chapter 06 avi

8/3/2019 Chapter 06 Avi

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Chapter 6-

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 aremost resistant to permanent deformation?

1

Toughness and ductility: What are they and howdo we measure them?

CHAPTER 6:

MECHANICAL PROPERTIES


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Chapter 6-

F

bonds

stretch

return to

initial

2

1. Initial 2. Small load 3. Unload

Elastic means reversible!

ELASTIC DEFORMATION


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Chapter 6- 3

1. Initial 2. Small load 3. Unload

Plastic means permanent!

F

linear

elasticlinear

elastic

plastic

PLASTIC DEFORMATION (METALS)


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Chapter 6- 4

Tensile stress, s: Shear stress, t:

s Ft

Aooriginal area

before loading Stress has units:N/m2 or lb/in2

ENGINEERING STRESS


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Chapter 6- 5

Simple tension: cable

os

F

A

Simple shear: drive shaft

o

t Fs

A

Note: t = M/AcR here.

Ski lift (photo courtesy P.M. Anderson)

COMMON STATES OF STRESS


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Chapter 6-

Canyon Bridge, Los Alamos, NM

6

Simple compression:

Ao

Balanced Rock, Arches

National Park

Note: compressivestructure member(s < 0 here).

(photo courtesy P.M. Anderson)

(photo courtesy P.M. Anderson)

OTHER COMMON STRESS STATES (1)


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Chapter 6- 7

Bi-axial tension: Hydrostatic compression:

Fish under waterPressurized tank

sz > 0

s > 0

s < 0h

(photo courtesyP.M. Anderson)

(photo courtesy

P.M. Anderson)

OTHER COMMON STRESS STATES (2)


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Chapter 6- 8

Tensile strain: Lateral strain:

Shear strain:/2

/2

/2 -

/2

/2

/2

L/2L/2

Lowo

= tan Strain is alwaysdimensionless.

ENGINEERING STRAIN


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Chapter 6-

Typical tensile specimen

9

Other types of tests:--compression: brittle

materials (e.g., concrete)

--torsion: cylindrical tubes,

shafts.

Typical tensiletest 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, TheStructure and Properties of Materials,Vol. III, Mechanical Behavior, p. 2, JohnWiley and Sons, New York, 1965.)

STRESS-STRAIN TESTING


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Chapter 6-

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

10

Hooke's Law:

s = Ee

Poisson's ratio, n:

metals: n ~ 0.33ceramics: ~0.25

polymers: ~0.40

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

LINEAR ELASTIC PROPERTIES


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Chapter 6-

Elastic Shearmodulus, G:

11

t

1G

t = G

Elastic Bulkmodulus, K:

Special relations for isotropic materials:

P

P P

M

M

G

E

2(1 n) K

E

3(1 2n)

simpletorsiontest

pressure

test: Init.vol =Vo.Vol chg.= DV

OTHER ELASTIC PROPERTIES


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Chapter 6- 120.2

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

10 0

200

600800

10 001200

400

Tin

Cu alloys

Tungsten

Si carbide

Diamond

PTFE

HDP E

LDPE

PP

Polyester

PSPET

CFRE( fibers) *

GFRE( fibers)*

GFRE(|| f ibers)*

AFRE(|| fibers)*

CFRE(|| fibers)*

Metals

Alloys

GraphiteCeramicsSemicond

PolymersComposites

/fibers

E(GPa)

10 9 Pa

Based on data in Table B2,Callister 6e.Composite data based onreinforced epoxy with 60 vol%of alignedcarbon (CFRE),aramid (AFRE), orglass (GFRE)fibers.

YOUNGS MODULI: COMPARISON


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Chapter 6-

Simple tension:

13

Simple torsion:

M=moment

=angle of twist

2r o

Lo

Material, geometric, and loading parameters allcontribute to deflection.

Larger elastic moduli minimize elastic deflection.

USEFUL LINEAR ELASTIC RELATIONS


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Chapter 6- 14

Simple tension test:

(at lower temperatures, T < Tmelt/3)PLASTIC (PERMANENT) DEFORMATION


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Chapter 6- 15

Stress at which noticeableplastic deformation hasoccurred.

when ep = 0.002tensile stress, s

engineering strain, e

sy

ep = 0.002

YIELD STRENGTH, sy


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Chapter 6- 16

Room T values

sy(ceramics) >>sy(metals) >> sy(polymers)

Based on data in Table B4,Callister 6e.a = annealedhr = hot rolledag = agedcd = cold drawncw = cold workedqt = quenched & tempered

YIELD STRENGTH: COMPARISON


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Chapter 6- 17

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.


TENSILE STRENGTH, TS


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Chapter 6- 18

Room T values

TS(ceram)

~TS(met)

~ TS (comp)

>> TS(poly)

Based on data in Table B4,Callister 6e.a = annealedhr = hot rolledag = aged

cd = cold drawncw = cold workedqt = quenched & temperedAFRE, GFRE, & CFRE =aramid, glass, & carbonfiber-reinforced epoxycomposites, with 60 vol%

fibers.

TENSILE STRENGTH: COMPARISON


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Chapter 6-

Plastic tensile strain at failure:

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Another ductility measure: %AR Ao A fAox100

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 f Lo

Lox100


DUCTILITY, %EL


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Chapter 6-

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

curve.

20

smaller toughness-

unreinforced

polymers

Engineering tensile strain, e

Engineering

tensile

stress, s

smaller toughness (ceramics)

larg er toughness(metals, PMCs)

TOUGHNESS


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Chapter 6-

Resistance to permanently indenting the surface.

Large hardness means:--resistance to plastic deformation or cracking in

compression.--better wear properties.

21

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


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Chapter 6-

An increase in sy due to plastic deformation.

22

Curve fit to the stress-strain response:

HARDENING


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Chapter 6-

Design uncertainties mean we do not push the limit.

Factor of safety, N

23

sworking syN

Often N isbetween1.2 and 4

Ex: Calculate a diameter, d, to ensure that yield doesnot occur in the 1045 carbon steel rod below. Use afactor of safety of 5.

sworking syN

220,000N

d2/ 4

5

DESIGN OR SAFETY FACTORS


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Chapter 6-

Stress and strain: These are size-independentmeasures of load and displacement, respectively.

Elastic behavior: This reversible behavior oftenshows 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 sy.

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Toughness: The energy needed to break a unitvolume of material.

Ductility: The plastic strain at failure.

Note: For materials selection cases related to

mechanical behavior, see slides 22-4 to 22-10.

SUMMARY


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Chapter 6-

Reading:

Core Problems:

Self-help Problems:

0

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