ce205 materials science · in most engineering materials, however, there will also exist a...

CE205

MATERIALS

SCIENCE

Dr. Mert Yücel YARDIMCIIstanbul Okan University

Deparment of Civil Engineering

PART_6

MECHANICAL PROPERTIES

Chapter Outline

Terminology for Mechanical Properties

The Tensile Test: Stress-Strain Diagram

Properties Obtained from a Tensile Test

True Stress and True Strain

The Bend Test for Brittle MaterialS

2

3

Questions to Think About

• 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?

• Ceramic Materials: What special provisions/tests

are made for ceramic materials?

BASIC TYPES OF LOADING

❑Tensile

❑Compressive

❑Shear

❑Torsion

4

STRESS AND STRAIN CONCEPTS(For Compression and Tension)

5

6

STRESS AND STRAIN CONCEPTS(For Shear and torsion)

7

The role of structural engineers is to determine

stresses and stress distributions within members that

are subjected to well-defined loads

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.

8

Stress-Strain TestTensile

test

specimen

Tensile testing machine

▪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

▪A specimen is deformed, usually to

fracture, with a gradually increasing

tensile load that is applied uniaxially

along the long axis of a specimen

d=12.8mm

9

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.

10

The output of such a tensile test is recorded (usually on a computer)

as load or force versus elongation.

These load–deformation characteristics are dependent on the

specimen size. For example, it will require twice the load to produce

the same elongation if the cross-sectional area of the specimen is

doubled.

To minimize these geometrical factors, load and elongation are

normalized to the respective parameters of engineering stress and

engineering strain.

Engineering stress Engineering strain

Engineering Stress and Strain

F

F

x

x

L0

F

F

x

x

L0

L1

Stress

σ = F / A

Elongation

ΔL = (L1 – L0)

Strain

ε = ΔL / L0

Cross-sectional

area A

F is the instantaneous load applied perpendicular to the specimen cross section (N).

A0 and is the original crosssectional area before any load is applied (mm2)

Engineering stress (stress) is in MPa (=1N/mm2=106N/m2)

L0 is the original length before any load is applied.

L1 is the instantaneous length.

12

Tensile Test

13

Important Mechanical Properties

from a Tensile Test

• Young's Modulus (Modulus of Elasticity): This is the slope of the linear portion of the stress-strain curve, it is usually specific to each material; a constant, known value.

• Yield Strength: This is the value of stress at the yield point, calculated by plotting young's modulus at a specified percent of offset (usually offset = 0.2%).

• Ultimate Tensile Strength: This is the highest value of stress on the stress-strain curve.

• Percent Elongation: This is the change in gauge length divided by the original gauge length.

Terminology

Load - The force applied to a material during

testing.

Strain gage or Extensometer - A device used for

measuring change in length (strain).

Engineering stress - The applied load, or force,

divided by the original cross-sectional area of the

material.

Engineering strain - The amount that a material

deforms per unit length in a tensile test.

Strain Stress Relation

P

P

Str

ess

(σ)

Strain (ε)

P

P


Str

ess

(σ)

Strain (ε)

P

P

Pla

stic

def

orm

atio

n

Elastic

def.


Str

ess

(σ)

Strain (ε)

P

P


Str

ess

(σ)

Strain (ε)

Pla

stic

def

orm

atio

n

Elastic

def.

Modulus of Elasticity or Young Modulus (E)S

tres

s (σ

)

Elastic

def.

Pla

stic

def

orm

atio

n

Strain (ε)

Stress and strain are linearly proportional

upto an elastic limit through the relationship

Hooke’s Law

σ = E ε

The constant of proportionality E

(GPa) is the modulus of elasticity,

or Young’s modulus. For most

typical metals the magnitude of this

modulus ranges between 45 Gpa, for

magnesium, and 407 GPa, for

tungsten. It is about 200 GPa for

structural steel

The slope of this linear segment corresponds to the modulus of

elasticity E

22

E modulus may be thought of as stiffness, or a material’s resistance to

elastic deformation. The greater the modulus, the stiffer the material, or

the smaller the elastic strain that results from the application of a given

stress.

The modulus is an important design parameter used for computing

elastic deflections.

23

▪Values of the modulus of elasticity for ceramic materials are

about the same as for metals; for polymers they are lower.

▪These differences are a direct consequence of the different types

of atomic bonding in the three materials types.

σ

ε

σ

ε

σ

ε

Lineer elastic N o n - L i n e e r e l a s t i c

There is no permanent deformation on the elastic

material after unloading!

Elastic Deformation

Deformation in which stress and strain are proportional is called

elastic deformation.

25

Elastic Deformation

For this nonlinear behavior, either tangent or secant modulus is normally used.

Tangent modulus is taken as the slope of the stress–strain curve at some

specified level of stress, while secant modulus represents the slope of a secant

drawn from the origin to some given point of the s– curve

Cast iron, concrete, many

polymers

28

F

bonds

stretch

return to

initial

1. Initial 2. Small load 3. Unload

Elastic means reversible.

Elastic Deformation

29

1. Initial 2. Small load 3. Unload

Plastic means permanent.

F

linear elastic

linear elastic

plastic

Plastic Deformation (Metals)

30

Typical stress-strain

behavior for a metal

showing elastic and

plastic deformations,

the proportional limit P

and the yield strength

σy, as determined

using the 0.002 strain

offset method (where there

is noticeable plastic deformation).

P is the gradual elastic

to plastic transition.

31

Yield Stress & Strain in different metallic materials

presenting and not presenting appearent yield point

Poisson’s Ratio

32

Poisson’s ratio is defined as the

ratio of the lateral and axial strains.

metals υ = ~ 0.33

ceramics (concrete) υ = ~ 0.25

Polymers υ = ~ 0.40

Max value is 0.5 (incompressible

material; rubber)

33

AnelasticityUpto now it has been assumed that;

Elastic deformation is time independent—that is, that an

applied stress produces an instantaneous elastic strain that

remains constant over the period of time the stress is

maintained.

Upon release of the load the strain is totally recovered—that is,

that the strain immediately returns to zero.

In most engineering materials, however,

there will also exist a time-dependent elastic

strain component.

34

In most engineering materials, however, there will also exist a

time-dependent elastic strain component. That is, elastic

deformation will continue after the stress application, and upon

load release some finite time is required for complete recovery.

This time-dependent elastic behavior is known as

anelasticity.

It is due to time-dependent microscopic and atomistic processes

that are attendant to the deformation. For metals the anelastic

component is normally small and is often neglected. However, for

some polymeric materials its magnitude is significant; in this case

it is termed viscoelastic behavior, which will be the topic of next

lectures.

Anelasticity

35

Plastic Deformation

(Permanent deformation)

• From an atomic perspective, plastic

deformation corresponds to the breaking of

bonds with original atom neighbors and

then reforming bonds with new neighbors.

• After removal of the stress, the large

number of atoms that have relocated, do

not return to original position.

• Yield strength is a measure of resistance

to plastic deformation.

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

• Localized deformation of a ductile material during a

tensile test produces a necked region.

• The image shows necked region in a fractured sample

38

Ductile failure

(The fracture surface is

more tortuous)

Brittle failure

(Fracture surface is

very sharp and smooth)

Permanent Deformation

• Permanent deformation for metals is

accomplished by means of a process called

slip, which involves the motion of

dislocations.

• Most structures are designed to ensure that

only elastic deformation results when stress

is applied.

• A structure that has plastically deformed, or

experienced a permanent change in shape,

may not be capable of functioning as

intended.39

tensile stress,

engineering strain,

y

p = 0.002

Yield Strength, y

40

41

BASIC PROPERTIES of STRESS-STRAIN

DIAGRAM of METALS

ε

σ

O

A

OA Portion:

Elastic Region.

The stress is linearly

proportional to the strain

in this region.

orεEσ =ε

σE =

εe

σe

B

C

D

42

ε

σ

O

A

B

AB Portion:

Non-lineer elastic or

Elastic-plastic transition region

The point A defines the initial

deviation from linearity of the

stress-strain curve. This point

sometimes is called as

propotional limit of the

material. Some materials exhibits

non-lineer elastic behavior in

between proportional limit (A)

and yield limit (Point B). 0.002

Yield point can be determined as the intersection of the curve and a

straight line drawn as parallel to elastic portion of the curve at a specified

strain offset of 0.002.

It is assumed that there is no permanent deformation on the material if

the sample is unloaded before reaching the yield point.

σy

C

D

43

ε

σ

O

A

B

0.002

C

BC Portion

After yielding, the stress

necessary to continue plastic

deformation in metals increases

to a maximum (point C) and

then decreases to the eventual

fracture (point D).

The tensile strength is the

stress at the maximum on the

engineering stress–strain curve.

This corresponds to the

maximum stress that can be

sustained by a structure in

tension; if this stress is applied

and maintained, fracture will

result.

D

If the material in

unloaded in between

BC, the curve will

follow back with the

same E

The maximum stress which the

material can support without

breaking is called tensile strength.

44

CD Portion

(Necking)

All deformation up to point C is

uniform throughout the narrow region

of the tensile specimen. However, at

this maximum stress, a small

constriction or neck begins to form at

some point, and all subsequent

deformation is confined at this neck.

This phenomenon is termed “necking”

and fracture ultimately occurs at the

neck. The fracture strength corresponds

to the stress at fracture (Point D). εO

A

B

0.002

C

D

45

• Stress-strain

behavior

found for

some steels

with yield

point

phenomenon.

46

Yield Stress & Strain in different metallic

materials

47

T

E

N

S

I

L

E

P

R

O

P

E

R

T

I

E

S

48

Room T valuesa = annealed

hr = hot rolled

ag = aged

cd = cold drawn

cw = cold worked

qt = quenched & tempered

Yield Strength: Comparison

49

In an undeformed

thermoplastic polymer

tensile sample,

(a) the polymer chains

are randomly

oriented.

(b)When a stress is

applied, a neck

develops as chains

become aligned

locally. The neck

continues to grow

until the chains in the

entire gage length

have aligned.

(c) The strength of the

polymer is increased

TENSILE RESPONSE OF POLYMERIC MATERIALS

50

Room T values

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

51

See tensile responses of various types of

metalic and polymeric materials.

http://www.wiley.com/college/callister/0470125373/vmse/strstr.htm

http://www.wiley.com/college/callister/0470125373/vmse/index.htm

Example 1

Tensile Testing of Magnesium

52

A specimen of magnesium having a

rectangular cross section of

dimensions 3.2 mm x 19.1 mm is

deformed in tension. Using the given

load–elongation data answer the

questions below.

a) Plot the data as engineering

stress vs. engineering strain.

b) Compute the modulus of

elasticity.

c) Determine the yield strength at a

strain offset of 0.002

d) Determine the tensile strength of

this material.

Example 1 SOLUTION

53

54

• Another ductility measure: 100% xA

AAAR

o

fo −=

• Ductility may be expressed as either percent elongation (%

plastic strain at fracture) or percent reduction in area.

• %AR > %EL is possible if internal voids form in neck.

100% xl

llEL

o

of −=

Ductility, %EL

Ductility is a measure of the

plastic deformation that has

been sustained at fracture:

A material that

suffers very

little plastic

deformation is

brittle.

56

Toughness

Lower toughness: ceramics

Higher toughness: metals

Toughness is

the ability to

absorb

energy up to

fracture.

“tough”

material has

strength and

ductility.

Approximated

by the area

under the

stress-strain

curve.

• Energy to break a unit volume of material

• Approximate by the area under the stress-strain

curve.

21

smaller toughness- unreinforced polymers

Engineering tensile strain,

Engineering

tensile

stress,

smaller toughness (ceramics)

larger toughness (metals, PMCs)

Toughness

58

Linear Elastic Properties

Modulus of Elasticity, E:

(Young's modulus)

• Hooke's Law: = E

• Poisson's ratio:metals: n ~ 0.33

ceramics: n ~0.25

polymers: n ~0.40

Units:

E: [GPa] or [psi]

n: dimensionless

n = x/y

x

y

59

Engineering Strain

Strain is dimensionless.

Axial (z) elongation (positive strain) and lateral (x and y) contractions

(negative strains) in response to an imposed tensile stress.

61

For isotropic materials, shear and elastic moduli are related to

each other and to Poisson’s ratio according to

Poisson’s Ratio

If the applied stress is uniaxial (only in the z direction), and the

material is isotropic, then A parameter termed Poisson’s ratio

is defined as the ratio of the lateral and axial strains, or

Theoretically, Poisson’s ratio for

isotropic materials should be ¼.

The maximum value is 0.50.

G is about 0.4E

= E

t = G g

avg = KDV

Vo

Stresses Strains

Elastic Constants

Normal

Shear

Volumetric

62

64

SAMPLE PROBLEM

After

loading

Before

loading

10

cm

10 cm

10

.00

4 c

m

9.999 cm

P=10000 kgf

Dimensions of the cube before and after the load application of 10000

kgf are given below. Determine modulus of elasticity (E) and the

Poisson’s ratio (υ) if the material response is entirely elastic and the

material is isotropic.

65

10cm

10cm

Δl/2=0.002cm

Δd/2=0.0005cm

10000 kgf

P=10000 kgf

P=10000kgf → σ=10*10

10000

E=σε =

100

0.0004= 250000 kgf/cm2

εlong=Δll0

= =0.00040.00410

εlat=Δdd0

= = -0.0001-0.001

10

ν = --0.0001

0.0004= 0.25

POISSON’S RATIO:

= 100 kgf/cm2

True Stress and True Strain

True stress The load divided by the actual cross-sectional

area of the specimen at that load.

True strain The strain calculated using actual and not

original dimensions, given by εt ln(l/l0).

•The relation between the true stress-

true strain diagram and engineering

stress-engineering strain diagram.

•The curves are identical to the yield

point.

69

Stress-Strain Results for Steel Sample

(1psi=0.00690MPa)

700.2

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)*

Metals

Alloys

Graphite

Ceramics

Semicond

PolymersComposites

/fibers

E(GPa)

109 Pa Composite data based onreinforced epoxy with 60 vol%

of aligned carbon (CFRE),

aramid (AFRE), or glass (GFRE)

fibers.

Young’s Moduli: Comparison

Example 3: True Stress and True Strain Calculation

72

Mechanical Behavior of Ceramics

• The stress-strain behavior of brittle ceramics

is not usually obtained by a tensile test.

Because;

▪ It is difficult to prepare a tensile test specimen

with a specific geometry.

▪ It is difficult to grip brittle materials without

fracturing them.

▪ Ceramics fail after roughly 0.1% strain;

Therefore the specimen have to be perfectly

aligned, it is very difficult...

For Brittle Materials, Bending test is used in determining tensile strength.

Bending test - Application of a force to the center of a bar

that is supported on each end to determine the

resistance of the material to a static or slowly applied

load.

Flexural strength or modulus of rupture -The stress

required to fracture a specimen in a bend test.

Flexural modulus - The modulus of elasticity calculated

from the results of a bend test, giving the slope of the

stress-deflection curve.


(a) The bend test often used for measuring the strength of brittle materials, and (b) the deflection δ obtained by bending

BENDING TEST


The stress-strain behavior of brittle materials compared with that of more ductile materials

76

• Schematic for a 3-point

bending test.

• Able to measure the

stress-strain behavior

and flexural strength of

brittle ceramics.

• Flexural strength

(modulus of rupture or

bend strength) is the

stress at fracture.

Flexural Strength

23

• Determination of E modulus from bending test is

Possible only in the elastic region of the loading.

MEASURING ELASTIC MODULUS

FROM BENDING TEST

E =F

L3

4bd3

For rectangular

Cross-section

FL/2 L/2

= midpoint

deflection

cross section

b

d

rectangular

78

THREE-POINT BENDING vs. FOUR-POINT BENDING

L/2 L/2 L/3 L/3 L/3

L L

P P/2 P/2Three-point bending Four-point bending

Three-point bending and four-point bending test on prismatic

samples is uased in determining the flexural properties of

brittle materials (as concrete)

79


L/2 L/2 L/3 L/3 L/3

L L

P P/2 P/2

P/2

-P/2

P/2

-P/2

(P.L/4)(P.L/6)

b

h

Three-point bending Four-point bending

+-

+-

+ +

[V] [V]

[M] [M]

𝑓𝑓𝑙𝑒𝑥 =3. 𝑃. 𝐿

2. 𝑏. ℎ2𝑓𝑓𝑙𝑒𝑥 =

𝑃. 𝐿

𝑏. ℎ2

80


L/2 L/2 L/3 L/3 L/3

L L

P P/2 P/2Three-point bending Four-point bending

The peak stress in 3-point bending test is at the specimen mid-

point as concentreted stress.

The peak stress in 4-point bending test is at an extended region of

the specimen in the mid-region. Hence, potantial to encounter a

defect or flaw on the maximum stress region is high. Therefore

testing the materials with 4-point bending provides more realistic

results particularly in heteregeneous materials like concrete.

81

--brittle response (microstructure: aligned chain, cross linked & networked case)

--plastic response (microstructure: semi-crystalline case)

Stress-Strain Behavior: Elastomers3 different responses

observed in polymers:

A – brittle failure

B – plastic failure

C - highly elastic (elastomer)

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