بسم الله الرحمن الرحیم. Materials Science. Chapter 7 Mechanical Properties

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1 بسم الله الرحمن الرحیم Materials Science Chapter 7 Mechanical Properties 1

2 Mechanical Properties Can be characterized using some quantities: 1. Strength, resistance of materials to (elastic+plastic) deformation; 2. Young s modulus and the elasticity limit (or plastic flow threshold): characterizes a material s elastic properties; 3. Toughness: accounts for the relative brittleness of a material; 4. Hardness: resistance of materials to plastic deformation. 2

3 Mechanical Properties Important factors: 1. Load or applied force: tension/ pressuer/ shear/ torsion; 2. How is applied load: cycling/ continuously; 3. Time; 4. Temperature. 3

4 Mechanical Properties ISSUES TO ADDRESS... Stress and strain: What are they and why are they used instead of load and deformation? Elastic behavior: When loads are small, how much deformation occurs? What materials deform least? Plastic behavior: At what point does permanent deformation occur? What materials are most resistant to permanent deformation? Toughness and ductility: What are they and how do we measure them? 4

5 Elastic Deformation 1. Initial 2. Small load 3. Unload bonds stretch δ Elastic means reversible! F F δ return to initial Linearelastic Non-Linearelastic 5

6 Engineering Stress Tensile stress, σ: Ft Shear stress, τ: Ft F Area, A o Area, A o Fs σ = F t lb f = 2 A o in Ft or N 2 m τ = F s A o Fs F Ft original area before loading Stress has units: N/m 2 or lb f /in 2 6

7 Common States of Stress Simple tension: cable F F Ao = cross sectional area (when unloaded) σ = F A o σ σ Torsion (a form of shear): drive shaft A c M 2R M Fs A o τ = F s A o Note: τ = M/A c R here. 7

8 Engineering Strain Tensile strain: ε = δ L o w o δ/2 L o Lateral strain: δ ε L = L w o Shear strain: θ x δ L /2 γ = x/y = tanθ y 90º 90º - θ Strain is always dimensionless. 8

9 Stress-Strain Testing Typical tensile test machine Typical tensile specimen extensometer specimen gauge length 9

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11 Linear Elastic Properties Modulus of Elasticity, E: (also known as Young's modulus) Hooke's Law: σ = E ε σ F E Linearelastic ε F simple tension test 11

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14 Elastic Deformation 1. Initial 2. Small load 3. Unload bonds stretch δ Elastic means reversible! F F δ return to initial Linearelastic Non-Linearelastic 14

15 Mechanical Properties Slope of stress strain plot (which is proportional to the elastic modulus) depends on bond strength of metal 15

16 Young s Moduli: Comparison E(GPa) 10 9 Pa Metals Alloys Tungsten Molybdenum Steel, Ni Tantalum Platinum Cu alloys Zinc, Ti Silver, Gold Aluminum Magnesium, Tin Graphite Ceramics Semicond Diamond Si carbide Al oxide Si nitride <111> Si crystal <100> Glass -soda Concrete Graphite Polymers Composites /fibers Polyester PET PS PC PP HDPE PTFE Carbon fibers only CFRE( fibers)* Aramid fibers only AFRE( fibers)* Glass fibers only GFRE( fibers)* GFRE* CFRE* GFRE( fibers)* CFRE( fibers) * AFRE( fibers) * Epoxy only Wood( grain) 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. 0.2 LDPE 16

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19 Poisson's ratio, n: Poisson's ratio, ν ε L ε ν = L ε ε metals: ν ~ 0.33 ceramics: ν ~ 0.25 polymers: ν ~ 0.40 Units: E: [GPa] or [psi] ν: dimensionless -ν > 0.50 density increases < 0.50 density decreases (voids form) 19

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21 Plastic Deformation (Metals) 1. Initial 2. Small load 3. Unload bonds stretch planes & planes still shear sheared δ elastic + plastic δ plastic F F Plastic means permanent! linear elastic δ plastic linear elastic δ 21

22 Plastic (Permanent) Deformation (at lower temperatures, i.e. T < T melt /3) Simple tension test: engineering stress, σ Elastic+Plastic at larger stress Elastic initially permanent (plastic) after load is removed ε p engineering strain, ε plastic strain 22

23 Yield Strength, σ y Stress at which noticeable plastic deformation has occurred. when ε p = σ y tensile stress, σ y = yield strength Note: for 2 inch sample = = z/z z = in ε p = engineering strain, ε 23

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25 Yield Strength : Comparison 2000 Metals/ Alloys Steel (4140) qt Graphite/ Ceramics/ Semicond Polymers Composites/ fibers Yield strength, σ y (MPa) Ti (5Al-2.5Sn) W (pure) a Cu (71500) cw Mo (pure) Steel (4140) a Steel (1020) cd Al (6061) ag Steel (1020) hr Ti (pure) a Ta (pure) Cu (71500) hr Al (6061) a, since in tension, fracture usually occurs before yield. Hard to measure, PC Nylon 6,6 PET humid PVC PP HDPE dry mposites, since before yield. Hard to measure, in ceramic matrix and epoxy matrix com in tension, fracture usually occurs b Room temperature values Based on data in Table B.4, Callister & Rethwisch 3e. a = annealed hr = hot rolled ag = aged cd = cold drawn cw = cold worked qt = quenched & tempered 10 Tin (pure) LDPE 25

26 Tensile Strength, TS Maximum stress on engineering stress-strain curve. TS y engine eering stre ess Typical response of a metal strain engineering strain F = fracture or ultimate strength Neck acts as stress concentrator Metals: occurs when noticeable necking starts. Polymers: occurs when polymer backbone chains are aligned and about to break. 26

27 Tensile Strength: Comparison Tensile strength, TS (MPa) Metals/ Alloys Steel (4140) qt W (pure) Ti (5Al-2.5Sn) Steel (4140) a a Cu (71500) Cu (71500) hr cw Steel (1020) Al (6061) Ti (pure) ag a Ta (pure) Al (6061) a Graphite/ Ceramics/ Semicond Diamond Si nitride Al oxide Si crystal <100> Glass-soda Concrete Graphite Polymers Nylon 6,6 PC PET PVC PP HDPE LDPE Composites/ fibers C fibers Aramid fib E-glass fib AFRE( fiber) GFRE( fiber) CFRE( fiber) wood( fiber) GFRE( fiber) CFRE( fiber) AFRE( fiber) wood ( fiber) Room temperature values Based on data in Table B4, Callister & Rethwisch 3e. 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. 27

28 Ductility L L o Plastic tensile strain at failure: %EL = x 100 L Engineering tensile stress, σ smaller %EL larger %EL L o f o A o A f L f Engineering tensile strain, ε Another ductility measure: A A %RA = f x 100 A o - o 28

29 Toughness Energy to break a unit volume of material Approximate by the area under the stress-strain curve. Engineering tensile stress, σ small toughness (ceramics) large toughness (metals) very small toughness (unreinforced polymers) Engineering tensile strain, ε Brittle fracture: elastic energy Ductile fracture: elastic + plastic energy 29

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32 Resilience, U r Ability of a material to store energy Energy stored best in elastic region U r 0 y d If we assume a linear stress-strain curve this simplifies to U r 1 2 σ y ε y 32

33 True Stress & Strain Note: S.A. changes when sample stretched True stress T F A i T 1 True strain T ln i o T ln 1 33

34 Elastic Strain Recovery σ yi D σ yo St tress 2. Unload 1. Load 3. Reapply load Strain Elastic strain recovery 34

35 Mechanical Properties of Ceramics 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 35

36 Flexural Tests Measurement of Elastic Modulus Room T behavior is usually elastic, with brittle failure. 3-Point Bend Testing often used. -- tensile tests are difficult for brittle materials. cross section b rect. d R circ. F L/2 L/2 Determine elastic modulus according to: F x slope = F δ δ linear-elastic behavior E E F F L 3 4bd L R 4 d= midpoint deflection (rect. cross section) (circ. cross section) 36

37 Flexural Tests Measurement of Flexural Strength 3-point bend test to measure room-t flexural strength. cross section b rect. d R circ. F L/2 L/2 location of max tension Adapted from Fig. 7.18, Callister & Rethwisch 3e. d= midpoint deflection Flexural strength: fs fs 3 2bd F f F f R L 3 L 2 (rect. cross section) (circ. cross section) Material Typical values: σfs(mpa) E(GPa) Si nitride Si carbide Al oxide glass (soda-lime) 69 Data from Table 7.2, Callister & Rethwisch 3e

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40 Dependence of modulus of elasticity on volume fraction porosity 40

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43 Hardness Resistance to permanently indenting the surface. Large hardness means: -- resistance to plastic deformation or cracking in compression. -- better wear properties. e.g., 10 mm sphere apply known force measure size of indent after removing load D d Smaller indents mean larger hardness. most plastics brasses Al alloys easy to machine steels file hard cutting tools nitrided steels diamond increasing hardness 43

44 Hardness: Measurement Rockwell No major sample damage Each scale runs to 130 but only useful in range Minor load 10 kg Major load 60 (A), 100 (B) & 150 (C) kg A = diamond, B = 1/16 in. ball, C = diamond HB = Brinell Hardness TS (psia) = 500 x HB TS (MPa) = 3.45 x HB 44

45 Hardness: Measurement Table

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48 Variability in Material Properties Elastic modulus is material property Critical properties depend largely on sample flaws (defects, etc.). Large sample to sample variability. Statistics Mean Standard Deviation x n n xi n where n is the number of data points s x n n x

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50 Design/Safety Factors Design stress: Estimated maximum load Design factor Yield Strength Safe stress: Factor of safety 50