition occurs

abruptly

Upper yield point:

decrease in stress

Lower yield point: stress

rises with strain increase

Yield Strength: taken as

average of lower yield

point

TENSILE STRENGTH (FIGURE 6.11)

Tensile Strength (TS):

Point M, maximum stress

Prior to M, deformation

is uniform throughout

specimen

At M, neck begins to

form

After M, fracture occurs

For building purposes,

yield strength is used as

opposed to tensile

strength (Why?)

EXAMPLE PROBLEM 6.3

EXAMPLE PROBLEM 6.3 CONTD.

DUCTILITY

Measure of the

degree of plastic

deformation that has

been sustained at

fracture

Material with little or

no plastic deformation

at fracture is brittle

High degree of plastic

deformation at

fracture is ductile

DUCTILITY

Percent Elongation:

Percent Reduction:

COLD WORKING VS HEAT TREATMENT

Plastically deforming metal at low temperatures

affects physical properties of metal – cold

working

Elevated temperature treatment, e.g. annealing

Recovery

Recrystallization

RECOVERY, RECRYSTALLIZATION, AND GRAIN

GROWTH

Plastically deforming metal at low temperatures

affects physical properties of metal

Elevated temperature treatment

Recovery

Recrystallization

FAILURE

Simple fracture is the separation of a body into

two or more pieces in response to an imposed

static stress (constant or slowly changing with

time) and at temperatures relatively low as

compared to the material’s melting point

FRACTURE

Stress can be tensile, compressive, shear, or

torsional

For uniaxial tensile loads:

Ductile fracture mode (high plastic deformation)

Brittle fracture mode (little or no plastic

deformation)

FRACTURE

“Ductile” and “brittle” are relative (ductility is based on percent elongation and percent reduction in area)

Fracture process involves two steps:

Crack formation & propagation in response to applied stress

Ductile fracture characterized by extensive plastic deformation in the vicinity of an advancing crack

Process proceeds slowly as crack length is extended.

FRACTURE

Stable crack: resists further extension unless there is

increase in applied stress

Brittle fracture: cracks spread extremely rapidly with

little accompanying plastic deformation (unstable)

Ductile fracture preferred over brittle fracture

Brittle fracture occurs suddenly and catastrophically without

any warning

Ductile fracture gives preemptive “warning” that fracture is

imminent

Brittle (ceramics), ductile (metals)

DUCTILE FRACTURE

Figure 8.1 (differences between highly ductile,

moderately ductile, and brittle fracture)

DUCTILE FRACTURE

Common type of fracture

occurs after a moderate

amount of necking

After necking commences,

microvoids form

Crack forms perpendicular

to stress direction

Fracture ensues by rapid

propagation of crack

around the outer

perimeter of the neck (45°

angle)

Cup-and-cone fracture

DUCTILE VS. BRITTLE FRACTURE – EXAMPLE

BRITTLE FRACTURE

Takes place without much deformation (rapid crack

propagation)

Crack motion is nearly perpendicular to direction of tensile

stress

Fracture surfaces differ:

V-shaped “chevron” markings

Lines/ridges that radiate from origin in fan-like pattern

Ceramics: relatively shiny and smooth surface

BRITTLE FRACTURE

BRITTLE FRACTURE

Crack propagation corresponds to the successive and repeated breaking of atomic bonds along specific crystallographic planes (cleavage)

Transgranular: fracture cracks pass through grains

Intergranular: crack propagation is along grain boundaries (only for processed materials)

BINARY PHASE DIAGRAMS

Temperature and composition of mixture are

varied at constant pressure

Describe how the microstructure of an alloy vary

Ni-Cu system

This system is isomorphous because of the

complete liquid and solid solubility of the two

components

EXAMPLE – COPPER-NICKEL PHASE DIAGRAM

BINARY ISOMORPHOUS SYSTEMS

Metallic alloys are designated by lowercase

Greek letters (α, γ, β, etc.)

Liquidus line: line separating L and α+L regions

Solidus line: line separating α and α+L regions

L is a homogeneous liquid solution composed

of both Cu and Ni

The α phase is an substitutional solid solution

consisting of both Cu and Ni atoms – FCC

crystal structure

LIQUIDUS AND SOLIDUS LINES

Intersect at composition extremities (melting

temperatures)

On the left axis, pure copper remains solid until

melting point (α→L)

Alloys have an extended melting phenomenon

(α→α+L→L)

Occurs over range of temperatures between solidus

and liquidus lines

Both solid α and liquid phases will be in equilibrium

in the region between solidus and liquidus lines

INTERPRETING PHASE DIAGRAMS

Information we get:

Phases, compositions, percentages of the phases

Locate these points:

60 wt% Ni - 40 wt% Cu @ 1100°C

35 wt% Ni - 65 wt% Cu @ 1250°C

PHASE COMPOSITIONS

Locate temperature-composition point on the

phase diagram

Easy to figure for α, L phase

More complicated for α+L phase

Both α and L within α+L are composed of varying

compositions of alloy metals

PHASE COMPOSITIONS

Within two-phase region:

Draw tie line (horizontal) at alloy temperature

Note the phase boundaries

Record compositions at each intersection (CL, Cα =

phase composition)

PHASE COMPOSITIONS

Example:

35 wt% Ni - 65 wt% Cu @

1250°C

CL = 31.5% Ni, 68.5% Cu

Cα = 42.5% Ni, 57.5% Cu

PHASE AMOUNTS

Easy within single phase regions α and L

(100%)

Within α+L region, use lever rule:

Find your tie line

Fraction of one phase: length of tie line from point

to other phase boundary divided by total tie length

Length = wt% or at% composition

PHASE AMOUNTS

Mass fractions:

PHASE AMOUNTS

BINARY EUTECTIC SYSTEMS


Example: Copper-silver system

Three single-phase regions (α,β,L)

Alpha(α): copper as solvent, FCC

Beta(β): silver as solvent, FCC

Pure copper and pure silver are considered to

be α and β phases respectively


Below BEG line: only a limited amount of metal

will dissolve in other metal for α, β phases

Solubility limit for α phase corresponds to

boundary line CBA

Notice maximum amount of silver possible for

α phase.

Increases to a certain temperature, then decreases

to zero at the melting point of pure copper


Solubility limit line separating α and α+β

phases is solvus line

Solubility limit line separating α and α+L

phases is solidus line

Solubility limit line separating β and α+β

phases is solvus line

Solubility limit line separating β and β+L

phases is solidus line


Horizontal line BEG can also be considered a

solidus line (lowest temperature at which liquid

exists for alloy at equilibrium)


Three two-phase regions: α+L, β+L, α+β

Tie-lines and lever rule stills apply to these

regions

COPPER-SILVER PHASE DIAGRAM

As silver is added to copper, temperature decreases at which alloy becomes liquid (melting point lowered by addition of silver)

Also works the other way around (liquidus lines meet at point E)

Invariant point: associated with composition (CE) and temperature (TE),

71.9 wt% Ag and 779°C


As temperature passes through invariant point (TE),

reaction occurs:

Liquid is transformed into two solid phases at TE

(opposite reaction upon heating)

Eutectic reaction (easily melted)

CαE, CβE are compositions of α and β phases at TE (tie-

line)

( ) ( ) ( )cooling

E E Eheating

L C C C

(71.9 % ) (8.0 % ) (91.2 % )cooling

heatingL wt Ag wt Ag wt Ag


General rules:

At most two phases may be in equilibrium within a

phase field (no α+β+L, only at equilibrium line)

Single phase regions are separated by two-phase

regions

Horizontal solidus line BEG at TE is called a

eutectic isotherm


If a binary eutectic solution is cooled through

the invariant point, direct solidification occurs

No intermediate “L” phase

For binary phase system, no more than two

phases may be in equilibrium within a phase

field

At points along a eutectic isotherm, three phases

may be in equilibrium (e.g. point B)


Lead-Tin (Pb-Sn) system:

Notice that 60-40 Sn-Pb melts at 185°C (365°F),

attractive for soldering.


These values add

up to 1.0

EUTECTIC ALLOY DEVELOPMENT

For Lead-Tin alloy at 1

wt% Sn decreasing in

temperature from L

phase:

Remains liquid until

crossing of liquidus

line at 330°C

Continued cooling

creates more α

Solidification is

completed at solidus

line

EUTECTIC ALLOY DEVELOPMENT

For Lead-Tin alloy at

15 wt% Sn

decreasing in

temperature from L

phase:

Past the solidus

line, small β-phase

particles form

Continued cooling

slightly increases

the presence of β

EUTECTIC MICROSTRUCTURE

For Lead-Tin alloy at 61.9 wt% Sn decreasing in

temperature from L phase (invariant point, CE):

No change until TE is reached

Liquid transforms into two phases α, β

(61.9 % Sn) (18.3 % Sn) (97.8 % Sn)cooling

heatingL wt wt wt


For Lead-Tin alloy at 61.9

wt% Sn:

Distribution of α & β phases

are accomplished by atomic

diffusion (alternating layers

of α & β, lamellae)

Eutectic Structure

Lead atoms diffuse towards

α-phase

Tin diffuses towards β-phase


For Lead-Tin alloy at 40 wt% Sn decreasing in

temperature from L phase:

α-phase is present both in a eutectic structure and

α+L region

α-phase in eutectic structure is called eutectic α

α-phase primary to eutectic isotherm is called

primary α


Microconstituent: an element of the

microstructure having an identifiable and

characteristic structure

In 40 wt% Sn, there exist two microconstituents in

the α+β phase (primary α and eutectic structure)


Computing the amounts of eutectic and primary α microconstituents:

Use lever rule from solvus line to eutectic composition

We, fraction of eutectic microconstituent is equal to fraction of liquid WL from which it transforms

Wα, fraction of primary α is equal to fraction of α phase in existence prior to transformation


Eutectic α Primary α

Total α (w.r.t entire solution)


Total β (w.r.t entire solution)

Total α (w.r.t entire solution)

INTERMEDIATE PHASES

EUTECTOID REACTIONS

Other invariant points exist involving three phases (Cu-

Zn system, 74 wt% Zn-26 wt% Cu)

Eutectoid (eutectic-like) reaction

One solid phase forms into two other solid phases

Point E is the eutectoid point, the corresponding tie line is the

eutectoid isotherm

cooling

heating

EUTECTOID REACTIONS

PERITECTIC REACTIONS

Upon heating, one solid phase transforms into a liquid

phase and another solid phase:

78.6 wt% Zn-21.4 wt% Cu

cooling

heatingL

CONGRUENT PHASE TRANSFORMATIONS

Congruent transformation: when there is no

change in the composition for phases involved

(Mg2Pb melts congruently)

Incongruent transformation: change occurs in

phase composition during transformation

(peritectic reaction)

CONGRUENT PHASE TRANSFORMATIONS

PHASE TRANSFORMATIONS

Alteration of microstructure

Three classifications:

Diffusion-dependent transformations (no change in

either number or composition of the phases

present)

Some alteration in phase compositions and number

of phases present

Diffusionless

KINETICS OF SOLID-STATE REACTIONS

At least one new phase is formed

Different physical/chemical properties and/or

different structure than parent phase

Transformations do not occur instantaneously

(obstacles impede course of reaction)

Diffusion is a time-dependent phenomenon

Increase in energy associated with phase

boundaries created between parent and

product phases

PHASE TRANSFORMATION

Stage 1, Nucleation: formation of very small

particles of new phase (capable of growing)

Likely to grow in imperfection sites

Stage 2, Growth: particles increase in size

(volume of parent phase disappears)

KINETICS OF SOLID-STATE REACTIONS

Time dependence of transformation rate

(kinetics)

Important for heat treatment of materials

Investigation of kinetics:

Temperature maintained as constant

Fraction of reaction is measured as function of time

KINETICS OF PHASE TRANSFORMATION

S-shaped curve (Avrami equation): Y = 1 – exp(-ktn)

k, n = time-independent constants for the reaction

Heating time (t) vs. Fraction of transformation (y)

Rate of transformation r = 1/t0.5

Reciprocal of time required for the transformation to proceed halfway to

completion

HARDENABILITY (HEAT TREATMENT OF STEELS)

Hardenability: Term used to describe the ability of an alloy to be hardened by the formation of martensite as a result of a given heat treatment

Hardenability is NOT “hardness,” rather it is the qualitative measure of the rate at which hardness drops off with distance into the interior of the material due to decreased martensite content

HARDENABILITY (HEAT TREATMENT OF STEELS)

Jominy end-quench test:

Determines hardenability

Cylindrical specimen austenized at specified temp and time

Remove from furnace and mount on fixture

Lower end is quenched by jet of water to room temp

Rockwell Hardness test (hardness v. position)

HARDENABILITY CURVES

Quenched end exhibits

maximum hardness

(100% martensite)

Cooling rates and

hardness decrease with

distance away from

quenched end

Hardness persists much

longer for 4340, 4140,

8640, 5140 steels than

for 1040 steel

RADIAL HARDNESS PROFILE

Water Oil

WHAT IS A POLYMER?

Poly mer many repeat unit

Adapted from Fig. 14.2, Callister & Rethwisch 9e.

C C C C C C

H H H H H H

H H H H H H

Polyethylene (PE)

Cl Cl Cl

C C C C C C

H H H

H H H H H H

Poly(vinyl chloride) (PVC)

H H

H H H H

Polypropylene (PP)

C C C C C C

CH3

H H

CH3 CH3 H

repeat

unit

repeat

unit

repeat

unit

ISOMERISM

Recall: different atomic configuration for same composition (butane/isobutane)

Stereoisomerism

Geometrical isomerism

STEREOISOMERISM

Isotactic (® groups on same side) Syndiotactic (® alternates sides)

Atactic (random)

ROTATION NOT ALLOWED! (must sever first)

Polymer can exhibit more than one configuration

3-D image

STEREOISOMERISM – ISOTACTIC

Isotactic – R groups on same side of the polymer chain

STEREOISOMERISM – SYNDIOTACTIC

Syndiotactic – R groups on alternate sides of the polymer chain

STEREOISOMERISM – ATACTIC

Atactic – R groups randomly positioned along the polymer chain

ISOMERISM

Geometrical Isomerism

Double bonds between C atoms

C atoms bonded to other atom or radical (side group)

Cis structure (same side, cis-polyisoprene)

Natural rubber

Trans structure (opposite sides, trans-polyisoprene)

Conversion from cis to trans not possible as bond rotation is not allowed – double bond is rigid

Cis Trans

POLYMER STRUCTURE CLASSIFICATION

Chemistry

Molecular size

Molecular weight

Molecular shape

Degree of twisting, coiling, bending

Molecular structure

The way units (mers) are joined together

ISOMERISM

Molecules having different atomic

arrangements

Example: Butane

Normal butane boils at -0.5°C

Isobutane boils at -12.3°C

Butane Isobutane

ISOMERISM

Isomerism

two compounds with same chemical formula can have

quite different structures

for example: C8H18

normal-octane

2,4-dimethylhexane

C C C C C C C CH

H

H

H

H

H

H

H

H

H

H

H

H

H

H

H

H

H H3C CH2 CH2 CH2 CH2 CH2 CH2 CH3=

H3C CH

CH3

CH2 CH

CH2

CH3

CH3

H3C CH2 CH3( )6

POLYMER MOLECULES

Polymer molecules are relatively large in size

(macromolecules) compared to hydrocarbon

molecules

Backbone of carbon chain polymer molecules

are carbon strings (long and flexible)

Side bonding allowed

Radical positioning

OTHER ORGANIC GROUPS

Contain radicals (groups of atoms that remain

intact during chemical reactions)

Alcohols (radical connected to OH)

Ethers (2 radical connected to O)

Acids (radical, OH, C/O double bond)

Aldehyde (radical, H, C/O double bond)

MER UNITS

Mer: successively repeated units along chain

Polymer: many mers

Monomer: stable molecule – small molecule from

which polymer is synthesized

MOLECULAR WEIGHT

• Molecular weight, M: Mass of a mole of chains.

Low M

high M

Not all chains in a polymer are of the same length

— i.e., there is a distribution of molecular weights

MOLECULAR WEIGHT

Large chains = large molecular weight

Average molecular weight:

Number-average molecular weight ( ):

Divide chains into different size ranges

Determine number of fraction chains within each size

range

Mi = mean molecular weight of size range i

xi = fraction of number of chains within size range

nM

n i iM x M=

MOLECULAR WEIGHT

Weight-average molecular weight ( ):

Mi = mean molecular weight of size range i

wi = weight fraction of molecules within

same size interval

wM

w i iM w M=

DEGREE OF POLYMERIZATION

n = average number of mer units in a chain

Number-average degree of polymerization (nn):

Weight-average degree of polymerization (nw):

m = mer molecular weight

ww

Mn

m=

nn

Mn

m=

EXAMPLE PROBLEM 14.1 (PG 542)

MOLECULAR WEIGHT

Melting temperature increases with increased

molecular weight (up to 100,000 g/mol)

Polymers with short chains (100 g/mol) are

liquids/gases at room temp

1000 g/mol (paraffin wax, soft resin)

10,000-several million g/mol (solid polymers)

ISOMERISM

Recall: different atomic configuration for same composition (butane/isobutane)

Stereoisomerism

Geometrical isomerism

STEREOISOMERISM

Isotactic (® groups on same side) Syndiotactic (® alternates sides)

Atactic (random)

ROTATION NOT ALLOWED! (must sever first)

Polymer can exhibit more than one configuration

3-D image

STEREOISOMERISM – ISOTACTIC

Isotactic – R groups on same side of the polymer chain

STEREOISOMERISM – SYNDIOTACTIC

Syndiotactic – R groups on alternate sides of the polymer chain

STEREOISOMERISM – ATACTIC

Atactic – R groups randomly positioned along the polymer chain

ISOMERISM

Geometrical Isomerism

Double bonds between C atoms

C atoms bonded to other atom or radical (side group)

Cis structure (same side, cis-polyisoprene)

Natural rubber

Trans structure (opposite sides, trans-polyisoprene)

Conversion from cis to trans not possible as bond rotation is not allowed – double bond is rigid

Cis Trans


Chemistry

Molecular size

Molecular weight

Molecular shape

Degree of twisting, coiling, bending

Molecular structure

The way units (mers) are joined together

151

THERMOPLASTICS AND THERMOSETS

Thermoplastic

can be reversibly cooled & reheated, i.e. recycled

heat until soft, shape as desired, then cool

ex: polyethylene, polypropylene, polystyrene.

• Thermoset

– when heated forms a molecular network (chemical reaction)

– degrades (doesn’t melt) when heated

– a prepolymer molded into desired shape, then

chemical reaction occurs

– ex: urethane, epoxy

ELECTRICAL CONDUCTION

153

ELECTRICAL CONDUCTION

• Ohm's Law: V = I R voltage drop (volts = J/C)

C = Coulomb

resistance (Ohms) current (amps = C/s)

• Conductivity, σ

• Resistivity, ρ:

-- a material property that is independent of sample size and

geometry cross-sectional area

of current flow

current flow

path length

154

ELECTRICAL PROPERTIES

Which will have the greater resistance?

Analogous to flow of water in a pipe

Resistance depends on sample geometry and

size.

D

2D

2

155

DEFINITIONS

Further definitions

J = σ E <= another way to state Ohm’s law

J current density

E electric field potential = V/

=current

surface area=

IA

like a flux

Electron flux conductivity voltage gradient

J = (V/ )

156

• Room temperature values (Ohm-m)-1 = (Ω - m)-1

Selected values from Tables 18.1, 18.3, and 18.4, Callister & Rethwisch 9e.

CONDUCTIVITY: COMPARISON

Silver 6.8 x 10 7

Copper 6.0 x 10 7

Iron 1.0 x 10 7

METALS conductors

Silicon 4 x 10 -4

Germanium 2 x 10 0

GaAs 10 -6

SEMICONDUCTORS

semiconductors

Polystyrene <10 -14

Polyethylene 10 -15 -10 -17

Soda-lime glass 10

Concrete 10 -9

Aluminum oxide <10 -13

CERAMICS

POLYMERS

insulators

-10 -10 -11

157

What is the minimum diameter (D) of the wire so that V < 1.5 V?

EXAMPLE: CONDUCTIVITY PROBLEM

Cu wire I = 2.5 A - +

V

Solve to get D > 1.87 mm

< 1.5 V

2.5 A

6.07 x 107 (Ohm-m)-1

100 m

4

2Dp

=100 m

ENGR 151: Materials of Engineering FINAL REVIEW · PDF fileFRACTURE Stable crack: resists...

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