1. Properties of Materials
Vikram K. Kuppa
Energy & Materials Engineering Program
SEEBME
University of Cincinnati
866 ERC
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Office Hours: MWF 10-11AM

2. Types of Stresses F
Tensile
Bending F F
Compressive F
Shear  F

3. Stress vs Strain

4. Representative Stress-strain curves

5. 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: ET = Eo – bTe-To/T
where Eo and b are empirical constants, T and To are temperatures
Units:
E: [GPa] or [psi]
 : dimensionless

6. 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.

7. True Stress & True Strain
True stress = F/A
True strain = ln(l/l0) = ln (A0/A)
(A must be used after necking)
Apparent softening

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

10. 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).

11. 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
Unique polymer struc-props xtal-amorphous

12. 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 sy.
• 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.

13. 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

14. 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.

15. 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 X1 X2 X4 C X1 X2 X4
Xi can be any entity ex H, O, another C, or even a similar monomer

16. Polymers – many repeating unitsC X1 X2 X4 C X1 X2 X4 +… + 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.

17. 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

18. Illustration backbone side-group a) & b) 3 dimensional models,
©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.
side-group
a) & b) 3 dimensional models,
c) Is a simpler 2-D representation

19. Chain Conformations

20. 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

21. 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.

23. Molecular weight distribution
The degree of polymerization (DP) = no. of monomers per polymer. It is determined from the ratio of the average molecular weight Mw of the polymer to the molecular weight of the repeat unit (MRP).
DP = Mw / MRP
where
Mw =  fi Mi : Mw = weight average molecular weight
Mn =  xi Mi : Mn = number average molecular weight
Mi = mean molecular weight of each range
fi = weight fraction of polymer having chains within that range
xi = fraction of total number of chains within each range

24. Molecular Weight Distributions

25. 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.Mm
where N is the number of monomers in that chain, ie the DP;
Mm 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 chain of N=100, ie mol. Wt. = 100
2 chains of N=50 each, ie mol. Wt. = 50
10 chains of N=10 each, ie mol. Wt. = 10
3 chains, 2 of N=25, and 1 of N=50

26. 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:
Take the simple numerical average, ie
( )/3.0 = (2x25 + 1x50)/3.0 = 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)
Take the average according to the weight fraction of each chain. What is the total weight ?
Mtotal=100
Wfraction50 = 50/100, ie ½ , Wfraction25=2*25/100 = 1/2
So, taking weight fractions, we get the average molecular weight as
Mw = 50*1/2 + 25*1/2 = = 37.5
So, numerical fractions, and weight fractions for mol. Wt. give different answers!
Mn = SUM(niMi)/Sum(ni) , where ni = no. of chains of length Mi
Mw = SUM(wiMi), where wi = weight fraction of chains of length Mi.
But, wi = niMi/SUM(niMi) 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

27. 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 Mn 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 Mw 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 Mw to Mn, called the Poly Dispersity Index (PDI) often determines properties.
* taken from “Polymer Physics” by M. Rubinstein & R. H. Colby, 1st edition, OUP

28. Polymer Architecture • Polymer = many mers
Polyethylene (PE)
mer Cl C H
Polyvinyl chloride (PVC)
mer
Polypropylene (PP) CH 3 C H
mer
• Covalent chain configurations and strength:
Direction of increasing strength

29. 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.

30. Isomerism – different structures, but same chemical composition
Isotactic
Syndiotactic
Atactic
Can’t Crystallize
Stereoisomerism

31. Polymer Architecture - Schematics
Random
If you have some red beads and some black beads, how can you make polymers out of them ?
Blocky
Alternating
Branched

32. 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.

33. 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

34. 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.

35. Vulcanization

36. Molecular weight, Crystallinity and Properties
• Molecular weight Mw: Mass of a mole of chains.
smaller M w
larger M w
• Tensile strength (TS):
--often increases with Mw.
--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.

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

38. Mechanical Properties of Polymers

39. 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

40. Cross-linking stops the sliding of chains
Viscosity of Polymers
Low entropy state
Elastic Deformation
creep
Slow Deformation
random
Cross-linking stops the sliding of chains

41. VISCOELASTIC RESPONSE
Viscous

42. Viscoelasticity: T Dependence
Temperature & Strain Dependence:
Low T & high strain rates = rigid solids
High T & low strain rates = viscous
medium times
Rubber-like Elastic
Deformation
Glassy (Elastic-high modulus)
Leathery
(Elastic-low modulus)
Thermoplastic (uncrosslinked) Tg Tm
Modulus of elasticity
Temp.
Rubbery Plateau
Elastic at high strain rate
Viscous at low strain rate
Long times
Slow
relaxation

43. Viscoelasticity: Structure Dependence
Effect of crosslinking
Effect of crystallinity Tg Tm
Log Mod. Of Elasticity
amorphous
50 % Crystalline
100 % crystalline
Thermoset
Heavy Crosslinking
Elastomer
Light crosslinking
Log Mod. Of Elasticity
Branched polymer
Thermoplastic
No crosslinking Tg Tm
Crystals act like crosslinks
Strain Induced Crystallization in NR
Crosslinked
Branched

44. TENSILE RESPONSE: ELASTOMER (ex: rubberband)
• Compare to responses of other polymers:
--brittle response (aligned, cross linked & networked case)
--plastic response (semi-crystalline case)

45. 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.

46. TIME-DEPENDENT DEFORMATION
• Stress relaxation test:
• Data: Large drop in Er
for T > Tg.
(amorphous
polystyrene)
--strain to eo and hold.
--observe decrease in
stress with time.
• Relaxation modulus:

47. Time-Temperature Superposition
Log Time
Log Relaxation Modulus
Lo T
Relaxation Modulus
Hi T

48. Relaxation Modulus s10 Stress, s Glass-like elasticity Rubber-like
Fluid-like
Viscous
10 s DL
time
Er(0)= E, Young’s Modulus
Er( )= 0