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/Twhere Eo and b are empirical constants, T and To are temperaturesUnits:E: [GPa] or [psi] : dimensionless
6 Stress-Strain Behavior (summary) Elastic deformationReversible:( For small strains)Stress removed material returns to original sizePlastic deformationIrreversible: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/ATrue strain = ln(l/l0) = ln (A0/A)(A must be used after necking)Apparent softening
9 ToughnessThe 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. FulayMaterials Science and Engineering: An IntroductionSixth Edition, Author: William D. Callister, Jr.The Science and Engineering of MaterialsFourth Edition, Authors: Askeland and Phule (Fulay ?)Introduction to Materials Science for EngineersSixth Edition, Author: James F. ShackelfordUnique 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 oftenshows a linear relation between stress and strain.To minimize deformation, select a material with alarge elastic modulus (E or G).• Plastic behavior: This permanent deformationbehavior occurs when the tensile (or compressive)uniaxial stress reaches sy.• Toughness: The energy needed to break a unitvolume 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, configurationsPolymers and inorganic glasses exhibit viscoelastic behavior(time and temperature dependant behavior)Polymers may act as an elastic solid or a viscous liquidi.e. Silly Putty (silicon rubber)- bounces, stretches, will flatten over long timesLow Strain RateHigh extension - failureresilient rubber ballElastic behavior rapid deformationVery low Strain rate - FlattenFlow like a viscous fluid
14 PolymersPolymer : 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 PolymersPolymer : Materials are made up of many (poly) identical chemical units (mers) that are joined together to construct giant molecules.Carbon – 1s22s22p2It 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)CX1X2X4CX1X2X4Xi can be any entity ex H, O, another C, or even a similar monomer
16 Polymers – many repeating units CX1X2X4CX1X2X4+…+CAnd 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
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 / MRPwhereMw = fi Mi : Mw = weight average molecular weightMn = xi Mi : Mn = number average molecular weightMi = mean molecular weight of each rangefi = weight fraction of polymer having chains within that rangexi = fraction of total number of chains within each range
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.Mmwhere 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. = 1002 chains of N=50 each, ie mol. Wt. = 5010 chains of N=10 each, ie mol. Wt. = 103 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=100Wfraction50 = 50/100, ie ½ , Wfraction25=2*25/100 = 1/2So, taking weight fractions, we get the average molecular weight asMw = 50*1/2 + 25*1/2 = = 37.5So, numerical fractions, and weight fractions for mol. Wt. give different answers!Mn = SUM(niMi)/Sum(ni) , where ni = no. of chains of length MiMw = 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)merClCHPolyvinyl chloride (PVC)merPolypropylene (PP)CH3CHmer• 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 IsotacticSyndiotacticAtacticCan’t CrystallizeStereoisomerism
31 Polymer Architecture - Schematics RandomIf you have some red beads and some black beads, how can you make polymers out of them ?BlockyAlternatingBranched
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 copolymersThe 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/heatingEx: 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 resinEx: car tyres, structural plasticscross-linking
34 VulcanizationIn 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.
36 Molecular weight, Crystallinity and Properties • Molecular weight Mw: Mass of a mole of chains.smaller Mwlarger Mw• Tensile strength (TS):--often increases with Mw.--Why? Longer chains are entangled (anchored) better.• % Crystallinity: % of material that is crystalline.--TS and E often increasewith % crystallinity.--Annealing causescrystalline regionsto grow. % crystallinityincreases.
39 Elasticity of Polymers Random arrangement = High EntropyStretched = Low EntropyEntropy is a measure of randomness: The more ordered the chains are, the loweris the entropy. Spontaneous processes always tend to increase the entropy, whichmeans that after stretching, the chains will tend to return to a high-entropy state
40 Cross-linking stops the sliding of chains Viscosity of PolymersLow entropy stateElastic DeformationcreepSlow DeformationrandomCross-linking stops the sliding of chains
42 Viscoelasticity: T Dependence Temperature & Strain Dependence:Low T & high strain rates = rigid solidsHigh T & low strain rates = viscousmedium timesRubber-like ElasticDeformationGlassy (Elastic-high modulus)Leathery(Elastic-low modulus)Thermoplastic (uncrosslinked)TgTmModulus of elasticityTemp.Rubbery PlateauElastic at high strain rateViscous at low strain rateLong timesSlowrelaxation
43 Viscoelasticity: Structure Dependence Effect of crosslinkingEffect of crystallinityTgTmLog Mod. Of Elasticityamorphous50 % Crystalline100 % crystallineThermosetHeavy CrosslinkingElastomerLight crosslinkingLog Mod. Of ElasticityBranched polymerThermoplasticNo crosslinkingTgTmCrystals act like crosslinksStrain Induced Crystallization in NRCrosslinkedBranched
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• Increasingstrain rate...--same effectsas decreasing T.
46 TIME-DEPENDENT DEFORMATION • Stress relaxation test:• Data: Large drop in Erfor T > Tg.(amorphouspolystyrene)--strain to eo and hold.--observe decrease instress with time.• Relaxation modulus:
47 Time-Temperature Superposition Log TimeLog Relaxation ModulusLo TRelaxation ModulusHi T
48 Relaxation Modulus s10 Stress, s Glass-like elasticity Rubber-like Fluid-likeViscous10 sDLtimeEr(0)= E, Young’s ModulusEr( )= 0