Mechanical Properties

5

Learning Objectives

4-2

Introduce the basic concepts associated with

mechanical properties of materials.

Stress and Strain (engineering and true stress, engineering and true strain)

Stress – Strain Curve

Elastic and Plastic deformation in metals

Types of Fracture: ductile and brittle

Common mechanical properties testing: hardness and

impact testing

Technological Importance

4-3

The materials used in sports equipment must be lightweight, stiff, tough, and impact resistant. (Courtesy of Getty Images.)

Aircraft, such as the one shown here, makes use of aluminum alloys and carbon-fiber-reinforced composites

Technological Importance

4-4

Terminology for Mechanical Properties

4-5

Stress - Force or load per unit area of cross-section over

which the force or load is acting.

Strain - Elongation change in dimension per unit length.

Young’s modulus - The slope of the linear part of the

stress-strain curve in the elastic region, same as

modulus of elasticity.

Shear modulus (G) - The slope of the linear part of the

shear stress-shear strain curve.

Viscosity ( ) - Measure of resistance to flow, defined as

the ratio of shear stress to shear strain rate (units Poise

or Pa-s).

Thixotropic behavior - Materials that show shear

thinning and also an apparent viscosity that at a

constant rate of shear decreases with time.

4-6

(a) Tensile, compressive, shear and bending stresses. (b) Illustration showing how Young’s modulus is defined for elastic material. (c) For nonlinear materials, we use the slope of a tangent as a variable quantity that replaces the Young’s modulus constant

(c)2

00

3 B

roo

ks/

Co

le, a

div

isio

n o

f T

ho

mso

n L

earn

ing,

Inc.

T

ho

mso

n L

earn

ing™

is

a tr

adem

ark u

sed h

erei

n u

nder

lic

ense

.

Stress – Strain

4-7

Engineering strain = oo

oi

l

l

l

ll

Ao : original cross sectional area li : instantaneous length lo : original length Strain has no unit

Engineering stress = oA

F

Tension and Compression The above definitions allow us to compare

test results for specimens of different cross

Sectional areas

Stress - Strain

4-8

Pure shear stress =

oA

F

Pure shear strain = tan

Shear

Stre

ss –

Stra

in T

est (T

ensile

Test)

4-9

(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein

under license.

4-1

0

(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.

Te

nsile

stre

ss-s

train

cu

rve

s fo

r diffe

ren

t ma

teria

ls

4-11

Stress – Strain Test (Tensile Test)

4-12

(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.

The stress-strain curve for an aluminum alloy from Table 6-1

Properties Obtained from Tensile Test

4-13

Elastic limit

Tensile strength, Necking

Hooke’s law

Poisson’s ratio

Modulus of resilience (Er)

Tensile toughness

Ductility

Elastic Deformation

4-14

Elastic Deformation is a non-permanent deformation where the material completely recovers to its original state upon release of the applied stress.

Hooke’s Law: = E

stress

Modulus of elasticity (Young’s modulus)

strain

E = slope in the linear region

For metals, typically E ~ 45 – 400 GPa

Measure of material’s resistance to elastic deformation (stiffness).

Elastic Deformation

4-15

F

bonds

stretch

return to

initial

1. Initial 2. Small load 3. Unload

Elastic means reversible! From Callister 6e resource CD.

Plastic Deformation

4-16

1. Initial 2. Small load 3. Unload

Plastic means permanent!

F

linear elastic

linear elastic

plasticFrom Callister 6e resource CD.

Yield Strength (y)

4-17

Is the strength required to produce a very slight yet specified amount of plastic deformation.

What is the specified amount of strain?

Strain offset method

0.002

1. Start at 0.002 strain (for most metals).

2. Draw a line parallel to the linear region.

3. y = where the dotted line crosses the

stress-strain curve. y

Elastic region

P P = proportional limit (beginning of deviation

from linear behavior.

Mixed elastic-plastic behavior

For materials with nonlinear elastic region: y is

defined as stress required to produce specific

amount of strain (e.g. ~0.005 for most metals).

Yield Strength (y)

4-18

(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.

(a) Determining the 0.2% offset yield strength in gray cast ion, and (b)

upper and lower yield point behavior in a low-carbon steel

Yield Strengths of Different Materials

4-19

Room T values

y(ceramics)

>>y(metals)

>> y(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

From Callister 6e resource CD.

Ultimate Tensile Strength (UTS)

4-20

Stress at the maximum of stress-strain curve.

0.002

y

Elastic region

P

TS M

F P = proportional limit y = yield strength

TS = tensile strength

M = max. stress

F = fracture point

Note: For most engineering materials, strength should be specified by

yield strength (not tensile strength). Why?

Necking

4-21

y P

TS M

F

• Necking starts at max stress (A decreases) • Past max stress, decreases • The material becomes weak (true or false?)

Necking

4-22

Engineering Stress = oA

F

Original cross

sectional area

True Stress = i

TA

F

Ai = instantaneous area

Tensile Test

4-23

(a) Original and final shape of a standard tensile-test specimen. (b)

Outline of a tensile-test sequence showing stages in the elongation of

the specimen.

Ductility

4-24

• Is measure of degree of plastic deformation that has been sustained at fracture.

• Ductile materials can undergo significant plastic deformation before fracture. • Brittle materials can tolerate only very small plastic deformation.

Types of Fracture

4-25

Cup & Cone in Al Brittle in mild steel

Highly ductile

Moderately ductile

Brittle

How to Measure Ductility?

4-26

% elongation = %100

o

of

l

ll

% reduction in area = %100

o

fo

A

AA

Ao and lo are initial.

Af and lf are at fracture.

Mechanical Properties of Materials

4-27

METALS (WROUGHT) E (GPa) Y (MPa) UTS (MPa) ELONGATION(%) in 50 mm

POISSONÕSRATIO (

Aluminum and its alloysCopper and its alloysLead and its alloysMagnesium and its alloysMolybdenum and its alloysNickel and its alloysSteelsStainless steelsTitanium and its alloysTungsten and its alloys

69-79105-150

1441-45

330-360180-214190-200190-20080-130

350-400

35-55076-1100

14130-30580-2070105-1200205-1725240-480344-1380550-690

90-600140-1310

20-55240-38090-2340345-1450415-1750480-760415-1450620-760

45-565-350-921-540-3060-565-260-2025-7

0

0.31-0.340.33-0.35

0.430.29-0.35

0.320.31

0.28-0.330.28-0.300.31-0.34

0.27

NONMETALLIC MATERIALS

CeramicsDiamondGlass and porcelainRubbersThermoplasticsThermoplastics, reinforcedThermosetsBoron fiberCarbon f ibersGlass f ibers (S, E)Kevlar fibers (29, 49, 129)Spectra f ibers (900, 1000)

70-1000820-1050

70-800.01-0.11.4-3.42-50

3.5-17380

275-41573-8570-11373-100

------------

140-2600-

140-

7-8020-12035-1703500

2000-53003500-46003000-34002400-2800

0-0-

1000-510-1

00

1-25

3-43

0.2-

0.240.5

0.32-0.40-

0.34-----

Note: In the upper table the lowest values for E, Y, and UTS and the highest values for elongation are for thepure metals. Multiply GPa by 145,000 to obtain psi, and MPa by 145 to obtain psi. For example, 100 GPa =14,500 ksi, and 100 MPa = 14,500 psi.

Hardness Testing

4-28

Hardness is defined as the resistance of a material to plastic penetration of its surface. That is the ability of a material to resist indentation, abrasion and wear

There are three main types of tests used to determine hardness:

Scratch tests, dynamic and static hardness tests

For engineering purposes, only the static hardness tests are used.

Hardness Testing

4-29

Higher values of hardness means:

Resistance to plastic deformation or cracking in

compression. Better wear properties.

Hardness test is: Simple (just press indent into material’s surface) Cheap (no need to machine the specimen, no big

equipment needed)

Hardness Testing

4-30

Apply known force (kg) Measure size of indenter

Smaller indents mean higher hardness

Indentation will depend not only on the material being tested but also

indenter composition and geometry.

Types of Hardness Tests

4-31

General characteristics of hardness testing methods. The Knoop test is known as a

microhardness test because of the light load and small impressions. Source: After H. W.

Hayden, W. G. Moffatt, and V. Wulff.

Types of Hardness Tests

4-32

Impact Testing: Toughness

4-33

• Toughness (notch toughness) is the ability of a

material to absorb energy

1. Material Toughness (slow absorption) - Not a readily observable property - Defined by the area under the stress-strain curve 2. Impact Toughness (rapid absorption) - Ability to absorb energy of an impact without

fracturing • Toughness, ductility and brittleness are related

Impact Testing: Toughness

4-34

Impact test - Measures the ability of a material to

absorb the sudden application of a load without

breaking.

Impact energy - The energy required to fracture a

standard specimen when the load is applied suddenly.

Impact toughness - Energy absorbed by a material,

usually notched, during fracture, under the conditions of

impact test.

Fracture toughness - The resistance of a material to

failure in the presence of a flaw.

Properties Obtained from the Impact Test

4-35

Ductile to brittle transition temperature (DBTT) - The

temperature below which a material behaves in a

brittle manner in an impact test.

Notch sensitivity - Measures the effect of a notch,

scratch, or other imperfection on a material’s

properties, such as toughness or fatigue life.

Impact Testing: DBTT

4-36

The Charpy V-notch properties for a BCC

carbon steel and a FCC stainless steel. The FCC crystal structure typically leads top higher absorbed energies and no transition temperature

(c)2

003 B

roo

ks/

Co

le, a

div

isio

n o

f T

ho

mso

n L

earn

ing,

Inc.

T

ho

mso

n L

earn

ing™

is

a tr

adem

ark u

sed h

erei

n u

nder

lic

ense

.

DBTT

Brittle Ductile

Rough surface

Smooth surface

Impact Testing

4-37

- At low temperature, where the material is brittle and

not strong, little energy is required to fracture the material.

- At high temperature, where the material is more ductile

and stronger, greater energy is required to fracture the

material

-The transition temperature is the boundary between brittle

and ductile behavior.

The transition temperature is an extremely important

parameter in selection of construction material.

Example of DBT failure

4-38

4-39

Charpy

Test

Izod Test

Fatigue Testing

4-40

Fatigue is the lowering of strength or failure of a material due

to repetitive or cyclic stress which may be above or below

the yield strength.

Aloha Airlines Flight 243, April 1988

Eschede train crash, Germany 1988

Fatigue Testing

4-41

Time Co

mp

res

sio

n Te

ns

ion

Time

max

min

Co

mp

res

sio

n Te

ns

ion

0

Time

max

min

Co

mp

res

sio

n T

en

sio

n

0

a r

m

Irregular or Random stress cycle

Reversed stress cycle Repeated stress cycle

Fatigue Testing

4-42

Fatigue Testing

4-43

(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a

trademark used herein under license.

Beach marks

Fatigue Testing

4-44