Chapter 6: Mechanical Properties

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Chapter 6 - 1

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 does permanent deformation occur? What materials are most

resistant to permanent deformation?

• Toughness and ductility: What are they and how do we measure them?

Chapter 6:

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Chapter 6 - 2

Elastic means

reversible

!

Elastic Deformation

2. Small load

F

bonds stretch

1. Initial

3. Unload

return to initial

F

Linear- elastic Non-Linear-elastic

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Chapter 6 - 3

Plastic means

permanent

!

Plastic Deformation (Metals)

F

linear elastic linear elastic plastic

1. Initial

2. Small load

3. Unload

planes

still

sheared

F

elastic + plastic

bonds

stretch

& planes

shear

plastic

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Chapter 6 - 4

Stress has units:

N/m

2

_{or lb}

f

/in

2

Engineering Stress

• Shear

stress, :

Area, A_o

F

_t

F

_t

F

_s

F

_s

=

F

s

A

_o

• Tensile

stress, :

original area before loading

=

F

t

A

_o

2 f 2

m

N

or

in

lb

=

Area, A_o

F

_t

F

_t

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Chapter 6 - 5

• Simple

tension: cable

Note: = M/AcR here.

Common States of Stress

o

F

A

o

F

s

A

M

_A

o

2R

F

_s

A

_c

• Torsion

(a form of shear): drive shaft

Ski liftP.M. Anderson) (photo courtesy

A_o = cross sectional area (when unloaded)

F

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Chapter 6 - 6 (photo courtesy P.M. Anderson)

Canyon Bridge, Los Alamos, NM

o

F

A

• Simple

compression:

Note: compressive structure member ( < 0 here).

(photo courtesy P.M. Anderson)

OTHER COMMON STRESS STATES (i)

A

_o

Balanced Rock, Arches National Park

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Chapter 6 - 7

• Bi-axial

tension:

• Hydrostatic

compression:

Pressurized tank

< 0

h (photo courtesy P.M. Anderson) (photo courtesy P.M. Anderson)

OTHER COMMON STRESS STATES (ii)

Fish under water

z

> 0

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Chapter 6 - 8

• Tensile

strain:

• Lateral

strain:

Strain is always

dimensionless.

Engineering Strain

• Shear

strain:

90º 90º -

y

x

_{= x/y = tan}

L

o

Adapted from Fig. 6.1(a) and (c), Callister & Rethwisch 8e.

/2

L

o

w

_o

L L

w

_o L

/2

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Chapter 6 - 9

Stress-Strain Testing

• Typical tensile test

machine

Adapted from Fig. 6.3, Callister & Rethwisch 8e. (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.)

specimen extensometer

• Typical tensile

specimen

Adapted from Fig. 6.2, Callister & Rethwisch 8e. gauge length

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Chapter 6 - 10

Linear Elastic Properties

• Modulus of Elasticity, E

:

(also known as Young's modulus)

• Hooke's Law

:

=

E

Linear-

elastic

E

F

simple tension test

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Chapter 6 - 11

Poisson's ratio,

• Poisson's ratio,

:

Units:

E: [GPa] or [psi]

: dimensionless

> 0.50 density increases < 0.50 density decreases (voids form) L

L metals: ~ 0.33 ceramics:

~ 0.25

polymers: ~ 0.40

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Chapter 6 - 12

Mechanical Properties

• Slope of stress strain plot (which is

proportional to the elastic modulus) depends

on bond strength of metal

Adapted from Fig. 6.7, Callister & Rethwisch 8e.

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Chapter 6 - 13

• Elastic

Shear

modulus, G:

G

= G

Other Elastic Properties

simple torsion test

M

• Special relations for isotropic materials:

2(1

)

E

G

3(1

2 )

E

K

• Elastic

Bulk

modulus, K:

pressure test: Init. vol =Vo. Vol chg. = V

P

P = -

K

V

V o

P

V

K

V

o

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Chapter 6 - 14 Metals Alloys Graphite Ceramics Semicond Polymers Composites /fibers E(GPa)

Based on data in Table B.2,

Callister & Rethwisch 8e.

Composite data based on reinforced epoxy with 60 vol% of aligned

carbon (CFRE), aramid (AFRE), or glass (GFRE) fibers.

Young’s Moduli: Comparison

10

9

_Pa

0.2 8 0.6 1 Magnesium, Aluminum Platinum Silver, Gold Tantalum Zinc, Ti Steel, Ni Molybdenum Graphite Si crystal Glass-soda Concrete Si nitride Al 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 2 0 4 0 6 0 8 0 10 0 2 00 6 00 8 00 10 00 1200 4 00 Tin Cu alloys Tungsten <100> <111> Si carbide Diamond PTF E HDP E LDPE PP Polyester PS PET CFRE( fibers) * GFRE( fibers)* GFRE(|| fibers)* AFRE(|| fibers)* CFRE(|| fibers)*

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Chapter 6 - 15

(at lower temperatures, i.e. T < Tmelt/3)

Plastic (Permanent) Deformation

• Simple tension test:

engineering stress, engineering strain, Elastic+Plastic at larger stress p plastic strain

Elastic

initially

Adapted from Fig. 6.10(a), Callister & Rethwisch 8e. permanent (plastic)

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Chapter 6 - 16

• Stress at which

noticeable

plastic deformation has

occurred.

when

_p

= 0.002

Yield Strength,

_y

y

= yield strength

Note: for 2 inch sample

= 0.002 = z/z

z = 0.004 in

Adapted from Fig. 6.10(a), Callister & Rethwisch 8e.

tensile stress,

engineering strain,

y

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Chapter 6 - 17

Room temperature

values

a = annealed hr = hot rolled ag = aged

cd = cold drawn cw = cold worked

qt = quenched & tempered

Yield Strength : Comparison

Graphite/ Ceramics/ Semicond Metals/ Alloys Composites/ fibers Polymers

Y

ie

ld

s

tre

ng

th,

y

(MPa)

PVC H ard t o m easure , since in te n sion , fract u re u su a lly o ccu rs b e fo re y ield . Nylon 6,6 LDPE 70 20 40 60 50 100 10 30 200 300 400 500 600 700 1000 2000 Tin (pure) Al (6061)a Al (6061)ag Cu (71500)hr Ta (pure) Ti (pure)a Steel (1020)hr Steel (1020)cd Steel (4140)a Steel (4140)qt Ti (5Al-2.5Sn) a W (pure) Mo (pure) Cu (71500)cw H ard to m eas ure, in ce ram ic m a trix a n d e p o x y m a trix co m p o site s, since in te n sion , fract u re u su a lly o ccu rs b e fo re y ield . HDPE PP humid dry PC PET ¨

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Chapter 6 - 18

Tensile Strength, TS

• Metals

: occurs when noticeable

necking starts.

• Polymers

: occurs when

polymer backbone chains are aligned and about to break.

y

strain

Typical response of a metal

F = fracture or ultimate strength Neck – acts as stress concentrator

en

gine

ering

TS

stress

engineering strain

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Chapter 6 - 19

Tensile Strength: Comparison

Si crystal <100> Graphite/ Ceramics/ Semicond Metals/ Alloys Composites/ fibers Polymers

T

en

si

le

st

re

ng

th,

TS

(MPa)

PVC Nylon 6,6 10 100 200 300 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) a W (pure) Cu (71500)cw LDPE PP PC PET 20 30 40 2000 3000 5000 Graphite Al oxide Concrete Diamond Glass-soda Si nitride HDPE wood( fiber) wood(|| fiber) 1 GFRE(|| fiber) GFRE( fiber) CFRE(|| fiber) CFRE( fiber) AFRE(|| fiber) AFRE( fiber) E-glass fib C fibers Aramid fib

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.

Room temperature

values

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Chapter 6 - 20

• Plastic tensile strain at failure:

Ductility

• Another ductility measure:

_x

₁₀₀

A

RA

%

o f o

-

=

x 100

L

EL

%

o o f

L

_f

A

_o

A

_f

L

_o

Engineering tensile strain, E ngineering

tensile stress,

smaller %EL

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Chapter 6 - 21

• Energy to break a unit volume of material

• Approximate by the area under the stress-strain curve.

Toughness

Brittle fracture: elastic energy

Ductile fracture: elastic + plastic energy

very small toughness (unreinforced polymers)

Engineering tensile strain, E ngineering

tensile stress,

small toughness (ceramics)

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Chapter 6 - 22

Resilience, U

_r

• Ability of a material to store energy

– Energy stored best in elastic region

If we assume a linear

stress-strain curve this

simplifies to

y y r

2

1 U

y

d

U

_r

0

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Chapter 6 - 23

Elastic Strain Recovery

St re ss Strain 3. Reapply load 2. Unload D Elastic strain recovery 1. Load y_o y_i

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Chapter 6 - 24

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

d

D Smaller indents mean larger hardness. increasing hardness most plastics brasses Al alloys easy to machine

steels file hard

cutting tools

nitrided

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Chapter 6 - 25

Hardness: Measurement

• Rockwell

– No major sample damage

– Each scale runs to 130 but only useful in range

20-100.

– Minor load 10 kg

– Major load 60 (A), 100 (B) & 150 (C) kg

• A = diamond, B = 1/16 in. ball, C = diamond

• HB = Brinell Hardness

– TS (psia) = 500 x HB

– TS (MPa) = 3.45 x HB

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Chapter 6 - 26

Hardness: Measurement

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Chapter 6 - 27

True Stress & Strain

Note: S.A. changes when sample stretched

• True stress

• True strain

i T

F

A

o i T

ln



ln

1

T T

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Chapter 6 - 28

Hardening

• Curve fit to the stress-strain response:

T

K

T n

“true” stress (F/A) “true” strain: ln(L/Lo)

hardening exponent:

n = 0.15 (some steels)

to n = 0.5 (some coppers)

• An increase in

_y

due to plastic deformation.

large hardening

small hardening

y

₀

y

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Chapter 6 - 29

Variability in Material Properties

• Elastic modulus is material property

• Critical properties depend largely on sample flaws

(defects, etc.). Large sample to sample variability.

• Statistics

– Mean

– Standard Deviation

s

n

x

_i

x

2

n 1

1 2

n

x

n n

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Chapter 6 - 30

• Design uncertainties mean we do not push the limit.

• Factor of safety, N

N

y working Often N is between 1.2 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

d

2

/ 4

5 N

y working 1045 plain carbon steel: y = 310 MPa TS = 565 MPa F = 220,000N

d

L o

d = 0.067 m = 6.7 cm

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Chapter 6 - 31

• 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 _y.