MASE 542/CHEM 442 BIOMATERIALS Spring 2012 H. Funda Yagci Acar Koç University İstanbul

Metals

Metals Metallic Bond Crystalline Alloy: Mixtures Close packed Unit cell Alloy: Mixtures . FCC Structure HCP Structure

fig_01_03 density fig_01_03

Metallic Crystal Structures Reasons for dense packing: Typically, only one element is present, so all atomic radii are the same. Metallic bonding is not directional. Nearest neighbor distances tend to be small in order to lower bond energy. Electron cloud shields cores from each other

Crystal structure

Body Centered Cubic Structure (BCC) Atoms touch each other along cube diagonals ex: Cr, W, Fe (), Tantalum, Molybdenum Coordination # = 8 2 atoms/unit cell: 1 center + 8 corners x 1/8 Adapted from Fig. 3.2, Callister & Rethwisch 8e.

Atomic Packing Factor: BCC 3 a a 2 length = 4R = Close-packed directions: 3 a Volume of atoms/unit cell in volume of unit cell APF = 4 3 p ( a/4 ) 2 atoms unit cell atom volume a APF = 0.68 Adapted from Fig. 3.2(a), Callister & Rethwisch 8e.

Hexagonal Close-Packed Structure (HCP) • ABAB... Stacking Sequence • 3D Projection • 2D Projection c a A sites B sites Bottom layer Middle layer Top layer Atomic packing number 6 atoms/unit cell • Coordination # = 12 APF = 0.74 ex: Cd, Mg, Ti, Zn • c/a = 1.633 Adapted from Fig. 3.3(a), Callister & Rethwisch 8e.

Theoretical Density, r Density =  = Cell Unit of Volume Total in Atoms Mass Density =  = VC NA n A  = where n = number of atoms/unit cell A = atomic weight VC = Volume of unit cell = a3 for cubic NA = Avogadro’s number = 6.022 x 1023 atoms/mol

Theoretical Density, r  = Ex: Cr (BCC) A = 52.00 g/mol R = 0.125 nm n = 2 atoms/unit cell a R a = 4R/ 3 = 0.2887 nm  = a3 52.00 2 atoms unit cell mol g volume 6.022 x 1023 theoretical = 7.18 g/cm3 ractual = 7.19 g/cm3 Adapted from Fig. 3.2(a), Callister & Rethwisch 8e.

Densities of Material Classes In general: r metals r ceramics r polymers > > Why? Metals have... • close-packing (metallic bonding) • often large atomic masses Ceramics have... • less dense packing • often lighter elements Composites have... • intermediate values Polymers have... • low packing density (often amorphous) • lighter elements (C,H,O)

Crystals as Building Blocks • Some engineering applications require single crystals: -- diamond single crystals for abrasives (Courtesy Martin Deakins, GE Superabrasives, Worthington, OH. Used with permission.) • Properties of crystalline materials often related to crystal structure. -- Ex: Quartz fractures more easily along some crystal planes than others.

Single vs Polycrystals E (diagonal) = 273 GPa E (edge) = 125 GPa • Single Crystals -Properties vary with direction: anisotropic. Data from Table 3.3, Callister & Rethwisch 8e. (Source of data is R.W. Hertzberg, Deformation and Fracture Mechanics of Engineering Materials, 3rd ed., John Wiley and Sons, 1989.) -Example: the modulus of elasticity (E) in BCC iron: • Polycrystals -Properties may/may not vary with direction. -If grains are randomly oriented: isotropic. (Epoly iron = 210 GPa) -If grains are textured, anisotropic. 200 mm Adapted from Fig. 4.14(b), Callister & Rethwisch 8e. (Fig. 4.14(b) is courtesy of L.C. Smith and C. Brady, the National Bureau of Standards, Washington, DC [now the National Institute of Standards and Technology, Gaithersburg, MD].)

Polycrystals overall component properties are not directional. Anisotropic • Most engineering materials are polycrystals. Adapted from Fig. K, color inset pages of Callister 5e. (Fig. K is courtesy of Paul E. Danielson, Teledyne Wah Chang Albany) 1 mm Isotropic • Nb-Hf-W plate with an electron beam weld. • Each "grain" is a single crystal. • If grains are randomly oriented, overall component properties are not directional. • Grain sizes typically range from 1 nm to 2 cm (i.e., from a few to millions of atomic layers).

Polymorphism Two or more distinct crystal structures for the same material (allotropy/polymorphism)     titanium   , -Ti carbon diamond, graphite BCC FCC 1538ºC 1394ºC 912ºC -Fe -Fe -Fe liquid iron system

Tin: allotropic transformation figun_03_p53a Tin: allotropic transformation Body-centered tetragonal Dimond cubic figun_03_p53a Slow process Volume increase 27% Disintegration into coarse powder Density decrease 7.3 to 5.77 g/cm3 1850 winter in russia. Very cold winter. Solders had white tin buttons At cold weather they crumbelled Tin disease Callister: figun_03_p53b

Composition

Composition Metal/element – generally pure Alloys – combination of different elements Amalgams – alloys of metals in mercury

Metal Alloys Impurity atoms are added intentionally to impart specific characteristics Usually to increase mechanical strength and corrosion resistance

Ti alloys a b transformation temp depends on impurity! V, Niobium, Molybdenum :decrease the temp (b- phase stabilizer) Four types of alloys Alpha: Al, tin ( superior creep, satisfactory stregth and thoughness Beta: V, Mo (Highly forgeable, high fracture thoughness) Alpha+beta (formable) Near alpha High temp reactivity RT: inert to aq, marine, air environment

Callister: page 413

Metals High tensile, fatigue and yield strengths load bearing implants internal fixation devices used for orthopedic applications dental implants Low reactivity and good ductility Good for stems of hip implant devices Their properties depend on the processing method and purity of the metal The selection of the material must be made appropriate to its intended use. Metals

MECHANICAL PROPERTIES Strength Modulus Thoughness Ductility ....

Strength = Maximum load / Area Strength: this is the maximum load that a material can withstand without breaking and is derived by dividing the maximum force by the cross sectional area of the material. Strength = Maximum load / Area

Strength Tensile strength is important for a material that is going to be stretched or under tension. Fibers need good tensile strength. Concrete is an example of a material with good compressional strength. flexural strength: Strength upon bending torsional strength: if it is strong when one tries to twist it. impact strength. A sample has impact strength if it is strong when one hits it sharply and suddenly, as with a hammer. Yield Strength - The stress a material can withstand without permanent deformation.

Strength Shear : Force parallel to the area megapascals (MPa) OR gigapascals (GPa). 1 MPa = 100 N/cm2, 1 GPa = 100,000 N/cm2, 1 GPa = 1,000 MPa. 1 N/cm2 = 1.45 psi.

Modulus = Stress / Strain (N/m2 ) “stiffness or resistance to deformation” when exposed to stress Modulus = Stress / Strain (N/m2 ) 1GPa =103MPa=109N/m2 Modulus of elasticity (E: GPa) (Young`s modulus)

What happens under stress? Bonds stretcth (small changes in the interatomic distance) Slope of stress strain plot (which is proportional to the elastic modulus) depends on bond strength of metal

Modulus of different materials Due to different types of bonding

Young’s Moduli: Comparison Graphite Ceramics Semicond Metals Alloys Composites /fibers Polymers 0.2 8 0.6 1 Magnesium, Aluminum Platinum Silver, Gold Tantalum Zinc, Ti Steel, Ni Molybdenum G raphite Si crystal Glass - soda Concrete Si nitride Al oxide PC Wood( grain) AFRE( fibers) * CFRE GFRE* Glass fibers only Carbon fibers only A ramid fibers only Epoxy only 0.4 0.8 2 4 6 10 00 1200 Tin Cu alloys Tungsten <100> <111> Si carbide Diamond PTF E HDP LDPE PP Polyester PS PET C FRE( fibers) FRE( fibers)* FRE(|| fibers)* E(GPa) Based on data in Table B.2, Callister & Rethwisch 8e. Composite data based on reinforced epoxy with 60 vol% of aligned carbon (CFRE), aramid (AFRE), or glass (GFRE) fibers. 109 Pa

Modulus of Metals

Elastic Deformation d F F Elastic means reversible! d bonds stretch 1. Initial 2. Small load F d bonds stretch 3. Unload return to initial F Linear- elastic Elastic means reversible! Non-Linear- elastic d

Temp dependence of modulus

Plastic (Permanent) Deformation • Simple tension test: Elastic+Plastic at larger stress engineering stress, s Elastic initially permanent (plastic) after load is removed ep plastic strain engineering strain, e Adapted from Fig. 6.10(a), Callister & Rethwisch 8e. (at lower temperatures, i.e. T < Tmelt/3)

Plastic deformation stress is not proportional to strain and non-recovarable! Perminent deformation Atomic perspective Bonds break and form again with new neighbours CRYSTALLINE: slip NONCRYSTALLINE: viscous flow

Yield Strength, sy y = yield strength sy tensile stress, s • Stress at which noticeable plastic deformation has occurred. when ep = 0.002 tensile stress, s engineering strain, e sy ep = 0.002 y = yield strength Note: for 2 inch sample  = 0.002 = z/z  z = 0.004 in Adapted from Fig. 6.10(a), Callister & Rethwisch 8e.

Yield strength : resistance to plastic deformation 35MPa: low strength Al Over 1400MPa for high stregth-steel yielding Yielding= where plastic deformation starts: important to know for function P: onset of plastic deformation in microscopic level Typical metal

Yield Strength : Comparison Graphite/ Ceramics/ Semicond Metals/ Alloys Composites/ fibers Polymers Yield strength, s y (MPa) PVC Hard to measure , since in tension, fracture usually occurs before yield. Nylon 6,6 LDPE 70 20 40 60 50 100 10 30 200 300 400 500 600 700 1000 2000 Tin (pure) Al (6061) a ag Cu (71500) hr Ta (pure) Ti Steel (1020) cd (4140) qt (5Al-2.5Sn) W Mo (pure) cw Hard to measure, in ceramic matrix and epoxy matrix composites, since in tension, fracture usually occurs before yield. H DPE PP humid dry PC PET ¨ Room temperature values Based on data in Table B.4, Callister & Rethwisch 8e. a = annealed hr = hot rolled ag = aged cd = cold drawn cw = cold worked qt = quenched & tempered

Tensile strength aligned and about to break. 50MPa: Al 3000 MPa : high stregth-steel Tensile strength Plastic Max plastic deformation fracture Elastic After M: it is useless necking • Metals: occurs when noticeable necking starts. • Polymers: occurs when polymer backbone chains are aligned and about to break. M: Max stress sustained under tension If you apply this much of stress it will fracture

Tensile Strength: Comparison Si crystal <100> Graphite/ Ceramics/ Semicond Metals/ Alloys Composites/ fibers Polymers Tensile strength, TS (MPa) PVC Nylon 6,6 10 100 200 300 1000 Al (6061) a ag Cu (71500) hr Ta (pure) Ti Steel (1020) (4140) qt (5Al-2.5Sn) W cw L DPE PP PC PET 20 30 40 2000 3000 5000 Graphite Al oxide Concrete Diamond Glass-soda Si nitride H wood ( fiber) wood(|| fiber) 1 GFRE (|| fiber) ( fiber) C FRE A FRE( fiber) E-glass fib Aramid fib Room temperature values Based on data in Table B.4, Callister & Rethwisch 8e. a = annealed hr = hot rolled ag = aged cd = cold drawn cw = cold worked qt = quenched & tempered AFRE, GFRE, & CFRE = aramid, glass, & carbon fiber-reinforced epoxy composites, with 60 vol% fibers.

brass

Ductility Degree of plastic deformation that has been sustained at fracture the ability of a material to deform before breaking Expressed quantitatively as % elongation or % area reduction Little or no plastic deformation: Brittle: 5% or less fracture strain

Ductility 100 x A RA % - = Engineering tensile strain, e E ngineering • Plastic tensile strain at failure: x 100 L EL % o f - = Adapted from Fig. 6.13, Callister & Rethwisch 8e. Engineering tensile strain, e E ngineering tensile stress, s smaller %EL larger %EL Lf Ao Af Lo • Another ductility measure: 100 x A RA % o f - =

fig_06_14 Ductility usally increases with temperature IRON fig_06_14

Resilience Capacity to absorb Energy when it is deformed elastically and then, upon unloading, to have this energy recovered. Energy/unit volume (J/m3) If resilient: High yield strength Low moduli of elasticity

fig_06_15 Thoughness Resistance to fracture when there is a crack Ability to absorb energy and plastically deform before fracture Energy/unit3

Toughness Engineering tensile strain, e E ngineering tensile stress, s • Energy to break a unit volume of material • Approximate by the area under the stress-strain curve. very small toughness (unreinforced polymers) Engineering tensile strain, e E ngineering tensile stress, s small toughness (ceramics) large toughness (metals) Adapted from Fig. 6.13, Callister & Rethwisch 8e. Brittle fracture: elastic energy Ductile fracture: elastic + plastic energy

Strength vs Toughness strength :how much force is needed to break a sample toughness : how much energy is needed to break a sample. Blue: takes lots of force to break it and it breaks Red: deformation cause E dissipation. Elongates and takes more E before breaking BRITTLE

Modulus “stiffness or resistance to deformation” when exposed to stress Modulus = Stress / Strain (N/m2 ). fibers plastics elastomers 1GPa =103MPa=109N/m2

Elongation ultimate elongation: amount you can stretch the sample before it breaks elastic elongation : percent elongation you can reach without permanently deforming your sample (snap back to its original length once you release the stress on it. ) Elastomers: 500 to 1000 % elongation

Elongation ultimate elongation: amount you can stretch the sample before it breaks elastic elongation : percent elongation you can reach without permanently deforming your sample (snap back to its original length once you release the stress on it. ) Elastomers: 500 to 1000 % elongation

Others Fatigue: A material failing at a lower stress value than the ultimate strength value due cyclic loading Hardness: the resistance of a material to surface abrasion.

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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.