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PHASE TRANSFORMATION IN CARBON COATED
TiNi ALLOY, WITH APPLICATION TO THE
DESIGN OF A PROSTHESIS FOR THE RECONSTRUCTION

OF THE ANTERIOR CRUCIATE LIGAMENT

BY

ASSEM HEDAYAT

A DISSERTATION

Submitted to Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Metallurgy, Mechanics, and Materials Science

1989

vs.

C

\cs "

ABSTRACT
PHASE TRANSFORMATION IN CARBON COATED TiNi ALLOY,
WITH APPLICATION TO THE DESIGN OF A PROSTHESIS
FOR THE RECONSTRUCTION OF THE ANTERIOR CRUCIATE LIGAMENT
BY

Assam Hedayat

The objective of this research is to study the effect
of surface constraint on the phase transformation of a near—
equiatomic nickel-titanium (50.1 at.%‘ N; - 49.9 at.% Ti)
shape memory alloy, Nitinol. ‘Ultra-low temperature
isotropic (ULTI) carbon was vapour deposited on the shape
memory alloy as part of a design of a composite prosthesis
for the reconstruction of the anterior cruciate ligament.

X-ray diffraction and surface. analytical techniques
indicated the formation of TiC at the carbon/Nitinol
interface. Differential scanning calorimetry studies showed

a marked decrease in the austenitic starting (A and the

s)
martensitic finishing- (Mf) temperatures of the surface
constrained alloy during phase transformation. A model that
describes this phenomenon is presented.

Cross-sectional specimens of the vapour deposited ULTI
carbon on Nitinol substrates were examined with transmission
electron microscopy. The phase transformation of the

surface constrained Nitinol was studied in-situ. It is

proposed that during nartensitic transformation, the last

martensite plates to form were close to the constrained
surface, and these are first to disappear during reverse
transformation. A model to calculate the strain energy
associated with the phase transformation of the surface
constrained Nitinol is proposed.

The development of the composite prosthesis for the
reconstruction of the anterior cruciate ligament required
testing of the new material in-vivo. The objective was to
study the growth of collagenous tissue on carbon coated
Nitinol. Thus, Nitinol filaments on which ULTI carbon was
vapour deposited were implanted in canine knees. Scanning
electron microscopy examination of the harvested filaments
revealed islands of reticular collagen on the surface of the

carbon coated filament.

To my mother and to the memory of my father.

ACKNOWLEDGEMENTS

The author would like to express his indebtedness to
both his advisors Dr. Kalinath Mukherjee and Dr. James
Rechtien for their inspiring guidance and counceling
throughout the development of this thesis.

Sincere gratitude is extended to Dr. Terrance Braden
for performing the surgery required in this study and for
serving as a member of the graduate guidance committee.

Special thanks is expressed. to Dr. Dahsin Liu for
serving as a member of the guidance committee.'

In addition, appreciation is expressed to Mr. Charles
Hovey' of 0.5. Nitinol for supplying' the nickel-titanium
alloy, and to Dr. Axel Haubold and Mr. Al Beavan of
Carbomedics, Inc. for performing the vapour deposition of
carbon on the Nitinol substrates.

Thanks also is extended to Ms. Jane Walsh for
performing the histological work, and for her unlimited aid
throughout the various stages of the experimental work.

Most of all, the author would like to express special
recognition and indebtedness to his brother Mr. Sherin
Hedayat for his genuine friendship and overwhelming support.

Moreover,.the author owes much to his sister Mrs. Amina
Khalil, and brother-in-law Dr. Hassan Khalil for their

continuous encouragement and sincere advice.

iii

Furthermore, the author wishes to express his
appreciation to Ms. Brenda Robinson for the effort she has
put into typing this thesis.

Finally, gratitude is expressed to the Composite
Materials and Structures Center at Michigan State University

for the financial support under account number 91-1006.

iv

tr

TABLE OF CONTENTS

LIST OF TABLES . . . . . . . . . . . . . . . . . . . .

LIST OF FIGURES. . . . . . . . . . . . . . . . . . . .
INTRODUCTION . . . . . . . . . . . . . . . . . . . . .
LITERATURE SURVEY. . . . . . . . . . . . . . . . . . .
A. THE ANTERIOR CRUCIATE LIGAMENT . . . . . . .
B. DRAWBACKS OF THE AVAILABLE TECHNIQUES USED
IN THE REPLACEMENT OR RECONSTRUCTION OF THE
ANTERIOR CRUCIATE LIGAMENT . . . . . . . . .
C. THE PHASE TRANSFORMATION OF NITINOL. . . . .
D. VAPOUR DEPOSITION OF THIN CARBON FILMS . . .
MATERIALS AND METHODS. . . . . . . . . . . . . . . . .
A. MATERIALS ANALYSIS . . . . . . . . . . . .
B. BIOLOGICAL TESTING . . . . . . . . . . . . .
EXPERIMENTAL RESULTS . . . . . . . . . . . . . . . . .
A. PHASE TRANSFORMATION STUDIES OF CARBON
COATED TiNi. . . . . . . . . . . . . . . . .
B. BIOLOGIC EVALUATION OF THE CARBON COATED
NITINOL. . . . . . . . . . . . . . . . . . .
DISCUSSION . . . . . . . . . . . . . . . . . . . . . .
A. PHASE TRANSFORMATION OF NITINOL. . . . . . .
B. DESIGN OF A PROSTHESIS FOR THE
RECONSTRUCTION OF THE ANTERIOR CRUCIATE
LIGAMENT . . . . . . . . . . . . . . . . . .
CONCLUSIONS. . . . . . . . . . . . . . . . . . . . .
APPENDIX 1 . . . . . . . . . . . . . . . . . . . . . .
APPENDIX 2 . . . . . . . . . . . . . . . . . . . . . .
APPENDIX 3 . . . . . . . . . . . . . . . . . . . .

vii

ix

10
14
26
29
29
38
42

42

86
92
92

117
123
125
130
135

APPENDIX 4 . . . . . . . . . . . . . . . . . . . . . . . 141

BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . 148

vi

LIST OF TABLES

Table 1. Thermodynamic Data of Selected Shape
Memory Effect Alloys. . . . . . . .

Table 2. Thermodynamic Data of a Near-Equiatomic
NiTi Alloy (50.1 at % Ni - 49.9 at % Ti)

Table 3. Heats of Transformation (AH) of Coated
and Uncoated Nitinol in the Unannealed
State (J/gm). . . . . . . . . . . . . .
APPENDIX 1

Table 1. Unconstrained Nitinol Sample - First
COOling CYCle O O O 0 O O O O O 0

Table 2. Constrained Nitinol Sample - First
Cooling Cycle . . . . . . . . . . .

‘Table 3. Unconstrained Nitinol Sample - First
Heating Cycle . . . . . . . . . . .

Table 4. Constrained Nitinol Sample - First
Heating Cycle . . . . . . . . . . .

APPENDIX 2

Table 1. Unconstrained Nitinol Sample — First
Cooling Cycle . . . . . . . . . . .

Table 2. Constrained Nitinol Sample - First
Cooling Cycle . . . . . . . . . . . . .

Table 3. Unconstrained Nitinol Sample - First
Heating Cycle . . . . . . . . . .

Table 4. Constrained Nitinol Sample - First
Heating Cycle . . . . . . . . . .

APPENDIX 3

Table 1. Unconstrained Nitinol Sample - First
Cooling Cycle . . . . . . . . . . . . .

Table 2. Constrained Nitinol Sample — First
Cooling Cycle . . . . . . . . . . . . .

vii

25

44

49

126

127

128

129

131

132

133

134

136

137

Table 3. Unconstrained Nitinol Sample - First
Heating Cycle . . . . . . . . . . .

Table 4. Constrained Nitinol Sample - First
Heating Cycle . . . . . . . . . . .

APPENDIX 4

Table 1. Unconstrained Nitinol Sample - First
Cooling Cycle . . . . . . . . . . .

Table 2. Constrained Nitinol Sample - First
Cooling Cycle . . . . . . . . . . .

Table 3. Unconstrained Nitinol Sample - First
Heating CYCle O O O O O O O O O I 0

Table 4. Constrained Nitinol Sample - First
Heating Cycle . . . . . . . . . . .

viii

138

139

142

143

145

146

Figure
Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure'

Figure

Figure

10.

11.

LIST OF FIGURES

Bones of the Knee. . . . . . . .
Ligaments of the Knee. . . . . . . .

Diagramatic Representation of the
Anterior Cruciate Ligament During
Extension and Flexion [16] . . . . .

Characteristic Force-Strain Diagram
of a Tensile Test on a Human Knee
Ligament [18]. . . . . ._. . . . . .

SEM Photomicrograph of Collagenous
Tissue Growth Around Carbon Fibers
(X 1000) as Shown by Weiss, et al.,
Clin. Orthop. Rel. Res., V. 196,
(1985):77 [42] . . . . . . . . . . .

Light Micrograph of a Longitudinal
Section of Collagenous Tissue Growth
Around Carbon Fibers (X 120) as Shown
by Claes, L., et al., Clin. Orthop.
Rel. Res., V. 196, (1985):99 [43]. .

Illustration of the Different Layers
of a Cross-Sectional TEM Specimen
Following Spark Cutting. . . . ...

DSC of Nitinol (50.1 at % Ni - 49.9
% Ti) (a) First Cooling Cycle,
(b) First Heating Cycle. . . . . .

DSC of Nitinol (50.1 at % Ni - 49.9
at % Ti) in the Cooling Cycle. (a)
First Cycle (b) Tenth Cycle (0)
Fortieth Cycle . . . . . . . . . . .

DSC Cooling Curves of Nitinol (First
Cycle) 3a) Uncoated (b) Coated with
a 3000 A Carbon Film. . . . . . . .

DSC Heating Curves of Nitinol (First

Cycle) (a) Uncoated (b) Coated with
a 3000 A0 Carbon Film. . . . . . . .

ix

15

15

37

43

45

47

48

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

DSC Cooling Curves of Nitinol (Tenth

Cycle) (a) Uncoated (b) Coated with a

3000 A0 Carbon Film. . . . . . . .

DSC Curves of the First Cooling Cycle
of Nitinol Samples (a) Uncoated and
Annealed at 700°C for 3 Hours (b)
Coated with a 3000 A0 Carbon Film and
Annealed at 700°C for 3 Hours. . . .

DSC Curves of the First Heating Cycle
of Nitinol Samples (a) Uncoated and
Annealed at 700°C for 3 Hours (b)
Coated with a 3000 A° Carbon Film and
Annealed at 700°C for 3 Hours. . . .

DSC Curves of the 10th Cooling Cycle
of Nitinol Samples (a) Uncoated and
Annealed at 700°C for 3 Hours (b)
Coated with a 3000 A° Carbon Film and
Annealed at 700°C for 3 Hours. . . .

DSC Curves of the 40th Cooling Cycle
of Nitinol Samples (a) Uncoated and
Annealed at 700°C for 3 Hours (b)
Coated with a 3000 A° Carbon Film and
Annealed at 700°C for 3 Hours. . .

DSC Curves of the First Cooling Cycle
of Nitinol Samples (a) Uncoated and

‘Annealed at 700°C for 6 Hours (b)

Coated with a 3000 A° Carbon Film and
Annealed at 700°C for 6 Hours. . . .

DSC Curves of the First Heating Cycle
of Nitinol Samples (a) Uncoated and
Annealed at 700°C for 6 Hours (b)
Coated with a 3000 A° Carbon Film and
Annealed at 700°C for 6 Hours. . . .

DSC Curves of the 10th Cooling Cycle
of Nitinol Samples (a) Uncoated and
Annealed at 700°C for 6 Hours (b)
Coated with a 3000 A° Carbon Film and
Annealed at 700°C for 6 Hours. . . .

DSC Curves of the 40th Cooling Cycle
of Nitinol Samples (a) Uncoated and
Annealed at 700°C for 6 Hours (b)

'Coated with a 3000 A° Carbon Film and

Annealed at 700°C for 6 Hours. . . .

X-ray Diffraction Pattern of Nitinol

(a) Uncoated (b) Coated with a 3000 A°

Carbon Film. . . . . . . . . . . . .

50

52

53

54

55

56

58

59

60

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Figure 22. X- ray Diffraction Pattern of a 3000 A°
Carbon Coated Nitinol Sample Heat
Treated at 700° C for 3 Hours After
Coating. . . . . . . . . . . . . . . . .

Figure 23. X- ray Diffraction Pattern of a 3000 A°
Carbon Coated Nitinol Sample Heat
Treated at 700°C for 6 Hours After
Coating. . . . . . . . . . . . . . . .

Figure 24. Vickers Hardness as a Function of
Annealing Time of a 3000 A° Carbon
Coated oNitinol Sample Heat Treated
at 700° C. Each Hardness Point is an
Average of 5 Readings. The Maximum
Deviation is 9.48% . . . . . . . . . . .

Figure 25. SEM Photomicrograph of an Uncoated,
Unannealed Nitinol Sample. . . . . . . .

Figure 26. SEM Photomicrograph of an Unannealed
3000 A° Carbon Coated Nitinol Sample . .

Figure 27. SEM Photomicrograph of an Uncoated
Nitinol Sample Heat Treated at 700°C
for 3 Hours. . . . . . . . . . . . . . .

Figure 28. SEM Photomicrograph of a 3000 A°
Carbon Coated Nitinol Sample that was
Heat Treated at 700° C for 3 Hours After
Coating. . . . . . . . . . . . . . . . .

Figure 29. Auger Signal of an Unannealed 3000 A°
Carbon Coated Nitinol Sample (a) One
Minute Argon Sputtering (b) 26 Minutes
Argon Sputtering . . . . . . . . . . .

Figure 30. Depth Profile of an Unannealed 3000 A°
Carbon Coated Nitinol Sample . . . . . .

Figure 31. SEM Photomicrograph of an Unannealed
3000 A° Carbon Coated Nitinol After 26
Minutes Argon Sputtering . . . . . . . .

Figure 32. Auger Signal of a 3000 A° Carbon Coated
Nitinol Sample Annealed at 700°C for One
Hour After Coating. (a) One Minute Argon
Sputtering (b) 40 Minutes Argon
°Sputtering . . . . . . . . . . . . . . .

Figure 33. Depth Profile of a 3000 A° Carbon Coated
Nitinol Annealed at 700°C for One Hour .

xi

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35.

36.

37.

38.

39.

40.

41.

42.

43.

44.

45.

46.

Auger Signal of a 3000 A° Carbon Coated
Nitinol Sample Annealed at 700°C for

Three Hours After Coating. (a)
Argon Sputtering (b) 40 Minutes Argon
Sputtering . . . . . . . . . . . . .

Depth Profile of a 3000 A° Carbon Coated
Nitinol Sample Annealed at 700°C for
Three Hours. . . . . . . . . . . . . . .

SEM Photomicrograph of 3000 A° OCarbon
Coated Nitinol Annealed at 7000 C for
Three Hours After 40 Minutes Argon
Sputtering . . . . . . . . . . . . . .

Auger Signal of a 3000 A° Carbon Coated
Nitinol Sample Annealed at 700°C for

Six Hours After Coating. (a) One Minute
Argon Sputtering (b) Thirty Five Minutes
Argon Sputtering . . . . . . . . . . .

Depth Profile of a 3000 A0 Carbon Coated
Nitinol Sample Annealed at 700°C for
Six Hours. . . . . . . . . . . . . . .

Bright Field Image of a Vertical Cross-
Section TEM Foil of a 3000 A° Carbon
Coated Nitinol Sample Heat Treated at
700°C for 3 Hours (a) 200, 000 x, (b)
500,000.. . . . . . . . . . . . . .

Electron Diffraction Pattern-of Nitinol
in the Martensitic phase, [110]m

Analysis of the Electron Diffraction
Pattern of Nitinol in the Martensitic
Phase, [110]m. . . . . . . . . . . .

Bright Field Image of a Carbon Flake

Electron Diffraction Pattern of a
Carbon Flake . . . . . . . . . . . . . .

Bright Field Image of TiC. . . . . . .

Electron Diffraction Pattern of TiC
[1231TiC . . . . . . . . . . . . . . .

Photographs Illustrating Part of the
Surgical Procedure Followed in the
Study. (a) Fascia Lata Before Pulling
it Through the Tibia, (b) Drilling a
Tunnel in the Tibia. . . . . . .

xii

One Minute

75

76

78

79

80

82

83

83
84

84
85

85

87

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

51.

56.

57.

Radiographs Showing the Carbon Coated
Nitinol Filaments in the Canine’s
Stifle Joint. (a) Anterior-Posterior
View, (b) Lateral-Medial View. . . . . .

SEM Photomicrographs of Collagen

Islands on the Surface of Carbon

Coated Nitinol Filaments. (a) 1000 X
(b) 1000 X . . . . . . . . . . . . . . .

Optical Photographs Illustrating the
Carbon Coated Nitinol Filaments in
Tissue. (a) Transverse Section,

(b) Longitudinal Section . . . . . . .

Percent of Martensite as a Function of
Temperature for 3000 A° Carbon

Coated oNitinol Samples Heat Treated

at 700° C for Three Hours . . . . . . . .

Percent of Martensite as a Function of
Temperature for 3000 A° Carbon Coated
Nitinol Samples Heat Treated at 7000 C
for Six Hours. . . . . . . . . . . . .

Percent of Austenite Present as a
Function of Temperature in the First
Cooling Cyclefor Coated and Uncoated
Nitinol Samples Heat Treated at 700°C
for (a) Three Hours (b) Six Hours. . .

Percent of Austenite Present as a
Function of Temperature in the First
Heating Cycle for Coated and Uncoated
Nitinol Samples Heat Treated at 7000 C

for (a) Three Hours (b) Six Hours. . . .
Schematic Representation of Gm as a
Function of Temperature [100]. . . . .

Driving Force as a Function of
Temperature for Unconstrained and
Constrained Samples Heat Treated at
700° C for Three Hours. . . . . . . . . .

Driving Force as a Function of
Temperature for Unconstrained and
Constrained Samples that were Heat
Treated at 7000 C for Six Hours . . . . .

Proposed Design of a Carbon Coated
Nitinol Prosthesis for the
Reconstruction of the Anterior

Cruciate Ligament. . . . . . . . . . . .

xiii

88

89

91

94

95

97

98

106

114

115

118

Figure 58.

Figure 59.

Figure 60.

Design Details of the Prosthesis
devised for the Reconstruction of the
Anterior Cruciate Ligament . . . . . . . 119

Illustration of a Measuring Device to
Measure the Lengths Between the
Surfaces of the Tibia and Femur. . . . . 121

Prosthesis in the Knee Joint (a)

Before Transformation (b) After
Transformation . . . . . . . . . . . . . 122

xiv

I . INTRODUCTION

The near~equiatomic nickel—titanium alloy, Nitinol,
belongs to a class of alloys that exhibits the shape memory
effect. This class includes binary alloys like Cu-Zn, Cu-
Sn, Au-Cd, Ni-Al, as well as ternary systems such as Cu-Al-
Ni, Cu-Zn-Si, and Ni-Ti-Cu [1]. These alloys change their
shape repeatedly with. heating and. cooling. Consequently,
they have been used in a variety of applications ranging
from. aircraft pipe couplings to orthodontic dental arch
wires [1].

Of all the shape memory alloys, Nitinol is most
commonly used ix) Ibiomedical applications. This, is
attributed to the fact that this material fulfills the two
requirements of a bio-implantable material, namely
biocompatibility and biofunctionability. With regards to
biocompatibility, in-vivo testing of Nitinol showed that the
material is biologically nontoxic. Not only does its
presence fail t1) generate allergic cu: carcinogenic
responses, there is also no clinical evidence of body
rejection or inflammation following its implantation [2].
On the other hand, prosthetic devices made of Nitinol proved
to be .biofunctionable. This is due to the material’s
outstanding fatigue and corrosion properties. Fatigue tests
showed that while bearing a load equal to four times their

yield strength, Nitinol specimens can be cycled thermally or
1

2
mechanically for 107 *cycles ’without failure» .Moreover,

Nitinol has an excellent corrosion resistence in saline
solutions, and is not susceptible to either stress corrosion
or crevice Corrosion [2].

The success of Nitinol as a biomaterial, encouraged
both engineers and physicians to use. it in developing new
prosthetic devices. For example, Nitinol 'is being
considered for use in the treatment of scoliosis. A Nitinol
Herrington rod is programmed to have bends along its length.
Following its. insertion, external heat to produce a
temperature change of about 3 to 5° C above body temperature
could be applied after. a few days and periodiCally
thereafter without producing further trauma. The rod gains
its undeformed shape, gradually over a period of time, and
corrects the spinal deformity without the need for further
surgical procedure [1,2]. The same concept is applicable in
the area of dentistry where a Nitinol wire could be used as
an orthodontic. dental arch to straighten out dental
malocclusions [1]. Another biomedical application of
Nitinol is in the area of orthopedics where Nitinol bone
plates for fraCture fixation were developed. The advantage
of these plates is that they promote rapid healing of the
fracture. This is attributed to the fact that when the
shape memory effect is triggered by body temperature, the
bone plate shrinks to a desired length, and the fractured
surfaces are brought together by a compressive load that

keeps the fixation rigid [1].

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3
In this research, a new application for Nitinol in the

biomedical field is proposed. The alloy will be used in the
development of a prosthetic device for the reconstruction of
the anterior cruciate ligament. The prosthesis is designed
to eliminate the problems associated with an earlier
technique that uses carbon fibers for the same application.
Carbon fibers were utilized in the other technique because
of their ability of bio-conduction of collagenous tissue
[3-12]. However, carbon fibers are follicular, extremely
brittle, and highly vulnerable to shearing forces. Thus, it
is difficult to anchor them to tissues and bones, as they
will not tolerate being knotted or stapled. Moreover, not
only do fragments of the broken fibers travel to the lymph
nodes, but also the process of fragmentation exposes new
surfaces of carbon that bio-conduct the growth. of more
tissue, leading to an uncontrolled growth of the ligament
[3].

The prosthesis design suggested in this research, for
the reconstruction of the anterior crucite ligament, is
mainly made .of Nitinol strips and filaments. A new
anchoring technique of the prosthesis to the tibia and femur
is proposed. The technique is based on the unique property
of Nitinol to change its shape with heating and cooling.
Moreover, ultra-low temperature isotropic (ULTI) carbon is
vapour depositd on the Nitinol filaments to induce the
growth of collagenous tissue.

Following the implantation of the prosthesis in the

knee joint, the carbon coated filaments will act as a

4
temporary replacement of the anterior cruciate ligament

until growth of the ligament is complete. At this stage,
the filaments will be. subjected to cyclic loading during
physical activities involving the knee joint. The external
stresses will cause the Nitinol filaments to experience
phase transformation from austenite to martensite. This
phenomenon is called stress induced martensite [14]. When
the stress is removed, the body temperature will transform
the martensite into austenite once again if the austenite
finish temperature is less than or equal to 35° C.

Phase transformation of Nitinol has been a subject of
great interest in) materials scientists. However, none of
the studies conducted in this area has dealt with ‘the
transformation of surface constrained Nitinol (or other
shape memory alloys). It is the the objective of this
research to .study the effect of surface constraint,
represented by a thin (ULTI) carbon film, on the phase
transformation of Nitinol. Some preliminary in-vivo canine
studies are also conducted with carbon coated TiNi filaments

to observe the nature of collagenous tissue growth on them.

(\‘

I I . LITERATURE SURVEY

The anterior cruciate ligament is a fibrous
connective tissue that links two bones in the knee: the
femur and the tibia (Figure 1 and 2) [15]. The ligament
originates at the surface of the lateral femoral condyle and
inserts 15mm posterior to the anterior edge of the tibial
plateau. It is made up of cells called'fibrocytes, and is
called cruciate because“ it crosses with the posterior
cruciate ligament [16].

The fibers constituting ‘the ligament are not all
parallel and longitudinal. l Actually, some fibers are
arranged spirally. Fibers emerging from the extreme
anterior and distal region of the femoral origin insert into
the extreme posterolateral region of the tibial attachment.
On the other hand, fibers arising from the most posterior
and proximal region of the lateral femoral condyle insert
into the extreme anterior and medial region of the tibia.
The ligament is narrowest at its most proximal region near
the femoral origin and fans out as it approaches the tibial
attachment. Accordingly, a portion of the anterior cruciate

ligament remains taut at all degrees of flexion [16]. Figure

Femur

 

 

Patella

 

 

Tibia

 

Fibula

 

 

Figure 1. Bones of the knee [15]

Posterior cruciate ligament ‘ . Anterior cruciate ligament

\Q
/ I .

Lateral collateral ligament \' \

  

' Medial collateral ligament

Figure 2. Ligaments of the knee [15]

I a-
.0 i. re a
l. I,

‘

.lI-i‘. to I

1
vi
v
4

7
3 is a diagramatic representation of the anterior cruciate

ligament during extension and flexion.
2. Fu gtion:

The anterior cruciate ligament is one of the most
important ligaments in the knee. It has average dimensions
of approximately 10 mm in diameter and 40 mm in length, and
is the primary static stabilizer of the knee against
anterior displacement of the tibia on the femur. Not only
is it responsible for the restraining force that keeps the
knee from being pulled forward, but also it keeps the knee
from rotating abnormally and from being pulled to the
outside [16].

'3. Biomeghanical Properties:
a. Tensile Behavior:

The characteristic tensile load versus extension
behavior of the knee ligament is shown in figure 4.
Although the elongation is of an elastic nature over a wide
range, the elastic line does not pass through the origin.
This is attributed to the fact that the fibrous structure of
the relaxed ligament does not have all the fibers pulled
straight and parallel. Actually, the fibers are buckled into
a wavy configuration. Therefore, for a small load, the
fibers are being straightened and aligned rather than
extended. The application of loads beyond the elastic limit

will lead to the deformation and rupture of the ligament

Anterior cruciate

l ligament
I I 73%;;

Extension Flexion

Figure 3. Diagramatic representation of the anterior

cruciate ligament during extension and flexion [16]

 

  

 

 

 

800
Rupture
Force at the linear force
600‘ limit
3
S2 400‘
8
200
0 . . , . 1
0 . S 10 15 20 25

STRAIN (%]

Figure 4. Characteristic force—strain diagram of a tensile

test on a human knee ligament [18]

10
[18].

b. Vieeeeleetie Effeet:

Similar tn) bones, ligaments exhibit viscoelastic
behavior. This behavior is characterized by the dependence
of the material properties on time. For example, if a
ligament is subjected to a strain which is applied suddenly
and held constant, the stress will decrease with time. On
the other hand, if the ligament is subjected to a stress
which is applied suddenly and held constant, the strain will
increase with time [19].

B. r w k f h Av ila l T hni

1 men or Re. n ru tion if h An eri r r i

Ligement:
1. Background

 

The anterior cruciate ligament is aux important
structure in the knee. Athletes with ruptured anterior
cruciate ligaments are usually unable to resume their
athletic activities. For some athletes, the anterior
cruciate ligament rupture and the knee instability
associated with it may prove disabling. This disability may
range from the knee catching and giving out with virtually
every step, to occasional swelling and pain if any sort of
athletics is attempted [15].

There are three major techniques employed in the
restoration of the ligament which are: replacement of the

ligament using autografts or allografts, ligament

11

substitution with an artificial .polymeric material, and
reconstruction of the ligament using ' carbon fibers.
Unfortunately, these methods proved Suboptimal due to

limitations in both application and design.

a. W
WW

The autograft technique [20—23] makes the use of the
patient's own fibrous tissue taken from the patellar tendon,
or iliotibial band. The harvested fibrous tissue is placed
into surgically produced tunnels in the femur and tibia in a
geometry consistent with the anterior cruciate function. A
more recent approach utilizes allografts of freeze dried
cadaver fascia lata or Achilles tendon or, possibly, even
anterior cruciate ligament available at tissue banks to
replace the ruptured ligament. The autograft technique is
suboptimal because the accurate length and position of the
reconstruction is difficult to achieve, and even when ideal,
the reconstruction might fail for lack of an adequate blood
supply [24-26]. Moreover, the structure from which the
autograft is taken becomes weaker. An example of that is
the patellar tendon of which the middle third is often used
as an autograft for the replacement of the anterior cruciate’
ligament. Experimental studies involving the patellar
tendons of canines indicate that the structural stiffness of
the remaining two thirds of the tendon was diminished

significantly post-surgery [27]. The allograft techniques

12
are still too new to provide definite failure data but,

clearly, these techniques will require significant
additional research before becoming an entirely satisfactory
solution. One can speculate that they too will lack
adequate circulation and will face the same problems that
bone replacements from ‘tissue banks encounter with

infectious disease transmission [28].

b. WW
wi ' ' i l

Considerable research is being conducted to develop an
acceptable artificial ligament. The problem of the anterior
cruciate ligament implant design is indeed a challenging one
to the bioengineer. The artificial material used should
imitate the natural mechanital properties of the biological
structure. Net only should the material be biocompatible,
but also it should be durable. Furthermore, some form of
fixation augmentation ’by tissue ingrowth must be provided
for long-term function. Finally, the pmosthetic ligament
should possess acceptable mechanical properties which are
essential for proper function. Such properties which must
be similar to that of the ligament are mainly yield
strength, creep, elongation recovery time, fatigue life and
modulus of elasticity [29-32].

Several investigators proposed different material
design for the prosthetic ligament. Dacron fabrics in

either woven, knitted, or velour form were used to replace

13
the anterior cruciate ligament [33-34]. Bicomponent brands

of dacron-kevlar or dacron-lykra were proposed as a new
design concept for anterior cruciate ligament replacement.
The strength of the braid can be adjusted by the
incorporation of chemically different bicomponent materials,
the composition of the bicomponents, the helix angle of the
sheath, and the core material [35]. Moreover, a composite
prosthesis, which consists of a compressible inner core
around which a dacron fiber is woven in a helical fashion,
was devised to replace the anterior cruciate ligament [36].
It is worth mentioning that artificial prostheses are
commercially available. Examples of these prostheses are
the Gortex graft [37], and the Richards Polyflex ligament
[38].

Long term results of the replacement of the anterior
cruciate ligament with an artificial polymeric material are
often unsatisfactory. This is attributed to the
insufficient strength of the materials, and the variability
in placement of the prosthesis. Usually, the artificial

ligaments fail by a fatigue mode [39].

c. R ns r i.rl of II An ri r

Ligament geing Certen Fitere

The ideal solution to the reconstruction of the
anterior cruciate ligament would be regrowth of the ligament
with its required blood supply since the appropriate

strength and other properties would be ideal for‘ the

14
ligament’s function. Carbon fibers are known to bioconduct

the formation of ligaments and tendons in both humans and
animals [3-12] and this has led to numerous research
attempts to construct a ligament prosthesis from. carbon
fibers (Figures 5 and 6). The carbon fibers' supporting
function is gradually replaced by new ligament formation
which is particularly prolific in the milieu created by the
active healing' process in the vicinity of the original
injury. Carbon, in general, is, among the most
biocompatible materials [40], but numerous difficulties have
prevented the success of this approach. The fibers are
extremely brittle and tend to break off, not only during
surgical implantation but also over a period of time, in
11.13. The latter process produces small fragments which
either produce local joint pain or migrate to the regional
lymph nodes [12]. The surgical anchoring of the pure carbon
fibers is also made difficult by their' brittleness and
stapling' attempts have failed [41]. Excessive ligament
regrowth usually occurs producing a new ligament six times
the optimal size [19]. iFurther, the .new ‘tissue fibers
generated tend to be straight and lack the spiral geometry
that allows the natural ligament to remain taut in multiple
configurations [3]. Thus, none of the current technologies
has produced a well accepted solution to the anterior

cruciate ligament injury problem.

Fig. 5.

Fig.

6.

15

 

SEM photomicrograph of collagenous tissue growth
around carbon fibers (X 1000) as shown by Weiss,
et al., Clin. Orthop. Rel. Res., V. 196, (1985):77
[42]

 

Light micrograph of a longitudinal section of
collagenous tissue growth around carbon fibers (X
120) as shown by Claes, L., et al., Clin. Orthop.
Rel. Res., V. 196, (1985):99 [43]

16

C. The Pheee Irenefetmetione ef Nitinol
1. In ion

The near-equiatomic nickel-titanium alloy is one
that exhibits the 'shape memory effect. This is a
characteristic by which the alloy can Change its shape
repeatedly, reversibly, and substantially with heating and
cooling [1]. The thermal cycling causes phase
transformation to proceed from one ordered structure to the
other reversibly. This transformation does not take place
by diffusional mixing of atoms. Instead, it occurs by shear
displacement of crystal segments. Although other alloys
like steels undergo diffusionless or martensitic
transformations, they do not exhibit the shape memory
effect. The reason is that the nertensitic transformation
in steel is non-thermoelastic [44].

Thermoelastic and non-thermoelastic phase
transformation can be contrasted with respect to the
mechanisms of transformation as well as the microstructural
changes associated with them. In thermoelastic phase
transformations, the shape recovery is attributed to the
fact that the strain introduced is reversible. Although a
shape change takes place, no permanent damage is made on the
microstructural scale. As a matter of fact, the
microstructure deforms by a mechanism of shearing regions of
the parent phase to martensite, or by detwinning within

individual martensite plates. These mechanisms are

 

 

17
different from the usual irreversible mechanisms of plastic

deformation experienced in non-thermoelastic transformations
such as slip and dislocation motion [44]. In shape memory
alloys, which exhibit thermoelastic phase transformation,
plates of martensite form continuouslywith cooling. If the
cooling is stopped and then resumed, the martensitic plates
will continue to grow because ‘the interface between the
parent and the martensitic phase is glissile. Growth will
only stop when_the_plates impinge with each other or with
grain boundaries. (hi heating, the plates will shrink and
completely revert to (‘the orientation of the parent phase.
In the case of non-thermoelastic, phase transformation, on
the other hand, plates of martensite will also form on
cooling. However, they will not grow beyond a certain size
because the interface becomes sessile. Moreover, on
heating, the plates will not shrink. Instead, the parent
phase will nucleate within them and grow by a diffusion
process, and the plate“ as a whole will not revert to the
orientation of the parent phase. The mechanism is governed
by the kinetics of the reaction, and involves nucleation and
growth [45].

The reversibility of thermoelastic martensite is
attributed to the inherently low elastic strains associated
with the change in the crystal structure of a shape memory
alloy. Thus, the elastic limit of the matrix of the parent
phase is not exceeded, and irreversible plastic deformation

does not take place. Moreover, as the martensite plates

18
grow, they are arranged in a mutually accommodating fashion,

and effectively cancel the distortions so that strains do
not accumulate. The martensite plate groups usually consist
of simple alternating stacks of platelets where cancellation
of strain vectors between neighboring platelets take place.
Moreover, the individual martensite plates are internally
faulted or twinned to accommodate the strains resulting from
the transformation. This is in contrast to non—
thermoelastic martensitic transformations in which high
inherent strains are associated with the martensitic phase.
These strains are too great to be accommodated, and this
renders the transformation irreversible [44].

During phase transformation of shape memory alloys, the
difference in the chemical free energy between the two
phases, which is the driving energy of the transformation,
and the elastic energy developed are in balance with each
other at all times. The interfacial energy is very small.
Consequently, either cooling or application of stress assist
the transformation to proceed in one direction, while
heating and releasing the stress will reverse it. The
mechanical analogue ta) the athermal (heating-cooling)
formation and reversion of martensite in shape memory alloys
is known as pseudoelastic behavior. This behavior is
characterized by the formation of martensite as the stress
increases. When the stress is removed, the transformation
reverses along the same microstructural path, and the shape

is recovered” IBoth the shape memory effect and

19
pseudoelasticity are complimentary to one anotherx For

example, on deforming a shape memory alloy, a fraction of
the strain is recovered on unloading (pseudoelastic
behavior), and the rest is recovered on heating (shape
memory effect) [44].

In Nitinol, the high temperature phase, which is called
the austenitic or the parent phase, has the structure of a
CsCl ordered lattice. In space group notation, the lattice
is denoted by 32, and has the lattice parameter a = 3.01 A°
[46]. The low temperature phase is called martensite. The
unit cell of 'that phase: is monoclinic, with the c~axis
slightly inclined ( = 97.78°). For a near-equiatomic TiNi
alloy, the unit cell structure has the space group of B19‘

[47], and the lattice parameters are [64]:

a = 2.989 A0
b = 4.108 A0
c = 4.646 A°

As the phase transformation of Nitinol proceeds in one
direction, abrupt changes in the physical properties of the
alloy can be observed. These Changes include mechanical
properties such as the yield Strength, Young's modulus and
eleCtrical resiStivity. While the yield strength and
Young's modulus increase with the martensitic transformation
[48], electrical resistivity' drops [49]. Moreover, ‘the
transformation from austenite to martensite is characterized

I 0\ I O
as belng exothermlc, and the reverse transformation 13

 

v.1.

20
endothermic [14]. Thus, several experimental techniques
based on the measured changes of these properties are
utilized to study the phase transformation of Nitinol and
other shape memory alloys. The main parameters used to
describe the transformation are the martensitic starting and
finishing temperatures as well as the austenite starting and
finishing temperatures; M Mf, A and Af, respectively.

8’ S’

2. W

As the transformation proceeds from austenite to
martensite, the Nitinol experiences a premartensitic
transition just above MS. 'The :lattice undergoes a
rhombohedral distortion which is the reason for referring to
the transition as the "R—phase" [50].

The R-phase can be detected in every experimental
technique used to study the martensitic transformation of
Nitinol. Electrical resistivity tests show an increase in
resistivity following thermal cycling of the alloy [49, 51,
52]. In addition, differential scanning calorimetry
measurements of thermally cycled Nitinol show the R-phase as
a separate exothermic peak just prior to the martensitic
peak [53]. Moreover, besides existing as diffuse streaks in
x-ray diffraction [46, 54], the R-phase is represented by
extra reflections located at one third positions in electron

diffraction patterns [52, 55]. Furthermore, the R-phase can

be detected also by its anomolous behavior in elasticity

 

21
[56, 57], magnetic properties [58], internal friction [57]

and heat capacity [59, 60].

The process by which the premartensitic phase, the R-
phase, forms is not completely understood. However, efforts
were made to interpret the transformation as a charge
density wave transition as follows. As the transformation
proceeds from the parent phase to the martensitic phase, a
periodic lattice distortion occurs giving rise to a three-
dimensional charge density wave. This wave forms on two
stages. First, an inconunensurate transition from the BZ
phase occurs with the decrease in temperature. Then, as the
temperature is decreased further, the incommensurate phase
locks into the conunensurate phase, which is the R-phase.
While the nomenclature incommensurate refers to a status
where the wave length is not a multiple of the lattice
parameter, commensurate denotes equality between them. It
is worth mentioning that while the transition from the 82
phase to the incommensurate phase is of the second order,
that from the incommensurate to the commensurate is of the
first order [50].

The R-phase has been studied extensively. Major
findings were that the commensurate R-phase corresponds to a
rhombohedral lattice with space group notation P31m [63].
Moreover, the history of the material including heat and
deformation affects the R-phase. The more residual stress
is present in the material, the more pronounced is the R-

phase [65]. Furthermore, the R-phase has four distinct

22

variants or orientations that can be correlated with each
other by twinning relationships [50, 66, 67]. These
variants are self accommodating and they produce a zero
macroscopic strain [66, 67]. This is in contrast to the
cubic parent phase to martensite transformation which has 24

variants [68].

3. Thermedynamiee of the pheee tranefermetiene in
TiNi elleye

The solid-state martensitic phase transformation in
Nitinol is categorized as being athermal. This type of
transformation is a function of temperature and not time.
The reaction proceeds only with the change in temperature.
If the temperature is held constant, the transformation will
not proceed with time. Accordingly, shape memory alloys are
studied thermodynamically rather than kinetically.

As mentioned earlier, during phase transformation, the
chemical free energy between the parent phase and the
martensitic phase is in balance at all times with non-
chemical energy, such as elastic energy and surface energy
[44, 45]. Since the interface between the martensite and
the parent phase is coherent in a thermoelastic
transformation, the surface energy is small. Thus, the
opposing non-chemical energy is mainly the elastic energy.
The phase transformation from the parent phase to the
martensitic phase, or visa versa, can be represented by the

following equation:

23

AG = AGC + AGnC (1)

where AGC is the chemical free energy or driving

energy
and AGnc is non-chemical energy.

For a first order phase transformation, a parent phase
is in equilibrium with the martensitic phase at an
equilibrium temperature To‘ This temperature corresponds
to AGC = 0 and is equivalent to (AS + MS)/2 [69]. For
Nitinol and other alloys that undergo thermoelastic
transformations, two equilibrium temperatures were
suggested. The first denoded by To corresponding AGC = 0
and is equivalent to (MS + Af)/2. The other is To, where
AGC + AGnc = 0 and is equivalent to (Mf + AS)/2 [70].
Moreover, for unstressed samples, the ratio of non-chemical

free energy AGnc to the enthalpy of the transformation AQ

could be estimated using the following formula [71]:
AGnC/AQ = (TO - TO‘)/TO (2)

Similarly, the ratio of energy change AG associated with the
cooling of an unstressed sample from MS to Mf, to the change

in the entropy of transformation was given as [72]:
AG/AS = 1/2 (Mf - MS) (3)

where AS = AQ/MS

 

24
Differential scanning calorimetry (DSC) and

differential thermal analysis (DTA) are two common
calorimetric techniques used in studying the phase
transformations of shape memory alloys [73-77]. While the
first technique measures the difference in energy between
the alloy and a reference material as a function of
temperature, the latter' measures the difference in
temperature.

Using the DSC, thermodynamic quantities like enthalpy,
heat capacity, and temperatures of transformations could be
measured. ~ Thus, it is usually preferred. The entropy of
the reactioncould also be calculated from DSC data using
the relation AS = AH/To where To is sometimes estimated as
the average temperature of AS and MS [78] or as the average
temperature of Af and MS when AS is below MS [70]. Selected
values of these parameters for a near equiatomic Nitinol are
given in Table 1. It is clear that the values may vary
although the composition of the alloy and its history might
be the same. The variation is attributed to the difference
in experimental conditions. The sensitivity of the"
apparatus used. is crucial in thermodynamic measurements.
The rate of cooling and heating at which transformation
occurs also affects the transformation temperatures [83].

Calorimetric studies of the phase transformation of
shape memory .alloys using DSC, clarified some of the
thermodynamical characteristics of the parent phase to

martensite reaction anui vice versa. During' cooling of

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26
Nitinol, as the BZ phase transforms into martensite, two

exothermic peaks result.’ The sum of enthalpy changes of the
two peaks is equal to the enthalpy change of the single
endothermic peak occurring with the martensite to BZ phase
reaction [14]. Moreover, for the thermoelastic trans-
formation of Nitinol, there is a linear relationship between
AH and To = 1/2 (A8 + M8) [81]. In addition, the fraction
of phase transformed as a function of temperature was given

by the formula [84]:

Msme
f(T) = l/AH I aAH/ T dT (4)
T

Furthermore, for a surface constrained single crystal of a
Cu-Al-Ni alloy undergoing martensitic phase transformation,
surface .nucleation. is inhibited. This results in
supercooling to lower temperatures for volume nucleation to
take place [85]. Finally, while complete cycling of Nitinol
substantially changes the transformation temperatures of the

alloy, incomplete cycling does not [86].

D. V r 1

Carbon coatings can be prepared by a variety of vacuum
processes. These processes include ion plating [87, 88],
sputtering [89], and laser evaporation [90]. The structure
of the 'carbon film, and: its “properties, depend “on the
technique used in the deposition process. Thus, carbon
films with an amorphous, crystalline, diamond like, or

turbostratic structures can be prepared [91]. The latter is

27
a subcrystalline structure in which no order exists between

the hexagonal layers of carbon as there is in graphite [92].
Of all the carbon films,, those with a turbostratic
structure have been singled out to be utilized in biomedical
applications.' «This- is attributed to the outstanding
biomechanical properties of this: class of carbon. The
complete randomness of the hexagonal carbon layers render
the material strong and tough. \ This is in comparison to
diamond like carbon films which are strong and stiff, and to
graphite films which are weak and flexible. Furthermore,
cyclic loading does not degrade the strength of turbostratic
carbons, and failure does not occur by a fatigue mode [91].
In this research, an ultra-low temperature isotropic
(ULTI) carbon is vapour deposited on the Nitinol substrates.
The ULTI carbon, which has a turbostratic structure, is
known commercially as Biolite‘R). It is prepared in a
hybrid vacuum process where a carbon-bearing gaseous
precursor in the presence of a catalyst is used to deposit
impermeable, isotropic carbon at high rates on cold
substrates. The advantage of this process is that the
deposition is performed at low pressure and ambient
temperature. Thus, the carbon can also be deposited on low-
melting-point materials such as polymers. During
deposition, the density, crystallite size and orientation of
the coating can be varied. Moreover, the carbon film is
less than one micron thick, and thus doesn't affect the
surface topography] or the mechanical properties of the

substrate [92].

 

 

.i.

 

 

28
Besides being biocompatible, ULTI carbon (Biolite(R))

is not susceptible to fluid friction erosion in either
turbulent or laminar flow. This property of the material is
indispensable in applications where it is exposed to fluid
flown An example of that type of application is the
Biolite(R* coatings applied to heart valves [91].

(R) to substrates of different

The adhesion of Biolite
materials was investigated. Studies show that Biolite‘R)
adheres best to carbide forming [88, 93, 94] metallic
materials like titanium and stainless steel. For example,
the bond strength between biolite and stainless steel was
found to be greater than 4700 psi [93]. Auger electron
spectroscopy (AE8) indicated the formation of titanium
carbide at the titanium/Biolite(R) interface [91, 93], and

(R) interface

iron carbide at ‘the stainless steel/Biolite
[88]. Moreover, Biolite(R) bonds well to polyamides.
Average bond strengths of 3000 psi were measured between
Biolite(R) and vespel which is a polyamide. It was
speculated that carbon-carbon type bonding could have

occurred between the carbon film and the polyamide substrate

[94].

III. MATERIALS AND METHODS

The experimental work in this study was divided into
two jparts: - (1) phase transformation “studies of carbon
coated TiNi, and (2) a preliminary biologic evaluation of
the carbon Coated Nitinol. The materials research focused
mainly on the effect of surface constraint, represented by a
thin film of. ‘ULTI carbon, on the phase transformation of
Nitinol. The biological study, on the other hand, involved
actual implantation of the composite material in a canine’s
knee. The objective of the implantation was to evaluate the
growth of fibroblasts, the constituent cells of collagen, on
the carbon coated filaments. The results from both studies
could possibly generate a design of a prosthetic device for

the replacement of the anterior cruciate ligament.

A. M ri l i

a. Nitinol

A near-equiatomic nickel—titanium (50.1 at % Ni - 49.9
at % Ti) shape memory alloy, Nitinol, was supplied by the
0.8. Nitinol, Saratoga, California. The alloy was produced
in the plate form, 2.5 mm thick, as well as in filament

form, 0.076 and 0.0152 mm in diameter. While Nitinol in the

29

30
plate form was used in the materials research, the Nitinol

filaments were used in the biological study.
b. - w m r ' n

The ULTI carbon, which has the commercial name of
Biolite‘R), was vapour deposited on the Nitinol substrates
at Carbomedics, Inc., Austin, Texas at a low pressure in a
hybrid process. A catalyst was used to deposit the biolite
at high rates from a carbon-bedring gaseous precursor, and
the temperature of the substrate was about 80°C. Thus, the
carbon was vapour hdeposited on: austenitic Nitinol. Two
thicknesses of carbon films were applied to two different
batches of Nitinol samples. The film thicknesses were 1500

A0 and 3000 A°.

2. Methods
a. il ' M

Film thickness measurements were done using a Dektak
IIA surface profile analyzer. Among every batch of Nitinol
substrates to be carbon coated, there was one specimen that
was partly covered. with a. heat resistant plastic tape.
Following vapour deposition, the plastic tape was removed,
creating a step between the coated and uncoated areas of the
sample. The surface profile analyzer measured the thickness
of that step which was actually the thickness of the carbon

film. The measurements showed that the thicknesses of the

I'\

31
films were roughly equal to those measured at Carbomedics,

Inc.

b. Qitfetegttel Seenning ‘Qeletimetty (DSC)
Measurements

To prepare samples for DSC measurements, the thickness
of the Nitinol: plates was reduced from 2.5 mm to 0.6 m
using a Penn rolling machine. Due to the explosive nature
of fracturing of Nitinol on cold working, the plates were
hot rolled. The samples were"'wet ground through 600 grit
SiC paper, and then cut with a shearing device to small
pieces, each weighing 25‘ mgm on the average. The samples
were placed in an alumina crucible and vacuum annealed at
550°C for one hour in a Cehtbrf‘vacuum furnace, model (M60 -
3 x 8 - W - D - 0484 - A - 20). They were rinsed in acetone
ultrasonically. Only 'one half of the samples were coated
with carbon. The film thiCknesses were 1500 A0 and 3000 A°.
Moreover, in order to promote the interfacial bond between
the ULTI carbon and the Nitinol, and to magnify the effect
of the surface constraint, some of the coated samples were
heat treated in vacuum at 700°C for three hours and others
for six hours. Uncoated samples were subjected to the same
heat treatments to establish a reference for the comparison
of experimental results between coated and uncoated samples
tested by DSC.

DSC measurements of the coated and uncoated samples
were performed using a DuPont Instruments 910 Differential

Scanning Calorimeter that is equipped with a 9900

r
7 v
.3—
) ’ n
J
. b ‘
,.\
' l
1 . 1
e

32
Computer/Thermal analyzer. The samples were placed in

DuPont Instruments 900786-901 aluminum pans and covered with
900779-901 aluminum lids. L Moreover, pure cathodic nickel,
which has approximately the same thermal mass of the Nitinol
samples, was used as the reference material.

Coated and uncoatedL Nitinol samples with identical
thermomechanical histories were tested using DSC. The
samples were thermally cycled between -40°C to 80°C. The
temperature stability was maintained by using a liquid
nitrogen cold stage. The ramp of heating and cooling for

all samples was fixed at 5°C/min.
c. X—tey Agelyeie

A General Electric model XRD-S x-ray diffractometer was
used to identify the phases present in the coated and the
uncoated Nitinol samples. A copper target was used at 25 KV
and 22 mA. The diffraction pattern was recorded for the 20
angle from 15° to 95° at a scanning rate of two degrees per
minute.

The Nitinol samples used in x-ray analysis were
prepared following the same procedure applied to the DSC
samples. However, the samples used in the x-ray study had a
larger area. Coated and uncoated samples with the same
thermomechanical histories were heat treated in vacuum at
700°C for one hour, three hours, and six hours prior to
being analyzed using the x-ray diffraction technique. It
was ensured by the vacuum annealing that all samples, coated

and uncoated, were fully transformed into austenite.

33

d. Migrghergneee Meaeurements

To confirm the formation of TiC at the carbon/Nitinol
interface as a result of heat treatment, microhardness
measurements were performed. Coated specimens identical to
those used in DSC measurements were used. Coated samples
that were heat treated in vacuum at 700°C for one hour,
three hours, and six hours, together with a coated sample
that was not heat treated, were tested. A Buehler
microindenter in the HV Vicker microhardness mode was used.
An 0.3 kgm force was applied for 15 seconds at a loading

speed of 50 microns/second.

e. Seanning Electron Microscopy gf the gerbgn
Coa ed TiNi Allo

Scanning electron microsc0py was used. to study the
topography of the vapour deposited ULTI carbon on the
Nitinol substrates. Nitinol substrates were cut from a
2.5mm thick plate using a Buehler Isomet low speed diamond
saw. The samples were wet ground through 600 grit SiC paper
and then polished through 0.3 micron alumina. The samples
were then rinsed in acetone ultrasonically, dried, and ULTI
carbon was vapour deposited on them. The surfaces of coated
specimens that were not heat treated, together with other
coated specimens that were vacuum heat treated at 700°C for

one hour, three hours, and six hours, were examined using

34
the scanning electron microscope. The microscope used was a

Hitachi S-415A, and was operated at 25 KV.

f. Auger Eleetrgn Speetrgeegpy

The study of the characteristics of the surfaces and
interfaces of the carbon coated Nitinol samples was
accomplished with Auger electron spectroscopy (AES). Coated
specimens, identical 1J1 their' thermomechanical. histories,
were analyzed with using a Perkin—Elmer PHI 660 Scanning
Auger microprobe equipped with a PHI 04-303 Sputter Ion Gun.
The analysis was performed on coated samples that were not
heat treated as well as on coated samples which were heat
treated in vacuum at 700°C for one hour, three hours, and
six hours.

The AES was operated, not only to characterize the
elements present at the surfaces and interfaces, but also to
give information of whether the elements are present in the
free or combined form. Depth profiling technique was
applied to determine the chemical profiles normal to the
surface of the carbon coated substrates. The AES was
operated at a base vacuum of 2 x lO'lOmbar, an electron beam
voltage of 30 KV, and an ion beam voltage of 3.5 KV. Argon
was used to sputter an area of 2 x 2mm at a sputter pressure
of 1 x 10'8mbar. Moreover, the sputter rate was calibrated
using a Si02 on Si standard, and was established to be about
80 A°/min. The data was analyzed using an Apollo 3500

workstation equipped with PHI AES software.

 

35
g. T mi ' El r n

Among the experimental methods used to study the effect
of surface constraint on the phase transformation of Nitinol
was the transmission electron microscope (TEM). Since the
material under study consisted of a thin carbon film vapour
deposited on Nitinol substrates, with TiC at the interfaCe,
conventional preparation. of TEM foils was inappropriate.
The preparation had to be pursued as outlined by the cross-
sectional transmission electron_ndcroscopy techniques [95,
96].

The preparation of TEM foils of the composite material
used in this study involved several stages. Nitinol
samples, 2.5 mm thick, 2.5 mm wide, and 20 mm long were cut
using a Buehler Isomet low speed diamond saw. The samples
were wet ground through 600 grit SiC paper, polished through
0.3 micron alumina, and then ultrasonically rinsed in
acetone. The samples were vacuum annealed at 550°C for one
hour,' and ULTI carbon was vapour deposited on their
surfaces. The carbon coated samples were then heat treated
in vaCuum at 700°C for three hours, and every two samples
were glued together along their 20 mm length using super
glue. Three hundred microns thick cross-sections were then
cut using a diamond saw.

The next step involved spark cutting of 3mm diameter
discs of the cross-sections. The diameter of the discs was
selected to coincide with the space separating the two

carbon coated surfaces of Nitinol facing each other. This

>1

36
configuration is illustrated in Figure 7. Spark cutting was

preferred to conventional mechanical techniques primarily
because it does not cause stress induced martensite to form
in the Nitinol samples. The cutting was performed using an
Agie electrical discharge (EDM) machine equipped with a 3mm
diameter graphite electrode, and operated at 100 volts and 9
amperes.

Preparation of the TEM foils required reduction of the
thicknesses of the cross-sectional samples. After an
ultrasonic acetone rinse, the discs were glued to Cu/Rh
grids, having 2 x l nun slits, using super glue. The discs
were then wet grouhd .through- 600 grit SiC paper to a
thickness of 80 microns. The foil thickness was measured
using a Gatan precision dimple grinder, model 656. The
dimpler was also used to grind the central area of the foil

down to 20 microns.

Two different transmission electron microscopes were
used in examining t‘he__cross-sectional foils to study the
effect of surface constraint on the phase transformation of
Nitinol. One of the microscopes was a Hitachi H-800
electron microscope. It was operated at 200 KV, which
corresponds to an electron wavelength (A) of 0.0251 A°, and
had a camera length of 160 cm. The other microscope was a
Jeol 100 CX II electron microscope equipped with a cold
stage. It was mainly used to examine the foils at cryogenic

temperatures where the Nitinol is fully transformed into

martensite. The microscope was operated at 120 KV,

-1
I
r'
‘ ,
.' ‘
' l
u
‘ r
t

, at

37

ULTI Carbon .

TIC - TIC

 

 

s—r
=F_,

 

 

Il"11fIJIL14111
LrLIIIJJIJFIFIJ

 

 

 

 

p

TIN]

Figure 7. Illustration of the different layers of a

cross-sectional TEM specimen following spark cutting

38
which corresponds to an eleCtron wavelength (A) of 0.0335

A°, and had a camera length of 55 cm.
B. BMW

As part of the design of a prosthesis for the
reconstruction of the anterior cruciate ligament, biolite
(ULTI carbon) was vapour deposited on Nitinol substrates.
The objective of the vapour deposition of carbon was to
induce the growth of collagenous tissue over the carbon
coated surfaces. Review of the literature indicated that
such a composite material has never been tested either in-
vitro or in-vivo. Thus, carbon coated Nitinol filaments
were tested by actual implantation in canine pelvic knees.
Although the study is aimed at reconstructing the human
anterior cruciate ligament, direct extrapolation of the

results from canines to humans is acceptable.
1. W

Nitinol filaments, 0.076 mm in diameter, were annealed
in vacuum at 550°C for one hour. The filaments were rinsed
ultrasonically in acetone, and then a thin film (3000 A°) of
ULTI carbon was vapour deposited on them. Moreover, the
coated filaments were sterilized by gaseous ethylene oxide
before their introduction into the canine’s knee joint.

The surgical technique was similar to that followed to
stabilize ruptured cruciate knees using fascia lata tissue
in the dog. The canine which was a female large breed, 52

lb. in weight, was conditioned for one month prior to

39
surgery. One stifle joint was asceptically surgically

approached. Tunnels were drilled in the condyles of the
tibia and femur. A long band of fascia lata tissue was cut
from the lateral side of the thigh and pulled through the
tunnels in the femur and tibia. Prior to the placement of
the tissue through the bone, carbon coated filaments were
incorporated with it in such a manner that the filaments
would be located in the stifle joint. After the tissue was
pulled out of the tibia anteriorly, it was anchored to the
patellar ligament. The wound. was closed and the operated
knee joint was then wrapped in soft padded bandage. After
surgery, the canine was housed in a ward with no restriction
to its motion. It was then euthanized 30 days post-
operatively with a T-61 intravenous injection, and the knee

joint was harvested [97, 98].

2. Scanning Electrgn Mieroscgpy gf Cgllagenoue Tieeue

Scanning electron. microsc0py was used. to study the
growth of collagenous tissue on the carbon coated Nitinol
filaments following harvesting them from the canine's knee.
To stop any degeneration of the harvested knee joint, it was
immersed in 10% formalin for three days.

Cross-sectional and longitudinal cuts of tflua coated
filaments adjacent to the patellar tendon and the
surrounding.tissue were made. The sections were dehydrated
at room temperature in a series of ethyl alcohol/water
mixtures with increasing concentrations of alcohol. The

starting concentration was 70% alcohol by volume and the

>0

40
final was 100% with 10% increments. The specimens were

immersed in each concentration for one hour. Treatment of
the tissue with the 100% alcohol concentration was repeated
three times to make sure that dehydration was complete. At
this stage, the tissue with the embedded filaments had to be
critically dried to remove any water present. Thus, a
critical point dryer using C02 gas was employed. The
filaments and annexed tissue were then cut to smaller pieces
and glued to aluminum SEM stubs using super glue. Since the
tissue is non-conductive, it had to be sputter coated with
gold before examination. The microscope used was a Hitachi
S-415A scanning electron microscope, and was operated at 20

KV.

3. Hietelggieel Evaluation

Tissue sections of the canine’s knee joint in which the
carbon coated Nitinol filaments were incorporated were
prepared for histological testing. The objective of this
test was also to study the growth of collagenous tissue on
the coated filaments. Longitudinal sections of the
filaments adjacent to the patellar tendon, and transverse
section of the filaments inserted in the tibia were made.
These sections were first dehydrated following the same
procedure used for the SEM specimens. The sections were
then embedded in a Polaron embedding medium which is glycol
methacrylate (GMA). Like dehydration, the embedding also
was performed on stages. The first embedding was in a mixed

solution of ethyl alcohol and GMA in the ratio of 1:1 by

41
volume. The second embedding was in a 1:3 solution and the

third. was in pure GMA” In each stage the tissue was
embedded in the solution for 24 hours. Once the last stage
of embedding was complete, benzoyl peroxide, which is a
catalyst, was added to the solution to polymerize and harden
the GMA. under vacuum. .At this stage, the tissue was
embedded in a hard casing of GMA and sections as thick as 30
microns could be cut with the diamond saw. Finally, the
sections were stained and then examined using a biological

microscope [99].

 

IV. EXPERIMENTAL RESULTS
A. W

Experimental results of the phase transformation
studies of carbon coated TiNi were categorized with respect
to the techniques used in the study. These techniques were
differential scanning calorimetry (DSC), x-ray analysis,
microhardness measurements, scanning electron microscopy
(SEM), Auger electron spectroscopy (ABS), and transmission

electron microscopy (TEM).

1. i r n ° nnin 1 r'm

A typical DSC curve of a TiNi shape memory alloy
annealed! for one hour at 550°C is illustrated in Figure 8
(a) and (b). The cooling cycle, which is shown in Figure
8(a), is exothermic, and is characterized by a martensitic
start and finish temperatures. The heating cycle, on the
other hand, is shown in Figure 8(b). This cycle is
endothermic and is characterized by an austenitic start and
finish temperatures. In both cases, the area under the
curves is the enthalpy of the transformation, and is denoted
by AH. Table 2 summarizes the data for the NiTi alloy under
study, which has a composition of 50.1 at % Ni - 49.9 at %

Ti. It is noted that the enthalpy of transformation of the

42

43

 

 

 

 

 

 

 

 

 

 

 

 

0.3
23.11'0
(a)
0.2-
13
\.
EE
3 OJ~
E
U
n
i
0.0-
23.05'D
23.74J/9
-001 ' T 1 I v I v ' '
-40 -2o 0 20 40 so so
Temperature (’0)
0.1
44.43'8
0.0" 24.!7J/I
\L I [:
E-p4~
15
3
o
E
g-oa
! .
-0.3~
51.14'8
“OMS 1 W '— V t a r v
-40 -20 o 20 40 so 80

 

 

Temperature (’0)

Figure 8. DSC of Nitinol (50.1 at % Ni - 49.9 % Ti) (a)
F1rst cooling cycle, (b) First heating cycle.

44

Thermodynamic Data of a Near-Equiatomic NiTi

Alloy (50.1 at % Ni - 49.9 at % Ti)

MS = 300 K
Mf = 271 K
AS = 296 x
Af = 327 K
AHcooling = 23.74 J/gm
Aflheating = 24.17 J/gm

cooling cycle is almost equal to the enthalpy of
transformation of the heating cycle.

Figure 9 (a), (b), and (c) illustrates the difference
in the cooling cycle for Nitinol as it was cycled one, ten,
and forty times, respectively. In the first cycle, the
martensitic transformation is characterized by a single
exothermic jpeak. 13: the tenth. cycle, Figure 9(b), two
exothermic peaks are formed. The first peak to appear is
associated with the premartensitic reaction and the
formation of the R-phase, while the second one is associated
with the martensitic phase. In the fortieth cycle, Figure
9(c), the premartensitic phase is characterized by a
separate exothermic peak that precedes the martensitic
transformation. However, the martensitic transformation
starts at a lower temperature, compared to that in the tenth

cycle.

455

o.3~ (a)

19.09J/fl

 

 

 

 

(b)

(ii/Oi
(a
T

20.89J/9

0.1-«

Hut Flew

 

 

(c)

0.1- ie.e7J/e

 

 

 

I ' T ' r '
20 40 60 DO
temperature ('C)

i
h
0

I
M
0
04

Figure 9. DSC of Nitinol (50.1 at % Ni - 49.9 at % Ti) in

the cooling cycle. (a) First cycle (b) Tenth
cycle (c) Fortieth cycle.

46
Although coating the Nitinol with carbon did not cause

any changes in the transformation temperatures of the
Nitinol, Changes in the heats of transformation in both the
heating and cooling cycles were noticed. Variation of the
thicknesses of the coatings did not affect the
transformation temperatures of Nitinol. Figure 10 (a) and
(b) shows the exothermic peaks of uncoated and coated
Nitinol samples, respectively, in the first cooling cycle.
Figure 11 (a) and (b) shows the endothermic peaks of the
uncoated. and coated. samples, respectively, in the first
heating cycle. The heats of transformation (AH) of uncoated
and coated Nitinol are given in Table 3. The data is given
for two different thicknesses of Biolite‘R), 1500 A° and
3000 .A°. For - the coated samples, two distinct
characteristics are associated with the phase
transformation. The first is that the carbon coating does
not inhibit the formation of the R-phase as shown in Figure
12(a) and (b). The second is that thermal cycling of the
coated Nitinol caused parts of the coating to flake out.
This meant that the carbon coating vapour deposited without
subsequent annealing was poorly bonded to the Nitinol
substrates. This led to the idea of annealing the carbon
coated Nitinol to enhance the bond at the carbon/Nitinol
interface.

The objective of annealing the coated samples was to
promote the interfacial bond between the TiNi and the ULTI
carbon coating, and to magnify the effect of the surface

constraint of Nitinol.) To establish a reference for the

47

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.4
( 2!.94'0
(a)
0.3-
a 02-4
\ a
‘ E
8
O
E
g 0.1-
0.0# u
26.09'C
19.09J/e
“0.! r T V 1 r— ' 1 ' 'r ‘
~40 --20 0 20 40 80 80
Temperature [’6]
0.5
J (b) R 23.49%:
0.4-*
E 0.3%
5
g .
£3
8 02
i O
o.i~ as.eé'c
22.21J/I
om . 1 - 1 - i. . .T , r -
-JO ~20 0 20 40 80 80

 

 

Temperature ('C)

Figure 10. DSC cooling curves of Nitinol (first cycle) (a)
Uncoated (b) Coated with a 3000 A° carbon film.

148

 

. ‘7

40.88'c
23.17J/o

Heat Flow (It/e)

 

 

-0.3~
(El) 45.19’8

 

 

 

OJ

. , _r .
~40 -20 20 40 60 80

Temperature t'c)

 

 

4:.7i'c
23.110/9 i

 

Heat Flew ill/e)

 

 

(b)

45.80'0

 

 

 

I“ ' r I' '
20 40 50 80
Temperature PC)

04

' ~40 ~20

I

Figure 11. DSC heating curves of Nitinol (first cycle) (a)
Uncoated (b) Coated with a 3000 A° carbon film.

49

IABLE.1

Heats of Transformation (AH) of Coated and
Uncoated Nitinol in the Unannealed State (J/gm)

(Substrate thickness - 600 um)

--‘---------—-------—-----—-—-------—------------’----

QEQIB

lst 20.09 19.53 23.54 23.32 24.12 24.32
10th 20.00 22.16 23.30 23.30 23.61 22.49
20th 19.81 22.76 22.70 22.70 23.0 21.76
30th 19.14 22.65 22.80 22.80 23.03 20.96
40th 18.82 22.77 22.59 22.59 23.01 20.90

50

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.4
a.” (a)
18.25’0
- I
“ 0 2
\ a
a
8
E
8 5,-
. g '
————'1 M
0.0-
18.33'C
20.89J/0
"' .1 v 1 r ' r" ' r 3 'r' V
o ~o0 ~20 3 20 40 so so
Temperature PC)
0.4
1
0.3.1
£7.02'C
g 002-
g .
l2
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i
q\ ‘ g M
0.0-
19.14%:
19.98.1/0
-0 ° 1~4 o ' ~50 6 20 ' 4'0 ' 60 C en

 

 

 

Temporature l'C)

Figure 12. DSC cooling curves of Nitinol (tenth cycle) (a)
Uncoated (b) Coated with a 3000 A° carbon film.

51
comparison of the DSC measurements of the coated samples,

uncoated Nitinol samples were subjected to the same heat
treatment, and tested using DSC. Figure 13 (a) and (b) show
the DSC curve in the first cooling cycle for an uncoated
3000 A0 carbon coated samples, respectively, that were each
heat treated three hours at 700°C. It is shown that
although the MS temperature remains the same for both the
coated and uncoated samples, the M1: temperature for the
coated 'and annealed sample dropped by about 20°C in
comparison to the uncoated sample. Figure 14 (a) and (b)
shows the DSC curve of the first heating cycle of an
uncoated Nitinol sample and a 3000 A° carbon coated sample,
respectively, each heat treated for three hours at 700°C.
It is shown that the Af temperature for the coated and
uncoated samples remains unchanged. However, in case of the
coated sample, the As temperature dropped by about 20°C in
comparison to the uncoated one. Moreover, both Figures 15
and 16 demonstrate how the surface constraint of Nitinol
inhibits the formation of R-phase. Figure 15 (a) and (b)
show the formation of the R-phase in the uncoated and the
3000 A° carbon coated Nitinol samples, respectively, in the
tenth cooling cycle. Figure 16 (a) and (b) show the same
effect for the uncoated and coated samples, respectively, in
the fortieth cooling cycle.

When DSC measurements were run for uncoated and 3000 A0
carbon coated samples, annealed at 700°C for six hours,
similar results were obtained. Figure 17 (a) and (b) show

the DSC cooling curve, of the first cycle for uncoated and

)1,

Ana

§

552

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.3
23.11'0
(a)
0.2-
1;
\
:5
57 o.:~
C.
u.
C
:2
0.0-
26.05’0 '
23.74J/9
-0 . 1—40 £0 ' (1 2'0 ' 4'0 I Si) 80
Temperature (’C)
0.4
(b)
o.3~
23.48'C
3E o.a~
a.
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,4
ll.
'2
. 0.1-
I
,4. ~
o.o~
25.33'c
““3. -5. a ' 2'0 ‘ :6 ' as ' so
Temperature I’C)
Figure 13. DSC curves of the first cooling cycle of

Nitinol samples. (a) Uncoated and annealed at
700°C for 3 hours (b) Coated with a 3000 A°
carbon film and annealed at 700°C for 3 hours.

'.
'4‘

£53

 

 

 

 

 

 

 

 

 

 

 

 

0.:
44.43’0
24.170/0 .
0.0~
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is
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Temperature PC)
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44.50’0
23.250/0
: l I
0.0-
35 -0.i~
5
3
O
63
‘2
i ~0.a~ 51.03%:
~0.3-
(b)
-0 ' 4... 0 ~50 ' 5 - 20 - 4'0 - BB . 60
Temperature (’12)
Figure 14. DSC curves of the first heating cycle of Nitinol

samples. (a) Uncoated and annealed at 700°C for
3 hours (b) Coated with a 3000 A° carbon film
and annealed at 700°C for 3 hours.

£54

 

 

 

 

 

 

 

 

 

 

 

0.4
(a)
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13 a
g 0‘2 14.05%:
5 J
E!
ii 0.1-
.£
0.0- L
17.95'0
21.7tJ/p
“0.1’ 1 1 r— V r ' r p
~40 ~20 0 20 40 so 30
Temperature (’6)
0.4
(b)
0.3
3? 0.2~
35 is.so°0
5
E:
u
I 0JJ
i
-.__..__3—+—~» '
0.0J
ta.9e°c
19.19010 .
~0.: . - - r. - r. - r ,
~40 ~20 3 20 40 an 00
Temperature ('0)
Figure 15. DSC curves of the 10th cooling cycle of Nitinol

samples. (a) Uncoated and annealed at 700°C for
3 hours (b) Coated with a 3000 A° carbon film
and annealed at 700°C for 3 hours.

555

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.4—
7
i a)
0.3-
3? 0.2—
is
I
E a. 20's
'3 0.i~
:£
.0.0- . a? _BJA
12.10'0
17.943/0
-°' 1 7 V "F r r r
~40 ~20 0 20 40 so 00
Temperature PC)
0 .4 y
1
(b)
0.3~
35 o.2~
E
g .
E e.02°c
i 04-
o 'o d M I
:1.3:°c.
15.030/0
'0 e 1 1 1 ' T _'_ —I" '
~4 ~20 0 20 40 00 00
Temperature ('8)
Figure 16. DSC curves of the 40th cooling cycle of Nitinol.

(a) Uncoated and annealed at 700

C for 3 hours

(b) Coated with a 3000 A° carbon film and

annealed at 700°C for 3 hours.

..A .

I)

556

 

 

 

 

 

 

 

 

 

 

 

0.4
(a)
.0.3~
23.34'0
35 0.a~
5
5 .
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g 0.1~
:£
0.0“ P/fl"
28.96'C
23.924/0
“o. 1 1 1 f r ' T ‘ Y '
-‘0 ~20 0 20 40 so 30
Temperature (’6)
6. A
(b)
0.3—
15 0.2—
g 23.59%:
I
O
E!
‘3 0 1
g .
0.0“ 1f \
25.55'c
~ 24.47J/g
~0.1 -+ 1 v 1 . _r l r _, r ,
~40 ~20 0 20 40 so so
' Temperature PC) ‘
Figure 17. DSC curves of the first cooling cycle of Nitinol

samples. (a) Uncoated and annealed at 700°C for
6 hours (b) coated with a 3000 A0 carbon film
and annealed at 700°C for 6 hours.

 

"II.

I‘

57
coated Nitinol samples, respectively. Figure 18 (a) and (b)

shows the DSC curves for the heating cycle. From both
Figures 17 and 18 it is shown that for the constrained
samples, the Mf and AS temperatures dropped markedly, while
the Ms and Af temperatures were unchanged.

Cycling the uncoated and coated samples that were heat
treated at 700°C for six hours was performed to study the
effect of surface constraint on the R-phase. It was found
out that the heat treatment promoted the surface constraint
and inhibited the formation of the R-phase. This is shown
in Figures 19 and 20, where the uncoated and coated samples

were cycled ten and forty times, respectively.
2. X-Rav Analysis:

X-ray analysis was made for the uncoated and 3000
A0 carbon coated Nitinol. The structure of the carbon
coating is turbostratic, which is a semicrystalline
structure. Thus, no peaks were recorded from the carbon
film. This is illustrated in Figure 21 (a) and (b) which
show the x-ray diffraction pattern of uncoated and carbon
coated Nitinol, respectively.

On annealing the carbon coated Nitinol, the thickness
of TiC formed at the carbon/Nitinol interface increases.
Consequently, peaks of TiC appear in the x-ray diffraction
pattern of annealed carbon coated Nitinol. Fig. 22 shows
the diffraction pattern of 21 3000 A0 carbon coated sample
that was annealed for three hours at 700°C. The intensities

of the TiC peaks are small in comparison to the TiNi peaks.

Heat Flew (We)

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a

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58

 

 

 

 

 

 

 

 

 

 

 

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Temperature (’CI

Figure 18. DSC curves of the first cooling cycle of Nitinol

samples. (a) Uncoated and annealed at 700°C for
6 hours (b) coated with a 3000 A0 carbon film
and annealed at 700°C for 6 hours.

£59

 

   

 

 

 

 

 

 

 

 

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Temperature (’0!

Figure 19. DSC curves of the 10th cooling cycle of Nitinol
samples. (a) Uncoated and annealed at 700°C for
6 hours (b) Coated with 3000 A0 carbon film and
annealed at 700°C for 6 hours.

‘l

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6()

 

 

 

 

 

 

 

 

 

 

 

 

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Temperature (‘0)
Figure 20. DSC curves of the 40th cooling cycle of Nitinol

samples.

(a) Uncoated and annealed at 700°C for

6 hours (b) Coated with 3000 A0 carbon film and
annealed at 700°C for 6 hours.

(1

61

 

nM
(a) cum

‘3
E
’3?
3
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I220)

 

 

 

 

15 20 25 30 35 40 48 50 55 BO 65 70 75 80 88 90 95
20 (degrees)

 

TIN!

(b) (um

11"
(211!

INTENSITY (arbitrary unite)

TIM
(220D

' V v r

15 20 28 30 35 40 45 50 55 BO 05 70 75 IO .5 .0 I!
20 (degrees)

 

 

f Y

 

 

Figure 21. X-ray diffraction pattern of Nitinol (a) .
Uncoated (b) Coated with a 3000 A0 carbon film.

.‘.r

62

 

 

 

 

mm
(110)
E
>.
E
E
3
11M
E (211)
U)
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(200)
no . TIM
(110 "C (220)
. (220) -

 

 

15 20 25 30 35 40 45 5O 55 50 55 70 75 80 85 90 95
20 (degrees)

Figure 22. X-ray diffraction pattern of a 3000 A0 carbon

coated Nitinol sample heat treated at 700°C for
3 hours after coating.

63
Annealing of the carbon coated samples at the same

temperature (700°C) for a longer period of time, six hours,
caused the TiC peaks to intensify. This effect is

illustrated in Figure 23.

3. i n M r m n :

Microhardness measurements were run on 3000 .A0
carbon coated Nitinol samples that were heat treated at
700°C. As the annealing time increased, the thickness of
the TiC at the carbon/TiNi interface increased.
Consequently, the surface hardness increased. This effect

is shown in Figure 24.

4. fioonning Elootron Miorosoooy of tho goroon Qootoo
TiNi Alloy

The electron microscope was used in the scanning
mode to evaluate both the microstructure and topography of
the uncoated and carbon coated Nitinol samples. The vapour
deposited ULTI carbon film was found to form a continuous
film on the Nitinol surface. Thicknesses of the carbon film
up to 3000 A0 did not change the topography of Nitinol, and
had no microstructural features. SEM photomicrographs of
unannealed. Nitinol are shown in Figures 25 and 26 for
uncoated and coated samples, respectively. Comparison of
the microstructure in both micrographs prove that the
coating is continuous and does not change the topography of
the Nitinol samples. On annealing uncoated and coated

Nitinol samples, the carbon film remained continuous and did

64

 

E

a

3

>

E

‘3? TIN)

3 (110)

t TIN)

a "C (211)

g (200)

.—

3- 110 mu
TIC (220) ( 220)

(111)

 

 

 

 

 

 

'7 f V V ' fi ' iv

15 20 25 30 35 40 45 50 .55 50 65 70 75 80 55 90 95
29 (degrees)

Figure 23. X-ray diffraction pattern of a 3000 A0 carbon
coated nitinol sample heat treated at 700°C for
6 hours after coating.

Figure 24.

65

 

170

180 .

150

VICKEHS HARDNESS

140

130 .

120

 

 

 

0 0'0 150 330
HEAT TREATMENT TIME ImInuIee)

Vickers hardness as a function of annealing time
of a 3000 A0 carbon coated Nitinol sample heat
treated at 700°C. Each hardness point is an
average of 5 readings. The maximum deviation is
9.48%.

 

Figure 25. SEM photomicrograph of an uncoated, unannealed
Nitinol sample.

 

Figure 26. SEM photomicrograph of an unannealed 3000 A0
carbon coated Nitinol sample.

67
not change the topography of the Nitinol surface. The

latter case is illustrated in Figures 27 and 28 for uncoated
and coated Nitinol samples, respectively, that were heat

treated at 700°C for three hours.

5. WWW

Elemental analysis of the carbon coated Nitinol
was done using Auger Electron Spectroscopy. The analysis
was done for 3000 A0 carbon coated Nitinol samples that were
unannealed, as well as for coated sample that were annealed
for one hour, three hours, and six hours. Concentration
profiles using the depth profiling technique were also
obtained for these samples.

Figure 29 (a) and (b) show the Auger spectrum of an
unannealed 3000 A0 carbon coated Nitinol sample after one
minute and 26 minutes argon sputtering, respectively. In
Figure 29 (a) it is illustrated that the surface of the
Nitinol is completely covered with carbon, while Figure 29
(b) show that carbon, nickel, titanium and oxygen are
present at the carbon/Nitinol interface. It is speculated
that the oxygen was present as a very thin layer over the
Nitinol surface prior to carbon deposition, or was
introduced to the Nitinol surface early in the deposition
process with carbon. Analysis of the carbon signal in the
Auger spectrum show that the carbon at the surface (Figure
29 (a)) is in the elemental form, while that close to the
interface (Figure 29 (b)) is in the compound form, titanium

carbide. Figure 30 show a depth profile of the unannealed

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68

 

Figure 27. SEM photomicrograph of an uncoated Nitinol
sample heat treated at 700°C for 3 hours.

 

Figure 28. SEM photomicrograph of a 3000 A0 carbon coated
Nitinol sample that was heat treated at 700°C
for 3 hours after coating.

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coated Nitinol sample (a) one minute argon

sputtering (b)

26 minutes argon sputtering.

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70

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om ooom anmocamas no mo maemoum aumoo .om musmflm

 

 

 

 

 

 

 

 

 

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3036-01-3030

‘ .4

71
3000 A0 carbon coated samples. It is illustrated how carbon

is concentrated at the surface, and then its concentration
drops after the carbon/Nitinol interface. On the other
hand, both nickel and titanium are concentrated in the bulk
of the material, and are depleted at the surface of the
sample. Considering the carbon film thickness, it is
estimated that the sputtering rate of the carbon film was
about 250 AO/min. Figure 31 is an SEM photomicrograph of
the argon sputtered surface of an unannealed carbon coated
Nitinol sample. The contrast between the carbon coating and
the TiNi phase shows a sharp interface area between the
carbon film and the substrate.

Auger analysis was also done on 3000 A0 carbon coated
samples annealed at 700°C for one hour, three hours, and six
hours. Figure 32 (a) and (b) shows the Auger spectrum for
the sample annealed for one hour after one minute and 40
minutes argon sputtering, respectiveLy. The depth profile
shown in Figure 33 shows that the annealing for one hour at
700°C broadened the TiC region at the carbon/Nitinol
interface. Similarly, Figure 34 (a) and (b) shows the Auger
spectrum for the sample annealed for three hours after one
minute and 40 minutes argon sputtering, respectively. It is
clear that the carbon still exists in the elemental form at
the surface. Moreover, Figure 35 shows the depth profile of
the three hour annealed carbon coated sample. It is clear
that the longer heat treatment broadened the TiC region at

the carbon/Nitinol interface as compared to one hour

N

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72

 

Figure 31. SEM photomicrograph of an unannealed 3000 A°
carbon coated Nitinol after 26 minutes argon
sputtering.

73

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W V I v v

 

 

 

 

 

 

 

 

 

 

   

 

 

 

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(a) ..
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10.0 110.0 210.0 310.0 410.0 510.0 010.0 710.0 010.0 010.0 1010.0
KINUIC ENERGY, eV
m e : : : : : : : : : : : : : : : : : : -
m. (b
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8 .
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10.0 110.1 215.4 314. 0 414. 1 513. 4 012.7 712.0 011.4 010.7 1010.0

Figure 32.

KliEllC ENERGY. eV

Auger signal of a 3000 Aocarbon coated Nitinol
sample annealed at 700°C for one hour after
coating. (3) One minute argon sputtering (b) 40
minutes argon sputtering.

«IQ!

74

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you occo> um Umammccm Hocwuflz Uwumou
conumuom ooom m mo maamoum aummo

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303d'01-30JJ

75

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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11.7 111.5 211.4 311.2 411.0 510.3 010.7 710.5 010.3 310.2 1010.0

Figure 34.

KDEIIC DUNN. 0V

Auger signal of a 3000 A0 carbon coated Nitinol
sample annealed at 700°C for three hours after
coating. (a) One minute argon sputtering (b) 40
minutes argon sputtering.

76

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um omamwccm mHmEMm Hocfluflz vmumoo

 

 

 

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.zu.MEupmflumm
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9H

flUJJ-UI-SUJJ

77
annealing. Figure 36 is an SEM photomicrograph illustrating

the presence of TiC at the carbon/Nitinol interface.

A six hour anneal was sufficient to make the 3000 A0
carbon film react with the substrate to form at the TiC
surface of the Nitinol substrate. This is illustrated in
Figure 37 (a) and (b) which shows the Auger spectrum after
'one minute and 35 minutes argon sputtering, respectively.
Analysis of the carbon signals in both Figure (a) and (b)
show that it exists in the compound form, TiC. Figure 38,
which is a depth profile of the sample, also shows that

titanium is present at the surface with carbon.

6. Transmission Electron Migrgsggpy:

Cross sectional specimens of vapour deposited
ultra—low temperature isotropic (ULTI) carbon on Nitinol
substrates were examined using transmission electron
microscopy. The :phase transformation of the surface
constrained Nitinol was studied in-situ using a cold stage.
The major findings of the study were that during martensitic
transformation, the last martensite to form was close to the
constrained surface. Also, the last martensite formed
disappeared first in the reverse transformation. The TEM
foil, which is made up of 3000 A° carbon coated Nitinol
samples heat treated at 700°C for three hours, was cooled to
about 240 K using the TEM cold stage. The temperature of
cooling was chosen to be below the Mf temperature to ensure

complete martensitic transformation of Nitinol. The cooling

was then stopped, and the TEM foil was left to warm up in

.v

78

 

Figure 36. SEM photomicrograph of 3000 A0 carbon coated
Nitinol annealed at 700°C for three hours after
40 minutes argon sputtering.

79

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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, 4..
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10.0 115.0 215.3 314.0 414.0 513.3 012.0 712.0 011.3 310.7 1010.0
' nmucmmm.w
Figure 37. Auger signal of a 3000 A0 carbon coated Nitinol

sample annealed at 700°C for six hours after
coating. (a) One minute argon sputtering (b)
Thirty five minutes argon sputtering.

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3036-01-3036

81
the column to about 300 K. Thus, partial austenitic

transformation of the Nitinol occurred. Figures 39 (a) and
(b) are bright fieldimages of the vertical cross-section
TEM foil at about 300 K. The micrographs (Figure 39 (a) and
(b)) show lathes of martensite present in the bulk of the
Nitinol sample, away from the constrained surface at that
temperature. Figure 40 is an electron diffraction pattern,
[llO]m, of the martensitic phase at about 240 K, and Figure

41 is the analysis of the [110]m electron diffraction

pattern.

Transmission electron microscopy was also used to
examine the microstructures of both the carbon thin film
vapour deposited on the Nitinol substrates, and the TiC
formed at the carbon/Nitinol interface in the heat treated
samples. Figure 42 shows the microstructure of a carbon
flake in a vertical cross-section TEM foil for a 3000 A0
carbon coated unannealed Nitinol samples. Figure 43 shows
the electronc diffraction pattern of the carbon flake.
Since the structure of carbon is semicrystalline
(turbostratic), a ring* pattern appears rather’ than
diffraction spots. The inner ring corresponds to the
angular position of (100) in graphite crystals while the
outer ring corresponds to the (002).

The TiC formed at the carbon/Nitinol interface was
investigated with an examination of a horizontal cross-
section TEM foil of a 3000 A0 carbon coated Nitinol sample
heat treated at 700°C for three hours. Figures 44 and 45

show the microstructure of TiC and the electron diffraction

 

82

 

 

(b)

Figure 39. Bright field image of a vertical cross-section
TEM foil of a 3000 A0 carbon coated Nitinol
sample heat treated at 700°C for 3 hours (a)
200,000 x, (b) 500,000 x.

83

 

Figure 40. Electron diffraction pattern of

Nitinol in the
martensitic phase, [110]m.

. ° (no). '(111) . - .

. . (002). . .(000) . .

Figure 41. Analysis of the electron diffraction_pattern of

Nitinol in the martensitic phase, [110]m.

84

 

h—q
0Ju

Figure 42. Bright field image of a carbon flake.

 

Figure 43. Electron diffraction pattern of a carbon flake.

85

 

Figure 44. Bright field image of TiC.

 

Figure 45. Electron diffraction pattern of Tic, [123]Tic.

In

(3

in.

f‘fl

te

(_)
In

86
pattern, [123]Tic, corresponding to it, respectively.

B. WM

The objective of the biologic study was to evaluate the
induced growth of collagenous tissue on non-annealed carbon
coated Nitinolsurfaces. Carbon coated Nitinol filaments,
0.076 mm in diameter, were incorporated into the fascia lata
which replaced the anterior cruciate ligament in a canine's
stifle joint. Figure 46 (a) and (b) show part of the
surgical procedure followed. Figure 46 (a) shows the fascia
lata before incorporating the carbon coated filament into
it, and Figure 46 (b) shows the process of drilling a tunnel
in the femur through which the fascia lata would be pulled.
Radiographs were also taken for the carbon coated Nitinol
filaments in the canine’s stifle joint. Figure 47 (a) and
(b) shows the anterior-posterior and lateral-medial views of
the operated knee joint, respectively.

Thirty days post-operatively, the canine was
euthanized, and the stifle joint was harvested. Scanning
electron microscopy examination of a wire section taken from
the fascia lata secured on the patellar tendon during
surgery showed the presence of islands of reticular collagen
on the surface of the carbon coated filaments. This is
illustrated in Figures 48 (a) and (b) which are SEM
photomicrographs of collagenous tissue over carbon coated
filaments harvested from an area adjacent to the patellar
tendon. However, histological evaluation at a magnification

of 100X could not reveal whether fibrocytes were formed on

\
f'

87

(a)

 

(b)

    

\
_fl!ir,,\,;_,_.x -, ,I

Figure 46. Photographs illustrating part of the surgical
procedure followed in the study. (a) Fascia
lata before pulling it through the tibia, (b)
drilling a tunnel in the tibia.

(a)

(b)

Figure 47.

 

88

Radiographs showing the carbon coated Nitinol
filaments in the canine’s stifle joint. (a)
Anterior-posterior view, (b) lateral-medial
view.

89

(a)

 

Figure 48. SEM photomicrographs of collagen islands on the
surface of carbon coated Nitinol filaments. (a)
1000 X (b) 1000 X.

90
the carbon coated filaments in either the transverse section

or the longitudinal section as shown in Figure 49 (a) and
(b), respectively. Thus, it is not conclusive whether the
reticular collagen viewed by SEM was induced by the carbon
coating, or occurred as a result of tissue healing in the

knee post-operatively.

91

(a)

 

Figure 49. Optical photographs illustrating the carbon
coated Nitinol filaments in tissue. (a)
Transverse section, (b) longitudinal section.

v. DISCUSSION
A. W

The objective of this research work was to study the
effect of surface constraint on the phase transformation of
Nitinol, with application to the design of a prosthesis for
the reconstruction of the anterior cruciate ligament. The
phase transformation studies Showed that the constraint in
the 3000 A0 ‘carbon coated and annealed Nitinol samples,
represented by TiC, caused both the Mf and the AS
temperatures to drop .markedly. The thicknesses of the
Nitinol samples and the vapour deposited carbon films were
600 um, and 0.3 um (3000 A°), respectively.

The transformation peaks of the thermally cycled coated
and uncoated Nitinol samples were analyzed. The 9900
computer/thermal analyzer with which the differential
scanning calorimeter is equipped, was used in the analysis.
For every' peak. in the heating or cooling cycle: of the
Nitinol sample tested, the percentage of the area under the
curve as a function of temperature was plotted. The plot
-also corresponded to the percentage of phase transformed in
both the cooling and heating cycles. The analysis with this
method was done for the transformation peaks of the coated
and uncoated samples on the first cycle of heating and

cooling. Since there was no distinct difference in the

92

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1A .
x . .
. .-
J
V .
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..
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11 0"
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o;
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IL .
a
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m.
C‘
L
11
. \
4
'\
.

93
transformation peaks of the unannealed samples, the analysis

was only performed for the coated and uncoated samples that
were annealed at 700°C for three and six hours. Figures 50
and 51 show the effect of surface constraint on the phase
transformation of Nitinol for samples annealed at 700°C for
three and six hours, respectively. Both figures represent
mapping of the percentage of martensitic phase present in
the heating and cooling cycles as a function of temperature.
A. distinctive characteristic of the figures is how: the
surface constraint causes the AS and Mf temperatures to drop
markedly. Consequently, the annealed coated samples undergo
a certain degree of supercooling to complete the
transformation, although both the MS and Af remain
unchanged.

It is Significant to point out that the phase
transformation of Nitinol will be affected by the ratio of
constraint thickness to sample's thickness. This can be
illustrated by comparing the DSC results for unannealed and
annealed carbon coated Nitinol samples. In the first case,
the TiC layer present at the carbon/Nitinol interface is too
thin compared to the substrate's thickness to affect its
transformation. In the latter case, it was shown that the
more the time of annealing, the thicker was the TiC layer

formed at the interface, and thus the more was the effect of

the constraint.on the phase transformation.

 

94

 

100 I

00.

60.

 

 

 

 

 

E
Elm
‘ HEY! TREATMENI' : 1023 K
20. 3 hours
-—~—- ®Mu1(0
o‘ --o-- Uncoated (U)
0 cu
11‘; 14‘
fi v v v v 3 fi 1 g r
243 253 263 273 283 293 303 313 323 333
THIPERA'IURE (K)
Figure 50. Percent of martensite as a function of

temperature for 3000 A0 carbon coated Nitinol
samples heat treated at 700°C for three hours.

 

95

 

moi

 

001

60<

 

 

 

 

E 3%
* 20
o ._.._. Coated (c1
- — o -— Uncoated (U)
MC'U AC'U
S f
W 1 fi v 1 l V Y 1 l V
243 253 263 273 283 293 303 313 323 333
TBIPERATURE (K)
Figure 51. Percent of martensite as a function of

temperature for 3000 A0 carbon coated Nitinol
samples heat treated at 700°C for six hours.

 

96
1. Mathematical Analyaia of tha Iransfgtmatign Data

Mathematical analysis was performed on the percentage
of phase transformed versus temperature data. A
mathematical empirical formula was obtained to fit the
experimental data. The formula was of the exponential form:
1-f=Aexp (-B (MS-TH (5)
for the martensitic transformation, and
f = A exp (-B (Af - T)) (6)
for the reverse transformation, where
f is the fraction of martensitic phase present at
the specific temperature (T),
1 - f is the fraction of austenitic phase present at
the specific temperature (T),
and
A, B are constants. '
Figure 52 (a) and (b) represents a comparison of the
percentage of the amount of austenitic phase present in
uncoated and coated samples as a function of temperature
during the first cooling cycle. . The figures show' the
percentage transformed for the samples heat treated at 700°C
for three hours and six hours, respectively. Similarly,
Figure 53 (a) and (b) represent a comparison of the amount
of austenitic phase present in uncoated and coated samples
as a function of temperature during the first heating cycle.
The figures Show the percentage transformed for the samples
heat treated at 700°C for three and Six hours, respectively.

In Figures 52, and 53, solid lines represent the empirical

A

1‘

1

97

 

 

   
  

 

 

 

 

 

 

 

100 O ."
BEAT TREATMENT: 700 C . 3 hours
00
to ---O--- Coated 1. - f - 1.05 exp (-0.1. (299.5 - 1))
g --o-v- Uncoated 1 - f - 1.15 exp (-O.17 (299.5 - TH
40
a
20
0
200 3'5) 250 203 268 211 270 201 200 29) 290 303
TEMPERAWRE 1K)
100 HEAT 51112111110111: 700°C . 6 hours .:0
.0
--I-- Coated l - f - 1.1 exp (-0.07S (299.5 - 1))
00
--O-- Uncoated l - f n 1.1 exp (-0.19 (299.5 - TH
.o 00
20
o .' .............. W-
240 233 250 301 200 270 270 201 200 293 290 301

Figure 52.

TEHPERATURE (K)

Percent of austenite present as a function of
temperature in the first cooling cycle for
coated and uncoated Nitinol samples heat treated
at 700°C for (a) three hours (b) six hours.

98

 

 

 

 

 

 

 

  
 
     

 

 

‘°° nan rmmsm: 100°C . 3 hours .0".
IO
‘0 --O-- Coated f - 1.05 exp(-0.095 (327 - TN
”‘0‘“ Uncoated l - 1.15 exp(-O.15 (327 - fl)
‘0
O
20
0
515 1:0 2:5 190 255 300 195 110 315 320 325 ”0
momentum: (It)
‘00 ”.0".
new: tnmmanm 100°C . 6 hours
.0
so --0-- Coated t - 1.05 exp (-0-07 (327 ' T”
‘0 --O-- Uncoated ! - 1.15 exp (-0.15 (321 - 7))
O
20
0
215 2:0 3le I;0 29'! 100 105 310 315 320 )2! 330
TEMPERATURE (K)
Figure 53. Percent of austenite present as a function of

temperature in the first heating cycle for
coated and uncoated Nitinol samples heat treated
at 700°C for (a) three hours (b) six hours.

99
values obtained mathematically to fit the experimental data.

The experimental results could be represented by two
exponential functions, one of which is only effective about
two to three degrees below the MS or the Af temperatures.
For simplification, one exponential term was used. Thus,
the Ms and Af temperatures used in equations (5) and (6) are
one and three degrees, respectively, lower than the actual
MS and Af values obtained from the experimental results.
The experimental and calculated data of the percentage of
austenite present as a function of temperature are tabulated
in Appendices 1.2nui 2 for uncoated and coated samples heat
treated at 700°C for three and six hours, respectively.
Equations 5 and 6 describe empirically the fraction of
austenite present in the martensitic and reverse
transformation, respectively, as a function of temperature.
However, as shown in Appendix 1 and 2, the values of the
constants A and B varied with the experimental conditions
such as the direction of transformation, the annealing time
of the uncoated or coated samples, and the presence of
surface constraint. Accordingly, it was deduced that the
constants A and B can be expressed in terms of physical or
thermodynamic parameters. These parameters differ from one
sample to the other depending on the sample's
thermomechanical history and the experimental conditions
under which it was tested. To find these parameters in the

martensitic transformation, equation (4) was employed.

100

where,

(4)

f is the fraction of martensite transformed,

and

AHT is the total heat of transformation of the reaction. It is

important to note that in these derivatives that the subscript, T,

does not signify a dependency on temperature.

Based on experimental curve fitting, a functional form of the

following type is proposed:

 

Qéfl = k e'al(Ms‘T) - k e-a2(MS-T)
8T 1 2
where,
a1 << 82
and
1 - k1 + A:2a # 0

(7)

(3)

101

Substitution of (7) into (4) yields

 

 

s -a (M -T) -a (M -T)
f - fig I [k1 e 1 s - k2 e 2 S ] dT (9)
T T
1 El 1 a1(M -T) E; 1 -a2(Ms-T)
- AH a ( - e ) a ( - )
T l 2
k -a (M -T) k -a (M
1 - £ - 1 - 1 ( 1 - e 1 s ) + ( 1 - e 2 5
AH a AH a
T l T 2

Since a1 << a2, experimental results suggest that for

 

 

 

-a?(Ms-T)
T << Ms , we have e ‘ z 0
k -a (M -T) k
l l s 2
1 - f z 1 - (l - e ) + (12)
AHTa1 AHTa2
Substitution of (8) in (12) yields
k -a (M -T)
1 - f - AH : (e 1 s ) (13)
T l

) (11)

The assumption in equation (8) is justified by the fact that equation

(13) agrees with the experimental results, as it will be shown later.

102

From experimental results, it was found out that

AH

 

 

a1 a T 2 (14)
R(MS - Mf)
and
AHTa1
where,

a is a unitless term close to unity depending on the accuracy of

the experimental data

(16)

From our understanding of activated processes, we know that an
expression of the following form can be written for the kinetics of a

transformation reaction:

1 - f = a e -Q/RT

where,

Q - AH

103

and

R - gas constant

We propose to define a normalized temperature, Tn

where

and the kinetic equation takes the form

- AHT Tn

R(M - M )
l - f - a e s f

which can also be written as:

- AHT(M§ - T)

2
f)

 

l - f = a e R(Ms - M

for the martensitic transformation.

Similarly, for the reverse transformation,

-a (A - T)
k (e l f )

AHTa1

 

where, from our experimental findings

(17)

(18)

104

31 a (19)

and,
2
k 9 —-EEI——— 20
1 ‘ R A - A ( )
f s

If we assume a normalized temperature Tm where,

n the kinetic equation takes the form

f - a e - A"'1' T

m
R(Af - As)

which can also be written as

- AH (A - T)

T f
2

f - o e R(A£ ‘ As) (21)

for the martensite to parent phase transformation.

105
2. F r Tr f ' '

Both the martensitic and reverse transformation of
Nitinol are characterized by no chemical compositional
change associated with them. Thus, both the parent and the
martensitic phase are considered to be a single component
system [100]. Figure 54 is a schematic representation of
the molar Gibbs chemical free energy for both the parent
phase (P) and the martensitic phase (M) as a function of
temperature. The figure illustrates that there exists a

single equilibrium temperature, T at which the difference

0'
in chemical free energy between the two phases is equal to
zero (AGP_M = 0) [100].

For the martensitic transformation to proceed, AGP_M
has to be negative, i.e. G: < GE. It would be expected that
the transformation would start at a temperature less than,

but very close to, T However, due to the presence of

o.
opposing elastic energies that are positive in magnitude,

the Nitinol undergoes supercooling below T The

0'
supercooling continues until the chemical driving force,
which is negative in magnitude, overcomes the opposing non-
chemical energies. Once a net negative energy is reached,
the martensitic transformation starts, and the temperature
at which this occurs is designated as MS. The chemical
driving force continues to increase from Ms to Mf at which
the transformation is complete [100]. Similarly, in the

reverse transformation, superheating above To is required.

The superheating allows the chemical driving force to

‘a

y.

106

    

 

)---——a—Q-‘—-

 

Z
.4
>

TUH‘ERA'IURB

Figure 54. Schematic representation of Gm as a function of
temperature [100].

107
overcome the non-chemical energies. Thus, the

transformation starts at the As temperature and is complete
at the Af temperature. Moreover, the chemical driving force
increases from As to Af.

Equations (13) and (18) were derived to express the
fraction of the parent phase present as a function of
.temperature during the martensitic and. the reverse
transformation, respectively. The heat of transformation at
a specific temperature during the heating or cooling cycle
is directly associated to a fraction of phase transformed.
Thus, the driving force for the martensitic transformation

or the reverse transformation can be calculated.

a. Driving Force Calculations of the Martensitic Transformation

 

 

k -a (M - T)
1 - f — AH : e 1 s (13)
T l
-a (M - T)
1 5
k1 e
f - 1 -
ART 31
Also,
AHT(f) = AH (22)

where AHT is the total heat of transformation,

and AH is the integrated enthalpy from the temperature T to

M .
s

108

 

 

 

 

l - a (M -T)
f AHT AHT - a l s
l
k -a M a T
AH - AHT - —1 e 1 S e 1 (23)
a
1
Using the Gibbs-Helmholtz equation
6(AG[T) _ _ _fl
61 T2 (2“)
a T
agAGgT) -AHT k1 -a M e 1
= ___ + l s (25)
BT a 2
2 1 T
T
-a M M
AC Ms AHT Ms kle 1 s S eal T
5‘ - + ___ + a 2 dT (26)
T T T 1 T T
-a M M
l s s a T
99 AG AH AH kle e
T - T - + - + a 2 (11‘ (27)
M T M T l T T
s 5
At M , AG - 0
M M M
J s ealT ea1 T s I s ea1 T
dT = - + a dT (28)
T T2 T T l T T

109

 

 

 

"3 a T M
e 1 alMs alT s alT
2 ———§—— dT — - e + e + a1 I e dT (29)
T T Ms T T T
But
M m
T
I s 811 dT 1 ( MS ) E (a1)i(M:-Ti)
-——-- = n - + . — (30)
T T T i=1 1 1!

which is not a closed form integral. Thus, the integral

 

s a T
I e 1 dT was calculated using the trapezoid rule of
T

 

-a M
AH AT k e 1 s alus 811
_AQ _ + T _ T + 1 _e + e
T T T a M T
l 5
Ms
ealT
+ a1 ——¥——— dT (31)
T

But, the martensitic transformation is an exothermic.reation. Thus,

both AHT and k1 are assigned negative signs.

110

 

The values for the driving force of the martensitic transformation of
(AC) of constrained and unconstrained samples in given in Appendices 3

and 4.

b. Driving_Force Calculations for the Martensite to Parent Phasg

Transformation

From equation (18):

k
1 - f - 1 - 73-5—1— (e'a1(Af'T’) (33)
a
1: 1
since, AHT(1 - f) - AH (22)

k -a (A -T)
-. All - AMT - -1 e 1 f (31.)
a1

111

Applying the Gibbs-Helmholtz equation

 

 

 

 

 

 

 

3(acgr) _ - _g (24)
6T T2
AM k -a (A -T)
QLAQLI) _ _ __I + 1 e 1 f (35)
31 T2 8 T2
1
A A a T
f f k -a A 1
As I _ A9 I - - I AHT 9% + I a1 e 1 f e 2 dT (36)
T Af T T T 1 1 1 T
A" “E k1 -alAf Af :1T
, _.I I 1 —— J 2 dT (37)
T T 81 1 T
An 1
T T
-— AG - AG - ———— - AH
Af Af T At. T
k 1 alAf ‘ 88111 e31T “1 :1T
+ -- e - + + a J dT (38)
a1 Af T l T T
1. AC AC AHTT AH le El - a1(Af-T)
A A ' T “ A ‘ T ' a A + a
f f f 1 f 1
A a T

 

-a A f
+ lee 1 fl 9 dT (39)
T

112

AGA can be calculated using the condition,
f

AG - 0 at A

With AGA known, AG can be calculated from:

f T

AllT kT k -a(A—T)
AG = %“ AG - T + AMT + 31A - 31 e 1 f
f f f 1f 1

 

 

 

dT (40)

where the integral I e dT

was calculated using the trapezoid rule of integration, and is

tabulated in Appendices 3 and h.

The values for the driving force of the constrained and unconstrained

samples in the martensite to parent phase transformation is given in

Appendices 3 and A.

113
The surface constraint was found to affect the driving

force. The calculated values of the driving force, G, for
the transformation of coated and uncoated samples that were
heat treated at 700°C for three and six hours are tabulated
in Appendices 3 and 4, respectively. Figures 55 and 56
illustrate the driving force as a function of temperature
for the unconstrained and constrained Nitinol samples. Both
figures show that for the martensitic transformation, MS is
the same for both the constrained and unconstrained sample.
However, as the transformation proceeds, the constraint
opposes the driving force in the surface constrained sample,
causing it to be lower than that for the unconstrained
sample. In order to overcome the constraint and the strain
energy associated with it, the constrained sample has to be
supercooled to achieve the same driving force required to
complete the transformation as in the unconstrained sample.
Thus, at any temperature during the martensitic
transformation other than Ms' the net driving force for the
constrained sample is lower than that for the unconstrained
one. Moreover, it is noticed from Figures 55 and 56 that
even though the constrained sample is supercooled to lower
temperatures, the net driving force at saturation is less
than that for the unconstrained sample. This is an
indication that complete transformation to martensite in the
cooling cycle is never achieved for the constrained sample.
It also indicates that for surface constrained samples,
martensitic transformation starts at the bulk and proceeds

to the surface with the decrease in temperature.

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116
In the martensite to parent phase transformation, the

As temperature for the surface constrained sample is lower
than that of the unconstrained one. This is attributed to
the fact that there is an increased amount of strain energy
associated with the surface constrained sample during the
martensitic transformation. Release of this stored energy
assists in the reverse transformation causing it to start
earlier, i.e. at a lower temperature. Thus, the driving
force is greater in the constrained sample in the reverse
transformation as compared to the unconstrained one at any
temperature during the reverse transformation. Since the
accommodation strain is largest for the martensite plates
formed near the constrained surface, the reverse
transformation of the surface constrained sample starts at
or near the surface and proceeds to the bulk with the
increase in temperature.

Finally, the strain energy associated with the surface
constraint of the Nitinol samples could be estimated.
Figures 55 and 56 show the differences in the driving force
between the unconstrained and constrained samples at a given
temperature during martensitic and reverse transformations.
This difference corresponds to the strain energy contributed
by the surface constraint. Although the strain energy is a
function of temperature, it can be estimated that the
maximum stored elastic energy difference between an
unconstrained and a constrained (thin Nitinol sample) is

estimated to be 3.5 J/gm.

117
B. D i n f Pr h i f r h R n ru i n of h

An ri r r i Li m nt

Scanning electron microscopy figures of the harvested
carbon coated filaments showed that islands of reticular
collagen formed on their surface thirty days post-operative.
However, the biological findings are inconclusive at that
early stage, and additional research is required. The
research should include a simple design of a prosthesis for
the reconstruction of the anterior cruciate ligament in
which the carbon coated Nitinol filaments are easily
anchored to the tibia and femur.

The design envisioned, which should be modified as
research progresses, uses the unique characteristic of
Nitinol to change its shape with temperature. The Nitinol
alloy chosen should have an austenitic finish temperature of
about 35°C, which is below the body temperature. Figure 57
shows the proposed design of the prosthesis. It is
illustrated how one prosthesis has the ends deflected to
illustrate the anchoring position with the tibia and femur
when the Nitinol transforms with body temperature.

The components of the prosthesis are illustrated in
Figure 58. It consists of two hollow cylindrical ends
connected with the carbon coated filaments. There are two
upset horizontal pins in each hollow end. The lower one is
for the filament attachment, while the upper one is for
surgical handling while pulling the ends of the prosthesis

through the bones.

118

cmpnmuqmumgmumg
SPEC.__ DATE

 

Figure 57. Proposed design of a carbon coated Nitinol
prosthesis for the reconstruction of the
anterior cruciate ligament.

119

 
  
   

‘~_~‘-““‘~—Hollow end of the
prosthesis (Nitinol)

/

Nitinol pins .i‘g“

 

 

 

Carbon coated

,,,,,,’~”””' nitinol filaments

 

Figure 58. Design details of the prosthesis devised for the
reconstruction of the anterior cruciate
ligament.

120
Figures 59 and 60 (a) and (b) illustrate the method by

which the prosthesis will be presented into the knee joint.
Following drilling tunnels in the condyles of the tibia and
femur, a flexible scale will be introduced to measure the
distance between the surfaces of the tibia and the femur at
the tunnel outlets (Figure 59). The prosthesis of the
desired length, which will be kept at low temperatures prior
to its use, will then be introduced in the knee joint. To
avoid transformation of the Nitinol prosthesis, the knee
will be cooled well below body temperature by ice packs.
Figure 60 (a) shows the prosthesis in the untransformed
configuration. The ice packs will be removed from around
the knee allowing it to warm to body temperature, which will
in turn heat the Nitinol prosthesis. Both ends of the
prosthesis will deflect, and the anchoring of it to the

tibia and femur is complete (Figure 60 (b)).

1231

 

Flexible
scale \\\

Tibia

 

Fibula __l

 

- -’/
~_f’
‘-

Figure 59. Illustration of a measuring device to measure
the lengths between the surfaces of the tibia
and femur.

122

Femur

 

(a)

Fibula Tibia

 

 

 

Femur

 

(b)

 

Fibula

 

Tibia

 

Figure 60. Prosthesis in the knee joint (a) before
transformation (b) after transformation.

VI. CONCLUSIONS

Surface constraint of Nitinol results in marked drop in

the AS and Mf temperatures for thin samples.

Unannealed coatings did not inhibit the NiTi phase
transformation regardless of the thickness of the

coatings.

The carbon coating did not change the topography of the

Nitinol surface.

TiC forms at the carbon/TiNI interface with annealing,
and the thickness increases with the time of heat

treatment.

The inhibition of the martensitic transformation
increases as the thickness of the TiC interface

increases.

The thicker the TiC interface was, the more the R-phase

was inhibited during the martensitic transformation.

It is proposed that for surface constrained samples,
the martensite plates last to form were close to the
surface, and these are first to disappear during

reverse transformation.

123

10.

124

The forward transformation can be described by an
equation of the form

1 — f = A exp (-B(MS — 1))
where A and B can be defined by thermodynamic

parameters.

The net driving force for the constrained sample was
lower in the martensitic transformation compared to
that of the unconstrained sample. The opposite is true

for the reverse transformation.

The maximum stored elastic energy difference between an
unconstrained and a constrained (thin Nitinol sample)

is estimated to be 3.5 J/gm.

APPENDICES

APPENDIX 1
Experimental and Calculated Data for the Percentage of
Austenite Present as a Function of Temperature for Uncoated
Nitinol Samples Heat Treated at 700°C for Three Hours, and
Carbon Coated Nitinol Samples Heat Treated at 700°C for

Three Hours After Coating.

125

126

TABLE 1

Unconstrained Nitinol Sample - First Cooling Cycle

T(K) % Austenite % Austenite
(Experimental) (Calculated*)
299.5 100 115
298.5 95 97
298.05 90 90
297.2 80 78
296.5 70 69
295.9 60 62
294.7 50 51
293.5 40 41
291.7 30 30
288.7 20 18
285.3 10 10
281.8 5 5
271.0 0 l

* % Austenite = 100 (l-f) = 100 x 1.15 exp [-0.17(299.5-T)].

127

TABLE 2

Constrained Nitinol Sample — First Cooling Cycle

T(K) % Austenite % Austenite
(Experimental) (Calculated*)
299.5 100 105
297.6 90 87
296.8 80 80
296.0 70 74
294.6 60 64
293.0 50 52
290.8 40 42
286.2 30 28
281.0 20 17
273.0 10 8
268.0 5 5
261.0 0 2

* % Austenite = 100 (l-f) = 100 x 1.05 exp [-0.1(299.5-T)].

128

Table 3

Unconstrained Nitinol Sample — First Heating Cycle

T(K) % Austenite % Austenite
(Experimental) (Ca1culated*)
327 100 115
326.3 95 103
325.7 90 94
324.7 80 81
323.7 70 70
322.8 ' 60 61
321.7 50 52
320.2 40 41
318.3 30 31
315.5 20 20
311.05 10 10
307.1 5 6
296 0 1

* % Austenite = 100 x f = 100 x 1.15 exp [-0.15(327-T)].

129

Table 4

Constrained Nitinol Sample - First Heating Cycle

T(K) % Austenite % Austenite
(Experimental) (Ca1culated*)
327 100 105
325.4 90 90
324.3 80 81
323.2 70 73
322.1 60 66
320.2 50 55
317.4 40 42
313.1 30 28
306.6 20 15
297.7 10 7
292.3 5 4
281.0 0 1

* % Austenite = 100 x f = 100 x 1.05 exp [-0.095(327-T)].

APPENDIX 2
Experimental and Calculated Data for the Percentage of
Austenite Present as a Function of Temperature for Uncoated
Nitinol Samples Heat Treated at 700°C for Six Hours, and
Carbon Coated Nitinol Samples Heat Treated at 700°C for Six

Hours After Coating.

130

131

Table 1

Unconstrained Nitinol Sample - First Cooling Cycle

T(K) % Austenite % Austenite
(Experimental) (Ca1culated*)
299.5 100 110
298.7 90 95
297.8 80 81
297.0 70 70
296.3 60 62
295.3 50 51
294.0 40 41
292.2 30 30
290.2 20 20
287.7 10 13
285.8 5 9
271.0 0 1

* % Austenite = lOOx(l-f) = 100 x 1.1 exp [-0.18(299.5-T)].

132

Table 2

Constrained Nitinol Sample - First Cooling Cycle

T(K) % Austenite % Austenite
(Experimental) (Ca1culated*)
299.5 100 110
296.9 90 90
295.7 80 83
293.9 70 72
291.3 60 59
288.5 50 48
285.2 40 38
281.4 30 28
276.7 20 20
270.7 10 12
266.3 5 9
255.0 0 4

* % Austenite = 100(1-f) = 100 x 1.1 exp [-0.075(299.5-T)].

133

Table 3

Unconstrained Nitinol Sample - First Heating Cycle

T(K) % Austenite % Austenite
(Experimental) (Ca1culated*)
327.0 100 115
326.7 95 110
325.5 90 92
324.5 80 79
323.5 70 68
322.6 60 59
321.4 50 50
319.9 40 40
318.1 30 30
315.9 20 22
312.7 10 13
310.3 5 9
296.0 0 1

* % Austenite = 100 x f = 100 x 1.15 exp [—0.15(327-T)].

134

Table 4

Constrained Nitinol Sample - First Heating Cycle

T(K) % Austenite % Austenite
(Experimental) (Ca1culated*)
327.0 100 105
326.0 95 98
324.8 90 90
323.0 80 79
321.3 70 70
319.6 60 62
316.4 50 50
313.0 40 39
308.3 30 28
303.8 20 21
297.4 10 13
293.1 5 10
281.0 0 4

* % Austenite = 100 x f = 100 x 1.05 exp [-0.07(327-T)].

APPENDIX 3
Driving Force of Phase Transformation as a Function of
Temperature for Uncoated Nitinol Samples Heat Treated at
700°C for Three Hours, and Carbon Coated Nitinol Samples

Heat Treated at 700°C for Three Hours After Coating.

135

136

Table 1

Unconstrained Nitinol Sample - First Cooling Cycle

T _eii MS __eiLT. dT AG
(K) T T T (J/gm)
299.5 4.32 x 1019 0 0
297.5 3.09 x 1019 4.32 x 1019 - 3.25
295.5 2.22 x 1019 7.41 x 1019 - 5.59
293.5 1.59 x 1019 9.63 x 1019 - 7.27
291.5 1.13 x 1019 11.2 x 1019 — 8.52
289.5 8.16 x 1018 12.35 x 1019 - 9.4
287.5 5.85 x 1018 13.16 x 1019 —10.07
285.5 4.19 x 1018 13.75 x 1019 -10.66
283.5 3.00 x 1018 14.17 x 1019 -10.94
281.5 2.15 x 1018 14.47 x 1019 —11.22
279.5 1.54 x 1018 14.68 x 1019 -11.47
277.5 1.10 x 1018 14.83 x 1019 ~11.66
275.5 7.94 x 1018 14.94 x 1019 —11.83
273.5 5.69 x 1018 15.02 x 1019 -11.95
271.5 4.08 x 1018 15.08 x 1019 -12.08

AHT = 23.8 J/gm
a1 = 0.17 K’1
K1 = 4.65 J/gm.K

137

Table 2

Constrained Nitinol Sample - First Cooling Cycle
T .J:_Ei? 1M3 _sLElI.dT AG
(K) T T T (J/gm)
299.5 3.39 x 1010 0 0
297.5 2.79 x 1010 3.39 x 1010 — 1.86
295.5 2.3 x 1010 6.18 x 1010 — 3.36
293.5 1.9 x 1010 8.48 x 1010 - 4.61
291.5 1.56 x 1010 10.38 x 1010 — 5.63
289.5 1.29 x 1010 11.94 x 1010 - 6.52
287.5 1.06 x 1010 13.23 x 1010 - 7.24
285.5 0.87 x 1010 14.29 x 1010 - 7.84
283.5 0.72 x 1010 15.16 x 1010 - 8.36
281.5 0.59 x 1010 15.88 x 1010 - 8.79
279.5 0.49 x 1010 16.47 x 1010 - 9.16
277.5 0.40 x 1010 16.96 x 1010 - 9.48
275.5 0.33 x 1010 17.36 x 1010 - 9.76
273.5 0.27 x 1010 17.69 x 1010 - 9.99
271.5 0.22 x 1010 17.96 x 1010 -10.20
269.5 0.18 x 1010 18.18 x 1010 -10.40
267.5 0.15 x 1010 18.36 x 1010 -10.56
265.5 0.12 x 1010 18.51 x 1010 -10.72
263.5 0.10 x 1010 18.63 x 1010 -10.85
261.5 0.087 x 1010 18.73 x 1010 -10.98

AHT = 21.38 J/gm

a1 = 0.1 K-1

K1 = 2.24 J/gm.K

138

Table 3

Unconstrained Nitinol Sample - First Heating Cycle

A

T _ejEE S f_§fl£gflf TAG
(K) T T T (J/gm)
327 6 13 x 1018 0 -14.18
325 4 57 x 1018 6 13 x 1018 -11 01
323 3 40 x 1018 10.7 x 1018 - 8 61
321 2 53 x 1018 14.1 x 1018 — 6 78
319 1.89 x 1018 16.63 x 1018 - 5.4
317 1.41 x 1018 18.52 x 1018 — 4.33
315 1.05 x 1018 19.93 x 1018 - 3.05
313 0.78 x 1018 20.98 x 1018 - 2.82
311 0.58 x 1018 21.76 x 1018 - 2.28
309 0.436 x 1018 22.34 x 1018 - 1.86
307 0.325 x 1018 22.776 x 1018 - 1.49
305 0.242 x 1018 23.101 x 1018 — 1.17
303 0.181 x 1018 23.343 x 1018 - 0.90
301 0.134 x 1018 23.524 x 1018 - 0.65
279 0.0865 x 1018 23.658 x 1018 - 0.42
297 0.075 x 1018 23.73 x 1018 — 0.19
295 0.056 x 1018 23.808 x 1018 0

AHT = 24.53 J/gm

a1 = 0.15 K‘1

K1 = 4.23 J/gm.K

139

Table 4

Constrained Nitinol Sample - First Heating Cycle

T _ea_1T SAf .323 dT AG

(K) T T T (J/gm)

327 9.48 x 1010 0 -13.72
325 7.88 x 1010 9.48 x 1010 -11.78
323 6.56 x 1010 17.36 x 1010 -10.17
321 5.46 1010 23.92 x 1010 8.8

319 4.54 1010 29.38 x 1010 7.64
317 3.78 1010 33.92 x 1010 6.66
315 3.14 1010 37.7 x 1010 5.82
313 2.62 1010 40.84 x 1010 5.1

311 2.18 1010 43.46 x 1010 4.47
309 1.81 1010 45.64 x 1010 3.92
307 1.51 1010 47.45 x 1010 3.47
305 1.25 1010 48.96 x 1010 3.03
303 1.04 1010 50.21 x 1010 2.65
301 0.871 1010 51.25 x 1010 2.31
299 0.725 1010 52.121 x 1010 2.01
297 0.603 1010 52.846 x 1010 1.72
295 0.502 1010 53.449 x 1010 1.47
293 0.418 1010 53.951 x 1010 1.23
291 0.348 1010 54.369 x 1010 0.98
289 0.290 1010 54.71 x 1010 0.78
287 0.241 1010 55.00 x 1010 0.57
285 0.201 1010 55.248 x 1010 0.37

140

TABLE 4 - (continued)

T 31T f a1T dT AG
(K) T T T (J/gm)
283 0.167 x 1010 55.449 x 1010 - 0.19
281 0.139 x 1010 55.616 x 1010 0
a1 = 0.095 K‘1

K1 2.23 J/gm.K

APPENDIX 4
Driving Force of Phase Transformation as a Function of
Temperature for Uncoated Nitinol Samples Heat Treated at
700°C for Six Hours, and Carbon Coated Nitinol Samples Heat

Treated at 700°C for Six Hours After Coating.

141

142

Table 1

Unconstrained Nitinol Sample - First Cooling Cycle

aTT 8M3 alT

T _e___ _e___dT AG

(K) T T T (J/gm)
299.5 8.63 x 1020 0 0
297.5 6.06 x 1020 8.63 1020 - 3.35
295.5 4.26 x 1020 14.69 1020 - 5.71
293.5 2.99 x 1020 18.95 1020 - 7.39
291.5 2.10 x 1020 21.94 1020 - 8.59
289.5 1.47 x 1020 24.04 1020 - 9.44
287.5 1.037 x 1020 25.51 1020 —10.07
285.5 0.729 x 1020 26.547 1020 -10.55
283.5 0.512 x 1020 27.276 1020 -10.9
281.5 0.360 x 1020 27.788 1020 -11.18
279.5 0.252 x 1020 28.148 1020 -11.39
277.5 0.177 x 1020 28.4 1020 -11.59
275.5 0.124 x 1020 28.577 1020 —11.72
273.5 0.0877 x 1020 28.701 x 1020 -11.87
271.5 0.0616 x 1020 28.7887 x 1020 -11.99
269.5 0.0433 x 1020 28.8503 x 1020 -12.11

AHT = 24.71 J/gm
a1 = 0.18 K"1

4.89 J/gm.K

SN
H
II

143

Table 2

Constrained Nitinol Sample - First Cooling Cycle

299.5
297.5
295.5
293.5
291.5
289.5
287.5
285.5
283.5
281.5
279.5
277.5
275.5
273.5
271.5
269.5
267.5
265.5
263.5
261.5
259.5

19.00
16.47
14.27
12.36
10.71
9.28
8.05
6.97
6.04
5.24
4.54
3.93
3.41
2.96
2.56
2.22
1.93
1.67
1.45
1.25
1.09

MS_(-::_dT
T
0

19.00 106
35.47 106
49.74 106
62.1 106
72.81 106
82.09 106
90.14 106
97.11 106
103.15 106
108.39 106
112.93 106
116.86 106
120.27 106
123.23 106
125.79 106
128.01 106
129.94 106
131.61 106
133.06 106
134.31 106

AG

(J/gm)

144

Table 2 (continued)

T e “T S ea‘T d'I’ AG
(K) T T T (J/gm)
257.5 0.94 x 106 135.4 x 106 -11.53
255.5 0.82 x 106 136.34 x 106 -11.66

AHT = 22.27 J/gm
31 = 0.075 K—1

K1

1.63 J/gm.K

145

Table 3

Unconstrained Nitinol Sample - First Heating Cycle

 

T fl; [Af e alT dT AG
(K) T T T (J/gm)
327 6 13 x 1018 0 -14 39
325 4 57 x 1018 6.13 x 1018 -11 16
323 3.4 x 1018 10.7 x 1018 - 8.73
321 2.53 x 1018 14.1 x 1018 - 6.89
319 1.89 x 1018 16.63 x 1018 - 5.48
317 1.41 x 1018 18.52 x 1018 — 4.30
315 1.05 x 1018 19.93 x 1018 - 3.54
313 0.78 x 1018 20.98 x 1018 - 2.88
311 0.58 x 1018 21.76 x 1018 - 2.32
309 0.436 x 1018 22.34 x 1018 - 1.88
307 0.325 x 1018 22.776 x 1018 - 1.5
305 0.242 x 1018 23.101 x 1018 - 1.19
303 0.181 x 1018 23.343 x 1018 - 0.91
301 0.134 x 1018 23.524 x 1018 - 0.65
299 0.0865 x 1018 23.658 x 1018 - 0.41
297 0.075 x 1018 23.73 x 1018 - 0.18
295 0.056 x 1018 23.808 x 1018 0

AHT = 24.92 J/gm
a1 = 0.15 K"1
K1 = 4.29 J/gm.K

146

Table 4

Constrained Nitinol Sample - First Heating Cycle

T __§_fjf IAf a‘T dT AG
(K) T T T (J/gm)
327 26.69 x 106 0 -13.44
325 23.35 x 106 26.69 x 106 -11.92
323 20.42 x 106 50.04 x 106 -10.59
321 17.86 x 106 70.46 x 106 - 9.45
319 15.63 x 106 88.32 x 106 - 8.41
317 13.67 x 106 103.95 x 106 - 7.47
315 11.96 x 106 117.62 x 106 — 6.51
313 10.46 x 106 129.58 x 106 — 5.92
311 9.15 x 106 140.04 x 106 - 5.27
309 8.01 x 106 149.19 x 106 - 4.67
307 7.01 x 106 157.2 x 106 — 4.13
305 6.13 x 106 164.21 x 106 - 3.65
303 5.36 x 106 170.34 x 106 - 3.2
301 4.69 x 106 175.7 x 106 - 2.8
299 4.11 x 106 180.39 x 106 - 2.51
297 3.59 x 106 184.5 x 106 - 2.09
295 3.15 x 106 188.09 x 106 - 1.77
293 2.75 x 106 191.24 x 106 - 1.47
291 2.41 x 106 193.99 x 106 - 1.19
289 2.11 x 106 196.4 x 106 — 0.92
287 1.84 x 106 198.57 x 106 — 0.67

285 1.61 x 106 200.35 x 106 - 0.44

147

Table 4 (continued)

 

 

T ealT JAf ea1T dT AG

(K) T T T (J/gm)

283 1.41 x 106 201.96 x 106 — 0.22

281 1.24 x 106 203.37 x 106 0
AHT = 22.27 J/gm

1.63 J/gm.K

79
H
II

10.

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The surgical procedure was summarized from:
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