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| Citation |
- Permanent Link:
- https://ufdc.ufl.edu/UFE0000711/00001
Material Information
- Title:
- Understanding microindentation in bone
- Creator:
- Johnson, Wesley M. ( Dissertant )
Rapoff, Andrew J. ( Thesis advisor )
Haftka, Raphael ( Reviewer )
Mecholosky, John ( Reviewer )
Critescu, Nicolae ( Reviewer )
Walsh, Edward ( Reviewer )
- Place of Publication:
- Gainesville, Fla.
- Publisher:
- University of Florida
- Publication Date:
- 2003
- Copyright Date:
- 2003
- Language:
- English
- Physical Description:
- xiv, 111 p.
Subjects
- Subjects / Keywords:
- Average linear density ( jstor )
Bones ( jstor )
Cattle ( jstor )
Hardness ( jstor )
Materials recovery ( jstor )
Microhardness ( jstor )
Moduli of elasticity ( jstor )
Monkeys ( jstor )
Teeth ( jstor )
Tooth enamel ( jstor )
Biomedical Engineering thesis,Ph.D ( local )
Dissertations, Academic -- UF -- Biomedical Engineering ( local )
Notes
- Abstract:
- The objective of my research was to improve understanding of microindentation in bone. Pursuit of that objective required that I: investigate the capability and limitations of a microindentation tool; investigate the tool effect on the bone surface; and apply the tool to derive hardness and elastic moduli of bone using the elastic recovery method (ERM). Microindentation hardness results were found to be sensitive to selection of applied mass on the tool. The previous value of minimum applied mass for bone (0.05 kg) was found to be too low and was replaced with a new value (0.1 kg). Observation of the post indentation affected region on the bone surface found differential elastic recovery between wet-indented and dry-indented specimens. Using a simple series spring model, an estimate of the wet-indented recovered material elastic modulus resulted in a value of about 1 GPa. Additionally, there was no observed pile-up at the indentation edges. The ERM, for deriving elastic modulus, was adapted from the materials' community for its first use in bone. It was applied, with a coordinate transformation process, to map elastic moduli and principal material direction along the mediolateral midline of a natural hole (foramen) in bone. The ERM based process detected the cortical to trabecular bone transition zone in the specimen. ERM based longitudinal elastic modulus results, over the initial distance from the foramen edge, compared favorably with correlation method (CM) derived elastic modulus map.
- Subject:
- elastic, foramen, fracture, microindentation, nutrient, recovery, toughness
- General Note:
- Title from title page of source document.
- General Note:
- Includes vita.
- Thesis:
- Thesis (Ph. D.)--University of Florida, 2003.
- Bibliography:
- Includes bibliographical references.
- General Note:
- Text (Electronic thesis) in PDF format.
Record Information
- Source Institution:
- University of Florida
- Holding Location:
- University of Florida
- Rights Management:
- Copyright Johnson, Wesley M. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
- Embargo Date:
- 9/9/1999
- Resource Identifier:
- 53177979 ( OCLC )
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UNDERSTANDING MICROINDENTATION IN BONE
By
WESLEY M. JOHNSON
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
2003
Copyright 2003
by
Wesley M. Johnson
This document is dedicated to my father, Fredrick Martin Johnson, the best natural
engineer I have ever known.
ACKNOWLEDGMENTS
I thank my wife Beth for the emotional and financial support she has so willingly
and consistently provided. Without her confidence and love I surely would not have
completed the rigorous course of study and the research captured in this dissertation.
I thank my faculty advisor and chair of my supervisory committee Dr. Andrew J.
Rapoff for his confidence, guidance, and support.
I thank each member of my supervisory committee for their willing and freely
given assistance: Dr. Raphael Haftka, Dr. John Mecholsky Jr., Dr. Nicolae Critescu, and
Dr. Edward Walsh.
Over the past 5 years my fellow students have been very helpful in my
understanding of difficult course subject material and acting as sounding boards during
considerations for the research detailed herein. Specifically I thank Jorge Zapata and
Barbara Garita for their assistance and friendship. I thank Mr. Matt Olszta for his
assistance in SEM imaging.
I am also grateful for the support provided by the following organizations:
Florida Foundation for Spinal Research and Disorders
Medtronic Sofamor Danek
Aero Chem Inc.
University of Florida Department of Mechanical and Aerospace Engineering
"When you can measure what you are speaking about, and express it in numbers, you
know something about it; but when you cannot express it in numbers, your knowledge is
of a meager and unsatisfactory kind; it may be the beginning of knowledge, but you have
scarcely, in your thoughts, advanced to the stage of science."
William Thompson, Lord Kelvin. Popular Lectures andAddresses, 1891-1894
TABLE OF CONTENTS
page
A C K N O W L E D G M E N T S ................................................................................................. iv
LIST OF TABLES ............................................................................. x
LIST OF FIGURES ......... ......................... ...... ........ ............ xi
A B S T R A C T .............................................. ..........................................x iii
CHAPTER
1 IN TR OD U CTION ............................................... .. ......................... ..
H isto ry ...................................................................2
M otivation............................................................... 3
M material Property Standards ........................................................ ............... 4
S c a le s .................................................................................................. . 4
S ig n ifican ce ....................................................... 5
2 MICROINDENTATIOIN IN BONE: HARDNESS VARIATION WITH FIVE
INDEPENDENT VARIABLES ...........................................................................9
Introduction..................................... ........................... ..... ..... ........ 9
A applied M ass ................................................................... ............... 11
D w ell T im e ............................................................... ...... .. ............ 11
R evidence Tim e .................................... ................ ................. 12
Time between Indentation and Measurement.....................................................12
Distance between Indentation and Pores..........................................................12
M materials and M methods ....................................................................... .................. 12
Specim ens and Preparation............................................ ........... ............... 12
Bovine m etacarpus ................................................... ............ ..13
B ov in e fem u r.....................................................13
M o n k ey to o th ......................................................................................... 14
Microindenter ................ .... ......... .............14
Indentation Procedures .............. ......... .........................15
Hardness variation with applied mass .......... .................................... 15
H ardness variation w ith dw ell tim e.......................................... ........... ...... 16
Interaction effect of applied mass and dwell time.....................................16
Hardness variation with residence time .............. ........................ .......... 16
Hardness variation with time between indentation and measurement .........17
Hardness variation with distance between indentation and pores ..............17
Intra-observer effect .......... .. ............... .1.. ..... ................ ... 18
Results ................. ..................................................18
Hardness Variation with Applied M ass.................................. ....................... 18
Hardness Variation with Dwell Time................................. ............. .............19
Applied M ass and Dwell Time Interaction ................................ ............... 19
Hardness Variation with Residence Tim e ..................................... .................... 19
Hardness Variation with Time between Indentation and Measurement .............19
Hardness Variation with Distance between Indentation and Pores....... ........ 19
Intra-ob server Effect ................................. .......... ...... .................... ... 20
Discussion ..................................... ........... .......................... 20
Hardness Variation with Applied M ass.................................... ............... 20
H ardness V ariation w ith D w ell Tim e ............................. ................................ 21
Applied M ass and Dwell Time Interaction ................................ ............... 21
Hardness Variation with Residence Time ................................ .....................22
Hardness Variation with Time between Indentation and Measurement .............22
Hardness Variation with Distance between Indentation and Pores ............... 22
Intra-ob server Effect ......... ........ ...................... .......... ...... .................... ... 23
3 INVESTIGATION OF THE MICROINDENTATION RESIDUAL
IM PR E SSIO N IN B O N E ........................................ ............................................30
In tro du ctio n .................................................................................. 3 0
Indentation Physical M odels................................................ ............ ............... 31
M materials and M methods ....................................................................... ..................32
M icroin d enter ...............................................................32
S p ecim en ....................................................... 3 2
P o lish in g ............. ................................................................................3 2
A d d itio n al cu ttin g ................................................................................... 3 3
Preparation for SEM ...................................................................33
D ry-indented specim en ........................................................ 33
Wet-indented specimen ............... ... ............ ......... .................. 34
Atomic force microscopy specimen .......... ...................................... ....34
Fracture toughness confirmation specimen ................................................35
Evaluation Procedures ........... .... .. .......... .. .... ...... .... ...... .......... ........36
Scanning electron microscope ...................... .........36
E plastic m odulus .................................. ...............................................36
F fracture toughness...................................................................... 38
R results ......... .................. ...................................... ..........39
C racks ................................. ........ ...... .................. ....39
C ro ss-sectio n ........................................................................................... 4 0
D iscu ssio n ......... .. ....... ....... .............. .......... ........................................ 4 1
Fracture T toughness .................................................... ................. ......... ... 4 1
Recovered Material Elastic Modulus ...................................................... 41
P ile-u p .......................................... .......... .......... .. 4 2
4 INVESTIGATION OF THE ELASTIC RECOVERY METHOD FOR
DERIVING ELASTIC MODULUS OF BONE, DENTIN, AND ENAMEL........... 53
In tro d u ctio n ............. .. ............. ................. ................................ 5 3
H isto ry ........................................................................................................... 5 3
M o tiv atio n ..................................................................................................... 5 5
M methods and M materials .............. ............... ..............................................................55
Adaptation of Elastic Recovery Method to Bone..........................................56
Elastic Recovery M ethod Validation........................................ ............... 57
Specimen Preparation and Indentation Procedures..........................................58
Glass ................ ......... ................... 58
P le x ig la s ................................................................................................. 5 9
Bovine femur.............................................59
Sensitivity evaluation of ERM equation ............ ................ 62
Application of ERM to Bone, Dentin, and Enamel............... ................ 62
Specimen Preparation and Indentation Procedures ..........................................62
B o v in e M C .................................................. ................ 6 3
Correlation m ethod (CM )...................................... .......................... ....... 63
Bovine foramen elastic modulus distribution.............................................63
M onkey teeth ................................................................... ............... 66
R e su lts .................. ...................................... ................. ................ 6 7
Elastic Recovery Method Validation........................................ 68
Elastic Recovery Method Equation Sensitivity .............................................68
Application of the Elastic Recovery Method ............. ..... .................69
Elastic C onstants D distribution ........................................ ......... ............... 69
M onkey T eeth .....................................................70
D discussion ............... ................... .....................................7 1
Elastic Recovery M ethod Validation........................................ ............... 71
Elastic Recovery M ethod Equation Sensitivity ......... ................................... 72
Application of the Elastic Recovery Method ...................................... 73
Elastic Constant and Principal Material Direction Distribution........................73
M onkey T eeth .....................................................74
D entin ..................................................................................................74
E n a m e l .................................................................. ................................7 5
5 FU TU RE RE SEAR CH ......................................................................... 100
B ovine Plexiform B one .................................................. .............................. 100
F racture T oughness.......... .............................................................. ......... ........ 100
M icroindentation Affected Region.......................................... ......... ... ............... 101
Elastic Recovery Method Constants...... ..................... ...............101
Principal Material Direction Mapping..... .................... ...............102
APPENDIX MODULUS ESTIMATE CALCULATION................ ................103
viii
L IST O F R E FE R E N C E S ......................................................................... ................... 108
BIOGRAPH ICAL SKETCH ............................................................. ............... .111
LIST OF TABLES
Table page
3-1 Values for dry-indented and wet-indented cross sections ......................................44
4-1 Values for ERM equation constants .................................................................77
4-2 Sensitivity of the ERM equation .................................................................. ...... 78
4-3 ERM elastic modulus validation results.............. ........ .............. 79
4-4 ERM derived elastic modulus results................................. ............... 80
4-5 Comparison of edge detection and optical microscopy. ......................................81
4-6 Comparison of ERM derived elastic modulus results............... ................ 82
4-7 Elastic constants descriptive statistics................................................................... 83
LIST OF FIGURES
Figure pge
1-1 Schematic representation of bone hierarchy ...................................................6
1-2 M acro and m icro structures in osteonal bone ........................................ ...............7
1-3 Schematic of monkey tooth cross section..... .......... ...................................... 8
2-1 Microindentation machine, Mitutoyo model HM-112................ ..................24
2-2 Typical microindentation residual impressions on bone ....................................25
2-3 A) Hardness variation with applied test mass in bone. B) Hardness
variation with applied test mass in monkey tooth dentin............ ...............26
2-5 Hardness variation with residence time ...................................... ............... 28
2-6 H ardness variation w ith distance ........................................ ........ ............... 29
3-1 Typical schematic accompanying indentation models .......................................45
3-2 Typical indentation set for SEM investigation ............................................... 46
3-3 Bovine m etacarpus ........... ... .................................. .... ...... .. .......... 47
3-4 A) Knoop residual impression array line B) Cross section of Knoop
m icroindentation short diagonal ........................................ ........................ 48
3-5 A) Knoop residual impression area. B) Cross section of the indentation.............49
3-6 Linear crack at the apex of the indentation residual impression............................50
3-7 Typical Knoop indentations in the fracture toughness confirmation specimen.....51
3-8 Plot of applied mass (Load) with crack length ............................................... 52
4-1 Bovine femur longitudinal specimen. ........................................ ............... 84
4-2 Bovine femur transverse specimen .............................................. .................. 85
4-4 Normalized sensitivity plots of the ERM equation variables ...............................87
4-5 Bovine M C distal dorsal specim en ............................................. ............... 88
4-6 A) Knoop indentation sets B) Schematic of indentation short diagonal ..............89
4-7 Vickers microindentations in bovine right MC distal dorsal foramen midline .....90
4-8 M onkey right side first molar and mandible............................... ............... 91
4-9 A) Buccolingual partial cross section of left side first monkey molar. B)
Buccolingual partial cross section of right side first monkey molar. ....................92
4-10 Left image Indentation pattern on posterior aspect of right first molar.
Right image Well-defined indentations in posterior aspect of right first
m o lar. ........................................................... ................ 9 3
4-11 Elastic Recovery M ethod validation plot................................... ..................94
4-12 ERM based derived elastic constants variation with distance ............................95
4-13 Coordinate rotation angle variation with distance ...........................................96
4-14 Correlation Method derived elastic modulus variation with distance ...................97
4-15 ERM derived longitudinal elastic modulus and CM derived elastic modulus.......98
4-16 Schematic of tooth enamel prism tube orientation .............................................99
Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
UNDERSTANDING MICROINDENTATION IN BONE
By
Wesley M. Johnson
May, 2003
Chair: Andrew J. Rapoff
Department: Biomedical Engineering
The objective of my research was to improve understanding of microindentation in
bone. Pursuit of that objective required that I: investigate the capability and limitations
of a microindentation tool; investigate the tool effect on the bone surface; and apply the
tool to derive hardness and elastic moduli of bone using the elastic recovery method
(ERM).
Microindentation hardness results were found to be sensitive to selection of applied
mass on the tool. The previous value of minimum applied mass for bone (0.05 kg) was
found to be too low and was replaced with a new value (0.1 kg).
Observation of the post indentation affected region on the bone surface found
differential elastic recovery between wet-indented and dry-indented specimens. Using a
simple series spring model, an estimate of the wet-indented recovered material elastic
modulus resulted in a value of about 1 GPa. Additionally, an estimate was made of bone
fracture toughness using a novel method through scanning electron microscopy.
The ERM, for deriving elastic modulus, was adapted from the materials'
community for its first use in bone. It was applied, with a coordinate transformation
process, to map elastic moduli and principal material direction along the mediolateral
midline of a natural hole foramenn) in bone. The ERM based process detected the
cortical to trabecular bone transition zone in the specimen. ERM based longitudinal
elastic modulus results, over the initial distance from the foramen edge, compared
favorably with correlation method (CM) derived elastic modulus map.
CHAPTER 1
INTRODUCTION
Designers of prostheses interfaced to bone rely on fundamental findings from bone
research. Information about bone mechanical properties and their temporal and spatial
variations govern prostheses material and fixation selection [McKoy 2000, pg 440]. One
important aspect of bone research is the effect of the prostheses on bone.
Microindentation is an experimental tool for interrogating material properties on the
surface of bone where it contacts a prostheses.
The objective of my work was to investigate microindentation as a tool to derive
material properties of bone. During the investigation I explored a variety of materials in
addition to bone. Investigation of the other materials was done to assess the accuracy,
precision and usefulness of the elastic recovery method for derivation of elastic modulus.
These materials were: glass; Plexiglas; and the dentin and enamel of monkey teeth.
Pursuit of my objective required investigation of the microindentation tool; the
microindentation tool effect on the bone; and microindentation techniques.
Microindentation is the action of forming an impression in a surface at the micro
(10-6 m) scale. That action uses a tool that applies a known load to a specimen through a
specific shaped point. The process leaves a residual impression in the material specimen.
Length dimensions of the residual microindentation impression in bone, dentin, and
enamel, about 20 to 200 [m, are measured through a microscope. The measurements are
used to derive specimen properties of hardness, elastic modulus, and fracture toughness.
Hardness is defined as resistance to penetration and is derived by dividing applied
load by the projected area of the residual impression. Hardness units are typically given
in kg/mm2. I have found typical values for bone to be about 45 kg/mm2. Elastic modulus
is the ratio of stress to strain in the linear region of the stress-strain curve. Elastic
modulus has units of Pascals, typically giga-Pascals (GPa) for bone. A typical value for
cortical bone is 20 GPa [Guo 2001, p. 10-7]. Fracture toughness is the resistance of a
brittle material to sudden failure. It can also be thought of as resistance to crack growth.
Fracture toughness is derived from length measurements of cracks associated with the
residual impression. The derivation uses the derived quantities of hardness and modulus
in empirical relationships. Fracture toughness units are typically given in MPa/m1/2. A
typical value for cortical bone is 2 MPa/m1/2 [Akkus et al. 2000].
History
Microindentation was first used in the 1920s [Amprino 1958]. Amprino [1958]
investigated bone hardness variation with applied microindentation load and found no
correlation. He also investigated hardness anisotropy and found no correlation between
the relative orientation of the indenter point and the grain of the specimen. Those
findings have been subsequently shown not to be accurate by Ramrakhiani et al. [1979],
Riches et al. [1997], and my work. Microindentation methods continued to be developed
and expanded.
During the 1970s and 1980s microindentation was used mostly to derive bone
hardness. In that period considerations of contact mechanics led to an indentation
method for measuring elastic modulus. Loubet et al. [1984] adapted Sneddon's [1965]
load and penetration flat ended cylindrical punch solution to the pyramidal Vickers
indenter point. Their treatment equated the Vickers projected contact area with the flat
punch area. The resulting equation describes the analytical relationship between load and
indenter penetration depth. The equation was differentiated with respect to penetration
depth and solved for reduced elastic modulus. That approach was a major step in
extending microindentation from hardness to elastic modulus measurement. I call the
method the load and displacement method (LDM).
In 1990 Currey et al. [1990] correlated microindentation hardness with elastic
modulus. Their method involved deriving hardness from a range of different bone types
from different species. They then performed macro uniaxial tension tests to derive elastic
modulus. Plotting hardness against elastic modulus, they found a correlation by linear
regression. I call this method the correlation method (CM).
Microindentation based derivation of elastic modulus, using only the residual
impression dimensions, has been mostly used in ceramics and polymer research [Lawn et
al. 1980, Amitay-Sadovsky and Wagner 1998]. The method has also been used in dental
[Meredith et al. 1996] and pharmaceutical research [Lum and Duncan-Hewitt 1996].
However, it had not been used in bone. The method uses the post indentation residual
impression dimensions and indenter point geometry. I describe the method in detail in
Chapter 4. I call that method the elastic recovery method (ERM).
Microindentation has been used to derive fracture toughness of ceramics and tooth
enamel [Lawn et al. 1980, Xu et al. 1998]. It also had not been used in bone.
Motivation
Hard biologic materials, like bone, dentin and tooth enamel, present challenges in
determination of their material properties. One challenge is no universal material
property standards exist for bone, dentin, or enamel. A second challenge is that biologic
material property derivations are performed at a variety of scales.
Material Property Standards
Material standards allow investigators to determine the accuracy and precision of
their results. Materials like ceramics, plastics, and crystals have standard values for their
material properties. Bone, dentin, and enamel on the other hand do not have such
standards. In determining whether a given set of bone hardness or elastic modulus results
are correct, reference must be made to published results from other researchers. Such a
situation is less than completely satisfying. However, an accepted set of hardness and
elastic modulus values for specific types of bone currently exists in available handbooks
[Huja 2000, p. 248; Guo 2001, p.10-7].
Handbooks also contain research results that are not accurate. Bone researchers
who rely on the incorrect information can report results that may not be reproducible.
Scales
Bone, dentin, and enamel are hierarchical structures (Figures 1-1, 1-2, 1-3). Scales
include: the macro scale of whole bones and teeth which is of several millimeters or
larger; the micro scale of osteons which is of hundredths of a millimeter; and the nano
scale of collagen fibers, fibrils, and mineral crystals of thousandths of a millimeter.
Selection of the scale for investigation is important because it is over that scale that
measurement results are averaged or homogenized. Microindentation homogenizes over
surface dimensions of about 200 |tm and indentation depth of about 6 |tm. I have shown
in Chapter 2 that the affected region around the indentation site in bone extends no more
than about 35 jtm from the edge of the residual impression. In specimens where the
spatial variations of bone microstructure is close to that of the residual impression
homogenization breaks down because the measured length reflects a single constituent.
Significance
The results of my research are significant because:
* I provide bone researchers who use microindentation, a new value for minimum
applied mass. The new value helps ensure reproducibility of results among
researchers.
* I provide bone researchers with new experimental evidence that bone does not pile
up at the edges of the indentation residual impression. This new evidence enhances
confidence that bone is a material that exhibits strain hardening behavior. It also
corrects the misinformation that bone exhibits pile-up as has been used in bone
research.
* I provide prostheses designers with new information about the material in the
indentation affected region. Specifically, I report an elastic modulus of about 1
GPa for bovine femur indentation recovered material. That value is more than a
factor of 10 less than the well-accepted average value of 16 GPa for bovine femur
[Guo 2001, p. 10-7].
* I provide bone researchers with new information on limitations and use of the ERM
for deriving elastic modulus. Specifically, I report that ERM derived elastic
modulus is not completely accurate for bone or dentin but is accurate for tooth
enamel, glass, and Plexiglas. I demonstrate that ERM can be used for relative
comparisons exploring bone, dentin, and enamel elastic anisotropy. I also
demonstrate use of the ERM, combined with edge detection image processing and a
coordinate transformation process, to map elastic moduli distribution and principal
material directions in the vicinity of a bone nutrient foramen.
* I report an average fracture toughness of 0.22 MPa/m2 0.03 (mean SD) for the
material in the indentation affected region on bone that has been processed for
scanning electron microscopy. The published mean value for unprocessed bone is
2.4 MPa/m2 0.7 (mean SD) [Akkus et al. 2000]. By determining the fracture
toughness of the material in the microindentation affected region, I have established
the foundation for future work on a more simple method of determining bone
fracture toughness. Such a method could save other researchers' resources.
Collagen
molecule
Cancellous bone
I Cullbr, 1
.-, .../ Collagen 7 ll
Lamella fiber i
Cor i,:n bone Bone
O(teon Haversiarn Cryqtals
canal
0.5 Jim
H 1 rn
10-500 pm 3-7 pm
Microstructure Nanostructure
Macrostructure Sub-microstructure Suh-nanosi ruirure
Figure 1-1 Schematic representation of bone hierarchy. Taken from: Rho JY, Kuhn-
Spearing L, Zioupos P. Mechanical properties and the hierarchical structure of
bone. Medical Engineering and Physics 1998. IPEM 1998
Osteon
(Haversian system)
I Circumferenthal -
lar-, :- vi.,-.
Iai-'.* ''i
I. I,. ,I., / '
i .a.
- 1 .. I
- ,.: l I, r.,. ...I ,'
, r, n. ,,rI I -I r .. 1,
,----. BI1oo vessel
Figure 1-2 Macro and micro structures in osteonal bone. Elaine N. Marieb. Human
Anatomy and Physiology. Benjamin/Cummings Science Publishing. 1998
[ ,' I,- ,, r
rods
dentin
tubules P
dentoenamel
S- junction
Figure 1-3 Schematic of monkey tooth cross section showing the macro and micro scale.
Tooth is approximately 2 cm in length. Dentine tubules are approximately 1
gm in diameter. Enamel tubes, approximately 5 gm diameter, begin at the
dentoenamel junction and end at the occlusal (biting) surface. E = enamel, D
= dentin, P = pulp cavity.
CHAPTER 2
MICROINDENTATION IN BONE: HARDNESS VARIATION WITH FIVE
INDEPENDENT VARIABLES
Introduction
The objective of the research described in this chapter was to investigate the
microindentation tool. Indentation at the micro scale is an often used and effective tool in
materials research [Amitay-Sadovsky and Wagner 1998, Lawn et al. 1980, Lum and
Duncan -Hewitt 1996, Marshall et al. 1982]. It is used to derive various material
properties including hardness, elastic modulus, and fracture toughness. More specifically
indentation has become a method of choice for deriving the hardness and elastic modulus
of bone and other hard tissue like tooth dentin and enamel [Currey et al. 1990, Meredith
1996, Xu 1998]. Bone hardness and elastic modulus are directly related to the
microstructure and composition of the material at the indentation site [Currey et al.
1990]. Bone is an anisotropic and inhomogeneous composite at the micro and nano
scale. The degree of anisotropy can vary and has been described as transversely isotropic
or orthotropic [Cowin 2001 p. 6-12 to 6-19] The constituents at the nano and micro
scales are hard calcium mineral crystals and a softer collagen matrix. While there are
observable macro, micro, and nano structures, estimation of material properties is far
from straightforward and requires a range of tools to elicit the bone properties at the
different scales.
The research reported in this chapter revisits microindentation as a method of
determining hardness. Hardness measurements are carried out with an indentation
machine (Figure 2-1). The fundamental process involves automatic placement of a
discretely selectable mass on the upper end of a pointed stylus. The point that contacts
the specimen can be spherical or pyramidal depending on the application. The mass is
applied to the specimen through the stylus for a predetermined duration (dwell time), then
automatically removed. The dimensions of the residual impression are then measured
and used to derive hardness at the indentation site. Customary units of hardness are mass
per unit projected area, typically given as kg/mm2
As part of my ongoing work with bovine bone, specifically the bovine metacarpus
(MC), I questioned the effect microindentation independent variables had on hardness
results. The question came up because I was concerned whether the current defacto
standard for applied mass [Huja et al. 2000 p. 252, Ramrakhiani et al. 1979, Riches et al.
1997] was appropriate for my fresh wet specimen. Ramrakhiani et al. [1979] used dry,
embalmed human bone.
In addition to hardness variation with applied mass, I chose to investigate hardness
variation with the following four microindentation independent variables: dwell time;
residence time on the instrument stage out of liquid; duration of time between indentation
and residual impression measurement; and distance between the indentation site and
pores. I also investigated the interaction effect on hardness of applied test mass and
dwell time. These two parameters are independently selectable on the microindentation
machine. Additionally, I performed an assessment of the intra-observer effect. Such an
assessment was needed to evaluate the variability and precision of my (observer) residual
impression dimension measurements.
Choice of appropriate values for the independent microindentation variables is of
importance in assuring reproducibility and measurement precision. Differences between
sets of measurements on the same specimen could be caused by time domain phenomena
such as creep and relaxation. Differences between sets of measurement on the same
specimen could also arise from the spatial domain due to pores. Testing machine setup,
calibration, and compliance (which can vary between indentation machines) is significant
at low applied mass values [Vander Voort and Lucas 1998]. Testing machine compliance
acts in series with the specimen compliance. If the machine compliance is relatively low
it can add to the compliance of the specimen producing a measurement error. In my case
these variables were not adjustable once the machine had been set up. Only those
variables over which I had control were chosen for investigation.
Applied Mass
Previous studies on bone showed no variation of hardness with applied load,
[Amprino 1958] yet a later study found a value of applied test mass (0.05 kg) below
which hardness measurements were not reliable [Ramrakhiani et al. 1979]. The later
value had acquired the status of a defacto standard through handbook reference [Huja et
al. 2000 p. 252] and use by other bone researchers [Riches et al. 1997].
Dwell Time
Due to the creep phenomenon, the duration of time the indenter point is applied to
the specimen, dwell time, could affect residual impression measurement results. Dwell
time of the microindentation machine used in my research is adjustable by the operator
between 5 and 99 seconds.
Residence Time
Because of my interest in wet specimens, the duration of time the specimen spends
out of the water-based liquid, or residence time on the microindenter stage, was
important. The duration of time out of the storage liquid could affect the residual
impression measurements because the specimen was drying out. Rho and Pharr [1999]
reported increased hardness with time out of liquid.
Time between Indentation and Measurement
Indentation site material relaxation, between the time the indentation impression is
made and when it is measured, could also affect the measurement of residual impression
dimensions. I was particularly concerned about the relaxation effect because my
specimens were wet. I thought that the collagen component of bone would relax more
wet than dry. Collagen behaves somewhat like a sponge, when wet it recovers more than
when dry.
Distance between Indentation and Pores
The distance between the indentation residual impression and nearby pores,
predominately Haversian and Volkmann's canals, could affect results because material
properties change spatially in the vicinity of pores.
Materials and Methods
Specimens and Preparation
The specimens described in this section were used for investigation of the effect on
hardness of microindentation independent variables. Specimens used were: a right
bovine metacarpus (MC); a right bovine femur; and a right first molar from a monkey
(Macacafascicularis). The array of specimens were available to me and presented a
range of hard biological material for assessment of their hardness variation with one or
more of my chosen microindentation independent variables. All procedures involving
animal tissue use were conducted under the approval and auspices of the Institutional
Animal Care and Use Committee.
Bovine metacarpus
One specimen from a previously fresh frozen bovine right MC was rough cut twice
with a 10" band saw (Delta Machinery; Jackson, TN) across the distal diaphysis to
produce a ring of bone approximately 30 mm in length. Additional fine cuts were made
(Low speed saw; Buehler; Lake Bluff, IL) longitudinally along the distal dorsal aspect.
The specimen was approximately 25 mm by 45 mm by 1 mm thick with the long
dimension parallel to the bone long axis. The length and width dimensions were dictated
by the polishing system capability. The specimen was polished after cutting, using a
semi-automated polishing system (Minimet 1000, Buehler, Lake Bluff, IL). Polishing
started with 6 |tm diamond slurry and finished with 0.05 |tm alumina and colloidal silica
suspension. After polishing a transverse cut was made to produce a specimen
approximately 25 mm by 10 mm by 1 mm thick. The bovine MC was supplied by the
University of Florida College of Veterinary Medicine from a donor of unknown age and
sex whose death was unrelated to this study.
Bovine femur
A specimen from a previously fresh frozen bovine right femur (Animal
Technologies Inc., Tyler Texas) was rough cut twice with a 10" band saw (Delta
Machinery; Jackson, TN) across the mid diaphysis to produce a ring of bone
approximately 30 mm in length. Subsequent longitudinal cuts were made (Low speed
saw; Buehler; Lake Bluff, IL) to produce a specimen approximately 25 mm by 25 mm by
1 mm thick. The specimen was polished in the same manner as the bovine MC specimen.
Monkey tooth
A tooth and accompanying mandible from a small monkey (Macacafascicularis)
were cut (Low speed saw; Buehler; Lake Bluff, IL) in the buccolingual plane on the right
side, between the premolar and the first molar. An additional cut was made on the
centerline of the first molar also in the buccolingual plane. The cuts produced a tooth
cross section specimen approximately 2 mm thick. After cutting the specimen was
manually polished using the same polishing sequence as the bovine specimens. The
monkey tooth specimen was only used for determination of hardness variation with
applied mass.
Microindenter
A microindenter (Model HM-112, Mitutoyo, Japan) fitted with a Vickers indenter
point was used for measuring: hardness variation with applied mass; hardness variation
with dwell time; and hardness variation with residence time out of solution on the bovine
metacarpal specimen. That indenter point was chosen because previous research by
others [Ramrakhiani et al. 1979] used the Vickers indenter point and its use provided a
basis for results comparison. A Knoop indenter point was chosen for all other
investigations of hardness variation with microindentation independent variables on the
bovine femur and monkey tooth specimens. I chose the Knoop indenter point because it
allows investigation of hardness [Riches et al. 1997] and elastic modulus anisotropy
[Rapoff et al. 2003].
The Vickers and Knoop indenter points are both four-sided pyramids. The
significant difference is that the Vickers point is a regular pyramid with equal diagonals
and the Knoop point has diagonals of two different lengths (Figure 2-2). The ratio of the
Knoop two different diagonals is 7.114 to 1 [Mitutoyo 1998]. Both indenter points
exhibit sensitivity to elastic anisotropy but the Knoop indenter point is much more
sensitive than the Vickers [Riches et al. 1997]. The increased sensitivity is due to the
ratio of diagonals and the corresponding apex angles. The long Knoop diagonal has an
acute angle at its ends while the short diagonal angles are obtuse. During indentation the
long diagonal does not change its length [Amitay-Sadovsky and Wagner 1998, Riester et
al. 2001] when the indenter point is removed from the specimen. However, the short
diagonal acts to spread or push the material away from the apex. That dimension does
change when the indenter point is removed. In fact the degree to which the residual
impression dimension departs from the actual point dimension can be used as a measure
of the indentation site material elastic modulus [Marshall et al. 1982, Amitay-Sadovsky
and Wagner 1998, Meredith et al. 1996, Lum and Duncan-Hewitt 1996].
Indentation Procedures
Hardness variation with applied mass
A series of five indentations was made on the wet bovine MC specimen for each of
five available masses (0.01 kg, 0.025 kg, 0.05 kg, 0.1 kg, 0.2 kg). A set of 3 indentations
was made in monkey tooth dentin at the same five available masses. The indentations in
the bovine MC were made with the Vickers indenter point while the indentations in
monkey dentin were made with the Knoop indenter point. An arbitrarily selected dwell
time of 10 s was used for the indentations. The interaction of applied mass and dwell
time was subsequently investigated and 10 s was found to be acceptable. I monitored the
time out of solution for each specimen to assure it did not exceed 30 minutes. I held the
time between indentation and residual impression measurement to less than 20 s for all
indentations. I also insured that each indentation was at least 100 [im from pores and
previous indentations.
Hardness variation with dwell time
One set of 5 indentations with the Vickers indenter point, at 5 dwell times (5 s, 10s,
15 s, 20 s, 30 s), was made in the bovine MC. An additional set of 5 indentations with
the Knoop indentation point each at 4 dwell times (5 s, 10 s, 15 s, 30 s) were also made in
bovine MC. The Knoop indenter point long diagonal was oriented parallel to the
specimen longitudinal direction. I compared the 5 sets of Vickers hardness with the
analysis of variation (ANOVA) procedure as well as the 4 sets of Knoop hardness results.
For all the indentation sets I used an indentation applied mass of 0.1 kg. I
monitored the time out of solution to assure it did not exceed 30 minutes. I held the time
between indentation and residual impression measurement to less than 20 s for all
indentations. I also insured that each indentation was at least 100 .im from pores and
previous indentations.
Interaction effect of applied mass and dwell time
A series of sixty indentations were made in the longitudinal aspect of bovine femur.
They were made with the Knoop indenter point short diagonal parallel to the bone
longitudinal direction. Applied masses of 0.01 kg, 0.05 kg, 0.1 kg, 0.2 kg, 0.3 kg and
dwell times of 5 s, 10 s, 20 s, 40 s were used. An ANOVA procedure was performed on
the resulting interaction data and then Scheffe's aposteriori test was preformed
(Statview, SAS Institute, Cary, NC).
Hardness variation with residence time
Seven sets of five indentations each were made in the longitudinal aspect of bovine
femur. I recorded the time each indentation was made over a period of 1.75 hours. I
made the 5 residual impression measurements approximately every 15 minutes during the
period. The indentations were made with the Vickers indenter point. I used an applied
mass of 0.1 kg and a dwell time of 10 s. I also assured that the distance between the
indentations and pores and other indentations was at least 100 am. I compared all 7 sets
with the ANOVA procedure.
After the residence time tests the specimen was allowed to equilibrate with the
laboratory environment for 47 hours. After 47 hours I made five additional Vickers
indentations and recorded derived hardness. The mean hardness of the previous 35
indentations was compared with the mean hardness of the 5 indentations performed after
47 hours using the ANOVA procedure.
Hardness variation with time between indentation and measurement
One indentation was made in bovine MC with the Knoop indenter point long
diagonal perpendicular to the specimen long axis. The specimen was maintained in a
bath surrounded by water solution. Based on results from hardness variation with applied
mass and hardness variation with dwell time, I used an applied mass of 0.1 kg and a
dwell time of 10 s. I also assured that the distance between the indentations and pores
and other indentations was at least 100 am.
I repeatedly measured the indentation starting 5 minutes after the indentation event
and repeated the measurement about every 15 minutes 3 additional times. The total
elapsed time between making the indentation and measuring it the last time was 57
minutes. I selected about 60 minutes because I did not expect measurements of
subsequent indentation sets to require more time.
Hardness variation with distance between indentation and pores
A series of 176 indentations were made on the bovine MC with the Knoop indenter
point short diagonal perpendicular to the bone longitudinal axis. The indentations were
made on the bovine bone in a regular pattern without regard to the location of pores. The
pattern consisted of 8 equally spaced rows of 22 equally spaced indentations each. The
spacing between the rows, measured between the center of adjacent indentations, was 240
lm. The spacing between indentations, measured between the center of neighboring
indentations, was 110 im.
The distance between the center of the indentation and the edge of the closest pore
was recorded for each indentation. The derived hardness and measured distance from the
indentations were plotted and analyzed with commercially available software (Excel,
Microsoft Corporation, Redmond, WA).
Intra-observer effect
One indentation was made in the longitudinal bovine femur specimen with the
Knoop indenter point long diagonal perpendicular to the specimen long axis. I measured
the indentation residual impression 5 times during a 5 minute period.
Results
Hardness Variation with Applied Mass
Hardness variation with applied mass and data variability was greatest at a low
value (0.01 kg) of applied mass for both specimens. I found hardness decreasing with
increasing applied mass. The hardness and applied mass curves for both specimens reach
a reasonably stable value at different applied masses (Figure 2-3). Range bars on the
figures were computed by taking the absolute value of the difference between the mean
and the greatest and least value.
An ANOVA for both specimen data sets resulted in statistical significance (p<0.05)
between hardness results at 0.01 kg and other results. However, I found no statistical
significance (p > 0.05) between derived hardness values at 0.05 kg and higher for bovine
bone and 0.025 kg and higher for the monkey dentin.
Hardness Variation with Dwell Time
Hardness variation with dwell time up to 30 seconds is not significant (ANOVA p
> 0.05) for either the Vickers or the Knoop indenter points (Figure 2-4).
Applied Mass and Dwell Time Interaction
There was a significant difference in the applied mass by dwell time interaction (p
< 0.05). Subsequent multiple comparison using Scheffe's aposteriori test showed that
the significance was limited to applied mass of 0.01. All other interactions were not
significant at the 0.05 level.
Hardness Variation with Residence Time
The duration of time the specimen was out of the solution was not significant
(Figure 2-5). One-way ANOVA results between the first data set taken at about 5
minutes after indentation and the last data set taken at about 1.6 hours later were not
significant (p>0.05).
The mean derived hardness of the specimen after 47 hours out of solution was 9%
greater than that measured within 1.75 hours. The mean derived hardness was 48.8
kg/mm2 with a standard deviation 1.5. One way ANOVA results were significant
between the 2 hour hardness results and the hardness at 47 hours (p<0.05).
Hardness Variation with Time between Indentation and Measurement
The mean derived hardness was 42.7 kg/mm2 with a standard deviation of 0.3.
Hardness Variation with Distance between Indentation and Pores
Microindentation distance between the center of the indentation and the edge of a
pore shows an effect at a distance of 73 irm and below (Figure 2-6). Two linear
regression lines were constructed to form a bi-linear plot. The lines reached the same
value at 73 tm. I fit a bi-linear function to the data. That function is:
0 < D < 73 pm HK = 0.15D +28.4; D > 73pm :HK = 39.5, where D = distance between the
center of the subject indentation and the edge of a pore expressed in rim; HK = Knoop
hardness expressed in kg/mm2.
Intra-observer Effect
The hardness mean was 51.5 kg/mm2 with a standard deviation of 0.5.
Discussion
Hardness Variation with Applied Mass
My results had some similarity to previous work by Ramrakhiani et al. [1979]
although my results were markedly different. The similarity was that the curves leveled
off at intermediate loads (Figure 2.3 A). The difference was that the previous work
reported increasing hardness with applied mass while I report decreasing hardness with
increasing applied mass. The other most striking observation was that one set of
Ramrakhiani et al. [1979] results did not support their own conclusion (Figure 2-3 A).
Inclusion of that data would have suggested a minimum applied mass value above about
0.7 kg. The excluded data was from a non silver plated specimen. Their conclusion was
based on only silver plated specimens.
For bovine MC hardness results were not significantly different at applied mass of
about 0.05 kg and above. The hardness results for the monkey tooth dentin were not
significantly different at applied mass of about 0.025 kg and above. Those results
suggests that for my Mitutoyo microindenter the applied mass values for bovine bone
could be as low as 0.05 kg for bovine and 0.025 kg for monkey dentin. However, taking
Ramrakhiani et al. [1979] data into consideration a higher minimum applied mass seems
appropriate. Hypothetically, if I used a minimum applied mass of 0.05 kg for indentation
of wet bovine bone, Ramrakhiani and colleagues would not be able to reproduce the test.
An additional consideration is the size of the indentation residual impression for
measurement. One of the advantages of microindentation is the ability to interrogate
small regions. The residual impression also needs to be large enough to measure with
precision. At low applied mass (0.01 kg) the long diagonal in a Knoop residual
impression is about 50 am. At an applied mass of 0.05 kg the residual impression long
diagonal is about 140 [am. While at an intermediate applied mass of 0.1 kg, the long
diagonal is about 200 am. Applied mass selection is governed by: the size of the region
of interest; the size of the residual impression; and the variation of hardness with applied
mass.
I conclude that a minimum applied mass of 0.1 kg is appropriate for bovine bone in
order to assure reproducible results among different microindentation machines.
Furthermore, noting the difference in hardness results between bovine specimen and the
monkey dentin I have also concluded that a hardness variation with applied mass study be
performed for each new material being tested.
Hardness Variation with Dwell Time
Dwell time from 5 s up to a limit of 60 s does not have statistical significance. I
have adopted 10 s as my typical dwell time in my subsequent research.
Applied Mass and Dwell Time Interaction
Significant interaction between applied mass and dwell time was limited to applied
mass of 0.01 kg. Results from the hardness variation with applied mass suggested that
use of applied mass of 0.01 kg is not appropriate. The interaction results confirm that
finding.
Based on the interaction result I chose not to investigate interactions between the
other microindentation variables. The only variability in any of the microindentation
independent variables is in derived hardness variation with applied mass. As long as the
minimum applied is greater than 0.05 kg for bone and 0.025 kg for dentin, there can be
little interaction between variables.
Hardness Variation with Residence Time
Derived hardness values did not significantly change with residence time out of
solution up to 1.75 hours. That result provided confidence that handling specimens out of
the water solution could be done for periods up to 1.75 hours. The result is important
because microindentation methods, such as the ERM for deriving elastic modulus,
require time to process. Subsequent to the finding I have adopted a maximum time of 30
minutes out of water solution for similar bone specimens in my subsequent work.
A 9 % increase in hardness values after 47 hours was similar to values obtained by
Rho and Pharr [1999]. They used nanoindentation on bovine femur and reported results
on a much finer scale than I used. They reported a 12.2 % hardness increase for
interstitial lamellae and 17.6 % increase for osteonal lamellae. Their specimen had been
dried for 14 days while mine was dried for 2 days.
Hardness Variation with Time between Indentation and Measurement
Because there was no significant difference in derived hardness with the time
between when the indentation was made and the long diagonal was measured, up to 30
minutes, I have arbitrarily chosen 10 minutes as a standard.
Hardness Variation with Distance between Indentation and Pores
Distance between the center of the subject indentation residual impression and the
edge of pores is significant with an effect at distances closer than about 70 nm. In my
subsequent microindentation work I have adopted the value of 100 [m between the
indentation center point and the closest pore edge or any neighboring indentation edge.
23
Intra-observer Effect
The results provided confidence in my ability to make repeated measurements with
precision.
eyepiece
specimen
stage
mass
selection
knob
Figure 2-1 Microindentation machine, Mitutoyo model HM-112.
,.
'i I
,.1 a>
I *
EEi" T Er
70.. i .Ip
I;*" ,i|
Pal ..-
Figure 2-2 Typical microindentation residual
Knoop on right).
S .100 pLm
impressions on bone (Vickers on left,
0.05 0.1
Mass (kg)
0.15 0.2
40
Mass (kg)
Figure 2-3 A) Hardness variation with applied test mass in bone. Shown are
Ramrakhiani et al.[1979] data from dry embalmed human rib (plotted from
their tabular data), solid line (triangles); and my data from wet bovine
metacarpus, dashed line (open circles). Range bars are also shown for my
data. A Vickers indenter point was used for all indentations. B) Hardness
variation with applied test mass in monkey tooth dentin. A Knoop indenter
point was used for the microindentations.
140
S.< ----- S- G ..... ........ (I
60
40
20
0
Dwell time (s)
40
S20
Dwell time (s)
Figure 2-4 A) Hardness variation with dwell time in wet bovine metacarpus showing
average values and range of results, Knoop microindentation point. B)
Hardness variation with dwell time in wet bovine metacarpus showing
average values and range of results, Vickers microindentation point.
60
" 40
-
-A
S20
0
Time (hrs)
Figure 2-5 Hardness variation with residence time (time out of solution) for bovine
metacarpus, Vickers microindentation point. Shown are the average values
and ranges for each data set.
+ +f O^ + t
60
0 40
S20
0
8
8%
0 0
0
oo
0 0
OK
}t
%0
0 0
) 100
Distance (fLm)
Figure 2-6 Hardness variation with distance measured between the center of the
microindentation and the edge of pores on wet bovine metacarpus. Bi-linear
plot lines have a common value at 73 am. Bi-linear function described by the
dotted lines is: 0 73mm :HK = 39.5
CHAPTER 3
INVESTIGATION OF THE MICROINDENTATION RESIDUAL IMPRESSION IN
BONE
Introduction
The objective of the work described in this chapter was to investigate the
interaction between the microindentation tool and the material bone. The specific aim of
this research was to describe the cross-sectional profile of the microindentation residual
impression both physically and materially. I used scanning electron microscopy (SEM)
and atomic force microscopy (AFM) images from both wet -indented and dry-indented
bone specimens in the work.
I used length and angle measurements from wet-indented microindentation residual
impression cross sections, from the SEM images, to model and derive elastic modulus of
the material in the residual impression. The value was lower than published values for
bone. I also used measurements of residual impression apex crack length, from the SEM
images, to derive a fracture toughness value of the vacuum dried bone. The value was
lower than that reported by other researchers for wet bone. I used AFM to search for
cracks in wet and dry bone that had not been prepared for and subjected to SEM. I found
no cracks.
From the SEM images I observed no material pile up in the residual impression
cross sections. Absence of pile up is an expected behavior for brittle material as
described by Marx and Balke [1997] and Cheng and Cheng [1998]. Previous
investigations by Ramrakhiani et al. [1979] reported pile up in dry embalmed human
bone that could not have existed. That report continues to be used in bone research
[Riches et al. 1997].
The work described in this chapter was motivated by my desire to experimentally
determine whether the physical descriptions of indentation models accurately reflect the
residual impression in bone. I was also motivated by the desire to provide material
property information to other bone researchers and prostheses designers.
Indentation Physical Models
Physical models of the residual impressions of micro and nano indentations in
ceramics, metals, and polymers have been developed. Researchers describing these
models typically include a schematic (Figure 3-1) of the indentation cross section [Cheng
and Cheng 1998; Dorner and Nix 1986; Marx and Balke 1997; Oliver and Pharr 1992].
In the schematic a residual impression is shown with an apex angle larger than that of the
indenter tip. The schematic may include a zone of pile-up at the residual impression
edge. In their schematic Marx and Balke [1997] depict a zone of pile-up for ductile
material and a zone of no pile-up for brittle material; Cheng and Cheng [1998] depict a
zone of material pile-up at the edge of the impression; while Dorner and Nix [1986] and
Oliver and Pharr [1992] do not depict pile-up.
In such schematics, and the model discussions that accompany them, the indenter is
depicted with a more acute angle than the residual impression. Such a model assumes the
area of contact between the indenter point and the specimen becomes less as the indenter
point is withdrawn. The contact area diminishes from initial full contact to only the very
tip during unloading.
Materials and Methods
Microindenter
A microindenter (Model HM-112, Mitutoyo Corporation, Japan) fitted with a
Knoop indenter point was used for all indentations. The Knoop indenter point was
chosen because it allows investigation of hardness and elastic anisotropy [Riches et al.
1997, Riester et al. 2000] and I used it in my other investigations. The Knoop indenter
point is a four sided pyramid with a long diagonal and a short diagonal. The aspect ratio
of diagonals is 7.114 [Mitutoyo 1998]. When an indentation residual impression is
observed it is an inverted pyramid with 2 diagonals one longer than the other (Figure 3-
2).
Specimen
One bovine right metacarpus (MC) was obtained from the University of Florida
College of Veterinary Medicine from a donor of unknown age and sex whose death was
unrelated to this study. After 2 transverse cuts with a 10 inch band saw (Delta
Machinery, Jackson, MS), the bone was longitudinally sectioned (Isomet Low Speed
Saw, Buehler, Lake Bluff, IL) from the distal dorsal aspect to produce a 1 mm thick by
25 mm wide by 45 mm long longitudinal slab (Figure 3-3). The specimen size was
controlled by the polishing system capabilities.
All procedures involving animal tissue use were approved by the Institutional
Animal Care and Use Committee.
Polishing
The most periosteal surface of the specimen slab, which was about 2 mm below the
periosteal surface, was polished in a progressive manner beginning with 6[tm diamond
slurry and final polish with 0.05 |tm alumina suspension (Minimet 1000, Buehler, Lake
Bluff, IL).
Additional cutting
Additional low speed saw cuts were made in the most proximal region of the
specimen slab. The cuts produced 2 pieces approximately one millimeter thick by 1 mm
wide by 25 mm long. The specimens were dried in equilibrium with the laboratory
environment and indented with the Knoop indenter short diagonal parallel to the bone
longitudinal axis in an ordered array (Figure 3-2 A). I used an applied mass of 0.1 kg and
dwell time of 10 s.
A wet specimen, taken from the same bone region, was cut with a low speed saw to
produce a specimen approximately 5 mm square by 1 mm thick. The specimen was
indented with the Knoop indenter short diagonal perpendicular to the bone longitudinal
axis in ordered arrays (Figure 3-2 B). I used an applied mass of 0.1 kg applied mass and
10 s dwell time.
Ordered indentation arrays were used because I did not have precise control over
subsequent cutting to obtain indentation short diagonal cross sections.
Preparation for SEM
Dry-indented specimen
In order to expose the cross-section of the residual impression, in a plane parallel to
the short Knoop indentation axis, each specimen piece was further divided to produce a
total of four pieces. One piece was manually fractured and the other sectioned with a low
speed saw. The 4 specimens were imaged in an optical microscope and two of the pieces
containing observable residual impressions were selected. The two selected specimens
were vacuum sputter coated with gold and imaged with SEM (JEOL 6400, Japan) using
15 kV excitation. Only the fractured specimen had a residual impression with an
unobstructed view of the cross-section at the mid point of the long diagonal (Figure 3-4).
That indentation was used in subsequent evaluations. The sectioned specimen residual
impression cross-sections were not clearly observable due to cutting debris on the
specimen edge. Additionally, the specimen had been sectioned with the indented face
surface perpendicular to the blade and in the same direction as the blade rotation. This
arrangement caused the bone material to rise up and obscure the indentation cross-
section. Sectioning of the subsequent wet-indented specimen was performed differently.
Wet-indented specimen
After indentation the specimen was sectioned with a low speed saw into 2 pieces to
expose the residual impression cross sections. The sectioning was done with the indented
surface facing the low speed saw blade. This arrangement was to ensure that the low
speed saw blade did not upset the bone material as it had done when sectioning the dry-
indented specimen.
After sectioning the cut planes were lightly polished by manually drawing them
across a dry polishing cloth (Texmet 1000, Buehler, Lake Park, IL) to remove cutting
debris. Following Zysset et al. [1999], the specimens were stored in a solution of 0.5-
mg/ml gentamicin sulfate in tap water at 20C when not undergoing indentation or imaging
to retard collagen biological degradation. Both pieces were vacuum sputter coated with
gold and imaged with SEM.
Atomic force microscopy specimen
Following discovery of indentation apex cracks in specimens previously indented
both wet and dry, an additional specimen, approximately 4 mm square by 1 mm thick,
was prepared. The specimen preparation was the same as previous specimens except it
was not prepared for SEM imaging. There was no vacuum gold sputter coating nor
bombardment by electrons in the SEM chamber. The specimen was indented at two
different times, once while wet and then again after 14 days drying time in equilibrium
with laboratory environment. A set of 5 indentations was made at a range of applied
mass (0.1 kg to 1.0 kg), with the Knoop indentation point short diagonal perpendicular to
the bone longitudinal axis. Another set of 5 indentations was made in the same specimen
after 14 days. The Knoop indenter point short diagonal was oriented parallel to the bone
longitudinal axis. Immediately post indentation, for both wet-indented and dry-indented
cases, the specimen was imaged with an optical microscope (BX-60; Olympus; Melville,
NY) and with an atomic force microscope (AFM) (Nanoscope III; Hysitron; Minneapolis,
MN).
Fracture toughness confirmation specimen
Fracture toughness of the bone subjected to SEM preparation and imaging was
derived using indentation apex crack length measurements from 3 wet-indented residual
impressions. The 3 indentations had been made at the same applied mass. In order to
determine whether the indentation apex cracks were artifacts of the SEM preparation and
imaging process or were related to the applied mass, an additional wet specimen was
prepared. The specimen was prepared in a manner as close to the original SEM wet-
indented specimen as possible.
The specimen was cut from the same region of the bovine MC specimen as the
original wet-indented SEM specimen. A Knoop indenter point was used with the short
diagonal perpendicular to the bone long axis. The specimen was indented with a range of
indentation masses (0.05 kg, 0.1 kg, 0.2 kg, 0.3 kg, 1.0 kg). Five indentations were made
at each mass level. The specimen was prepared for and imaged using the same
equipment as the original SEM specimens.
Evaluation Procedures
Scanning electron microscope
Optical evaluation of the SEM images revealed that 3 of the wet-indented specimen
cross sections were clearly observable at the midpoint of the long diagonal. One typical
cross section is shown in Figure 3-5. The average length, width, and depth of the 3
indentations were used in subsequent evaluations. Only one of the dry-indented cross
sections was measurable (Figure 3-4).
Elastic modulus
The difference in residual impression side-wall angles between the wet-indented
and dry-indented cross sections suggested that an estimate of wet recovered material
elastic properties could be made. The difference between the wet and dry indentation
depths could be due to the material recovering more when wet than dry. More recovery
in the wet-indented specimen suggested to me that the recovered material (that material
between the maximum indentation depth and the final residual indentation depth) has a
different elastic modulus than the bone outside the indentation affected region.
Hengsberger et al. [2002] suggested that damaged bone does not recover its intact elastic
modulus like metals after indentation. They [Hengsberger et al. 2002] also pointed out
that the degree of elastic modulus recovery for bone is likely a function of indentation
depth and collagen architecture.
I calculated the maximum depth for both indentations using the simple geometric
relationship between the length of the Knoop diagonal and depth. The calculated value
was about 6 itm for both wet-indented and dry-indented residual impressions The actual
difference in maximum depths was about 5%. However, the wet-indented depth
recovered 5 gtm while the dry-indentation depth recovered 4 inm. The wet-indented
measurements were used to estimate the elastic modulus of the recovered material.
For the first estimate of the wet-indented recovered material elastic modulus, I used
the derivation reported by Loubet et al. [1984]. That derivation assumes simple elasticity
although bone is known to have a degree of viscoelasticity. I have not added viscoelastic
behavior to the model in order to preserve simplicity. The following equations were
taken from Dorner and Nix [1986]:
Er dP 1 -l (1
E dh -2 A(1)
E = (1 v2) 1, (2)
E, E,
dP
where Er = reduced modulus, =slope of load and displacement plot, A = projected
dh
area of the indenter residual (recovered) impression, i = indenter point material, v =
dzd2
Poisson's ratio, E = elastic modulus. For the Knoop indenter point, A = 2 where d,
2
= length of long diagonal, d2 = length of recovered short diagonal.
dP
I calculated the load and displacement slope, from 2 data points. The first was
dh
at the maximum indentation depth (6 itm) and maximum applied mass (0.1 kg). The
second was at the final indentation depth (1 tm ) and final applied mass (0.0 kg). I then
computed the reduced elastic modulus, Er, using equation (1). I used equation (2) to
computed the elastic modulus with an assumed Poisson's ratio of 0.3 for the specimen. I
also used a Poisson's ratio of 0.2 and an elastic modulus of 925 GPa for the diamond
indenter [MatWeb 2003].
A refinement of the recovered material elastic modulus derivation for the wet-
indented specimen was made through a simple elastic model. Equation (1) assumes that
the modulus found was for the entire elastic half space. In reality there is a spectrum of
elastic moduli ranging from that of the intact bone to that of the material in the immediate
indentation affected region. Observation of a typical load -displacement data [Oliver and
Pharr 1992] shows the changing slope of the load-displacement curve. I constructed a
simple model that estimated the thickness of a finite column equivalent to the elastic half
space. Then I divided that column into two regions, one of competent bone and one of
recovered material. I then used a simple two series springs model for the two materials.
I assumed that the modulus of bone was 11 GPa [Guo 2001 p. 10-7] because the wet
specimens were indented with the short Knoop diagonal perpendicular to the bone
longitudinal direction. A sensitivity evaluation was also performed to determine
variation of results with the value of crush depth. The recovered material depth was not
known. I estimated the depth to be twice the maximum depth of the Knoop indentation
point at full load. That value was chosen based on the extensive modeling work by
Giannakopoulos et al. [1994]. They [Giannakopoulos et al. 1994] had shown that the
maximum tensile residual stress was located close to twice the indentation maximum
depth for strain hardening material after complete unloading. Details of the elastic
modulus estimation procedure are contained in the Appendix.
Fracture toughness
Cracks in the dry SEM prepared specimens were very small and I was unable to
measure their width or length. Wet-indented crack lengths were 91 [tm + 4 [tm (mean +
SD). The measured crack lengths were used in an empirical equation to derive fracture
toughness. The relationship between fracture toughness and crack length, taken from Xu
et al. [1998] was:
XP
K= (3)
c2
where Kc = fracture toughness (MPa /mm2), X = 0.076, P = indentation load (N), 2c =
total crack length (mm). The constant, X, depends on the hardness to modulus ratio of
the material. I assumed that the material was brittle after SEM preparation and imaging.
I also assumed that it had a hardness to modulus ratio similar to other brittle materials
like ceramics and dental enamel. Based on those assumptions I selected x to be the same
(0.76) as that used by Xu et al. [1998] in their ceramic and tooth enamel investigations.
Results
The results fall into two major categories. The first relates to the observation of
cracks in the apices of SEM specimens and the second to the physical description of the
microindentation residual impression cross section.
Cracks
Midline cracks were observed along the apex of the residual impression long axis
for both wet-indented and dry-indented SEM specimens (Figure 3-5). There were no
cracks observed in the AFM specimens whether they were wet-indented or dry-indented,
regardless of indentation point (Vickers or Knoop) or test mass.
Cracks in the first SEM specimens (Figure 3-6) were measured optically and
resulted in a mean fracture toughness of 0.22 MPa/m1l2 0.01 (mean SD) using
equation (3). The average of results from the fracture toughness confirmation specimen
(Figure 3-7) was 0.22 MPa/ml/2 0.04 (mean SD). The crack length is directly
proportional to applied mass (Figure 3-8). A one way ANOVA was performed on the
fracture toughness confirmation data. There was no significant difference between the
fracture toughness at any value of applied mass (p > 0.05).
Cross-section
The computed estimate of elastic moduli were 3.2 GPa and 4.8 GPa wet and dry
respectively. The detailed calculation is provided in the Appendix. The result for the
wet-indented specimen, 3.2 GPa, represents a modulus between that of cortical bone (11
to 20 GPa) [Guo 2001 p. 10-7] and demineralized bone (0.2 to 0.9 GPa) [Catanese et al.
1999]. A further refinement using the series spring model resulted in elastic modulus
value of 1.0 GPa. That value was based on an assumed recovered material depth of twice
the maximum indentation depth. That depth was taken from Giannakopoulos et al.
[1994] and is the point of maximum tensile stress. It is at this point that maximum bone
damage would be expected.
Measured residual impression sidewall angles of 153 and 168, dry and wet
respectively, were greater than the 1300 of indenter tip geometry (Figures 3-4, 3-5).
There was no evidence of pile-up on the short diagonal sides of the residual
impression where the sidewalls meet the initial material surface (Figures 3-3, 3-4). In
fact there was no indication of pile-up on any of the several hundred indentations made in
the course of this study.
Also notable was the unevenness of the polished specimen surface and lack of well-
defined edge or boundary between the impression and the initial surface (Figure 3-5).
Discussion
In this section I discuss: fracture toughness of SEM prepared specimens; the
derived elastic modulus of the recovered material in the indentation affected region; and
absence of pile-up on the residual impression edge.
The objective of this study was to better understand microindentation through
investigation of the residual impression indentation site. The observations and simple
calculations in this study appear to verify that post indentation material at the indentation
site is not representative of the undisturbed bone as suggested by Hengsberger et al.
[2002].
Fracture Toughness
The microindentation residual impression site was investigated through SEM and
optical microscopy. Cracks in the SEM prepared specimens were directly related to the
applied mass. The relationship between the fracture toughness values derived in this
work and that of unprocessed bone is unknown. Future research could help understand
the relationship.
It may be possible to more easily derive fracture toughness of bone through
development of a regression model. Specimens from bones with a range of fracture
toughness could be tested macroscopically and compared with fracture toughness values
derived using SEM preparation and crack length measurement. A good regression
relation (R2 > 0.8) could greatly simplify derivation of fracture toughness for a wide
range of bones.
Recovered Material Elastic Modulus
The estimated elastic modulus of the wet-indented recovered material can be
interpreted as the modulus of a material that is not intact bone, it is damaged. I could not
determine the nature of the damage. The results of my work can only estimate an elastic
modulus for the material. My method assumed a depth of the damaged material. A
difference of 1 tm in assumed depth is equivalent to about 90 MPa estimated modulus.
Future research could examine that assumption.
The objective of the future work described in Chapter 5, is to experimentally
determine the depth of the recovered (damaged) bone material and use it in finite element
models like those developed by Giannakopoulos et al. [1994], for ultimate use as a bone
model. Such a model could provide a better value for the elastic modulus of the material
in the microindentation affected region.
Pile-up
Some time ago other researchers had found evidence of pile-up during
microindentation hardness tests when the applied mass was above 0.1 kg [Ramrakhiani et
al. 1979]. Their result was likely due to the silver plate they had applied to the bone
specimen. Bone, as a brittle material, exhibits strain hardening behavior with a relatively
large strain hardening exponent of about 0.7. The strain hardening exponent, n, comes
from the stress-strain relationship after the material yields. The constitutive law is
expressed as: o = EFs Materials with large strain hardening exponents over about 0.5,
are not expected to exhibit pile-up [Cheng and Cheng 1998], they sink in. Therefore,
pile-up should not have been expected in bone microindentation. The absence of pile-up
provides additional confirmation that bone behaves as a work hardening (brittle) material.
Absence of pile-up also suggests that bone compacts, sinks in, under the
microindentation point because material is conserved. The compaction or sinking in
suggests that the material under the microindenter tip is different than the intact material.
Extending this idea to elastic modulus measurement methods it seems reasonable that the
ERM measures different material than does the LDM. I suggest it may be so because the
ERM takes its measurements after all recovery is complete while the LDM takes its
measurements when the indenter point is in full and intimate contact with the specimen.
The compacted material is between the indenter point and the intact material and remains
compacted. During the very first part of the unloading while the indenter point is in full
contact with the specimen the elastic response of the intact material will be manifest in
the load and displacement measurements. It is the initial unloading slope of the load
displacement curve that is used to derive elastic modulus.
Such an interpretation would predict that ERM derived elastic modulus values of
bone would be less than LDM derived elastic modulus values. Such a prediction has in
fact been demonstrated in my related work described in Chapter 4.
Table 3-1 Values for dry-indented and wet-indented cross sections. Measured quantities
are: angle = angle between side-walls, brec = recovered short diagonal, a =
long diagonal, h = depth of residual indentation, P = applied load. Derived
quantities are: HK = Knoop hardness, E = elastic modulus.
SEM Specimen Parameters
Quantity Dry-indented Wet-indented
Angle (0) 153 168
HK (kg/mm2) 40 36
brec (pm) 20.5 22.8
a (pm) 188.3 198.7
h (pm) 2.5 1.2
P (N) 0.98
E (GPa) elastic half 4.8 3.2
space model
E (GPa) series n/a 1.0
spring model
initial surface
pile up
Sp unloaded
surface profile loaded
Figure 3-1 Typical schematic accompanying indentation models. A region of material
pile up is not shown on all such schematics. It is shown for models of ductile
material. Brittle materials do not exhibit material pile up.
B
S v j .i
r;
Figure 3-2 Typical indentation set for SEM investigation prior to SEM preparation.
Indentations made with the Knoop indenter point. Scale is the same in A and
B. A) Dry-indented bovine MC specimen B) Wet-indented bovine MC
specimen
Figure 3-3 Bovine metacarpus. Dashed boxes indicate area from which indentation
specimens were taken.
B
Figure 3-4 A) Knoop residual impression array line containing 9 microindentations.
Indentations made in dry specimen with short Knoop diagonal parallel to the
bone long axis. One observable indentation is indicated by the dashed box. B)
Cross section of Knoop microindentation short diagonal of the indentation
with approximate side-wall angle depicted by dashed lines.
49
A
B
Figure 3-5 A) Knoop residual impression area. Indentations made in wet specimen with
short Knoop diagonal perpendicular to the bone long axis. One of the
observable indentations is indicated by the dashed box. B) Cross section of
the indentation with approximate side-wall angle depicted by dashed lines.
\\
N.
N J~
N ~ ttv
..o
r
* ,'
"
**, ;r )Ce
:~:f.*~ S=
v,
c-- ~
7r?~,~
r
v
.I~*' ,
Figure 3-6 Linear crack at the apex of the indentation residual impression. Other non
indentation related cracks can be seen in the lower left section of the image.
Note lack of well defined edge. Specimen was indented wet. Dotted lines
indicate the edge of half of the indentation residual impression. Solid circles
indicate approximate end of residual impression long diagonal. Note that the
apex crack is shorter than the long diagonal of the indentation.
~JI.
"''
'~"
:*
-r,~.
r
:i
.. .
1
Figure 3-7 Typical Knoop indentations in the fracture toughness confirmation specimen.
Specimen was indented wet with the Knoop short diagonal perpendicular to
the bone longitudinal axis. Cracks appear as white lines. Other non
indentation related cracks are visible on the left side of the image.
52
1 0
ii O
0.oE-H)0 1.OE-06 2.OE-06 3.OE-06 4.OE-06
3/2
C1.5 (0.5
C^0.5 (m342)
Figure 3-8 Plot of applied mass (Load) with crack length, where "C" is the total
measured crack length divided by 2. Dotted line is linear regression, R2=0.98.
CHAPTER 4
INVESTIGATION OF THE ELASTIC RECOVERY METHOD FOR DERIVING
ELASTIC MODULUS OF BONE, DENTIN, AND ENAMEL
Introduction
The objective of the work described in this chapter was to evaluate the elastic
recovery method (ERM) for deriving elastic modulus of bone, dentin, and enamel. The
aims were to: adapt and validate the ERM using well documented material (glass,
Plexiglas, bovine femur); and apply the ERM to bone, dentin, and enamel.
In addition to those aims I used the ERM to map elastic modulus distribution in the
mediolateral direction along the centerline of bovine metacarpus nutrient foramen and I
investigated the elastic anisotropy of monkey dentin and enamel.
History
The ERM was originally developed within the materials research community and
used on ceramics by Marshall et al. [1982]. Marshall et al. [1982], using the Knoop
indenter point, had observed a relationship between the post indentation ratio of short to
long Knoop diagonal measurements and the hardness to elastic modulus ratio. Using a
spectrum of ceramic materials, with a range of hardness and moduli, they constructed a
mathematical relationship. The relationship equated elastic modulus to hardness divided
by a measure of departure from perfect elasticity. Their resultant equation for elastic
modulus was:
E= CHK / C2- b (1)
I aJa
where E = elastic modulus, Cl and C2 = constants, HK = Knoop hardness (MPa), brec
= recovered short diagonal, a = long diagonal. The constants were chosen through curve
fitting from a plot of microindentation residual impression dimensions ratio (brec/a) and
hardness to elastic modulus ratio (HK/E). Constant Cl is the slope of the linear
regression and constant C2 is the intercept on the brec/a ordinate. The resulting linear
regression equation as taken from Marshall et al. [1982] is:
be = C2 C1HK (2)
a E
Subsequent work by Amitay-Sadovsky and Wagner [1998] extended ERM to
polymers. They also used a spectrum of polymers with a range of hardness to modulus
ratios. Their constants, Cl and C2 in equation (2), were also derived through curve
fitting. Amitay-Sadovsky and Wagner [1998] concluded that the ERM was applicable
for polymers. Use of appropriate indentation applied mass was their only caveat because
they had found a dependence of derived hardness on applied indentation load while
Marshall et al. [1982] had found none for ceramics.
In addition to work in polymers the ERM has been applied in dental research by
Meredith et al. [1996] and pharmacological work by Lum and Duncan-Hewitt [1996].
Lum and Duncan-Hewitt compared ERM derived elastic modulus results with those
derived from use of ultrasonic methods. They criticized ERM for producing negative
values of elastic moduli. Meredith et al.[1996] reported that their ERM derived elastic
modulus results were limited by enamel cracking. They also reported success with
deriving dentin elastic modulus. Such cracks did not allow measurement of the
microindentation residual impression dimensions. During the period from 1982 to my
research, the ERM had not been used in bone.
Motivation
Success of the ERM in ceramics, polymers, and dentin, reported by Marshall et al.
[1982], Amitay-Sadovsky and Wagner [1997], and Meredith et al. [1996], encouraged me
to use the method in bone. Equipment required by the ERM was available to me and the
method appeared to be reasonably straightforward. I also wanted to explore the tooth
enamel limitation reported by Meredith et al. [1996].
In addition I wanted to use the ERM to map elastic modulus distribution on the
mediolateral midline of the bovine metacarpus dorsal foramen.
Methods and Materials
This section is divided into 3 subsections. The first describes the method used in
adapting the ERM for use in bone. The second describes the methods and materials used
in validation of the ERM. The third describes the methods and materials used in
application of the ERM to bone, dentin, and enamel.
A microindenter (Model HM-112, Mitutoyo, Japan), equipped with a Knoop
indenter point, was used for all microindentations unless otherwise stated. The Knoop
indenter point was selected because it allows investigation of elastic anisotropy as
demonstrated by Riches et al. [1997] and Riester et al. [2000].
For bovine and monkey specimens, I used a dwell time of 10s and followed the
limitations on: time out of solution; time between indentation and measurement; and
distance between the indentation and pores from Chapter 2. I did not perform hardness
variation with independent variables evaluations for bovine or monkey specimens except
applied mass.
Animal tissue from bovine and monkey were used in the work described in this
chapter. All procedures involving animal tissue use were approved by our Institutional
Animal Care and Use Committee.
Adaptation of Elastic Recovery Method to Bone
Adaptation of the ERM for use in bone involved the selection of constants Cl and
C2 for equation (1). In this subsection I describe my selection of those constants.
The constant Cl, as derived by Marshall et al. [1982] and Amitay-Sadovsky and
Wagner [1998], is the slope of a linear curve fitted through the brec/a and HK/E data
(Equation (2)). Derivation of the constant Cl requires that the value of hardness to
modulus ratio be known for the material being indented. The values for forming the ratio
brec/a are simply measured from the microindentation residual impression.
While I could measure the residual impression dimensions in bone, I did not know
the HK/E values for bone. Indeed, it was the elastic modulus that I was trying to find.
Moreover, I did not have available a range of bone specimens with known elastic moduli
with which to work.
Without a range of bone specimens from which to determine a value for Cl, I
decided to use a simple linear relationship between the value of the constant C for
ceramics and the value of the constant Cl for polymers. It also turned out that the ERM
equation is sensitive to the value of Cl (Figure 4-4). I chose the ordinate to be the value
of Cl and for the abscissa I chose the corresponding average value of elastic modulus for
the subject material. The first data point set was the value of Cl for ceramics (0.45)
[Marshall et al. 1982] at an elastic modulus of 70 GPa. The second data point set was the
value of Cl for polymers (0.473) [Amitay-Sadovsky and Wagner 1998] at an elastic
modulus of 2.6 GPa. An elastic modulus of 70 GPa was selected for the material glass as
it is representative of ceramics. The value for elastic modulus of 2.6 GPa was selected
for the material acrylic polymer as it is representative of polymers. The values for elastic
modulus were taken from an available internet source [Mat Web 2003]. The resulting
equation was:
Cl= 0.4739- 0.0003(E), (3)
where Cl = constant, E = elastic modulus (GPa). I then used an elastic modulus of 16
GPa to pick off a value for Cl. I chose the value of 16 GPa because it is the average
value of bovine femur elastic modulus [Guo 2001, p 10-7]. I chose the bovine femur
values for the computation because I planned to use that bone for ERM validation. I then
computed a value of 0.47 for the constant Cl for use in deriving the elastic modulus of
bone (Table 4-1).
In selecting the value for the constant C2, I again did not have a range of specimens
with known elastic moduli from which to find the ordinate intercept. I selected the value
of 0.14 for the constant C2 following Marshall et al. [1982] and Meredith et al. [1996].
Marshall et al. [1982] and Meredith et al. [1996] had used 0.14 because it is the largest
physically possible value for brec/a. That value follows directly from the geometry of the
Knoop indenter.
Elastic Recovery Method Validation
In this subsection: I state the hypotheses for the ERM validation; describe specimen
preparation and indentation procedure for each specimen; and provide the method for
ERM equation sensitivity evaluation.
Hypotheses
The null hypotheses for ERM validation were:
1. Glass specimen.
a. Mean value of ERM derived elastic modulus is equal to the mean
published value.
b. Mean value of ERM derived elastic modulus, using edge detection,
is equal to the mean ERM derived elastic modulus, using optical
measurements alone.
2. Mean value of ERM derived elastic modulus for Plexiglas is equal to the
mean published value.
3. Bovine femur longitudinal specimen.
a. Mean value of ERM derived elastic modulus is equal to the mean
published value.
b. There is no difference in the mean value of ERM derived elastic
modulus between indentation orientations.
4. Bovine femur transverse specimen.
a. Mean value of ERM derived elastic modulus is equal to the mean
published value of elastic modulus.
b. There is no difference in the mean value of ERM derived elastic
modulus between indentation orientations.
The alternate hypotheses were all two-tailed.
Specimen Preparation and Indentation Procedures
Glass
A glass slide, 27 x 46 x 1.25 mm (Petrographic slides, Buehler, Lake Bluff, IL),
was cleaned with 100% ethyl alcohol and air dried. A range of indentation applied mass
was evaluated against derived hardness. That investigation resulted in selection of 0.3 kg
as the minimum appropriate applied mass for subsequent indentations. A dwell time of
10 seconds was used based on my experience and other related work (Chapter 2).
Ten indentations were performed in 2 groups of 5. The microindentation residual
impressions were well defined which resulted in ease of short diagonal measurement
using optical means. The indentation residual impressions were measured with the
installed measuring system of the microindenter. Edge detection was evaluated on the
specimen to access its accuracy. Two groups of 3 indentations were made for optical and
edge detection measurement.
Plexiglas
A piece of transparent optical acrylic polymer (Plexiglas) approximately 36 mm by
40 mm by 12 mm thick was cleaned with tap water and blotted dry with paper wipes.
Again, a range of indentation applied mass were evaluated against the derived hardness.
The investigation resulted in selection of 0.1 kg as the applied load for subsequent
indentations.
Ten indentations were performed and the elastic modulus results averaged. The
indentation residual impressions were well defined and the short diagonal easy to
measure with optical means.
Bovine femur
In this subsection I describe: the specimen preparation; indentation procedure; and
indentation residual impression evaluation with edge detection image processing. The
image processing used for the these specimens was also used on the glass and Plexiglas
specimens.
Two bovine femur specimens were used in ERM validation. Specimen size was
dictated by specimen mounting and polishing requirements. The specimens were sized to
fit on a standard petrographic slide (Buehler, Lake Park, IL). The specimens were taken
from a previously fresh frozen right femur in the mid diaphysis anterior aspect (Animal
Technologies Inc., Tyler Texas). One of these specimens was sectioned parallel to the
long bone axis, longitudinal (Figure 4-1) and the other was sectioned transverse to the
long bone axis (Figure 4-2). Both specimens were approximately 25 mm by 45 mm by 1
mm thick.
After cutting to size the specimens were polished using a semi automated polishing
system (Minimet 1000, Buehler, Lake Bluff IL). Both specimens were polished
progressively beginning with 6 |tm diamond slurry and finishing with 0.05 |tm alumina
and colloidal silica suspension. Following Zysset et al. [1999], the specimens were
stored in a solution of 0.5 mg/ml gentamicin sulfate in tap water at 20 C when not
undergoing indentation or imaging to retard collagen biological degradation.
A series of 10 indentations each were made in the transverse (Figure 4-1) and
longitudinal specimens (Figure 4-2). For the longitudinal specimen 5 indentations were
made with the short Knoop diagonal perpendicular to the bone long axis (L1, Figure 4-3)
and the other 5 with the short Knoop diagonal parallel to the bone long axis (L2, Figure
4-3). For the transverse specimen 5 indentations were made with the short Knoop
diagonal perpendicular to the bone circumferential direction (T1, Figure 4-3) and 5
indentations were made with the Knoop short diagonal parallel (T2, Figure 4-3) to the
bone circumferential direction.
Knoop hardness (kg/mm2) and long diagonal (pm) were recorded for each
indentation. Optical microscopy images of each indentation were then taken within about
20 minutes. Use of strictly optical measurement means introduced subjectivity into the
measurements. Reproducible measurement of the short Knoop diagonal length was not
possible. In order to minimize the subjectivity an edge detection step was added to the
indentation procedure for bone.
The optical microscopy images were converted to grayscale and subjected to edge
detection with image processing software (MatLab, MathWorks, Inc., Natick, MA). A
variety of edge detection filters are available in the software. Each filter was used on a
representative residual impression grayscale image of the bovine femur. The Canny filter
was selected for subsequent edge detection due to its superior ability to detect edges of
this type.
The significant difference between the Canny filter and other available filters is an
edge linking feature. This feature links discrete picture elements (pixels) into chains to
form lines. One weakness of the Canny filter occurs at junctions of several lines. The
linking function fails to enhance the edge at these junctions. The critical measurements
for ERM are between large angles across the short diagonal. The linking function does
not appear to fail at these junctions.
The differences between all other filters and the Canny filter were obvious and
profound. The edge-detected images were used in image handling software (Paint Shop
Pro, JASC, Eden Prairie, MN). The short diagonal (brec) and long diagonal (a)
measurements were made using pixels and the known value of pixels per im for the
given optical microscope magnification. The diagonal length measurements were made
by identifying and subtracting pixel location coordinates and dividing by the known
pixels per im. Identification of pixel location was a manual task and involved some
degree of subjectivity.
Sensitivity evaluation of ERM equation
A sensitivity analysis was performed on the ERM equation (Equation (1)) to
determine the variation of elastic modulus results to a + 5% change in each of the 5
equation variables. The evaluation used reference values for the equation variables from
1 representative indentation residual impression on the bovine femur longitudinal
specimen.
Application of ERM to Bone, Dentin, and Enamel
In this subsection I describe the methods and materials used for application of the
ERM. Three different materials from 2 different specimens were used: bovine
metacarpus (MC); and monkey tooth dentin and enamel.
I also describe the methods used to investigate the ERM derived elastic modulus
distribution in the mediolateral direction along the centerline of the bovine MC foramen
minor axis.
Hypotheses
Three hypotheses were tested for the application of ERM.
1. The mean ERM derived value of elastic modulus for bovine MC was equal to
the correlation method (CM) derived elastic modulus for bovine MC;
2. The mean ERM derived value of monkey tooth dentin elastic modulus was
equal to the mean published value;
3. The mean ERM derived value of monkey tooth enamel elastic modulus was
equal to the mean published value.
Specimen Preparation and Indentation Procedures
In this subsection I describe: specimen preparation; indentation procedures and
correlation method used for answering the 1st hypothesis; specimen preparation and
indentation procedures for answering the 2nd and 3rd hypotheses; and indentation
procedures used for investigation of the nutrient foramen elastic modulus distribution.
Bovine MC
One bovine right metacarpus (MC) was obtained from the University of Florida
College of Veterinary Medicine from a donor of unknown age and sex whose death was
unrelated to this study. After 2 transverse cuts with a 10 inch band saw (Delta
Machinery, Jackson, MS), the bone was longitudinally sectioned (Isomet Low Speed
Saw, Buehler, Lake Bluff, IL) from the distal dorsal aspect to produce a 1 mm thick by
25 mm wide by 45 mm long longitudinal slab (Figure 4-5). The specimen size was again
controlled by the polishing system capabilities. The specimen was polished in the same
manner as the bovine femur specimens. The specimen was to be used to map elastic
properties along the mediolateral midline through the foramen minor axis.
Correlation method (CM)
In mapping elastic constants, along the midline of the bovine MC foramen, I
compare ERM derived results with those obtained by CM. I use the linear correlation of
Vickers hardness with elastic modulus developed by Currey et al. [1990]. The equation
is:
E 0.58+0.36Hv, (R2=0.93) (4)
where E = elastic modulus (MPa), Hv = Vickers hardness (kg/mm2).
Bovine foramen elastic modulus distribution
A series of 19 sets of 4 indentations each was made along the bovine MC foramen
midline in the lateromedial direction, parallel to the foramen minor radius (Figures 4-6).
Each of the 4 indentations were made at angles of 0, 450, 90, and 110 as measured
between the bone longitudinal axis and the Knoop short diagonal.
Ideally all indentations would be made at the same point. Placing the 4
indentations in the same place would overlap them. Measurements of the residual
impressions would represent the effect of other indentations and not the bone itself. For
that reason the indentations were grouped as close together as reasonable allowing for
pores. In general a spacing of at least 70 .im was maintained between the short diagonals
of the neighboring Knoop indentations within a group. This distance has been found in
previous work (Chapter 2) to eliminate the effect of one indentation on another.
Mapping of ERM derived elastic modulus based results for elastic constants
distribution on the bovine MC lateromedial midline consisted of the following steps.
1. Locating a representative distance from the foramen edge for each set of 4
indentations.
2. Deriving elastic modulus values for each of the 76 indentations.
3. Calculating the principal longitudinal and transverse elastic moduli and
shear modulus for each of the 19 indentation sets.
Mapping the CM derived elastic modulus distribution on the bovine MC
mediolateral midline involved making microindentations with the Vickers indenter point.
A set 44 indentations was made along the midline of the foramen in the mediolateral
direction (Figure 4-7).
Representative Distance from Foramen Edge
I chose the distance between the edge of the foramen and the center of the
indentation made at 450 as reasonable representative of the indentation set distance. The
decision was based on inspection of the completed indentation sets.
Deriving Elastic Modulus for Indentations
Elastic moduli values were computed for each indentation except one. The one
exception was the 450 indentation in set 2. I was unable to obtain a reproducible
measurement of the residual impression short diagonal. That left 18 viable indentation
sets with all 4 ERM derived values of elastic modulus.
Principal Elastic Moduli Calculation
The principal longitudinal and transverse elastic moduli and the shear modulus
were calculated using an iterative process. The process was constructed because I did not
know the principal material directions. The apparent material directions were evident for
some indentation sets but not for all.
The first step in the iterative process was to use an in-plane coordinate
transformation to obtain values for longitudinal, transverse, and shear elastic moduli at
coordinate rotation angles between 00 and 900. The transformation equation was taken
from Rapoff et al. [2003]:
1 1 [(sin4(Q+0))-(2v)(cos2 (+0)sin2 (+0))]
E' (0) EL (5)
(5)
+1 (cos4 (+0))+ (cos2( +0)sin2 + ))
ET GLT
where E' (0) = measured modulus at angle 0, 0 = angle between the Knoop short
diagonal and the transverse axis of the specimen (Figure 4-6 B), 4 = angle of in-plane
coordinate transformation rotation, EL = elastic modulus in the principal material
direction, E, = elastic modulus in the transverse principal material direction, GLT
shear modulus, v = Poisson's ratio.
For each of the 18 viable indentation sets, 3 of the 4 values (0 = 00, 450, 900) of
ERM derived elastic modulus were used, with an assumed Poisson's ratio of 0.3, to form
a set of 3 linear equations in 3 unknowns. Poisson's ratio of 0.3 is representative of
bovine long bones. Values of EL, ET, and GLT were calculated as the angle of rotation, 4,
was iterated from 0 through 900, in 5 steps. These calculations resulted in a range of
physically possible values for EL, ET, and GLT. In order to select the best set of values,
the 4th data point (110) in each of the 18 indentation sets, was used. At each angle of
rotation, ), the predicted value of elastic modulus at 1100 was calculated using the same
transformation equation. The result of the calculation was compared with the actual
ERM derived value to determine the percent error. I established criteria to select the best
angle and the corresponding values for EL, ET, and GLT. That criteria was: the values
were possible (0 < EL > GLT, ET > GLT > 0); the error between the ERM derived value
and calculated value was <5%; and that the minimum error were single valued, that is
there was only one minimum in the interval 0 to 900. The computations were carried out
with a commercially available software (Mat Lab, MathWorks, Inc, Natick, MA). The
best angle was the angle corresponding to the principal material direction. An angle of 0
means a principal direction parallel to the bone longitudinal axis.
Monkey teeth
I describe the specimen preparation and indentation procedures for both tooth
dentin and enamel because the dentin and enamel are part of the same specimen.
The first molars from both sides of a skeletally mature female monkey (Macaca
fascicularis) were sectioned from a previously cleaned and fresh mandible using a
diamond blade saw (Low Speed Saw, Buehler, Lake Park, IL). On each side one cut was
made in the buccolingual plane between the premolar and the first molar. A second cut
on each side was made also in the buccolingual plane at the centerline of the first molar.
A third cut was made again on both sides in the buccolingual plane between the first and
second molars. These cuts produced four specimens about 2 mm thick, with both a cross
section and an exterior surface. The right side specimens are shown in Figure 4-8.
The posterior aspect of the first right side molar was particularly flat and afforded
the opportunity to indent the exterior surface of enamel with minimum removal of
material through cutting and polishing. These specimens were manually polished using
the same polishing and storage protocol used with the bovine specimens.
In order to determine the appropriate microindentation applied mass for dentin and
enamel I followed the same hardness variation with applied mass method I described in
Chapter 2, I found an appropriate applied mass of 0.1 kg for used for dentin and 0.2 kg
for enamel. The indentations made at 0.1 kg applied mass in dentin were also used to
answer the 2nd hypothesis. The indentations made at 0.2 kg applied mass in enamel were
also used to answer the 3rd hypothesis.
In the dentin of the right side first molar cross section, 2 sets of 5 indentations were
made. One set of 5 with the short Knoop diagonal parallel and the second set of 5
perpendicular to the dentin tubule orientation (Figure 4-9). The indentations were used to
investigate in-plane elastic anisotropy.
A series of 3 indentations were made in the cross section of enamel with the short
diagonal approximately perpendicular to the enamel prism tubes in the crown of the
tooth. These indentations cracked and were not useable for ERM (Figure 4-9 A).
Two series of 3 indentations were made in the surface enamel on the posterior
aspect of the right first molar. The first series was with the short diagonal approximately
parallel to the occlusal surface and the second with the short diagonal 900 from the first
set (Figure 4-10). One indentation in the first series exhibited cracking and was not used.
Results
This section is divided into 2 major subsections. In the first subsection I report
results from the ERM validation activities. In the second subsection I report the results of
the ERM application to bovine MC elastic modulus mapping and monkey dentin and
enamel.
Elastic Recovery Method Validation
In this subsection I report the results of hypotheses tests and ERM equation
sensitivity evaluation.
Hypotheses Tests
Glass
The mean ERM derived elastic modulus was not significantly different (ANOVA,
p > 0.05) from the published value (Table 4-3).
The ERM derived elastic modulus using optical measurement of the residual
impression dimension, was not significantly different (ANOVA, p > 0.05) from the ERM
derived elastic modulus results using edge detection (Table 4-4).
Plexiglas
The ERM derived elastic modulus was not significantly different (ANOVA, p >
0.05) from the published value (Table 4-3).
Bovine Femur
The ERM derived elastic modulus was significantly different (ANOVA, p < 0.05)
from published values for both longitudinal and transverse specimens (Table 4-3). There
was no significant difference (ANOVA, p > 0.05) in ERM derived elastic modulus
between Knoop indenter point orientations for either the longitudinal or transverse
specimens (Table 4-4).
Elastic Recovery Method Equation Sensitivity
The least sensitive variables are constant Cl and Knoop hardness. The most
sensitive variables are constant C2, measured long diagonal, a, and measured short
diagonal, brec (Table 4-2). Results are also provided graphically as normalized sensitivity
plots for each of the 5 variables (Figure 4-4).
Application of the Elastic Recovery Method
In this subsection, for the bovine MC foramen region, I report, : the ERM derived
elastic modulus based results for elastic constants distribution; the distribution of
principal material directions; and the CM derived elastic modulus distribution. I also
report ERM derived elastic modulus results for monkey tooth dentin and enamel.
Elastic Constants Distribution
The distribution of longitudinal elastic modulus (EL), transverse elastic modulus
(ET), and shear modulus (GLT), with distance from the foramen edge in the lateromedial
direction, is shown on Figure 4-12. Longitudinal elastic modulus had the most variability
(Table 4-7). That variability occurs between 1 and 2 foramen radii from the foramen
edge. Shear modulus had the least variability.
The distribution of coordinate rotation angle variation with distance from the
foramen edge in the lateromedial direction, is shown on Figure 4-13. The coordinate
rotation angle was least (0) at about 1 foramen radii from the edge of the foramen. The
greatest coordinate rotation angle occurred at about 1.5 foramen radii from the foramen
edge.
The distribution of CM derived elastic modulus with distance from the foramen
edge in the mediolateral direction, is shown on Figure 4-13. The maximum value
occurred at approximately 1.5 foramen radii from the foramen edge.
The values of longitudinal modulus (ET) and CM derived elastic modulus, between
the foramen edge and a distance of 1 foramen radius, are significantly different
(ANOVA, p < 0.05). The values of longitudinal modulus (ET) and CM derived elastic
modulus, between the foramen edge and a distance of 2.3 foramen radii, are not
significantly different (ANOVA, p> 0.05).
Monkey Teeth
In this subsection I report the results of hypotheses tests for dentin and enamel. I
also report results of investigation of dentin and enamel elastic anisotropy. I describe my
experience with enamel cracking during testing.
There was significant difference (ANOVA, p=0.05) between ERM derived elastic
modulus of dentin compared with ERM derived elastic modulus results reported by
Meredith et al. [1996]. There was significant pair wise difference between (ANOVA
p<0.05 for each pair) ERM derived elastic modulus and elastic modulus derived by the 2
load-displacement methods (Table 4-6). The standard deviation was greater in my
measurements than others. My data contained 10 points while Meredith et al. [1996] data
contained 5. Data from the load displacement methods in inherently less variable due to
its automated nature.
There was no significant difference (ANOVA p>0.05) between ERM derived
elastic modulus of enamel and the published values (Table 4-6).
There was no significant difference (ANOVA p>0.5) in the dentin ERM derived
elastic modulus either parallel to or perpendicular to the dentin tubules. These results
agree with those of Kinney et al. [2001], who used small angle X-ray scattering (SAXS)
to investigate dentin microstructural anisotropy.
There was no significant difference (ANOVA p>0.5) in enamel ERM derived
elastic modulus either parallel or perpendicular to the ends of the enamel prisms.
Indentations in the buccolingual cross-section exhibited cracking, and I was unable
to measure the short diagonal of the residual indentation with accuracy. Therefore, I have
no enamel elastic modulus results in that plane. That result is similar to Meredith et al.
[1996]. However, indentations in the posterior surface of the first molar were generally
well defined with little evidence of cracking (Figure 4-10)
Discussion
In this section I discuss: results from ERM validation; ERM equation sensitivity;
and the application of the ERM to bovine MC and monkey tooth dentin and enamel.
Elastic Recovery Method Validation
Agreement between the mean values of ERM derived elastic modulus and
published values for glass and Plexiglas was good (Table 4-3). Agreement was also good
between the mean values of ERM results using optical microscopy and edge detection for
glass (Table 4-4). Those results provided confidence in the ERM technique and edge
detection method.
Agreement between ERM derived elastic modulus results and published values for
the bovine femur was not good (Table 4-3). The Bovine femur results seemed reversed
between the longitudinal and transverse specimens based on an elastically transverse
isotropic or orthotropic model. The lack of significant difference in elastic modulus,
between indentation orientations for both the longitudinal and transverse specimens,
implies elastic isotropy in those planes. In Knoop indentations the short diagonal
surfaces spread the indented material. For these bovine specimens it was easier for the
indenter to spread the material on the longitudinal surface than on the transverse surface.
Such a difference could be due to directionally dependent mineralization in the plexiform
bone. Higher mineralization means harder bone. In addition to higher mineralization
some unidentified microstructural features may reduce post indentation material
recovery.
Elastic Recovery Method Equation Sensitivity
For the representative values used in the evaluation, the most sensitive are: C2, the
linear regression intercept; the long diagonal length, a; and the recovered short diagonal
length, brec. Of these variables C2 is chosen based on the physical limits of the indenter
geometry. Once chosen it is no longer a source of variation in the derivation of elastic
modulus. The long residual impression length, a, is easy to measure. I have shown, in
intra-observer effect evaluation (Chapter 2), that the measurement has little error.
However, the short diagonal, brec, is not easy to measure.
Operationally, the ERM results rely on the accuracy of measuring the short
diagonal. The measurement is made between the apices of 2 obtuse angles (Figure 4-3
B). The angle formed by the edges of the diamond tool on the specimen at the short
diagonal is about 1300. As previously described (Chapter 3) I found the residual
indentation impression edges are rounded where they meet the virgin material. In glass
and Plexiglas the surfaces are uniform or can be made uniform with polishing. The
uniform polished surface allows for well-defined indentation edges, that is, the distance
between the large angle apices can be measured with repeatable accuracy. The bovine
specimens used in this work (MC and femur) do not present a uniform surface nor well
defined indentation edges for indentation. Polishing removes softer material
preferentially leaving the harder material proud. The polished surface is uneven and
difficult to accurately determine the residual impression edge. Measurement of the short
diagonal is problematic and care should be exercised in acquiring the dimension.
The least sensitive variables were Cl (linear regression slope) and Knoop hardness
(HK). Again, once the constant has been selected it is no longer an operational variable.
Knoop hardness derivation relies on measurement of the long diagonal, a. Measurement
of the long diagonal is not problematic as I previously mentioned.
Application of the Elastic Recovery Method
In this subsection, for the bovine MC foramen I discuss: the ERM derived elastic
modulus based results for elastic constants distribution; the distribution of principal
material directions; and the CM derived elastic modulus distribution. I also discuss the
ERM derived elastic modulus results for monkey tooth dentin and enamel.
Elastic Constant and Principal Material Direction Distribution
The transition zone between cortical and trabecular bone, on the lateromedial side
(right side of the foramen in Figure 4-5), occurs between 1 and 2 foramen radii from the
foramen edge. That distance corresponds to the rapid change in both longitudinal and
transverse elastic moduli (Figure 4-12) and with the largest coordinate rotation angle
(Figure 4-13).
On the mediolateral side (left side of the foramen in Figure 4-5), there is no cortical
to trabecular transition zone along the minor axis midline.
There was statistically significant difference, at the 0.05 level, between the
longitudinal elastic modulus (ET) and the CM derived elastic modulus over the distance
of 1 foramen radius. However, the attained significance level of 0.47, was very close to
the apriori level of 0.05. That result suggests that there is some degree of similarity
between the elastic modulus derivation methods (Figure 4-15). Had I chosen 0.01 as the
a priori level of significance, I would have concluded that the results of both methods
were not significantly different. Agreement between the method results adds confidence
in the ERM.
I conclude that the ERM, with edge detection on sets of 4 indentations and the
iterative computations based on rotational planar coordinate transformation, can be useful
for mapping principal material directions and elastic constants in bone, based on the
following:
1. The symmetry between ERM based longitudinal elastic modulus (ET) and
CM derived elastic modulus.
2. ERM based elastic constants mapping detection of the cortical to trabecular
bone transition zone.
The CM has an advantage in operational simplicity. However, while the ERM
based elastic constants mapping process has many steps, it provides more information.
The ERM based process provides: longitudinal (ET) and transverse (EL) elastic moduli
and shear modulus; and principal material directions. The CM provides only elastic
modulus with no sense of direction.
Monkey Teeth
In this subsection I discuss the ERM derived elastic modulus results of dentin and
enamel.
Dentin
The lack of elastic anisotropy in dentin was of some surprise. I expected, noting
the dentin tubules and enamel prism tubes, was to expect elastic anisotropy, as found in
osteonal bone with its analogous repeating structural tubuless" (the osteons). Other
researchers have found strength anisotropy in dentin [Lertchirakam et al. 2001]. Dentin
tubules are small, about 1 [m diameter compared with osteons (about 200 [m) or osteon
lamellae (about 5 pm). The Knoop microindentation residual impression size,
approximately 165 [m by 19 [im, was much greater than the dentin tubule diameter.
While I found isotropy there must be some structural basis for strength anisotropy. The
ERM, at the microindentation scale, may not be small enough to determine the basis for
strength anisotropy.
Enamel
Our measured elastic modulus of enamel from averaged 103.9 GPa. There was no
statistical evidence (p = 0.37) to conclude that there was a difference in elastic modulus
measured parallel or perpendicular to the occlusal surface. We also found that
microindentations made in the enamel surface specimen did not experience cracking that
confounded measurements in the transverse specimen reported by Meredith et al. [1996].
Cracking of enamel during indentation occurred predominantly on the enamel cross
section surface and was minimal on the posterior surface. The difference between the
surfaces is the orientation of the enamel prisms. In the cross section the prisms appear as
the side of a tube bundle. On the posterior surface, or any occlusal surface, the ends of
the tubes are at the surface (Figure 4-16). Indentations made against the ends of the tubes
are less likely to crack because the prism tubes are in compression. Indentations in the
cross section subject the slender tubes to bending. Meredith et al. [1996] also
experienced difficulty with cracking of the molar enamel during indentation. However,
their specimens were all in the buccolingual cross section.
The absence of elastic anisotropy in the surface enamel seemed reasonable due to
enamel prism tube orientation. The posterior surface had been cut and polished and
presented the prism tube ends to indentation. The posterior surface indentations were
made against the ends of enamel prism tubes while the cross section indentations were
made across the enamel prism tubes (Figure 4-16). The microstructural architecture
clearly leads to my observed isotropic results.
76
I conclude that the ERM is an effective tool for investigation of the enamel elastic
modulus but is limited to occlusal surfaces.
77
Table 4-1 Values for ERM equation constants. Values for ceramics (glass) were taken
from Marshall et al. [1982]. Values for polymer were taken from Amitay-Sadovsky and
Wagner [1998].
Ceramics
Constant Cramcs Polymers Bone
(glass)
C1 0.45 0.473 0.47
C2 0.14 0.148 0.14
Table 4-2 Sensitivity of the ERM equation (1) to a 5% change in each variable taken
one at a time. Percent difference is with respect to the reference. A value
greater than 0.14 for C2 is not physically possible.
Elastic
Elac Elastic Modulus
Modulus
Mo s Difference (%)
(GPa)
Reference
Variable Reference Reference +5% -5%
Value
C1 0.47 16.9 4.7 -5.3
HK (MPa) 585 16.9 4.7 -5.3
C2 0.14 16.9 n/a 75
brec (m) 19.1 16.9 -61 28
a (ur) 154.4 16.9 27 -66
Table 4-3 ERM elastic modulus validation results. Significance levels computed
through ANOVA procedure. (* = MatWeb 2002, ** = Guo 2001 p. 10-7)
Bovine Femur
Longitudinal Transverse
ERM(GPa) 69.8 9.0 9.3 + 1.3 18.3 5.5 2.6 0.3
Mean SD
Published
published 68* 20** 11** 2.6*
(GPa)
Significance
Significance > 0.05 < 0.05 < 0.05 > 0.05
level (p)
Table 4-4 ERM derived elastic modulus results for 2 indentation orientations in bovine
femur specimens. Knoop indenter short diagonal orientation was either
parallel or perpendicular to the long axis of the bone for the longitudinal
specimen and parallel or perpendicular to the radial direction of the transverse
specimen.
Longitudinal Transverse
Specimen Specimen
Parallel (GPa) 9.1 + 1.9 18.3 + 7.0
Mean SD
Perpendicular 9.3 1.3 18.4 + 5.0
Mean SD
Significance (p) 0.9 0.99
81
Table 4-5 Comparison of edge detection and optical microscopy measurement precision
in glass specimen. Significance level determined by ANOVA procedure.
Optical (GPa) 69.7 9.0
Mean SD
Edge detection (GPa) 68.4 5.4
Mean SD
Significance level (p) 0.76
Table 4-6 Comparison of ERM derived elastic modulus results for monkey tooth dentin
and enamel results with 3 published sources. (LDM-m = Load displacement
method with microindentation, LDM-n = Load displacement method with
nano indentation.)
Monkey Tooth
Enamel Dentin
ERM(GPa) 73.6 14.0 15.6 5.4
Mean SD
Meredith et al. [1996]
(ERM) --- 10.3 + 1.0
Mean SD
Mahoney et al. [2000]
(LDM-m) 80 + 8 20 2.0
Mean SD
Marshall et al. [2001]
(LDM-n) 64 2 20 + 1.0
Mean SD
83
Table 4-7 Elastic constants descriptive statistics
Constant Mean SD
EL 14.2 + 5.0
ET 7.3 2.8
GLT 3.2 1.7
Figure 4-1 Bovine femur longitudinal specimen. Insets show sets of 5 indentations
with the Knoop indentation short diagonal perpendicular to the bone
longitudinal direction (upper) and with the short Knoop diagonal parallel
to the bone longitudinal direction (lower). Double-ended arrows indicate
the approximate local apparent principal material direction.
Figure 4-2 Bovine femur transverse specimen. Insets show sets of 5 indentations
with the Knoop indentation short diagonal parallel to the bone
circumferential direction (upper) and with the short Knoop diagonal
parallel to the bone radial direction (lower). The double-ended arrows
indicate the approximate apparent principal material direction.
short diagonal (brec)
obtuse angle
long diagonal (a)
Figure 4-3 A) Schematic of bone cube depicting locations and orientations of Knoop
indentations. The vertical double ended arrow indicates the longitudinal
axis of the bone. The horizontal double ended arrow indicates the bone
circumferential direction. T1 and T2 represent indentation on the
transverse plane. L1 and L2 represent indentations on the longitudinal
plane. EL indicates the direction of the longitudinal elastic modulus and
ET indicates the direction of the transverse elastic modulus. B) Schematic
of Knoop indentation residual impression.
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UNDERSTANDING MICROINDENTATION IN BONE By WESLEY M. JOHNSON A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2003
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Copyright 2003 by Wesley M. Johnson
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This document is dedicated to my father, Fredrick Martin Johnson, the best natural engineer I have ever known.
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iv ACKNOWLEDGMENTS I thank my wife Beth for the emotional and financial support she has so willingly and consistently provided. Without her confidence and love I surely would not have completed the rigorous course of study and th e research captured in this dissertation. I thank my faculty advisor and chair of my supervisory committee Dr. Andrew J. Rapoff for his confidence, guidance, and support. I thank each member of my supervisor y committee for their willing and freely given assistance: Dr. Raphael Haftka, Dr. John Mecholsky Jr ., Dr. Nicolae Critescu, and Dr. Edward Walsh. Over the past 5 years my fellow students have been very helpful in my understanding of difficult course subject ma terial and acting as sounding boards during considerations for the research detailed herein. Specifica lly I thank Jorge Zapata and Barbara Garita for their assistance and frie ndship. I thank Mr. Matt Olszta for his assistance in SEM imaging. I am also grateful for the support provided by the following organizations: Florida Foundation for Spinal Research and Disorders Medtronic Sofamor Danek Aero Chem Inc. University of Florida Department of Mechanical and Aerospace Engineering
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v “When you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind; it ma y be the beginning of knowledge, but you have scarcely, in your thoughts, advanc ed to the stage of science.” — William Thompson, Lord Kelvin. Popular Lectures and Addresses 1891-1894
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vi TABLE OF CONTENTS page ACKNOWLEDGMENTS.................................................................................................iv LIST OF TABLES...............................................................................................................x LIST OF FIGURES...........................................................................................................xi ABSTRACT.....................................................................................................................xi ii CHAPTER 1 INTRODUCTION........................................................................................................1 History........................................................................................................................ ..2 Motivation..................................................................................................................... 3 Material Property Standards..................................................................................4 Scales.....................................................................................................................4 Significance..................................................................................................................5 2 MICROINDENTATIOIN IN BONE: HARDNESS VARIATION WITH FIVE INDEPENDENT VARIABLES...................................................................................9 Introduction................................................................................................................... 9 Applied Mass.......................................................................................................11 Dwell Time..........................................................................................................11 Residence Time...................................................................................................12 Time between Indentation and Measurement......................................................12 Distance between Indentation and Pores.............................................................12 Materials and Methods...............................................................................................12 Specimens and Preparation..................................................................................12 Bovine metacarpus.......................................................................................13 Bovine femur................................................................................................13 Monkey tooth...............................................................................................14 Microindenter......................................................................................................14 Indentation Procedures........................................................................................15 Hardness variation with applied mass..........................................................15 Hardness variation with dwell time..............................................................16 Interaction effect of applied mass and dwell time........................................16 Hardness variation with residence time.......................................................16 Hardness variation with time between indentation and measurement.........17
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vii Hardness variation with distance between indentation and pores................17 Intra-observer effect.....................................................................................18 Results........................................................................................................................ .18 Hardness Variation with Applied Mass...............................................................18 Hardness Variation with Dwell Time..................................................................19 Applied Mass and Dwell Time Interaction.........................................................19 Hardness Variation with Residence Time...........................................................19 Hardness Variation with Time betw een Indentation and Measurement.............19 Hardness Variation with Distance between Indentation and Pores.....................19 Intra-observer Effect............................................................................................20 Discussion...................................................................................................................20 Hardness Variation with Applied Mass...............................................................20 Hardness Variation with Dwell Time..................................................................21 Applied Mass and Dwell Time Interaction.........................................................21 Hardness Variation with Residence Time...........................................................22 Hardness Variation with Time betw een Indentation and Measurement.............22 Hardness Variation with Distance between Indentation and Pores.....................22 Intra-observer Effect............................................................................................23 3 INVESTIGATION OF THE MICROINDENTATION RESIDUAL IMPRESSION IN BONE...........................................................................................30 Introduction.................................................................................................................30 Indentation Physical Models.......................................................................................31 Materials and Methods...............................................................................................32 Microindenter......................................................................................................32 Specimen.............................................................................................................32 Polishing.......................................................................................................32 Additional cutting.........................................................................................33 Preparation for SEM.....................................................................................33 Dry-indented specimen................................................................................33 Wet-indented specimen................................................................................34 Atomic force microscopy specimen.............................................................34 Fracture toughness confirmation specimen..................................................35 Evaluation Procedures.........................................................................................36 Scanning electron microscope......................................................................36 Elastic modulus............................................................................................36 Fracture toughness........................................................................................38 Results........................................................................................................................ .39 Cracks..................................................................................................................39 Cross-section.......................................................................................................40 Discussion...................................................................................................................41 Fracture Toughness.............................................................................................41 Recovered Material Elastic Modulus..................................................................41 Pile-up..................................................................................................................42
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viii 4 INVESTIGATION OF THE EL ASTIC RECOVERY METHOD FOR DERIVING ELASTIC MODULUS OF BONE, DENTIN, AND ENAMEL............53 Introduction.................................................................................................................53 History.................................................................................................................53 Motivation...........................................................................................................55 Methods and Materials...............................................................................................55 Adaptation of Elastic Recovery Method to Bone................................................56 Elastic Recovery Method Validation...................................................................57 Specimen Preparation and Indentation Procedures.............................................58 Glass.............................................................................................................58 Plexiglas.......................................................................................................59 Bovine femur................................................................................................59 Sensitivity evaluation of ERM equation......................................................62 Application of ERM to B one, Dentin, and Enamel.............................................62 Specimen Preparation and Indentation Procedures.............................................62 Bovine MC...................................................................................................63 Correlation method (CM).............................................................................63 Bovine foramen elastic modulus distribution...............................................63 Monkey teeth................................................................................................66 Results........................................................................................................................ .67 Elastic Recovery Method Validation...................................................................68 Elastic Recovery Meth od Equation Sensitivity...................................................68 Application of the Elastic Recovery Method......................................................69 Elastic Constants Distribution.............................................................................69 Monkey Teeth......................................................................................................70 Discussion...................................................................................................................71 Elastic Recovery Method Validation...................................................................71 Elastic Recovery Meth od Equation Sensitivity...................................................72 Application of the Elastic Recovery Method......................................................73 Elastic Constant and Principal Ma terial Direction Distribution..........................73 Monkey Teeth......................................................................................................74 Dentin...........................................................................................................74 Enamel..........................................................................................................75 5 FUTURE RESEARCH.............................................................................................100 Bovine Plexiform Bone............................................................................................100 Fracture Toughness...................................................................................................100 Microindentation Affected Region...........................................................................101 Elastic Recovery Method Constants.........................................................................101 Principal Material Direction Mapping......................................................................102 APPENDIX MODULUS ESTIMATE CALCULATION..............................................103
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ix LIST OF REFERENCES.................................................................................................108 BIOGRAPHICAL SKETCH...........................................................................................111
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x LIST OF TABLES Table page 3-1 Values for dry-indented and wet-indented cross sections........................................44 4-1 Values for ERM equation constants.........................................................................77 4-2 Sensitivity of the ERM equation..............................................................................78 4-3 ERM elastic modulus validation results...................................................................79 4-4 ERM derived elastic modulus results.......................................................................80 4-5 Comparison of edge detec tion and optical microscopy...........................................81 4-6 Comparison of ERM derive d elastic modulus results..............................................82 4-7 Elastic constants descriptive statistics......................................................................83
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xi LIST OF FIGURES Figure page 1-1 Schematic representation of bone hierarchy............................................................6 1-2 Macro and micro structures in osteonal bone..........................................................7 1-3 Schematic of monkey tooth cross section................................................................8 2-1 Microindentation machine, Mitutoyo model HM-112...........................................24 2-2 Typical microindentatio n residual impressions on bone.......................................25 2-3 A) Hardness variation with appl ied test mass in bone. B) Hardness variation with applied test mass in monkey tooth dentin.......................................26 2-5 Hardness variation with residence time.................................................................28 2-6 Hardness variation with distance...........................................................................29 3-1 Typical schematic accompanying indentation models..........................................45 3-2 Typical indentation se t for SEM investigation......................................................46 3-3 Bovine metacarpus.................................................................................................47 3-4 A) Knoop residual impression arra y line B) Cross section of Knoop microindentation short diagonal............................................................................48 3-5 A) Knoop residual impression area. B) Cross section of the indentation.............49 3-6 Linear crack at the apex of th e indentation residual impression............................50 3-7 Typical Knoop indentations in the fracture toughness confirmation specimen.....51 3-8 Plot of applied mass (Load) with crack length......................................................52 4-1 Bovine femur longitudinal specimen.....................................................................84 4-2 Bovine femur transverse specimen........................................................................85 4-4 Normalized sensitivity plots of the ERM equation variables................................87
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xii 4-5 Bovine MC dist al dorsal specimen........................................................................88 4-6 A) Knoop indentation sets B) Sche matic of indentation short diagonal...............89 4-7 Vickers microindentations in bovine ri ght MC distal dorsal foramen midline.....90 4-8 Monkey right side first molar and mandible..........................................................91 4-9 A) Buccolingual partial cross section of left side first monkey molar. B) Buccolingual partial cross section of right side first monkey molar.....................92 4-10 Left image Indentation pattern on po sterior aspect of right first molar. Right image Well-defined indentations in posterior aspect of right first molar......................................................................................................................93 4-11 Elastic Recovery Method validation plot...............................................................94 4-12 ERM based derived elastic cons tants variation with distance...............................95 4-13 Coordinate rotation angl e variation with distance.................................................96 4-14 Correlation Method derived elastic modulus variation with distance...................97 4-15 ERM derived longitudinal elastic mo dulus and CM derived elastic modulus.......98 4-16 Schematic of tooth enamel prism tube orientation................................................99
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xiii Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy UNDERSTANDING MICROINDENTATION IN BONE By Wesley M. Johnson May, 2003 Chair: Andrew J. Rapoff Department: Biomedical Engineering The objective of my research was to impr ove understanding of microindentation in bone. Pursuit of that objective required that I: investigate the capability and limitations of a microindentation tool; investigate the t ool effect on the bone surface; and apply the tool to derive hardness and elastic moduli of bone using the elastic recovery method (ERM). Microindentation hardness results were found to be sensitiv e to selection of applied mass on the tool. The previous value of minimum applied mass for bone (0.05 kg) was found to be too low and was replaced with a new value (0.1 kg). Observation of the post indentation a ffected region on the bone surface found differential elastic recovery between wet-inde nted and dry-indented specimens. Using a simple series spring model, an estimate of the wet-indented recovered material elastic modulus resulted in a value of about 1 GPa. Additionally, an estimate was made of bone fracture toughness using a novel method through scanning electron microscopy.
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xiv The ERM, for deriving elastic modulus was adapted from the materials' community for its first use in bone. It wa s applied, with a coor dinate transformation process, to map elastic moduli and principa l material direction along the mediolateral midline of a natural hole (foramen) in bone The ERM based process detected the cortical to trabecular bone transition z one in the specimen. ERM based longitudinal elastic modulus results, over the initial distance from the foramen edge, compared favorably with correlation method (CM) derived elastic modulus map.
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1 CHAPTER 1 INTRODUCTION Designers of prostheses interfaced to bone rely on fundamental findings from bone research. Information about bone mechanical properties and their temporal and spatial variations govern prostheses material a nd fixation selection [McKoy 2000, pg 440]. One important aspect of bone research is the effect of the prostheses on bone. Microindentation is an experi mental tool for interrogati ng material properties on the surface of bone where it contacts a prostheses. The objective of my work was to investigat e microindentation as a tool to derive material properties of bone. During the inves tigation I explored a variety of materials in addition to bone. Investigation of the othe r materials was done to assess the accuracy, precision and usefulness of the elastic recovery method for de rivation of elastic modulus. These materials were: glass; Plexiglas; and the dentin and enamel of monkey teeth. Pursuit of my objective required investig ation of the microindentation tool; the microindentation tool effect on the b one; and microindentation techniques. Microindentation is the action of forming an impression in a surface at the micro (10-6 m) scale. That action uses a tool that applies a known load to a specimen through a specific shaped point. The process leaves a re sidual impression in the material specimen. Length dimensions of the residual microi ndentation impression in bone, dentin, and enamel, about 20 to 200 m, are measured through a microscope. The measurements are used to derive specimen properties of har dness, elastic modulus, and fracture toughness.
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2 Hardness is defined as resistance to penetr ation and is derived by dividing applied load by the projected area of the residual impression. Hardne ss units are typically given in kg/mm2. I have found typical values for bone to be about 45 kg/mm2. Elastic modulus is the ratio of stress to strain in the linear region of the stress-strain curve. Elastic modulus has units of Pascals, typically giga-Pascals (GPa) for bone. A typical value for cortical bone is 20 GPa [Guo 2001, p. 10-7]. Fracture toughness is the resistance of a brittle material to sudden failure It can also be thought of as resistance to crack growth. Fracture toughness is derived from length meas urements of cracks as sociated with the residual impression. The derivation uses the derived quantities of hardness and modulus in empirical relationships. Fracture to ughness units are typically given in MPa/m1/2. A typical value for cortical bone is 2 MPa/m1/2 [Akkus et al. 2000]. History Microindentation was first used in the 1920s [Amprino 1958]. Amprino [1958] investigated bone hardness va riation with applied microi ndentation load and found no correlation. He also investigated hardne ss anisotropy and found no correlation between the relative orientation of the indenter point and the gr ain of the specimen. Those findings have been subsequently shown not to be accurate by Ramrakhiani et al. [1979], Riches et al. [1997], and my work. Microindentation methods continued to be developed and expanded. During the 1970s and 1980s microindentati on was used mostly to derive bone hardness. In that period c onsiderations of c ontact mechanics led to an indentation method for measuring elastic modulus. L oubet et al. [1984] ad apted SneddonÂ’s [1965] load and penetration flat ended cylindrical punch solution to the pyramidal Vickers indenter point. Their treatment equated the Vi ckers projected contact area with the flat
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3 punch area. The resulting equation describes th e analytical relationship between load and indenter penetration depth. The equation was differentiated with respect to penetration depth and solved for reduced elastic modulus That approach was a major step in extending microindentation from hardness to elastic modulus measurement. I call the method the load and displacement method (LDM). In 1990 Currey et al. [1990] correlated mi croindentation hard ness with elastic modulus. Their method involved deriving har dness from a range of different bone types from different species. They then performed macro uniaxial te nsion tests to derive elastic modulus. Plotting hardness against elastic modulus, they found a correlation by linear regression. I call this met hod the correlation method (CM). Microindentation based derivation of el astic modulus, using only the residual impression dimensions, has been mostly used in ceramics and polymer research [Lawn et al. 1980, Amitay-Sadovsky and Wagner 1998]. The me thod has also been used in dental [Meredith et al. 1996] and pharmaceutical research [Lum and Duncan-Hewitt 1996]. However, it had not been used in bone. The method uses the post indentation residual impression dimensions and indenter point geom etry. I describe the method in detail in Chapter 4. I call that method the elastic recovery method (ERM). Microindentation has been used to derive fracture toughness of ceramics and tooth enamel [Lawn et al. 1980, Xu et al. 1998]. It also had not been used in bone. Motivation Hard biologic materials, like bone, dentin and tooth enamel, present challenges in determination of their material properties. One challenge is no universal material property standards exist for bone, dentin, or en amel. A second challenge is that biologic material property derivations are performed at a variety of scales.
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4 Material Property Standards Material standards allow investigators to determine the accuracy and precision of their results. Materials like ceramics, plastics, and crystals have sta ndard values for their material properties. Bone, dentin, and enamel on the other hand do not have such standards. In determining whether a given se t of bone hardness or elastic modulus results are correct, reference must be made to publishe d results from other researchers. Such a situation is less than completely satisfying. However, an accepted set of hardness and elastic modulus values for sp ecific types of bone currently exists in avai lable handbooks [Huja 2000, p. 248; Guo 2001, p.10-7]. Handbooks also contain research results th at are not accurate. Bone researchers who rely on the incorrect info rmation can report results th at may not be reproducible. Scales Bone, dentin, and enamel are hierarchical st ructures (Figures 1-1, 1-2, 1-3). Scales include: the macro scale of whole bones and teeth which is of several millimeters or larger; the micro scale of osteons which is of hundredths of a millimeter; and the nano scale of collagen fibers, fibrils, and mineral crystals of thousandths of a millimeter. Selection of the scale for investigation is im portant because it is over that scale that measurement results are averaged or homoge nized. Microindentation homogenizes over surface dimensions of about 200 m and indentation depth of about 6 m. I have shown in Chapter 2 that the affected region around th e indentation site in bone extends no more than about 35 m from the edge of the residual impression. In specimens where the spatial variations of bone mi crostructure is close to th at of the residual impression homogenization breaks down because the measur ed length reflects a single constituent.
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5 Significance The results of my research are significant because: I provide bone researchers who use mi croindentation, a new value for minimum applied mass. The new value helps ensure reproducibility of results among researchers. I provide bone researchers with new expe rimental evidence that bone does not pile up at the edges of the indent ation residual impression. This new evidence enhances confidence that bone is a material that exhi bits strain hardening behavior. It also corrects the misinformation that bone exhibi ts pile-up as has been used in bone research. I provide prostheses designers with new information about the material in the indentation affected region. Specifically, I report an elastic modulus of about 1 GPa for bovine femur indentation recovered material. That value is more than a factor of 10 less than the well-accepted average value of 16 GPa for bovine femur [Guo 2001, p. 10-7]. I provide bone researchers with new info rmation on limitations and use of the ERM for deriving elastic modulus. Specificall y, I report that ER M derived elastic modulus is not completely accurate for bone or dentin but is accurate for tooth enamel, glass, and Plexiglas. I demonstrate that ERM can be used for relative comparisons exploring bone, dentin, a nd enamel elastic anisotropy. I also demonstrate use of the ERM, combined with edge detection image processing and a coordinate transformation pr ocess, to map elastic modu li distribution and principal material directions in the vici nity of a bone nutrient foramen. I report an average fracture toughness of 0.22 1 2MPa/m 0.03 (mean SD) for the material in the indentation affected re gion on bone that has been processed for scanning electron microscopy. The publishe d mean value for unprocessed bone is 2.4 1 2MPa/m 0.7 (mean SD) [Akkus et al. 2000]. By determining the fracture toughness of the material in the microindent ation affected region, I have established the foundation for future work on a more simple method of determining bone fracture toughness. Such a method could save other researchers' resources.
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6 Figure 1-1 Schematic representation of bone hierarchy. Taken from: Rho JY, KuhnSpearing L, Zioupos P. Mechanical propert ies and the hierarch ical structure of bone. Medical Engineering and Physics 1998. IPEM 1998
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7 Figure 1-2 Macro and micro structures in os teonal bone. Elaine N. Marieb. Human Anatomy and Physiology. Benjamin /Cummings Scien ce Publishing. 1998
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8 Figure 1-3 Schematic of monkey tooth cross se ction showing the macro and micro scale. Tooth is approximately 2 cm in length. Dentine tubules are approximately 1 m in diameter. Enamel tubes, approximately 5 m diameter, begin at the dentoenamel junction and end at the occlus al (biting) surface. E = enamel, D = dentin, P = pulp cavity. dentin tubules enamel rods dentoenamel junction P D E
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9 CHAPTER 2 MICROINDENTATION IN BONE: HARDNESS VARIATION WITH FIVE INDEPENDENT VARIABLES Introduction The objective of the research described in this chapter was to investigate the microindentation tool. Indentati on at the micro scale is an ofte n used and effective tool in materials research [Amitay-Sadovsky a nd Wagner 1998, Lawn et al. 1980, Lum and Duncan –Hewitt 1996, Marshall et al. 1982]. It is used to derive various material properties including hard ness, elastic modulus, and fractur e toughness. More specifically indentation has become a method of choice fo r deriving the hardness and elastic modulus of bone and other hard tissue like tooth dentin and enamel [Currey et al. 1990, Meredith 1996, Xu 1998]. Bone hardness and elastic modulus are directly related to the microstructure and composition of the material at the indentation site [Currey et al. 1990]. Bone is an anisotropic and inhom ogeneous composite at the micro and nano scale. The degree of anisotropy can vary and has been described as transversely isotropic or orthotropic [Cowin 2001 p. 6-12 to 6-19] The constituents at the nano and micro scales are hard calcium mineral crystals and a softer collagen matrix. While there are observable macro, micro, and nano structures, estimation of ma terial properties is far from straightforward and requires a range of tools to elicit the bone properties at the different scales. The research reported in this chapter re visits microindentation as a method of determining hardness. Hardness measuremen ts are carried out with an indentation
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10 machine (Figure 2-1). The fundamental pr ocess involves automatic placement of a discretely selectable mass on th e upper end of a pointed stylus The point that contacts the specimen can be spherical or pyramida l depending on the application. The mass is applied to the specimen through the stylus for a predetermined duration (dwell time), then automatically removed. The dimensions of the residual impression are then measured and used to derive hardness at the indentati on site. Customary units of hardness are mass per unit projected area, typically given as kg/mm2. As part of my ongoing work with bovine bone, specifically the bovine metacarpus (MC), I questioned the effect microindentation independent variables had on hardness results. The question came up because I was concerned whether the current de facto standard for applied mass [Huja et al. 2000 p. 252, Ramrakhiani et al. 1979, Riches et al. 1997] was appropriate for my fresh wet speci men. Ramrakhiani et al. [1979] used dry, embalmed human bone. In addition to hardness variation with app lied mass, I chose to investigate hardness variation with the following four microindent ation independent vari ables: dwell time; residence time on the instrument stage out of liquid; duration of tim e between indentation and residual impression measurement; and di stance between the indentation site and pores. I also investigated the interaction effect on har dness of applied test mass and dwell time. These two parameters are inde pendently selectable on the microindentation machine. Additionally, I performed an assessment of the intra-observer effect. Such an assessment was needed to evaluate the variabil ity and precision of my (observer) residual impression dimension measurements.
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11 Choice of appropriate values for the inde pendent microindentati on variables is of importance in assuring reproducibility and m easurement precision. Differences between sets of measurements on the same specimen could be caused by time domain phenomena such as creep and relaxation. Differences between sets of measurement on the same specimen could also arise from the spatial domain due to pores. Testing machine setup, calibration, and compliance (which can vary be tween indentation machines) is significant at low applied mass values [Vander Voort and Lucas 1998]. Testing machine compliance acts in series with the specimen compliance. If the machine compliance is relatively low it can add to the compliance of the specimen producing a measurement error. In my case these variables were not adjustable once the machine had been set up. Only those variables over which I had contro l were chosen for investigation. Applied Mass Previous studies on bone showed no vari ation of hardness with applied load, [Amprino 1958] yet a later study found a value of applied test mass (0.05 kg) below which hardness measurements were not relia ble [Ramrakhiani et al. 1979]. The later value had acquired the status of a de facto standard through handbook reference [Huja et al. 2000 p. 252] and use by other bone researchers [Riches et al. 1997]. Dwell Time Due to the creep phenomenon, the duration of time the indenter point is applied to the specimen, dwell time, could affect re sidual impression measurement results. Dwell time of the microindentation machine used in my research is adjustable by the operator between 5 and 99 seconds.
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12 Residence Time Because of my interest in wet specimens, the duration of time the specimen spends out of the water-based liquid, or residen ce time on the microindenter stage, was important. The duration of time out of the storage liquid could affect the residual impression measurements because the speci men was drying out. Rho and Pharr [1999] reported increased hardness with time out of liquid. Time between Indentation and Measurement Indentation site material relaxation, betw een the time the indentation impression is made and when it is measured, could also a ffect the measurement of residual impression dimensions. I was particularly concerned about the relaxation effect because my specimens were wet. I thought that the co llagen component of bone would relax more wet than dry. Collagen behaves somewhat lik e a sponge, when wet it recovers more than when dry. Distance between Indentation and Pores The distance between the indentati on residual impression and nearby pores, predominately Haversian and VolkmannÂ’s canals, could affect results because material properties change spatially in the vicinity of pores. Materials and Methods Specimens and Preparation The specimens described in this section were used for investigation of the effect on hardness of microindentation independent variables. Sp ecimens used were: a right bovine metacarpus (MC); a right bovine femur; and a right first molar from a monkey (M acaca fascicularis ). The array of specimens were available to me and presented a range of hard biological materi al for assessment of their ha rdness variation with one or
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13 more of my chosen microindentation independe nt variables. All procedures involving animal tissue use were conducte d under the approval and ausp ices of the Institutional Animal Care and Use Committee. Bovine metacarpus One specimen from a previously fresh fr ozen bovine right MC was rough cut twice with a 10" band saw (Delta Machinery; J ackson, TN) across the distal diaphysis to produce a ring of bone approximately 30 mm in length. Additional fine cuts were made (Low speed saw; Buehler; Lake Bluff, IL) l ongitudinally along the distal dorsal aspect. The specimen was approximately 25 mm by 45 mm by 1 mm thick with the long dimension parallel to the bone long axis. The length and width dimensions were dictated by the polishing system capability. The sp ecimen was polished after cutting, using a semi-automated polishing system (Minimet 1000, Buehler, Lake Bluff, IL). Polishing started with 6 m diamond slurry and finished with 0.05 m alumina and colloidal silica suspension. After polishing a transverse cut was made to produce a specimen approximately 25 mm by 10 mm by 1 mm th ick. The bovine MC was supplied by the University of Florida College of Veterina ry Medicine from a donor of unknown age and sex whose death was unrelated to this study. Bovine femur A specimen from a previously fresh frozen bovine right femur (Animal Technologies Inc., Tyler Texas) was rough cut twice with a 10" band saw (Delta Machinery; Jackson, TN) across the mid diaphysis to produce a ring of bone approximately 30 mm in length. Subsequent longitudinal cuts were made (Low speed saw; Buehler; Lake Bluff, IL) to produ ce a specimen approximately 25 mm by 25 mm by 1 mm thick. The specimen was polished in the same manner as th e bovine MC specimen.
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14 Monkey tooth A tooth and accompanying mandible from a small monkey (M acaca fascicularis ) were cut (Low speed saw; Buehler; Lake Blu ff, IL) in the buccolingual plane on the right side, between the premolar and the first mo lar. An additional cut was made on the centerline of the first molar also in the bucco lingual plane. The cuts produced a tooth cross section specimen approximately 2 mm thick. After cutting the specimen was manually polished using the same polishing se quence as the bovine specimens. The monkey tooth specimen was only used for de termination of hardness variation with applied mass. Microindenter A microindenter (Model HM-112, Mitutoyo, Ja pan) fitted with a Vickers indenter point was used for measuring: hardness vari ation with applied ma ss; hardness variation with dwell time; and hardness variation with residence time out of solution on the bovine metacarpal specimen. That indenter point was chosen because previous research by others [Ramrakhiani et al. 1979] used the Vi ckers indenter point and its use provided a basis for results comparison. A Knoop i ndenter point was chosen for all other investigations of hardness va riation with microindentation independent variables on the bovine femur and monkey tooth specimens. I chose the Knoop indenter point because it allows investigation of hardness [Riches et al. 1997] and elastic modulus anisotropy [Rapoff et al. 2003]. The Vickers and Knoop indenter points ar e both four-sided pyramids. The significant difference is that the Vickers point is a regular pyramid with equal diagonals and the Knoop point has diagonals of two differe nt lengths (Figure 2-2). The ratio of the Knoop two different diagonals is 7.114 to 1 [Mitutoyo 1998]. Both indenter points
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15 exhibit sensitivity to elastic anisotropy but the Knoop indenter point is much more sensitive than the Vickers [Riches et al. 1997] The increased sensitivity is due to the ratio of diagonals and the corresponding apex angles. The long Knoop diagonal has an acute angle at its ends while the short diagona l angles are obtuse. During indentation the long diagonal does not change its length [Amitay-Sadovsky and Wagner 1998, Riester et al. 2001] when the indenter point is remove d from the specimen. However, the short diagonal acts to spread or push the material away from the apex. That dimension does change when the indenter point is removed. In fact the degree to which the residual impression dimension departs from the actual point dimension can be used as a measure of the indentation site material elastic modulus [Marshall et al. 1982, Amitay-Sadovsky and Wagner 1998, Meredith et al. 1996, Lum and Duncan-Hewitt 1996]. Indentation Procedures Hardness variation with applied mass A series of five indentations was made on the wet bovine MC specimen for each of five available masses (0.01 kg, 0.025 kg, 0.05 kg, 0.1 kg, 0.2 kg). A set of 3 indentations was made in monkey tooth dentin at the same five available masses. The indentations in the bovine MC were made with the Vickers indenter point while the indentations in monkey dentin were made with the Knoop indent er point. An arbitr arily selected dwell time of 10 s was used for the indentations. The interaction of applied mass and dwell time was subsequently investigated and 10 s was found to be acceptable. I monitored the time out of solution for each specimen to assu re it did not exceed 30 minutes. I held the time between indentation and residual impre ssion measurement to less than 20 s for all indentations. I also insured that each indentation was at least 100 m from pores and previous indentations.
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16 Hardness variation with dwell time One set of 5 indentations with the Vickers indenter point, at 5 dwell times (5 s, 10s, 15 s, 20 s, 30 s), was made in the bovine MC. An additional set of 5 indentations with the Knoop indentation point each at 4 dwell times (5 s, 10 s, 15 s, 30 s) were also made in bovine MC. The Knoop indenter point long diagonal was oriented parallel to the specimen longitudinal direction. I compared the 5 sets of Vickers hardness with the analysis of variation (ANOVA) procedure as well as the 4 sets of Knoop hardness results. For all the indentation sets I used an indentation applied mass of 0.1 kg. I monitored the time out of solution to assure it did not exceed 30 minutes. I held the time between indentation and residual impression measurement to less than 20 s for all indentations. I also insured that each indentation was at least 100 m from pores and previous indentations. Interaction effect of ap plied mass and dwell time A series of sixty indentations were made in the longitudinal aspect of bovine femur. They were made with the Knoop indenter po int short diagonal pa rallel to the bone longitudinal direction. Applied masses of 0.01 kg, 0.05 kg, 0.1 kg, 0.2 kg, 0.3 kg and dwell times of 5 s, 10 s, 20 s, 40 s were used. An ANOVA procedure was performed on the resulting interaction data and then ScheffeÂ’s a posteriori test was preformed (Statview, SAS Institute, Cary, NC). Hardness variation with residence time Seven sets of five indentations each were made in the longitudinal aspect of bovine femur. I recorded the time each indentat ion was made over a period of 1.75 hours. I made the 5 residual impression measurements approximately every 15 minutes during the period. The indentations were made with the Vickers indenter point. I used an applied
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17 mass of 0.1 kg and a dwell time of 10 s. I also assured that th e distance between the indentations and pores and othe r indentations was at least 10 0 m. I compared all 7 sets with the ANOVA procedure. After the residence time tests the specimen was allowed to equilibrate with the laboratory environment for 47 hours. After 47 hours I made five additional Vickers indentations and recorded derived hardness. The mean hardness of the previous 35 indentations was compared with the mean ha rdness of the 5 indentations performed after 47 hours using the ANOVA procedure. Hardness variation with time between indentation and measurement One indentation was made in bovine MC with the Knoop i ndenter point long diagonal perpendicular to the specimen long axis. The specimen was maintained in a bath surrounded by water solution. Based on re sults from hardness variation with applied mass and hardness variation with dwell time, I used an applied mass of 0.1 kg and a dwell time of 10 s. I also assured that th e distance between the indentations and pores and other indentations was at least 100 m. I repeatedly measured the indentation star ting 5 minutes after th e indentation event and repeated the measurement about every 15 minutes 3 additional times. The total elapsed time between making the indentati on and measuring it the last time was 57 minutes. I selected about 60 minutes because I did not expect measurements of subsequent indentation sets to require more time. Hardness variation with distance between indentation and pores A series of 176 indentations were made on the bovine MC with the Knoop indenter point short diagonal perpendicular to the bone longitudinal axis. The indentations were made on the bovine bone in a regular pattern w ithout regard to the location of pores. The
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18 pattern consisted of 8 equally spaced rows of 22 equally spaced indentations each. The spacing between the rows, measured between the center of adjacent indentations, was 240 m. The spacing between indentations, m easured between the center of neighboring indentations, was 110 m. The distance between the center of the inde ntation and the edge of the closest pore was recorded for each indentation. The deri ved hardness and measured distance from the indentations were plotted a nd analyzed with commercially available software (Excel, Microsoft Corporation, Redmond, WA). Intra-observer effect One indentation was made in the longit udinal bovine femur specimen with the Knoop indenter point long diagona l perpendicular to the specimen long axis. I measured the indentation residual impression 5 times during a 5 minute period. Results Hardness Variation with Applied Mass Hardness variation with applied mass and data variability was greatest at a low value (0.01 kg) of applied mass for both spec imens. I found hardness decreasing with increasing applied mass. The hardness and applied mass curves for both specimens reach a reasonably stable value at different applied masses (Fig ure 2-3). Range bars on the figures were computed by taking the absolute value of the difference between the mean and the greatest and least value. An ANOVA for both specimen data sets re sulted in statistical significance (p<0.05) between hardness results at 0.01 kg and other results. However, I found no statistical significance (p > 0.05) between derived hardness values at 0.05 kg and higher for bovine bone and 0.025 kg and higher for the monkey dentin.
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19 Hardness Variation with Dwell Time Hardness variation with dwell time up to 30 seconds is not significant (ANOVA p > 0.05) for either the Vickers or the Knoop indenter poin ts (Figure 2-4). Applied Mass and Dwell Time Interaction There was a significant difference in the applied mass by dwell time interaction (p < 0.05). Subsequent multiple comparison using ScheffeÂ’s a posteriori test showed that the significance was limited to applied mass of 0.01. All ot her interactions were not significant at the 0.05 level. Hardness Variation with Residence Time The duration of time the specimen was out of the solution was not significant (Figure 2-5). One-way ANOVA results between the first data set taken at about 5 minutes after indentation and the last data set taken at about 1.6 hours later were not significant (p>0.05). The mean derived hardness of the specime n after 47 hours out of solution was 9% greater than that measured within 1.75 hours. The mean derived hardness was 48.8 kg/mm2 with a standard deviation 1.5. On e way ANOVA results were significant between the 2 hour hardness results a nd the hardness at 47 hours (p<0.05). Hardness Variation with Time between Indentation and Measurement The mean derived hardness was 42.7 kg/mm2 with a standard deviation of 0.3. Hardness Variation with Distance between Indentation and Pores Microindentation distance between the cente r of the indentation and the edge of a pore shows an effect at a distance of 73 m and below (Figure 2-6). Two linear regression lines were constructed to form a bi-linear plot. The lines reached the same value at 73 m. I fit a bi -linear function to the data. That function is:
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20 K0D73m:H0.15D28.4; KD73m:H39.5, where D = distance between the center of the subject indentation a nd the edge of a pore expressed in m; HK = Knoop hardness expressed in kg/mm2. Intra-observer Effect The hardness mean was 51.5 kg/mm2 with a standard deviation of 0.5. Discussion Hardness Variation with Applied Mass My results had some similarity to prev ious work by Ramrakhiani et al. [1979] although my results were markedly different. The similarity was that the curves leveled off at intermediate loads (Figure 2.3 A). The difference was that the previous work reported increasing hardness with applied ma ss while I report decr easing hardness with increasing applied mass. The other most st riking observation was that one set of Ramrakhiani et al. [1979] results did not s upport their own conclusion (Figure 2-3 A). Inclusion of that data would have sugges ted a minimum applied mass value above about 0.7 kg. The excluded data was from a non silv er plated specimen. Their conclusion was based on only silver plated specimens. For bovine MC hardness results were not si gnificantly different at applied mass of about 0.05 kg and above. The hardness results for the monkey tooth dentin were not significantly different at applied mass of about 0.025 kg and above. Those results suggests that for my Mitutoyo microindenter the applied mass values for bovine bone could be as low as 0.05 kg for bovine and 0.025 kg for monkey dentin. However, taking Ramrakhiani et al. [1979] data into consid eration a higher minimum applied mass seems appropriate. Hypothetically, if I used a mi nimum applied mass of 0.05 kg for indentation of wet bovine bone, Ramrakhiani and colleagues would not be able to reproduce the test.
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21 An additional consideration is the size of the indentation residual impression for measurement. One of the advantages of mi croindentation is the ability to interrogate small regions. The residual impression also needs to be large enough to measure with precision. At low applied mass (0.01 kg) the long diagonal in a Knoop residual impression is about 50 m. At an applie d mass of 0.05 kg the residual impression long diagonal is about 140 m. While at an in termediate applied mass of 0.1 kg, the long diagonal is about 200 m. Applied mass select ion is governed by: the size of the region of interest; the size of the re sidual impression; and the variat ion of hardness with applied mass. I conclude that a minimum applied mass of 0.1 kg is appropriate for bovine bone in order to assure reproducible results am ong different microindentation machines. Furthermore, noting the difference in hardne ss results between bovine specimen and the monkey dentin I have also concluded that a hardness variation with applied mass study be performed for each new material being tested. Hardness Variation with Dwell Time Dwell time from 5 s up to a limit of 60 s does not have statistical significance. I have adopted 10 s as my typical dwe ll time in my subsequent research. Applied Mass and Dwell Time Interaction Significant interaction between applied mass and dwell time was limited to applied mass of 0.01 kg. Results from the hardness va riation with applied mass suggested that use of applied mass of 0.01 kg is not appropria te. The interaction results confirm that finding. Based on the interaction result I chose not to investigate interactions between the other microindentation variables. The only variability in any of the microindentation
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22 independent variables is in de rived hardness variation with applied mass. As long as the minimum applied is greater than 0.05 kg for bone and 0.025 kg for dentin, there can be little interaction between variables. Hardness Variation with Residence Time Derived hardness values did not significantly change w ith residence time out of solution up to 1.75 hours. That result provide d confidence that handling specimens out of the water solution could be done for periods up to 1.75 hours. The result is important because microindentation methods, such as the ERM for deriving elastic modulus, require time to process. Subsequent to th e finding I have adopted a maximum time of 30 minutes out of water solution for similar bone specimens in my subsequent work. A 9 % increase in hardness values after 47 hours was similar to values obtained by Rho and Pharr [1999]. They used nanoindent ation on bovine femur and reported results on a much finer scale than I used. Th ey reported a 12.2 % hardness increase for interstitial lamellae and 17.6 % in crease for osteonal lamellae. Their specimen had been dried for 14 days while mine was dried for 2 days. Hardness Variation with Time between Indentation and Measurement Because there was no significant difference in derived hardness with the time between when the indentation was made a nd the long diagonal was measured, up to 30 minutes, I have arbitrarily chos en 10 minutes as a standard. Hardness Variation with Distance between Indentation and Pores Distance between the center of the subject indentation residual impression and the edge of pores is significant with an ef fect at distances cl oser than about 70 m. In my subsequent microindentation work I have adopted the value of 100 m between the indentation center point and th e closest pore edge or any neighboring indentation edge.
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23 Intra-observer Effect The results provided confidence in my ability to make repeated measurements with precision.
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24 Figure 2-1 Microindentation m achine, Mitutoyo model HM-112. specimen stage mass selection knob eyepiece
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25 Figure 2-2 Typical microinde ntation residual impressions on bone (Vickers on left, Knoop on right). 70 m 100 m
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26 Figure 2-3 A) Hardness variation with applied test mass in bone. Shown are Ramrakhiani et al.[1979] data from dr y embalmed human rib (plotted from their tabular data), solid line (triangles); a nd my data from wet bovine metacarpus, dashed line (open circles). Range bars are also shown for my data. A Vickers indenter point was used for all inde ntations. B) Hardness variation with applied test mass in monkey tooth dentin. A Knoop indenter point was used for the microindentations. 0 20 40 60 80 00.050.10.150.2Mass (kg)HV (kg/mm2) 0 20 40 60 80 00.050.10.150.2Mass (kg)HK (kg/mm2) A B
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27 Figure 2-4 A) Hardness variation with dwell time in wet bovine metacarpus showing average values and range of results Knoop microindentation point. B) Hardness variation with dwell time in wet bovine metacarpus showing average values and range of resu lts, Vickers microindentation point. 0 20 40 60 0102030 Dwell time (s)HK (kg/mm2) 0 20 40 60 0102030 Dwell time (s)HV (kg/mm2) B A
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28 Figure 2-5 Hardness variati on with residence time (time out of solution) for bovine metacarpus, Vickers microindentation point. Shown are the average values and ranges for each data set. 0 20 40 60 00.511.52 Time (hrs)HV (kg/mm2) Figure 3 – Vickers hardness variation with time out of solution. 0 20 40 60 00.511.52 Time (hrs)HV (kg/mm2)
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29 Figure 2-6 Hardness variati on with distance measured be tween the center of the microindentation and the edge of pores on wet bovine metacarpus. Bi-linear plot lines have a common value at 73 m. Bi-linear function described by the dotted lines is: K0D73m:H0.15D28.4 ; KD73m:H39.5 0 20 40 60 050100150 Distance (m)HK (kg/mm2)
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30 CHAPTER 3 INVESTIGATION OF THE MICROINDENT ATION RESIDUAL IMPRESSION IN BONE Introduction The objective of the work described in this chapter was to investigate the interaction between the microi ndentation tool and the materi al bone. The specific aim of this research was to describe the cross-sec tional profile of the mi croindentation residual impression both physically and materially. I used scanning electron microscopy (SEM) and atomic force microscopy (AFM) images from both wet –indented and dry-indented bone specimens in the work. I used length and angle measurements fr om wet-indented microindentation residual impression cross sections, from the SEM images to model and derive elastic modulus of the material in the residual impression. The value was lower than published values for bone. I also used measurements of residual impression apex crack length, from the SEM images, to derive a fracture toughness value of the vacuum dried bone. The value was lower than that reported by other researcher s for wet bone. I used AFM to search for cracks in wet and dry bone that had not been prepared for and subjected to SEM. I found no cracks. From the SEM images I observed no materi al pile up in the residual impression cross sections. Absence of pile up is an expected behavior for brittle material as described by Marx and Balke [1997] a nd Cheng and Cheng [1998]. Previous investigations by Ramrakhiani et al. [1979] reported pile up in dry embalmed human
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31 bone that could not have existed. That repo rt continues to be used in bone research [Riches et al. 1997]. The work described in this chapter was mo tivated by my desire to experimentally determine whether the physical descriptions of indentation models accurately reflect the residual impression in bone. I was also mo tivated by the desire to provide material property information to other bone re searchers and prostheses designers. Indentation Physical Models Physical models of the residual impressi ons of micro and nano indentations in ceramics, metals, and polymers have been developed. Researchers describing these models typically include a sche matic (Figure 3-1) of the in dentation cross section [Cheng and Cheng 1998; Dorner and Nix 1986; Marx and Balke 1997; Oliver and Pharr 1992]. In the schematic a residual impression is shown with an apex angle larger than that of the indenter tip. The schematic may include a z one of pile-up at th e residual impression edge. In their schematic Marx and Balke [1997] depict a zone of pile-up for ductile material and a zone of no pile-up for brittle material; Cheng and Cheng [1998] depict a zone of material pile-up at the edge of th e impression; while Dorner and Nix [1986] and Oliver and Pharr [1992] do not depict pile-up. In such schematics, and the model discussi ons that accompany them, the indenter is depicted with a more acute angle than the re sidual impression. Such a model assumes the area of contact between the i ndenter point and the specimen becomes less as the indenter point is withdrawn. The contact area diminishes from initial full contact to only the very tip during unloading.
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32 Materials and Methods Microindenter A microindenter (Model HM-112, Mitutoyo Corporation, Japan) fitted with a Knoop indenter point was used for all inde ntations. The Knoop indenter point was chosen because it allows inve stigation of hardness and elas tic anisotropy [Riches et al. 1997, Riester et al. 2000] and I used it in my other investigations. The Knoop indenter point is a four sided pyramid with a long dia gonal and a short diagonal. The aspect ratio of diagonals is 7.114 [Mitutoyo 1998]. When an indentation residual impression is observed it is an inverted pyramid with 2 diagonals one longer than the other (Figure 32). Specimen One bovine right metacarpus (MC) was obt ained from the University of Florida College of Veterinary Medi cine from a donor of unknown ag e and sex whose death was unrelated to this study. After 2 transver se cuts with a 10 inch band saw (Delta Machinery, Jackson, MS), the bone was long itudinally sectioned (Isomet Low Speed Saw, Buehler, Lake Bluff, IL) from the di stal dorsal aspect to produce a 1 mm thick by 25 mm wide by 45 mm long l ongitudinal slab (Figure 3-3). The specimen size was controlled by the polishing system capabilities. All procedures involving animal tissu e use were approved by the Institutional Animal Care and Use Committee. Polishing The most periosteal surface of the specimen slab, which was about 2 mm below the periosteal surface, was polished in a progressive manner beginning with 6m diamond
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33 slurry and final polish with 0.05 m alumina suspension (Minimet 1000, Buehler, Lake Bluff, IL). Additional cutting Additional low speed saw cuts were made in the most proximal region of the specimen slab. The cuts produced 2 pieces approximately one millimeter thick by 1 mm wide by 25 mm long. The specimens were dr ied in equilibrium with the laboratory environment and indented with the Knoop inde nter short diagonal parallel to the bone longitudinal axis in an ordered array (Figure 3-2 A). I used an applied mass of 0.1 kg and dwell time of 10 s. A wet specimen, taken from the same bone region, was cut with a low speed saw to produce a specimen approximately 5 mm square by 1 mm thick. The specimen was indented with the Knoop indenter short dia gonal perpendicular to the bone longitudinal axis in ordered arrays (Figure 3-2 B). I used an applied mass of 0.1 kg applied mass and 10 s dwell time. Ordered indentation arrays were used b ecause I did not have precise control over subsequent cutting to obtain indent ation short diagonal cross sections. Preparation for SEM Dry-indented specimen In order to expose the cross-se ction of the residual impressi on, in a plane parallel to the short Knoop indentation axis, each speci men piece was further divided to produce a total of four pieces. One piece was manually fr actured and the other sectioned with a low speed saw. The 4 specimens were imaged in an optical microscope and two of the pieces containing observable residual impressions we re selected. The two selected specimens were vacuum sputter coated with gold a nd imaged with SEM (JEOL 6400, Japan) using
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34 15 kV excitation. Only the fractured speci men had a residual impression with an unobstructed view of the cross-section at the mi d point of the long diagonal (Figure 3-4). That indentation was used in subsequent ev aluations. The sectioned specimen residual impression cross-sections were not clearly observable due to cutting debris on the specimen edge. Additionally, the specimen had been sectioned with the indented face surface perpendicular to the blade and in the same direction as the blade rotation. This arrangement caused the bone ma terial to rise up and obscu re the indentation crosssection. Sectioning of the subsequent wetindented specimen was performed differently. Wet-indented specimen After indentation the specimen was sectione d with a low speed saw into 2 pieces to expose the residual impression cross sections. The sectioning was done with the indented surface facing the low speed saw blade. This arrangement was to ensure that the low speed saw blade did not upset the bone mate rial as it had done when sectioning the dryindented specimen. After sectioning the cut planes were li ghtly polished by manually drawing them across a dry polishing cloth (Texmet 1000, Bueh ler, Lake Park, IL) to remove cutting debris. Following Zysset et al. [1999], the sp ecimens were stored in a solution of 0.5mg/ml gentamicin sulfate in tap water at 2 C when not undergoing i ndentation or imaging to retard collagen biological degradation. Both pieces were vacuum sputter coated with gold and imaged with SEM. Atomic force microscopy specimen Following discovery of indentation apex cr acks in specimens previously indented both wet and dry, an additional specimen, approximately 4 mm square by 1 mm thick, was prepared. The specimen preparation was the same as previous specimens except it
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35 was not prepared for SEM imaging. Ther e was no vacuum gold sputter coating nor bombardment by electrons in the SEM chambe r. The specimen was indented at two different times, once while wet and then agai n after 14 days drying time in equilibrium with laboratory environment. A set of 5 i ndentations was made at a range of applied mass (0.1 kg to 1.0 kg), with the Knoop indentat ion point short diagonal perpendicular to the bone longitudinal axis. Another set of 5 indentations was made in the same specimen after 14 days. The Knoop indenter point short diagonal was oriented parallel to the bone longitudinal axis. Immediately post indenta tion, for both wet-indent ed and dry-indented cases, the specimen was imaged with an optic al microscope (BX-60; Olympus; Melville, NY) and with an atomic force microscope (AFM) (Nanoscope III; Hysitron; Minneapolis, MN). Fracture toughness confirmation specimen Fracture toughness of the bone subjected to SEM preparation and imaging was derived using indentation apex crack length m easurements from 3 wet-indented residual impressions. The 3 indentations had been made at the same applied mass. In order to determine whether the indentation apex cracks were artifacts of th e SEM preparation and imaging process or were related to the a pplied mass, an additional wet specimen was prepared. The specimen was prepared in a manner as close to the original SEM wetindented specimen as possible. The specimen was cut from the same region of the bovine MC specimen as the original wet-indented SEM specimen. A Knoop indenter point was used with the short diagonal perpendicular to the bone long axis. The specimen was indented with a range of indentation masses (0.05 kg, 0.1 kg, 0.2 kg, 0.3 kg, 1.0 kg). Five indentations were made
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36 at each mass level. The specimen was pr epared for and imaged using the same equipment as the original SEM specimens. Evaluation Procedures Scanning electron microscope Optical evaluation of the SEM images reveal ed that 3 of the wet-indented specimen cross sections were clearly obs ervable at the midpoint of th e long diagonal. One typical cross section is shown in Figure 3-5. Th e average length, width, and depth of the 3 indentations were used in subsequent evalua tions. Only one of the dry-indented cross sections was measur able (Figure 3-4). Elastic modulus The difference in residual impression side -wall angles betwee n the wet-indented and dry-indented cross sections suggested th at an estimate of wet recovered material elastic properties could be ma de. The difference between the wet and dry indentation depths could be due to the material recoveri ng more when wet than dry. More recovery in the wet-indented specimen suggested to me that the recovered material (that material between the maximum indentation depth and th e final residual inde ntation depth) has a different elastic modulus than the bone outside the indentatio n affected region. Hengsberger et al. [2002] suggested that dama ged bone does not recover its intact elastic modulus like metals after indentation. They [Hengsberger et al. 2002] also pointed out that the degree of elastic modul us recovery for bone is like ly a function of indentation depth and collage n architecture. I calculated the maximum depth for both i ndentations using the simple geometric relationship between the length of the Knoop diagonal and depth. The calculated value was about 6 m for both wet-indented and dry-indent ed residual impressions The actual
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37 difference in maximum depths was about 5%. However, the wet-indented depth recovered 5 m while the dry-indentation depth recovered 4 m. The wet-indented measurements were used to estimate the elastic modulus of the recovered material. For the first estimate of the wet-indented recovered material elastic modulus, I used the derivation reported by Loubet et al. [1984] That derivation assumes simple elasticity although bone is known to have a degree of visc oelasticity. I have not added viscoelastic behavior to the model in order to preserve simplicity. The following equations were taken from Dorner and Nix [1986]: rdP1 E dh2A (1) 1 2 2 i ri11 E(1) EE (2) where rE = reduced modulus, dP dh = slope of load and displacement plot, A = projected area of the indenter residua l (recovered) impression, i = indenter point material, = PoissonÂ’s ratio, E= elastic modulus. For th e Knoop indenter point, 12dd A 2, where 1d = length of long diagonal, 2d = length of recove red short diagonal. I calculated the load and displacement slope, dP dh from 2 data points. The first was at the maximum indentation depth (6 m) and maximum applied mass (0.1 kg). The second was at the final indentation depth (1 m ) and final applied mass (0.0 kg). I then computed the reduced elastic modulus, rE, using equation (1). I used equation (2) to computed the elastic modulus with an assumed Poisson's ratio of 0.3 for the specimen. I
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38 also used a Poisson's ratio of 0.2 and an elastic modulus of 925 GPa for the diamond indenter [MatWeb 2003]. A refinement of the recovered material elastic modulus derivation for the wetindented specimen was made through a simple elastic model. Equation (1) assumes that the modulus found was for the entire elastic half space. In reality th ere is a spectrum of elastic moduli ranging from that of the intact bone to that of the material in the immediate indentation affected region. Observation of a typical load –displacement data [Oliver and Pharr 1992] shows the changing slope of the load-displacement curve. I constructed a simple model that estimated the thickness of a fi nite column equivalent to the elastic half space. Then I divided that column into two regions, one of competent bone and one of recovered material. I then used a simple two series springs model for the two materials. I assumed that the modulus of bone was 11 GPa [Guo 2001 p. 10-7] because the wet specimens were indented with the shor t Knoop diagonal perpendicular to the bone longitudinal direction. A sensitivity ev aluation was also performed to determine variation of results with the value of crush depth. The r ecovered material depth was not known. I estimated the depth to be twice th e maximum depth of the Knoop indentation point at full load. That value was chosen based on the extensive modeling work by Giannakopoulos et al. [1994]. They [Gianna kopoulos et al. 1994] had shown that the maximum tensile residual stress was located close to twice the indentation maximum depth for strain hardening ma terial after complete unloading. Details of the elastic modulus estimation procedure ar e contained in the Appendix. Fracture toughness Cracks in the dry SEM prepared specimen s were very small and I was unable to measure their width or length. We t-indented crack lengths were 91 m 4 m (mean
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39 SD). The measured crack lengt hs were used in an empirical equation to derive fracture toughness. The relationship between fracture toughness and crack length, taken from Xu et al. [1998] was: 3 2cKP c, (3) where Kc = fracture toughness ( 1 2MPa/mm), = 0.076, P = indentation load (N), 2c = total crack length (mm). The constant, depends on the hardness to modulus ratio of the material. I assumed that the material wa s brittle after SEM preparation and imaging. I also assumed that it had a hardness to modul us ratio similar to other brittle materials like ceramics and dental enamel. Ba sed on those assumptions I selected to be the same (0.76) as that used by Xu et al. [1998] in their ceramic and tooth enamel investigations. Results The results fall into two major categories. The first relates to the observation of cracks in the apices of SEM specimens and th e second to the physical description of the microindentation residual im pression cross section. Cracks Midline cracks were observe d along the apex of the resi dual impression long axis for both wet-indented and dry-indented SE M specimens (Figure 3-5). There were no cracks observed in the AFM specimens whether they were wet-indented or dry-indented, regardless of indentation point (Vic kers or Knoop) or test mass. Cracks in the first SEM specimens (Figur e 3-6) were measured optically and resulted in a mean fract ure toughness of 0.22 MPa/m1/2 0.01 (mean SD) using equation (3). The average of results from the fracture toughness confirmation specimen
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40 (Figure 3-7) was 0.22 MPa/m1/2 0.04 (mean SD). The crack length is directly proportional to applied mass (Figure 3-8) A one way ANOVA was performed on the fracture toughness confirmation data. There was no significant di fference between the fracture toughness at any value of applied mass (p > 0.05). Cross-section The computed estimate of elastic moduli were 3.2 GPa and 4.8 GPa wet and dry respectively. The detailed calculation is provided in the Appendix. The result for the wet-indented specimen, 3.2 GPa, represents a modulus between that of cortical bone (11 to 20 GPa) [Guo 2001 p. 10-7] and demineralized bone (0.2 to 0.9 GPa) [Catanese et al. 1999]. A further refinement us ing the series spring model resulted in elastic modulus value of 1.0 GPa. That value was based on an assumed recovered material depth of twice the maximum indentation depth. That de pth was taken from Giannakopoulos et al. [1994] and is the point of maxi mum tensile stress. It is at this point that maximum bone damage would be expected. Measured residual impression sidewall an gles of 153 and 168, dry and wet respectively, were greater than the 130 of indenter tip geomet ry (Figures 3-4, 3-5). There was no evidence of pile-up on the short diagonal sides of the residual impression where the sidewalls meet the initia l material surface (Figures 3-3, 3-4). In fact there was no indication of pile-up on any of the several h undred indentations made in the course of this study. Also notable was the unevenness of the po lished specimen surface and lack of welldefined edge or boundary between the impre ssion and the initial surface (Figure 3-5).
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41 Discussion In this section I discuss: fracture t oughness of SEM prepared specimens; the derived elastic modulus of the recovered materi al in the indentation affected region; and absence of pile-up on the residual impression edge. The objective of this study was to better understand micr oindentation through investigation of the residual impression inde ntation site. The observations and simple calculations in this study appear to verify that post indentation materi al at the indentation site is not representative of the undisturbed bone as sugge sted by Hengsberger et al. [2002]. Fracture Toughness The microindentation residual impression site was investigated through SEM and optical microscopy. Cracks in the SEM prepar ed specimens were directly related to the applied mass. The relationship between the fracture toughness values derived in this work and that of unprocessed bone is unknown. Future research could help understand the relationship. It may be possible to more easily de rive fracture toughness of bone through development of a regression model. Speci mens from bones with a range of fracture toughness could be tested macroscopically a nd compared with fract ure toughness values derived using SEM preparation and crack length measurement. A good regression relation (R2 > 0.8) could greatly simplify deri vation of fracture toughness for a wide range of bones. Recovered Material Elastic Modulus The estimated elastic modulus of the we t-indented recovered material can be interpreted as the modulus of a material that is not intact bone, it is damaged. I could not
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42 determine the nature of the damage. The resu lts of my work can only estimate an elastic modulus for the material. My method assu med a depth of the damaged material. A difference of 1 m in assumed depth is equivalent to about 90 MPa estimated modulus. Future research could examine that assumption. The objective of the future work describe d in Chapter 5, is to experimentally determine the depth of the rec overed (damaged) bone material a nd use it in finite element models like those developed by Giannakopoulos et al. [1994], for ultimate use as a bone model. Such a model could provide a better value for the elastic modulus of the material in the microindentation affected region. Pile-up Some time ago other researchers had found evidence of pile-up during microindentation hardness tests when the a pplied mass was above 0.1 kg [Ramrakhiani et al. 1979]. Their result was likely due to the silver plate they had applied to the bone specimen. Bone, as a brittle material, exhibits strain hardening behavi or with a relatively large strain hardening exponent of about 0.7. The strain hardening exponent, n, comes from the stress-strain relationship after the material yields. The constitutive law is expressed as: nE Materials with large strain hardening exponents over about 0.5, are not expected to exhibit pile-up [Cheng and Cheng 1998], they sink in. Therefore, pile-up should not have been expected in bone microindentation. The absence of pile-up provides additional confirmation that bone behave s as a work hardening (brittle) material. Absence of pile-up also suggests th at bone compacts, sinks in, under the microindentation point because material is conserved. The compaction or sinking in suggests that the material under the microindenter tip is different than the intact material.
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43 Extending this idea to elastic modulus meas urement methods it seem s reasonable that the ERM measures different material than does the LDM. I suggest it may be so because the ERM takes its measurements after all recove ry is complete while the LDM takes its measurements when the indenter point is in full and intimate contact with the specimen. The compacted material is between the indenter point and the intact material and remains compacted. During the very first part of the unloading while the indent er point is in full contact with the specimen the elastic response of the intact material will be manifest in the load and displacement measurements. It is the initial unloading slope of the load displacement curve that is used to derive elastic modulus. Such an interpretation would predict that ERM derived elastic modulus values of bone would be less than LDM de rived elastic modulus values. Such a prediction has in fact been demonstrated in my rela ted work described in Chapter 4.
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44 Table 3-1 Values for dry-indented and wet-i ndented cross sections. Measured quantities are: angle = angle between side-walls, brec = recove red short diagonal, a = long diagonal, h = depth of residual indentation, P = applied load. Derived quantities are: HK = Knoop har dness, E = elastic modulus. SEM Specimen Parameters Quantity Dry-indented Wet-indented Angle () 153 168 HK (kg/mm2) 40 36 brec (m) 20.5 22.8 a (m) 188.3 198.7 h (m) 2.5 1.2 P (N) 0.98 E (GPa) elastic half space model 4.8 3.2 E (GPa) series spring model n/a 1.0
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45 Figure 3-1 Typical schematic accompanying in dentation models. A region of material pile up is not shown on all such schematics. It is shown for models of ductile material. Brittle materials do not exhibit material pile up. s urface profile loaded unloaded i nitial surface p ile up
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46 Figure 3-2 Typical indentati on set for SEM investigation prior to SEM preparation. Indentations made with the Knoop indenter point. Scale is the same in A and B. A) Dry-indented bovine MC spec imen B) Wet-indented bovine MC specimen 1 mm A B 200 m
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47 Figure 3-3 Bovine metacarpus. Dashed boxe s indicate area from which indentation specimens were taken.
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48 Figure 3-4 A) Knoop residual impression a rray line containing 9 microindentations. Indentations made in dry specimen w ith short Knoop diagona l parallel to the bone long axis. One observable indentati on is indicated by the dashed box. B) Cross section of Knoop mi croindentation short dia gonal of the indentation with approximate side-wall angle depicted by dashed lines. 153 20 m A B
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49 Figure 3-5 A) Knoop residual im pression area. Indentations made in wet specimen with short Knoop diagonal perpendicular to the bone long axis. One of the observable indentations is indicated by the dashed box. B) Cross section of the indentation with approximate side-w all angle depicted by dashed lines. 168 20 m A B
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50 Figure 3-6 Linear crack at the apex of the indentation residual im pression. Other non indentation related cracks can be seen in the lower left section of the image. Note lack of well defined edge. Specimen was indented wet. Dotted lines indicate the edge of half of the indentation residual impression. Solid circles indicate approximate end of residual im pression long diagonal. Note that the apex crack is shorter than the long diagonal of the indentation. apex crack residual impression edge
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51 Figure 3-7 Typical Knoop inde ntations in the fracture tough ness confirmation specimen. Specimen was indented wet with the Knoop short diagonal perpendicular to the bone longitudinal axis. Cracks appear as white lines. Other non indentation related cracks are visible on the left side of the image. apex crack cracks
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52 Figure 3-8 Plot of applied mass (Load) with crack length, where “C” is the total measured crack length divided by 2. Dotted line is linear regression, R2=0.98. 0 0.5 1 0.0E+001.0E-062.0E-063.0E-064.0E-06C^1.5 (m3/2)Load (kg)
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53 CHAPTER 4 INVESTIGATION OF THE ELASTIC RECOVERY M ETHOD FOR DERIVING ELASTIC MODULUS OF BONE, DENTIN, AND ENAMEL Introduction The objective of the work described in this chapter was to evaluate the elastic recovery method (ERM) for deriving elastic modulus of bone, dentin, and enamel. The aims were to: adapt and validate the ER M using well documented material (glass, Plexiglas, bovine femur); and apply the ERM to bone, dentin, and enamel. In addition to those aims I used the ERM to map elastic modulus distribution in the mediolateral direction along the centerline of bovine metacarpus nutrient foramen and I investigated the elastic anisotr opy of monkey dentin and enamel. History The ERM was originally deve loped within the materials research community and used on ceramics by Marshall et al. [1982]. Marshall et al. [1982], using the Knoop indenter point, had observed a relationship betw een the post indentati on ratio of short to long Knoop diagonal measurements and the hard ness to elastic modulus ratio. Using a spectrum of ceramic materials, with a range of hardness and moduli, they constructed a mathematical relationship. The relationship equated elastic modulus to hardness divided by a measure of departure from perfect elasti city. Their resultant equation for elastic modulus was: recKb EC1/C2 aH (1)
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54 where E = elastic modulus, C1 and C2 = constants, KH = Knoop hardness (MPa), rec b = recovered short diagonal, a = long diagonal. The constants were chosen through curve fitting from a plot of microindentation residual impression dimensions ratio (brec/a) and hardness to elastic modulus ratio (HK/E). Constant C1 is the slope of the linear regression and constant C2 is the intercept on the brec/a ordinate. The resulting linear regression equation as taken from Marshall et al. [1982] is: rec Kb H C2C1 aE (2) Subsequent work by Amitay-Sadovsky and Wagner [1998] extended ERM to polymers. They also used a spectrum of pol ymers with a range of hardness to modulus ratios. Their constants, C1 and C2 in e quation (2), were also derived through curve fitting. Amitay-Sadovsky and Wagner [1998] concluded that the ERM was applicable for polymers. Use of appropriate indentati on applied mass was their only caveat because they had found a dependence of derived har dness on applied inde ntation load while Marshall et al. [1982] had found none for ceramics. In addition to work in polymers the ERM has been applied in dental research by Meredith et al. [1996] and pharmacological work by Lum and Duncan-Hewitt [1996]. Lum and Duncan-Hewitt compared ERM deri ved elastic modulus results with those derived from use of ultrasonic methods. They criticized ERM for producing negative values of elastic moduli. Meredith et al .[1996] reported that thei r ERM derived elastic modulus results were limited by enamel cr acking. They also reported success with deriving dentin elastic modulus. Such cracks did not allow measurement of the microindentation residual impression dime nsions. During the period from 1982 to my research, the ERM had not been used in bone.
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55 Motivation Success of the ERM in ceramics, polymers, and dentin, reported by Marshall et al. [1982], Amitay-Sadovsky and Wagner [1997], and Meredith et al. [ 1996], encouraged me to use the method in bone. Equipment requir ed by the ERM was available to me and the method appeared to be reasonably straightforw ard. I also wanted to explore the tooth enamel limitation reported by Meredith et al. [1996]. In addition I wanted to use the ERM to map elastic modulus distribution on the mediolateral midline of the bovine metacarpus dorsal foramen. Methods and Materials This section is divided into 3 subsections. The first describes the method used in adapting the ERM for use in bone. The second describes the methods and materials used in validation of the ERM. The third de scribes the methods and materials used in application of the ERM to bone, dentin, and enamel. A microindenter (Model HM-112, Mitu toyo, Japan), equipped with a Knoop indenter point, was used for all microindent ations unless otherwise stated. The Knoop indenter point was selected because it allo ws investigation of elastic anisotropy as demonstrated by Riches et al. [1997] and Riester et al. [2000]. For bovine and monkey specimens, I used a dwell time of 10s and followed the limitations on: time out of solution; time between indentation and measurement; and distance between the indentation and pores fr om Chapter 2. I did not perform hardness variation with independent va riables evaluations for bovine or monkey specimens except applied mass.
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56 Animal tissue from bovine and monkey were used in the work described in this chapter. All procedures i nvolving animal tissue use were approved by our Institutional Animal Care and Use Committee. Adaptation of Elastic Recovery Method to Bone Adaptation of the ERM for use in bone i nvolved the selection of constants C1 and C2 for equation (1). In this subsection I describe my selection of those constants. The constant C1, as derived by Marsha ll et al. [1982] and Amitay-Sadovsky and Wagner [1998], is the slope of a linear curve fitted through the brec/a and HK/E data (Equation (2)). Derivation of the constant C1 requires that the value of hardness to modulus ratio be known for the material being indented. The values for forming the ratio brec/a are simply measured from the mi croindentation residual impression. While I could measure the re sidual impression dimensi ons in bone, I did not know the HK/E values for bone. Indeed, it was the el astic modulus that I was trying to find. Moreover, I did not have available a range of bone specimens with known elastic moduli with which to work. Without a range of bone specimens from which to determine a value for C1, I decided to use a simple linear relationship between the value of the constant C1 for ceramics and the value of the constant C1 for polymers. It also turned out that the ERM equation is sensitive to the value of C1 (Figur e 4-4). I chose the ordinate to be the value of C1 and for the abscissa I chose the corre sponding average value of elastic modulus for the subject material. The first data point set was the value of C1 for ceramics (0.45) [Marshall et al. 1982] at an el astic modulus of 70 GPa. The second data point set was the value of C1 for polymers (0.473) [Amitay-Sadovsky and Wagner 1998] at an elastic modulus of 2.6 GPa. An elastic modulus of 70 GPa was selected for the material glass as
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57 it is representative of ceramics. The value for elastic modulus of 2.6 GPa was selected for the material acrylic polymer as it is representative of polymers. The values for elastic modulus were taken from an available inte rnet source [Mat Web 2003]. The resulting equation was: C10.47390.0003(E) (3) where C1 = constant, E = elastic modulus (GPa ). I then used an elastic modulus of 16 GPa to pick off a value for C1. I chose th e value of 16 GPa because it is the average value of bovine femur elastic modulus [Guo 2001, p 10-7]. I chose the bovine femur values for the computation because I planned to use that bone for ERM validation. I then computed a value of 0.47 for the constant C1 for use in deriving the elastic modulus of bone (Table 4-1). In selecting the value for the constant C2, I again did not have a range of specimens with known elastic moduli from which to find the ordinate intercept. I selected the value of 0.14 for the constant C2 following Marshall et al. [1982] and Meredith et al. [1996]. Marshall et al. [1982] and Meredith et al. [ 1996] had used 0.14 because it is the largest physically possible value for brec/a. That value follows directly from the geometry of the Knoop indenter. Elastic Recovery Method Validation In this subsection: I state the hypotheses for the ERM validation; describe specimen preparation and indentation procedure for each specimen; and provide the method for ERM equation sensitivity evaluation. Hypotheses The null hypotheses for ERM validation were:
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58 1. Glass specimen. a. Mean value of ERM derived elas tic modulus is equal to the mean published value. b. Mean value of ERM derived elas tic modulus, using edge detection, is equal to the mean ERM derived elastic modulus, using optical measurements alone. 2. Mean value of ERM derived elastic modulus for Plexiglas is equal to the mean published value. 3. Bovine femur longitudinal specimen. a. Mean value of ERM derived elas tic modulus is equal to the mean published value. b. There is no difference in the mean value of ERM derived elastic modulus between indentation orientations. 4. Bovine femur transverse specimen. a. Mean value of ERM derived elas tic modulus is equal to the mean published value of elastic modulus. b. There is no difference in the mean value of ERM derived elastic modulus between indentation orientations. The alternate hypotheses were all two-tailed. Specimen Preparation and Indentation Procedures Glass A glass slide, 27 x 46 x 1.25 mm (Petrogra phic slides, Buehler, Lake Bluff, IL), was cleaned with 100% ethyl al cohol and air dried. A range of indentation applied mass was evaluated against derived hardness. That investigation resulted in selection of 0.3 kg
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59 as the minimum appropriate applied mass for s ubsequent indentations. A dwell time of 10 seconds was used based on my experien ce and other related work (Chapter 2). Ten indentations were performed in 2 gr oups of 5. The microindentation residual impressions were well defined which resulted in ease of short diagonal measurement using optical means. The indentation resi dual impressions were measured with the installed measuring system of the microindenter. Edge de tection was evaluated on the specimen to access its accuracy. Two groups of 3 indentations were made for optical and edge detection measurement. Plexiglas A piece of transparent optical acrylic polym er (Plexiglas) approximately 36 mm by 40 mm by 12 mm thick was cleaned with tap water and blotted dry with paper wipes. Again, a range of indentation applied mass we re evaluated against th e derived hardness. The investigation resulted in selection of 0.1 kg as the applied load for subsequent indentations. Ten indentations were performed and the elastic modulus results averaged. The indentation residual impressi ons were well defined and the short diagonal easy to measure with optical means. Bovine femur In this subsection I describe: the specimen preparation; indentation procedure; and indentation residual impression evaluation with edge detec tion image processing. The image processing used for the these specimens was also used on the glass and Plexiglas specimens. Two bovine femur specimens were used in ERM validation. Specimen size was dictated by specimen mounting a nd polishing requirements. The specimens were sized to
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60 fit on a standard petrographic s lide (Buehler, Lake Park, IL). The specimens were taken from a previously fresh frozen right femur in the mid diaphysis anterior aspect (Animal Technologies Inc., Tyler Texas). One of thes e specimens was sectioned parallel to the long bone axis, longitudinal (Fi gure 4-1) and the other was se ctioned transverse to the long bone axis (Figure 4-2). Both specimens were approximately 25 mm by 45 mm by 1 mm thick. After cutting to size the specimens were polished using a semi automated polishing system (Minimet 1000, Buehler, Lake Bluff IL). Both specimens were polished progressively beginning with 6 m diamond slurry and finishing with 0.05 m alumina and colloidal silica suspension. Following Zysset et al. [1999], the specimens were stored in a solution of 0.5 mg/ml gentamicin sulfate in tap water at 2 C when not undergoing indentation or imaging to reta rd collagen biological degradation. A series of 10 indentations each were ma de in the transverse (Figure 4-1) and longitudinal specimens (Figure 4-2). For th e longitudinal specimen 5 indentations were made with the short Knoop dia gonal perpendicular to the bone long axis (L1, Figure 4-3) and the other 5 with the short Knoop diagonal parallel to th e bone long axis (L2, Figure 4-3). For the transverse specimen 5 inde ntations were made with the short Knoop diagonal perpendicular to the bone circumfe rential direction (T1, Figure 4-3) and 5 indentations were made with the Knoop short diagonal parallel (T2, Figure 4-3) to the bone circumferential direction. Knoop hardness (kg/mm2) and long diagonal ( m) were recorded for each indentation. Optical microscopy images of each indentation were then taken within about 20 minutes. Use of strictly optical measurement means introduced subjectivity into the
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61 measurements. Reproducible measurement of the short Knoop diagonal length was not possible. In order to minimize the subjectivit y an edge detection st ep was added to the indentation procedure for bone. The optical microscopy images were convert ed to grayscale and subjected to edge detection with image processing software (M atLab, MathWorks, Inc., Natick, MA). A variety of edge detection filters are availabl e in the software. Each filter was used on a representative residual impression grayscale image of th e bovine femur. The Canny filter was selected for subsequent edge detection due to its superior ability to detect edges of this type. The significant difference between the Canny f ilter and other available filters is an edge linking feature. This feature links discrete picture elements (pixels) into chains to form lines. One weakness of the Canny filter oc curs at junctions of several lines. The linking function fails to enhance the edge at these junctions. The critical measurements for ERM are between large angles across th e short diagonal. Th e linking function does not appear to fail at these junctions. The differences between all other filte rs and the Canny filter were obvious and profound. The edge-detected images were us ed in image handling software (Paint Shop Pro, JASC, Eden Prairie, MN). The short diagonal rec b and long diagonal a measurements were made using pixels and the known value of pixels per m for the given optical microscope magnification. Th e diagonal length measurements were made by identifying and subtracting pixel locat ion coordinates and dividing by the known pixels per m. Identification of pixel location was a manual task and involved some degree of subjectivity.
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62 Sensitivity evaluation of ERM equation A sensitivity analysis was performed on the ERM equation (Equation (1)) to determine the variation of elastic modulus results to a 5% change in each of the 5 equation variables. The evaluation used refe rence values for the equation variables from 1 representative indentation residual im pression on the bovine femur longitudinal specimen. Application of ERM to Bone, Dentin, and Enamel In this subsection I describe the methods and materials used for application of the ERM. Three different materials from 2 different specimens were used: bovine metacarpus (MC); and monkey tooth dentin and enamel. I also describe the methods used to i nvestigate the ERM deri ved elastic modulus distribution in the mediolater al direction along th e centerline of the bovine MC foramen minor axis. Hypotheses Three hypotheses were tested fo r the application of ERM. 1. The mean ERM derived value of elas tic modulus for bovine MC was equal to the correlation method (CM) derive d elastic modulus for bovine MC; 2. The mean ERM derived value of mo nkey tooth dentin elastic modulus was equal to the mean published value; 3. The mean ERM derived value of monkey tooth enamel elastic modulus was equal to the mean published value. Specimen Preparation and Indentation Procedures In this subsection I describe: specimen pr eparation; indentation procedures and correlation method used for answering the 1st hypothesis; specimen preparation and indentation procedures for answering the 2nd and 3rd hypotheses; and indentation procedures used for investigation of the nut rient foramen elastic modulus distribution.
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63 Bovine MC One bovine right metacarpus (MC) was obt ained from the University of Florida College of Veterinary Medi cine from a donor of unknown ag e and sex whose death was unrelated to this study. After 2 transver se cuts with a 10 in ch band saw (Delta Machinery, Jackson, MS), the bone was l ongitudinally sectioned (Isomet Low Speed Saw, Buehler, Lake Bluff, IL) from the di stal dorsal aspect to produce a 1 mm thick by 25 mm wide by 45 mm long long itudinal slab (Figure 4-5). The specimen size was again controlled by the polishing system capabilitie s. The specimen was polished in the same manner as the bovine femur specimens. The specimen was to be used to map elastic properties along the mediolateral mid line through the foramen minor axis. Correlation method (CM) In mapping elastic constants, along the midline of the bovine MC foramen, I compare ERM derived results with those obtai ned by CM. I use the linear correlation of Vickers hardness with elastic modulus deve loped by Currey et al. [1990]. The equation is: VE0.580.36H (R2=0.93) (4) where E = elastic modulus (MPa), HV = Vickers hardness (kg/mm2). Bovine foramen elasti c modulus distribution A series of 19 sets of 4 indentations each was made along the bovine MC foramen midline in the lateromedial direction, parallel to the foramen minor ra dius (Figures 4-6). Each of the 4 indentations were made at an gles of 0, 45, 90, and 110 as measured between the bone longitu dinal axis and the Knoop short diagonal. Ideally all indentations would be made at the same point. Placing the 4 indentations in the same place would overl ap them. Measurements of the residual
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64 impressions would represent the effect of othe r indentations and not the bone itself. For that reason the indentations were grouped as close together as reasonable allowing for pores. In general a sp acing of at least 70 m was maintained between the short diagonals of the neighboring Knoop indent ations within a group. This distance has been found in previous work (Chapter 2) to eliminate the effect of one indentation on another. Mapping of ERM derived elastic modulus based results for elastic constants distribution on the bovine MC lateromedial midline consisted of the following steps. 1. Locating a representative distance fro m the foramen edge for each set of 4 indentations. 2. Deriving elastic modulus values for each of the 76 indentations. 3. Calculating the principal longitudi nal and transverse elastic moduli and shear modulus for each of the 19 indentation sets. Mapping the CM derived elastic modul us distribution on the bovine MC mediolateral midline involved making microindent ations with the Vickers indenter point. A set 44 indentations was made along the midline of the foramen in the mediolateral direction (Figure 4-7). Representative Distance from Foramen Edge I chose the distance between the edge of the foramen and the center of the indentation made at 45 as reasonable represen tative of the indentation set distance. The decision was based on inspection of the completed indentation sets. Deriving Elastic Modulus for Indentations Elastic moduli values were computed for each indentation except one. The one exception was the 45 indentation in set 2. I was unable to obta in a reproducible measurement of the residual impression short diagonal. That left 18 viable indentation sets with all 4 ERM derived values of elastic modulus.
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65 Principal Elastic Moduli Calculation The principal longitudinal and transverse elastic moduli and the shear modulus were calculated using an iterative process. The process was construc ted because I did not know the principal material directions. The a pparent material direc tions were evident for some indentation sets but not for all. The first step in the iterative process was to use an in-plane coordinate transformation to obtain values for longitudina l, transverse, and shear elastic moduli at coordinate rotation angles between 0 and 90. The transformation equation was taken from Rapoff et al. [2003]: 422 L 422 TLT11 sin2cossin EE 11 coscossin EG (5) where 'E = measured modulus at angle = angle between the Knoop short diagonal and the transverse axis of the specimen (Figure 4-6 B), = angle of in-plane coordinate transformation rotation, LE = elastic modulus in the principal material direction, TE = elastic modulus in the transver se principal material direction, LTG = shear modulus, = Poisson's ratio. For each of the 18 viable indentation sets, 3 of the 4 values ( = 0, 45, 90) of ERM derived elastic modulus were used, with an assumed Poisson's ratio of 0.3, to form a set of 3 linear equations in 3 unknowns. Po isson's ratio of 0.3 is representative of bovine long bones. Values of EL, ET, and GLT were calculated as the angle of rotation, was iterated from 0 through 90, in 5 steps. These calculations resulted in a range of physically possible values for EL, ET, and GLT. In order to select the best set of values,
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66 the 4th data point (110) in each of the 18 indent ation sets, was used. At each angle of rotation, the predicted value of elastic modulus at 110 was calculated using the same transformation equation. The result of th e calculation was compared with the actual ERM derived value to determine the percent error. I established criteria to select the best angle and the corresponding values for EL, ET, and GLT. That criteria was: the values were possible (0 < EL > GLT, ET > GLT > 0); the error betwee n the ERM derived value and calculated value was 5%; and that the minimum error were single valued, that is there was only one minimum in the interval 0 to 90. The computa tions were carried out with a commercially available software (Mat Lab, MathWorks, Inc, Natick, MA). The best angle was the angle corresponding to the prin cipal material direction. An angle of 0 means a principal direction parall el to the bone longitudinal axis. Monkey teeth I describe the specimen preparation and indentation procedures for both tooth dentin and enamel because the dentin and enamel are part of the same specimen. The first molars from both sides of a skeletally mature female monkey (Macaca fascicularis) were sectioned from a previously cleaned and fresh mandible using a diamond blade saw (Low Speed Saw, Buehler, Lake Park, IL). On each side one cut was made in the buccolingual plane between the premolar and the first molar. A second cut on each side was made also in the buccolingual plane at the centerline of the first molar. A third cut was made again on both sides in the buccolingual plane between the first and second molars. These cuts produced four sp ecimens about 2 mm thick, with both a cross section and an exterior surf ace. The right side specimens are shown in Figure 4-8.
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67 The posterior aspect of the first right side molar was particularly flat and afforded the opportunity to indent the exterior su rface of enamel with minimum removal of material through cutting and polishing. These specimens were manually polished using the same polishing and storage protoc ol used with the bovine specimens. In order to determine the appropriate mi croindentation applied mass for dentin and enamel I followed the same hardness variati on with applied mass method I described in Chapter 2, I found an appropriate applied ma ss of 0.1 kg for used for dentin and 0.2 kg for enamel. The indentations made at 0.1 kg applied mass in dentin were also used to answer the 2nd hypothesis. The indentations made at 0.2 kg applied mass in enamel were also used to answer the 3rd hypothesis. In the dentin of the right si de first molar cross section, 2 sets of 5 indentations were made. One set of 5 with th e short Knoop diagonal parallel and the second set of 5 perpendicular to the dentin tubu le orientation (Figure 4-9). Th e indentations were used to investigate in-plane elastic anisotropy. A series of 3 indentations were made in the cross section of enamel with the short diagonal approximately perpendicular to the enamel prism tubes in the crown of the tooth. These indentations cracked and were not useable for ERM (Figure 4-9 A). Two series of 3 indentations were made in the surface enamel on the posterior aspect of the right first molar. The first se ries was with the short diagonal approximately parallel to the occlusal surface and the sec ond with the short diagonal 90 from the first set (Figure 4-10). One indentation in the firs t series exhibited crack ing and was not used. Results This section is divided into 2 major subs ections. In the firs t subsection I report results from the ERM validation activities. In the second subsection I re port the re sults of
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68 the ERM application to bovi ne MC elastic modulus mapping and monkey dentin and enamel. Elastic Recovery Method Validation In this subsection I report the resu lts of hypotheses tests and ERM equation sensitivity evaluation. Hypotheses Tests Glass The mean ERM derived elastic modulus was not significantly different (ANOVA, p > 0.05) from the published value (Table 4-3). The ERM derived elastic modulus using optical measurement of the residual impression dimension, was not significantly different (ANOVA, p > 0.05) from the ERM derived elastic modulus results us ing edge detection (Table 4-4). Plexiglas The ERM derived elastic modulus was not significantly different (ANOVA, p > 0.05) from the published value (Table 4-3). Bovine Femur The ERM derived elastic modulus was si gnificantly different (ANOVA, p < 0.05) from published values for both longitudinal and transverse specimens (Table 4-3). There was no significant difference (ANOVA, p > 0.0 5) in ERM derived elastic modulus between Knoop indenter point orientations fo r either the longitudinal or transverse specimens (Table 4-4). Elastic Recovery Method Equation Sensitivity The least sensitive variables are constant C1 and Knoop hardness. The most sensitive variables ar e constant C2, measur ed long diagonal, a, and measured short
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69 diagonal, brec (Table 4-2). Results are also provid ed graphically as normalized sensitivity plots for each of the 5 variables (Figure 4-4). Application of the Elastic Recovery Method In this subsection, for the bovine MC fo ramen region, I report, : the ERM derived elastic modulus based results for elastic c onstants distribution; the distribution of principal material directions; and the CM de rived elastic modulus distribution. I also report ERM derived elastic modulus results for monkey tooth dentin and enamel. Elastic Constants Distribution The distribution of longitudinal elastic modulus (EL), transverse elastic modulus (ET), and shear modulus (GLT), with distance from the foramen edge in the lateromedial direction, is shown on Figure 412. Longitudinal elastic modulu s had the most variability (Table 4-7). That variability occurs betw een 1 and 2 foramen radii from the foramen edge. Shear modulus ha d the least variability. The distribution of coordina te rotation angle variati on with distance from the foramen edge in the lateromedial directi on, is shown on Figure 4-13. The coordinate rotation angle was least (0) at about 1 forame n radii from the edge of the foramen. The greatest coordinate rotation a ngle occurred at about 1.5 foramen radii from the foramen edge. The distribution of CM deri ved elastic modulus with distance from the foramen edge in the mediolateral direction, is shown on Figure 4-13. The maximum value occurred at approximately 1.5 foramen radii from the foramen edge. The values of longitudinal modulus (ET) and CM derived elastic modulus, between the foramen edge and a distance of 1 fora men radius, are significantly different (ANOVA, p < 0.05). The values of longitudinal modulus (ET) and CM derived elastic
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70 modulus, between the foramen edge and a distance of 2.3 foramen radii, are not significantly different (ANOVA, p> 0.05). Monkey Teeth In this subsection I report the results of hypotheses tests for dentin and enamel. I also report results of investigation of dentin and enamel elastic anisotropy. I describe my experience with enamel cracking during testing. There was significant difference (ANOVA, p=0.05) between ERM derived elastic modulus of dentin compared with ERM de rived elastic modulus results reported by Meredith et al. [1996]. There was signifi cant pair wise difference between (ANOVA p<0.05 for each pair) ERM derived elastic modul us and elastic modulus derived by the 2 load-displacement methods (Table 4-6). Th e standard deviation was greater in my measurements than others. My data contained 10 points whil e Meredith et al. [1996] data contained 5. Data from the load displacement methods in inherently less variable due to its automated nature. There was no significant difference (ANOVA p>0.05) between ERM derived elastic modulus of enamel and th e published values (Table 4-6). There was no significant difference (ANO VA p>0.5) in the dentin ERM derived elastic modulus either parallel to or perpe ndicular to the dentin tubules. These results agree with those of Kinney et al. [2001], w ho used small angle X-ray scattering (SAXS) to investigate dentin microstructural anisotropy. There was no significant difference ( ANOVA p>0.5) in enamel ERM derived elastic modulus either parallel or perpendi cular to the ends of the enamel prisms. Indentations in the buccolingual cross-se ction exhibited cracking, and I was unable to measure the short diagonal of the residual in dentation with accuracy. Therefore, I have
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71 no enamel elastic modulus results in that plane. That result is simila r to Meredith et al. [1996]. However, indentations in the posterior surface of th e first molar were generally well defined with little evid ence of cracking (Figure 4-10) Discussion In this section I discuss: results from ERM validation; ERM equation sensitivity; and the application of the ERM to bovine MC and monkey tooth dentin and enamel. Elastic Recovery Method Validation Agreement between the mean values of ERM derived elastic modulus and published values for glass and Plexiglas was good (Table 4-3). Agreement was also good between the mean values of ERM results usi ng optical microscopy and edge detection for glass (Table 4-4). Those results provided confidence in the ERM technique and edge detection method. Agreement between ERM derived elastic m odulus results and published values for the bovine femur was not good (Table 4-3). Th e Bovine femur results seemed reversed between the longitudinal and transverse speci mens based on an elastically transverse isotropic or orthotropic mode l. The lack of significant difference in elastic modulus, between indentation orientations for both the longitudinal and transverse specimens, implies elastic isotropy in those planes. In Knoop indentations the short diagonal surfaces spread the indented material. Fo r these bovine specimens it was easier for the indenter to spread the material on the longit udinal surface than on the transverse surface. Such a difference could be due to directiona lly dependent mineralization in the plexiform bone. Higher mineralization means harder bon e. In addition to higher mineralization some unidentified microstruc tural features may reduce post indentation material recovery.
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72 Elastic Recovery Method Equation Sensitivity For the representative values used in the evaluation, the most sensitive are: C2, the linear regression intercept; the long diagonal length, a; and the recovered short diagonal length, brec. Of these variables C2 is chosen ba sed on the physical limits of the indenter geometry. Once chosen it is no longer a sour ce of variation in the derivation of elastic modulus. The long residual impression length, a, is easy to measure. I have shown, in intra-observer effect evaluation (Chapter 2) that the measurement has little error. However, the short diagonal, brec, is not easy to measure. Operationally, the ERM results rely on the accuracy of measuring the short diagonal. The measurement is made between the apices of 2 obtuse angles (Figure 4-3 B). The angle formed by the edges of the diamond tool on the specimen at the short diagonal is about 130 As previously described (C hapter 3) I found the residual indentation impression edges are rounded where they meet the virgin material. In glass and Plexiglas the surfaces are uniform or can be made uniform with polishing. The uniform polished surface allows for well-define d indentation edges, that is, the distance between the large angle apices can be meas ured with repeatable accuracy. The bovine specimens used in this work (MC and femur) do not present a uniform surface nor well defined indentation edges for indentati on. Polishing removes softer material preferentially leaving the harder materi al proud. The polished surface is uneven and difficult to accurately determine the residual impression edge. Measurement of the short diagonal is problematic and care should be exercised in acquiring the dimension. The least sensitive variables were C1 ( linear regression slope) and Knoop hardness (HK). Again, once the constant has been select ed it is no longer an operational variable.
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73 Knoop hardness derivation relies on measuremen t of the long diagonal, a. Measurement of the long diagonal is not problem atic as I previously mentioned. Application of the Elastic Recovery Method In this subsection, for the bovine MC fora men I discuss: the ERM derived elastic modulus based results for elastic constants distribution; the dist ribution of principal material directions; and the CM derived elas tic modulus distribution. I also discuss the ERM derived elastic modul us results for monkey t ooth dentin and enamel. Elastic Constant and Principal Ma terial Direction Distribution The transition zone between cortical a nd trabecular bone, on the lateromedial side (right side of the foramen in Figure 4-5), o ccurs between 1 and 2 fo ramen radii from the foramen edge. That distance corresponds to the rapid change in both longitudinal and transverse elastic moduli (Figure 4-12) and with the largest coordinate rotation angle (Figure 4-13). On the mediolateral side (lef t side of the foramen in Figure 4-5), there is no cortical to trabecular transition zone along the minor axis midline. There was statistically significant diffe rence, at the 0.05 level, between the longitudinal elastic modulus (ET) and the CM derived elastic modulus over the distance of 1 foramen radius. However, the attained significance level of 0.47, was very close to the a priori level of 0.05. That result suggests that there is some degree of similarity between the elastic modulus derivation methods (Figure 4-15). Had I chosen 0.01 as the a priori level of significance, I would have c oncluded that the results of both methods were not significantly different. Agreement between the method results adds confidence in the ERM.
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74 I conclude that the ERM, with edge dete ction on sets of 4 indentations and the iterative computations based on rotational planar coordinate transformation, can be useful for mapping principal material directions and elastic constants in bone, based on the following: 1. The symmetry between ERM based longitudinal elastic modulus (ET) and CM derived elastic modulus. 2. ERM based elastic constants mapping dete ction of the cortical to trabecular bone transition zone. The CM has an advantage in operational simplicity. However, while the ERM based elastic constants mapping process has ma ny steps, it provides more information. The ERM based process provides: longitudinal (ET) and transverse (EL) elastic moduli and shear modulus; and principal material directions. The CM provides only elastic modulus with no sense of direction. Monkey Teeth In this subsection I discuss the ERM derive d elastic modulus results of dentin and enamel. Dentin The lack of elastic anisotropy in dentin was of some surprise. I expected, noting the dentin tubules and enamel prism tubes, wa s to expect elastic anisotropy, as found in osteonal bone with its analogous repeating st ructural “tubules” (the osteons). Other researchers have found strength anisotropy in dentin [Lertchirakarn et al. 2001]. Dentin tubules are small, about 1 m diameter compared with osteons (about 200 m) or osteon lamellae (about 5 m). The Knoop microindentation residual impression size, approximately 165 m by 19 m, was much greater than th e dentin tubule diameter. While I found isotropy there must be some stru ctural basis for stre ngth anisotropy. The
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75 ERM, at the microindentation scale, may not be small enough to determine the basis for strength anisotropy. Enamel Our measured elastic modulus of enamel from averaged 103.9 GPa. There was no statistical evidence (p = 0.37) to conclude that there wa s a difference in elastic modulus measured parallel or perpendicular to th e occlusal surface. We also found that microindentations made in the enamel surface specimen did not experience cracking that confounded measurements in the transverse specimen reported by Meredith et al. [1996]. Cracking of enamel during indentation occu rred predominantly on the enamel cross section surface and was minimal on the poste rior surface. The difference between the surfaces is the orientation of the enamel prisms In the cross section the prisms appear as the side of a tube bundle. On the posterior su rface, or any occlusal surface, the ends of the tubes are at the surface (Fi gure 4-16). Indentations made against the ends of the tubes are less likely to crack because the prism t ubes are in compression. Indentations in the cross section subject the sl ender tubes to bending. Me redith et al. [1996] also experienced difficulty with cracking of the molar enamel during indentation. However, their specimens were all in the buccoli ngual cross section. The absence of elastic anisotropy in the surface enamel seemed reasonable due to enamel prism tube orientation. The poste rior surface had been cut and polished and presented the prism tube ends to indentati on. The posterior surface indentations were made against the ends of enamel prism tube s while the cross section indentations were made across the enamel prism tubes (Figure 4-16). The microstructural architecture clearly leads to my observed isotropic results.
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76 I conclude that the ERM is an effective t ool for investigation of the enamel elastic modulus but is limited to occlusal surfaces.
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77 Table 4-1 Values for ERM equation constants. Values for ceramics (glass) were taken from Marshall et al. [1982]. Values for polymer were taken from Amitay-Sadovsky and Wagner [1998]. Constant Ceramics (glass) Polymers Bone C1 0.45 0.473 0.47 C2 0.14 0.148 0.14
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78 Table 4-2 Sensitivity of the ERM equation (1 ) to a 5% change in each variable taken one at a time. Percent difference is w ith respect to the reference. A value greater than 0.14 for C2 is not physically possible. Elastic Modulus (GPa) Elastic Modulus Difference (%) Variable Reference Value Reference +5% -5% C1 0.47 16.9 4.7 -5.3 HK (MPa) 585 16.9 4.7 -5.3 C2 0.14 16.9 n/a 75 brec (m) 19.1 16.9 -61 28 a (m) 154.4 16.9 27 -66
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79 Table 4-3 ERM elastic modulus validation results. Significance levels computed through ANOVA procedure. (* = MatWeb 2002, ** = Guo 2001 p. 10-7) Bovine Femur Glass Longitudinal Transverse Plexiglas ERM (GPa) Mean SD 69.8 9.09.3 1.3 18.3 5.5 2.6 0.3 Published (GPa) 68* 20** 11** 2.6* Significance level (p) > 0.05 < 0.05 < 0.05 > 0.05
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80 Table 4-4 ERM derived elastic modulus results for 2 indentation orientations in bovine femur specimens. Knoop indenter s hort diagonal orientation was either parallel or perpendicular to the long axis of the bone for the longitudinal specimen and parallel or perpendicular to the radial direction of the transverse specimen. Longitudinal Specimen Transverse Specimen Parallel (GPa) Mean SD 9.1 1.9 18.3 7.0 Perpendicular Mean SD 9.3 1.3 18.4 5.0 Significance (p) 0.9 0.99
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81 Table 4-5 Comparison of edge detection and optical microscopy measurement precision in glass specimen. Significance le vel determined by ANOVA procedure. Optical (GPa) Mean SD 69.7 9.0 Edge detection (GPa) Mean SD 68.4 5.4 Significance level (p) 0.76
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82 Table 4-6 Comparison of ERM derived elastic modulus results for monkey tooth dentin and enamel results with 3 published s ources. (LDM-m = Load displacement method with microindentation, LDM-n = Load displacement method with nano indentation.) Monkey Tooth Enamel Dentin ERM (GPa) Mean SD 73.6 14.0 15.6 5.4 Meredith et al. [1996] (ERM) Mean SD --10.3 1.0 Mahoney et al. [2000] (LDM-m) Mean SD 80 8 20 2.0 Marshall et al. [2001] (LDM-n) Mean SD 64 2 20 1.0
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83 Table 4-7 Elastic consta nts descriptive statistics Constant Mean SD EL 14.2 5.0 ET 7.3 2.8 GLT 3.2 1.7
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84 Figure 4-1 Bovine femur longitudinal specime n. Insets show sets of 5 indentations with the Knoop indentation short di agonal perpendicu lar to the bone longitudinal direction (upper) and with the short Knoop diagonal parallel to the bone longitudinal direction (low er). Double-ended arrows indicate the approximate local apparent principal material direction.
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85 Figure 4-2 Bovine femur transverse specime n. Insets show sets of 5 indentations with the Knoop indentation short diagonal parallel to the bone circumferential direction (upper) and with the short Knoop diagonal parallel to the bone radial directi on (lower). The double-ended arrows indicate the approximate apparent principal material direction.
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86 Figure 4-3 A) Schematic of bone cube depi cting locations and orientations of Knoop indentations. The vert ical double ended arrow in dicates the longitudinal axis of the bone. The horizontal double ended arrow indicates the bone circumferential direction. T1 a nd T2 represent in dentation on the transverse plane. L1 and L2 represent indentations on the longitudinal plane. EL indicates the direction of the longitudinal elastic modulus and ET indicates the direction of the tran sverse elastic modulus. B) Schematic of Knoop indentation residual impression. ET EL L1 L2 T2 T1 short diagonal (brec) obtuse angle long diagonal (a) A B
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87 Figure 4-4 Normalized sens itivity plots of the ERM equation variables for bovine femur transverse specimen. 0 0.5 1 1.5 2 0.911.1C2Modulus 0 0.5 1 1.5 2 0.911.1brec Modulus CD 0 0.5 1 1.5 2 0.911.1aModulus E 0 0.5 1 1.5 2 0.911.1C1Modulus A 0 0.5 1 1.5 2 0.911.1HK Modulus B
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88 Figure 4-5 Bovine MC di stal dorsal specimen. The numbers correspond to longitudinal cuts made to produce the specimen shown on the right inset. Double ended arrow indicates the long itudinal axis of the bone. Foramen is located on the distal region of th e bovine MC specimen. Right Inset The most periosteal surface specime n. The horizontal line indicates the foramen mediolateral midline. The dark freehand line below the foramen is the approximate location of th e transition between cortical and trabecular bone. 1 2 3 foramen transition line
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89 Figure 4-6 A) Knoop indentati on sets (first 5 of 19) in lateromedial direction in bovine right MC distal dorsal fora men midline. Double ended arrow indicates the longitudinal axis of the bone. Horizontal arrow indicates the lateromedial direction. B) Schema tic of indentatio n short diagonal orientation with respect to th e specimen transverse axis (T). 1 2 345 Foramen edge 200 m A T B
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90 Figure 4-7 Vickers microindentations in bovine right MC distal dorsal foramen midline mediolateral direction. Double -ended arrow indicates long axis of the bone, horizontal arrow indicat es the mediolateral direction. 100 m Foramen edge
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91 Figure 4-8 Monkey right side first molar and mandible. The posterior section is shown on the left. Left side first mola rs appear very similar. The dotted line indicates the tooth.
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92 Figure 4-9 A) Buccolingual partial cross se ction of left side first monkey molar. The dentine tubules (DT) are the fine lines in the dentine (D) emanating from the pulp cavity (PC). The upper su rface of enamel (E) is occlusal. Cracked indentations in enamel just left of “E” and upper center most dentine indentations not used. B) Buccolingual partial cross section of right side first monkey molar. The de ntine tubules (DT) are the fine lines in the dentine (D) emanating from the pulp cavity. The upper surface of enamel (E) is occlusal and indentatio ns are visible and well defined in the dentine. E PC DT D 200 m Not used 200 m PC E D E D DT 200 m A B
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93 Figure 4-10 Left image Indent ation pattern on posterior asp ect of right first molar. Upper surface is occlusal. Parallel cutti ng lines can be seen. Right inset Well-defined indentations in posterior aspect of right first molar. Note cracking on uppermost indentation. That indentation was not used. 100 m 100 m cutting lines occlusal surface
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94 Figure 4-11 Elastic Recovery Method va lidation plot comparing results with published values. Mean values and ranges are shown. Dotted line represents equality between ER M results and published values. 0 30 60 90 0306090Published (GPa) ERM (GPa) Plexiglas Bovine Femur Glass
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95 Figure 4-12 ERM based derive d elastic constants variation with distance from the foramen edge expressed in normalized foramen radii. Circles (EL = longitudinal elastic modulus), triangles (ET = transverse elastic modulus), squares (GLT = shear modulus). 0 5 10 15 20 25 30 0123Lateromedial distance from foramen edge (1/r)Modulus (GPa)
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96 Figure 4-13 Coordinate rotati on angle (principal material direction) variation with distance from the foramen edge expressed in normalized foramen radii. 0 30 60 90 0123Lateromedial distance from foramen edge (1/r)Coordinate rotation (degrees )
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97 Figure 4-14 Correlation Method derived elastic modulus variation with distance from the foramen edge expressed in normalized foramen radii. 0 10 20 30 0123Mediolateral distance from foramen edge (1/r)Modulus (GPa)
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98 Figure 4-15 ERM derived longitudinal elas tic modulus (squares) and CM derived elastic modulus (circles). The va lues are plotted on together for comparison. The CM derived elastic modulus results are really a mirror image. 0 10 20 30 0123Distance from foramen edge (1/r)Elastic Modulus (GPa)
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99 Figure 4-16 Schematic of tooth enamel pris m tube orientation with respect to the Dentoenamel Junction (DEJ) and the occlusal (biting) surface. Dentoenamel Junction enamel prism tubes occlusal surface Cross section
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100 CHAPTER 5 FUTURE RESEARCH My research has suggested 5 future research projects. The pur pose of the suggested research is to extend my findings to continue improvements in understanding microindentation in bone. Bovine Plexiform Bone Investigate 2 ERM observations. The fi rst is planar isotropy in both the longitudinal and transverse planes in bovine femur. The second is the larger elastic modulus on the transverse plane than the long itudinal plane. A similar finding was made in monkey mandible. The second observation has not been previously reported in the literature. The investigation would in clude: scanning electron micr oscopy (SEM); X-ray and optical microscopy determination of mi neral density; microindentation; and nanoindentation. The causes for the observations could include directionally dependent mineralization. There could also be microstr uctural features that account for the reduced material recovery on the bovine femur transver se plane. In the ERM reduced material recovery results in larger derived elastic modulus. Fracture Toughness Fracture toughness correlation in bone. Th e objective of this future work is to investigate the hypothesis that there is no correlation between fracture toughness
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101 determined through macro specimen method and fracture toughness determined through microindentation and scanning el ectron microscopy method in bone. Perform traditional macro fracture toughness tests for Mode I crack in both the longitudinal and transverse dire ctions. At least 4 different bone types from different species should be selected. These specimens must differ in their hardness and elastic modulus. Using specimens from the same re gion of bone, perform microindentations in both longitudinal and transverse planes with the Knoop indent er. Prepare the specimens for scanning electron microscopy (SEM). From the images measure the apex crack length and determine the fracture toughness. Plot the results of each test against the macro test results on the ordinate and the microindentation results on the abscissa. Determine the best curve fit. If the null hypothesis can not be accepted and the coeffi cient of determination (R2) is large (>0.8), the resulting regression equa tion would represent a more simple method for derivation of fracture toughness in bone. Microindentation Affected Region Model the microindentation affected region. The objective of th e research is to experimentally determine the depth of the recovered (damaged) bone material and use it in finite element models [Giannakopoulos et al. 1994] for ultimate use as a bone model. Such a model could provide a better value for the elastic modulus of the material in the microindentation affected region. Elastic Recovery Method Constants Elastic recovery method (ERM) derived elas tic modulus results are generally lower than those derived by other methods. The ma in reason I found for the difference is the elastic modulus of the recovered compresse d material in the indentation region.
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102 However, another reason could be selection of the constants in the empirical equation used to compute elastic modulus. A set of experiments on bones with a range of harnesses and moduli could help apportioning the cause between the 2 competing explanations. The method for performing the tests are outlined by Amita y-Sadovsky and Wagner [1998] and Marshall et al. [1982]. Principal Material Direction Mapping The objective of the work is to compare the ERM based derived elastic moduli and iterative coordinate rotation method (ERMR) results with polarized light microscopy method results for mapping principal material directions in bone. A set of experiments on the same bone region mapping the principal material directions. Use the well documented equine MC foramen region. Prepare 2 longitudinal specimens by sectioning the bone into 2 slab s. One specimen should be approximately 100 m thick for transmission plane polarized light images. The other specimen should be approximately 1 mm thick for microindentation.
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103 APPENDIX MODULUS ESTIMATE CALCULATION This appendix provides the calculation details for estimation of the recovered indentation material elastic modulus. The pro cedure involved 2 steps: using the residual impression measured dimensions and applied load for a first estimate then using an equivalent column model to refine the estimate. For the first estimate of the wet-indented recovered material elastic modulus, I used the derivation reported by Loubet et al. [1984]. Their deriva tion adapted SneddonÂ’s [1965] load and penetration solution for a fl at ended cylindrical punch to the pyramidal Vickers indenter point. Their treatment e quated the Vickers projected contact area with the flat punch area. The resulting equation de scribed the analytical relationship between load and indenter penetration depth. They th en differentiated the equation with respect to penetration depth and solved for reduced elastic modulus. I took the following relationships from Dorner and Nix [1986] and Oliver and Pharr [1992]: rdP1 E dh2A (1) 22 i ri11 1 EEE (2) 1 2 2 i ri11 E(1) EE (3)
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104 where rE = reduced modulus, i = indenter, dP dh = slope of load displacement plot, A = projected area of the inde nter residual impression. Fo r the Knoop indenter point, based on simple geometry, 12dd A 2 where 1d = length of long diagonal, 2d = length of short diagonal. Two areas are computed one for the wet indentation and one for dry. The second term in equation (2) was ignored due the large difference in elastic modulus between the specimen and the indenter diamond. A maximum depth of 6.4 m for the wet-indented specimen was computed from the measured long diagonal (198.7 m) using the known angle of 172.5 between the two long diagonals. Another calculation, using the measured residual impression side-wall angles resulted, in a residual wet-indented depth of 1.2 m. The differential depth was computed by subtracting the residual im pression from the maximum depth. The projected elastic area (A) was computed fr om the measured residual impression long and short diagonals. The maximum indentation load was 0.1 kg (0.98 N). The wet –indented slope was 0.19 E6 N/m (Figure A-1). It was computed by dividing the maximum indentation load by the differential depth. W ith the assumption of 0.3 for Poisson’s ratio hw hd hm original surface hw = wet-indented depth hd = dry-indented depth hm = maximum indentation depth
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105 and the calculated projected el astic area from the measured diagonals, the elastic modulus from equation (1) was 3.2 GPa fo r the wet-indented specimen. Figure A-1 Load displacement plot The calculated elastic modulus is an estim ate of the recovere d material in the indentation site. The calculated value was larg er than actual because it assumed that the elastic half space was composed totally of the recovered material. In actuality the material is composed of two ma terials, one is the recovered material and the other is the intact bone. A refinement to the first estimate value involved constructing a simple model to find the effective thickness of the elastic ha lf space that would yield the same result. Then using that thickness an estimate is ma de of a new modulus ba sed on two regions in the effective thickness with an effective elas tic modulus equal to that estimated in the first step. The problem then becomes a simple series spring configuration. 0 0.4 0.8 1.2 02468Depth ( m)Load (N)
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106 Figure A-2 Schematic of the 2 material model. To find the effective thickness we set the indentation depth h from the (1) equal to the depth of a column and solv e for the effective thickness: P1 E h2A (3) P1 h E2A (4) effL P E Ah (5) effPL h EA (6) eff1 LA 2 (7) I then estimate the modulus of the recovere d material assuming the recovered material and bone are two springs in series: effcb111 kkk (8) where c c cEA k L b b effcEA k LL I then solve for cE: Leff = effective thickness keff = effective spring constant Lc = crushed material thickness kc = crushed material spring constant Lb = bone thickness kb = bone spring constant Ld, kcLb, kc Leff, keff
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107 1 effeff c effcbcLL 11 E1 ELEL (9) For my specific case; effE3.2GPa effL42m cL12m bE11GPa The result is 1154 MPa. The result sensitivity to the estimate of crushed material depth cL, is about 6% for a 0.5 m difference either increase or decrease. The range of recovered material elastic modulus estimate from these calculations is 889 MPa to 1154 MPa, given a recovered material depth range of 9 to 12 m.
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108 LIST OF REFERENCES Akkus O, Jepsen KJ, Rimnac CM. Microstruc tural aspects of the fracture process in human cortical bone. Journal of Materials Science 2000;35:6065-74. Amitay-Sadovsky E, Wagner HD. Evaluation of Young's Modulus of polymers from Knoop microindentation. Polymer Communications 1998;39(11):2387-90. Amprino R. Investigations on some physical properties of bone tissue. Acta Anatomica 1958;34:161-86. Catanese III J, Iverson EP, Ng RK, Keave ny TM. Heterogeneity of the mechanical properties of demineralized bone. Jo urnal of Biomechanics 1999;32:1365-9. Cheng Y, Cheng C. Scaling approach to conica l indentation in elastic-plastic solids with work hardening. Journal of A pplied Physics 1998;84(3):1284-1291. Cowin SC. Mechanics of materials. In: Co win SC, editor. Bone Mechanics, 2nd Edition. 2001, CRC Press. p. 6-12-6-19. Currey JD, Brear K. Hardness, Young's modulus and yield stress in mammalian mineralized tissue. Journal of Material Sc ience Material in Me dicine, 1990;1:14-20. Dorner MF, Nix WD. A method for interpreting the data from depth-sensing indentation instruments. Journal of Materi al Research 1984; 1(4): 601-9. Giannakopoulos AE, Larsson P.-L, Vestergaar d R. Analysis of Vickers indentation. International Journal of Solid s and Structures 1994;19:2679-708. Guo XE. Mechanical Properties of cortical bone and cancellous bone tissue. In: Cowin SC, Ed. Bone Mechanics, 2nd Edition. Boca Raton:, CRC Press, 2001. p. 10-1-23. Hensberger S, Kulik A, Zysset PH. Nanoindent ation discriminates the elastic properties of individual human bone lamella under dry and physiological conditions. Bone 2002;30(1):178-84. Huja SS, Katona TR, Roberts WE. Microha rdness testing of bone. In: An YH, Draughn RA, editors. Mechanical test ing of bone and the bone-implant interface. Boca Raton (FL): CRC Press; 2000. p. 247-256
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109 Kinney JH, Pople JA, Marshall GW, Marshall SJ. Collagen orientation and crystallite size in human dentin: A small angle X-ra y study. Calcified Tissue International 2001;69:31-7. Lawn BR, Evans AG, Marshall DB. Elastic/Plastic damage in ceramics: The median/radial crack system. Journal of the American Ceramic Society 1980;63(910):574-81. Lertchirakarn V, Palamara JE, Messer HH. Anis otropy of tensile streng th of root dentin. Journal of Dental Research 2001;80(2):453-6. Loubet JL, Georges JM, Marche sini O, Meille G. Vicker s indentation curves of magnesium-oxide (MgO). Journa l of Tribology 1984;106(1):43-8. Lum SK, Duncan-Hewitt WC. A comparison of elastic moduli derived from theory, microindentation, and ultrasonic testing. Ph armaceutical Research 1996;13(11):1739-45. Mahoney E, Holt A, Swain M, Kilpatrick N. The hardness and modulus of elasticity of primary molar teeth: an ultra-micro-inde ntation study. Journal of Dentistry 2000;28:58994. Marieb EN. Human Anatomy and Physio logy. Menlo Park, CA: Benjamin/Cummings Science Publishing; 1998. p. 170 Marshall DB, Noma T, Evans AG. A simple method for determining elastic-modulus-to hardness ratios using Knoop indentation measurements. Communication of The American Ceramic Society 1982;65:175-6. Marshall Jr. GW, Balooch M, Gallager RR, Gansky SA, Marshall SJ. Mechanical properties of the dentoenamel junction: AF M studies of nanohardness, elastic modulus, and fracture. Journal of Biomedi cal Materials Res earch, 2001;54:87-95. Marx V, Balke H. A critical investigation of the unloading behavior of sharp indentation. Acta mater. 1997;45(9):3791-3800. MatWeb. The On-line Materials Inform ation Source. Available from URL: http://www.matweb.com/. Site last visited January 2003. Meredith N, Sherrif M, Setchell DJ, Swan son SAV. Measurement of the microhardness and YoungÂ’s modulus of human enamel and de ntine using an inde ntation technique. Archives of Oral Biology 1996;40(6):539-45. McKoy BE, An YH, Friedman. Factors aff ecting the strength of the bone-implant interface. In: An YH, Draughn RA, editors. Mechanical testing of bone and the boneimplant interface. Boca Raton (FL): CRC Press; 2000. p. 439-462 Mitutoyo Corporation. Instruction manual for micro hardness testing machine model: HM-112. Japan: Mitutoyo; 1998.
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110 Oliver WC, Pharr GM. An improved techni que for determining hardness and elastic modulus using load and displacement sensi ng indentation experiments. Journal of Material Research 1992;7(6):1564-83. Ramrakhiani M, Pal D, Murty TS. Micro-i ndentation hardness studies on human bones. Acta Anatomica 1979;103:358-62. Rapoff AJ, Fontanel O, Venkatara man S. Proceedings of the 51st Bioengineering Division Conference of the American Society of M echanical Engineers, Key Biscayne, FL. 2003. Riches PE, Everitt NM, Heggie, McNally DS. Microhardness anisotropy of lamellar bone. Journal of Biomechanics 1997;30(10):1059-61. Riester L, Bell TJ, Fischer-Cripps AC. Analysis of depth-sensing inde ntation tests with a Knoop indenter. Journal of Mate rials Research 2001;16(6):1660-7 Riester L, Blau PJ, Lara-Curzio E, Breder K. Nanoindentation with Knoop indenter. Thin Solid Films 2000;(377-378):635-9. Rho JY, Kuhn-Spearing L, Zioupos P. Mechan ical properties and the hierarchical structure of bone. Medical Engineeri ng and Physics 1998; 20(2): 92-102. Rho JY, Pharr GM. Effects of drying on th e mechanical properties of bovine femur measured by nanoindentation. Journal of Mate rials Science: Mate rials in Medicine 1999;10:485-8. Sneddon IN. The relation between load and pene tration in the axisymmetric Boussinesq problem for a punch of arbitrary profile. Inte rnational Journal of Engineering Science 1965; 3: 47-57. Vander Voort GF, Lucas GM. Microindentati on hardness testing. Advanced Materials and Processes 1998;154 (3):21-25. Xu HHK, Smith DT, Jahanmir S, Romberg E, Kelly JR, Thompson VP, Rekow ED. Indentation damage and mechanical propertie s of human enamel and dentin. Journal of Dental Research, 1998;77(3):472-80. Zysset PK, Guo XE, Hoffler CE, Moore KE, Go ldstein SA. Elastic modulus and hardness of cortical and trabecular bone lamellae measured by nanoindentation in the human. Journal of Biomechanics 1999;32(10):1005-1012.
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111 BIOGRAPHICAL SKETCH Born in Paterson, NJ, Wes was raised by his grandmother until age 8. During the 12 years of primary and secondary schooling he attended 14 different schools. Joining the US Navy at age 17, after graduating high sc hool, Wes served aboard conventional and nuclear powered submarines as an electronics technician and reac tor operator. After completing 7 years service, during the Viet Na m era, he attended college and received a B.S. in Nuclear Engineering with honors in 1974 from the University of Florida. Wes then spent 24 years in the nuclear power plant industry wh ich included various positions from safety engineer to departmental and plant manager. During that time Wes attended and graduated from The Humanist Institute and became a certified Humanist Minister. He returned to university in 1998 to purs ue graduate education in biomedical engineering. Wes received several honors dur ing his graduate studies including election to the national Aeronautical Engineering Honorary Society and winning the Costello Award fellowship for excellence in biomedical engineering.
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