# Chapter 7 Mechanical Properties of Solids.

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Chapter 7 Mechanical Properties of Solids

Mechanical Properties of Solids

Mechanical Properties of Solids
mechanical testing experiment data experiment result mechanical properties Tension test [Universal Testing Machine (UTM)] Load, F Elongation,  Surface area, Ao Poisson’s ratio, v Engineering stress,  Engineering strain,  True stress, T True strain, T Modulus of elasticity, E Yield strength,  Tensile strength TS Fracture strength F Ductility %RA) Toughness (area under graph) Consider: Linear elastic deformation Typical tension test Typical stress-strain curves for hypothetical materials strain Typical response of a metal Neck – acts as stress concentrator y TS F specimen extensometer gauge length Adapted from Fig. 7.2, Callister & Rethwisch 3e. Concept of engineering stress Concept of engineering strain q 90º 90º - q y x 1. Tensile stress, s: Ao F t s 2. Shear stress, t: d /2 L o w 1. Tensile strain: Ao F t e = d L o F t = F s A o s = t A o 2. Lateral strain: original area before loading Stress has units: N/m2 or lbf /in2 - d e L = w o 3. Shear strain: g = Dx/y = tan q

Mechanical Properties of Solids
mechanical testing experiment data experiment result mechanical properties Tension test [Universal Testing Machine (UTM)] Load, F Elongation,  Surface area, Ao Poisson’s ratio, v Engineering stress,  Engineering strain,  True stress, T True strain, T Modulus of elasticity, E Yield strength,  Tensile strength TS Fracture strength F Ductility %RA) Toughness (area under graph) Elastic deformation region Metals Alloys Graphite Ceramics Semicond Polymers Composites /fibers Based on data in Table B.2, Callister & Rethwisch 3e. Composite data based on reinforced epoxy with 60 vol% of aligned carbon (CFRE), aramid (AFRE), or glass (GFRE) fibers. E (GPa) 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)* 1. Modulus of Elasticity, E (also known as Young's modulus) E values for selected materials s Linear- elastic E e E = Units: E: [GPa] or [psi] n: dimensionless 2. Poisson's ratio,n eL e -n e n = - L metals: n ~ 0.33 ceramics: n ~ 0.25 polymers: n ~ 0.40

Mechanical Properties of Solids
mechanical testing experiment data experiment result mechanical properties Tension test [Universal Testing Machine (UTM)] Load, F Elongation,  Surface area, Ao Poisson’s ratio, v Engineering stress,  Engineering strain,  True stress, T True strain, T Modulus of elasticity, E Yield strength,  Tensile strength TS Fracture strength F Ductility %RA) Toughness (area under graph) Plastic deformation region 1. Yield strength,  Stress at which noticeable plastic deformation has occurred. when ep = 0.002 = 0.2% offset Elastic+Plastic at larger stress Elastic initially sy engineering stress, s engineering stress, s permanent (plastic) after load is removed ep e engineering strain, e engineering strain, e p = 0.002 plastic strain Adapted from Fig (a), Callister & Rethwisch 3e. y strain Typical response of a metal F = fracture or ultimate strength Neck – acts as stress concentrator engineering TS stress engineering strain 2. Tensile Strength, TS Maximum stress on engineering stress-strain curve. Metals: occurs when noticeable necking starts. Polymers: occurs when polymer backbone chains are aligned & about to break.

Mechanical Properties of Solids
mechanical testing experiment data experiment result mechanical properties Tension test [Universal Testing Machine (UTM)] Load, F Elongation,  Surface area, Ao Poisson’s ratio, v Engineering stress,  Engineering strain,  True stress, T True strain, T Modulus of elasticity, E Yield strength,  Tensile strength TS Fracture strength F Ductility %RA) Toughness (area under graph) Plastic deformation region  & TS values for selected materials (room temperature) 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 Si crystal <100> Graphite/ Ceramics/ Semicond Metals/ Alloys Composites/ fibers Polymers 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 strength, TS (MPa) Tensile

Mechanical Properties of Solids
mechanical testing experiment data experiment result mechanical properties Tension test [Universal Testing Machine (UTM)] Load, F Elongation,  Surface area, Ao Poisson’s ratio, v Engineering stress,  Engineering strain,  True stress, T True strain, T Modulus of elasticity, E Yield strength,  Tensile strength TS Fracture strength F Ductility %RA) Toughness (area under graph) Plastic deformation region 3. Ductility 4. Toughness Plastic tensile strain at failure. -- shows a significant plastic deformation before rupture. Energy to break a unit volume of material. Approximate by the area under the stress-strain curve. Engineering L - L tensile small toughness (ceramics) % EL = f o x 100 stress, s L large toughness (metals) o Lo Ao Af Lf A - A = o f % RA x 100 A very small toughness o (unreinforced polymers) Engineering tensile strain, e Adapted from Fig. 7.13, Callister & Rethwisch 3e. Engineering tensile strain, e E ngineering tensile stress, s smaller %EL larger %EL Brittle fracture: elastic energy Ductile fracture: elastic + plastic energy

Stress-Strain curves for typical polymers
Mechanical Properties of Solids mechanical testing experiment data experiment result mechanical properties Tension test [Universal Testing Machine (UTM)] Load, F Elongation,  Surface area, Ao Poisson’s ratio, v Engineering stress,  Engineering strain,  True stress, T True strain, T Modulus of elasticity, E Yield strength,  Tensile strength TS Fracture strength F Ductility %RA) Toughness (area under graph) Stress-Strain curves for typical polymers True Stress & Strain Note: Surface area, A changes when sample stretched. True stress True strain brittle polymer plastic elastomer elastic moduli – less than for metals Adapted from Fig. 7.22, Callister & Rethwisch 3e. Fracture strengths of polymers ~ 10% of those for metals. Deformation strains for polymers > 1000% – for most metals, deformation strains < 10%. Adapted from Fig. 7.16, Callister & Rethwisch 3e. 8 8

Mechanical Properties of Solids
mechanical testing experiment data experiment result mechanical properties Flexural test [Universal Testing Machine (UTM)] Load, F Elongation,  (deflection) Modulus of elasticity, E Flexural strength, fs - ceramic materials are more brittle than metals. Why is this so? - consider mechanism of deformation -- in crystalline, by dislocation motion. -- in highly ionic solids, dislocation motion is difficult. * few slip systems. * resistance to motion of ions of like charge (e.g., anions) past one another. Flexural test… - most common test for ceramics. Flexural test… - materials with room T behavior is usually elastic but with brittle failure. -- show little plastic deformation before failure. - 3-Point Bend Testing often used. -- tensile tests are difficult for brittle materials. Typical 3 point bend test F L/2 d = midpoint deflection cross section R b d rect. circ. Adapted from Fig. 7.18, Callister & Rethwisch 3e. Determine elastic modulus according to: Flexural strength: (rect. cross section) (circ. cross section) Typical values: F x linear-elastic behavior d slope = Si nitride Si carbide Al oxide glass (soda-lime) 69 304 345 393 Material s fs (MPa) E(GPa) (rect. cross section) (circ. cross section) Data from Table 7.2, Callister & Rethwisch 3e.

Mechanical Properties of Solids
mechanical testing experiment data experiment result mechanical properties Hardness test [hardness machine] Hardness number (HN) Covert to  , TS, E Hardness… - Resistance to permanently indenting the surface. - Large hardness means: -- resistance to plastic deformation or cracking in compression. -- better wear properties. Type of hardness test Brinell hardness test Rockwell hardness test Vickers microhardness test Knoop microhardness test General procedure… Press the indenter that is harder than the metal Into metal surface. Withdraw the indenter Measure hardness by measuring depth or width of indentation. Typical rockwell hardness tester e.g., 10 mm sphere apply known force measure size of indent after removing load d D Smaller indents mean larger hardness. increasing hardness most plastics brasses Al alloys easy to machine steels file hard cutting tools nitrided diamond

Detail of hardness testing techniques & measurement
Mechanical Properties of Solids mechanical testing experiment data experiment result mechanical properties Hardness test [hardness machine] Hardness number (HN) Covert to  , TS, E Detail of hardness testing techniques & measurement Table 7.5 11

Design or Safety Factors
• Design uncertainties mean we do not push the limit. • Factor of safety, N Often N is between 1.2 and 4 • Example: Calculate a diameter, d, to ensure that yield does not occur in the 1045 carbon steel rod below. Use a factor of safety of 5. 1045 plain carbon steel: s y = 310 MPa TS = 565 MPa F = 220,000N d L o 5 d = m = 6.7 cm 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. 13

End of Chapter 7 14