Properties of Materials

Properties of Materials

Vikram K. Kuppa Vikram K. Kuppa

Energy & Materials Engineering Program Energy & Materials Engineering Program SEEBME

SEEBME

University of Cincinnati University of Cincinnati 866 ERC

866 ERC

Ph: 513-556-2059

Ph: 513-556-2059

Vikram.kuppa@uc.edu

Vikram.kuppa@uc.edu

www.uc.edu/~kuppavm

www.uc.edu/~kuppavm

Office Hours: MWF 10-11AM

Office Hours: MWF 10-11AM

Types of Stresses

F F

Tensile

F Bending

F F

Compressive

F

Shear



F

Stress vs Strain



stress force area strain length

length

Representative Stress-

strain curves

Young’s Modulus (E)

• The slope of the stress-strain curve in the elastic region.

– Hooke’s law: E =  /

• A measure of the stiffness of the material.

• Larger the value of E, the

more resistant a material is to deformation.

• Note: E

= E

– bTe

where E

and b are empirical constants, T and T

are

temperatures

Units:

E: [GPa] or [psi]

: dimensionless

Stress-Strain Behavior (summary)

Elastic deformation Reversible:

( For small strains)

Stress removed  material returns to original size

Plastic deformation Irreversible:

Stress removed  material does not return to original dimensions.

Yield Strength (y)

• The stress at which plastic deformation becomes noticeable (0.2% offset).

• P the stress that divides the elastic and plastic behavior of the material.

True Stress & True Strain

0 0 0

strain

g Engineerin

stress

g Engineerin

l l l

A F

 









• True stress = F/A

• True strain = ln(l/l

)

= ln (A

/A)

(A must be used after necking)

Apparent softening



True Strain _t  dl l

L o



True Stress  t  Load

A  Load A₀ AL  A_oL_o

_t  ln 1  

_t  1  

• The total area under the true stress-strain curve which measures the energy absorbed by the specimen in the process of breaking.

Toughness



Toughness    d 

Tensile properties: Ductility

The total elongation of the specimen due to plastic deformation, neglecting the elastic stretching (the broken ends snap back and separate after failure).

Textbooks

Essentials of Materials Science & Engineering Second Edition

Authors: Donald R. Askeland & Pradeep P. Fulay Materials Science and Engineering: An Introduction

Sixth Edition, Author: William D. Callister, Jr.

The Science and Engineering of Materials

Fourth Edition, Authors: Askeland and Phule (Fulay ?)

Introduction to Materials Science for Engineers

Sixth Edition, Author: James F. Shackelford

• Stress and strain: These are size-independent measures of load and displacement, respectively.

• Elastic behavior: This reversible behavior often shows a linear relation between stress and strain.

To minimize deformation, select a material with a large elastic modulus (E or G).

• Plastic behavior: This permanent deformation behavior occurs when the tensile (or compressive)

uniaxial stress reaches 

.

• Toughness: The energy needed to break a unit volume of material.

• Ductility: The plastic strain at failure.

Note: materials selection is critically related to mechanical behavior for design

applications.

SUMMARY

Viscoelastic Behavior

Polymers have unique mechanical properties vs. metals & ceramics.

Why?

Bonding, structure, configurations

Polymers and inorganic glasses exhibit viscoelastic behavior (time and temperature dependant behavior)

Polymers may act as an elastic solid or a viscous liquid i.e. Silly Putty (silicon rubber)

- bounces, stretches, will flatten over long times

Low Strain Rate High extension - failure resilient rubber ball

Elastic behavior rapid deformation

Very low Strain rate - Flatten Flow like a viscous fluid

Polymers

Polymer : Materials are made up of many (poly) identical chemical units (mers) that are joined together to construct giant molecules.

Plastics - deformable, composed of polymers plus additives. E.g. a variety of films, coatings, fibers, adhesives, and foams. Most are distinguished by their chemical form and composition.

The properties of polymers is related to their structures, which in turn,

depend upon the chemical composition. Many of these molecules contain backbones of carbon atoms, they are usually called "organic" molecules and the chemistry of their formation is taught as organic chemistry.

The most common types of polymers are lightweight, disposable, materials for use at low temperatures. Many of these are recyclable. But polymers are also used in textile fibers, non-stick or chemically resistant coatings,

adhesive fastenings, bulletproof windows and vests, and so on.

Polymers

Polymer : Materials are made up of many (poly) identical chemical units (mers) that are joined together to construct giant molecules.

Carbon – 1s²2s²2p²

It has four electrons in its outermost shell, and needs four more to make a

complete stable orbital. It does this by forming covalent bonds, up to 4 of which can be formed.

The bonds can be either single bonds, ie one electron donated by each participating element, or double bonds (2 e^- from each), or triple bonds (3 from each)

C ^X

X

X

X

X_i can be any entity ex H, O, another C, or even a similar monomer

C ^X

X

X

X

Polymers – many repeating units

C ^X

X

X

X

+ C ^X

X

X

X

+…

C C

C C C

And so on… if the bonds can keep getting formed, entire string-like structures (strands, or chains) of the repeating units are created. C is the most common element in polymers. Occasionally, Si may also participate in such bonding.

Classes of Polymers

Thermoplastics:

Consist of flexible linear molecular chains that are tangled together like a plate of spaghetti or bucket

of worms. They soften when heated.

Thermosets:

Remain rigid when heated & usually consist of a highly cross-linked, 3D network.

Elastomers:

Consist of linear polymer chains that are lightly cross-linked. Stretching an elastomer causes chains

to partially untangle but not deform permanently (like the thermoplastics).

Of all the materials, polymers are perhaps the most versatile, not only because the properties can be drastically modified by simple chemistry, but the behavior is also

dependent on the architecture of the chains themselves.

From proteins to bullet-proof jackets to bottles, polymers are INDISPENSIBLE to life as we know it

Illustration

©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.

a) & b) 3 dimensional models, c) Is a simpler 2-D representation

backbone

side-group

Chain Conformations

Polymer Synthesis - I

Addition

in which one “mer” is added to the structure at a time.

This process is begun by an initiator that "opens up" a C=C double bond, attaches itself to one of the resulting single bonds, & leaves the second one dangling to repeat the process

Polymer Synthesis - II

Condensation

in which the ends of the precursor molecules lose atoms to form water or alcohol, leaving bonds that join with each other to form bits of the final large molecules. An example is shown in the Detail - the formation of nylon.

Molecular weight distribution

The degree of polymerization (DP) = no. of monomers per polymer. It is determined from the ratio of the average molecular weight M_w of the polymer

to the molecular weight of the repeat unit (M_RP).

DP = M_w / M_RP where

M_w =  f_i M_i : M_w = weight average molecular weight M_n =  x_i M_i : M_n = number average molecular weight

M_i = mean molecular weight of each range

f_i = weight fraction of polymer having chains within that range xi = fraction of total number of chains within each range

Molecular Weight Distributions



M _n  x_iM_i

i



M _w  w_iM_i

i



i



x_i  n_i n_i

i





Degree of Polymerization n_n  M_n

m ; n_w  M_w m

m  "mer" molecular weight

Degree of polymerization & molecular weight

Degree of polymerization (DP)- number of monomers per polymer chain, ie no. of repeat units.

Obviously, the weight (either in AMU, or in g/mol) is the same for each repeat unit. Then, the total weight of the polymer chain, ie its molecular weight is :-

mol. Wt. = N.M_m

where N is the number of monomers in that chain, ie the DP;

M_m is the weight of the monomer.

In a polymer sample synthesized from monomers by either condensation or addition polymerization, one always has a distribution of DPs amongst the resulting chains.

So let us consider that we have 100 monomers. Let the weight of each monomer be 1g/mol (in reality, this is Hydrogen !) Let us see some ways in which we can arrange this:

1)1 chain of N=100, ie mol. Wt. = 100 2)2 chains of N=50 each, ie mol. Wt. = 50 3)10 chains of N=10 each, ie mol. Wt. = 10 4)3 chains, 2 of N=25, and 1 of N=50

Degree of polymerization & molecular weight

3 chains, 2 of N=25, and 1 of N=50.

Now, to calculate the average molecular weight, we have two methods:

1) Take the simple numerical average, ie

(25+25+50)/3.0 = (2x25 + 1x50)/3.0 = 33.33. This value is according to the number fraction of each type of chain (1/3 of the chains are of N=50, and 2/3 have N = 25)

2) Take the average according to the weight fraction of each chain. What is the total weight ?

Mtotal=100

W_fraction⁵⁰ = 50/100, ie ½ , W_fraction²⁵=2*25/100 = 1/2

So, taking weight fractions, we get the average molecular weight as Mw = 50*1/2 + 25*1/2 = 25+12.5 = 37.5

So, numerical fractions, and weight fractions for mol. Wt. give different answers!

M_n = SUM(n_iM_i)/Sum(n_i) , where n_i = no. of chains of length M_i

M_w = SUM(w_iM_i), where w_i = weight fraction of chains of length M_i.

But, w_i = n_iM_i/SUM(n_iM_i) ie the weight of that polymer (i), divided by total weight.

So, in the previous example, W⁵⁰ = 50/100, W²⁵₁ = 25/100, W²⁵₂ = 25/100

Degree of polymerization & molecular weight

Suppose we want to find out the average population of each state.*

We can go to each senator of each state and find out what the population of their state is, and then divide that number by 100.

This number is the number-average population for each state. This is exactly similar to the M_n that we calculated earlier, ie no. av. Mol. wt.. Problem ?

Yes, of course. What do we do about say, CA and AK ?

Now, senators are busy, so we ask congressmen from each state. Then, we take the value that each congressman/congresswoman gives us, and then divide by the number of congresscritters. What value do we get ? Certainly one different from our earlier attempt ! Problem ?

Now the value is much higher than before. This is exactly similar to the M_w that we calculated earlier, ie to weight av. mol. Wt.

Is this value MUCH more representative (eh eh !) of the average population of each state ? Well, not really. But at least, it is an average.

We learn about these differences, because different measurement techniques measure different averages, and the ratio of M_w to M_n, called the Poly Dispersity Index (PDI) often determines properties.

* taken from “Polymer Physics” by M. Rubinstein & R. H. Colby, 1^st edition, OUP

• Polymer = many mers

• Covalent chain configurations and strength:

Direction of increasing strength

Branched Cross-Linked Network Linear

secondary

bonding

C C C C C C H H H H H H

H H H H H H

Polyethylene (PE)

mer

Cl

Cl Cl

C C C C C C H H

H

H H H H H H

Polyvinyl chloride (PVC)

mer

Polypropylene (PP)

CH3

C C C C C C

H H

H

H H

H H

H H

CH3 CH3 mer

Polymer Architecture

Structure of polymers strongly affects their properties; e.g., the ability of chains to slide past each other (breaking Van der Waals bonds) or to arrange themselves in regular crystalline patterns.

Some of the parameters are: the extent of branching of the linear polymers;

the arrangement of side groups. A regular arrangement (isotactic) permits the greatest regularity of packing and bonding, while an alternating pattern (syndiotactic) or a random pattern (atactic) produces poorer packing which lowers strength & melting temperature.

Polymer Architecture - II

Stereoisomerism

C C H H

R H C

C H H

R H C

C H H

R H C

C H H

R H C

C H H

R H

C C H H

R H C

C H H

H R C

C H H

R H C

C H H

H R C

C H H

R H

C C H H

R H C

C H H

H R C

C H H

R H C

C H H

R H C

C H H

R H

Isotactic

Syndiotactic

Atactic

Can’t Crystallize

Isomerism – different structures, but same chemical composition

Polymer Architecture - Schematics

Random

Alternating

Branched

If you have some red beads and some black beads, how can you make polymers out of them ?

Blocky

We have discussed polymers comprised of a single kind of a monomer, ie just one repeating entity. However, this is not unique: we can

synthesize polymers that consist of different repeating units, and such polymers are called copolymers

The combination of different mers allows flexibility in selecting properties, but the way in which the mers are combined is also

important. Two different mers can be alternating, random, or in blocks along the backbone or grafted on as branches.

Polymer Architecture - III

Thermoplastic & Thermosetting Polymers

• Thermoplastics:

--little cross-linking --ductile

--soften w/heating

Ex: grocery bags, bottles

• Thermosets:

--large cross-linking (10 to 50% of mers) --hard and brittle

--do NOT soften w/heating --vulcanized rubber, epoxies,

polyester resin, phenolic resin Ex: car tyres, structural plastics

cross-linking

Vulcanization

In thermoset, the network is inter-connnected in a non-regular fashion. Elastomers belong to the first category. Polyisoprene, the hydrocarbon that constitutes raw natural

rubber, is an example. It contains unsaturated C=C bonds, and when vulcanizing rubber, sulfur is added to promote crosslinks. Two S atoms are required to fully saturate

a pair of –C=C— bonds and link a pair of adjacent molecules (mers) as indicated in the reaction.

Without vulcanization, rubber is soft and sticky and flows viscously even at room temperature. By crosslinking about 10% of the sites, the rubber attains mechanical stability while preserving its flexibility. Hard rubber materials contain even greater sulfur

additions.

Vulcanization

• Molecular weight M

: Mass of a mole of chains.

• Tensile strength (TS):

--often increases with M

.

--Why? Longer chains are entangled (anchored) better.

• % Crystallinity: % of material that is crystalline.

--TS and E often increase with % crystallinity.

--Annealing causes crystalline regions

to grow. % crystallinity increases.

crystalline region

amorphous region

smaller Mw larger Mw

Molecular weight, Crystallinity

and Properties

“Semicrystalline” Polymers

~10 nm spacing

Oriented chains with long-range order

Amorphous disordered polymer chains in the “intercrystalline” region

Mechanical Properties of Polymers

Elasticity of Polymers

Random arrangement = High Entropy Stretched = Low Entropy

Entropy is a measure of randomness: The more ordered the chains are, the lower is the entropy. Spontaneous processes always tend to increase the entropy, which means that after stretching, the chains will tend to return to a high-entropy state

Viscosity of Polymers

Elastic Deformation

creep

Cross-linking stops the sliding of chains

random Slow Deformation

Low entropy state

Elastic

Viscous Viscoelastic

VISCOELASTIC RESPONSE

Viscoelasticity: T Dependence

Temperature & Strain Dependence:

Low T & high strain rates = rigid solids High T & low strain rates = viscous

Rubber-like Elastic Deformation

Slow relaxation Glassy (Elastic-high modulus)

Leathery

(Elastic-low modulus) Thermoplastic (uncrosslinked)

T_g T_m

Modulus of elasticity

Temp.

Rubbery Plateau Elastic at high strain rate Viscous at low strain rate

medium times

Long times

Crosslinked Branched Effect of crosslinking

Thermoset Heavy Crosslinking

Elastomer Light crosslinking

Effect of crystallinity

Tg Tm

Log Mod. Of Elasticity

amorphous

50 % Crystalline 100 % crystalline

Tm

Log Mod. Of Elasticity

Thermoplastic No crosslinking Tg

Branched polymer

Crystals act like crosslinks

Strain Induced Crystallization in NR

Viscoelasticity: Structure Dependence

• Compare to responses of other polymers:

--brittle response

--plastic response

TENSILE RESPONSE: ELASTOMER (ex: rubberband)

initial: amorphous chains are kinked, heavily cross-linked.

final: chains are straight,

still cross-linked

0 20 40 60

0 2 4 6

(MPa)



x x

x

elastomer plastic failure brittle failure

Deformation is reversible!

• Decreasing T...

--increases E --increases TS --decreases %EL

• Increasing strain rate...

--same effects as decreasing T.

20 40 60 80

0 0 0.1 0.2 0.3

4°C

20°C 40°C

60°C to 1.3

(MPa)



Data for the

semicrystalline polymer: PMMA (Plexiglas)

T & STRAIN RATE: THERMOPLASTICS

(ex: plastic bottles or containers)

• Stress relaxation test:

E

(t)  (t)



--strain to 

and hold.

--observe decrease in stress with time.

• Relaxation modulus:

• Data:

Large drop in E

for T > T

.

103 101 10-1 10-3 105

60 100 140 180 rigid solid

(small relax)

viscous liquid (large relax)

transition region

T(°C) Tg

Er(10s) in MPa

TIME-DEPENDENT DEFORMATION

time strain tensile test



( ) t

Time-Temperature Superposition

Log Time

Log Relaxation Modulus Relaxation Modulus

Hi T

Lo T

Relaxation Modulus

time

Stress, 

10 s



L



_fixed  L L_o

E_r(0)= E, Young’s Modulus E_r( )= 0

Glass-like elasticity

Rubber-like elasticity

Fluid-like Viscous



Viscoelstic modulus

Modulus of elasticity E_r(10s) = (10)

_fixed Relaxation Modulus