Mechanical Properties of Solids

Mechanical Properties of

Solids

Chapter 7


Solids

Mechanical properties of materials… - reflect the relationship between its response or deformation to an applied load. -- its behavior when subjected to external load (shows elastic & plastic deformation before failure). - measure using various mechanical testing.

Why study mechanical properties?as a mechanical engineer…- how to measure mechanical properties

& what these properties represent. -- may be used to design structures @ components using predetermined materials such that unacceptable levels of deformation or failure will not occur.

as a structural engineer…- how to determine stresses & stresses distributions within members that are subjected to loads. -- analyze & predict various stresses using experimental & structural analysis.

as a materials & metallurgical engineer…- concerned with producing & fabricating materials to meet service requirements as predicted by these stress analysis. -- understand relationship between microstructure of the materials & their mechanical properties.

Common mechanical properties… Hardness Ductility Yield strength Toughness Brittleness Tensile strength Modulus of Malleability Fracture strength elasticity Flexural strength

Some mechanical testing…

Tension test Hardness test

Compression test Impact test

Flexural test Fatigue test

Shear/Torsion test Creep test

will cover in Chapter 9: Failure of Materials

Ela

stic

de

form

atio

n

Pla

stic

de

form

atio

n

2. Small load

F

d

bonds stretch

1. Initial 3. Unload

return to initial

elastic

F

d

Linear- elastic

Non-linear elastic

d = deformation/elongation/deflection

1. Initial 2. Small load 3. Unload

planes still sheared

F

delastic + plastic

bonds stretch & planes shear

dplastic

F

dlinear elastic

linear elastic

dplastic

Concept of elastic deformationmaterials return to its

original dimension after tensile force is removed.

Concept of plastic deformationmaterials are deformed to such an extent such that it cannot return to its original dimension.

Elastic means reversible!


Solids

Concept of engineering stress

Tension test [Universal Testing Machine (UTM)]

Modulus of elasticity, E Yield strength, Tensile strength TS Fracture strength F Ductility (%EL @ %RA)Toughness (area under graph)

Load, FElongation, Surface area, Ao

experiment datamechanical testing mechanical propertiesexperiment result

Poisson’s ratio, vEngineering stress, Engineering strain, True stress, T True strain, T

specimenextensometer

Adapted from Fig. 7.2,Callister & Rethwisch 3e.

gauge length

2. Lateral strain:

-deL= L

w o

d/2

L ow o

dL/2

Concept of engineering strain1. Tensile strain:

e = d

Lo

q

90º

90º - qy

x

q

3. Shear strain:

g = Dx/y = tan

1. Tensile stress, s:

original area before loading

s =FtA o

Ao

Ft

Ft

Ao

Ft

Ft

Fs

F

F

Fs

2. Shear stress, t:

t =FsA o

Stress has units: N/m2 or lbf /in2

Typical tension test

strain

Typical response of a metal

Neck – acts as stress concentrator

y

TS

F

Consider: Linear elastic deformation

Typical stress-strain curves for hypothetical materials


Solids



experiment datamechanical testing experiment result



mechanical properties

1. Modulus of Elasticity, E (also known as Young's modulus)

s

Linear- elastic

E

e

2. Poisson's ratio,neL

e

-n

en = - L

e

E =

metals: n ~ 0.33ceramics: n ~ 0.25polymers: n ~ 0.40

Units:E: [GPa] or [psi]n: dimensionless

MetalsAlloys

GraphiteCeramicsSemicond

PolymersComposites

/fibers

Based on data in Table B.2,Callister & Rethwisch 3e. Composite data based onreinforced epoxy with 60 vol%of alignedcarbon (CFRE),aramid (AFRE), orglass (GFRE)fibers.

E (

GP

a)

0.2

8

0.6

1

Magnesium,Aluminum

Platinum

Silver, Gold

Tantalum

Zinc, Ti

Steel, NiMolybdenum

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

10 0

200

600800

10 001200

400

Tin

Cu alloys

Tungsten

<100>

<111>

Si carbide

Diamond

PTFE

HDPE

LDPE

PP

Polyester

PSPET

CFRE( fibers) *

GFRE( fibers)*

GFRE(|| fibers)*

AFRE(|| fibers)*

CFRE(|| fibers)*

Elastic deformation region

E values for selected materials


Solids







1. Yield strength, Plastic deformation region

Adapted from Fig. 7.10 (a),Callister & Rethwisch 3e.

en

gin

ee

ring

str

ess

, s

engineering strain, e

Elastic+Plastic at larger stress

ep

plastic strain

Elastic initially

permanent (plastic) after load is removed

Stress at which noticeable plastic deformation has occurred.

engineering strain, e

sy

ep = 0.002

when ep = 0.002 = 0.2% offset

Maximum stress on engineering stress-strain curve.

2. Tensile Strength, TS

Metals: occurs when noticeable necking starts.Polymers: occurs when polymer backbone chains are aligned & about to break.

en

gin

ee

ring

str

ess

, s

y

strain

Typical response of a metal

F = fracture or

ultimate

strength

Neck – acts as stress concentrator e

ng

ine

erin

g

TS s

tre

ss

engineering strain


Solids







Plastic deformation region & TS values for selected materials (room temperature)

Graphite/ Ceramics/ Semicond

Metals/ Alloys

Composites/ fibersPolymers

Yie

ld s

tre

ng

th, s y

(MP

a)

PVC

Har

d to

mea

sure

, si

nce

in te

nsio

n, fr

actu

re u

sual

ly o

ccur

s be

fore

yie

ld.

Nylon 6,6

LDPE

70

20

40

6050

100

10

30

200

300

400500600700

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

Har

d to

mea

sure

, in

cer

amic

mat

rix a

nd e

poxy

mat

rix c

ompo

site

s, s

ince

in te

nsio

n, fr

actu

re u

sual

ly o

ccur

s be

fore

yie

ld.

HDPEPP

humid

dryPC

PET

¨ Si crystal<100>

Graphite/ Ceramics/ Semicond

Metals/ Alloys

Composites/ fibersPolymers

PVC

Nylon 6,6

10

100

200300

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

20003000

5000

Graphite

Al oxide

Concrete

Diamond

Glass-soda

Si nitride

HDPE

wood ( fiber)

wood(|| fiber)

1

GFRE (|| fiber)

GFRE ( fiber)

CFRE(|| fiber)

CFRE( fiber)

A FRE(|| fiber)

AFRE( fiber)

E-glass fib

C fibersAramid fib

str

en

gth

, T

S (M

Pa

)Te

nsi

le


Solids







Plastic deformation region

3. DuctilityPlastic tensile strain at failure.-- shows a significant plastic deformation before rupture.

x 100L

LLEL%

o

of-

=

100xA

AARA%

o

fo-

=

LfAo Af

Lo

Adapted from Fig. 7.13, Callister & Rethwisch 3e.

Engineering tensile strain, e

Engineering tensile stress, s

smaller %EL

larger %EL

4. Toughness

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

very small toughness (unreinforced polymers)

Engineering tensile strain, e

Engineering tensile stress, s

small toughness (ceramics)

large toughness (metals)

Brittle fracture: elastic energyDuctile fracture: elastic + plastic energy

Stress-Strain curves for typical polymers

Fracture strengths of polymers ~ 10% of those for metals.

Deformation strains for polymers > 1000% – for most metals, deformation strains < 10%.

brittle polymer

plasticelastomer

elastic moduli – less than for metals



Solids







True Stress & Strain

Note: Surface area, A changes when sample stretched.

True stress

True strain

iT AF

oiT ln

1ln

1

T

T



Solids

Flexural test [Universal Testing Machine (UTM)]

Load, FElongation, (deflection)


Modulus of elasticity, E Flexural strength, fs


- ceramic materials are more brittle than metals.

Why is this so?- consider mechanism of deformation

-- in crystalline, by dislocation motion.

-- in highly ionic solids, dislocation motion is

difficult.

* few slip systems.

* resistance to motion of ions of like charge (e.g., anions) past one another.

Flexural test…- most common test for ceramics.

Flexural test…- materials with room T behavior is usually elastic but with brittle failure. -- show little plastic deformation before failure.- 3-Point Bend Testing often used. -- tensile tests are difficult for brittle materials.

FL/2 L/2

d = midpoint deflection

cross section

R

b

d

rect. circ.


Determine elastic modulus according to:

F

x

linear-elastic behavior

d

F

dslope =

3

3

4bd

LFE

(rect. cross

section)

4

3

12 R

LFE

(circ. cross

section)

Flexural strength:

22

3

bd

LFffs (rect. cross section)

(circ. cross section)3R

LFffs

Typical values:

Data from Table 7.2, Callister & Rethwisch 3e.

Si nitrideSi carbideAl oxideglass (soda-lime)

250-1000100-820275-700

69

30434539369

Material sfs (MPa) E(GPa)

Typical 3 point bend test


Solids

Hardness test [hardness machine]

Hardness number (HN)


Covert to , TS, E


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

Type of hardness test

Brinell hardness test

Rockwell hardness test

Vickers microhardness test

Knoop microhardness test

Press the indenter thatis harder than the metal

Into metal surface.

Withdraw the indenter

Measure hardness by measuring depth orwidth of indentation.

General procedure…

Typical rockwell hardness tester

Detail of hardness testing techniques & measurement

Table 7.5


Solids

Hardness test [hardness machine]

Hardness number (HN)


Covert to , TS, E


• Design uncertainties mean we do not push the limit.• Factor of safety, N

Ny

working

Often N isbetween1.2 and 4

• Example: 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.

Design or Safety Factors

220,000N

d2 / 4 5

Ny

working

1045 plain

carbon steel: y = 310 MPa

TS = 565 MPa

F = 220,000N

d

Lo

d = 0.067 m = 6.7 cm

• 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).

• Toughness: The energy needed to break a unit volume of material.

• Ductility: The plastic strain at failure.

Summary

• Plastic behavior: This permanent deformation behavior occurs when the tensile (or compressive) uniaxial stress reaches sy.

End of Chapter

7

Mechanical Properties of Solids

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