Properties of Materials

Vikram K. Kuppa Energy & Materials Engineering Program SEEBME University of Cincinnati 866 ERC Ph: 513-556-2059 [email protected]

www.uc.edu/~kuppavm Office Hours: MWF 10-11AM

Types of Stresses

F Tensile F Bending F F Compressive F



F Shear F

 stress  strain  force area  length length

Stress vs Strain

Representative Stress-strain curves

Young’s Modulus (E)

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

– Hooke’s law:

E =

the material.

deformation.

• Note: where

E E T

o =

E

o

and

–

b bTe

 / 

• A measure of the stiffness of • Larger the value of E, the more resistant a material is to

-To/T

are empirical constants,

T

temperatures and

T

o

are



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 original dimensions.

not return to

•

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

• True stress • True strain

= ln (A 0 /A) = F/A = ln(l/l 0 ) (A must be used after necking) Engineerin g stress   Engineerin g strain   

F A

0 

l



l

0

l

0 Apparent softening

True Strain

 

t



L o L



dl l

 ln

L L o True Stress

 

t



Load A



Load A

0

AL



t

 

A o L o

    

t

   1   



Toughness

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

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

SUMMARY

• 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



y .

• 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.

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 resilient rubber ball Elastic behavior rapid deformation Low Strain Rate High extension - failure 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 – 1s 2 2s 2 2p 2

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 -

X 2

from each), or triple bonds (3 from each)

X 2 X 4 C X 1 X 4 C X 1 X 4 X 4

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

X 4 X 2 C X 4

Polymers – many repeating units

X 1 + X 4 X 2 C X 4 X 1 +… 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

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

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 to the molecular weight of the repeat unit (M RP ).

of the polymer M i

DP = M w / M RP

where M w M n = =  

f

i M

x

i M i i : M : M n w = weight average molecular weight = number average molecular weight = 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

 

M w



x i M i i



w i M i i x i

 

n i n i i

  

i x i M i

2

number fraction



Degreeof Polymerization n n m

 

M n m

;

n w



M w 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 fraction 50 = 50/100, ie ½ , W fraction 25 =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 M w = SUM(n i M i )/Sum(n i ) , where n i = SUM(w i M i ), where w i = no. of chains of length M i = weight fraction of chains of length M i .

But, w i weight.

= n i M i /SUM(n i M i ) ie the weight of that polymer (i), divided by total So, in the previous example, W 50 = 50/100, W 25 1 = 25/100, W 25 2 = 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 we calculated earlier, ie to weight av. mol. Wt.

that 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 Dispersity Index (PDI) often determines properties.

to M n , called the Poly * taken from “Polymer Physics” by M. Rubinstein & R. H. Colby, 1 st edition, OUP

Polymer Architecture

• Poly mer H H mer H H = many mers H H C C C C C C H H H H H H Polyethylene (PE) H H mer H H H H H H H mer H H H C C C C C C H Cl H Cl H Cl Polyvinyl chloride (PVC) C C C C C C H CH3 H CH3 H CH3 Polypropylene (PP) • Covalent chain configurations and strength: Direction of increasing strength

Polymer Architecture - II

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.

Isomerism – different structures, but same chemical composition

Isotactic Syndiotactic Atactic H H H H H H H H H H C C R H C C C C C C C C R H R H R H R H H H C C H H C C H C H H C H H H C C C C H R H H H H R H H R H H H H R H H R H H C C C C C C C C C C R H H R R H R H R H Can’t Crystallize

Stereoisomerism

Polymer Architecture - Schematics

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

Alternating Blocky Branched

Polymer Architecture - III

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.

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, Crystallinity and Properties

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

smaller Mw larger Mw • Tensile strength (TS): --often increases with M w .

--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

“Semicrystalline” Polymers

Oriented chains with long-range order Amorphous disordered polymer chains in the “intercrystalline” region ~10 nm spacing

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

Low entropy state

Elastic Deformation creep

Slow Deformation

random Cross-linking stops the sliding of chains

VISCOELASTIC RESPONSE

Elastic Viscoelastic Viscous

Viscoelasticity: T Dependence

Temperature & Strain Dependence:

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

Thermoplastic (uncrosslinked)

Glassy (Elastic-high modulus) medium times Leathery (Elastic-low modulus) Rubbery Plateau Elastic at high strain rate Viscous at low strain rate Long times Rubber-like Elastic Deformation Slow relaxation T g Temp.

T m

Viscoelasticity: Structure Dependence

Effect of crosslinking

Thermoset Heavy Crosslinking Elastomer Light crosslinking

Effect of crystallinity

100 % crystalline Branched polymer 50 % Crystalline Thermoplastic No crosslinking amorphous Tg Tm Tg Tm Crosslinked Branched Crystals act like crosslinks Strain Induced Crystallization in NR

TENSILE RESPONSE: ELASTOMER (ex: rubberband)

• Compare to responses of other polymers: --brittle response --plastic response (aligned, cross linked & networked case) (semi-crystalline case)

T & STRAIN RATE: THERMOPLASTICS (ex: plastic bottles or containers)

• Decreasing T...

--increases E --increases TS --decreases %EL • Increasing strain rate...

--same effects as decreasing T.

TIME-DEPENDENT DEFORMATION

• Stress relaxation test : --strain to

 o

and hold.

--observe decrease in stress with time.

• Data: Large drop in E r for T > T g .

• Relaxation modulus :

E r (t )   (t )  o

Time-Temperature Superposition

Lo T Hi T Log Time

  L 

fixed

 

L L o

Relaxation Modulus

 10 Glass-like elasticity Rubber-like elasticity Fluid-like Viscous 10 s time 

Viscoelstic modulu s Modulus of elasticity r ( 10s ) =

 

( 10 ) fixed Relaxation Modulus

E r (0)= E, Young’s Modulus E r (  )= 0