Effect Load to Materials

8/3/2019 Effect Load to Materials

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Effect of Load to

Materials

MECHANICAL

PROPERTIES

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Cha ter Outline

Terminolo for Mechanical Pro erties

The Tensile Test: Stress-Strain Diagram

True Stress and True Strain

Hardness of Materials


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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 muchdeformation occurs? What materials deform least?

Plastic behavior: At what point do dislocations

cause permanent deformation? What materials aremost resistant to permanent deformation?

Toughness and ductility: What are they and how

o we measure em Ceramic Materials: What special provisions/tests

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are ma e or ceram c ma er a s


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-

specimen

4

machine


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Tensile Test

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Important Mechanical Properties

Young's Modulus: This is the slope of the linearpor on o e s ress-s ra n curve, s usua yspecific to each material; a constant, known value.

yield point, calculated by plotting young's modulus

at a specified percent of offset (usually offset =. .

Ultimate Tensile Strength: This is the highestvalue of stress on the stress-strain curve.

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

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Terminology Load - The force applied to a material during

.

Strain gage or Extensometer- A device used for

.

Engineering stress - The applied load, or force,v e y e or g na cross-sec ona area o e

material.

Engineering strain - The amount that a materialdeforms per unit length in a tensile test.


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Elastic Deformation

1. Initial 2. Small load 3. Unload

bondsstretch

initial

F F Linear-elastic

Elastic means reversible.Non-Linear-elastic

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Plastic Deformation (Metals)

1. Initial 2. Small load 3. Unload

bonds

p anes

stillsheared

stretch& planes

F

e as c + p as c

linear linear

F

9

.

plastic


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T ical stress-strainbehavior for a metal

showin elastic and

plastic deformations,the ro ortional limit P

and the yield strength

, as determined usingthe 0.002 strain offset

method (where there isnoticeable plastic deformation).

P is the gradual elastic

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to plastic transition.


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Plastic Deformation (permanent)

From an atomic perspective, plastic

bonds with original atom neighbors and.

After removal of the stress, the large

,

not return to original position.

e s reng s a measure o res s anceto plastic deformation.

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(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

The image shows necked region in a fractured sample


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Permanent Deformation

Permanent deformation for metals is

accom lished b means of a rocess called

slip, which involves the motion ofdislocations.

Most structures are designed to ensure that

is applied.

,experienced a permanent change in shape,

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intended.


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Yield Strength, y

tensile stress,

ytensile stress,Elastic+Plasticat larger stress

Elastic

initially

en ineerin strain

permanent (plastic)after load is removed

engineering strain,p = 0.002

plastic strain

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Stress-Strain Diagram (cont)

Elastic Region (Point 1 2)

- The material will return to its ori inal sha e

after the material is unloaded( like a rubber band).- The stress is linearly proportional to the strain in

this region.

E

E or

: Stress(psi)

E :Elastic modulus (Youngs Modulus) (psi)

: Strain (in/in)

- Point 2 : Yield Strength : a point where permanent

e orma on occurs. s passe , e ma er a w

no longer return to its original length.)


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Strain Hardening

- ,

curve will follow back to Point 3 with the same

Elastic Modulus (slope).

- The material now has a higher yield strength ofPoint 4.

- Raisin the ield stren th b ermanentl

straining the material is called Strain

.


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Tensile Strength (Point 3)

-

Tensile Strength(TS) or Ultimate Tensile Strength

- It is the maximum stress which the material can

.

Fracture (Point 5)

- If h m ri l i r h d nd P in h r

decreases as necking and non-uniform deformation

occur.

- Fracture will finally occur at Point 5.


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The stress-strain curve for an aluminum alloy.



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Stress-strain

found for

some steels

point

phenomenon.

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T

E

N

S

I

L

E

P

R

P

E

R

T

I

22

E

S


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Yield Strength: Comparison

Ceramics/Semicond

Metals/Alloys

Composites/fibers

Polymers

2000Steel (4140)qt

MPa

)

eforeyie

ld.

500600700

1000

Ti (5Al-2.5Sn)aW (pure)

Mo (pure)Cu (71500)cw

osites

,since

oreyield

.

h,y

(

as

ure

,

allyoccurs

200

300

400

Al (6061)ag

Ti (pure)aSteel

(1020)hr

Steel (1020)cdee (4140)

ea

sure,

matrixcomp

llyoccursbe

Room T values

reng

Hardtom

n,

fractureus

N lon 6 67060

100

Cu (71500)hr

Hardto

trixandepox

fractureusua

dry

PC

a = annealedhr = hot rolledag = agedcd = cold drawn

ields

PVC

inceintensio

4050

30

nceramicm

a

intension

,

HDPEPP

humidPET cw = co wor e

qt = quenched & tempered

23

s

LDPE

10 Tin (pure)

i


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Tensile Strength, TS

After yielding, the stress necessary tocontinue plastic deformation in metals

increases to a maximum point (M) and

point (F). All deformation up to the maximum

sample.

However, at max stress, a small

constriction or neck be ins to form.

Subsequent deformation will be

confined to this neck area.

Fracture strength corresponds to the

stress at fracture.Region between M and F:

Metals: occurs when noticeable necking starts.

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Ceramics: occurs when crack propagation starts.

Polymers: occurs when polymer backbones are aligned and about to break.


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n an un e ormethermoplastic polymer

tensile sample,

are randomlyoriented.

b When a stress is

applied, a neck

develops as chains

become alignedlocally. The neck

continues to grow

until the chains in the

ent re gage engthave aligned.

(c) The strength of the

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Tensile Strength: Comparison

Ceramics/Semicond

Metals/Alloys

Composites/fibers

Polymers

) 30005000

E-glass fib

C fibersAramid fib

(MP

a1000

Steel (4140) a

Steel (4140) qt

Ti (5Al-2.5Sn) aW (pure)

Cu (71500) cw

2000

Diamond

Si nitride

GFRE(|| fiber)CFRE(|| fiber)

AFRE(|| fiber)

Room T values

Si crystalth

,TS

100

200

300

Al (6061) a

Al (6061) ag

Cu (71500)

Ta (pure)Ti (pure)a

Steel (1020) Al oxide

wood(|| fiber) Based on data in Table B4, Callister 6e.

treng

PVC

y on ,

PP

PC PET

20

3040

Graphite

Concrete

Glass-soda

HDPE

GFRE( fiber)CFRE( fiber)AFRE( fiber)

a = annea e

hr = hot rolled

ag = aged

cd = cold drawn

cw = cold worked

sile 10

qt = quenched & temperedAFRE, GFRE, & CFRE =

aramid, glass, & carbon

fiber-reinforced epoxy

26Te wood( fiber)

1

,

fibers.


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Engineering Stress

Tensile stress, : Shear stress, :Ft Ft F

Area, A Area, A Fs

Ft

Ft FtF Fs

original areabefore loading

o

27Stress has units: N/m2 or lb/in2


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

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

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Example 1

Convert the change in length data in the table to engineering-


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Example 1 SOLUTION


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ToughnessToughness is

Lower toughness: ceramics

Higher toughness: metals

absorb

energy up to

rac ure (energy

per unit volume ofmaterial).

A tough

material has

ductility.

pprox ma eby the area

under the

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stress-strain

curve.


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Toughness

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

curve.

Engineering smaller toughness (ceramics)

-

tensilestress,

larger toughness(metals, PMCs)

unreinforcedpolymers

Engineering tensile strain,

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Linear Elastic PropertiesF

Hooke's Law: = E

Poisson's ratio:metals: ~ 0.33

Fsimpletension

xy

ceramics: ~0.25polymers: ~0.40

Modulus of Elasticity, E:

'1

E

Linear-elastic

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Units:

E: [GPa] or [psi]

: dimensionless


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Engineering Strain

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Strain is dimensionless.


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

contractions (negative strains) in response to an imposed

tensile stress.

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True Stress and True Strain

True stress The load divided by the actual cross-sectional

area of the specimen at that load.

original dimensions, given by

t ln(l/l0).

The relation between the true stress-rue s ra n agram an eng neer ng

stress-engineering strain diagram.

The curves are identical to the yield

oint.


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Stress-Strain Results for Steel Sample

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Example 2:


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Example 2:Youngs Modulus - Aluminum Alloy

From the data in Example 1, calculate the modulus ofelasticity of the aluminum alloy.


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Example 2: Youngs Modulus - Aluminum Alloy - continued

Use the modulus to determine the length after

deformation of a bar of initial length of 50 in.

Assume that a level of stress of 30,000 psi is applied.


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Youngs Moduli: Comparison

1200

MetalsAlloys

GraphiteCeramicsSemicond

PolymersComposites

/fibers

Steel, Ni

Molybdenum Si nitrideAl oxide Carbon fibers only

200

600800

1000

400 Tungsten

< >

Si carbide

Diamond

CFRE(|| fibers)*E GPa

Eceramics

> Emetals>> E

Magnesium,

Aluminum

Platinum

Silver, GoldZinc, Ti

Si crystal

Glass-soda

Concrete

Glass fibers only

Aramid fibers only

40

6080

100

Tin

Cu alloys

GFRE(|| fibers)*

AFRE(|| fibers)*

8

Graphite

AFRE( fibers)*

CFRE*

GFRE*

6

10

20

CFRE( fibers)*

GFRE( fibers)*

10 Pa Composite data based onreinforced epoxy with 60 vol%of aligned carbon (CFRE),aramid (AFRE), or glass (GFRE)

1

PC Epoxy only

0.8

2

4

HDPEPP

PS

PET fibers.

410.2

0.6 Wood( grain)

0.4PTFE

LDPE

Example 3: True Stress and True Strain


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Example 3: True Stress and True StrainCalculation

Compare engineering stress and strain with true stress andstrain for the aluminum alloy in Example 1 at (a) themaximum load. The diameter at maximum load is 0.497in. and at fracture is 0.398 in.

Example 3 SOLUTION


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Strain Hardening

plastic deformation.

large hardening

small hardeningy0

y1

un

loa

re

loa

d

hardening exponent:=

T C T

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

.to n=0.5 (some copper)


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The Bend Test for Brittle Materials

-

that is supported on each end to determine theresistance of the material to a static or slowly applied

oa .

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.


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The stress-strain behavior of brittle materials compared withthat of more ductile materials


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a The bend test often used for measurin the stren th

of brittle materials, and (b) the deflection obtained bybending

Flexural Strength


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Flexural Strength

Schematic for a 3-

point bending test.

stress-strain behavior

and flexural strength

of brittle ceramics.

Flexural strength

(modulus of rupture or

bend stren th is thestress at fracture.

See Table 7.2 for more values.

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MEASURING ELASTIC MODULUS

Room T behavior is usually elastic, with brittle failure. 3-Point Bend Testing often used.

-- ens e es s are cu or r e ma er a s.

FL/2 L/2cross section

= midpoint

deflection

brect. circ.

Determine elastic modulus according to:

F L3

F L3F

4bd3 12R4rect. circ.

F

slope =

23

section

sectionlinear-elastic behavior


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MEASURING STRENGTH

3-point bend test to measure room T strength.

Fcross section

R

bd

. .

location of max tension

exura s reng :

fs mfail

1.5FmaxL

FmaxL

yp. va ues:Material fs(MPa) E(GPa)

Si nitride 700-1000 300

rect.

xF

FmaxSi carbideAl oxideglass (soda)

550-860275-55069

43039069

24max

Data from Table 12.5, Callister 6e.


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-

3 different responses:

r e a ure

B plastic failureC - highly elastic (elastomer)

60

(MPa)

xbrittle failure

20

40

x

x

elastomer

plastic failure

initial: amorphous chains arekinked, heavily cross-linked.

are straight,

stillcross-linked

00 2 4 6 8

Deformationis reversible!

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

--plastic response (semi-crystalline case)


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Hardness of Materials

ar ness es - easures e res s ance o a ma er a o

penetration by a sharp object. Macrohardness - Overall bulk hardness of materials

measured using loads >2 N.

Microhardness Hardness of materials typically measured

usin loads less than 2 N usin such test as Knoo(HK).

Nano-hardness - Hardness of materials measured at 1

forces.

H d


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Hardness

Hardness is a measure of a materials resistance

to localized lastic deformation a small dent or

scratch). Quantitative hardness techni ues have been

developed where a small indenter is forced into

the surface of a material. The depth or size of the indentation is measured,

and corresponds to a hardness number.

The softer the material, the larger and deeper theindentation (and lower hardness number).

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Hardness


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Hardness

Resistance to permanently indenting the surface.

Large hardness means:--

compression.--better wear properties.

e.g.,10mm sphere

apply known force(1 to 1000g)

measure sizeof indent afterremoving load

dDSmaller indentsmean largerhardness.

mostplastics brassesAl alloys easy to machinesteels file hard cuttingtools nitridedsteels diamond

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ncreas ng ar ness

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.)

H d T t


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Hardness Testers

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Conversion of


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Conversion of

ar nessScales

-Volume 03.01

Standard Hardness Conversion

Tables for Metals Relationship

Among Brinell Hardness, Vickers

Hardness, Rockwell Hardness,

Superficial Hardness, Knoop

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,

Hardness

Correlation


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Correlation

e weenHardness and

Tensile

Stren th

Both hardness and tensile

a metals resistance to

plastic deformation.

,

brass, the two are roughlyproportional.

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Tensile strength (psi) =

500*BHR


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Summary


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Summary

Stress and strain: These are size-independent

measures of load and dis lacement res ectivel .

Elastic behavior: This reversible behavior often

shows a linear relation between stress and strain.,

large elastic modulus (E or G).

Plastic behavior: This permanent deformation

e av or occurs w en e ens e or compress ve

uniaxial stress reaches y.

Toughness: The energy needed to break a unit

volume of material.

Ductility: The plastic strain at failure.

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