Mechanical Session1_Dr Willy

8/2/2019 Mechanical Session1_Dr Willy

1/19

2/14/201

Testing Machine User Workshop

Session 1

Mechanical Properties of Materials

2

Elastic means reversible!

Elastic Deformation1. Initial 2. Small load 3. Unload

F

d

bonds

stretch

return to

initial

F

d

Linear-

elastic

Non-Linear-

elastic


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Plastic means permanent!

Plastic Deformation (Metals)

F

dlinearelastic linearelasticdplastic

1. Initial 2. Small load 3. Unload

planes

still

sheared

F

delastic + plastic

bondsstretch

& planes

shear

dplastic

4

Stress has units:

N/m2 or lbf/in2

Engineering Stress Shear stress, t:

Area,A

Ft

Ft

Fs

F

F

Fs

t =Fs

Ao

Tensile stress, s:

original area

before loading

Area,A

Ft

Ft

s= FtAo

2

f

2m

Nor

in

lb=


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Simple tension: cable

Note: t = M/AcR here.

Common States of Stress

Ao= cross sectional

area (when unloaded)

FF

o

s= FA

o

t =FsA

ss

M

M Ao

2R

Fs

Ac

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

6

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

o

s= FA

Simple compression:

Note: compressive

structure member

(s < 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

s < 0h

(photo courtesy

P.M. Anderson)

(photo courtesy

P.M. Anderson)

OTHER COMMON STRESS STATES (2)

Fish under water

sz > 0sq > 0

8

Tensile strain: Lateral strain:

Shear strain:

Strain is always

dimensionless.

Engineering Strain

q

90

90 - qy

x qg = x/y= tan

e = dL o

-deL = L

wo

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

d/2

dL

/2

L owo


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Stress-Strain Testing Typical tensile test

machine

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 tensile

specimen

Adapted from

Fig. 6.2,

Callister 7e.

gauge

length

10

Linear Elastic Properties Modulus of Elasticity, E:

(also known as Young's modulus)

Hooke's Law:

s = Ee s

Linear-

elastic

Ee

F

Fsimpletensiontest


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Poisson's ratio, n Poisson's ratio, n:

Units:E: [GPa] or [psi]

n: dimensionless

n > 0.50 density increases

n < 0.50 density decreases(voids form)

eL

e-n

en=- L

emetals: n ~ 0.33

ceramics: n~ 0.25

polymers: n ~ 0.40

12

Mechanical Properties Slope of stress strain plot (which is

proportional to the elastic modulus)

depends on bond strength of metal

Adapted from Fig. 6.7,

Callister 7e.


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Elastic Shear

modulus, G:

tG gt = Gg

Other Elastic Properties

simpletorsion

test

M

M

Special relations for isotropic materials:

2(1+n)E

G =3(1-2n)

EK =

Elastic Bulk

modulus, K:

pressure

test: Init.

vol =Vo.Vol chg.

= V

P

P PP = - K

VVo

PV

K Vo

14

Metals

Alloys

Graphite

Ceramics

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

2 0

4 0

6 08 0

10 0

2 00

6 008 00

10 001200

4 00

Tin

Cu alloys

Tungsten

Si carbide

Diamond

PTF E

HDP E

LDPE

PP

Polyester

PSPET

CFRE( fibers) *

GFRE( fibers)*

GFRE(|| fibers)*

AFRE(|| fibers)*

CFRE(|| fibers)*


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Simple tension:

d=FL oEAo dL =-nFwoEAo

Material, geometric, and loading parameters all

contribute to deflection.

Larger elastic moduli minimize elastic deflection.

Useful Linear Elastic Relationships

FAo d/2

dL

/2

Lo

wo

Simple torsion:

a=2MLopro4GM = moment

a= angle of twist

2ro

Lo

16

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

Simple tension test:

engineering stress, s

engineering strain, e

Elastic+Plastic

at larger stress

permanent (plastic)

after load is removed

epplastic strain

Elastic

initially

Adapted from Fig. 6.10 (a),

Callister 7e.


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Stress at which noticeableplastic deformation has

occurred.when ep = 0.002

Yield Strength, sy

sy= yield strength

Note: for 2 inch sample

e = 0.002 = z/z

z = 0.004 in

Adapted from Fig. 6.10 (a),

Callister 7e.

tensile stress, s

engineering strain, e

sy

ep= 0.002

18

Room Tvalues


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,

sy(MPa)

PVC

Hardtomeasure

,

sinceintension,fractureusuallyo

ccursbeforeyield.

Nylon 6,6

LDPE

70

20

40

6050

100

10

30

2 00

3 00

4 00

5 006 007 00

10 00

2 0 00

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,

inceramicmatrixandepoxymatr

ixcomposites,since

intension,fractureusuallyoc

cursbeforeyield.

HDPEPP

humid

dry

PC

PET


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19

Tensile Strength, TS

Metals: occurs when noticeable necking starts.

Polymers: occurs when polymer backbonechains are

aligned and about to break.

Adapted from Fig. 6.11,Callister 7e.

sy

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.

20

Tensile Strength : Comparison

Si crystal

Graphite/

Ceramics/

Semicond

Metals/

Alloys

Composites/

fibersPolymers

Tensile

strength

,TS

(MPa)

PVCNylon 6,6

10

100

200

300

1000

Al (6061) a

Al (6061) ag

Cu (71500) hr

Ta (pure)Ti (pure) a

Steel (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. values


Callister 7e.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.


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Plastic tensile strain at failure:


Callister 7e.

Ductility

Another ductility measure: 100xA

AARA%

o

fo-

=

x 100L

LLEL%

oof -=

Engineering tensile strain, e

Engineering

tensile

stress, s

smaller %EL

larger %ELLf

AoAf

Lo

22

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, e

Engineeringtensile

stress, ssmall toughness (ceramics)

large toughness (metals)


Callister 7e.


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23

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.

yyr21U es@

e

es= y dUr0

24

Elastic Strain Recovery


Callister 7e.


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25

True Stress & StrainNote: S.A. changes when sample stretched

True stress

True Strain

iT AF=s

oiT ln=e

e+=e

e+s=s

1ln

1

T

T


Callister 7e.

26

Hardening

Curve fit to the stress-strain response:

sT

= K eT n

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 sydue to plastic deformation.

s

e

large hardeningsmall hardeningsy

0sy

1


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27

Design uncertainties mean we do not push the limit.

Factor of safety, N

N

y

working

s=s

Often N isbetween

1.2 and 4

Example: 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.

Design or Safety Factors

40002202 /d

N,

p5

N

y

working

s=s 1045 plain

carbon steel:

sy = 310 MPaTS = 565 MPa

F= 220,000N

d

L o

d= 0.067 m = 6.7 cm

Includes Glossary of Terms-Force, load

- Displacement/ elongation

- Stress

- Strain

- How to calculate stress, strain, elongation

- Gauge Length

- Units of measurement

- Stress vs Strain Curve

- Force vs Displacement Curve

- Modulus of Elasticity or Youngs Modulus

- Yield Point, Upper & Lower Yield Point, Yield

Strength

- Maximum Force, Stress

- Break Point

- Elongation At Break Point


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Specimen Must follow the standards

Crucial especially needed to calculate the

stress and strain needed for stress vs strain

plot.

Specimen size and dimension affecting the

calculation of the stress.

o

s= FA


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Typical tensile

specimen

Adapted from

Fig. 6.2,

Callister 7e.

gauge

length


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Load Cell and extensometer

Strain gauges


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Case study

38

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 (Eor 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 sy.

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Mechanical Session1_Dr Willy