Properties of Materials Vikram K. Kuppa Energy & Materials Engineering Program SEEBME University of Cincinnati 866 ERC Ph: 513-556-2059 Vikram.kuppa@uc.edu www.uc.edu/~kuppavm Office Hours: MWF 10-11AM

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

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 = / 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

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

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

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 Unique polymer struc-props xtal-amorphous

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.

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

Polymers – many repeating units C 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.

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, ©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

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 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

Molecular Weight Distributions

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

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 (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) 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 = 25+12.5 = 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

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

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

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 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 ? Blocky Alternating 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 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.

“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

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

VISCOELASTIC RESPONSE Viscous

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

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

TENSILE RESPONSE: ELASTOMER (ex: rubberband) • Compare to responses of other polymers: --brittle response (aligned, cross linked & networked case) --plastic response (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: • Data: Large drop in Er for T > Tg. (amorphous polystyrene) --strain to eo and hold. --observe decrease in stress with time. • Relaxation modulus:

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

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