Chapter 8 -

ME 254: Materials Engineering

Chapter 6: Mechanical

Properties of Metals

1st Semester 1435-1436 (Fall 2014)

Dr. Hamad F. Alharbi, harbihf@ksu.edu.sa

November 3, 2014

mailto:harbihf@ksu.edu.sa

Chapter 8 -

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?

Mechanical Properties of Metals

Chapter 8 - 3

Elastic means reversible!

Elastic Deformation

2. Small load

F

δ

bonds

stretch

1. Initial 3. Unload

return to

initial

F

δ

Linear-elastic

Chapter 8 -

Plastic means permanent!

Plastic Deformation (Metals)

F

δ

linear elastic

linear elastic

δplastic

1. Initial 2. Small load 3. Unload

planesstill sheared

F

δelastic + plastic

bonds stretch & planes shear

δplastic

Chapter 8 -

Stress has units:

Pa = N/m2

Engineering Stress

• Shear stress, τ:

Area, Ao

Ft

Ft

Fs

F

F

Fs

τ =Fs

Ao

• Tensile stress, σ:

original cross-sectional area

before loading

σ =Ft

Ao m2

N=

Area, Ao

Ft

Ft

Chapter 8 -

• Simple tension: cable

Common States of Stress

o

σ =F

A

o

τ =Fs

A

σσ

M

M Ao

2R

FsAc

• Torsion (a form of shear): drive shaft

Ao = cross-sectional

area (when unloaded)

FF

Chapter 8 -

o

σ =F

A

• Simple compression:

Note: compressive

structure member

(σ < 0 here).

OTHER COMMON STRESS STATE

Ao

Balanced Rock, Arches National Park

Chapter 8 - 8

• Tensile strain: • Lateral strain:

Strain is always

dimensionless.

Engineering Strain

• Shear strain:

θ

90º

90º - θy

x γ = Δx/y = tan θ

e =δ

Lo

δ/2

Lowo

- δeL =

L

wo

δL/2

Chapter 8 - 9

Linear Elastic Properties

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

• Hooke's Law:

σ = E e σ

Linear-

elastic

E

e

F

Fsimple tension test

Chapter 8 - 10

Mechanical Properties

Slope of stress strain plot (which is proportional to the

elastic modulus) depends on bond strength of metal

F

d

bonds

stretch

return to

initial

Chapter 8 -

Chapter 8 - 12

Metals

Alloys

Graphite

Ceramics

Semicond

PolymersComposites

/fibers

E(GPa)

Young’s 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)*

Chapter 8 -

Chapter 8 -

See Example 6.1

Chapter 8 - 15

• Elastic Shear

modulus, G:

τG

γ

τ = G γ

Other Elastic Properties

simple

torsion

test

M

M

• Special relations for isotropic materials:

2(1 + ν)

EG =

3(1 -2ν)

EK =

• Elastic Bulk

modulus, K: pressuretest: Init.

vol =Vo.

Vol chg.

= ΔV

P

P PP = -K

ΔVVo

P

ΔV

KVo

Chapter 8 - 16

Poisson's ratio, ν

• Poisson's ratio, ν:

Units:

E: [GPa] or [psi]

ν: dimensionless

eν = - L

e

metals: ν ~ 0.33

ceramics: ν ~ 0.25

polymers: ν ~ 0.40

Chapter 8 -

See Example 6.2

Chapter 8 -

Mechanical properties of metals

For Elastic Deformation

Chapter 8 -

Mechanical properties of metals

Anelasticity

Time-dependent elastic deformation

Viscoelastic deformation

Chapter 8 - 20

Plastic (Permanent)

Deformation

Chapter 8 - 21

Plastic (Permanent) Deformation

• Simple tension test:

engineering stress,σ

engineering strain, e

Elastic+Plastic at larger stress

ep

plastic strain

Elastic initially

permanent (plastic) after load is removed

Chapter 8 -

Mechanical properties of metals

Permanent deformation

Breaking bonds, moving

atoms, & reforming bonds

Elastic strain, ε ~ 0.5 %

(0.005)

Mechanism (metals):Slip

(1) Yield strength σy0.2% strain offset can be

used to find σy

Plastic deformation

Chapter 8 - 23

• Stress at which noticeable plastic deformation has

occurred.

Yield Strength, σy

y = yield strengthtensile stress, σ

engineering strain, e

σy

ep = 0.002

Chapter 8 - 24

Values at room

temperature

a = annealed

hr = hot rolled

ag = aged

cd = cold drawn

cw = cold worked

qt = quenched & tempered

Yield Strength : ComparisonGraphite/ Ceramics/ Semicond

Metals/ Alloys

Composites/ fibers

Polymers

Yie

ld s

tre

ng

th, σ

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

¨

Chapter 8 -

VMSE: Virtual Tensile Testing

25

Chapter 8 - 26

Tensile Strength, TS

• Metals: occurs when noticeable necking starts.

y

strain

Typical response of a metal

F = fracture or

ultimate

strength

Neck – acts

as stress

concentrator

en

gin

ee

rin

g

TSstr

ess

engineering strain

• Maximum stress on engineering stress-strain curve.

Chapter 8 -

Mechanical properties of metals

(2) Tensile

strength, TS

(3) Fracture

strength

Chapter 8 - 28

Tensile Strength: Comparison

Si crystal

Graphite/ Ceramics/ Semicond

Metals/ Alloys

Composites/ fibers

Polymers

Ten

sile

str

eng

th,

TS

(MP

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) 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

Room temperature

values

Chapter 8 -

Mechanical properties of metals

(4) Ductility: A measure of degree of plastic deformation without fracture

Ductility

measure:

Chapter 8 - 30

• Plastic tensile strain at failure:

Ductility

• Another ductility measure: 100xA

AARA%

o

fo-

=

x 100L

LLEL%

o

of-

=

LfAo

AfLo

Engineering tensile strain, e

Engineering

tensile

stress, σ

smaller %EL

larger %EL

Chapter 8 -

Mechanical properties of metals

(5) Toughness

A measure of the ability of a material to absorb energy

up to fractureApproximate by the area under the stress-strain curve

Metals: Tough => High strength + Good ductility

smaller toughness-unreinforcedpolymers

Engineering tensile strain, e

Engineering

tensile

stress, s

smaller toughness (ceramics)

larger toughness(metals, PMCs)

Chapter 8 - 32

• Energy to break a unit volume of material

Toughness

Brittle fracture: elastic energy

Ductile fracture: elastic + plastic energy

very small toughness (unreinforced polymers)

Engineering tensile strain, e

Engineering

tensile

stress, σ

small toughness (ceramics)

large toughness (metals)

Chapter 8 -

Mechanical properties of metals

(6) Resilience:

It is the capacity of a material

to absorb energy when it is

deformed elastically

Modulus of resilience, Ur

Chapter 8 - 34

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

yyr2

1U eσ≅

ey

Chapter 8 - 35

Elastic Strain Recovery

Str

ess

Strain

3. Reapplyload

2. Unload

D

Elastic strain

recovery

1. Load

σyo

σyi

Chapter 8 -

Hardness

Method:

A small indenter is forced into the

surface of a material to be tested,

under controlled conditions of load

and rate of application. The size of

the resulting indentation is measured,

which in turn is related to a hardness

number.

Softer material >> larger indentation

> lower hardness index number

A measure of a material’s resistance to

localized plastic deformation (e.g., a small

dent or a scratch)

Chapter 8 - 37

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

dDSmaller indents mean larger hardness.

increasing hardness

most plastics

brasses Al alloys

easy to machine steels file hard

cutting tools

nitrided steels diamond

Chapter 8 - 38

Hardness: Measurement

Chapter 8 - 39

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

Chapter 8 -

Correlation Between Hardness and Tensile Strength

(empirical)

Chapter 8 - 41

True Stress and

True Strain

Chapter 8 -

Mechanical properties of metals

True stress: The load F divided by the instantaneous cross-sectional area

True strain: The natural logarithmof the ratio of instantaneous gauge length to

original gauge length of a specimen

It is obtained by integrating

the incremental strain

Constant volume:

>>>

Valid only to the onset of necking

Chapter 8 -

Mechanical properties of metals

Chapter 8 - 44

Hardening

• Curve fit to the stress-strain response:

σT = 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 σy due to plastic deformation.σ

e

large hardening

small hardeningσy0

σy1

Chapter 8 -

Mechanical properties of metals

The region of the true stress–strain curve from the

onset of plastic deformation to the point at which necking

begins may be approximated by

K and n are

constant.

n: strain hardening

exponent

Chapter 8 -

Mechanical properties of metals

See Example 6.5

Chapter 8 -

Problems

6.4, 6.8, 6.9, 6.16, 6.21, 6.24,

6.25, 6.26, 6.27, 6.28, 6.30,

6.37, 6.38, 6.39, 6.40, 6.41,

6.44, 6.45