Mechanical Properties chapter 6 pdf - ÖZLEM ATEŞ

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 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?

CHAPTER 6:

MECHANICAL PROPERTIES

• Ceramic Materials:

What special provisions/tests are

made for ceramic materials?

Many materials, when in service, are subjected to forces
or loads; examples include the aluminum alloy from which
an airplane wing is constructed and the steel in an
automobile axle.

In such situations it is necessary to know the

characteristics of the material and to design the member
from which it is made such that any resulting deformation
will not be excessive and fracture will not occur.

The mechanical behavior of a material reflects the
relationship between its response or deformation
to an applied load or force.Key mechanical design
properties are stiffness, strength, hardness, ductility, and
toughness.

Factors to be considered include the nature of the
applied

load

and

its

duration,

well

the

environmental conditions.

It is possible for the load to be tensile, compressive, or
shear, and its magnitude may be constant with time, or it
may fluctuate continuously.

Application time may be only a fraction of a second, or it
may extend over a period of many years.

Service temperature may be an important factor.

Elastic deformation
is the deformation in which stress and
strain are linearly proportional.

So, the slope of line is E which may be thought as
the stiffness or material’s resistance
to elastic deformation.

Elastic deformation is reversible (nonpermanent),
specimen returns to its original shape when
applied load is released



bonds
stretch

return to
initial

1. Initial

2. Small load

3. Unload

Elastic means

reversible

ELASTIC DEFORMATION

For most metallic materials, elastic deformation persists only to
strains of about 0.005.

As the material is deformed beyond this point, the stress and
strains are no longer linearly proportional
(Hook’s law is not valid) and permanent (nonrecoverable) or
plastic deformation occurs

1. Initial

2. Small load

3. Unload

Plastic means

permanent



linear
elastic

plastic

PLASTIC DEFORMATION

(METALS)

If a load is static or changes relatively slowly with time and
is applied uniformly over a cross section or surface of a
member, the mechanical behavior may be ascertained by
a simple stress

–strain test; these are most commonly

conducted for metals at room temperature.

There are three principal ways in which a load may
be applied: namely, tension, compression, and shear.

One of the most common mechanical stress

–strain tests

is performed in tension. The tension test can be used to
ascertain several mechanical properties of materials that
are important in design.

Engineering stress is defined as the instantaneous load
divided by the original specimen cross-sectional area.

Engineering strain is expressed as the change in length
(in the direction of load application) divided by the
original length.

•

Tensile

stress,

•

Shear

stress,

s 

original area
before loading

Stress has units:
N/m

or lb/in

ENGINEERING STRESS

F is the instantaneous load applied perpendicular to the specimen cross section,
in units of newtons (N) or pounds force (lbf)

•

Tensile

strain:

•

Lateral

strain:

•

Shear

strain:

/2

/2

/2 - 

/2

/2



 = tan



Strain is always
dimensionless.

ENGINEERING STRAIN

is the original length

before any load is
applied,

the

instantaneous length.

A standard tensile specimen is shown in Figure.

Normally, the cross section is circular, but rectangular
specimens are also used. This

“dogbone” specimen

configuration

was

chosen

that,

during

testing,

deformation is confined to the narrow center region
(which has a uniform cross section along its length), and
also to reduce the likelihood of fracture at the ends of the
specimen.

The tensile testing machine is designed to elongate the
specimen at a constant rate and to continuously and
simultaneously measure the instantaneous applied load (with a
load cell) and the resulting elongations (using an extensometer).
A stress–strain test typically takes several minutes to perform
and is destructive; that is, the test specimen is permanently
deformed and usually fractured.

• Typical tensile specimen

• Other types of tests:

--compression:

brittle

materials (e.g., concrete)

--torsion:

cylindrical tubes,

shafts.

• Typical tensile

test machine

Adapted from Fig. 6.2,

Callister 6e.

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.)

STRESS-STRAIN TESTING

Stress

–Strain Behavior

• A material that is stressed first undergoes elastic, or
nonpermanent, deformation.
• When most materials are deformed elastically, stress and strain
are proportional

— that is, a plot of stress versus strain is linear.

• For tensile and compressive loading, the slope of the linear
elastic region of the stress

–strain curve is the modulus of elasticity

(E), per

Hooke’s law.

• For a material that exhibits nonlinear elastic behavior, tangent
and secant moduli are used.
• On an atomic level, elastic deformation of a material corresponds
to the stretching of interatomic bonds and corresponding slight
atomic displacements.
• For shear elastic deformations, shear stress and shear strain are
proportional to one another.The constant of proportionality is the
shear modulus (G).
• Elastic deformation that is dependent on time is termed
anelastic.

Another elastic parameter, Poisson’s ratio (v),
represents the negative ratio of transverse and
longitudinal strains

•

Modulus of Elasticity, E

(also known as Young's modulus)

•

Hooke's Law

s =

•

Poisson's ratio,

metals:

n ~ 0.33

ceramics: ~0.25
polymers: ~0.40

Units:
E: [GPa] or [psi]

n: dimensionless

LINEAR ELASTIC PROPERTIES

• Elastic

Shear

modulus, G:



t =



• Elastic

Bulk

modulus, K:

• Special relations for isotropic materials:



2(1

 n)



3(1

 2n)

simple
torsion
test

pressure
test: Init.
vol =V

Vol chg.

OTHER ELASTIC PROPERTIES

0.2

0.6

Magnesium,

Aluminum

Platinum

Silver, Gold

Tantalum

Zinc, Ti

Steel, Ni

Molybdenum

Graphite

Si crystal

Glass-soda

Concrete

Si nitride

Al oxide

Wood( grain)

AFRE( fibers)*

CFRE*

GFRE*

Glass fibers only

Carbon fibers only

Aramid fibers only

Epoxy only

0.4

0.8

100

200

600

800

1000

1200

400

Tin

Cu alloys

Tungsten

<100>

<111>

Si carbide

Diamond

PTFE

HDPE

LDPE

Polyester

PET

CFRE( fibers)*

GFRE( fibers)*

GFRE(|| fibers)*

AFRE(|| fibers)*

CFRE(|| fibers)*

Metals
Alloys

Graphite
Ceramics
Semicond

Polymers

Composites

/fibers

E(GPa)

109 Pa

YOUNG’S MODULI:

COMPARISON

• Simple tension test:

(at lower temperatures, T < T

melt

/3)

PLASTIC (PERMANENT)

DEFORMATION

• Stress at which

noticeable

plastic deformation has

occurred.

when

= 0.002

tensile stress,

engineering strain,

ep = 0.002

YIELD STRENGTH,

Room T values

sy(ceramics)

sy(metals)

sy(polymers)

Based on data in Table B4,

Callister 6e

a     = annealed
hr   = hot rolled
ag  = aged
cd  = cold drawn
cw = cold worked
qt   = quenched & tempered

YIELD STRENGTH: COMPARISON

• Maximum possible engineering stress in tension.

• Metals:

occurs when noticeable

necking

starts.

• Ceramics:

occurs when

crack propagation

starts.

• Polymers:

occurs when

polymer backbones

are

aligned and about to break.

Adapted from Fig. 6.11,

Callister 6e.

TENSILE STRENGTH, TS

Room T values

TS(ceram)

(met)

TS(comp)

TS(poly)

Based on data in Table B4,

Callister 6e

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.

TENSILE STRENGTH:

COMPARISON

Ductility

is another important mechanical property. It

is a measure of the degree
of plastic deformation that has been sustained at
fracture. A metal that experiences
very little or no plastic deformation upon fracture is
termed brittle.

• Plastic tensile strain at failure:

• Another ductility measure:

%AR



 A

x100

• Note:

%AR and %EL are often comparable.

--Reason: crystal slip does not change material volume.
--%AR > %EL possible if internal voids form in neck.

%EL



 L

x100

Adapted from Fig. 6.13,

Callister 6e.

DUCTILITY, %EL

Toughness

is a mechanical term that may be used in several

contexts. For one, toughness (or more specifically, fracture
toughness) is a property that is indicative of a material’s
resistance to fracture when a crack (or other stress-
concentrating defect) is present.

Because it is nearly impossible (as well as costly) to

manufacture materials with zero defects (or to prevent damage
during service), fracture toughness is a major consideration for
all structural materials.

Another way of defining toughness is as the ability of a material
to absorb energy and plastically deform before fracturing.

• Energy to break a unit volume of material
• Approximate by the area under the stress-strain

curve.

smaller toughness-
unreinforced
polymers

Engineering tensile strain,

Engineering
tensile
stress,

smaller toughness (ceramics)

larger toughness
(metals, PMCs)

TOUGHNESS

Another mechanical property that may be important to
consider is

hardness,

which is a measure of a

material’s

resistance to localized plastic deformation (e.g., a small dent
or a scratch).

Early hardness tests were based on natural minerals with a
scale constructed solely on the ability of one material to
scratch another that was softer.

A qualitative and somewhat arbitrary hardness indexing
scheme was devised, termed the Mohs scale, which ranged
from 1 on the soft end for talc to 10 for diamond.

Quantitative hardness techniques have been developed over
the years in which a small indenter is forced into the surface
of a material to be tested, under controlled conditions of load
and rate of application.

• An increase in

due to plastic deformation.

• Curve fit to the stress-strain response:

HARDENING

•

Room T behavior is usually elastic, with brittle failure.

•

3-Point Bend Testing

often used.

--tensile tests are difficult for brittle materials.

•

Determine elastic modulus according to:





4bd





R

rect.

cross

section

circ.

cross

section

Adapted from Fig.
12.29,

Callister 6e.

MEASURING ELASTIC MODULUS

•

3-point bend test to measure room T strength.

L/2

cross section

rect.

circ.

location of max tension

•

Flexural strength:

rect.

 s

fail



1.5F

max



max

R

•

Typ. values:

Material

sfs(MPa) E(GPa)

Si nitride
Si carbide
Al oxide
glass (soda)

700-1000

550-860
275-550

300
430
390

Adapted from Fig.
12.29,

Callister 6e.

Data from Table 12.5,

Callister 6e.

MEASURING STRENGTH

• Compare to responses of other polymers:

--brittle response

(aligned, cross linked & networked case)

--plastic response

(semi-crystalline case)

Stress-strain curves
adapted from Fig.
15.1,

Callister 6e.

Inset figures along
elastomer curve
(green) adapted from
Fig. 15.14,

Callister

6e. (Fig. 15.14 is from
Z.D. Jastrzebski,

The

Nature and Properties

of Engineering

Materials, 3rd ed.,
John Wiley and Sons,
1987.)

TENSILE RESPONSE: ELASTOMER

CASE

• Decreasing T...

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

• Increasing

strain rate...

--same effects

as decreasing T.

Adapted from Fig. 15.3,

Callister 6e. (Fig. 15.3 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.)

T AND STRAIN RATE:

THERMOPLASTICS

•

Stress relaxation test

(t )



s(t )

--strain to

and hold.

--observe decrease in

stress with time.

•

Relaxation modulus

• Data:

Large drop in E

for T > T

(amorphous
polystyrene)

•

Sample T

(C) values:

PE (low M

)

PE (high M

)

PVC
PS
PC

-110
- 90
+ 87
+100
+150

Adapted from Fig.
15.7,

Callister 6e.

(Fig. 15.7 is from
A.V. Tobolsky,

Properties and

Structures of

Polymers, John
Wiley and Sons,
Inc., 1960.)

Selected values
from Table 15.2,

Callister 6e.

TIME DEPENDENT

DEFORMATION

• Resistance to permanently indenting the surface.
• Large hardness means:

--resistance to plastic deformation or cracking in

compression.

--better wear properties.

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.)

HARDNESS

• Design uncertainties mean we do not push the limit.
•

Factor of safety, N

working



Often N is
between
1.2 and 4

• Ex:

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.

working



220, 000N

 d

/ 4













DESIGN OR SAFETY FACTORS

Thermal Expansion

Materials change size when temperature

is changed

)

(

initial

final

initial

final









linear coefficient of
thermal expansion (1/K or 1/

°C)

initial

final



initial



final

initial

Atomic Perspective: Thermal Expansion

Asymmetric curve:

-- increase temperature,
-- increase in interatomic

separation

-- thermal expansion

Symmetric curve:

-- increase temperature,
-- no increase in interatomic

separation

-- no thermal expansion

Coefficient of Thermal Expansion: Comparison

• Q: Why does



generally decrease
with increasing
bond energy?

Polypropylene

145-180

Polyethylene

106-198

Polystyrene

90-150

Teflon

126-216

• Polymers

• Ceramics

Magnesia (MgO)

13.5

Alumina (Al

)

7.6

Soda-lime glass

Silica (cryst. SiO

)

0.4

• Metals

Aluminum

23.6

Steel

Tungsten

4.5

Gold

14.2



(10

-6

C)

at room T

Material

Polymers have larger



values because of

weak secondary bonds

inc

ing



• Occur due to:

-- restrained thermal expansion/contraction
-- temperature gradients that lead to differential

dimensional changes

Thermal Stresses



 Ea (T

T

)

 Ea DT

Thermal stress

s

•

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).

•

Plastic

behavior: This permanent deformation

behavior occurs when the tensile (or compressive)
uniaxial stress reaches

•

Toughness

: The energy needed to break a unit

volume of material.

•

Ductility

: The plastic strain at failure.

SUMMARY