chapter 7: 機械性質 ( mechanical properties)

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Chapter 7: 機械性質 (Mechanical Propertie

s) • Tensile & Hardness Testing;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.

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7.2 應力和應變 (Stress and Strain) 的觀念

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拉力試驗

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• Simple tension: cable

Note: R × ×Ac= M here.

Common States of Stress

o F

A

o

FsA

M

M Ao

2R

FsA

c

• Torsion (a form of shear): drive shaft

Ao = cross sectional

area (when unloaded)

FF

5

(photo courtesy P.M. Anderson)Canyon Bridge, Los Alamos, NM

o F

A

• Simple compression:

Note: compressivestructure member( < 0 here).(photo courtesy P.M. Anderson)

OTHER COMMON STRESS STATES (i)

Ao

Balanced Rock, Arches National Park

6

• Bi-axial tension: • Hydrostatic compression:

Pressurized tank

< 0h

(photo courtesyP.M. Anderson)

(photo courtesyP.M. Anderson)

OTHER COMMON STRESS STATES (ii)

Fish under water

z > 0

> 0

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Stress has units: N/m2 or lbf /in2

Engineering Stress• Shear stress, :

Area, Ao

Ft

Ft

Fs

F

F

Fs

= Fs

Ao

• Tensile stress, :

original area before loading

=Ft

Ao2f

2m

Nor

in

lb=

Area, Ao

Ft

Ft

8

• Tensile strain: • Lateral strain:

Strain is alwaysdimensionless.

Engineering Strain

• Shear strain:

90º

90º - y

x = x/y = tan

Lo

Adapted from Fig. 7.1 (a) and (c), Callister & Rethwisch 3e.

/2

Lowo

L L

wo

L/2

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

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Elastic means reversible!

Elastic Deformation2. Small load

F

bonds stretch

1. Initial 3. Unload

return to initial

F

Linear- elastic

Non-Linear-elastic

12

Linear Elastic Properties• Modulus of Elasticity, E: (also known as Young's modulus)

• Hooke's Law:

= E

Linear- elastic

E

F

Fsimple tension test

13

Plastic means permanent!

Plastic Deformation (Metals)

F

linear elastic

linear elastic

plastic

1. Initial 2. Small load 3. Unload

planes still sheared

F

elastic + plastic

bonds stretch & planes shear

plastic

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• 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.

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MetalsAlloys

GraphiteCeramicsSemicond

PolymersComposites

/fibers

E(GPa)

Based on data in Table B.2,Callister & Rethwisch 3e. Composite data based onreinforced epoxy with 60 vol%of alignedcarbon (CFRE),aramid (AFRE), orglass (GFRE)fibers.

Young’s Moduli: Comparison

109 Pa

0.2

8

0.6

1

Magnesium,Aluminum

Platinum

Silver, Gold

Tantalum

Zinc, Ti

Steel, NiMolybdenum

Graphite

Si crystal

Glass -soda

Concrete

Si nitrideAl oxide

PC

Wood( grain)

AFRE( fibers) *

CFRE*

GFRE*

Glass fibers only

Carbon fibers only

Aramid fibers only

Epoxy only

0.4

0.8

2

4

6

10

20

40

6080

100

200

600800

10001200

400

Tin

Cu alloys

Tungsten

<100>

<111>

Si carbide

Diamond

PTFE

HDPE

LDPE

PP

Polyester

PSPET

CFRE( fibers) *

GFRE( fibers)*

GFRE(|| fibers)*

AFRE(|| fibers)*

CFRE(|| fibers)*

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7.4 滯彈性 (Anelasticity)

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7.5 材料的彈性性質 (Poission’s Ratio)

22

Poisson's Ratio, • Poisson's ratio, :

Units:E: [GPa] or [psi]: Dimensionless

> 0.50 density increases

< 0.50 density decreases (voids form)

L

-

L

metals: ~ 0.33ceramics: ~ 0.25polymers: ~ 0.40

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• Elastic Shear modulus, G:

G

= G

Other Elastic Properties

simpletorsiontest

M

M

• Special relations for isotropic materials:

2(1 )EG

3(1 2)

EK

• Elastic Bulk modulus, K:

pressuretest: Init.

vol =Vo. Vol chg. = V

P

P PP = -K

VVo

P

V

K Vo

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b

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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.

7.6 拉力性質 ( 塑性變形 )

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(at lower temperatures, i.e. T < Tmelt/3)Plastic (Permanent) Deformation

• Simple tension test:

engineering stress,

engineering strain,

Elastic+Plastic at larger stress

p

plastic strain

Elastic initially

Adapted from Fig. 7.10 (a),Callister & Rethwisch 3e.

permanent (plastic) after load is removed

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• Stress at which noticeable plastic deformation has occurred.

when p = 0.002

Yielding and Yield Strength, y

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.

tensile stress,

engineering strain,

y

p = 0.002

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Tensile Strength, TS

• Metals: occurs when noticeable necking starts.• Polymers: occurs when polymer backbone chains are aligned and about to break.

Adapted from Fig. 7.11, Callister & Rethwisch 3e.

y

strain

Typical response of a metal

F = fracture or

ultimate

strength

Neck – acts as stress concentrator

eng

inee

ring

TS s

tres

s

engineering strain

• Maximum stress on engineering stress-strain curve.

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Room temperature values

Based on data in Table B.4,Callister & Rethwisch 3e. a = annealedhr = hot rolledag = agedcd = cold drawncw = cold workedqt = quenched & tempered

Yield Strength : ComparisonGraphite/ Ceramics/ Semicond

Metals/ Alloys

Composites/ fibers

Polymers

Yie

ld s

tren

gth,

y

(MP

a)

PVC

Har

d to

mea

sure

,

sin

ce in

te

nsi

on

, fr

act

ure

usu

ally

occ

urs

be

fore

yie

ld.

Nylon 6,6

LDPE

70

20

40

6050

100

10

30

200

300

400500600700

1000

2000

Tin (pure)

Al (6061) a

Al (6061) ag

Cu (71500) hrTa (pure)Ti (pure) aSteel (1020) hr

Steel (1020) cdSteel (4140) a

Steel (4140) qt

Ti (5Al-2.5Sn) aW (pure)

Mo (pure)Cu (71500) cw

Har

d to

mea

sure

, in

ce

ram

ic m

atr

ix a

nd

ep

oxy

ma

trix

co

mp

osi

tes,

sin

cein

te

nsi

on

, fr

act

ure

usu

ally

occ

urs

be

fore

yie

ld.

HDPEPP

humid

dry

PC

PET

¨

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Tensile Strength: Comparison

Si crystal<100>

Graphite/ Ceramics/ Semicond

Metals/ Alloys

Composites/ fibers

Polymers

Ten

sile

stre

ngth

, TS

(M

Pa)

PVC

Nylon 6,6

10

100

200300

1000

Al (6061) a

Al (6061) agCu (71500) hr

Ta (pure)Ti (pure) aSteel (1020)

Steel (4140) a

Steel (4140) qt

Ti (5Al-2.5Sn) aW (pure)

Cu (71500) cw

LDPE

PP

PC PET

20

3040

20003000

5000

Graphite

Al oxide

Concrete

Diamond

Glass-soda

Si nitride

HDPE

wood ( fiber)

wood(|| fiber)

1

GFRE(|| fiber)

GFRE( fiber)

CFRE(|| fiber)

CFRE( fiber)

AFRE(|| fiber)

AFRE( fiber)

E-glass fib

C fibersAramid fib

Based on data in Table B4,Callister & Rethwisch 3e. a = annealedhr = hot rolledag = agedcd = cold drawncw = cold workedqt = quenched & temperedAFRE, GFRE, & CFRE =aramid, glass, & carbonfiber-reinforced epoxycomposites, with 60 vol%fibers.

Room temperature values

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Ductility(延性 )

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• Plastic tensile strain at failure:

Ductility

• Another ductility measure: 100xA

AARA%

o

fo -=

x 100L

LLEL%

o

of

Lf

Ao AfLo

Adapted from Fig. 7.13, Callister & Rethwisch 3e.

Engineering tensile strain,

Engineering tensile stress,

smaller %EL

larger %EL

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Resilience( 彈性能 , 回彈性 ), Ur

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Resilience, Ur

• Ability of a material to store energy – Energy stored best in elastic region

If we assume a linear stress-strain curve this simplifies to

Adapted from Fig. 7.15, Callister & Rethwisch 3e.

yyr2

1U

y dUr 0

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• Energy to break a unit volume of material• Approximate by the area under the stress-strain curve.

Toughness( 韌性 )

Brittle fracture: elastic energyDuctile fracture: elastic + plastic energy

Adapted from Fig. 7.13, Callister & Rethwisch 3e.

very small toughness (unreinforced polymers)

Engineering tensile strain,

Engineering tensile stress,

small toughness (ceramics)

large toughness (metals)

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7.7 真應力與真應變

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7.8 塑性變形期間之彈性回復

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Elastic Strain Recovery

Adapted from Fig. 7.17, Callister & Rethwisch 3e.

Str

ess

Strain

3. Reapplyload

2. Unload

D

Elastic strainrecovery

1. Load

yo

yi

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7.10 Fexural Strength of Ceramics)

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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

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• Room T behavior is usually elastic, with brittle failure.• 3-Point Bend Testing often used. -- tensile tests are difficult for brittle materials.

Adapted from Fig. 7.18, Callister & Rethwisch 3e.

Flexural Tests – Measurement of Elastic Modulus

FL/2 L/2

= midpoint deflection

cross section

R

b

d

rect. circ.

• Determine elastic modulus according to:

Fx

linear-elastic behavior

F

slope =

3

3

4bd

LFE

(rect. cross section)

4

3

12 R

LFE

(circ. cross section)

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• 3-point bend test to measure room-T flexural strength.

Adapted from Fig. 7.18, Callister & Rethwisch 3e.

Flexural Tests – Measurement of Flexural Strength

FL/2 L/2

= midpoint deflection

cross section

R

b

d

rect. circ.

location of max tension

• Flexural strength: • Typical values:

Data from Table 7.2, Callister & Rethwisch 3e.

Si nitrideSi carbideAl oxideglass (soda-lime)

250-1000100-820275-700

69

30434539369

Material fs (MPa) E(GPa)

22

3

bd

LFffs (rect. cross section)

(circ. cross section)3R

LFffs

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7.16 硬度 (Hardness) 與硬度試驗

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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

21

2

1

n

xxs i

n

n

xx n

n

where n is the number of data points

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• 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).

• Toughness: The energy needed to break a unit volume of material.

• Ductility: The plastic strain at failure.

Summary

• Plastic behavior: This permanent deformation behavior occurs when the tensile (or compressive) uniaxial stress reaches y.