Ch-9 [Compatibility Mode]

7/28/2019 Ch-9 [Compatibility Mode]

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Chapter: 9

Mechanical Properties


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ISSUES TO ADDRESS...ISSUES TO ADDRESS...ISSUES TO ADDRESS...ISSUES TO ADDRESS... Stress and strain: What are they and why are

they used instead of load and deformation?

MECHANICAL PROPERTIES

Elastic behavior: When loads are small, how muchdeformation occurs? What materials deform least?

Plastic behavior: At what point do dislocations

cause permanent deformation? What materials are

most resistant to permanent deformation?

Toughness and ductility: What are they and how

do we measure them?


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Introduction

To know the characteristics of material

To design the member To avoid the failure

To concern to variety of parties

To study distributions

To study the requirement


4/43

bondsstretch

return toinitial

1. Initial 2. Small load 3. UnloadELASTIC DEFORMATION

F

Elastic means reversible!

F

Linear-

elasticNon-Linear-elastic


5/43

1. Initial 2. Small load 3. Unload

planes

stillsheared

bondsstretch

& planesshear

PLASTIC DEFORMATION (METALS)

Plastic means permanent!

F

linearelastic

linearelastic

plastic

F

elastic + plastic plastic


6/43

Tensile stress, : Shear stress, :

Area, A

Ft

Area, A

Ft

Fs

F

ENGINEERING STRESS

Ft =

FtA

ooriginal areabefore loading

FtF

Fs

=Fs

AoStress has units:

N/m2 or lb/in2


7/43

Simple tension: cable

=F

Ao = cross sectionalArea (when unloaded)

FF

COMMON STATES OF STRESS

o

Simple shear: drive shaft

o =

Fs

A

Note: = M/AcR here.

Ski lift (photo courtesy P.M. Anderson)

M

M Ao

2R

Fs

Ac


8/43

Simple compression:

Ao

OTHER COMMON STRESS STATES (1)

Canyon Bridge, Los Alamos, NM

Balanced Rock, ArchesNational Park o =

F

A

Note: compressive

structure member( < 0 here).

(photo courtesy P.M. Anderson)

(photo courtesy P.M. Anderson)


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Bi-axial tension: Hydrostatic compression:

OTHER COMMON STRESS STATES (2)

Fish under waterPressurized tank

z > 0

> 0

< 0h

(photo courtesy

P.M. Anderson)

(photo courtesy

P.M. Anderson)


10/43

Tensile strain: Lateral strain:

/2

/2

Lowo =

Lo L =

L

wo

ENGINEERING STRAIN

Shear strain:/2

/2

/2 -

/2

LL

= tan Strain is always

dimensionless.


11/43

Typical tensile specimen Typical tensile

test machineload cell

extensometerspecimen

Adapted from Fig. 6.2,

Callister 6e.

STRESS-STRAIN TESTING

Other types of tests:--compression: brittle

materials (e.g., concrete)

--torsion: cylindrical tubes,

shafts.

gaugelength

(portion of sample withreduced cross section)

=

moving cross head

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.)


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Shear test

Shear and flexural test are performed bythree-point or four point beam

tested is subjected to a concentrated load

The experiment may be conducted on UTM

and Tensometer using suitable attachments,or on a machine specially meant for it.

M/I=E/R=f/y =VQ/bIzz


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Torsion tests

T

Ability of material to resist twisting

moment is determine by a torsion test

G/L=T/J=/r

= 16T/d3


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Geometric Considerations of the Stress

State


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Geometric Consideration of the Stress

State

CED

2

2'

)

2

21('

SinCosSinSin

BE

BEBCSinBE

CosCos

BE

BCCosBCBE

====

+===

AB


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

Hooke's Law: = E

Poisson's ratio, : L

F

Linear-elastic

1

E

LINEAR ELASTIC PROPERTIES

metals: ~ 0.33

ceramics: ~0.25

polymers: ~0.40

= L

1-

Fsimpletension

testUnits:

E: [GPa] or [psi]

: dimensionless


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Non-linear and Interatomic relation ME

temp


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Force versus interatomic separation

Fc or Ft=-F=dP/dr where P= - A/rn+B/rm

Hence A,B, m and n are constant in whichm>n

E-dF/dr=d2P/dr2


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Linear Strain and shear strain

,2

1)

1(

2

1)

2

1)(

2

1(

451'1)1(

=

=

AB

BB

AB

BB

BD

CosBB

BD

BB

BD

BDDBd

B1 B C1C

q

B

( )

)1(2

1

.221

+=

+=

+=

==

GE

Eqd

E

q

E

qd

Gqd

AD

q


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ANELASTICITY

Time dependent elastic behavior is knownas anelasticity

Time dependent microscopic and atomstic

processes that are attendant to thedeformation

For metal normally small and is often

neglected however for some polymericmaterials its magnitude is significant


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Elastic Shear

modulus, G:

1

G

= G

M

M

simple

torsion

test

OTHER ELASTIC PROPERTIES

modulus, K:

P= -KVVo

V

1-K

Vo

Special relations for isotropic materials:

P P

G =

E

2(1+ ) K =

E

3(1 2)

pressure

test: Init.

vol =Vo.Vol chg.

= V


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Platinum

Silver, Gold

Tantalum

Zinc, Ti

Steel, Ni

Molybdenum

Si crystal

Si nitrideAl oxide Carbon fibers only

Aramid fibers only

80100

200

600

80010001200

400

Cu alloys

Tungsten

Si carbide

Diamond

AFRE fibers *

CFRE(|| fibers)*

Metals

Alloys

Graphite

Ceramics

Semicond

PolymersComposites

/fibers

E(GPa)

Eceramics

> Emetals>> Epolymers

YOUNGS MODULI: COMPARISON

0.2

8

0.6

1

Magnesium,

um num

Graphite

-

Concrete

PC

Wood( grain)

AFRE( fibers)*

CFRE*

GFRE*

Glass fibers only

Epoxy only

0.4

0.8

2

4

6

10

20

40

60

Tin

PTFE

HDPE

LDPE

PP

Polyester

PSPET

CFRE( fibers)*

GFRE( fibers)*

GFRE(|| fibers)*

109 Pa

,

Callister 6e.Composite data based on

reinforced epoxy with 60 vol%

of aligned

carbon (CFRE),

aramid (AFRE), or

glass (GFRE)

fibers.


27/43

Simple tension:

= FLoEA

o

L

= FwoEA

o

/2

F

Ao

Simple torsion:

M=moment =angle of twist

=2MLoro

4G

USEFUL LINEAR ELASTIC RELATIONS

/2

L/2

L/2

Lowo

2ro

Lo

Material, geometric, and loading parameters all

contribute to deflection.

Larger elastic moduli minimize elastic deflection.


28/43

Simple tension test:

(at lower temperatures, T < Tmelt/3)

tensile stress,

Elastic+Plastic

at larger stress

PLASTIC (PERMANENT) DEFORMATION

engineering strain,

initiallypermanent (plastic)after load is removed

p

plastic strain


29/43

Stress at which noticeableplastic deformation has

occurred.

when p = 0.002tensile stress,

y

YIELD STRENGTH, y

engineering strain,

p = 0.002


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Graphite/Ceramics/Semicond

Metals/Alloys

Composites/fibers

Polymers

y(MPa

)

cursbeforeyield.

400

500600700

1000

2000

Steel (1020)cdSteel (4140)a

Steel (4140)qt

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

Mo (pure)Cu (71500)cw

,

composites,si

nce

rsbeforeyield.

y(ceramics)

>>y(metals)

>> y(polymers)

YIELD STRENGTH: COMPARISON

Yieldstrength,

PVC

Hardtomeasu

re

sinceintensio

n,

fractureusually

oc

Nylon 6,6

LDPE

70

20

40

60

50

100

10

30

200

Tin (pure)

Al (6061)a

Al (6061)ag

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

Hardtomeas

ur

inceramicmatrixandepoxyma

trix

intension,

fractureusuallyo

cc

HDPEPP

humid

dry

PC

PET

oom va ues

Based on data in Table B4,

Callister 6e.

a = annealed

hr = hot rolled

ag = aged

cd = cold drawncw = cold worked

qt = quenched & tempered


31/43

Maximum possible engineering stress in tension.


Callister 6e.

TENSILE STRENGTH, TS

eering

ess

TS

Metals: occurs when noticeable necking starts.

Ceramics: occurs when crack propagation starts.

Polymers: occurs when polymer backbones are

aligned and about to break.

strain

engin

st

Typical response of a metal


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Graphite/Ceramics/Semicond

Metals/Alloys

Composites/fibers

Polymers

TS(MP

a)

300

1000

Al (6061)ag

Cu (71500)hr

Ti (pure)a

Steel (1020)

Steel (4140)a

Steel (4140)qt

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

Cu (71500)cw

2000

3000

5000

Al oxide

Diamond

Si nitride

GFRE(|| fiber)CFRE(|| fiber)

AFRE(|| fiber)

E-glass fib

C fibersAramid fib TS(ceram)

~TS(met)

~ TS(comp)

>> TS(poly)

TENSILE STRENGTH: COMPARISON

Si crystal

Tensilestrength

,

PVC

Nylon 6,6

10

100 Al (6061)a

a pure

LDPE

PP

PC PET

20

3040

Graphite

Concrete

Glass-soda

HDPE

wood( fiber)

wood(|| fiber)

1

GFRE( fiber)CFRE( fiber)AFRE( fiber)

Based on data in Table B4,

Callister 6e.

a = annealed

hr = hot rolled

ag = aged

cd = cold drawn

cw = cold workedqt = quenched & tempered

AFRE, GFRE, & CFRE =

aramid, glass, & carbon

fiber-reinforced epoxy

composites, with 60 vol%

fibers.


33/43

Plastic tensile strain at failure:

Engineeringtensilestress,

smaller %EL

(brittle if %EL5%)

Another ductility measure:

%AR =

Ao A f

Aox100

Note: %AR and %EL are often comparable.--Reason: crystal slip does not change material volume.

--%AR > %EL possible if internal voids form in neck.


Callister 6e.


34/43

Resilience

Capacity of material to absorbenergy when it is deformed

elastically and then, upon

un oa ng, to ave t s energy

recovered.


35/43

Energy to break a unit volume of material

Approximate by the area under the stress-strain

curve.

Engineeringtensile

smaller toughness (ceramics)

larger toughness

TOUGHNESS

smaller toughness-unreinforcedpolymers

Engineering tensile strain,

, ,


36/43

Resistance to permanently indenting the surface.

Large hardness means:--resistance to plastic deformation or cracking in

compression.--better wear properties.

e.g.,apply known force(1 to 1000g)

measure sizeof indent after

HARDNESS

mm sp ere

removing load

dDSmaller indentsmean largerhardness.

increasing hardness

mostplastics

brassesAl alloys

easy to machinesteels file hard

cuttingtools

nitridedsteels diamond

Adapted from Fig. 6.18, Callister 6e. (Fig. 6.18 is adapted from G.F. Kinney, Engineering Properties

and Applications of Plastics, p. 202, John Wiley and Sons, 1957.)


37/43

An increase in y due to plastic deformation.

large hardening

small hardening

ad

ad

y0

y1

HARDENING

Curve fit to the stress-strain response:

u

nl

re

lo

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)


38/43

Design uncertainties mean we do not push the limit.

Factor of safety, N

working=

y

N

Often N is

between

1.2 and 4

Ex: Calculate a diameter, d, to ensure that yield does

DESIGN OR SAFETY FACTORS

.

factor of safety of 5.

1045 plaincarbon steel:

y=310MPa

TS=565MPa

F = 220,000N

d

Loworking =

y

N

220,000N d2/ 4

5


39/43

Stress and strain: These are size-independent

measures of load and displacement, respectively.

Elastic behavior: This reversible behavior oftenshows a linear relation between stress and strain.

To minimize deformation, select a material with a

large elastic modulus (E or G).

SUMMARY

Plastic behavior: This permanent deformationbehavior occurs when the tensile (or compressive)

uniaxial stress reaches y.

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 22-4 to 22-10.


40/43

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

cross section

Rd

Adapted from Fig.

12.29, Callister 6e.

MEASURING ELASTIC MODULUS

9

deflection

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 =


41/43

3-point bend test to measure room T strength.

FL/2 L/2

cross section

Rb

d

rect. circ.

Adapted from Fig.

12.29, Callister 6e.

MEASURING STRENGTH

10

Flexural strength:

rect.

fs = mfail =

1.5FmaxL

bd

2=

FmaxL

R

3

xF

Fmax

max

Typ. values:Material fs(MPa) E(GPa)

Si nitride

Si carbideAl oxide

glass (soda)

700-1000

550-860275-550

69

300

430390

69Data from Table 12.5, Callister 6e.


42/43

Elevated Temperature Tensile Test (T > 0.4 Tmelt).

creep test

x

slope = ss = steady-state creep rate.

MEASURING ELEVATED T RESPONSE

11

Generally,

time

ssceramics < ss

metals


43/43

Ceramic materials have mostly covalent & someionic bonding.

Structures are based on:

--charge neutrality--maximizing # of nearest oppositely charged neighbors.

Structures may be predicted based on:

SUMMARY

12

-- .

Defects--must preserve charge neutrality

--have a concentration that varies exponentially w/T.

Room T mechanical response is elastic, but fracture

brittle, with negligible ductility. Elevated T creep properties are generally superior to

those of metals (and polymers).

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