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 do dislocations cause permanent deformation? What materials are most resistant to permanent deformation?

1

• Toughness and ductility: What are they and how do we measure them?

CHAPTER 7: MECHANICAL PROPERTIES

• Ceramic Materials: What special provisions/tests aremade for ceramic materials?

F

bonds stretch

return to initial

2

1. Initial 2. Small load 3. Unload

Elastic means reversible!

F

Linear- elastic

Non-Linear-elastic

ELASTIC DEFORMATION

3

1. Initial 2. Small load 3. Unload

Plastic means permanent!

F

linear elastic

linear elastic

plastic

planes still sheared

F

elastic + plastic

bonds stretch & planes shear

plastic

PLASTIC DEFORMATION (METALS)

4

• Tensile stress, : • Shear stress, :

Area, A

Ft

Ft

FtAo

original area before loading

Area, A

Ft

Ft

Fs

F

FFs

FsAo

Stress has units:N/m2 or lb/in2

ENGINEERING STRESS

8

• Tensile strain: • Lateral strain:

• Shear strain:/2

/2

/2 -

/2

/2

/2L/2L/2

Lowo

LoL L

wo

= tan Strain is alwaysdimensionless.

ENGINEERING STRAIN

• Typical tensile specimen

9

• Other types of tests: --compression: brittle materials (e.g., concrete) --torsion: cylindrical tubes, shafts.

gauge length

(portion of sample with reduced cross section)=

• Typical tensile test machine

load cell

extensometer specimen

moving cross head

Adapted from Fig. 6.2, Callister 6e.

Adapted from Fig. 6.3, Callister 6e. (Fig. 6.3 is taken from H.W. Hayden, W.G. Moffatt, and J. Wulff, The Structure and Properties of Materials, Vol. III, Mechanical Behavior, p. 2, John Wiley and Sons, New York, 1965.)

STRESS-STRAIN TESTING

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

10

• Hooke's Law: = E

• Poisson's ratio, :

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

L

L

1-

F

Fsimple tension test

Linear- elastic

1E

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

LINEAR ELASTIC PROPERTIES

• Elastic Shear modulus, G:

12

1G

= G

• Elastic Bulk modulus, K:

P= -KVVo

PV

1-K Vo

• Special relations for isotropic materials:

PP P

M

M

G

E2(1 )

K E

3(1 2)

simpletorsiontest

pressuretest: Init.vol =Vo. Vol chg. = V

OTHER ELASTIC PROPERTIES

130.2

8

0.61

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

46

10

20

406080100

200

6008001000

1200

400

Tin

Cu alloys

Tungsten

<100><111>

Si carbide

Diamond

PTF E

HDPE

LDPE

PP

PolyesterPSPET

CFRE( fibers)*

GFRE( fibers)*

GFRE(|| fibers)*

AFRE(|| fibers)*

CFRE(|| fibers)*

MetalsAlloys

GraphiteCeramicsSemicond

Polymers Composites/fibers

E(GPa)

Eceramics > Emetals >> Epolymers

109 Pa

YOUNG’S MODULI: COMPARISON

15

• Simple tension test:

(at lower temperatures, T < Tmelt/3)

tensile stress,

engineering strain,

Elastic initially

Elastic+Plastic at larger stress

permanent (plastic) after load is removed

pplastic strain

PLASTIC (PERMANENT) DEFORMATION

16

• Stress at which noticeable plastic deformation has occurred.

when p = 0.002 tensile stress,

engineering strain,

y

p = 0.002

YIELD STRENGTH, y

17

Graphite/ Ceramics/ Semicond

Metals/ Alloys

Composites/ fibersPolymers

Yiel

d st

reng

th,

y (M

Pa)

PVC

Hard

to m

easu

re,

since

in te

nsion

, fra

ctur

e us

ually

occ

urs b

efor

e yie

ld.

Nylon 6,6

LDPE

70

20

40

6050

100

10

30

200300400500600700

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

Hard

to m

easu

re,

in c

eram

ic m

atrix

and

epo

xy m

atrix

com

posit

es, s

ince

in te

nsion

, fra

ctur

e us

ually

occ

urs b

efor

e yie

ld.

HDPEPP

humid

dryPCPET

¨Room T values

y(ceramics) >>y(metals) >> y(polymers)

Based on data in Table B4,Callister 6e.a = annealedhr = hot rolledag = agedcd = cold drawncw = cold workedqt = quenched & tempered

YIELD STRENGTH: COMPARISON

18

• Maximum possible engineering stress in tension.

• Metals: occurs when noticeable necking starts.• Ceramics: occurs when crack propagation starts.• Polymers: occurs when polymer backbones are aligned and about to break.

Adapted from Fig. 6.11, Callister 6e.

TENSILE STRENGTH, TS

strain

eng

inee

ring

stre

ssTS

Typical response of a metal

19

Room T valuesSi crystal

<100>

Graphite/ Ceramics/ Semicond

Metals/ Alloys

Composites/ fibersPolymers

Tens

ile s

treng

th, T

S (M

Pa)

PVCNylon 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

PPPC PET

20

3040

200030005000

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 fibC fibersAramid fib TS(ceram)

~TS(met) ~ TS(comp) >> TS(poly)

Based on data in Table B4,Callister 6e.a = annealedhr = hot rolledag = agedcd = cold drawncw = cold workedqt = quenched & temperedAFRE, GFRE, & CFRE =aramid, glass, & carbonfiber-reinforced epoxycomposites, with 60 vol%fibers.

TENSILE STRENGTH: COMPARISON

• Plastic tensile strain at failure:

20

Engineering tensile strain,

Engineering tensile stress,

smaller %EL (brittle if %EL<5%)

larger %EL (ductile if %EL>5%)

• Another ductility measure: %AR

Ao A fAo

x100

• Note: %AR and %EL are often comparable. --Reason: crystal slip does not change material volume. --%AR > %EL possible if internal voids form in neck.

Lo LfAo Af

%EL

L f LoLo

x100

Adapted from Fig. 6.13, Callister 6e.

DUCTILITY, %EL

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

21

smaller toughness- unreinforced polymers

Engineering tensile strain,

Engineering tensile stress,

smaller toughness (ceramics)larger toughness (metals, PMCs)

TOUGHNESS

• An increase in y due to plastic deformation.

22

• Curve fit to the stress-strain response:

large hardening

small hardeningun

load

relo

ad

y 0y 1

T C T n“true” stress (F/A) “true” strain: ln(L/Lo)

hardening exponent: n=0.15 (some steels) to n=0.5 (some copper)

HARDENING

23

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

FL/2 L/2

= midpoint deflection

cross sectionR

bd

rect. circ.

• Determine elastic modulus according to:

E

F

L3

4bd3 F

L3

12R4rect. cross

section

circ. cross

section

Fx

linear-elastic behavior

F

slope =

Adapted from Fig. 12.29, Callister 6e.

MEASURING ELASTIC MODULUS

24

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

L/2 L/2cross section

Rb

d

rect. circ.location of max tension

• Flexural strength:

rect. fs m

fail 1.5FmaxLbd2

FmaxLR3

xFFmax

max

• Typ. values:Material fs(MPa) E(GPa)Si nitrideSi carbideAl oxideglass (soda)

700-1000550-860275-550

69

30043039069

Adapted from Fig. 12.29, Callister 6e.

Data from Table 12.5, Callister 6e.

MEASURING STRENGTH

25

• Compare to responses of other polymers: --brittle response (aligned, cross linked & networked case) --plastic response (semi-crystalline case)

Stress-strain curves adapted from Fig. 15.1, Callister 6e. Inset figures along elastomer curve (green) adapted from Fig. 15.14, Callister 6e. (Fig. 15.14 is from Z.D. Jastrzebski, The Nature and Properties of Engineering Materials, 3rd ed., John Wiley and Sons, 1987.)

TENSILE RESPONSE: ELASTOMER CASE

initial: amorphous chains are kinked, heavily cross-linked.

final: chains are straight,

still cross-linked

0

20

40

60

0 2 4 6

(MPa)

8

x

x

x

elastomer

plastic failure

brittle failure

Deformation is reversible!

26

• Decreasing T... --increases E --increases TS --decreases %EL

• Increasing strain rate... --same effects as decreasing T.

Adapted from Fig. 15.3, Callister 6e. (Fig. 15.3 is from T.S. Carswell and J.K. Nason, 'Effect of Environmental Conditions on the Mechanical Properties of Organic Plastics", Symposium on Plastics, American Society for Testing and Materials, Philadelphia, PA, 1944.)

20

40

60

80

00 0.1 0.2 0.3

4°C

20°C

40°C

60°C to 1.3

(MPa)

Data for the semicrystalline polymer: PMMA (Plexiglas)

T AND STRAIN RATE: THERMOPLASTICS

27

• Stress relaxation test:

Er(t)

(t)o

--strain to and hold.--observe decrease in stress with time.

• Relaxation modulus:

• Data: Large drop in Er for T > Tg.

(amorphouspolystyrene)

• Sample Tg(C) values:PE (low Mw)PE (high Mw)PVCPSPC

-110- 90+ 87+100+150

103

101

10-1

10-3

105

60 100 140 180

rigid solid (small relax)

viscous liquid (large relax)

transition region

T(°C)Tg

Er(10s) in MPa

Adapted from Fig. 15.7, Callister 6e. (Fig. 15.7 is from A.V. Tobolsky, Properties and Structures of Polymers, John Wiley and Sons, Inc., 1960.)

Selected values from Table 15.2, Callister 6e.

TIME DEPENDENT DEFORMATION

time

straintensile test

ot( )

• Resistance to permanently indenting the surface.• Large hardness means: --resistance to plastic deformation or cracking in compression. --better wear properties.

28

e.g., 10mm sphere

apply known force (1 to 1000g) measure size

of indent after removing load

dDSmaller indents mean larger hardness.

increasing hardness

most plastics

brasses Al alloys

easy to machine steels file hard

cutting tools

nitrided steels diamond

Adapted from Fig. 6.18, Callister 6e. (Fig. 6.18 is adapted from G.F. Kinney, Engineering Propertiesand Applications of Plastics, p. 202, John Wiley and Sons, 1957.)

HARDNESS

• Design uncertainties mean we do not push the limit.• Factor of safety, N

29

working yN

Often N isbetween1.2 and 4

• Ex: 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: y=310MPa TS=565MPa

F = 220,000N

d

Lo working yN

220,000N d2 /4

5

DESIGN OR SAFETY FACTORS

25

Thermal ExpansionMaterials change size when temperature is changed

)(α initialfinalinitial

initialfinal TT

linear coefficient ofthermal expansion (1/K or 1/°C)

Tinitial

Tfinal

initial

final

Tfinal > Tinitial

26

Atomic Perspective: Thermal Expansion

Asymmetric curve: -- increase temperature, -- increase in interatomic separation -- thermal expansion

Symmetric curve: -- increase temperature, -- no increase in interatomic separation -- no thermal expansion

27

Coefficient of Thermal Expansion: Comparison

• Q: Why does

generally decrease with increasing bond energy?

Polypropylene 145-180 Polyethylene 106-198 Polystyrene 90-150 Teflon 126-216

• Polymers

• CeramicsMagnesia (MgO) 13.5Alumina (Al2O3) 7.6Soda-lime glass 9Silica (cryst. SiO2) 0.4

• MetalsAluminum 23.6Steel 12 Tungsten 4.5 Gold 14.2

(10-6/C)at room T

Material

Polymers have larger values because of weak secondary bonds

incr

easi

ng

28

• Occur due to: -- restrained thermal expansion/contraction -- temperature gradients that lead to differential

dimensional changes

Thermal Stresses

E(T0 Tf ) ETThermal stress

• 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 y.

30

• Toughness: The energy needed to break a unit volume of material.• Ductility: The plastic strain at failure.

Note: For materials selection cases related to mechanical behavior, see slides 20-4 to 20-10.

SUMMARY