LECTURE 6 Mechanical Properties

8/2/2019 LECTURE 6 Mechanical Properties

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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?

LECTURE 6

Mechanical Properties


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Elastic means reversible!

Elastic Deformation

1. Initial 2. Small load 3. Unload

F

bonds

stretch

return toinitial

F Linear-elastic

Non-Linear-elastic


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Plastic means permanent!

Plastic Deformation (Metals)

F

linearelastic

linearelastic

plastic

1. Initial 2. Small load 3. Unload

planesstillsheared

F

elastic + plastic

bondsstretch& planesshear

plastic


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Stress has units:

N/m2 or lbf/in2

Engineering Stress

Shearstress, :

Area, A

Ft

Ft

Fs

F

F

Fs

=Fs

Ao

Tensile stress, :

original area

before loading

Area, A

Ft

Ft

= FtAo

2f

2mNor

inlb=


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Simple tension: cable

Note: = M/AcRhere.

Common States of Stress

Ao = cross sectional

area (when unloaded)

FF

o

FA

o

Fs

AM

M Ao

2R

FsAc

Torsion (a form of shear): drive shaftSki lift (photo courtesyP.M. Anderson)


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

oF

A

Simple compression:

Note: compressivestructure member

( < 0 here).(photo courtesy P.M. Anderson)

OTHER COMMON STRESS STATES (1)

Ao

Balanced Rock, ArchesNational Park


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Bi-axial tension: Hydrostatic compression:

Pressurized tank

< 0h

(photo courtesyP.M. Anderson)

(photo courtesy

P.M. Anderson)

OTHER COMMON STRESS STATES (2)

Fish under water

z > 0

> 0


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Tensile strain: Lateral strain:

Shearstrain:

Strain is always

dimensionless.

Engineering Strain

90

90 -y

x = x/y= tan

LoL

L

wo

Adapted from Fig. 6.1 (a) and (c), Callister 7e.

/2

L/2

Lowo


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Stress-Strain Testing

Typical tensile testmachine

Adapted from Fig. 6.3, Callister 7e. (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.)

specimenextensometer

Typical tensilespecimen

Adapted from

Fig. 6.2,Callister 7e.

gauge

length


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Linear Elastic Properties

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

Hooke's Law:

= E

Linear-elastic

EF

Fsimpletensiontest


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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: ~ 0.33

ceramics: ~ 0.25

polymers: ~ 0.40


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Mechanical Properties

Slope of stress strain plot (which isproportional to the elastic modulus) depends

on bond strength of metal

Adapted from Fig. 6.7,

Callister 7e.


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MetalsAlloys

GraphiteCeramics

Semicond

PolymersComposites

/fibers

E(GPa)

Based on data in Table B2,

Callister 7e.

Composite data based on

reinforced epoxy with 60 vol%

of aligned

carbon (CFRE),

aramid (AFRE), or

glass (GFRE)fibers.

Youngs Moduli: Comparison

109 Pa

0.2

8

0.6

1

Magnesium,

Aluminum

Platinum

Silver, Gold

Tantalum

Zinc, Ti

Steel, Ni

Molybdenum

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

Si carbide

Diamond

PTFE

HDPE

LDPE

PP

Polyester

PSPET

CFRE( fibers) *

GFRE( fibers)*

GFRE(|| fibers)*

AFRE(|| fibers)*

CFRE(|| fibers)*


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

Plastic (Permanent) Deformation

Simple tension test:

engineering stress,

engineering strain,

Elastic+Plasticat larger stress

permanent (plastic)after load is removed

p

plastic strain

Elasticinitially

Adapted from Fig. 6.10 (a),

Callister 7e.


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Stress at which noticeable plastic deformation hasoccurred.

when p = 0.002

Yield Strength, y

y= yield strength

Note: for 2 inch sample

= 0.002 = z/z

z= 0.004 in

Adapted from Fig. 6.10 (a),

Callister 7e.

tensile stress,

engineering strain,

y

p = 0.002


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Room Tvalues

Based on data in Table B4,

Callister 7e.

a = annealed

hr = hot rolled

ag = aged

cd = cold drawn

cw = cold worked

qt = quenched & tempered

Yield Strength : ComparisonGraphite/Ceramics/Semicond

Metals/

Alloys

Composites/

fibersPolymers

Yieldstrength,

y(MPa)

PVC

H

ardtomeasure

,

sinceintension,fractureusuallyoccursbeforeyield.

Nylon 6,6

LDPE

70

20

40

6050

100

10

30

200

300

400

500600700

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

Hardtomeasure,

inceramicmatrix

andepoxymatrixcomposites,since

intension,frac

tureusuallyoccursbefore

yield.

HDPEPP

humid

dry

PCPET


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Tensile Strength, TS

Metals: occurs when noticeable necking starts.

Polymers: occurs when polymer backbone chains arealigned and about to break.


Callister 7e.

y

strain

Typical response of a metal

F= fracture or

ultimate

strength

Neck acts

as stress

concentratorengineering

TS

stress

engineering strain

Maximum stress on engineering stress-strain curve.


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Tensile Strength : Comparison

Si crystal

Graphite/Ceramics/

Semicond

Metals/

Alloys

Composites/

fibers

Polymers

Tensilestrength,

TS

(MPa)

PVC

Nylon 6,6

10

100

200

300

1000

Al (6061) a

Al (6061) ag

Cu (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

2000

3000

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

Room Temp. valuesBased on data in Table B4,

Callister 7e.

a = annealed

hr = hot rolled

ag = aged

cd = cold drawncw = cold worked

qt = quenched & tempered

AFRE, GFRE, & CFRE =

aramid, glass, & carbon

fiber-reinforced epoxy

composites, with 60 vol%

fibers.


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Plastic tensile strain at failure:


Callister 7e.

Ductility

Another ductility measure: 100xA

AARA%

o

fo-

=

x 100L

LLEL%o

of

Engineering tensile strain,

Engineering

tensile

stress,

smaller %EL

larger %ELLf

AoAfLo


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

curve.

Toughness

Brittle fracture: elastic energy

Ductile fracture: elastic + plastic energy

very small toughness(unreinforced polymers)

Engineering tensile strain,

Engineering

tensile

stress,

small toughness (ceramics)

large toughness (metals)


Callister 7e.


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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


Callister 7e.

yyr2

1U

y dU

r 0


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Elastic Strain Recovery


Callister 7e.


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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 sizeof indent afterremoving load

dDSmaller indentsmean largerhardness.

increasing hardness

mostplastics

brassesAl alloys

easy to machinesteels file hard

cuttingtools

nitridedsteels diamond


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Hardness: Measurement

Rockwell

No major sample damage

Each scale runs to 130 but only 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


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Hardness: MeasurementTable 6.5


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True Stress & Strain

Note: S.A. changes when sample stretched

True stress

True Strain

iT AF

oiT ln

1ln

1

T

T


Callister 7e.


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Hardening

Curve fit to the stress-strain response:

T K Tn

true stress (F/A) true strain: ln(L/Lo)

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

An increase in ydue to plastic deformation.

large hardening

small hardeningy0

y1


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Design uncertainties mean we do not push the limit.

Factor of safety, N

N

y

working

Often Nis

between

1.2 and 4

Example: Calculate a diameter, d, to ensure that yield doesnot occur in the 1045 carbon steel rod below. Use a

factor of safety of 5.

Design or Safety Factors

4000220

2 /d

N,

5

N

y

working

1045 plain

carbon steel:

y= 310 MPaTS = 565 MPa

F= 220,000N

d

Lo

d= 0.067 m = 6.7 cm


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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 (EorG).

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.

LECTURE 6 Mechanical Properties

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