Mechanical Properties Phenomena related to mechanical properties Fundamentals

Mechanical Properties Phenomena related to mechanical properties Fundamentals of Materials Science 1

Mechanical Properties Why mechanical properties? • Need to design materials that will withstand applied load and in-service uses for… Bridges for autos and people MEMS devices skyscrapers Space exploration Fundamentals of Materials Science Space elevator? 2

Mechanical Properties Objectives • Define Stress and strain: Normalized force and displacements. • Define Elastic constants: Ability to be deformed elastically. • Understand Elastic behavior: When loads are small. • Understand Plastic behavior: dislocations and deformation • Toughness, ductility, resilience, toughness, and hardness: Define and how do we measure? • Mechanical behavior of the various classes of materials. Fundamentals of Materials Science 3

Stress: Dilation Fundamentals of Materials Science

Shear deformation Fundamentals of Materials Science

Tensile stress Fundamentals of Materials Science

Shear stress Fundamentals of Materials Science

Stress and Strain Stress: Force per unit area arising from applied load. Tension, compression, shear, torsion or any combination. Stress = σ = force/area Strain: ε – physical deformation response of a material to stress, e. g. , elongation. Fundamentals of Materials Science 8

Pure Tension Pure Compression stress strain Elastic response stress Pure Shear strain Elastic response Pure Torsional Shear Fundamentals of Materials Science 9

Common States of Stress • Simple tension: cable • Simple shear: drive shaft Ski lift (photo courtesy P. M. Anderson) Note: t = M/Ac. R here. Fundamentals of Materials Science 10

Common States of Stress • Simple compression: (photo courtesy P. M. Anderson) Note: compressive structural member (σ < 0). (photo courtesy P. M. Anderson) Fundamentals of Materials Science 11

Common States of Stress • Bi-axial tension: • Hydrostatic compression: (photo courtesy P. M. Anderson) Pressurized tank (photo courtesy P. M. Anderson) σh < 0 Fundamentals of Materials Science 12

Engineering Strain • Tensile strain: • Lateral (width) strain: • Shear strain: Strain is always dimensionless. Fundamentals of Materials Science 13

Elastic Deformation 1. Initial 2. Small load 3. Unload bonds stretch return to initial d F F Linearelastic Elastic means reversible! d Fundamentals of Materials Science Non-Linearelastic 14

Plastic Deformation of Metals 1. Initial 2. Small load bonds stretch & planes shear 3. Unload planes still sheared δplastic δelastic + plastic F F Plastic means permanent! linear elastic δplastic εelastic Fundamentals of Materials Science d 15

Strain Testing • Tensile specimen • Tensile test machine Often 12. 8 mm x 60 mm Adapted from Fig. 7. 2, Callister & Rethwisch 3 e. extensometer specimen gauge length • Other types: -compression: brittle materials (e. g. , concrete) -torsion: cylindrical tubes, shafts. Fundamentals of Materials Science 16

Linear Elasticity • Modulus of Elasticity, E: Units: E [GPa] or [psi] (also known as Young's modulus) • Hooke's Law: σ = E ε s Axial strain E Linearelastic Fundamentals of Materials Science e Width strain 17

Example: Hooke’s Law • Hooke's Law: σ=Eε (linear elastic behavior) Copper sample (305 mm long) is pulled in tension with stress of 276 MPa. If deformation is elastic, what is elongation? For Cu (polycrystalline), E = 110 GPa. Axial strain Width strain Hooke’s law involves axial (parallel to applied tensile load) elastic deformation. Fundamentals of Materials Science 18

Comparison of Elastic Moduli Silicon (single xtal) 120 -190 (depends on crystallographic direction) Glass (pyrex) 70 Si. C (fused or sintered) 207 -483 Graphite (molded) ~12 High modulus C-fiber 400 Carbon Nanotubes ~1000 Normalize by density, 20 x steel wire. strength normalized by density is 56 x wire. Fundamentals of Materials Science 19

Young’s Modulus, E Metals Alloys Graphite Ceramics Polymers Semicond Composites /fibers E(GPa) Based on data in Table B 2, Callister 6 e. Composite data based on reinforced epoxy with 60 vol% of aligned carbon (CFRE), aramid (AFRE), or glass (GFRE) fibers. Fundamentals of Materials Science 20

Yield Stress, σY • Stress where noticeable plastic deformation occurs. When εp = 0. 002 For metals agreed upon 0. 2% tensile stress, σ σY P Elastic recovery • P is the proportional limit where deviation from linear behavior occurs. Strain off-set method for Yield Stress • Start at 0. 2% strain (for most metals). • Draw line parallel to elastic curve (slope of E). • σY is value of stress where dotted line crosses stress-strain curve (dashed line). Eng. strain, ε εp = 0. 002 Fundamentals of Materials Science Note: for 2 in. sample ε = 0. 002 = Δz/z Δz = 0. 004 in 21

Compare Yield Stress, σYS Room T values Based on data in Table B 4, Callister 6 e. a = annealed hr = hot rolled ag = aged cd = cold drawn cw = cold worked qt = quenched & tempered Fundamentals of Materials Science 22

(Ultimate) Tensile Strength, σTS • Maximum possible engineering stress in tension. TS F = fracture or ultimate strength engineering stress y Typical response of a metal strain engineering strain Neck – acts as stress concentrator • Metals: occurs when necking starts. • Ceramics: occurs when crack propagation starts. • Polymers: occurs when polymer backbones are aligned and about to break. Fundamentals of Materials Science 23

Compare Tensile Strength, σTS Metals/ Alloys Tensile strength, TS (MPa) 5000 3000 2000 1000 300 200 100 40 30 20 Graphite/ Ceramics/ Semicond Polymers Composites/ fibers C fibers Aramid fib E-glass fib Steel (4140) qt W (pure) Ti (5 Al-2. 5 Sn)aa Steel (4140)cw Cu (71500) hr Steel (1020) Al (6061) ag Ti (pure) a Ta (pure) Al (6061) a AFRE(|| fiber) GFRE(|| fiber) CFRE(|| fiber) Diamond Si nitride Al oxide Si crystal <100> Glass-soda Concrete Graphite Nylon 6, 6 PC PET PVC PP HDPE wood(|| fiber) GFRE( fiber) CFRE( fiber) AFRE( fiber) LDPE Based on data in Table B 4, Callister & Rethwisch 3 e. 10 wood ( 1 Room T values Fundamentals of Materials Science fiber) 24

Example for Metals: Determine E, YS, and TS Stress-Strain for Brass • Young’s Modulus, E (bond stretch) • 0 ffset Yield-Stress, YS (plastic deformation) • Max. Load from Tensile Strength TS • Gage is 250 mm (10 in) in length and 12. 8 mm (0. 505 in) in diameter. • Subject to tensile stress of 345 MPa (50 ksi) • Change in length at Point A, Δl = εl 0 = (0. 06)250 mm = 15 mm Fundamentals of Materials Science 25

Temperature matters (see Failure) Most metals are ductile at RT and above, but can become brittle at low T bcc Fe cup-and-cone fracture in Al Fundamentals of Materials Science brittle fracture in mild steel 26

Stress-Strain in Polymers brittle polymer plastic elastomer elastic moduli – less than for metals Adapted from Fig. 7. 22, Callister & Rethwisch 3 e. • Fracture strengths of polymers ~ 10% of those for metals. • Deformation strains for polymers > 1000%. – for most metals, deformation strains < 10%. Fundamentals of Materials Science 27

Hardness • Resistance to permanently indenting the surface. • Large hardness means: --resistance to plastic deformation or cracking in compression. --better wear properties. Adapted from Fig. 7. 18. Fundamentals of Materials Science 28

Hardness: Measurement • Rockwell – No major sample damage – Each scale runs to 130 (useful in range 20 -100). – 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 Fundamentals of Materials Science 29

Hardness: Measurement Fundamentals of Materials Science 30

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. Fundamentals of Materials Science 31