CHE 3166: HANDOUT 3

Stresses, Deformation and Fracture

LEARNING OBJECTIVES: Part I

• Stress and Strain

• Elastic Deformation

• Plastic Deformation

• Ductility

• Toughness

Stress and Stress Types

Stress (s): Force (F) / Cross-sectional Area (A)

s= F / A

States / Types of Stress

Tension

Compression

Shear / Torsion

Engineering Stress and Strain

s0=Ft

Aooriginal area

before loading

Area, A

Ft

FtUnits of Stress:

N/m2 or lb/in2

Engineering stress, s0:

e =d

Lo

δ = (L-L0)

Engineering strain, e : d/2

dL/2

Lowo

True Stress and Strain

True stress, sT:

Load F divided by the

instantaneous cross-sectional

area Ai (after deformation)i

TA

F=s

True strain, eT:

0

lnl

liT =e

Elastic Deformation

1. Initial 2. Small load 3. Unload

F

d

bonds

stretch

return to

Initial

F

d

Linear-

elastic

Non-Linear-

elastic

Elastic Deformation

is reversible

Plastic Deformation

Plastic Deformation

is NOT reversible

1. Initial 2. Small load 3. Unload

planes still sheared

F

delastic + plastic

bonds stretch & planes shear

dplastic

F

d

linear elastic

linear elastic

dplastic

Linear Elastic Behaviour

When stress (s) is proportional to strain (e)s

Linear-

elastic

E

e

F

Fsimple tension test

Hooke's Law:

s = E e

E: Slope, a Constant, also known as:

• Modulus of Elasticity or Young’s Modulus

• Stiffness of the materials

• Materials resistance to elastic deformation

Young’s Modulus (E) of Different Material Types

0.2

8

0.6

1

Magnesium,

Aluminum

Platinum

Silver, Gold

Tantalum

Zinc, Ti

Steel, Ni

Molybdenum

G raphite

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

10 0

200

600800

10 001200

400

Tin

Cu alloys

Tungsten

<100>

<111>

Si carbide

Diamond

PTF E

HDP E

LDPE

PP

Polyester

PSPET

CFRE( fibers) *

G FRE( fibers)*

G FRE(|| fibers)*

A FRE(|| fibers)*

CFRE(|| fibers)*

Metals

Alloys Ceramics PolymersComposites

/fibers

E

(GPa,

109 Pa)

Young’s

Modulus (E):

Metals:

40 – 400 GPa

Polymers:

0.2 – 4GPa

Ceramics:

80 – 1200 GPa

1GPa = 103 MPa = 109 N/m2

Effect of Temperature on Young’s Modulus (E)

E decreases with increase in temperature

Yield strength

• A plastically deformed structure, will experience permanent change in shape and may not be intended for good functionality.

• Stress level at which plastic deformations begins is known as yielding.

• It is the point of linearity of stress-straincurve, shown as proportional limit.

Yield Strength of Different Material Types

Ceramics Metals/ Alloys

Composites/fibre

Polymers

Yie

ld s

tre

ng

th,s

y(M

Pa)

PVC

Ha

rd to

me

asu

re,

sin

ce

in t

en

sio

n, fr

actu

re u

su

ally

occu

rs b

efo

re y

ield

.

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

Ha

rd to

me

asu

re,

in c

era

mic

ma

trix

an

d e

po

xy m

atr

ix c

om

po

sites, sin

ce

in te

nsio

n, fr

actu

re u

su

ally

occu

rs b

efo

re y

ield

.

HDPEPP

humid

dry

PC

PET

¨

Room Temp. Data

Based on data in

Table B4,

Callister 7e.

a = annealed

hr = hot rolled

ag = aged

cd = cold drawn

cw = cold worked

qt = quenched &

tempered

Tensile Strength (TS) or

Ultimate Tensile Strength (UTS)

sy

strain

Typical response of a metal

F = fracture or

ultimate

strength

Neck – acts

as stress

concentrator

Eng

inee

ring

TS

str

ess

Engineering strain

TS / UTS: Maximum stress on an engineering stress-strain curve

Adapted from Fig. 6.11,

Callister 7e.

• Metals: when noticeable necking starts.

Tensile Strength of Different Material Types

Room Temp. Data

Si crystal<100>

Ceramics/ Metals/Alloys

Composites/fibres

Polymers

Ten

sile

str

en

gth

, T

S(M

Pa)

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) 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

a = annealed

hr = hot rolled

ag = aged

cd = cold drawn

cw = cold worked

qt = quenched & tempered

COMPOSITES:

AFRE = aramid-fiber reinforced

GFRE = glass-fiber reinforced

CFRE = carbon-fiber reinforced

(each with 60 vol% fibers).

Ductility• Ductility is a measure of degree of plastic

deformation that has been sustained at fracture.

• A material that experiences very little or no plastic deformation upon fracture is termed brittle.

• Ductility may be expressed quantitatively as percent elongation or percent reduction in area.

• %EL is the percentage of plastic strain at fracture.

Ductility

Plastic tensile strain at failurex 100

L

LLEL%

o

of-

=

Lf

AoAf

Lo

Engineering tensile strain, e

Engineering

tensile

stress, s

smaller %EL

larger %EL

• Another ductility measure: 100xA

AARA%

o

fo-

=

Brittle fracture: elastic energy

Ductile fracture: elastic + plastic energy

Very low toughness:unreinforced polymers

Engineering tensile strain, e

Engineering

tensile

stress, s

Low toughness: ceramics

High toughness: metals

Toughness / Fracture Toughness

• Energy to break a unit volume of material

• Approximated by the area under the stress-strain curve

Why are metals/alloys

and reinforced plastic

so popular as structural

materials?

Mechanical Properties and Testing

LEARNING OBJECTIVES: Part II

Material’s response to:

• Excessive Loading: Tensile Test

• Localized Loading: Hardness Test

• Sudden Intense Loading: Impact Test

• Loading at High Temperatures: Creep Test

• Cyclic Loading: Fatigue Test

Excessive loading: Tensile Test

Tensile Test

• Tests are performed as per the ASTM, BS or Australian Standards.

• A tensile test measures the resistance of a material to a static or slowly applied force.

• A machined specimen is placed in the testing machine and load is applied.

• A strain gage or extensometer is used to measure elongation.

• The stress obtained at the highest applied force is the Tensile Strength.

Test provides data: strength,stiffness,ductility

Tensile Test

Other Tensile Test Data

• Yield Strength: The stress at which a prescribed amount of plastic deformation (commonly, 0.2%) is produced.

• Elongation: The extent to which the specimen stretches before fracture.

Cup and Cone Fracture

Fracture: Different Types of Material

Brittle fracture

Cup and cone fracture

a) Highly ductile

b) Moderately ductile

c) Brittle

Tensile Properties: Effect of Temperature