Chapter 7:機械性質(Mechanical Properties) Tensile & Hardness Testing; Macroscopic Behavior; Elastic Deformation; Elastic Modulus; Proportional Limit; Poisson's Ratio; Plastic deformation; Yielding and Yielding Strength; Tensile Strength; Fracture Strength; Ductility; Resilience; Toughness Property Variability; Design Safety Factors. 1 1

7.2 應力和應變(Stress and Strain)的觀念 c07f01 c07f01

拉力試驗 c07f03 c07f03

Common States of Stress • Simple tension: cable A o = cross sectional area (when unloaded) F o s = F A s • Torsion (a form of shear): drive shaft M A o 2R F s c o t = F s A Note: R × t ×Ac= M here. 4 4

OTHER COMMON STRESS STATES (i) • Simple compression: A o Balanced Rock, Arches National Park (photo courtesy P.M. Anderson) Canyon Bridge, Los Alamos, NM o s = F A Note: compressive structure member (s < 0 here). (photo courtesy P.M. Anderson) 5 5

OTHER COMMON STRESS STATES (ii) • Bi-axial tension: • Hydrostatic compression: Fish under water Pressurized tank (photo courtesy P.M. Anderson) (photo courtesy P.M. Anderson) s z > 0 q s < 0 h 6 6

Engineering Stress s = F A F t s = A m N or in lb • Tensile stress, s: original area before loading s = F t A o 2 f m N or in lb Area, Ao • Shear stress, t: Area, Ao F t s = A o  Stress has units: N/m2 or lbf /in2 7 7

Engineering Strain L w e = d L - d e = w q g = Dx/y = tan • Tensile strain: d /2 L o w • Lateral strain: e = d L o - d e L = w o d L /2 • Shear strain: q 90º 90º - q y x g = Dx/y = tan Strain is always dimensionless. Adapted from Fig. 7.1 (a) and (c), Callister & Rethwisch 3e. 8 8

c07f04 c07f04

彈性變形(Elastic Deformation) 7.3 應力-應變行為(Stress-Strain behavior) c07f05 c07f05

Elastic Deformation d F F d 1. Initial 2. Small load 3. Unload bonds stretch 3. Unload return to initial F Linear- elastic Elastic means reversible! Non-Linear- elastic d 11 11

Linear Elastic Properties • Modulus of Elasticity, E: (also known as Young's modulus) • Hooke's Law: s = E e s Linear- elastic E e F simple tension test 12 12

Plastic Deformation (Metals) 1. Initial 2. Small load 3. Unload planes still sheared F d elastic + plastic bonds stretch & planes shear plastic F d linear elastic plastic Plastic means permanent! 13 13

c07f06 c07f06

c07f07 c07f07

Slope of stress strain plot (which is proportional to the elastic modulus) depends on bond strength of metal Adapted from Fig. 7.7, Callister & Rethwisch 3e. 16 16

c07f08 c07f08

c07tf01 c07tf01

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 3e. Composite data based on reinforced epoxy with 60 vol% of aligned carbon (CFRE), aramid (AFRE), or glass (GFRE) fibers. 109 Pa 19 19

7.4 滯彈性(Anelasticity) c07f26 c07f26

7.5 材料的彈性性質(Poission’s Ratio) c07f09 c07f09

Poisson's Ratio, n eL e -n e n = - • Poisson's ratio, n: Units: metals: n ~ 0.33 ceramics: n ~ 0.25 polymers: n ~ 0.40 Units: E: [GPa] or [psi] n: Dimensionless  > 0.50 density increases  < 0.50 density decreases (voids form) 22 22

Other Elastic Properties simple torsion test M t G g • Elastic Shear modulus, G: t = G g • Elastic Bulk modulus, K: pressure test: Init. vol =Vo. Vol chg. = DV P P = - K D V o • Special relations for isotropic materials: 2(1 + n) E G = 3(1 - 2n) K 23 23

c07prob c07prob

c07f10ab 7.6 拉力性質(塑性變形) Mechanical Properties: Macroscopic Behavior; Elastic Deformation; Elastic Modulus; Proportional Limit; Poisson's Ratio; Plastic deformation; Yielding and Yielding Strength; Tensile Strength; Fracture Strength; Ductility; Resilience; Toughness. c07f10ab

Plastic (Permanent) Deformation (at lower temperatures, i.e. T < Tmelt/3) • 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. 7.10 (a), Callister & Rethwisch 3e. 26 26

Yielding and Yield Strength, y • Stress at which noticeable plastic deformation has occurred. when ep = 0.002 tensile stress, s engineering strain, e sy p = 0.002 y = yield strength Note: for 2 inch sample  = 0.002 = z/z  z = 0.004 in Adapted from Fig. 7.10 (a), Callister & Rethwisch 3e. 27 27

c07f11 c07f11

Tensile Strength, TS TS engineering stress strain engineering strain • Maximum stress on engineering stress-strain curve. y strain Typical response of a metal F = fracture or ultimate strength Neck – acts as stress concentrator engineering TS stress engineering strain Adapted from Fig. 7.11, Callister & Rethwisch 3e. • Metals: occurs when noticeable necking starts. • Polymers: occurs when polymer backbone chains are aligned and about to break. 29 29

c07f33 c07f33

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 3e. a = annealed hr = hot rolled ag = aged cd = cold drawn cw = cold worked qt = quenched & tempered 31 31

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 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. 32 32

Ductility(延性) c07f13 c07f13

Ductility x 100 L EL % - = • Plastic tensile strain at failure: Lf Ao Adapted from Fig. 7.13, Callister & Rethwisch 3e. 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 - = 34 34

c07f14 c07f14

c07tf02 c07tf02

Resilience(彈性能, 回彈性), Ur c07f15 c07f15

Resilience, Ur 2 1 U e s @ Ability of a material to store energy Energy stored best in elastic region If we assume a linear stress-strain curve this simplifies to y r 2 1 U e s @ Adapted from Fig. 7.15, Callister & Rethwisch 3e. 38 38

Toughness(韌性) • 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. 7.13, Callister & Rethwisch 3e. Brittle fracture: elastic energy Ductile fracture: elastic + plastic energy 39 39

7.7 真應力與真應變 c07f16 c07f16

c07tf04 c07tf04

7.8 塑性變形期間之彈性回復 c07f17 c07f17

Elastic Strain Recovery syi D syo Elastic strain recovery 2. Unload Stress 1. Load 3. Reapply load Strain Adapted from Fig. 7.17, Callister & Rethwisch 3e. 43 43

7.10 Fexural Strength of Ceramics) c07f18 c07f18

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 45 45

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. 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: F x linear-elastic behavior d slope = (rect. cross section) (circ. cross section) 46 46

Flexural Tests – Measurement of Flexural Strength • 3-point bend test to measure room-T flexural strength. F L/2 d = midpoint deflection cross section R b d rect. circ. location of max tension Adapted from Fig. 7.18, Callister & Rethwisch 3e. • Flexural strength: • Typical values: Data from Table 7.2, Callister & Rethwisch 3e. Si nitride Si carbide Al oxide glass (soda-lime) 250-1000 100-820 275-700 69 304 345 393 Material s fs (MPa) E(GPa) (rect. cross section) (circ. cross section) 47 47

c07f19 c07f19

c07f20 c07f20

c07f21 c07f21

7.16 硬度(Hardness)與硬度試驗 c07tf05 c07tf05

c07f30 c07f30

c07f31 c07f31

c07tf06b c07tf06b

c07tf07 c07tf07

7.19 Property Variability and Design Safety Factors Elastic modulus is material property Critical properties depend largely on sample flaws (defects, etc.). Large sample to sample variability. Statistics Mean Standard Deviation All samples have same value Because of large variability must have safety margin in engineering specifications 56 where n is the number of data points 56

c07f32 c07f32

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. 58 58