Tensile strain - Spada UNS - Universitas Sebelas Maret

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Mohammad Masykuri - Universitas Sebelas Maret

SIFAT MEKANIK POLIMER

(Mechanical Properties of Polymers)

Dr. Mohammad Masykuri, M.Si.

PROGRAM STUDI PENDIDIKAN KIMIA FAKULTAS KEGURUAN DAN ILMU PENDIDIKAN

UNIVERSITAS SEBELAS MARET Email: [email protected]

Website: https://mmasykuri.wordpress.com

Kimia Polimer

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Mechanical Properties

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?

Stress: Tegangan Strain: Regangan

Toughness: Kekakuan

Ductility: Kegetasan

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Elastic Deformation

Elastic means reversible!

2. Small load

F d

bonds stretch

1. Initial 3. Unload

return to initial

F

d

Linear- elastic

Non-Linear-

elastic

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Plastic Deformation

Plastic means permanent!

F

d

linear

elastic linear

elastic

d plastic

1. Initial 2. Small load 3. Unload planes still

sheared

F

d elastic + plastic bonds

stretch

& planes shear

d plastic

(5)

 Stress has units:

N/m2 or lbf /in2

Engineering Stress

• Shear stress, t:

Area, A

_o

Ft Ft

Fs F

F Fs t = F s

A o

• Tensile stress, s:

original area before loading

s = F t

A o 2

f

m 2

or N in

= lb

Area, A

_o

Ft

(6)

• Tensile strain: • Lateral strain:

Strain is always dimensionless.

Engineering Strain

• Shear strain:

q

90º

90º - q

y

x g = x/y = tan q e = d

L o

d/2

L o

w o

e L = -d L w o

d L /2

(7)

Stress-Strain Testing

• Typical tensile test machine

Adapted from Fig. 7.3, Callister & Rethwisch 3e. (Fig. 7.3 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.)

specimen extensometer

• Typical tensile specimen

Adapted from Fig. 7.2, Callister &

Rethwisch 3e.

gauge

length

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Linear Elastic Properties

• Modulus of Elasticity, E:

(also known as Young's modulus)

• Hooke's Law:

s = E e

s

Linear- elastic

E

e

F

simple F

tension

test

(9)

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)

e L

e -n

n = - e e L

metals: n ~ 0.33

ceramics: n ~ 0.25

polymers: n ~ 0.40

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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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Metals Alloys

Graphite Ceramics Semicond

Polymers Composites /fibers

E(GPa)

Based on data in Table B.2, Callister & Rethwisch 3e.

Composite data based on reinforced epoxy with 60 vol%

of aligned

carbon (CFRE), aramid (AFRE), or glass (GFRE) fibers.

Young’s Moduli: Comparison

10

⁹

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 nitride Al 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

PETPS

CFRE( fibers) * GFRE( fibers)*

GFRE(|| fibers)*

AFRE(|| fibers)*

CFRE(|| fibers)*

(12)

• Simple tension:

d = FL o EA o

d L = - n Fw o EA o

• Material, geometric, and loading parameters all contribute to deflection.

• Larger elastic moduli minimize elastic deflection.

Useful Linear Elastic Relationships

F

Ao d/2

d L /2

L

_o

w o

• Simple torsion:

a = 2ML o

 r o 4 G

M = moment

a = angle of twist

2r

_o

L

_o

(13)

(at lower temperatures, i.e. T < T

melt

/3)

Plastic (Permanent) Deformation

• Simple tension test:

engineering stress, s

engineering strain, e Elastic+Plastic

at larger stress

e p

plastic strain

Elastic initially

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

permanent (plastic)

after load is removed

(14)

• Stress at which noticeable plastic deformation has occurred.

when e p = 0.002

Yield Strength, s y

s y = yield strength

Note: for 2 inch sample e = 0.002 = z/z

 z = 0.004 in

Adapted from Fig. 7.10 (a),

tensile stress, s

engineering strain, e

s y

e p = 0.002

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Room temperature values

Based on data in Table B.4, Callister & Rethwisch 3e.

a = annealed hr = hot rolled ag = aged

cd = cold drawn cw = cold worked

qt = quenched & tempered

Yield Strength : Comparison

Graphite/

Ceramics/

Semicond Metals/

Alloys

Composites/

fibers Polymers

Y ie ld s tr en gt h, s y (M P a)

PVC

H ar d to m ea su re

, since in tension, fracture usually occurs before yield.

Nylon 6,6

LDPE

70

20 40 60 50 100

10 30 200 300 400 500 600 700 1000 2000

Tin (pure) Al (6061)a Al (6061)ag

Cu (71500)hr Ta (pure)Ti (pure) aSteel (1020)hr Steel (1020)cd Steel (4140)a Steel (4140)qt

Ti (5Al-2.5Sn) a W (pure) Mo (pure) Cu (71500)cw

H ar d to m ea su re ,

in ceramic matrix and epoxy matrix composites, since in tension, fracture usually occurs before yield.

HDPE PP

humid dry

PC PET

¨

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Tensile Strength, TS

• Metals: occurs when noticeable necking starts.

• Polymers: occurs when polymer backbone chains are

s

_y

strain

Typical response of a metal

F = fracture or ultimate strength Neck – acts as stress concentrator

e ng in ee rin g

TS

s tr e ss

engineering strain

• Maximum stress on engineering stress-strain curve.

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Tensile Strength: Comparison

Si crystal

<100>

Graphite/

Ceramics/

Semicond Metals/

Alloys

Composites/

fibers Polymers

T en si le st re ng th , T S (M P a)

PVC Nylon 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) a W (pure) Cu (71500)cw

LDPE PP

PC PET

20 30 40 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 fibers Aramid fib

Based on data in Table B4, Callister & Rethwisch 3e.

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.

Room temperature

values

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• Plastic tensile strain at failure:

Ductility

• Another ductility measure: x 100

A A RA A

%

o f o -

=

x 100 L

L EL L

%

o o f -

=

L

_f

A

_o

A

_f

L

_o

Engineering tensile strain, e Engineering

tensile stress, s

smaller %EL

larger %EL

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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, e Engineering

tensile stress, s

small toughness (ceramics)

large toughness (metals)

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Resilience, U r

• 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,

y y

r 2

U @ 1 s e

 e s e

= y d U r

0

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Elastic Strain Recovery

S tr es s

Strain

3. Reapply load 2. Unload

D

Elastic strain recovery 1. Load

s

_y_o

s

_y_i

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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.

Flexural Tests – Measurement of Elastic Modulus

L/2 F L/2

d = midpoint deflection cross section

R b

d

rect. circ.

• Determine elastic modulus according to:

F x

linear-elastic behavior d

F

slope = d

(rect. cross section)

(circ. cross section)

3 3

4bd L E F

= d

4 3

12 R L E F

d 

=

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

Flexural Tests – Measurement of Flexural Strength

L/2 F L/2

d = 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 nitride Si carbide Al oxide

glass (soda-lime)

250-1000 100-820 275-700

69

304 345 393 69 Material s fs (MPa) E(GPa)

(rect. cross section)

(circ. cross section)

2 2

3 bd

L F f

fs = s

R 3

L F f

fs = 

s

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Mechanical Properties of Polymers – Stress-Strain Behavior

• Fracture strengths of polymers ~ 10% of those for metals

• Deformation strains for polymers > 1000%

– for most metals, deformation strains < 10%

brittle polymer

plastic

elastomer elastic moduli

– less than for metals

Adapted from Fig. 7.22, Callister & Rethwisch 3e.

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• Decreasing T...

-- increases E -- increases TS -- decreases %EL

• Increasing

strain rate...

-- same effects

as decreasing T.

Adapted from Fig. 7.24, Callister & Rethwisch 3e. (Fig. 7.24 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.)

Influence of T and Strain Rate on Thermoplastics

20 40 60 80

0 0 0.1 0.2 0.3

4°C

20°C 40°C

60°C to 1.3

s (MPa)

e

Plots for

semicrystalline

PMMA (Plexiglas)

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• Representative T g values (C):

PE (low density) PE (high density) PVC

PS PC

- 110 - 90 + 87 +100 +150

Selected values from Table 11.3, Callister

& Rethwisch 3e.

• Stress relaxation test:

-- strain in tension to e o

and hold.

-- observe decrease in stress with time.

• Relaxation modulus:

Time-Dependent Deformation

time strain tensile test

e

_o

s(t)

• There is a l arge decrease in E r for T > T g . (amorphous

polystyrene)

Adapted from Fig.

7.28, Callister &

Rethwisch 3e. (Fig.

7.28 is from A.V.

Tobolsky, Properties and Structures of Polymers, John Wiley and Sons, Inc., 1960.)

10

³

10

¹

10

^-1

10

^-3

10

⁵

60 100 140 180

rigid solid (small relax)

transition region

T(°C) T

_g

E

_r

(10 s) in MPa

viscous liquid (large relax)

o r

t t

E e

= s ( ) )

(

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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 size of indent after removing load

d

D Smaller indents

mean larger hardness.

increasing hardness

most

plastics brasses

Al alloys easy to machine

steels file hard cutting

tools nitrided

steels 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: Measurement

Table 7.5

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True Stress & Strain

Note: S.A. changes when sample stretched

• True stress

• True strain

i

T = F A

s e T = ln   i  o  e s T = = ln s   1 1   e e  

T

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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 s

_y

.

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