A Study of the effects of strain on NiTi shape memory alloy

Rochester Institute of Technology

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A Study of the effects of strain on NiTi shape

memory alloy

Bret Oltmans

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Recommended Citation

A STUDY OF THE EFFECTS OF STRAIN

ON NiTi SHAPE MEMORY ALLOY

by

Bret Allen Oltmans

A Thesis Submitted in

Partial Fulfillment of the

Requirement for the

MASTER OF SCIENCE

IN

MECHANICAL ENGINEERING

Approved by:

Dr. Surendra K. Gupta

Department of Mechanical Engineering

Dr. Hany Ghoneim

Department of Mechanical Engineering

Dr. Andreas Langner

Department of Chemistry

Dr. Satish G. Kandlikar

Department Head of Mechanical Engineering

(Thesis advisor)

DEPARTMENT OF MECHANICAL ENGINEERING

ROCHESTER INSTITUTE OF TECHNOLOGY

Thesis Reproduction Permission Statement

A

Study of the Effects of Strain on NiTi Shape Memory Alloy

I, Bret Oltmans, hereby grant permission to the Wallace Library of the Rochester

Institute of Technology to reproduce my thesis

in whole or in part. Any reproduction

will

not be for commercial use or profit.

Date:

/

Dh

>/zt7l:Jb

Abstract

Shape

memory

alloys are materialsthatare capable of

returning

toanoriginal

shape after

large deformations

in

responsetoastimulus.

Shape memory

alloys can

be

metals, ceramics,polymers and gels.

This

thesisstudiesthechanges of various properties

of

NiTi

metal as samples are prestrained variousamounts.

After conducting

various

characterization

techniques,

relationshipswere

developed for

thechanges

in

transformation

temperatures,

Knoop

hardness

number, andcrystal

lattice

parameters.

Through

theuse of

differential scanning calorimetry

and

dynamic

mechanical

analysisthe transformation temperatureswere

determined. It

wasobserved

in

both

experimentsthatthe

initial

austenite start

temperature(As)

increased parabolically

while

austenite

finish

temperature

(Af)increased

linearly

withprestrain.

Also,

DSC

showedthat

Martensite

starttemperature

(Ms)

increased

linearly

with_prestrain,

however,

DMA

did

not show

any

trend

for Ms.

Knoop

hardness

testsas well as

deformation

testswere performedto

investigate

changes

in

themechanical propertiesof

NiTi

with

increased

prestrain.

It

was

found

that

the

Knoop

hardness

number

increased

linearly

with

increased

prestrain.

Additionally,

from

tensile

data

collected

during

the

deformation

testing,

it

was

found

that themaximum

flow

stressat each strain amount

follows

a parabolictrend.

Also

from

thestress-strain

data,

it

was

found

that

NiTi

has

a

higher

strain

hardening

coefficientthanmost materials.

When

Knoop

hardness

numbers were comparedto the true stress_values,

it

was

found

that

the

hardness

number

increased

following

a cubictrendwith

increasing

stress.

Using X-Ray

diffracton,

thecrystalstructureofthe

NiTi

was

found

to

be

monoclinic with

lattice

_parameters,a=

2.884,

b

=

4.637,

c =

4.101,

y

=

97.7.

It

_wasalso

observedthat the volumeoftheunitcellremainedconstant regardlessofprestrain.

Using

an opticalmicroscope,

large

grainswithstripesperpendicularto the

prestrain

direction

were observed.

The

occurrenceand sizeofthesegrains

increased

with

theamount of prestrain.

Surface

scans

using

atomic

force microscopy

showedthatthese

stripes were all

approximately

thesame

depth

and

regularly

spaced.

These

grains

appearedto

be

self-accommodated martensite regions

but

could not

be

fully

characterized

Acknowledgements

First I

would

like

to

say

a

huge

thankyouto

my

family

and

friends for

supporting

methrough theups and

downs

of

my

research.

I

also owea

debt

ofgratitudeto

Dr.

Gupta for serving

as

my

thesisadvisor.

Without his

extensive

knowledge

and experience

in

thematerials science

field,

this thesis

wouldnot

have

been

possible.

I

would also

like

to thank

him

for

encouraging

meto

participate

in

the

Undergraduate Materials Research Initiative

sponsored

by

the

Materials

Research

Society

in

which

I

wasawardedan

honorable

mention

for

an

initial

proposalof

my

research.

I

would also

like

to thank

Dr. Langner for

letting

meuse

his lab

equipment and

for

spending many hours

teaching

me

how

to use

DSC

and

DMA.

Also,

both Dr. Langner

and

Dr. Ghoneim

deserve

a

huge

thankyou

for

taking

Table

of

Contents

Title Page i

Thesis Reproduction Permission Statement ii

Acknowledgements v

TableofContents vi

IndexofFigures vii

ListofTables viii

ListofTerms&Symbols ix

Introduction 1

Shape

Memory

Effect 2

Crystallography

oftheShape

Memory

Effect 4

Mechanical PropertiesofNiTi 9

OtherCharacteristicsofNiTi 15

Experimental Plan 17

Materials 17

Specimen Preparation 17

Differential

Scanning Calorimetry

20

Dynamic MechanicalAnalysis 22

X-ray

Diffraction 26

Hardness

Testing

29

Optical

Microscopy

32

Atomic Force

Microscopy

33

Data/Processing

Method 34

DeterminationofModulusof

Elasticity

34

DeterminationofTransformation Temps 35

Differential

Scanning

Calorimetry

35

Dynamic Mechanical Analysis 37

Hardness 39

Strain

Hardening

Exponent 39

Results/Discussion 41

Differential

Scanning Calorimetry

41

Dynamic MechanicalAnalysis 46

Hardness

Testing

50

Mechanical

Testing

52

X-Ray

Diffraction 58

Optical

Microscopy

60

AtomicForce

Microscopy

62

VerificationofDeveloped Correlations 64

Conclusions 75

Appendicies 78

Appendix A 78

Appendix B 80

AppendixC 83

AppendixD 88

AppendixE 89

Index

of

Figures

Figure 1 Shape

Memory

Process 3

Figure2 Diagramof phases asNiTiis heatedand cooled 4

Figure 3 Lattice Parametersof aCrystal System 5

Figure4 Crystal StrucureofB19'NiTi 6

Figure5 Exampleof aTwin

Boundary

8

Figure6

Twinning during heating

and_cooling 8

Figure7 Exampleof self-accommodation 9

Figure8 SpecimeninTension 1 1

Figure9 Stress-Strain Curve for NiTi 13

Figure 10 Tension Apparatus

Setup

18

Figure 1 1

Polishing

Disk Dimensions 19

Figure 12 Typical DSC ScanofNiTi 20

Figure 13 Three DSC Cycles 21

Figure 14 Elastic Response

Analogy

23

Figure 15 Dynamic Responseof aMaterial 24

Figure 16 Three-point

Bending

Apparatus 25

Figure 17 DiffractionofX-Rays

by

a crystal 27

Figure 18

Knoop

Indentor 30

Figure 19

Knoop

Indentation in NiTiSurface 30

Figure 20 DeterminationofTransformation Temperatures from DSC 37

Figure 21 DeterminationofTransformation TemperaturesfromDMA 38

Figure 22 ExampleofShiftof

As

and

Af

42

Figure 23 TrendofInitial

As

Temperatures 43

Figure 24 Absenceof peaks wheninitial

As

and

Af

not surpassed 44

Figure 25 Average

Ms

temperaturesas afunctionof prestrain 45

Figure 26

Af

Temperatureas afunctionof prestrain 46

Figure 27 Initial

As

as afunctionof prestrain(from

DMA)

47

Figure 28 Average

Ms

temperatureas afunctionof prestrain(from

DMA)

48 Figure 29 Initial

Af

temperaturesas afunctionof prestrain(from

DMA)

49

Figure 30 KHNas afunctionofPrestrain 52

Figure 31 Max True StressvsTrue Strain 53

Figure32

Knoop

Hardness NumberVs True Stress 54

Figure 33 Powercurvefittoplasticdeformationregionof15%sample 56 Figure 34 Powercurvefittoplastic region of20%sample 56 Figure35 Brightfield ImageofStriped Grain at500X 61

Figure 36 Brightfield ImageofStripedGrain at 1000X 61

Figure 37 2-Dimensional AFM Image 62

Figure 38 3-Dimensional AFM Image 63

Figure39 Section ViewofAFM Image 63

Figure 40 Initial

As

as afunctionof prestrainfrom DSC 65

Figure41 DMA

Heating

Curves for 17% Sample 66

Figure 42 Initial

As

from DMA 67

Figure 43 Average Ms from DSC 68

Figure44 Average

Ms

temperaturesfromDMA 68

Figure 45 Initial

Af

TemperaturefromDSC 69

Figure46 Initial

Af

TemperaturefromDMA 70

Figure47 Powercurvefor 17%sample 72

Figure 48 Maximumtruestress values 73

Figure 49 KHNasafunctionof prestrain 74

Figure 50 KHNasafunctionoftruestress 75

List

of

Tables

Table 1. Specimen Lengths 18

Table2 Transformation Temperatures fromDSCin C 41

Table3 Initial Austenitic Transformation Temperatures 42

Table4 Final KHNValues 51

Table5 Modulusof

Elasticity

ValuesFound From Tensile

Testing

54

Table 6 Strain

Hardening

Exponents forvarious materials 57

Table7 Springbackvalues upon_unloading 58

Table8 Monoclinic Lattice Parameters 58

Table9 Transformationtemperaturesfor17%samplefromDSC 70

Table 10 Transformationtemperatures for17%samplefromDMA 70 Table1 1 Modulusof

Elasticity

determined fromtensiledata for 17%sample 71

Table12 Strain

hardening

exponent 71

List

of

Terms

&

Symbols

A

Instantaneous

Area

ofthe

Specimen

Ao

Original Area

ofthe

Specimen

Af

Austenite Finish Temperature

AFM

Atomic Force

Microscopy

As

Austenite

Start Temperature

Av

Area

ofthe

Specimen

at

Yield Point

D

Interplanar

Spacing

5

Change in Specimen Length

DMA

Dynamic Mechanical Analysis

DSC

Differential

Scanning Calorimetry

E*

Complex Modulus

E,E'

Modulus

of

Elasticity

(Young's

Modulus)

E"

Imaginary

Loss Modulus

Save

Average Strain

et

True

Strain

KHN

Knoop

Hardness Number

L

Instantaneous Length

ofthe

Specimen

Lo

Original Length

ofthe

Specimen

Lf

Final Length

ofthe

Specimen

Lv

Length

ofthe

Specimen

at

Yield Point

Mf

Martensite Finish Temperature

Ms

Martensite

Start Temperature

v

Poisson's Ratio

SE

Superelasticity

SMA

Shape

Memory

Alloy

SME

Shape

Memory

Effect

^eng

Engineering

Tensile Stress

0"trae

True Tensile

Stress

t

Instantaneous Thickness

ofthe

Specimen

to

Original Thickness

ofthe

Specimen

e

Bragg

Angle

w

Instantaneous

width ofthe

Specimen

w0

Original

width ofthe

Specimen

XRD

X-ray

Diffraction

Introduction

Shape

Memory

Alloys

(SMA)

are

very

interesting

alloysthat

have become

apart

of

everyday

life

for

many

peoplewithoutthemeven

knowing

it. Shape memory

alloys

gettheirname

because

oftheirunique

ability

to"remember"theiroriginal shape even afterthe

alloy is apparently plastically deformed. The

shapethata

SMA

remembers

is

determined

by

_{the user,} and

it

can

be easily

changedwith proper

heat

treatment.

Depending

onthecertain characteristicsof_{the alloy,}

it

can recoverthe

deformation

once

it is heated

above acertain_{temperature or,}

it

will

automatically

returnto

its

original

shape oncethestress

is

removed.

In

thecase

of

thematerialusedinthis study, the

alloy

remembers

its

original shape afterit is

heated

above a certain temperature.

The

first

recorded

incident

of amaterial

exhibiting

shape

memory

characteristicswas

in

1951,

and

thematerialwasan

Au-Cd

alloy.

Later

in 1963

atthe

Naval

Ordinance

Laboratory

(NOL),

theshape

memory

phenomenon was observed

in

anequiatomic

NiTi

alloy, and

the

alloy

wasgiventheacronym

NiTi-NOL

or

Nitinol1.

Since its

discovery

in

1963,

NiTi

has beeen

used

in many different

applicationssuch aspipe_{couplings, antennas, actuators,}

and

they

arealso

being

used

extensively in

themedical and

dental fields.

The

shape

memory

phenomenon occurs

because

of a

crystallographically

reversible martensitic phasetransformation.

The

transformation

is

difiusionless,

where

theatoms shift small

distances from

an ordered

high

temperaturephase

(austenite)

to a

lower energy

phase

(martensite). Another

interesting

characteristic of

NiTi

is

superelasticity

(SE). In

SE,

large

stress

induced

deformations

are recovered whenthe

The

shape

memory

phenomenon and

superelasticity

will

be

discussed

atagreater

length

in

thesubsequentpages.

The

goal ofthisresearch

is

to

study

thechangesofvarious properties of shape

memory NiTi

when specimens are prestrained

different

amounts.

The

propertiesthatwill

be investigated

are

hardness,

transformation

temperatures,

modulus ofelasticity, and

microstructure.

Different

characterizationtechniqueswill

be

usedtorecordthechanges

in

theseproperties asthepre-strain amount

is

varied.

Shape

Memory

Effect

The

mechanism

behind SME is

ashear-like

deformation

where a

difiusionless

phasetransformationoccurs.

This

transformation

is

a

crystallographically

reversible

martensitictransformation.

Figure 1

is

asimple schematic

showing

the shape

memory

process

from

amicroscopic point of view.

Depending

onthe

temperature,

the

SMA

can

either

be

austenite or_{martensite, the}

latter

being

the

low energy

(temperature)

phase.

Assuming

the

SMA is

atatemperature

below

themartensitetransformation

finish

temperature

(Mf)

temperatureand_undeformed,the

SMA

will

be in

the twinned

Austenite

i

?

Heating

Cooling

Deformed Martensite

[image:13.514.158.360.46.250.2]

Twinned Martensite

Figure 1 Shape

Memory

Process1

In

_{twinned martensite, there}

may

be

many

regions of martensitethat

have

the

same structure

but

areoriented

differently,

andtheseare calledcorrespondencevariants.

When

astress

is

applied_{to the twinned martensite,}

it deforms

by

themovement oftwin

boundaries. As

thestress

is

increased,

the variants

begin

toorientthemselves

into

a

preferredorientationthatpermitsthe

largest

deformation.3

In

thecase ofa single crystal

as

in Figure 1

, onesingle variantcan

be

produced as shown

by

the

deformed

martensite

stage.

If

the

SMA

is

then

heated,

reversetransformationwilltakeplace andthe

martensitewilltransform

into

theparent

austenite.1"3

Ifthe

SMA

is

thencooled_again,

self-accommodatingmartensite will

be

formed,

andthe

SMA

will

be in

thesame state as

the

beginning

ofthe

description

ofthe shape

memory

process.

If

theunstrained

self-accommodatedmartensite

is

heated,

it

will still revertto theparent austenite eventhough

no deformationtakesplace.

It

is

thereversetransformation

from

the

deformed

martensite

Something

not mentioned

in

theprevious example

is

that thesetransformations

start and end at certaintemperatures.

The

transformation

from

parent austeniteto

martensite

begins

atthe

Ms

temperatureand

is

completed atthe

Mf

temperature.

The

transformation

from

martensitetoaustenite

begins

at

As

and

finishes

at

Af. Figure 2

graphically

portraysthephasethat

NiTi

is in

as

it is

heated

andcooled.

It

is

important

to

noticethatwhenthe temperatureof

NiTi

falls between

either

Ms

and

Mf

or

As

and

Af,

both

phases arepresent.

B19'

-i

BlS'frP3

Completely

Austeaite

Phases

During Cooling

B2

B19' B19'

Completely Martensite

BI9'

B19'&B2

12

Mf

M,

Phases

During Heating

Af

Figure 2 Diagramof phases asNiTiis heatedand cooled

Another important

thing

tonotice

is

thatthere

is

a

hysteresis

associatedwiththe

phasetransformations.

This

meansthatthe

forward

andreversetransformation temperaturesare

different.

Typically

NiTi

has

a

20

-

40C

hysteresis,

but

it

is extremely

alloy dependent.

Crystallography

of

the

Shape

Memory

Effect

The

shape

memory

effect occurs

because

a

SMA

undergoes a

crystallographically

different

phasesthat

it

can

be in.

In

its

high-temperature

form,

NiTi

is in

its

parent

austinitic state which

has

a

CsCl

body

centered cubic

(BCC)

crystal structure which

is

denoted

by

B2.

The B2 CsCl

crystal

has

side

lengths

where a=

b

=

c=

0.301

-0.302nm

anda=

(5

=

y

=90.3

See Figure 3 for

thesideand angle

designations.

Figure 3 Lattice Parametersof aCrystalSystem4

In

its low

temperaturestate,

NiTi

is

in

a

low energy

martensiticphase which

has

a

monoclinic structure which

is denoted

by

B19'

with

lattice

parameters a*

b

*_c,and

a=

y

= 90

*

p. For

amonoclinic _{crystal, the}

lattice

parametersreported

by

Sinclair

et al

were,a=

0.2885

nm,

b

=

0.4622

nm,c =

0.4120

nm, and

y

=96.80.5

As

mentionedpreviously, theshape

memory

effect and

superelasticity

depend

heavily

onamartensitictransformation

(MT). In

MT,

theatomsmove_{cooperatively,}

often

by

ashear-like mechanism.

The

martensitictransformation

begins from

theordered

parent austenite phase andendswiththe

lower symmetry

monoclinic phase.

Previously

it

wasmentionedthat

low

temperaturemartensite

may

consist of

many

regions withthe

parent phase.

It

has

also

been

proventhat

MT

is

a

linear

transformation.

To

see

this,

one

can gothroughallthe

linear

algebra

behind

MT2,

orone cantakeasingle crystal

SMA

and scratch a straight

line in

thesurface andallow

it

to cool.

Upon

cooling, the

line

will

change

direction

andremainstraight.

Since

a

line

anda surface

become

a

different

line

and_surface,

it

demonstrates

thatashape changeassociated with

MT

is

linear.

In

termsof_{crystallography,} each

(110)

planeoftheparentphase

deforms nearly

to a

hexagonal

network and shifts

in

the

[1 1

0]

direction

by

ashear_resulting

in

a

stacking

arrangement as shown

in Figure 4.

IstUyer

\0

\0Nl

[100]

O

L

o

\

O

0th Layer \?68'

[001]

Figure 4 CrystalStrucureofB19*NiTi6

It

was

previously

mentionedthat

during

thephasetransformation

from

theparent

austenite phasetothemartensite phasethatself-accommodation occurs.

Self-accommodation

is

the

ability

ofthemicrostructuretochange phases without

changing

shape.

In

a_{self-accommodating}micro_{structure, there}

is

a coherent arrangement of

martensite variants_occupyingaregion whose

boundary

suffersno

displacement

with [image:16.514.174.348.261.466.2]

materials

because

it

aids

in

making

thetransformationtomartensite reversible or

thermoelastic.

Since

most shape

memory

materials

in

useare_{polycrystalline,}

self-accommodation

greatly

facilitates

the

reversibility

ofphasetransformations.

In

a

polycrystalline

SMA

thereare a

large

number of

randomly

oriented grains.

Since

these

grains areall

randomly

_oriented,

any

change

in

shape would

develop

internal

stressesor

possibly

cracks

because

ofthemismatchofthegrain

boundaries. Since internal

stresses

wouldoppose the

reversibility

ofthephase

transformation,

thematerial accommodates

these

differences

which

is

known

as

"self-accommodation". Because

ofthe

accommodation_phenomenon,

it

would

be

possibletoput a

self-accommodating

microstructurewithinaustenitewithout

introducing

macroscopicstresses.

Similarly,

for

thesame_reason, martensite cannucleate withinaustenite

during

cooling in

a stress-free

manner,whicheasesthe transition

from

austenitetomartensite.

A

key

part of self-accommodationthatallowsthematerialtochangeshape

is

"twinning."

Generally,

thereare

only

twomechanisms

by

which amaterial

deforms: slip

andtwinning.

Slip

is

a permanent processand

is

common

in many

martensites.

Obviously

since

slip is

apermanent phenomenonwhereastheshape

memory

effect

is

reversible,

it

is

clearthat

NiTi

undergoes

twinning

toaccommodatethenew structure

upontransformation.

Twin

boundaries

are planesacross whichthere

is

a mirror

image

misorientation ofthe

lattice

structure4.

A

schematic of atwin

boundary

can

be

seen

in

Figure 5. Atoms

thatare

along

the twin

boundary

seethesamenumber andtypesof

Twin

Boundary

Figure 5 Exampleof aTwin

Boundary

Twin Boundaries

are capable of

interfering

withthe

slip

process and

increase

thestrength

ofthematerial.

Another

key

property

oftwin

boundary

is

that

they

areof a

very low

activation

energy

and arequitemobile.

The energy is low because

theatomsthatare

along

the

boundary

are

bonded very similarly

to those that arenot

along

the

boundary.

This

bonding

causesthe

boundaries

to

be very

mobile.

In

most_materials,themovement

oftwin

boundaries

can causethematerialto

deform,

but in

SMA,

twinning

allowsthe

materialtochange phases without

changing

thevolume or

causing any internal

stresses.

One

ofthereasonsthat

NiTi

does

not undergo

slip

to accommodatemartensite

is because

slip

requires atomic

bonds

to

be

broken,

and

twinning

allowsall atomic

bonds

to remain

intact.

Above

Af

%&

m

Parent

Phase

Un-de formed

Below

Mf

Deformation

Above

Af

iXXXM)

Parent

Phase

Figure6

Twinning during heating

and

Figure

6

shows a microscopic explanationof

twinning

througha

heating-cooling-heating

cycle.

From

the

left,

thematerial starts

in

theordered parentstatethen

is

cooledand

self-accommodatedmartensite

is formed.

Upon

deformation,

thetwin

boundaries easily

move and converttoa

different

orientationthat

better

accommodatesthestress.

When

thematerial

is

then

heated

above

Af,

it

returnsto theorderedparent austenite phase.

Figure 7

demonstrates

thisphenomenon

in Cu-Al-Ni. As

onecan see

from

this

figure,

thetwin

boundaries

move and converttoa

different

preferred orientation

according

to the

applied stress.

This

processof

condensing many

twinvariants

into

a single

favored

variant

is

called

detwinning.

'

Figure 7 Exampleof

self-accommodation2

The

occurrence of_{self-accommodating}martensite and

deformation

twinning

in SMA

leads

to

interesting

mechanical properties.

Mechanical Properties

of

NiTi

strain andtruestrain.

Engineering

strain

is defined

astheratio ofthechange

in length

to

theoriginal

length.

"

ave

j j

x '

A)

A)

True

strain, which

is

the

instantaneous

change

in linear dimension divided

by

the

instantaneous

value ofthe

dimension,

is

extremely

usefitl when

dealing

with plastic

deformation8.

L'rdL

,

Lf

<=)T=t

(2)

Another

conceptthat

is

key

to

studying

mechanics

is

stress.

Again

there aretwo

types,

engineering

stress andtrue stress.

Engineering

stress

is

the

load divided

by

the

cross-sectionalarea oftheunloaded material.

True

stress

is

the

load divided

by

the

instantaneous

cross-sectional area.

P

<7=T

(3)

p

otrue =

(

4

)

A

Given

theprevious

definitions,

thetensileproperties ofa materialcan

be

studied.

When

an axialtensile

load is

appliedto a_{metal, the}metalgoesthroughseveral stagesof

deformation.

During

the

first

stageof

deformation,

thespecimen exhibits elastic

behavior. This

meansthatthespecimen willrecover

its

original

dimensions

whenthe

load is

removed.

This recovery

should not

be

confusedwiththeshape

recovery

process

or superelasticityof

NiTi.

Elastic recovery in

most metals occursat

fractions

of a percent

strain, whilesuperelastic

NiTi

is

capable of

recovering up

to

approximately 8%

strain

uponunloading. '

[image:21.514.202.354.42.284.2]

Figure 8 Specimen in Tension

When

mostmaterialsare

deformed

elastically, the

resulting

stress

is

proportionaltothe

strain and

is

governed

by

Hooke's Law.

(j=

Es

(5)

Also in

theelastic_{region, the}contraction

in

the

y

and z-directions

(Figure

8)

is

directly

proportionalto theelongation

in

thex-directions.

sx

-vsy

=-ve,

(

6

)

Using

theprevious_equation, expressions

for

the

instantaneous

length,

width,and

thicknesscan

be developed.

L

=

L0(\+sx)

(7)

w=

w0(l-vsx)

(8)

t=

tQ(l-Vx)

(9)

Since

an_engineeringstress-straincurve

does

not

completely

depict

the

true stress

from

equations

(2)

and

(4). For

truestressthe

instantaneous

area

is

needed,

and

it is found

by

multiplying

the

instantaneous

widthandthickness.

A

=

w0t0{\-vexf

(10)

Using

this equation, the

final

equation

for

truestress

is,

^=7~y

(11)

This

elastic

behavior

continuesuntilthe

load

reachestheelastic

limit. When

the

elastic

limit is

_{exceeded, the}second stage

is

encountered where

yielding

occurs,which

meansthematerialwill notreturnto

its

original

dimensions

whenthe

load

is

_completely

removed.

This is

called plastic

deformation. In

thisstage of

deformation,

thematerial

deforms

uniformly.

Although

the

deformation

is

uniform, the strain

is

no

longer

directly

proportionalto the stress, so equation

10

no

longer correctly describes

the

instantaneous

area.

A better

representation oftheareacomes

from

the assumptionthat thevolumeof

thespecimenremainsconstantafter_yieldingoccurs.

This

assumptionallowsan

expression

for instantaneous

areato

be

_written,

Vv

=

V

=

Constant

LyAy=LA

where

Vy, Ly,

and

Ay

arethe volume,

length

and areaattheelastic

limit.

Solving

for

instantaneous

area

(A),

A

=

Ay-f

(12)

With

anewexpression

for

area, thenew equation

for

true stress

in

the uniform plastic

region

is,

Gtrae

=

PL

Ay

Ly

(13)

Once

thematerial reaches

its

ultimatestrength, the

deformation becomes

unstable

and

necking

_occurs, andthis

is

the third stage of

deformation.

Necking

is

a

localized

deformation

wherethe

increase

in

stress

is

due

to a

decrease

in

thecross-sectionalarea,

andthe

deformation

is

no

longer

uniform.

In

this study, thespecimensnever enteredthe

necking

regionsothisstage will not

be discussed

at

length.

In

NiTi,

thestress-strain

diagram looks

quite a

bit different

thanastandard

stress-straincurvethatone would see

for

atypical

ductile

material.

Martensitic NiTi

exhibits

thestress-strain characteristicsthatare shown

in Figure 9. As

one can_{see, the}material

appearsto

initially

deform

like

a standard

ductile

material,untilpoint

A.

According

to

Liu

et_{al, this}

deformation

is

due

to theelasticaccommodationoftwinbands.11

Elastic Deformation cf

Detwinned Martensite

JnselofMartensite Detwinning

Strain

[image:23.514.66.462.353.629.2]

1112

At

point

A,

the twinnedmartensiteundergoes martensite variantreorientation '

untilthemartensite

is

fully

detwinned (point B). After

themartensite

has become

fully

detwinned,

it

exhibits a

secondary

elastic

deformation.

During

this stage,

it

is

the

detwinned

martensitethat

deforms

elastically1.

At

point

C,

slip begins

andthe

deformation is

no

longer completely

reversible upon

unloading

orwhen

heated

above

Af.

Point C falls

atabouteight percent

for

thematerial used

in

this

study

which

is

consistent

withthe

generally

acceptedvalue

for

maximumrecoverable strain

in NiTi.

Other Characteristics

of

NiTi

NiTi

also

has

severalother

important

characteristicsthatarenot explored

in

this

research.

One

ofthesecharacteristics

is

called_{superelasticity}

(SE).

Superelasticity

occurs when a material recovers

from

large

deformations

upontheremoval ofthestress.

Essentially

SE is

thesameas shape

memory

_effect,

but

no

heating

is

requiredto recover

the originalshape.

In NiTi SE

occurswhenthematerial

is in its

parentaustenitic state.

The

parent state can

be

achieved

by heating

abovethe

Af,

or

it

can occur attemperatures

below

roomtemperature

depending

onthe atomiccomposition.

SE

occurs

because

of

stress

induced

martensitewhich reverts

back into

theparent austenite phase whenthe

stress

is

removed.

Essentially,

thestress actsthesameastemperature

does for

SME,

where a

decrease in

temperature

is

equivalenttoan

increase

in

stress.'

As

with

SME,

one

preferred martensite variant will

form

asthematerial

is deformed.

Another

interesting

characteristic of

SMA is

what

is known

as

two-way

memory

effect.

As

one might guess

from

thename, a

two-way

SMA

is

capable of

remembering

two

different

shapes.

The

shapesthatareremembered aretheparentaustenite_shape, as

in

standard

one-way

memory, andtheother

is

the

deformed

martensite shape.

When

the

alloy

is

above

Af,

it

takes theshapeoftheparentaustenite,thenwhen

it is

cooled

below

Mf,

it

takestheshapeofthe

deformed

martensite.

Special

thermomechanical treatments

arerequiredto producethiseffect.

This

training

introduces

microstressesthattendto

bias

thenucleationandgrowth ofmartensite,andthesemicrostresses causethematerial

totransform

from

parent austenite

directly

into deformed

martensite.1

The last

characteristicthatwill

be

mentioned

in

thissection

is

the

intermediate

lengths because

thisphase

did

not occur

in

the

alloy

studied.

This intermediate

phase

is

calledthe

R-phase because it has

arhombohedral crystal structure.

To determine

if

the

R-phase

occurs

during

the

cooling

of

NiTi,

a

DSC cooling

scancould

be

takenwherethe

alloy is

cooled

from

above

Af

to

below Mf. If

two exothermicpeaks appearonthe scan,

there

is

evidencethat the

R-phase

has

occurred.

The R-phase

producesamuch smaller

peakthanthemartensitic

transformation,

and

it

occurs at a

higher

temperature.

The

typical

hysteresis

ofthe

R-phase is only

a couple of

degrees Celsius. As

noted

before,

the

material used

in

thisresearch

does

not transitionthroughthe

R-Phase because

there

is

no

additionalpeakevidentonthe

DSC cooling

curve.

Also,

the

R-Phase

is

_usuallynot

evident

in Titanium

rich

NiTi

alloys.

Experimental

Plan

Materials

The

materialused

for

thisresearchwas

alloy BH from

Memry

Corporation in

the

form

of

0.432mm

x

1 1.379mm

ribbon.

According

to

Memry,

thecomposition ofthe

alloy

was

54.5

wt

% Ni

and

it

was coldrolled.

From

theweight percentage, theatomic

percentage of nickelwas

determined

to

be 49.4

at

% Ni.

Specimen Preparation

Six

sampleswerecut

from

theas receivedribbon_usingasmallshear.

The

sampleswere

approximately 125mm

long by

1 1mm

wide.

Since

theribbon received

from

Memry

Corporation

was

in

acold-worked_state,

it

was

necessary

to anneal all

samples at

850C

for 30

minutes.

Before

thespecimenswere placed

in

the

furnace,

all

greaseand

dirt

was removed

by

wiping

themwith methanol.

To

minimize_{oxidation, the}

samples were placed

between

aluminaplates and a steel weightwas placedon

top

ofthe

plates.

Following

the

annealing

treatment,

thespecimens werequenched

in

water at

roomtemperature.

A

second

heat

treating

process was neededto "teach"thespecimens a

shape andto givethemtheshape

memory

ability.

At

this

step

thesampleswerecleaned

againwith methanolandplaced

between

thealumina plates.

They

werethenplaced

in

the

furnace

at

350C for 30

minutes and allowedto aircool.

Once

thespecimens

had

air-cooled,

they

were prestrained

using

a

Instron

Universal

testing

machine whilethestrain was measured withan

MTS

extensometer.

Figure 10

showstheconfiguration ofthesample and extensometer

in

the

testing

machine.

specimens_{were strained with a crosshead speed of}

1.25

mm/min, andthestrainwas also

released at

1.25

mm/min.

Load

and extension

data

wererecorded

using Testworks

in

English

units and convertedto

SI

units afterthe

data

was exported

into

an

Excel

spreadsheet.

After

each specimen receivedtheproper strain_amount,

they

wereseparated

and

labeled

with

MEM850XX,

wherethe

XX

stands

for

theamount ofprestrainthe

specimen received.

After

thespecimens

had been

_prestrained,

they

werecut

into

sections

for

each

experiment.

Table 1 lists

therequired

lengths

for

each experiment.

NiTi

Specimen

Instron

Crips

MTS

Extensometer

Figure 10 Tension Apparatus

Setup

Table 1. SpecimenLengths

Experiment

Length

of

Specimen

Dynamic Mechanical Analysis

50

mm

X-Ray

Diffraction

15

mm

Microhardness

13

mm

Optical

Microscopy

13

mm

Differential

Scanning

Calorimetry

5

mm

Samples

for

X-Ray

Diffraction,

hardness

testing

andoptical_microscopy

had

to

be

mechanically

polished

before

analysis.

To

polishthe samples,sample

holders had

to

be

fabricated.

The

holders

consistedofa

32mm Bakelite

disk

with a

0.650mm

deep

groove

milled

in

one ofthe

flat

surfaces

(Figure 11). The

othersurface wasuse

for

sample

identification.

10.0

|M

0.64

Figure 11

Polishing

Disk Dimensions

Each

specimen was glued

into

thegroovewith a

drop

of superglue.

The

mechanical

polishing

was

done using

a

Rotopol-1

1,

RotoForcel

and

Multidoser

all purchased

from

Struers. For

microhardness

testing

and optical_{microscopy, the} sampleswere

left

attachedto the

Bakelite

disk,

while_{the x-ray}sample was removedwith a

drop

ofacetone

andthenmounted on aglass slide_using

double-sided

cleartape.

The DMA

samplewas

wet sanded on

#220

grit sandpapertoremove

any

oxidethatresulted

from

the

heat

treatmentprocess.

An

8-10 mg

sample wascut

from

each

DSC 5mm

piece

using

a shear

Differential

Scanning

Calorimetry

Differential scanning calorimetry

(DSC)

is

usedto

find

thermochemicaland

thermophysical

characteristicsof a substance.

The DSC

measures

heat flow into

(endothermic)

or out

(exothermic)

of a material as

it

is

heated

at a

defined

rate.

If

the

material undergoes a phase

transformation,

therewill

be

a change

in

the

heat

flow

depending

onthe typeof

transformation.

Since it

is

well

known

that

SMA

experience a

phase

change, DSC

is

an excellent choice

for monitoring

the

heat flow

of a specimen as

it

transforms

into

either austenite or martensiteoreven a

different

phase.

Another

reason

that

DSC is

excellent

for characterizing

the transformation temperatures

is

that the

sample remains unstressedthroughout theentire_experiment, and

it has been

shownthat

stress

has

a

large

effectonthe transformation temperatures. 913

A

typicalchart of

heat

flow

versustemperaturecan

be

found

in Figure 12

Temperature(C)

Figure12 Typical DSCScanofNiTi

[image:30.514.96.430.382.615.2]

From

thisscan

it is

important

_{tonoticethat there}

is

only

oneexothermic peakand

oneendothermicpeakevident

in

the

heating/cooling

cycles.

This

provesthatthis

alloy

does

nottransform

from

austeniteto the

intermediate

R-phase before

transforming

into

martensite.

In

_{this study,}samples of

8-10

mg

were cut

from

theprestrainedspecimensand

analyzed

in

a

TA

Instruments DSC 2010

differential scanning

calorimeter.

After

the

specimens were cut,

they

were cleaned withmethanoland sealed

in

aluminum specimen

pans.

Prior

to

starting

the

heating

and

cooling

_cycles,a specimen wasplaced

inside

the

calorimeter aswellas an

empty

specimen_pan,whichserved asthereferencematerial.

For

the

first

cycle, the

initial

transformation temperatureswere estimated andthe

DSC

was setto

heat

30-50C beyond

thoseestimates andcoolto

10C

atarateof

10C

per

minute.

For

thesecond and_{third cycles, the} specimenwas

heated

to 150 and cooledto

10C

at a rateof

10C

per minute.

An

exampleofthe three

heating/cooling

cycles can

be

seen

in Figure 13. All

heating

and

cooling

was

done

undera constant

flow

of nitrogenat

50ml/min.

Temperature (C)

Dynamic Mechanical

Analysis

Dynamic

mechanical analysis

(DMA)

is

a

very

usefultool

for characterizing

various materials.

DMA is

identified

by

various names suchas,

forced

oscillatory

measurements,

dynamic

mechanicalthermalanalysis

(DMTA),

dynamic

thermomechanical analysis,and

dynamic

rheology.

Lately,

DMA has been

used

extensively

on polymersto

determine different

propertiessuchas glasstransition

temperatures,

elasticity

and resistanceto creep.

Glass

transition temperaturescould also

be

measured

using

differential

scanning calorimetry

(DSC),

but in

some materialsthe

transition temperaturesaretoo

faint

to

be

detected

by

DSC. DMA

is

muchmore

sensitive so

it is

ableto

detect

the slightest changes

in

material response.

The

basic

principle

behind DMA

is

analyzing

a material's responseto an

oscillating

force.

Based

on a material'sresponsetoa sinusoidal_{stress, the}stiffness

(modulus)

can

be

calculated

from

thesample_recovery, andthe

tendency

to

flow

(viscosity)

is

calculated

from

thephase

lag. Transition

temperaturescan

be

found

through

drastic

changes

in

thematerial'smodulus.

The

stiffness

describes

the

ability

of

thematerialto recover

from

a

deformation,

andthe

viscosity

describes

the

ability

ofthe

materialto

lose

_energy

in

the

form

of

heat (damping). DMA

outputs amoduluswhich

differs from

the

Young's

modulus of elasticity.

Young's

Modulus,

from Hooke's

law,

is

defined

astheratio of stressto strainasshown

in

equation

14.14

E

=

-(14)

E

can

be

determined

by

plottingseveral points

in

the

linear

region of stress-strain curve

and

finding

theslope ofthe

line

throughthepoints.

As previously

stated,

DMA does

not

measure

Young's Modulus

directly,

it

outputs a complex modulus

denoted

by

E*.

E*

is

defined

_as,

E*=E'+iE"

(15)

whereE'

is

theelastic storagemoduluswhich

is

ameasure ofthematerials

ability

to

store or return_energy, andE"

is

the

imaginary

loss

moduluswhich

is

thematerial's

ability

to

lose

energy.

A

good

analogy

of whatE' andE"

is best

thoughtof as a

ball

bouncing

as shown

in

Figure

1415. The

height

that

is

recovered after a

bounce is

E',

the

Energy

Loss

In Internal

Motion

Elastic

Response

Figure 14 Elastic ResponseAnalogy15

elastic_response,andthe

difference between

theoriginal

height

andthe second

height

represents

E",

the

energy lost due

to

internal

motion.

An

expression

for

E'

is,

E'=

^

v*,

cos

5

= Jo

Kbkj

cosS

(16)

where

fo

is

the

force

applied,

b

is

thesample

geometry

term,

k

is

thesample

displacement

atthepeak and

5 is

thephase

difference between

thematerial andtheapplied stress. [image:33.514.81.432.277.480.2]

result

if

a

different

sample

is

used andthe

forces

are not adjustedto

be

thesame.

The

imaginary

(viscous)

loss

modulus

is described

by

equation

17.

E"=

^

Ke _J

sin = Jo

ybkj

sin5

(17)

where

b,

k,

and

5

are thesame asthoseusedto calculate

E'. Figure 15

gives agraphical

representation of

how

k

and

8

are

found from

theresponse.

Another

important

property

that

DMA

measures

is

the tangentofthephase

difference.

This quantity

is

called

damping

and

it

represents

how

efficiently

thematerial

loses energy

to

internal friction

and molecular rearrangements.

Tan

8 is defined

as,

+

_

E" 77* e"

tanS~ = = ₍₁₈

)

E' rj" s1

where n'

is

the

energy

loss

portion of

viscosity

and n"

is

thestorage_portion, s'

is

the

in

phase strain and s"

is

theoutof phase strain.

Force

Force(Djnamic)

JT\

Force_(Static)

t

Time

Phase

MaterialResponse J ,

r*x

ft

Angle=6

J\

\

/

/

Amplitude= k

Stress

\\tCS

Time

Figure 15 Dynamic Responseof aMaterial

Since

tan

8 is

theratio ofthe

loss

to thestorage_modulus,

it is

independent

of

geometry

and can also

be

used as a check

for

possible measurement errors

in

atest.9

To

testa specimen

dynamically,

a

Seiko Instruments

DMS1 10

three-point

bending

machine was used.

Displacement

Clamp

NiTi

^End

Clamp

Specimen

Figure 16 Three-point

Bending

Apparatus

Figure 16

gives a

close-up

view ofthe three-point

bending

fixture

ofthe

DMS1 10. The

specimens were

heated

in 2 C

steps wherethe temperaturewas

held

constant

for

threeminutes

between

steps.

The

temperatureranges used

for

heating

varied

between

specimens

because

ofthe

higher

initial

As

and

Af

temperatures.

The

heating

rate

was

kept

constant at

2

C

per

step

regardlessofthe temperaturerangeused.

The

temperatureranges

for

the

heating

and

cooling

runswere estimated

from

the transition

temperatures

found from DSC

curves.

For

thesecond andthird

trials,

a general

heating

range

from 70C

to

150C

wasused sincethe transformation temperatures stabilized after

the

initial

heating

above

Af. After

a

heating

run

had

_{completed, the}specimen wasthen

steps.

There

was no shift

in

the

Ms

and

Mf

temperatures

during

cooling

sothisrangewas

used across allspecimens.

A

constant

flow

of

300ml/min

of

Nitrogen

wasused

during

all

heating

and

cooling

_cycles.

X-ray

Diffraction

X-ray

diffraction is

an

important

characterization method

for

determining

the

structures of crystalline

materials,

and

it is

appropriately

named

because

it

uses

diffracted

x-raysto makethese

determinations.

A

diffracted

x-ray is

similartoreflected

light,

but

thereare some significant

differences,

for

example,

light

reflects at

any

angle of

incidence,

while

diffraction

ofx-raystakesplace at certainanglesonly.

Another

difference is

that the

intensity

of reflected

light is

almostthesameasthe

incident

light,

but

the

intensity

of

diffracted

x-rays

is

much

less

thanthe

incident

x-rays.

The

reason

that thereare

only diffracted

x-rays at certain angles

is

because

there

is

constructive and

destructive interference between diffracted

x-rays.

When

a

x-ray hits

an_atom,

it is

scattered

in

all

directions,

andwhenthere are atoms arranged_{periodically,}such as

in

a

crystalline_material,

many

ofthescatteredx-rays

destructively

interfere

with each_other,

whileothers_{constructively}

interfere

withone another.

The

constructive

interference

occurs

because

thereare parallel

beams

thatare

integer

multiples of

x-ray

wavelength out

of phase witheach other

(essentially

they

are

in

_phase),andthephase

difference

comes

from

the

different distances

the

beams

travel.

It

is

theconstructive

interference

thatmake

x-ray diffraction

possible.

To

understand

how

_x-ray

diffraction

works,consider a set of parallel planes

spaced a

distance

d'

apart, suchas

in

acrystallinematerial

(Figure

17). In

the

figure,

a

beam

with

known

wavelength

(X)

is incident

onthecrystal at an angle

0. This

angle

is

known

asBragg's angle and

it is

measured

between

thecrystal planes andthe

beam.

Considering

beams

1

and

2, they

strike atoms

K

and

L

and are scattered

in

all

directions,

S _L

Figure 17 DiffractionofX-Rays

by

a

crystal16

but only in

the

1

'

and2'

directions

willthescattered

beams be in

phase.

The

phase

difference

is

relatedto thepath

difference,

and

it

can

be described

by,

ML

+

LN

=

d'sin0

₊

d'sm 9

This

is

also thepath

difference for

theraysscattered

by

S

and

P because

there

is

nopath

difference between S

and

L

or

P

and

K. Since

therays

1

'

and2' will

be

in

_phase,

equation

(19),

which was

first

written

by

W.L.

Bragg

can

be

used.

nAX=

2d'sw.O

(19)

This

relation

is known

as

Bragg'

s

law. This

expression

is

generally

found in

the

form

ofEquation

20,

wherethesubstitutionof

d

=

d'/n

is done for

convenience.

X

=

2d

_sin

6

From

thisexpressionwe can seethat the angle

6

is

a

function

ofthe

spacing

between

planes as well asthewavelength ofthex-rays.

In

thecaseof

x-ray

diffraction,

the

interplanar

spacing

d,

is

found

by

exposing

acrystalto x-raysof

known

wavelength

and

measuring

theangles at which

diffraction

occurs.

To

measuretheangles at which

diffraction

takes place,a

diffractometer

is

used.

A

diffractometer

consists ofan

x-ray

_source, a_stage, and a counter.

The x-ray

source

is

a

cathode

ray

tubewhich provides characteristic_radiation,thestage

is

theareawherethe

specimen

is

_mounted,andthecounter measuresthe

intensity

ofthe

diffracted beams.

The x-ray

tuberemains

stationary

at alltimeswhile thestage

is

rotated

in

placeandthe

counter

is

rotated aroundthestage.

Typically

theangle

between

the

incident beam

and

the

diffracted

beam is

measured ratherthan

0. It

is

known

that theangle

between

the

incident

and

diffracted

beam

is

29.

16

The

counterthenmeasuresthe

intensity

ofthe

diffracted

beam. The final

outputofthe

diffractometer

is

a plot of

diffracted beam

intensity

versus

20.

For

this study, the crystallographic structure ofthe

NiTi

ribbonwas

determined

through

x-ray diffraction using

a

Rigaku

DMAX-IIB diffractometer

with

Cu

K<x

radiation

at

40kV

and

35mA.

13mm

specimens were cut

from

eachstrained sample and

mechanically polished, andthenmountedto a glassslide with

double-sided

tape.

Scans

began

at

10 degrees

and ended at

80 degrees

witha

scanning

rate of

1

.2

deg/min.

The

slit

configuration

defining

the x-rayoptics was set witha

divergent

slit of

1,

a

scattering

slit

of

1

,

a_receivingslit of

0. 1

5mm,

andanickel

filter.

From

the

XRD

scans, peakswere

identified

andthe

corresponding

d-spacings

werecalculated.

From

thesepeaks, the

lattice

parameters

for

aB19' monoclinic unit cell

were calculated

using

linear

regressionas well asExcel'ssolver.

To

solve

for

these

parameters, theequation

for

theplane spacingsofamonoclinic cell

had

to

be

used.16

1

1

ft-2

d2

sin2/?

h1

k2sm2/3

I2

2hlcos/3

a ac

(21)

In

orderto use

Equation

21

withthe

known

parameters

from

pdf

35-1281,

it

had

to

be

rearranged

replacing

theangle

p

with_y,andthe

resulting formula

_was,

J_

d2

1

(h2 k2 ,2^2 n .,,- A

sin

y

a2 b2

I

sin

fi

2hkcosy

c2

ab

(22)

Hardness

Testing

The

Knoop

hardness

testwas

developed in

1939,

and

it

usesa_preciselyshaped

diamond indenter

andvarious

loads

to

determine

hardness

characteristics of materials

thatcannot

be

tested

by

conventionaltechniques.

The

indenter,

as shown

in Figure 1

8,

produces arhombic-shaped

indentation

(Figure

19)

wheretheratio

between

long

and

short

diagonals is

_{approximately}

7

to

1

whilethe

depth

ofthe

indentation

is

approximately

1/30

ofthe

length

ofthe

long

diagonal.

A

Knoop

indenter

was chosen

Figure18

Knoop

Indentor

I

Figure19

Knoop

Indentationin NiTiSurface

The

Knoop

hardness

number

(KHN)

is

theratio of the

load

appliedto theunrecovered

projected area.

KHN

er

(23)

In

theprevious_equation,

P

is

the

load

applied

in

kg,

1

is

the

length

ofthe

long

diagonal in

mm and

C is

the

indenter

constant

relating

theprojected area ofthe

indentation

to thesquareofthe

length

ofthe

long

diagonal. Since

the

long

diagonal

is

typically

measured

in

urnandthe

load

applied

is

in

_grams, a moreconvenientequation

for

calculating

the

KHN

can

be

written.

14229P

KHN= '

(24)

where

Pi

is

the

load in

gf and

di

is

the

length

ofthe

long

diagonal

in

urn.

Hardness

testing

is

a

very

valuabletool

because

it

relatesthe

hardness

numberto

other properties ofamaterial.

It

is

a measure oftheresistance ofthematerialtoplastic

deformation.

In

the

hardness

test,

the

indenter is

pressed

into

thesurface andthematerial

deforms

plastically

leaving

an

indentation,

which

is

thenmeasured.

As

aresultofthe

plastic

deformation

thematerialwork-hardens.17

Since

there

is

_{work-hardening}aswellas

plastic

deformation

occurring

during

a

hardness

test

it is

evidentthat the

hardness

number

is

relatedto theyield stressofthematerial aswell asthestrain

hardening

coefficient.

Also,

the

hardness

number

is

relatedto themodulus of

elasticity

ofthematerial

because

there

is

some elastic

spring back

ofthematerialwhenthe

indenter

is

withdrawn.

This

elastic

spring

back

makes

determining

hardness

values

for

some

SMA very difficult.

Depending

onthetemperature at whichthe test

is

conducted_{at, the}

SMA

could recover

some ofthe

indentation if

not all of

it,

whichwould give erroneous values.

For

this

research, the

NiTi

was

known

to

be in

themartensitic phase

during

testing

based

on

DSC

scans.

The hardness

testing

for

thisresearchwas

done in

accordance with

ASTM

standard

E384.18

All hardness

testing

was performed ona

Mitutoyo MVK-H1

hardness

testing

machineatroomtemperature.

A

Knoop

Indenter

witha

100

gram

load

was used

for

all

indentations. The duration

ofthe

indentation

was

12

seconds.

After

the

indentation

wasmade,the

indent

was

brought

into

focus

at

40X

magnification.

Prior

to measuring the

length

ofthe

long

diagonal,

the

indentation

was checked

for

symmetry.

An indent

was consideredsymmetric

if

therewas

less

thana

20%

thespecimen was adjustedtomake surethat thesurface wasperpendicularto the

indenter

and another

indent

was made and checked.

The

long

diagonal

wasmeasured

by

placing

the

inside

edge oftheocular

lines just into

contact withtheedges ofthe

long

diagonal.

The

hardness

testerconvertedthe

length

ofthe

indent into

the

Knoop

hardness

number

using

equation

23. Three

separate

hardness

valuesweretaken

for

each

indentation.

Indentations

were made untilthe

KHN

were within

10,

and at

least 5 indentations

were

madepersample.

Optical

Microscopy

Optical microscopy is

a valuabletool thatmetallurgistsuseto

identify

surface

characteristics of a material.

In

_{this research,}

brightfield

images

ofthe

NiTi

surfacewere

taken.

Brightfield

images

usenormal

lighting

wherethe

image is

reflected

vertically

from

thesurfacethrough the

lenses. Images

werethenextracted

using

avideocapture

systemwitha

gray

scalecamera.

Prior

to

viewing

thespecimensunder_{the microscope,}

the

NiTi

samples were

mechanically

polishedto a

0.04

urn

finish. No etching

was

performed.

Atomic Force

Microscopy

Atomic Force

Microscopy

is

an

imaging

technique

developed

in

1986. AFM

uses

an

extremely

small

sharp

tip

that

is

affixed or

integrated into

acantilever.

The

radiusof

the

tip

greatly

effectstheresolution ofthescanned surface so

for

the

best

resolution,

ideally

a single atom

tip

should

be

used.

The

tip

used

in

thisresearch

had

aradiusof

less

than

lOnm.

Depending

onthemodethat the

AFM

set

to,

eitherthe

tip

is

dragged

across

thesurface of_{the test piece,} orthe

tip

taps thesurface.

The

method used

for

thisresearch

was

tapping

mode wherethe

tip

lightly

taps thesurface.

The

tapping

mode

is

advantageous

because

the

tip

does

notremain

in

contactwiththesurface sothere

is less

damage

to thesample andthe tip.

In

tapping

_{mode, the}cantilever

is

oscillated at

its

natural

frequency by

a

piezoelectric crystaland

it is

movedtowards the surfaceuntil

it begins

to

tap

thesurface.

When

the

tip

contactsthe surface, the

energy

ofthe

oscillating

cantilever

is dissipated

andtheamplitude ofthecantilever

is

reduced.

To

keep

aconstant_{oscillation, the}surface

to

tip

distance is

adjusted.

The

change

in

oscillation amplitude

is

what

is

usedto

identify

and measure surface

features. The

amplitude

is

measured

by

laser beam

deflection.

A

laser

is

focused

onthe

backside

ofthecantilever andthe

beam

reflects and strikes a

photodetector.

This

methodofmeasurement allows sub-angstrom

measurements.19'20

AFM

was performed_usinga

Digital

Instruments Dimension 3000

atomic

force

microscope

in

tapping

mode.

A

scansizeof

15um

wastakenat arate of

0.6 Hz in

ambientconditions.

Prior

to

scanning

the

NiTi strip

was

mechanically

polishedtoa

0.04

urn

finish

andcleaned with alcohol.

The

areasof

interest

onthe

NiTi

surface were

Data/Processing

Method

Determination

of

Modulus

of

Elasticity

According

to

Hooke's law

(5),

themodulus of

elasticity

is

the

proportionality

constant

between

stress and strain

in

theelasticregion of

deformation,

therefore,

an

easy

way

to calculatethemodulus

is

to

find

theslopeofthe

linear

elastic region.

To

do

this

one can perform atensile teston a specimen and calculatethestresses andstrains within

the

linear

elastic range and

fit

a straight

line

_{to this region,} wheretheslopeofthe

line is

themodulusofelasticity.

Also,

it has been found

that

if

a material

is loaded into

the

plastic region and_{then unloaded, the} stress

decreases in

a

linear fashion

and

it is

parallel

to the

linear

elasticregion.14

Since both

regions are

linear

andthemodulus of

elasticity is

the

first derivative

ofthe

fitted

line,

an alternative

for

finding

themodulus

is

touse

numericalmethods to

find

the

first

derivative

ofthe

data

points.

One

drawback

to

numerically

differentiating

experimental

data is

that the

data

contains noisethat

is

characteristicofthe equipment used

during

theexperiment.

Because

ofthis noise,

it is difficult

to

directly

apply

thestandard

formulas

for

forward,

central, and

backward difference.

Alternatively,

there

have been

severalmethods

generated_{to numerically}

differentiate

experimental

data using FORTRAN

programs.21'22.

These

methodsalso

apply

_smoothingtechniquesto tninimize errors.

The FORTRAN

program used

for

thisresearchcan

be

found

in Appendix C.

The

numericaldifferentiationmethod chosen

is known

asthe

Anderssen-Bloomfield-Cullummethod21.

To implement

this method, the observed

data

must

first be

arranged

into

a

function,

(xi? ),

i

=

1

...N.

Next

the

function

is

transformedso that

it is

zeroat_xi andxN.

After

the

transformation,

the

Fourier

coefficients are calculated

using

Goertzel's

methodcombinedwith

Reinsch's

modifications21.

Then

thevalue of athat

minimizesthe

function

L(a)

is

calculated.

The

function

L(a)

is:

ft-r A

L{a)

=

(N-l)ln

Jjft-Wj)

-j>(l-Mr)

ft=i

)

N-\

where

Yj

denotes

the

finite Fourier

coefficients,

and

Wj

thevalueof

wy

with

^

=_7r/(N

-1).

Finally

the

derivative

values are

found from

the

following

equation:

fif)

=

fJYJwJfJsm{(j>Jt+T^-where,

m 2k

'P i=0

To

find

the

first

derivative

oftheelasticregionstress and strainvalues

for 0

to

0.1%

strainwere considered.

For

the

unloading

region, the strains

from

themaximum

strainto

0.2% below

that strain were considered.

Also,

the

first

threepoints ofthe

unloading

curvewere neglectedto remove

any Hertzian

effects.

Theoretically

the

resulting derivative

should

be

constant acrossall strains sincetheregion

is

linear,

but

due

tonoisethevalue

fluctuates

sotheaverage ofrangewill

be

reported

along

withthe

maximum,minimum, and standard

deviation

ofthe

derivatives.

Determination

of

Transformation

Temps

Differential

Scanning Calorimetry

Previously

it

was mentionedthat thereare

definite

temperaturesat whichthe

forward

andreversetransformationsoccur.

To

characterizethese

temperatures,

one

slightly between

every experiment,

and

both

DSC

and

DMA,

which were used

in

this

study

are noexception.

To

characterizethe

transformation

temperatures

using

DSC,

a methodsimilarto

the

ASTM standard,

ASTM

El

356-91,

_{was used}

for

determining

theglasstransition

temperatures

ofpolymers.23

The first

step

takenwasto take theraw

data

from DSC

and

separate

heating

cycles andthe

cooling

cycles and plotthe

heat

flow

asa

function

of

temperature.

The

austenitetransformation temperaturesarethen

determined

from

the

heating

cycle andthemartensitictransformation temperaturesare

determined from

the

cooling

cycles.

The

transformation temperaturesarethen

found

based

onthe

location

of

theexothermic or endothermic peaks.

To