core.ac.uk · Acknowledgements . I am greatly indebted to my supervisor, A/Prof. Adrian Yap U Jin,...

BIOMECHANICAL CHARACTERIZATION OF

DENTAL COMPOSITE RESTORATIVES – A MICRO-INDENTATION APPROACH

CHUNG SEW MENG (B.Eng(Hons), M.Eng, NUS)

A THESIS SUBMITTED

FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

DEPARTMENT OF RESTORATIVE DENTISTRY

NATIONAL UNIVERSITY OF SINGAPORE

2008

Acknowledgements

I am greatly indebted to my supervisor, A/Prof. Adrian Yap U Jin, for his

continuous offering of guidance, encouragement and advice throughout the course

of my research work. Despite his busy schedule, he always made time for

discussion and sharing his expertise. He had truly motivated me to complete this

PhD thesis.

I would also like to express my appreciation to my co-supervisors, A/Prof. Tsai

Kuo Tsing and A/Prof. Lim Chwee Teck for contributing their invaluable

engineering knowledge towards this research project.

I would like to thank A/Prof. Neo Chiew Lian, Head of the Department of

Restorative Dentistry for her support and giving me the opportunity to undertake

this research.

I am thankful to A/Prof Zeng Kai Yang for his advice and assistance in

developing the indentation test method. Special thanks to Prof. Dietmar W

Hutmacher for helping me to proof-read the thesis. I would also like to thank all

staffs and students from the Faculty of Dentistry and Department of Mechanical

Engineering for their help in the experimental work.

Finally, I am particularly grateful to my wife Hwee Kheng, for her wonderful

support, concern and sacrifies all this while especially during the course of writing

up this thesis.

Preface

Sections of the results related to the research in this thesis have been presented and published.

1. Chung SM, Yap AU, Koh WK, Tsai KT, Lim CT. Measurement of

Poisson's ratio of dental composite restorative materials. Biomaterials 2004;25(13):2455-60.

2. Chung SM, Yap AU, Chandra SP, Lim CT. Flexural strength of dental composite restoratives: comparison of biaxial and three-point bending test. J Biomed Mater Res B Appl Biomater 2004;71(2):278-83.

3. Chung SM, Yap AU, Tsai KT, Yap FL. Elastic modulus of resin-based

dental restorative materials: a microindentation approach. J Biomed Mater Res B Appl Biomater 2005;72(2):246-53.

4. Chung SM, Yap AU. Effects of surface finish on indentation modulus and

hardness of dental composite restoratives. Dent Mater 2005;21(11):1008-16.

5. Yap AU, Chung SM, Rong Y, Tsai KT. Effects of aging on mechanical

properties of composite restoratives: a depth-sensing microindentation approach. Oper Dent 2004;29(5):547-53.

6. Yap AU, Chung SM, Chow WS, Tsai KT, Lim CT. Fracture resistance of

compomer and composite restoratives. Oper Dent 2004;29(1):29-34.

http://www.ncbi.nlm.nih.gov/pubmed/14751729?ordinalpos=10&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVDocSum�






i

Table of Contents

Acknowledgment

Preface

Table of Contents i

Abstract iv

List of Tables vii

List of Figures ix

List of Symbols xi

1. Introduction 1

2. Literature Review 2.1 Mechanical Characterization of Resin-based Dental Materials

2.1.1 Introduction 6 2.1.2 Dental composite restoratives and their

characterization 6 2.1.3 Clinical relevance of material properties 9 2.1.4 Plastic properties – Hardness 10 2.1.5 Elastic properties – Modulus 11 2.1.6 Strength properties 13 2.1.7 Fracture properties – Toughness 14

2.2 Depth-sensing Indentation Method

2.2.1 Introduction 15 2.2.2 Determination of elastic properties by depth- sensing indentation method 15 2.2.3 Determination of yield strength by depth-sensing

indentation method 22 2.2.4 Errors associated with depth-sensing indentation 26 2.2.5 Indentation fracture mechanics 33

3. Objective and Research Program 3.1 Objectives 39 3.2 Research Program 40

ii

4. Development of Depth-sensing Micro-indentation Test Method for Resin-based Dental Materials 4.1 Introduction 45 4.2 Instrumentation for Depth-sensing Micro-indentation Test 45 4.3 Poisson’s ratio of Dental Composite Restoratives

4.3.1 Introduction 49 4.3.2 Materials and method 49 4.3.3 Results and discussion 52

4.4 Effects of Surface Roughness


4.5 Effects of Experimental Variables

4.5.1 Introduction 64 4.5.2 Materials & method 66 4.5.3 Results and discussion 67

5. Elasto-plastic and Strength Properties of Dental Composite Restoratives 5.1 Introduction 79 5.2 Determination of Flexural Properties of Dental Composites by ISO 4049 Test Method


5.3 Determination of Micro-hardness and Elastic Modulus of Dental Composites using Depth-sensing Indentation Method


5.4 Determination of Yield Strength of Dental Composites


6. Indentation Fracture of Dental Composite Restoratives 6.1 Introduction 110 6.2 Determination of KIC of Dental Composites by Three-point Bend Test


iii

6.3 Determination of KIC of Dental Composites by Indentation Fracture Test


7. Conclusions and Recommendations 7.1 Conclusions

7.1.1 Depth-sensing micro-indentation methodology 130 7.1.2 Experimental and specimen-related variables 130 7.1.3 Elasto-plastic properties 131 7.1.4 Indentation fracture 132

7.2 Recommendations 7.2.1 Direct Amax measurement 133 7.2.2 Indentation fracture equation for dental composite restoratives 134

Bibliography 135

iv

Abstract

The clinical success of dental restorative materials is dependent on a wide

range of factors ranging from the selection of materials to the placement

technique. From the material point of view, mechanical characterization of

restorative materials is of utmost importance in order to understand their

deformation behavior when subjected to different loading in vitro. From a clinical

point of view, such data sets are important to clinicians when it comes to the

selection of appropriate material for restoring tooth at different locations or

different class of cavities. The current test standard for resin-based dental

restorative materials testing is documented in ISO 4049. Within this standard, the

flexural test method requires large beam specimens which have no clinical

relevance. Furthermore, such specimens are technically difficult to prepare and

hence expensive. In view of the increasing clinical demands to apply dental

composite restoratives, there is a need to develop a more reliable and user-friendly

test method which is based on clinically-relevant size specimens for the

mechanical characterization. The current research aims to develop and apply the

indentation method as a single test platform for determining the four fundamental

mechanical properties namely hardness, modulus, strength and fracture toughness

of dental composite restoratives.

A customized indentation head that was capable of measuring the load and

displacement with high accuracy was developed in collaboration with Instron

Singapore. The instrumentation set-up was first used to investigate various

v

experimental and specimen-related variables in the depth-sensing indentation test

of dental composite restoratives. The variables investigated included surface

roughness, maximum indentation load, loading/unloading strain rate, and load

holding period. Five materials (3M ESPE: Z100, Z250, F2000, A110 and Filtek

Flow) representing the spectrum of composite restoratives currently available

were selected for the experimental investigations. At the peak indentation load of

10N, both the surface roughness and loading/unloading strain rate have no effects

on all the materials investigated. The indentation size effects and creep have

negligible effects on the measured hardness and modulus of brittle dental

composite restoratives. The depth-sensing indentation protocol was established as

follows; test specimen (3x3x2 mm3) is loaded at 0.0005 mm/s until Pmax of 10 N is

attained and then held for a period of 10 seconds, it is then unloaded fully at a rate

of 0.0002 mm/s.

Subsequently, the indentation hardness, modulus, yield strength and

fracture toughness were measured and calculated for all composite materials. The

indentation modulus and fracture toughness values were then compared and

correlated with the test data obtained from the conventional three-point bend test

method. The indentation hardness and modulus results were highly reproducible.

A significant, positive and strong correlation was found between the flexural and

indentation modulus. Correlation for KIC between SENB and indentation fracture

testing was not significant. It was found that the empirical constant for modelling

KIC of conventional micro and minifilled composites differs from that of flowable

composites and compomers. Within the limitation of the current research, the

vi

results support the original hypotheses of this PhD project that depth-sensing

indentation method has the potential to be an alternate test method for determining

the elastic modulus of resin-based dental composite restoratives. The semi-

empirical method used to determine the indentation yield strength has been shown

useful as a measure of the incipient point of yielding in these resin-based dental

materials. The application of indentation fracture test on dental composite

materials warrants further research.

vii

List of Tables

Table 4.1 Specifications of materials investigated.

Table 4.2 Mean Poisson’s ratio of the composite materials (n=8) determined by tensile test method.

Table 4.3 Comparison of Poisson’s ratio between materials.

Table 4.4 Polishing protocol for dental composite restoratives.

Table 4.5 Mean surface roughness (Ra), indentation hardness (H) and modulus (Ein) of materials investigated.

Table 4.6 Comparison of surface roughness, hardness and indentation modulus of dental composites investigated.

Table 4.7 Indentation modulus (Ein) and hardness (H) of dental composites at different loading/unloading rate.

Table 4.8 Indentation modulus (Ein) and hardness (H) of dental composites at different indentation load.

Table 4.9 Indentation modulus (Ein) and hardness (H) of dental composites at different load holding time.

Table 4.10 Comparison of hardness and indentation modulus of various dental composites at different test variables investigated.

Table 5.1 Mean flexural strength and modulus of the composite materials after the two conditioning periods.

Table 5.2 Comparison of flexural strength and modulus between materials.

Table 5.3 Mean hardness, indentation and flexural modulus of the various composites after 7 days and 30 days of conditioning.

Table 5.4 Comparison of hardness, indentation and flexural modulus.

Table 5.5 Mean yield strength of the various composites determined using power and polynomial curve fitting method.

Table 5.6 Comparison of yield strength of various dental composites.

Table 6.1 Mean KIC of the composite materials determined by three-point bending test method.

viii

Table 6.2 Validity test of the KIC values determined by three-point bending test method.

Table 6.3 Mean KIC of the composite materials determined by three-point bending test and indentation fracture method.

Table 6.4 Comparison of KIC between materials obtained from different methods.

Table 6.5 Determination of the empirical constant (ξ) using different indentation fracture mechanics equations.

ix

List of Figures Fig. 2.1 A load-displacement graph for an indentation experiment. Fig. 2.2 Determination of weight factor θ from the indentation P-h

data Fig. 2.3 Schematic representation of (a) radial-median or half-penny and

(b) Palmqvist crack system with c, a and l being the indent-crack length.

Fig. 3.1 Experimental design roadmap for the research program. Fig. 4.1 Experimental set-up for the depth-sensing micro-indentation

test. Fig. 4.2 Correlation between Poisson’s ratio and filler vol. of dental

composites. Fig. 4.3 SEM photographs of specimen surfaces with different

polishing methods. Fig. 4.4 Cross-sectional view of the indent impression for composite

F2000. Fig. 4.5 Load-displacement (P-h) profiles and creep data from a 10-N

indent with T=10 s into various materials.

Fig. 4.6 Effects of strain rate on indentation modulus and hardness.

Fig. 4.7 Effects of load on indentation modulus and hardness.

Fig. 4.8 Effects of holding time on indentation modulus and hardness.

Fig. 5.1 Load-displacement curves of various materials when tested under ISO 4049 three-point bending test.

Fig. 5.2 Load-displacement (P-h) curves of various materials obtained

in the depth-sensing micro-indentation test.

Fig. 5.3 Photographs of the indent impressions (Pmax = 10 N) for various dental composite restoratives.

x

Fig. 5.4 Correlation between the modulus and filler volume content of

dental composite restoratives. Fig. 5.5 Load to h2 relationship of a typical indent. The lower portion

of the plot deviates from linearity. Fig. 5.6 Curve fitting for F2000 using P=C”h2+y. Fig. 5.7 Correlation between flexural strength and indentation yield

strength. Fig. 5.8 (a) Compressive stress-strain curves, (b) Comparison of

flexural, yield and compressive strength of dental composites, (c) Normalised strength plots.

Fig. 6.1 Three-point bend test set-up for determining the KIC. Fig. 6.2 Residual impression of corner cube indentation fracture

showing characteristics dimensions c and a of radial-median crack.

Fig. 6.3 (a) KIC of dental composite restoratives obtained from

different methods and (b) its normalized plot. Fig. 6.4 KIC correlation plot for different groups of dental composites.

xi

List of Symbols

E Young’s modulus,

Ef flexural modulus,

Ein indentation modulus,

Eo elastic modulus of indenter,

Er Reduced modulus,

ν Poisson’s ratio,

ν o Poisson’s ratio of indenter,

G shear modulus,

B bulk modulus,

H hardness,

A area,

Ac projected contact area,

Amax maximum projected contact area,

Fmax maximum flexure load prior to fracture,

P indentation load,

Pr concentrated load,

Pmax maximum indentation load,

h displacement or penetration depth,

hmax maximum penetration depth,

hc contact depth,

hf final or residual depth,

hi initial depth of penetration,

∆h change in penetration depth,

xii

t thickness of the specimen,

W width of the specimen,

L the distance between the supports in three-point bend test,

S slope of the indentation P-h graph, or dP/dh,

C loading curvature,

Ra surface roughness,

KIC fracture toughness or stress intensity factor (mode 1),

co crack length measured from the center of the indent to the end of crack,

χr dimensionless parameter represents the stress field intensity at Pr,

ξ empirical constant,

η numerical constant and is equal to 6 for Vickers indeter,

ε empirical constant and is equal to 0.75 for Vickers indentation,

σf flexural stress,

σy yield stress.

1

Chapter 1

1. Introduction

During the last two decades, the use of dental composites has increased

exponentially in restorative dentistry due to increasing aesthetic demands and

concerns of mercury toxicity associated with amalgam. In the formulation and

development of dental composite restoratives, it is of paramount importance to

understand their intrinsic mechanical properties in order to achieve the best

clinical results. For mechanical testing of dental restorative materials, the plastic

(hardness), elastic (modulus), strength and fracture properties are most often being

evaluated to determine the deformation behaviour of these materials under

different loading regimes.

The hardness measures the resistance of the material to permanent plastic

deformation. The elastic modulus yields useful information as it determines the

stress-strain behaviour of the material under loading. Ideally, the elastic modulus

of the restorative materials must be closely matched to that of enamel and/or

dentin. This would then allow a more uniform stress distribution across the

restorations-enamel/dentin interface during mastication. An imperfect match of

the elastic values between the materials and the surrounding hard tissues will lead

to marginal adaptation and fracture problems (Lambrechts et al., 1987). During

the preparation and placement of dental composite restoratives, imperfections

such as voids and micro-cracks inevitably exist within the materials to some

extent. Strength measures the maximum stress that a material can withstand prior

2

to failure. The fracture toughness or the stress intensity factor is a crucial

parameter which measures the resistance of the materials to crack propagation

before leading to catastrophic failures.

The current worldwide standard screening criterion for resin-based dental

restorative materials is documented in ISO 4049. For mechanical determination,

it only covers the procedure for determining elastic modulus and strength in a

flexural three-point bend test. The ISO flexural test requires beam specimens with

dimensions (25 x 2 x 2) mm. It is technically difficult to prepare these large

specimens and the specimens are very susceptible to flaws such as voids.

Moreover, at least three overlapping irradiations are required for visible-light-

cured composites resulting in specimens which may not be homogeneous. The

above may influence the stress distribution when the specimens are loaded, which

may in turn affect the experimental results. Apart from material and time

consumption, these large specimens may not be clinically realistic, considering the

size of mesio-distal width of molars to be only about 11 mm. In view of the

drawbacks associated with flexural test, there is a need to develop a better and

more reliable screening test that involves specimens that are of appropriate size-

scale.

The development of indentation testing methodologies has been rapid in

the area of thin films and microelectronics industries. During an indentation test,

an indenter, usually made of a hard material typically diamond, is pressed into the

specimen. From the specimen’s deformation in response to the indentation load,

various mechanical properties of the specimen can be deduced. Indentation test is

3

a popular method for determining the hardness of a wide range of materials like

metals, glass, ceramics, and thin film surface coatings because it is fast and

inexpensive. It can also be effectively used on small volumes of materials. In the

development of depth-sensing indentation methodology, which involves the

continuous tracking of applied load and indenter’s displacement, the elastic

properties of the material can also be deduced. This technique relies on the fact

that the materials undergo elastic recovery when the indenter is withdrawn from

the indented material. With the advancement in technology, many commercially

available indentation test systems are capable of measuring load and displacement

with superior accuracy and precision. Apart from instrumentation, much research

(Doerner and Nix, 1986; Oliver & Pharr, 1992; Pharr et al., 1992; Giannakopoulos

and Suresh, 1999; Dao et al., 2001) has been carried out to improve and refine the

indentation methodology so as to make this measurement technique a reliable and

accurate means to determine the elasto-plastic properties of materials. In 2001,

Zeng and Chiu proposed a semi-empirical method to determine the yield strength

of a material from the indentation test data. As compared to other methods

(Giannakopoulos and Suresh, 1999; Dao et al., 2001), Zeng and Chiu’s method

was more generalized and it had been verified on spectrum of materials ranging

from ductile metals to brittle ceramic materials. This method was established

based on an observation that the stress-strain relation of elastic-plastic materials

was between that of elastic and elastic perfect-plastic. As dental composites differ

greatly from metals and pure ceramics, its application on this group of complex

material has yet to be researched.

4

In dentistry, the indentation test method has been employed to determine

the mechanical properties of hard tissues (Meredith et al., 1996; Xu et al., 1998;

Marshall et al., 2001; Poolthong et al., 2001; Kishen et al., 2000), investment

materials (Low and Swain, 2000), and composites (Xu et al., 2002). Most of

these studies were in nanometer scale. Micro-indentation test which is required to

determine the bulk material properties of dental composite materials has not been

reported, yet.

The use of indentation fracture technique to determine the fracture

toughness (KIC) of materials has been well established in brittle materials such as

glass and ceramic (Lawn and Marshall, 1979; Anstis et al., 1981). The indentation

fracture method involves the understanding of the contact stress field within

which the cracks evolve. Such fields are primarily determined by the indenter

geometry and intrinsic material properties which include hardness, modulus and

toughness. Among various crack system, the radial-median cracks produced by

sharp pyramidal indenter is the most widely used fracture testing methodologies

for brittle material (Lawn, 1993). With correct measurement of the crack

morphology and material properties, the indentation fracture method provides a

user friendly, cost effective and reliable way in determining the fracture toughness

of materials. In the evaluation of the fracture toughness of dental composite

restoratives, the three-point bend test method with using single-edge notched

beam (SENB) specimen (ASTM E-399 and ASTM D-5045) were most commonly

being employed (Bonilla et al., 2001; Bonilla et al., 2003). This test method

which involves large specimens suffers the same drawbacks as discussed earlier.

Furthermore, the need to initiate a sharp Chevron notch on the dental composite

5

specimen is experimentally difficult and resulting in highly deviated test results.

The use of indentation fracture theory to determine the KIC of dental restorative

materials has not been well established, yet.

Given the fact that the restoratives are subjected to compressive load

primarily in vivo, the compressive nature of the indentation test may be more

relevant. Also in considering the drawbacks associated with the three-point bend

test as discussed earlier, it is hypothesized that the micro-indentation has potential

to be an alternative test method in the mechanical characterization of resin-based

dental composite restoratives. Micro-indentation can be arbitrarily defined as an

indent which has diagonal length of less than 100 µm (Samuels, 1984).

Considering the size of the filler particles of dental composites which is typically

less than 5 µm, micro-indentation is the appropriate size-scale for determining the

bulk intrinsic material properties of this group of material. Thus, this research

project aims to evaluate if the depth-sensing micro-indentation test is suitable to

determine the elasto-plastic, strength and fracture properties of resin-based dental

composite restoratives.

6

Chapter 2

2. Literature Review

2.1 Mechanical Characterization of Resin-based Dental Materials

2.1.1 Introduction

Some basic knowledge of the formulation of dental composite restoratives is

essential in order to understand their mechanical properties. In this chapter, the

composition of dental composites and its relations to various mechanical

properties will be presented. Following this, the current mechanical

characterization method for resin-based dental composite materials and its

drawbacks will be discussed. In section 2.1.3, the effects of some critical

mechanical properties on the clinical performance of dental composite restoratives

will be described. Lastly, the various measurement methods for determining the

elasto-plastic, strength and fracture properties of dental bio-composites will be

reviewed.

2.1.2 Dental composite restoratives and their characterization

Dental composite consists of organic resin-based polymer, inorganic fillers as

reinforcement, and silane coupling agent. Currently, it is the most popular

material being used in modern dentistry because it combines both the functions of

esthetics and ease of use due to its light polymerizable base. Similar to other

composite structures, the type and composition of the resin matrix as well as the

filler particles have strong influence on the material properties, which ultimately

determines the clinical performance of these materials.

7

In particular, the filler particle size and type have strong influence on the

mechanical and wear properties of the materials. The filler particles size can be

classified into three main categories: midifills (average size = 1 - 5 µm), minifills

(average size = 0.6 - 1.0 µm), and microfills (average size = 0.04 µm) (Ferracane,

1995). Filler particles greater than 50 microns are rarely used today. Fillers are

used in dental composites to increase strength (Ferracane et al., 1987; Chung and

Greener, 1990), increase stiffness (Braem et al.,1989; Kim et al., 1994), reduce

polymerization contraction and thermal expansion, provide radiopacity (van

Dijken et al., 1989), enhance esthetics, and improve handling. In general, the

physico-mechanical properties of composites are improved in direct relationship

to the amount of filler added. Composite wear decreases as the filler level

increases (Condon and Ferracane, 1997). Both fatigue resistance and flexural

strength of composites were also found to increase with increased filler level (Xu

et al., 2000). Braem and others (1989) have also reported that modulus and

hardness of composite increased monotonically with filler level. The elastic

modulus and other mechanical properties such as tensile strength, diametral

tensile strength, fracture toughness and many others are important in determining

the resistance to occlusal forces and longevity of composite restoratives.

The current worldwide standard screening criterion for resin-based dental

restorative materials is documented in ISO 4049. In the mechanical evaluation, it

covers only the procedure for determining flexural strength and modulus by the

three-point bend test method. The ISO flexural test requires beam specimens with

dimensions 25 x 2 x 2 mm3. In this test, the beam specimen is freely supported on

two ball contacts at a span of 20 mm. The axial load is applied on top and at the

8

centre of the specimen at a rate of 0.5 mm/min until the specimen is fractured.

The load and displacement information up to the point of fracture are to be

recorded continuously in an universal testing system. The flexural strength (σf)

and modulus (Ef) was calculated using the following equation:

2max

23

WtLF

f =σ …….. (2.1a)

= 3

3

4WtL

DFE f …….. (2.1b)

Where

Fmax is the maximum load prior to fracture, in newtons;

L is the distance, in millimeters, between the supports (20 mm);

F /D is the slope of the load-displacement graph, in newtons/millimeters;

W is the width, in millimeters, of the specimen measured prior to testing; and

t is the thickness, in millimeters, of the specimens measure prior to testing.

In the flexural test, the tensile stress developed at the bottom of the

specimen is more predominant. Therefore, the measured flexural modulus would

have value close to that of the tensile modulus of the material. However the

dental restoratives are subjected to compressive stresses primarily in vivo. Apart

from the requirement of large beam specimen as discussed earlier, this test also

suffers another drawback of being destructive in nature. Hence, larger amount of

materials are required for this test which deem this method non cost-effective.

Furthermore, multiple overlapping curing is necessary to polymerize the large

beam specimen which may lead to inhomogeneity of specimens. Within the

overlapping irradiation zones, more radicals are generated from the reaction

between the activator and the photo-initiator, which results in higher degree of

9

polymerization as compared to the adjacent region (Flores et al., 2000). Finally, it

is technically difficult to prepare flaws-free specimen at this length. Any voids or

irregularities present in the materials would result in uneven stress distribution

within the specimen which may influence the test result.

2.1.3 Clinical relevance of mechanical properties

In the evaluation and selection of dental restorative materials, biological,

chemical, mechanical and physical properties must be considered. Apart from not

causing any harmful effects in the mouth, dental restorative materials should also

possess suitable mechanical strength, rigidity, hardness and wear resistance.

Although the physico-mechanical performance of composite resins has been

improved substantially since the introduction of BIS-GMA resin by Bowen

(1956), the mechanical properties of composite resins are still not adequate for

high stress-bearing posterior restorations (Wilson et al., 1997). Polymerization

shrinkage remains the greatest problem with dental composites. The main clinical

failures associated with dental composite include marginal degradation (Bryant

and Hodge, 1994; Ferracane et al., 1997; Ferracane and Condon, 1999) and

fractures within the body of restorations (Roulet, 1988).

The close marginal adaptation between the restoration and enamel and/or

dentin is important for the prevention of secondary caries, reduction of marginal

staining and breakdown. Thus, it is important to understand materials

deformation behaviour under different loading conditions. If the elastic properties

of composites could be matched to those of the tissue, either enamel or dentin,

10

with which the materials are in contact, marginal separation by mechanical

deformation during mastication would be minimal. The loading stresses would be

transmitted more uniformly across the restoration-tooth interfaces. Therefore, the

modulus of the dental restorative materials is an important mechanical parameter

which could influence the longevity of the material. It must possess an adequate

value of elasticity so that the restorative materials do not deform permanently after

the masticatory load is being removed.

In view of its brittle nature, fracture is one of the common clinical failures

associated with dental composite restoratives, especially in the stress-bearing

posterior restorations (Roulet, 1988). As the posterior restorations are subjected

to high load conditions, the material must have sufficient mechanical

characteristics to withstand the marginal chipping and body bulk fracture (Roulet,

1987). Such destructions are related to the resistance of the material to fracture or

crack formation and propagation (Bonilla et al., 2001). Occurring either naturally

in a material or during the length of service, micro-cracks and flaws developed in

the restorative materials can lead to catastrophic crack propagation which results

in marginal fracture and surface degradation (Leinfelder, 1981).

2.1.4 Plastic properties – Hardness

Hardness (H) is defined as the resistance to permanent indentation or penetration.

It is, however, difficult to formulate a definition that is completely acceptable,

since any test method will involve complex interaction of stresses in the material

being tested from applied force. Despite this condition, the most common concept

11

of hard and soft substances is the relative resistance they offer to indentation

(Craig, 1993). Since it is measuring the contact pressure, hardness can be defined

as the ratio of the indentation force over the projected contact area. Among the

properties that are related to the hardness of a material are strength, proportional

limit, and ductility. Hardness measurement can be defined as macro-, micro- or

nano- scale according to the forces applied and displacements obtained.

Rockwell, Brinell, Berkovich, Vickers, Knoop and Shore hardness are the

different types of hardness methods available with both Vickers and Knoop

hardness among the most common test methods used for the measurement of

dental restorative materials.

In dentistry, hardness has been commonly used as a quick test parameter to

evaluate any possible change in mechanical properties when the material is

subjected to different environmental conditions (McKinney et al., 1987;

Mohamed-Tahir et al., 2005). In addition, hardness has also been used to predict

the wear resistance of a material and its ability to abrade or be abraded by

opposing dental structures and materials (Anusavice, 1996).

2.1.5 Elastic properties – Modulus

Elastic modulus which refers to the relative stiffness or rigidity of a material is a

measurement of the slope of the elastic region of the stress-strain curve

(Anusavice, 1996). It relates the deformation behaviour of a material to the

applied stress and the corresponding strain within the proportional limit.

12

The modulus of a material can be measured using both dynamic and static

methods. The three-point bending flexural test being employed in ISO 4049 is

among the static methods used to determine the elastic modulus of resin-based

dental restorative materials. Other test methods include mechanical resonance

frequencies technique (Spinner and Tefft, 1961), dynamic mechanical thermal

analysis (Wilson and Turner, 1987; Jacobsen and Darr, 1997) and the ultrasonic

method (Jones and Rizkallah, 1996). However, most of these techniques involved

either complicated set-up or elevated range of temperature. In addition, the

requirement of large sample sizes of (35x5x1.5 mm3) for dynamic modulus

(Braem et al., 1987) and (2x2x25 mm3) for static modulus are major

disadvantages.

Apart from the above, depth-sensing indentation method is a novel method

to determine the elastic property of a material. This technique utilises small

specimens and relies on the fact that the materials undergo elastic recovery when

the indenter is withdrawn from the indented material. In dentistry, the indentation

test method has been employed to determine the elastic modulus of dental hard

tissues (Meredith et al., 1996, Xu et al., 1998, Kishen et al., 2000), investment

materials (Low and Swain, 2000), and composites (Xu et al., 2002). Most of

these studies were on the nanometer scale. Micro-indentation test which is

required to determine the bulk material properties of dental composite materials

has not been reported.

13

2.1.6 Strength properties

Strength measures the maximum stress of a material at the point of failure. It is

not an intrinsic mechanical property, but rather a conditional property which

depends largely on the loading mode and the resulting stress state. Flexural

strength is most often being measured in the mechanical characterization of resin-

based dental composite materials. This test method is documented in ISO 4049 in

which the strength is determined in a three-point bending test. Apart from flexural

test, diametral tensile (Della et al., 2008; Lu et al., 2006; Soares et al., 2005) and

compressive tests (Silva and Dias, 2009; Yüzügüllü et al., 2008) are among other

methods being used in determining the strength properties of dental materials.

Yield strength or yield point has been known to relate to the plastic

properties or hardness of a material, especially in the case of metals. It measures

the stress at which a material begins to deform plastically. In the literatures, few

analytical and empirical methods (Giannakopoulos et al., 1994; Giannakopoulos

and Suresh, 1997; Giannakopoulos and Suresh, 1999; Dao et al., 2001) have been

reported in extracting the yield strength and strain hardening component of a

material from the indentation test data. Most of these studies were carried out on

metals which had different stress-strain behavior as compared to dental composite

materials. In 2001, Zeng and Chiu proposed a more generalized semi-empirical

method in determining the yield strength of a material. This method relied on the

fact that the stress-strain relation of elastic-plastic materials was between that of

elastic and elastic perfect-plastic. Its accuracy when apply to dental composite

materials has yet to be verified.

http://www.ncbi.nlm.nih.gov/sites/entrez?Db=pubmed&Cmd=Search&Term=%22Dias%20KR%22%5BAuthor%5D&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_DiscoveryPanel.Pubmed_RVAbstractPlus�

14

2.1.7 Fracture properties – Toughness

Fracture toughness measures the resistance of a material to crack propagation. It

is defined as the critical stress intensity level at which catastrophic failure occurs

due to a critical micro defect and is one of the most important properties of

material for virtually all design applications. While high fracture toughness refers

to materials undergoing ductile fracture, low fracture toughness value is

characteristic of brittle fracture of materials. The lower the fracture toughness, the

lower is the clinical reliability of the restorative materials. Dental composites

have considerable low fracture toughness because of the presence of its resin

matrix with relatively low toughness. In view of the vast clinical applications, the

fracture toughness of dental composite restoratives should be tested before

introducing into the market.

Both bending test using single-edge notched beam (SENB) specimens

(Zhao et al., 1997; Watanabe et al., 2007) and indentation fracture (Kvam, 1992;

Maehara et al., 2005) are among the different test methods commonly used for the

evaluation of the fracture toughness of dental materials. Although the bending

test is easy to perform, it requires large beam specimen which is technically

difficult to prepare. The other drawback is the difficulty to initiate an infinitely

sharp crack tip which is required by the bending stress equation. On the other

hand, the indentation fracture test is faced with the problem of accurate

calculation based on the raw data obtained by the indentation test. In the literature

(Matsumoto, 1987; Ponton and Rawlings, 1989a; Fischer and Marx, 2002),

discrepancies between the indentation fracture toughness of materials and its

fracture toughness measured by the conventional SENB method has been reported

15

frequently. This is attributed to a variety of phenomena, including: (1) the

dependence of crack geometry in response to different indentation load and the

material properties, (2) the influence of complex deformation behaviour such as

lateral cracking, and (3) the effects of other mechanical parameter such as

Poisson’s ratio and hardness measurement (Gong, 1999).

2.2 Depth-sensing Indentation Method

2.2.1 Introduction

In view of the shortcomings of the ISO 4049 test as discussed earlier, it provides

the motivation for the current research to investigate the potential of the depth-

sensing indentation test as an alternative test method for the mechanical

characterization of resin-based dental restoratives. This section firstly covers the

theoretical framework of the depth-sensing indentation test and its derivation of

the elastic modulus from the first principle. Following this, the application of

indentation technique to determine the yield strength and fracture toughness of the

dental restorative materials will be presented.

2.2.2 Determination of elastic properties by depth-sensing indentation method

In an indentation test, penetration load is applied to the materials under study by a

rigid punch or indenter. The resulting deformation is attributed to the combination

of both elastic and plastic. Rubber-like materials can deform elastically over a

larger range as compared to metals. In metals, the deformation is both elastic and

plastic with the latter being more predominant and often involves considerable

16

permanent deformation (Tabor, 2000). When using an indenter with known

geometry, the indentation hardness of a material can be determined by measuring

the resistance force to deformation over the projected contact area (Ac).

H = P/Ac …….. (2.2)

If the displacement information of the indenter is made available, this

technique can be further applied to measure the elastic modulus of the material.

The latter is referred to depth-sensing indentation method. Tabor (1948) first used

the indentation method to determine the hardness of various metals deformed by a

hardened spherical indenter. To investigate the behaviour of different indenter, a

similar study was further undertaken by Stillwell and Tabor (1961) with using a

conical indenter. In both studies, it was shown that the shape of the unloading

curve and the total amount of recovered displacement accurately related to the

elastic modulus of the materials and the area of the contact impression (Oliver and

Pharr, 1992). This important observation has pillared the foundation for all depth-

sensing indentation works. Bulychev et al. (1975 & 1976) first adopted the load

and displacement sensing methods to determine the elastic properties of materials.

The techniques rely on the fact that the displacement recovered during unloading

is largely elastic where elastic punch theory can be applied to determine the

indentation modulus (Ein) from analyses of load-displacement data (Pharr et al.,

1992). This term was introduced in distinction to the Young’s modulus (E) of a

material which to be measured in a tensile test. A typical load-displacement (P-h)

graph of dental bio-composite is presented in Fig. 2.1.

17

Fig. 2.1. A load-displacement graph for an indentation experiment where hmax is

the maximum indenter displacement at peak indentation load (Pmax), dhdP is the

slope of the P-h curve during the initial unloading stage, hf and hc are the final (residual) and contact depth of the hardness impression respectively.

To relate load and penetration, Sneddon (1965) developed the analytical

solution for a rigid flat punch with cylindrical profile. For the indentation of an

elastic half space by a flat cylindrical punch, the total load P required to produce a

penetration h is given by

)1(4

ν−=

GrhP …….. (2.3)

Where

ν = Poisson’s ratio,

P-h Curve of Dental Bio-composite

0.0

1.0

2.0

3.0

4.0

5.0

0.000 0.005 0.010 0.015 0.020 0.025 0.030

Displacement, h (mm)

Load

, P

(N)

Pmax

hmax hf

dhdP

LOADING P = Ch2

UNLOADING P = α(h – hf)n

hc

hc hf hmax

18

G = shear modulus of the indented material and is related to the elastic modulus

(E) through E = 2G(1 + ν), and

r = radius of the cylinder.

Since the contact area of the cylinder, A = πr2, Eqn. (2.3) can be rearranged in the

form

)1(

22νπ

−=

AhEP …….. (2.4)

Differentiating P in Eqn. (2.4) with respect to penetration h and yields

)1(2

2νπ −==

EASdhdP …….. (2.5)

From Eqn. (2.5), it is observed that the contact stiffness is related to the

modulus and contact area of the indented profile. Hence the elastic modulus of

the material can be computed if independent measurements of the Poisson’s ratio

and contact area are available. In the indentation test, the indenter has finite

elastic constants, E0 and νo. To account for the indenter’s contribution to the

measured displacement, the term Reduced Modulus (Er) is used to define the

modulus of the indenter-and-indented materials system (Sneddon, 1965) which is

given by

EEE o

o

r

)1()1(1 22 νν −+

−= …….. (2.6)

Where

Eo = elastic modulus of the indenter,

19

vo = Poisson ratio of the indenter,

E = elastic modulus of the indented material of interests, and

v = Poisson ratio of the indented material of interests.

For most indenters which are made of diamond, Eo = 1141 GPa and vo =

0.07 (Simmons and Wang, 1971). For bulk indentation, Eqn. (2.5) becomes

(Stilwell and Tabor, 1961; Pharr et al., 1992)

rEAdhdPS

π2

== …….. (2.7)

Combining equations (2.6) and (2.7), the elastic modulus, Ein, of the indented

material of interest can be determined through the following equation

−−

−=

o

oin

ESA

E)1(2

12

2

νπ

ν …….. (2.8)

In general, the indenters can be classified into spherical, conical,

cylindrical and pyramidal in profiles. In Sneddon’s analysis, the flat punch

approximation is derived for indenter which can be described as a solid of

revolution of a smooth function (e.g., cone, sphere, and paraboloid of revolution

which can be infinitely differentiable). It was also important to note that this does

not preclude singularities at the tip, so the analysis also applies to conical and

spherical punches (Pharr et al., 1992). Sneddon (1965) had also established the

load-penetration relationship for conical indenters with the inclusion of its apex

angle. Buylchev et al. (1975 & 1976) had shown that the above equations hold

equally well for spherical and conical indenters. However most common

20

indenters used in indentation testing such as Vickers, Knoop and Berkovich

cannot be described as bodies of smooth revolution. To test the validity of the

analytical solutions to these geometries, finite element analysis was performed by

King (1987) to evaluate the load-displacement characteristic of flat-ended punches

with circular, triangular and square profiles. The latter two profiles are the flat-

ended equivalents of the Berkovich and Vickers indenters. In his numerical

calculations, the unloading stiffness for different indenter geometries was

determined to be:

Circular: rEAdhdP

π2000.1= ……. (2.9)

Triangular: rEAdhdP

π2034.1= …….. (2.10)

Square: rEAdhdP

π2012.1= …….. (2.11)

From the results shown above, it can be observed that Eqs. (2.5) and (2.6)

are valid for almost any axisymmetric indenters and the relation between the

initial unloading contact stiffness and contact area is geometry independent (Pharr

et al., 1992). The geometric correction factor for triangular-based and square-

based indenter profiles was 1.034 and 1.012 respectively. Therefore it was

concluded that the analytical solutions was rather universal and not just limited to

flat punch geometry.

In the derivation of flat-punch approximation, it was also assumed that the

unloading behaviour is linear. In indentation experiments conducted by Oliver

and Pharr (1992) on materials included metals (aluminium and tungsten),

21

amorphous glasses (soda lime glass and fused silica) and crystalline ceramics

(sapphire and quartz), it was found that the unloading characteristics of all these

materials were non-linear. The unloading profiles are reasonably well described

by power law relations [P=α(h – hf)n] and the power law exponents (n) for the six

materials were found to be in the range of 1.25 to 1.6 (Pharr et al. 1992; Oliver

and Pharr, 1992). In the literatures, Doerner and Nix (1986) reported linear

behaviour was observed for most metals over the unloading range. This was not

entirely true as illustrated by Oliver and Pharr (1992) that when replotted those

unloading curves on logarithmic axes, power law exponents (n) of greater than

one (n > 1) were revealed for almost all materials which implied non-linearity.

Due to the scaling of the axes, the unloading curves sometimes appeared to be

linear.

In a continuous stiffness measurement that employed a dynamic technique,

it was found that the stiffness changes instantly and continuously when the

indenter was withdrawn from the specimen during unloading (Oliver and Pharr,

1992). This has lead to an important concern on the validity of the flat-punch

approximation. Nonetheless, the analytical solutions have often been applied with

primary justification that at least the initial portion of the unloading curve was

linear which behaves like a flat punch. In determining the initial unloading

stiffness, it is practically difficult to determine the number of data points that

should be included in the linear fit of the unloading curve. It was suggested that

the unloading contact stiffness (S) to be computed from the upper one-third of the

unloading curves (Doerner and Nix, 1986). In some studies, the initial unloading

stiffness was determined from the first derivative of the power law equation that

22

fitted to the unloading curve at the peak indentation load (Oliver and Pharr, 1992).

The later was found to be a more appropriate technique as it was less sensitive to

creep and other unloading errors. In the treatment of the analytical solutions, it

was assumed that the punch was flat-ended. As discussed earlier, the use of

pyramidal or non flat-ended indenters would not affect the validity of Eqn. (2.7)

provided that indenters were axisymmetric.

2.2.3 Determination of yield strength by depth-sensing indentation method

As previously described in Section 2.1.6, Zeng and Chiu (2001) proposed a semi-

empirical method in computing the yield strength of a material from the

indentation test data. This method was based on the fact that the unloading curve

of a general elastic-plastic material is bounded by two lines, corresponding to the

indentation of fully elastic and elastic perfect-plastic, as shown in Fig. 2.2. For a

fully elastic material, the indentation-unloading curve will be similar to that of the

loading one which can be described as a parabolic curve P~h2. On the other hand,

the unloading curve will be close to a straight line if the material is an elastic

perfect-plastic one. Zeng and Chiu (2001) had verified this method on a wide

spectrum of glass ceramic and metals with elastic modulus ranged from 3 to 650

GPa and hardness ranged from 0.1 to 30 GPa. Although the modulus of elasticity

and hardness of dental composite materials are well within the range of the above

materials being evaluated, the validity of this empirical method as well as its

underlying assumptions remain a big question as dental composites have complex

polymeric structure possess different deformation response. The derivation of the

yield strength from this empirical method is presented as follows.

23

Fig. 2.2 Determination of weight factor θ from the indentation P-h data

In Sneddon’s flat punch analysis, it was found that the loading part of an

instrumented sharp indentation can be expressed as

P = Ch2 …….. (2.12)

where P and h are the indentation load and penetration depth respectively, and C

is a constant depending on the indenter’s geometry and material properties. In

various numerical simulations (Giannakopoulos et al., 1994; Larsson et al., 1996),

the constant C for sharp Vickers indentation on an elastic material was cited as,

22

32

)1()1862.01737.01655.01(0746.2 hEP

νννν

−−−−= …….. (2.13)

and that on an general elastic-plastic material,

24

22 3

22tanln11)22(tan

273.1 hEP yyy

u σσσ

σ

°+

+

°= …….. (2.14)

where ν is the Poisson’s ratio, E is elastic modulus, σy is the yield strength, σu is

the stress at 29% strain, and ratio σy/σu is used to represent strain-hardening

property of materials. In the empirical method proposed by Zeng and Chiu (2001)

as described earlier, it was suggested that the unloading curve for elastic-plastic

material could be written as a linear combination of the results of the two extreme

cases, namely the fully elastic and elastic perfect-plastic as below.

)()()1( 2chhSEhfP −+−= θνθ …….. (2.15)

where f(ν) = )1(/)1862.01737.01655.01(0746.2 232 νννν −−−− , hc is the contact

depth, and the weight θ is dependent on the strain hardening parameter σy/σu. It

has a value of between 0 to 1 corresponding to a pure elastic (σy = 0) and elastic

perfectly-plastic (σy= σu) solution respectively. The above is purely empirical.

For sharp indentation, the maximum projected contact area for Vickers indenter is

given by

Amax = 24.56hc2 …….. (2.16)

Combining equations (2.5), (2.11) and (2.16), Eqn. (2.15) can be rewritten as

)()1(

66.5)()1( 22

cc hhhEEhfP −−

+−=νθνθ …….. (2.17)

The above equation has three unknowns namely E, θ and hc which can

solved using non-linear algorithm when a polynomial curve of P = ah2 + bh +c is

25

fitted to the unloading curve. Alternatively, it can be estimated graphically as

illustrated in Fig. 2.2. The constant C was determine by fitting the curve of

P=Ch2 to the loading curve of the indentation data. With known θ and modulus

(E) of the material from the first part of the indentation experiment, the yield

strength (σy) can thus be computed using Eqn. (2.14). The above empirical

method is based on speculation with several underlying assumptions. Firstly, it

was assumed that θ = σy/σu which has no theoretical justification. Secondly, it

was also assumed that the first few points of the unloading curve behaved in a

linear manner (P = S[h – hc]) as suggested by Doerner and Mix (1986). Therefore,

the elastic perfectly-plastic boundary line can be established by fitting to the first

two to three points of the initial unloading curve. Lastly, the loading curve was

assumed to follow the relationship of P=Ch2. In view of the above, its application

on other materials such as dental composites would require careful examination.

The indentation test is an easy test to conduct, but however the contact

mechanics is rather complex. For instance, the aforementioned analytical solution

did not consider the frictional force at the contact interface which is difficult to

account for. In order to obtain an accurate elastic modulus value, one has to be

extremely careful in measuring parameters such as the true penetration depth (not

that due to strain hardening effect or compliance of the system) which is required

for the calculation of the intrinsic material property. There are many sources of

error associated with this technique and they will be discussed in details in the

next section.

26

2.2.4 Errors associated with depth-sensing indentation test

All measurements have errors and their accuracy is always the key concern.

Indentation measurement is no exception. The sources of errors associated with

indentation tests had been discussed extensively by Menčik and Swain (1995). In

view of the high sensitivity of the technique, it is important to understand the

factors which would affect the accuracy of the indentation method. A false

interpretation would eventually lead to false conclusions. The main sources of

errors during indentation tests are as follows.

1) Load and displacement measurement devices

2) Compliance of the system

3) Shape of the indenter tip

4) Initial depth of penetration

5) Surface roughness

6) Shape of the indented impression

7) Elastic constant of the indenters

8) Noise of the system

9) Thermal drift

In view of the developmental nature of this research project, the various

sources of errors associated with the instrumentation, surface preparation of dental

composite materials and test parameters will be discussed in greater details as

follow.

Load and displacement measurement devices (transducers) – like all other

measurements, there are errors inherent with the load and displacement

27

transducers of the testing system itself. This will affect the accuracy of the load-

displacement (P-h) curve of the indentation profile. With today’s technology

advancement, most load and displacement measuring devices are capable to

measure its physical parameters with high resolution and precision. However one

has to be cautious when selecting the load transducer for the indentation test at

desired load range. The selected load transducer must be of appropriate capacity

in order to detect the minimum load. Measurement at low load over the dead zone

of the load transducer will result in high non-linearity error. Calibration of the

measurement devices must be checked periodically to ensure measurement

accuracy.

Compliance of the system – in an indentation test, only the deformation of the

materials in response to load is of interest, and not that due to the load transducer,

the loading frame and other associated fixtures. The stiffness associated with all

these components must be compensated when calculating the unloading stiffness

from the P-h curve during the indentation test. The compliance of a component is

the inverse of its stiffness and has a unit of mm/N. The total compliance (CT)

measured from the slope of the initial unloading curve is the sum of the

compliance of the specimen (CS) and the compliance of other components (CC).

CST CCC += …….. (2.18)

CST

CdhdP

dhdP

+

=

−− 11

…….. (2.19)

CTS

CdhdP

dhdP

−

=

−− 11

…….. (2.20)

28

Upon the compliance correction, Eqn. (2.9) becomes

rS

EAdhdPS

π2

=

= …….. (2.21)

From the above, it can be observed that the rigidity of components used in

an indentation test set-up has strong influence on the deformation results. This

error is more pronounced when performing the indentation measurement at low

load or low penetration depth. Therefore the compliance of all components

including the load transducer, clamping and mounting fixtures, and load frame has

to be known prior to the indentation test. Apart from the above, the substrate

which used to embed or hold the specimen will also have an influence on the

compliance of the indented material. The compliance effects of using different

mounting methods on quartz specimen have been shown by Wolf (2000). In

indentation test, it is proposed that the thickness of the indented materials must be

at least 10 times larger than the indentation depth in order to eliminate the

substrate effect (Chudoba et al., 2000). This is commonly known as the one-tenth

rule.

Shape of the indenter tip and initial depth of penetration. In the analysis, the

tip of the pyramidal indenters has always been assumed ideally sharp. However

there is always certain degree of blunting at the tip of three- or four-sided

indenters. This is referred as the indenter size effect (ISE) or indenter tip offset

(Trindade et al., 1994). As a consequence, this results in a difference between the

measured and actual depth of penetration as illustrated by Menčik and Swain

(1995). In the depth-sensing indentation test, the contact area is calculated as a

function of the penetration depth, A(h), thus the error contributes to an apparent

29

change in the measured indentation hardness and modulus. This error is more

significant at smaller depths of penetration. As reported in the literatures (Mencik

and Swain, 1995; Halitim et al., 1997), the ISE will result in the indentation

modulus changes with different indentation load. Theoretically, the elastic

modulus is an intrinsic material property which is independent of the indentation

load or depth. After considering the tip defect in Halitim’s experiment, the

corrected elastic modulus curve became almost uniform with respect to the

indentation depth.

Several ways to overcome this problem have been proposed in the

literature. One simple way to determine the indenter area function was to make a

series of indents at different depths on a material (preferably metal) with known

properties. The contact area of the indent impression was then measured directly

by using imaging techniques and expressed as a function of the penetration depths

(Oliver et al., 1984; Doerner and Nix, 1996). The other method (Oliver and Pharr,

1992) was to derive the area function by performing indentation on a material

with known E. The unloading stiffness was calculated for indents at different

depth and a polynomial function was then fitted to relate the contact area and

depth of penetration. In sharp indentation, it is assumed that the blunting tip

radius, r has negligible effects on the P-h curve if the maximum depth of

penetration, hmax > r/40 (Giannakopoulos and Suresh, 1999). Dental composite is

a complex structure which consists of polymeric matrix with reinforced filler

particles. Hence, in the measurement of the indentation modulus of dental

composite restoratives, it is critical to determine the appropriate peak indentation

30

load and the corresponding penetration depth so that the material will respond to

its bulk behaviour with minimal ISE.

Surface Roughness. No surface is perfectly smooth no matter how well it is

being polished. Surface undulations can range from few nanometers to several

microns or more in peak heights. Therefore, the depth of penetration in an

indentation test must be sufficiently “deep” so that the materials will response in

accordance to its true bulk material properties. Indentation tests for which the

depth of penetration of less than 50 nm are considered as less reliable (Menčik and

Swain, 1995). At low penetration depth, the indenter may only touch few peaks

and the apparent stiffness of the material is lower. An attempt (Joslin and Oliver,

1990) has been made to study the influence of surface roughness on the

measurement of indentation hardness and modulus, but the results were

inconclusive. In the context of dental composite materials, the specimen surface

preparation protocol has not been well established as it is not a critical parameter

in many engineering test methods. However in the micro-indentation test which is

sensitive to the surface properties, it has to be dealt with carefully.

Shape of the indented impression – if a metal is highly work hardened it will

tend to “pile-up” towards the edge of the indentation. If it is heavily annealed it

will tend to “sink-in” near the indentation. These changes seriously affect the

elastic analysis due to the error in contact area measurement (Stillwell and Tabor,

1961). In the event of piling up, the contact area is appeared larger and therefore

the apparent values of elastic modulus and hardness are higher than actual ones.

In a sensitivity analysis conducted by Venkatesh et al. (2000), it was found that

31

the elasto-plastic properties estimated in the inverse (reverse) problem exhibited

strong sensitivity to variations in the maximum contact area. To account for pile-

up or sink-in due to strain hardening (plastic) effects, various numerical models

have been derived in the literatures (Giannakopoulos et al., 1994; Giannakopoulos

and Suresh, 1999; Suresh et al., 1996) to relate the indentation depth to the true

(projected) contact area in sharp indentation of elasto-plastic materials. However

the model is derived for metals which have small elastic deformation range and its

validity on dental composite materials warrants further investigation.

Elastic constant of the indenters – as shown in Eqn. (2.8), the reduced modulus

(Er) calculated from the indentation P-h curve is a function of the isotropic

material properties (elastic modulus and Poisson ratio) of the indenter and the

indented material. Therefore an incorrect value used for the indenter will

introduce error in the calculation. In the literatures, a value of between 900-1200

GPa was usually assumed for elastic modulus of diamond indenter. In a

sensitivity analysis performed using Eqn. (2.8), a 10% error in Ei will result in

0.44 to 0.54% error of E for Er/Eo = 0.05, and 3.4 to 4.5% for Er/Eo = 0.3. It is

important to note that the compliance of the indenter has stronger influence on the

error in E when the indented material has stiffness close to that of the indenter. In

an indentation measurement, this error can be assumed to be negligible for E/Ei <

0.2 (Menčik and Swain, 1995).

Noise of the system – both intrinsic and extrinsic noises can influence the

accuracy of the indentation measurement. A fluctuating or tortuous P-h curve is

an indication of the presence of noises especially during low force and depth

32

indentation measurement. There are numerous sources for the noises which

include instruments, mechanical vibration, thermal effects, after effects in the

indented materials during the first few steps of unloading due to creeps, stick-slip

effects between the indenter and the indented material, and many others. Most of

the noises are random and therefore technically difficult to eliminate them

completely in an indention measurement. One can only minimize this error by

observing the proper instrument set-up and having good understanding on the

various sources of the noises. The instrument noises are rather random and can be

due to improper shielding, unregulated voltage, and mechanical vibrations which

affect the output signals. To minimize the unloading error, the first few points in

the initial unloading curve should be omitted in the calculation of the stiffness

value.

Thermal drift – contraction or expansion of the specimens, which caused by

change in temperature of the surrounding or the measurement devices, will affect

the measurement accuracy. For instance, the apparent modulus will be higher as a

result of contraction of specimen due to a decrease in temperature during

unloading. In hardness measurement, the measured penetration depth (h) will be

larger when the specimen contracts due to a decrease in temperature. As a result,

the apparent hardness will be lower. Therefore it is important to ensure that the

thermal conditions are stable during the test. The thermal effect is more

predominant when the test is done at ultra-low load level such as in nano-

indentation testing.

33

2.2.5 Indentation fracture mechanics

In an indentation P-h curve as presented earlier, the loading portion is hardness-

controlled while the unloading portion is modulus-controlled which is purely

elastic. In the last two decades, this method has further being applied to perform

fracture characterization of brittle materials. The contact of a sharp indenter with

brittle surface results in some irreversible deformation and leaves a residual

impression from which the indentation hardness can be measured. Upon the

removal of the indentation load, an invariable appearance of so called radial

cracks emanating from the impression corners had led to the discovery of

distinctive indentation crack patterns (Marshall and Lawn, 1986). It then becomes

clear that with accurate control of the crack size and geometry arising from

advanced instrumentation, quantitative information on fracture can be obtained

through a hardness testing facility. This forms the basis of the indentation fracture

test methodology.

The starting point in understanding the indentation fracture mechanics is

the characterization of the elastic-plastic stress fields, with particular focus on the

residual stress component. The analysis for this phenomenon is extremely

difficult as the contact stress fields at the indentation tip are far more complex

than one can imagine. However, this problem can be simplified by representing

the far field by a simple “point” force solutions when the crack is at the fully

propagating stage (Lawn and Wilshaw, 1975; Lawn and Evans, 1977). In the

continuum based plastic model, the deformation process under a sharp indenter

are dominated by a cumulation of discrete shear events. It is this series of shear

events that acts as an embryonic nuclei for crack formation when the developed

34

stress field reaches certain critical intensity level. Ultimately, the irreversible

component of the resulting critical stress field provides the dominant driving force

for fracture.

In general, two crack systems can be observed in the indentation fracture

mechanics. Firstly, radial cracks emanated from the residual impression corners

that are oriented normal to the specimen surface. Since this is coincident with the

median plane of the impression’s diagonal, it is also referred to as the radial-

median crack system. It has a half-penny configuration with its centre at the

contact point. Hence, it is also commonly known as a half-penny crack. The

second set is called the Pamqvist crack, extends from the end of the residual

impression into the subsurface. The crack system is presented in Fig. 2.3.

Deriving from first principles and based on the empirical solution

developed by Palmqvist (1962), the contact pressure of the loading and unloading

cycle can be represented in the form

Fig. 2.3 Schematic representation of (a) radial-median or half-penny and (b) Palmqvist crack system with c, a and l being the indent-crack length. (Adapted from Gong, 1999)

35

Loading: P α Hh2 …….. (2.22)

Unloading: P α E(h2 – hf2) …….. (2.23)

The requirement of the capability for these two equations at maximum

depth, hmax, yields the relation

−=

EH

hhf η1

2

max

…….. (2.24)

where η is a numerical constant and the ratio of (H/E) has an important place in

the specification of the elastic-plastic stress field. As previously mentioned, the

residual component of the stress field during the unloading half-cycle provides the

principal crack driving force for the radial crack to develop. This component can

be evaluated in terms of a concentrated force, Pr, centered at the contact origin. It

has been shown that Pr = χrP, which means the crack-opening force is directly

proportional to the contact load with χr being a dimensionless parameter which

represents the field intensity (Lawn and Marshall, 1979). For an ideal elastic-

plastic material in which the irreversible deformation is volume conserving,

analysis (Lawn et al., 1980; Anstis et al., 1981) gives

3/22/1

)(cot φαχ

HE

r …….. (2.25)

where φ is the indenter’s half angle.

In the fracture mechanics formulation, the stress intensity factor, K is used

to express the intensity of the stress field concentrated at the tip of extending crack

36

(Lawn et al., 1980, Evan and Charles, 1976). For half-penny cracks, the intensity

stress factor can be expressed as

2/3cPK χ= …….. (2.26)

where c is the characteristic crack size and χ α χr. Assuming the absence of time-

dependent crack-growth effect and at equilibrium where K = KIC, the fracture

toughness (KIC) of a material can be deduced from the indentation crack profile

through the following relationship (Lawn et al., 1980; Marshall and Lawn, 1986),

3/2

=

ICo K

Pc χ …….. (2.27)

where co is the crack length at equilibrium which measured from the center of the

indent to the end of crack. Combining equations (2.25) to (2.27), the fracture

toughness or critical stress intensity factor (KIC) of the material is given by (Lawn

et al., 1980)

5.10

5.0

cP

HEKIC

=ξ …….. (2.28)

where P, E and H are to be obtained experimentally from indentation P-h data,

and ξ is an empirical constant which is dependent on the indenter geometry.

Equation (2.28) is commonly known as the LEM (Lawn-Evans-Marshall) model.

This model has the unique feature that the complex elastic-plastic stress field is

being resolved into a reversible elastic component and an irreversible residual

component (Gong, 1999) in a radial-median crack system. To better represent the

fully developed radial-median or half-penny crack configuration, Lankford (1982)

37

proposed a more generalized equation which was based on early test data and is

given by

56.1

5.1

5/2

,

=− c

aaP

HEK PennyHalfIC ξ …….. (2.29)

where a is the half-length of the indent. In Palmqvist crack system, the crack

length, l which measured from the indent corner to the end of the crack (Fig. 2.3)

was reckoned as the characteristic crack length instead of c (Ponton and Rawlings,

1989b). Nihara et al. (1982) proposed the Palmqvist crack as semielliptical

surface flaws and derived the following relationship

2/1

5/2

, alP

HEK PalmqvistIC

=ξ for 0.25 < l/a < 2.5 …….. (2.30)

Equations (2.28) to (2.30) are the most straightforward approach to

determine the fracture toughness of a brittle material in relating to either the post-

indentation crack size (c) and the crack length (l), which are to be measured

immediately after the indenter has been removed. Apart from providing a simple

means to determine toughness, this method involves small specimens and multiple

measurements can be made on a single surface.

In conclusions, the micro-indentation method appears to be a potential

alternative test method to the ISO 4049 test. However its applications on resin-

based dental composite materials have yet to be evaluated carefully as this method

has not been widely used in dental restorative materials. Various experimental

and specimen-related variables have to be investigated to ensure the method

38

would provide accurate and reproducible measurements of mechanical

parameters. In the next chapter, the objectives and research program of the

current PhD thesis will be presented.

39

Chapter 3 3.1 Objectives The current mechanical characterization of resin-based dental restoratives requires

the use of different test methods with a variety of test set-ups. Apart from their

destructive nature, the utilization of large beam specimens is another shortcoming

of conventional test methods such as ISO 4049. In view of the continuous

development of tooth-coloured dental composite restoratives, a single mechanical

test platform that can provide fast, accurate and reliable results for screening of

these materials is most valuable. In the current research, the various mechanical

properties namely the hardness, elastic modulus, strength and fracture toughness,

will be evaluated with using a single test platform i.e. the depth-sensing

indentation method. The objectives of the research were:

1. To develop depth-sensing micro-indentation methodologies that can yield

accurate elastic and plastic properties of resin-based dental composite

restoratives.

2. To assess the critical specimen and test-related test parameters which affect

the accuracy of the micro-indentation test on resin-based dental materials.

3. To perform a correlation study on the elastic modulus obtained by

instrumented indentation method and ISO 4049 testing.

4. To apply indentation fracture mechanics to determine the fracture properties

of resin-based dental composite restoratives.

40

3.2 Research Program

Materials Selection

The dental composite materials evaluated in the current investigation have been

selected to represent the wide range of commercial materials available. As the

materials vary widely in their filler and resin content, the measured mechanical

properties exhibit a wide range of values to facilitate comparison and statistical

analysis. Based on previous research projects and material’s data sheets, five

materials from the same manufacturer (3M ESPE) have been selected for the

studies of the PhD thesis. They include microfill (A110), minifill (Z100 and

Filtek Z250), poly-acid modified (F2000), and flowable (Filtek Flowable [FF])

composites.

Determination of Strength and Modulus using ISO 4049 Test Method

The strength and modulus of the above selected materials will be first evaluated

using the flexural test method as documented in ISO 4049. The elastic modulus

obtained will serve as reference values for the subsequent depth-sensing

indentation tests. The flexural strength is another mechanical parameter which

can be determined from this test. The strength value is to be used to validate the

plane strain toughness test in the fracture experiment. To improve the test

accuracy, a custom test jig and specimen mould are required to be designed and

fabricated.

Measurement of the Poisson’s Ratio

Apart from modulus, Poisson’s ratio is one of the mechanical parameters which is

required to fully describe the elastic property of a dental composite material. It

41

has a value of 0 to +0.5 depending on the compressibility of a material. Although

the Poisson’s ratio had been reported to have little effect on the measurement of

indentation modulus, this intrinsic material property should be measured as

accurate as possible in the effort to minimize the error in computing the modulus.

Instrumentation for the Depth-sensing Micro-indentation Test

Upon considering the various sources of errors in association with the depth-

sensing indentation test, it is of paramount importance that the force and

displacement measurement devices in the mechanical test set-up are of ultra-high

precision and accuracy. In overcoming the compliance issue, the displacement

has to be measured directly in corresponding to the indenter’s penetration into the

material of interest. To allow for the examination and measurement of the indent

impression on the specimen, a digital optical imaging system has to be

incorporated into the instrumentation setup. In view of the complexity of the

above, the indentation head has to be custom designed and fabricated for the

current research.

Assessment of Critical Test and Specimen-related Parameters

In an effort to propose the depth-sensing indentation technique as an alternative

test method for the mechanical characterization of dental composite restoratives, it

is important to establish the test protocols in order to make this test reproducible

and hence reliable. Due to the lack of literature in the indentation test of resin-

based dental materials, it is critical to identify key experimental and specimen-

related parameters such as peak indentation load, strain rate and surface roughness

which may influence the test accuracy significantly.

42

Calibration of the Indenter’s Area Function, A(hc)

An important aspect of the depth-sensing indentation experiment is to provide an

independent contact area measurement prior to the analysis. Instrumentation set-

up which can provide direct absolute measurement of the projected contact area is

still not available and is a setback for the depth-sensing indentation test. In the

current determination of the indentation modulus, the contact area is often being

estimated empirically from the obtained force-displacement graph with certain

degree of limitations. In the literature, the various methods used in determining

the project contact area for metallic and ceramic materials have been well

established. To select the most adequate model in the contact analysis of resin-

based dental restorative materials, various developed empirical methods in the

literature will be evaluated in consideration of their test assumptions and

limitations.

Correlation studies. Upon establishing the test methodology, the hardness and

indentation modulus of the five selected dental composite materials will be

determined using the newly developed depth-sensing indentation test set-up. To

validate the micro-indentation test method, correlation studies will be performed

between the indentation modulus and the flexural modulus determined in the

previous ISO testing. As an attempt, the yield strength of the dental composite

materials will be estimated from a developed empirical method. The results will

be analyzed and compared with the flexural strength values.

Determination of KIC using the Three-point Bend Test Method. In view of the

structure and presence of brittle filler particles in the dental composite system, the

43

existence of any critically sized voids and micro cracks will lead to failure of the

material in the clinical application. Thus, the measurement of the resistance of the

material to crack propagation or fracture toughness (KIC) is critical to prevent

catastrophic failures of the materials under service. The KIC values of the five

dental composite materials under current investigation will be first determined in a

three-point bend test set-up with using single-edge notched specimens in

accordance to ASTM E399 and ASTM D5045. The KIC values will be validated

to ensure plain-strain measurement and they will serve as the reference values for

the subsequent indentation fracture experiments as well as correlation studies.

Indentation Fracture Toughness. The main drawbacks of the ASTM E399

fracture toughness test in the context of dental composite materials include the

utilization of large beam specimens and technical difficulties in inducing the sharp

Chevron V-notch. Hence, the experimental results obtained from the three-point

bending test may be highly deviated. In association with the aim of the current

research, it is hypothesized that the indentation fracture test is a potential

alternative test method in determining the fracture properties of the resin-based

dental materials. In the current research, indentation fracture mechanics based on

the established classical half-penny crack system will be employed to determine

the KIC of dental composite materials. This method requires the accurate

measurement of the crack length produced under sharp indentation and the ratio of

the modulus over hardness (E/H) of the materials which has been obtained from

the first part of the indentation experiment. Indentation fracture test protocols for

the complex dental composite material have yet to be established to initiate

adequate crack system for the contact stress analysis. To study the validity of the

44

indentation fracture test, the indentation fracture toughness will be correlated to

the K1c values obtained from the previous three-point bending test. The

experimental design roadmap is presented in Fig. 3.1.

Fig. 3.1 Experimental design roadmap for the research program.

Elastic (E) and Plastic (H) Properties

ISO 4049

Poisson Ratio (v)

Test parameters 1. Surface roughness 2. Indentation load 3. Holding period 4. Strain rate

Depth-sensing Indentation Method

H Correlation Study

Fracture (KIC) Property

Ein

SENB (3-pt bending test)

Indentation Fracture Test

KIC KIC

E/H

Correlation Study

Ef σf

Validation

σy

Comparison Study

45

Chapter 4 4. Development of Depth-sensing Micro-indentation Test Method for Resin-based Dental Materials

4.1 Introduction

The depth-sensing indentation test is easy to conduct but the test mechanics is

very complex and susceptible to many sources of errors as reported previously.

Firstly, it is important that the instrumentation setup is capable of measuring the

load and corresponding displacement values accurately and precisely. It has been

reported that various experimental parameters including loading rate, holding time

at maximum load and the maximum indentation load contributed to creep

deformation in the plastic regime and affects the calculation of the indentation

modulus and hardness of materials (Guo and Kagawa, 2004, Simoes et al., 2002,

Chudoba and Richter, 2001). In view of the polymeric nature of dental composite

materials, the aforementioned test variables are of concern in the current depth-

sensing indentation test. In this chapter, the customized instrumentation and

experimental setup for the depth-sensing micro-indentation test will first be

presented. Following this, various specimen and experimental related variables

include surface roughness, loading and unloading strain rate, indentation load and

the load holding time will be investigated. These investigations will lead to the

standardization of the micro-indentation test protocol for resin-based dental

restorative materials which will be used in all the subsequent experiments.

46

4.2 Instrumentation for depth-sensing micro-indentation test

Notably from Section 2.2.4, the experimental set-up and instrumentation, which

used to carry out the depth-sensing indentation test, play an extremely important

role in determining the accuracy of this test method. After considering the various

sources of errors as discussed earlier, a material testing system (model 5848,

Instron Corp., MA, USA) mounted with a custom-designed indentation head unit

as shown in Fig. 4.1 was employed to perform the depth-sensing micro-

indentation test. This instrumentation setup was designed and developed in

collaboration with Instron Singapore Pte. Ltd. A static load cell of 1 kN capacity

(Instron Corp., CA, USA) was built into the indentation head unit for force

measurement. The penetration depth was directly measured by a Linear Variable

Differential Transducer (LVDT) which was in contact with the specimen surface

through a surface referencing probe. This surface referencing technique was

employed to eliminate the compliance issues associated with the test frame.

Hence the measured displacement was solely the deformation of the specimen in

response to the indentation load. The displacement resolution of the LVDT is

2nm. To avoid the indenter tip offset error, the indenter was first inspected under

the microscope for any tip blunting before taking actual measurement. The

clamping fixture was designed to ensure that the specimen surface was oriented in

perpendicular to the indentation load. To achieve this, the fixture was designed

with two finger clamps rigidly fixed to the test frame. The bottom side of the

finger clamps was designed and fabricated with tight control on its geometrical

tolerance to ensure that it is perpendicular to the vertical axis of the test system.

During mounting of the specimen, the acrylic mould was raised freely from the

bottom until it pressed firmly against bottom side of the finger clamps.

47

A digital imaging system was incorporated into the indentation head unit

(Fig. 4.1). It consisted of a custom-designed optical transmission unit (Moritex

Corp., Tokyo, Japan), an illumination light source (MHF-M1002, Moritex Corp.,

Tokyo, Japan), a microscope digital camera system (DP12, Olympus Optical Co.

Ltd., Tokyo, Japan) and the image analysis software (Micro Image 4.0, Media

Cybernetics, Maryland, USA). The imaging system was used to inspect the

specimen surface and indent impression before and after the indentation test

respectively. Besides inspection, the imaging system could also be used to

measure the size of the indent upon calibration. A pneumatic actuating system

was used to toggle between the indenter and the objective lens (CF Plan 10-50X,

Nikon Corp., Tokyo, Japan), which was mounted to the imaging system (Fig. 4.1).

The specimen block was mounted onto computer-controlled xy-motorised stages.

This allowed the distance between each indent to be controllable and to carry out

the indentation test in a more organized manner.

48

Fig. 4.1 Experimental set-up for the depth-sensing micro-indentation test.

Surface referencing probe (connect to LVDT)

xy-motorized stages

Load cell

Vickers indenter

Specimen Acrylic mould Clamping

fixture

Optical transmission

unit

Image Analysis Software

Digital Imaging System Indentation Head Unit

Pneumatic control

Objective lens

Force

Motorized xy-stage

Clamping fixture

Indenter LVDT

Loadcell

Digital imaging system

49

4.3 Poisson’s ratio of Dental Composite Restoratives

4.3.1 Introduction

Poisson’s ratio is one of the several mechanical parameters required to fully

describe the elastic property of a material. It can be defined as the ratio of

transverse strain (contraction) to axial strain (elongation) obtained in a uniaxial

test. It has a value of between 0 and +0.5 depending on the compressibility of a

material. For elastomeric materials which have high bulk modulus relative to

Young’s modulus, the Poisson’s ratio has a value of close to 0.5.

The Poisson’s ratio of a dental composite material is essential for

determining other mechanical properties such as the indentation modulus.

Poisson’s ratio has been conveniently assumed to be between the values of 0.24 to

0.35 for dental composite materials (Wei et al., 2002; Braem et al., 1987). In a

sensitivity analysis, it was found that an error of 20% in Poisson’s ratio would

lead to errors of 4.4% in computation of indentation modulus. In an effort to

minimize errors, it is desirable to accurately determine this intrinsic material

property. The work in this chapter aimed to determine the Poisson’s ratio of some

dental composites used in restorative dentistry by employing the classical tensile

test method.

4.3.2 Materials and methods

The materials evaluated and their technical specifications are presented in Table

4.1. They comprise a microfill composite (A110), two minifill composites (Z100

and Z250), a polyacid-modified composite (F2000) and a flowable composite

50

(Filtek Flow, FF). All materials were from the same manufacturer (3M ESPE)

and of the A2 shade. These materials were used in all the subsequent experiments

for the current research.

Table 4.1 Specifications of materials investigated.

Material Cure time (s)

Resin Filler Filler size (µm)

Filler Content

% by volume

Filtek A110 (Lot no.

20001128) 40 BisGMA

TEGDMA Colloidal

Silica

0.01

- 0.09

40

Z100 (Lot no.

20010208) 40 BisGMA

TEGDMA Zirconia / Silica

0.01 - 3.5 66

Filtek Z250 (Lot no.

20010306) 20

BisGMA UDMA BisEMA

Zirconia / Silica

0.01 - 3.5 60

F2000 (Lot no.

20010122) 40 CDMA

GDMA

Fluroaluminosilicate

glass, silica 3 - 10 67

Filtek Flow, FF

(Lot no. 20010410)

20 BisGMA TEGDMA

Zirconia / Silica

0.01 - 6 47

BisEMA = Ethoxylated bisphenol-A-glycidyl methacrylate BisGMA = Bisphenol-A-glycidyl methacrylate CDMA = Dimethacrylate functional oligomer derived from critic acid GDMA = Glyceryl methacrylate TEGDMA = triethylene glycol dimethacrylate UDMA = Urethane dimethacrylate

Two rectangular test specimens (55 mm long x 11 mm wide x 1 mm thick)

of the various restoratives were fabricated in a customized mould. The

restoratives were placed into the mould, which was positioned on top of a glass

slide. A second glass slide was then placed on top of the mould. Finger pressure

51

was then applied to extrude excess material and to minimize voids or porosity in

the specimens which may affect the homogeneity. The top surface was then light

polymerized in nine overlapping irradiations of 20 to 40 seconds each (depending

of manufacturer's recommendations) using a curing light (Spectrum, Dentsply

Caulk, Milford, DE 19963) with an exit window of 13 mm and an output intensity

≥ 420 mW/cm2 as assessed with a curing radiometer (Cure Rite, EFOS Inc.,

Ontario, Canada). Nine irradiations, with five over the gauge length and four over

the clamping areas, were applied so that the materials would be fully polymerised

over the entire length. After light polymerization, the specimens were placed in a

water bath for 15 minutes to allow the material to stabilize and eliminate any post-

cure effects. The test specimens were then carefully removed from the mould and

the edges were smoothened with grade 1200 sandpaper. The specimens were

stored in distilled water at 37 ± 1°C for one week prior to the tensile test.

After one week conditioning period, a 90o tee-rosette strain gauge (KFG-5-

120-D16-23, Kyowa Electronic Instruments Co. Ltd, Tokyo, Japan) was then

attached to the center of the specimens using the appropriate cement (CC-33A,

Kyowa Electronic Instruments Co. Ltd, Tokyo, Japan), aligned to the axial and

transverse directions. A foil-connecting terminal was used as a junction point

joining the strain gauge to the data logger (Model TDS-302, Tokyo Sokki

Kenkyujo Co. Ltd, Tokyo, Japan). Tensile test was conducted using a uniaxial

testing system (Instron 4302, Instron Corp., MA, USA) with a crosshead speed of

0.5 mm/min. The specimen was held in a non-slip 30kN wedge grip (Instron

Corp., MA, USA) with gauge length of 35 mm. Due to the complexity of dental

composites and need to account for the non-linear stress-strain behaviour, 0.2%

52

axial strain was used as the yield point or elastic limit. During the tensile test, the

specimen was pulled up to about 0.3% axial strain of the material. The specimen

was then unloaded fully and subjected to 30 seconds holding period before the

next force application. This was to allow relaxation and diminishing of time-

dependent properties. The test was conducted at room temperature (23.0 ± 1.0 °C).

A total of eight measurements (n=8) were made for each material.

The Poisson’s ratio is calculated as the ratio of transverse (lateral) to the

longitudinal (axial) strain obtained from the data logger, up to 0.2% axial strain.

Inter-material Poisson’s ratio was compared using One-Way Analysis Of

Variance (ANOVA)/post-hoc Scheffe’s test at 0.05 level. Correlation between

the Poisson’s ratio and the filler volume fraction of the dental composites was

done using Pearson’s correlation at significance level of 0.05.

4.3.3 Results and discussion

The mean Poisson’s ratio of the various materials is shown in Table 4.2. Results

of statistical analysis are tabulated in Table 4.3. Mean Poisson’s ratio for the five

materials ranged from 0.30 to 0.39. The reproducibility of this test was good as

evident from the low standard deviation of the test results.

Table 4.2 Mean Poisson’s ratio of the composite materials (n=8) determined by tensile test method. Material Poisson’s Ratio

A110 0.372 (0.014)

Z100 0.302 (0.008)

Z250 0.308 (0.004)

53

F2000 0.318 (0.017) FF 0.393 (0.004) Standard deviations in parenthesis. Table 4.3 Comparison of Poisson’s ratio between materials. Statistical analysis FF > all other composites

A110 > Z100, Z250, F2000

Results of one-way ANOVA/Scheffe's test at significance level 0.05. > indicates statistically significant difference in Poisson’ s ratio

The Poisson’s ratio of FF was significantly higher than all other

composites evaluated, and A110 was significantly higher than Z100, Z250 and

F2000 restorative materials. In Pearson’s correlation analysis, positive and good

correlation (R = 0.88) was found between the Poisson’s ratio and filler volume

fraction of dental composites. The correlation graph is plotted in Fig. 4.2.

Fig. 4.2 Correlation between Poisson’s ratio and filler vol. of dental composites.

R2 = 0.77R = 0.88

0.00

0.10

0.20

0.30

0.40

0.50

35 40 45 50 55 60 65 70 75Filler volume fraction (%)

Pois

son'

s ra

tio

54

The materials being tested have filler particle size which ranged from 0.01-

0.09 µm in microfill (A110) to as large as 3-10 µm as those found in flowable

composites (FF). The selected materials also had vast difference in filler volume

fraction from 40% found in A110 to 67% in poly-acid modified composite

(F2000) as shown in Table 4.1. The materials were selected to represent the range

of commercial composite currently available and for comparative reasons.

Pearson’s correlation analysis revealed strong interaction between

Poisson’s ratio and filler volume fraction. Composites materials with lower

volume fraction (FF and A100) were found to have higher Poisson’s ratio and

suggested that these materials were less compressible as compared to materials

with higher filler content since ν = 0.5 – E/6B, where E and B are Young’s and

bulk modulus of the material respectively. The above observation was consistent

with other studies on dental composite materials (Wei et al., 2002; Whiting and

Jacobsen, 1980). This was attributed to the lower modulus of the materials with

lower filler content that had been reported previously. An increase in the filler

content will provide higher resistance to deformation during the tensile test (Wei

et al., 2002). Based on the above, dental composites with lower Poisson’s ratio

are recommended for use in the stress bearing areas in view of their higher

resistance to deformation.

In the literature (Nakayama et al., 1974; Whiting and Jacobsen, 1980;

Craig, 1993; Chabrier et al., 1999), the Poisson’s ratio of various dental

composites was found to range from 0.23 to 0.44. In the present study, the

Poisson’s ratio for the five materials investigated was found to range from 0.30 to

55

0.39, which fell within the range of the values reported in the literature. These

values were in agreement with the finite-element study on particulate-reinforced

composites with varying filler volume fraction (Wei et al., 2002).

Although the uniaxial tensile test is an established method in the

evaluation of engineering materials, it has not been widely used in the testing of

dental materials. One reason is the requirement of large beam specimen which is

the main limitation of dental materials. The specimen size used in the current

study was 55x11x1 mm. This was the optimum size in order to accommodate for

the mounting of strain gauges and the required specimen gauge length.

Overlapping irradiation was used in photo-initiating the dental composite

specimens to ensure complete cure. In the experiment, appropriate

adhesive/cement was used to mount the strain gauge to minimize the gauge

stiffness effect. Although this test was experimentally difficult to perform, with

extra care and efforts in specimen preparation and experimental set-up, this

classical test method could still yield a very satisfactory result as evident in the

low standard deviation obtained.

4.4 Effects of surface roughness

4.4.1 Introduction

When dental composites are being polished, surface finish is one of the variables

which would influence interpretation of indentation results especially at low

penetration depth (Barber and Ciavarella, 2000, Bec et al., 1996, Wang et al,

2002). As the surface roughness is increased, the hardness measured at depths

56

comparable with the roughness scale deviates increasingly from the actual

hardness (Bobji and Biswas, 1999). This is because at low penetration depth, the

indenter may only touch a few peaks and the apparent stiffness of the material is

lower. Regardless of the degree of polishing, real contacting surfaces are rough to

a certain extent. Surface undulations can be ranged from few nanometers to

several microns. Therefore, the depth of penetration in an indentation test must be

sufficiently “deep” so that the materials will response in accordance to its true

bulk material properties. Polishing reduces the amplitude of roughness. However,

in the indentation test on dental composite restoratives, the extent to which the

specimens have to be polished is not standardized and remains a question to

answer during an experiment. It was noted that the effect of roughness on

material surface estimation is negligible if the indentation depth is much greater

than the surface roughness (Tabor, 2000). However this effect has to be

quantified by considering the size of the reinforced filler particles in dental

composite resins as well as the bulk material response. The experiment of this

part of the thesis was to investigate the effects of surface finish, as a result of

different polishing methods, on the indentation modulus and hardness of various

dental composite restoratives.

4.4.2 Materials & Methods

The materials investigated in this study were of A2 shade and produced by the

same manufacturer (3M ESPE, MN, USA). They included microfill (A110),

minifill (Z100) and poly-acid modified (F2000) composites. The materials used

57

were selected to represent composite restoratives of various composition, filler

particle size and volume fraction.

In the experiment, forty-two specimens for each material were placed into

the square recesses (3 mm long x 3 mm wide x 2 mm deep) of customized acrylic

molds. The specimens were then covered with acetate strips (Hawe-Neos Dental,

Bioggio, Switzerland). A glass slide was placed on top of the moulds and gentle

pressure was applied to extrude excess materials. The surface of the specimen

was light polymerized using a curing unit (Spectrum, Dentsply Caulk, Milford,

DE, USA) with an exit window of 8 mm. The intensity of the curing light was

423.2 ± 3.8 mW/cm2, as verified with a curing radiometer (Cure Rite, EFOS Inc.,

Ontario, Canada). The duration for curing was 40 seconds in accordance to

manufacturer’s instructions. After curing, the specimens were conditioned in

distilled water at 37 ± 1 °C for one week.

After one week of conditioning, the materials were randomly divided into

six groups namely A, B, C, D, E and F (Control) with seven specimens in each

group. To achieve different surface roughness, the specimens were polished

successively using a twin-wheeled grinder (L30520, Buehler GmbH, Düsseldorf,

Germany) at 200 rpm with 240, 600 and 1200 grit lapping disks (L30520, Buehler

GmbH, Düsseldorf, Germany) and water-based diamond suspensions (3 µm and

1µm ) on a soft polishing disc (Metadi, Buehler Ltd., IL, USA) as summarized in

Table 4.4. The specimens were then further conditioned in distilled water at 37 ± 1

°C for 1 week prior to the micro-indentation testing. This was to simulate the

58

body temperature and also help to alleviate the residual stress which were induced

during the polishing.

Table 4.4 Polishing protocol for dental composite restoratives.

Groups 240-grit

for 2 min

600-grit for

2 min

1200-grit for

3 min

3 µm diamond suspension for

3 min

1 µm diamond suspension for

3 min A √ B √ √ C √ √ √ D √ √ √ √ E √ √ √ √ √

F (Control) Non-polished (acetate strip finished)

After one week conditioning, 1 mm line scans (4 samplings at length of

0.25 mm each) across the center of the specimens were made using a surface

profilometer (Surftest, Mitutoyo Corp., Tokyo, Japan). The arithmetic mean of

surface roughness (Ra) was then recorded. Following this, indentation modulus

and hardness were determined using the Instron Microtester (Instron 5848, Instron

Corp., MA, USA) and instrumentation set-up shown in Fig. 4.1. The depth-

sensing micro-indentation test was carried out using a four-sided pyramidal

Vickers indenter at peak load of 10 N with a resolution of 3.8 x 10-3 N. During

indentation, specimens were loaded at a rate of 0.5 µm/s or approximately 10

seconds to reach the peak load and then held for 10 seconds. The specimens were

then unloaded at the same rate as during loading. The penetration depth was

measured directly by a LVDT which was mounted onto the indentation head unit

as described previously. The indentation modulus (Ein) and hardness (H) were

determined using the analytical equations as presented previously in Section 2.2.

59

max

max

APH = …….. (4.1)

−−

−=

o

o

inin

ESA

E)1(142.1

12

max

2

ν

ν …….. (4.2)

where

Pmax = maximum indentation load,

Amax = maximum projected contact area,

S = unloading contact stiffness,

Eo = elastic modulus of the indenter,

vo = Poisson ratio of the indenter,

Ein = elastic modulus of the indented material of interests, and

vin = Poisson ratio of the indented material of interests.

The parameters Pmax, hmax, and S were obtained from the load-displacement

(P-h) curve. The unloading contact stiffness, S was derived from the first

derivative of the fitted power-law equation [P=α(h – hf)m] at Pmax of the unloading

curve (Oliver and Pharr, 1992). To minimize unloading error, only the portion of

the unloading curve at between 50 to 90% of the Pmax was used for the curve

fitting. The Poisson’s ratio for each material was obtained in an independent

tensile test (Chung et al., 2004) and their values are tabulated in Table 4.2. For a

diamond indenter, Eo = 1141 GPa and vo = 0.07 (Simmons and Wang, 1971).

Oliver and Pharr’s (O&P) method (Oliver and Pharr, 1992) was used to estimate

the maximum projected contact area. In this method, the contact area at peak load

was estimated through the indenter’s area function and the contact depth (hc).

60

SPhhc

maxmax ε−= …….. (4.3)

Where,

ε is an empirical constant and is equal to 0.75 for Vickers indentation (Oliver and

Pharr, 1992). Assuming that the indenter itself does not deform significantly and

the blunting of the tip is negligible, the maximum projected contact area for

Vickers indenter is given by

Amax = 24.5hc2 …….. (4.4)

The results were analyzed using a statistical software, SPSS (V11.5, SPSS

Inc., USA). Comparisons were conducted using one-way analysis of variance

(ANOVA)/post-hoc Scheffé’s test at significance level 0.05.


The polished specimens had surface roughness ranging from 0.02 to 0.81 µm.

The roughness of F2000 was significantly higher than A110 and Z100. This was

due the larger filler particle size of F2000. The Ein and H for Z100 ranged from

14.02 to 14.83 GPa and 1.18 to 1.27 GPa respectively. Ein for F2000 and A110

ranged from 12.25 to 13.82 GPa and 5.26 to 5.52 GPa and hardness ranged from

0.89 to 0.98 GPa and 0.52 to 0.55 GPa respectively. The results are summarized

in Table 4.5. The SEM micrograph of the polished specimen surfaces is shown in

Fig. 4.3.

61

Table 4.5 Mean surface roughness (Ra), indentation hardness (H) and modulus (Ein) of materials investigated.

Materials (n = 7) Z100 F2000 A110

Polishing Method

Ra (µm)

H (GPa)

Ein (GPa)

Ra (µm)

H (GPa)

Ein (GPa)

Ra (µm)

H (GPa)

Ein (GPa)

A 0.61 (0.06)

1.18 (0.05)

14.02 (0.51)

0.81 (0.05)

0.91 (0.11)

12.25 (1.58)

0.57 (0.06)

0.54 (0.04)

5.26 (0.29)

B 0.22 (0.01)

1.21 (0.05)

14.13 (0.73)

0.40 (0.04)

0.97 (0.03)

13.65 (0.87)

0.29 (0.04)

0.55 (0.02)

5.39 (0.26)

C 0.10 (0.01)

1.25 (0.07)

14.22 (0.88)

0.25 (0.01)

0.89 (0.04)

12.53 (0.85)

0.07 (0.02)

0.52 (0.01)

5.22 (0.11)

D 0.02 (0.00)

1.27 (0.09)

14.72 (0.85)

0.09 (0.03)

0.98 (0.06)

13.40 (0.45)

0.03 (0.00)

0.54 (0.02)

5.45 (0.18)

E 0.02 (0.01)

1.25 (0.07)

14.12 (1.04)

0.06 (0.00)

0.94 (0.03)

13.22 (0.90)

0.04 (0.01)

0.55 (0.03)

5.52 (0.22)

F (Control)

0.04 (0.01)

1.21 (0.05)

14.83 (0.55)

0.08 (0.01)

0.90 (0.06)

13.82 (0.56)

0.08 (0.01)

0.53 (0.02)

5.52 (0.13)

Standard deviation in parenthesis

No statistical significance (p < 0.05) was found in the indentation modulus

and microhardness for all specimens with varying surface roughness (Table 4.6).

This suggested that the indentation load employed and the corresponding

penetration depth in the current experiment was appropriate to overcome surface

effects on the indentation test accuracy. In the pilot study, the indentation load of

10 N was selected so that it would produce a penetration depth of 20 to 35 µm for

composite restoratives to ensure that the measured hardness and modulus

approximate that of bulk composite. This was further verified by the SEM

micrograph (Fig. 4.4) on F2000 composite which clearly showed the indentation

depth had penetrated through the depth of 6 to 7 fillers. Among all the dental

composites being tested, F2000 has the largest filler particle size ranged between

3 to 10 µm. With this, the ratio of the specimen thickness (t = 2mm) over the

maximum indentation depth was more than 60, which surpasses the one-tenth rule

as stipulated in the UK National Physical Laboratory’s recommendation’s to

suppress the substrate effect (Peggs and Leigh,1983).

62

Fig. 4.3 SEM photographs of specimen surfaces with different polishing methods.

F (Control)

E

D

C

B

A

a

g

f e d

b

n m

l k j

i h

r q p

o

c

Materials Z100 F2000 A110

63

Fig. 4.4 Cross-sectional view of the indent impression for composite F2000.

Table 4.6 Comparison of surface roughness, hardness and indentation modulus of dental composites investigated.

Comparison of Ra values between materials for the various groups

Significance

A F2000 > A110 & Z100 B F2000 > A110 > Z100 C F2000 > Z100 > A110 D F2000 > Z100 & A110 E F2000 > A110 > Z100 Control F2000 & A110 > Z100 Comparison of hardness between treatment groups for the various materials

Significance

Z100 NS F2000 NS A110 NS Comparison of indentation modulus between treatment groups for the various materials

Significance

Z100 NS F2000 NS A110 NS > indicates statistically difference (p < 0.05) NS indicates no significant difference

64

From the above results, it was concluded that the indentation modulus and

hardness of dental composite restoratives were independent of the surface finish

provided indenter penetration is sufficiently deep. The polishing protocol in

Group D will be adopted for all the subsequent experiments. The Group D

protocol was selected because of its optimum surface finish and ability to remove

the resin-rich layers revealing the composite structure clearly as evidenced in Fig.

4.3.

4.5 Effects of Experimental Variables

4.5.1 Introduction

Apart from surface finish, it has been reported that various experimental

parameters such as indentation load, holding period and loading rate can influence

the calculation of the indentation modulus and hardness of some materials (Guo

and Kagawa, 2004, Simoes et al., 2002, Chudoba and Richter, 2001). Therefore

the aforementioned test variables are of concern in the current depth-sensing

indentation test of polymer-based dental composite materials.

The rate applied during loading and unloading may affect the indentation

test in several aspects. For some materials, the loading rate would have an effect

on the creep rate of the materials, which may in turn influence the maximum

depth as well as the slope of the unloading curve (Chudoba and Richter, 2001).

This will affect the accuracy of the modulus which is to be derived from the

unloading contact stiffness. The loading and unloading rate could also affect the

65

resolution of the data during the acquisition depending on the sampling frequency.

It had been reported that the number of points on the initial unloading curve

included in the curve fitting would affect the compliance of the contact stiffness,

and thus the modulus results (Oliver and Pharr, 1992). In the event of fast

unloading rate and low sampling frequency, the resulting discrete data points will

certainly affect the curve fitting process. However this shall not be a major

concern with the advancements in technology in which the sampling frequency

can be well controlled.

The holding period between loading and unloading is to diminish the time

dependent or creep behaviour of the material. To shorten the experimental and

measurement time, a 10 to 15 seconds holding time is commonly being applied in

most indentation and hardness testing. However this holding period may not be

sufficient for some materials which have higher creep rate. This can have a

remarkable influence on the hardness and modulus results especially for

polymeric and composite materials. Since the holding time is materials dependent,

a short holding period but sufficiently long enough to suppress the creep behavior

of dental composite restoratives has yet to be identified for productivity and

accuracy reasons.

The maximum indentation load (Pmax) to be applied during an indentation

test is dependent on the hardness of the material. For resin-based dental

composite restoratives, the optimum Pmax is yet to be investigated in such a way

that the resulting penetration depth is sufficiently deep for measuring the bulk

material properties and without initiating any cracks on the materials at the same

66

time. The aim of this phase of the research is to determine the effects of loading

and unloading rate, holding period and maximum indentation load on the hardness

and indentation modulus of resin-based dental composite restoratives.

4.5.2 Materials and method

The materials used were same as previous investigation which included minifill

(Z100, 3M ESPE), microfill (A110, 3M ESPE) and poly-acid modified (F2000,

3M ESPE) composites. The variables investigated were the loading and

unloading rate (0.2, 0.5, 1.0 and 2.0 µm/min), indentation load (10, 15, 25 and 50

N) and the load holding time (2, 5, 7.5, 10, 25, 50, 100, 250 and 500 sec). In the

experiment, twenty-one specimens for each material were placed into the square

recesses (3 mm long x 3 mm wide x 2 mm deep) of customized acrylic molds.

The specimens were prepared, cured and conditioned as previously described in

Section 4.4.2.

After conditioning, the materials were randomly divided into three groups

with seven specimens (n=7) in each group. To remove any surface flaws, the

specimens were polished successively using the Group D protocol in which 3µm

diamond suspension was used as the final polish media (Table 4.4). The

specimens were then further conditioned in distilled water at 37 ± 1 °C for 1 week

prior to the micro-indentation testing. At the end of the conditioning period,

indentation modulus (Ein) and hardness (H) were determined using the

instrumentation set-up and analytical equations as described previous1y. The

depth-sensing micro-indentation test was carried out using a Vickers indenter with

load and displacement resolution of 3.8 x 10-3 N and 2.0 x 10-9 m, respectively.

67

To investigate the effects of loading rate, depth-sensing micro-indentation test was

conducted at peak load of 10 N and holding period of 10 s. The loading rate

employed was 0.2, 0.5, 1.0 and 2.0 µm/min and unloading was carried out at a

similar rate as loading. The creep effects on Ein and H were investigated at

different holding period of 2, 5, 7.5, 10, 25, 50, 100, 250 and 500 s at peak

indentation load of 10 N and loading/unloading rate of 2.0 µm/min. The effects of

indentation load was evaluated at 10, 15, 25 and 50 N at loading/unloading rate of

2.0 µm/min with load holding period of 10 s. Comparisons were conducted using

one-way analysis of variance (ANOVA)/post-hoc Scheffé’s test at significance

level 0.05.


The mean indentation modulus and hardness for various composites investigated

at different loading rate, indentation load and holding period are tabulated in

Table 4.7, 4.8 and 4.9 respectively. The effects of test variables investigated on

the modulus and hardness are plotted in Fig. 4.5 to 4.8. The statistical analysis

results are presented in Table 4.10.

Table 4.7 Indentation modulus (Ein) and hardness (H) of dental composites at different loading/unloading rate with peak load = 10 N and holding period = 10 s.

Material Z100 A110 F2000 Loading rate

(µm/min) E (GPa) H (GPa) E (GPa) H (GPa) E (GPa) H (GPa)

0.2 15.22 (1.13)

1.20 (0.04)

5.74 (0.26)

0.52 (0.02)

14.42 (1.70)

0.98 (0.11)

0.5 15.23 (1.27)

1.22 (0.05)

5.73 (0.28)

0.54 (0.02)

14.14 (1.91)

0.96 (0.10)

1.0 15.31 (1.48)

1.22 (0.06)

5.91 (0.31)

0.57 (0.04)

14.32 (1.67)

0.97 (0.10)

2.0 15.36 (1.33)

1.21 (0.07)

5.84 (0.30)

0.54 (0.01)

15.57 (2.79)

1.11 (0.27)

68

Table 4.8 Indentation modulus (Ein) and hardness (H) of dental composites at different indentation peak load with loading/unloading rate = 2.0 µm/min and holding period = 10 s

Material Z100 A110 F2000 Load (N) E (GPa) H (GPa) E (GPa) H (GPa) E (GPa) H (GPa)

10.0 15.19 (0.86)

1.23 (0.05)

5.74 (0.18)

0.53 (0.02)

13.82 (0.79)

0.92 (0.07)

15.0 14.29 (0.59)

1.15 (0.05)

5.59 (0.24)

0.51 (0.02)

12.98 (0.92)

0.87 (0.05)

25.0 13.50 (1.03)

1.17 (0.15)

5.38 (0.69)

0.50 (0.03)

12.20 (1.22)

0.84 (0.04)

50.0 11.69 (1.17)

1.04 (0.17)

5.08 (0.84)

0.48 (0.02)

11.07 (1.39)

0.79 (0.09)

Table 4.9 Indentation modulus (Ein) and hardness (H) of dental composites at different load holding time with indentation peak load = 10 N and loading/unloading rate = 2.0 µm/min

Material Z100 A110 F2000 Holding time

(sec) E (GPa) H (GPa) E (GPa) H (GPa) E (GPa) H (GPa)

2.0 13.14 (0.29)

1.06 (0.01)

4.97 (0.20)

0.46 (0.01)

13.58 (0.39)

0.87 (0.02)

5.0 13.38 (0.27)

1.07 (0.02)

4.88 (0.08)

0.45 (0.01)

13.49 (0.20)

0.89 (0.02)

7.50 13.65 (0.11)

1.07 (0.01)

4.88 (0.08)

0.45 (0.01)

12.98 (0.46)

0.86 (0.05)

10.0 13.59 (0.17)

1.05 (0.01)

4.88 (0.08)

0.45 (0.01)

12.58 (0.79)

0.83 (0.04)

25.0 13.50 (0.16)

1.03 (0.01)

4.79 (0.07)

0.43 (0.01)

12.20 (0.06)

0.79 (0.01)

50.0 13.28 (0.08)

0.97 (0.01)

4.74 (0.12)

0.42 (0.00)

12.55 (0.29)

0.75 (0.04)

100.0 13.39 (0.08)

0.96 (0.01)

4.64 (0.13)

0.39 (0.01)

12.86 (0.47)

0.79 (0.01)

250.0 13.28 (0.24)

0.92 (0.01)

4.55 (0.18)

0.37 (0.01)

13.42 (0.29)

0.79 (0.00)

500.0 13.43 (0.15)

0.91 (0.02)

4.52 (0.20)

0.36 (0.01)

13.19 (0.13)

0.74 (0.01)

69

Fig. 4.5 Load-displacement (P-h) profiles and creep data from a 10-N indent with T=10 s into various materials.

A110

0

2

4

6

8

10

0 0.01 0.02 0.03 0.04h (Displacement)

P (L

oad)

0.2 um/s0.5 um/s1.0 um/s2.0 um/s

A110

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0.0018

0.002

0 2 4 6 8 10Time (s)

Dep

th c

hang

e (m

m)

0.2 um/s0.5 um/s1.0 um/s2.0 um/s

F2000

0

2

4

6

8

10

0 0.01 0.02 0.03Displacement (h)

Load

(P)

0.2 um/s0.5 um/s1.0 um/s2.0 um/s

F2000

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0 2 4 6 8 10

Time (s)

Dep

th c

hang

e (m

m)

0.2 um/s0.5 um/s1.0 um/s2.0 um/s

Z100

0

2

4

6

8

10

0 0.01 0.02 0.03Displacement (mm)

Load

(P)

0.2 um/s0.5 um/s1.0 um/s2.0 um/s

Z100

0

0.0002

0.0004

0.0006

0.0008

0.001

0 2 4 6 8 10Time (s)

Dep

th c

hang

e (m

m)

0.2 um/s0.5 um/s1.0 um/s2.0 um/s

70

Fig. 4.6 Effects of strain rate on indentation modulus and hardness.

Modulus at different strain rate

02468

101214161820

0 0.5 1 1.5 2

Strain rate (um/min)

Mod

ulus

(GPa

)

Z100A110F2000

Hardness at different strain rate

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.5 1 1.5 2

Strain rate (um/min)

Har

dnes

s (G

Pa)

Z100A110F2000

71

Fig. 4.7 Effects of load on indentation modulus and hardness.

Modulus at different indentation load

0

2

4

6

8

10

12

14

16

18

0 10 20 30 40 50

Indentation Load (N)

Mod

ulus

(GPa

)

Z100A110F2000

Hardness at different indentation load

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 10 20 30 40 50

Load (N)

Har

dnes

s (G

Pa)

Z100A110F2000

72

Fig. 4.8 Effects of holding time on indentation modulus and hardness.

Modulus at different holding time

0

2

4

6

8

10

12

14

16

0 100 200 300 400 500

Holding Time (sec)

Mod

ulus

(GPa

)

Z100A110F2000

Hardness at different holding time

0

0.2

0.4

0.6

0.8

1

1.2

0 100 200 300 400 500

Holding Time (sec)

Har

dnes

s (G

Pa)

Z100A110F2000

73

Table 4.10 Comparison of hardness and indentation modulus of various dental composites at different test variables investigated. Comparison of modulus and hardness between different strain rate (µm/min) for the various materials

Significance

Modulus Hardness

Z100 NS NS A110 NS NS F2000 NS NS Comparison of modulus and hardness between different indentation load (N) for the various materials

Significance

Modulus Hardness

Z100 10 > 25 & 50, 15 > 50 NS A110 10 & 15 > 50 10 > 50 F2000 10 & 15 > 50 10 > 50 Comparison of modulus and hardness between different holding time (sec) for the various materials

Significance

Modulus Hardness

Z100 NS

2,5,7.5,10 & 25 > 50,100,250 & 500 50 > 250 & 500 100 > 500

A110 NS

2 > 25,50,100,250 & 500 5 > 50,100,250 & 500 25 > 100,250 & 500 50 > 250 & 500 100 > 500

F2000 NS 5 > 50,250 & 500 2 > 50 & 500

> indicates statistically difference (p < 0.05) NS indicates no significant difference

74

The loading and unloading rate has no effects on Ein and H of all materials

investigated. Quantitatively, the Ein and H decreased with increasing indentation

load. For all materials, the modulus computed at 10 N was significantly higher

than those obtained at 50 N. Except for Z100, the H at 10 N was significantly

higher (p<0.05) than those obtained at 50 N. The modulus of dental composites

was insensitive to the load holding time. The hardness was higher at shorter

holding time due to the plasticity effects of creep. The indentation modulus of

dental composite restoratives was independent of the strain rate and load holding

time, but it decreased with increasing load or depth of penetration. Strain rate has

no effects on hardness, which was indentation load and holding time dependent.

The indentation hardness is related to the yield stress of the material under

testing. At macro level, the hardness is indeed a material constant or called the

true hardness which reflects the bulk material property. However at micro level,

past and present experimental evidences (Gao and Fan, 2002; Halitim et al, 1997)

have shown that the indentation micro-hardness is a function of the indent size,

the applied indentation load, or the penetration depth. As previously discussed in

Section 2.2.4, this is commonly known as the indentation size effects (ISE), which

is more pronounced in the surface characterization of thin films and surface

coatings especially at nano level (Gao and Fan, 2002). In the analysis, the tip of

the pyramidal indenters has always been assumed to be ideally sharp. However, a

certain degree of blunting at the tip of three- or four-sided indenters cannot be

avoided. As a consequence, this results in a difference between the measured and

actual depth of penetration as illustrated by Menčik and Swain (1995). In the

depth-sensing indentation test, the maximum contact area is calculated as a

75

function of the penetration depth, A(h), thus the error contributes to an apparent

change in the measured indentation hardness as well as modulus. This error is

more significant at smaller depths of penetration.

In the current research, the ISE had slight effects on the micro-hardness

measurement for varying maximum indention load and load holding period.

Except for maximum indentation load, no significance difference was found in the

indentation modulus of dental composites at different loading/unloading strain

rate and load holding time.

In general, the results suggest that the current indentation test was being

carried out at an appropriate size-scale level to surpass the ISE. Through the

extensive experimental investigations and results obtained, it was concluded that a

maximum indentation load of 10 N was appropriate for the micro-indentation of

dental composite restoratives. Hence, it was decided to use this value in all the

subsequent experiments. Within the limitations of the current experiment, the

results were highly reproducible at this load level when compared to Pmax at 50N

(Table 4.8) which has higher standard deviations for both Ein and H obtained.

Experimentally, it takes less than 10 seconds (based on loading rate of 0.5 µm/s)

to attain Pmax at 10 N which is more cost and time effective when compared to

higher load levels. In addition, cracks were being initiated in some dental

composites when a maximum indentation load of 50 N was applied.

As shown in Fig. 4.8 and Table 4.10, a load holding period of more than

10 seconds has little effects on the calculated Ein and H. The low depth change

76

(∆h) during the holding period (Fig. 4.5) further suggest that polymer-based dental

composite restoratives does not pose a complex issue associated with visco-

elasticity effects in the current depth-sensing micro-indentation test. The dental

composite materials investigated had filler content of between 40 to 67%. This

amount of filler loading has provided adequate reinforcement to the composite

structure and makes it less susceptible to the time-dependent effects. Among the

three materials being investigated, composite A110 with the lowest filler content

(40%) had the highest depth change of approximately 0.002 mm over the 10

seconds holding period at Pmax of 10 N. Corresponding to the maximum

penetration depth (hmax) of approximately 33 µm, the ratio of ∆h /hmax is calculated

to about 6%. This would be the highest visco-elasticity effects to be expected as

most of the dental composite restoratives available commercially nowadays have

filler content of at least 60%.

The load holding time has no significant effects on the indentation

modulus of dental composite restoratives, while the micro-hardness decreased

with increasing load holding period. This was due to the plasticity effects of the

material and the ISE as discussed previously. Although the load holding period

has a known effect on the measured micro-hardness, a load holding period of 10

seconds was chosen for all the subsequent investigations. As shown in Fig. 4.5,

this time interval was adequate to allow time dependent effects to diminish and

hence reduce time dependent non-elastic effects. Analysing the current dental

composite literature, it can be concluded that indentation modulus is of greater

interest than hardness. To facilitate materials comparison, the measurement of

77

micro-hardness should be carried out on the same load holding period to isolate

time-dependent effects.

In view of the creep behaviour of the dental composite restoratives, the

loading and unloading rate has no significant effects on the indentation modulus

and hardness as shown in Table 4.10. As a result, a loading and unloading strain

rate of 0.5 µm/s and 0.2 µm/s respectively was chosen for all the subsequent

experiments. With this loading rate, it took approximately 10 seconds for the

depth-sensing indentation to reach Pmax of 10N. A lower rate was used during the

unloading so that it captured more data points and hence improved the

measurement resolution of the indentation modulus.

From the experimental results obtained in this chapter, the test protocols

for the micro-indentation testing of composite resins were established and

summarized below. This test protocol should form the basis in the standardization

for the depth-sensing indentation test of resin-based dental composite restoratives

and will be used in all the subsequent experiments.

- Test specimen is loaded at 0.5 µm/s until Pmax of 10 N was attained;

- Pmax is held for a period of 10 seconds;

- it is then unloaded fully at a rate of 0.2 µm/s.

To minimize the unloading error, the first few points in the initial

unloading curve should be omitted in the calculation of the stiffness value. These

after-effects in the indented materials could be due to creeps, stick-slip effects

between the indenter and the indented material, and many others. From the

78

literature and current experimental results, it was concluded that the portion of the

unloading curve at between 50 to 90% of the Pmax was appropriate for the

determination of indentation modulus of resin-based dental composite.

With the experimental protocols obtained from this part of the research,

the indentation modulus of the selected 3M dental composites will be evaluated in

the next chapter. The modulus values will then be compared and correlated to the

flexural modulus obtained from the ISO 4049 test method to study the potential of

the micro-indentation test as an alternate test method for the mechanical

characterization of resin-based dental composite restoratives.

79

Chapter 5 5. Elasto-plastic and Strength Properties of Dental Composite Restoratives

5.1 Introduction

The strength, hardness and elastic modulus of dental composites are key

mechanical properties which may influence the length of service of these

materials. In the context of dental restorative materials, hardness of the dental

restorative materials should be of less concern than its elastic property. This is

because the material is hardly deformed beyond the proportional limit in vivo

during mastication. On the other hand, the elastic property of the restoratives,

which measures the ability of the materials to restore to its original shape when

the load is being removed, could be a more important mechanical property to be

evaluated. The modulus of elasticity is directly related to the amount of

deformation when the material is subjected to external forces. Hence, dental

composites used in posterior restorations must possess an adequate modulus value

in order to withstand the high forces during mastication (Lambrenchts et al., 1987).

As described in Section 2.1.3, the elastic modulus of the dental restorative

materials should be close to that of the enamel and dentin to allow better stress

distribution. The existence of large modulus gradient between restorative

materials and dental hard tissues may lead to fracture and marginal failure

(Lambrechts et al., 1987).

80

As discussed previously, the current worldwide standard for the

mechanical characterization of resin-based dental restorative materials is

documented in ISO 4049 in which the flexural strength and modulus are

determined using three-point bending test method. There are several drawbacks in

association with the use of large beam specimens with dimensions of 25x2x2 mm3

as required in this test method. Firstly, it is time and materials consuming to

prepare these large specimens, which are very susceptible to flaws such as voids.

Secondly, at least three overlapping irradiations are required for visible-light-

cured composites resulting in specimens which may not be homogeneous. This

may influence the stress distribution when the specimens are loaded, which may

in turn affect experimental results. Lastly, the large specimens do not reflect the

clinical situation, considering the mesio-distal width of molars is only about 11

mm. Hence, there is a need to develop better and more reliable screening tests

that based on specimens of clinically appropriate size.

Given the fact that the restoratives are subjected to primarily compressive

load in vivo, the compressive nature of the indentation test may be more relevant.

In view of the drawbacks associated with the ISO three-point bending test as

discussed previously, it is of current research interest to investigate the potential

of the micro-indentation test method for the characterization of resin-based dental

composite restoratives. Micro-indentation can be arbitrarily defined as an indent

which has diagonal length of less than 100 µm (Samuels, 1984). As the filler

particle size of dental composites is typically less than 5 µm, micro-indentation is

the most appropriate size-scale for determining the bulk intrinsic material

properties of this group of material. The research project presented in this chapter

81

aimed to determine the elastic modulus of various resin-based dental composite

restoratives using the depth-sensing micro-indentation method. The results were

then compared with the modulus values obtained from the flexural test. In Section

5.4, an attempt was made to estimate the yield strength of the polymeric dental

composite materials using a developed empirical method from the literature.

5.2 Determination of Flexural Strength and Modulus of Dental Composites by ISO 4049 test method 5.2.1 Introduction

Clinically, composites restorations can be subjected to considerable amount of

flexural stresses (Anusavice, 1996). The required flexural properties are highly

dependent on the clinical applications. In Class I, II, III and IV restorations, where

stresses are significant, high flexural strength and modulus are desired. Materials

with low modulus will deform more during mastication, resulting in catastrophic

failures and destruction of the marginal seal between the composites and tooth

substance (McCabe, 1994; Lambrechts et al., 1987). In some studies (Heymann et

al., 1991, Yap et al., 2002), it was found that composites with lower modulus are

desired for Class V restorations as they are capable of flexing during tooth

function. The latter may reduce the stresses along the bonding agent interface and

likelihood of de-bonding. The objective of this section was to evaluate the

flexural strength and modulus of five selected dental composites with wide

variation of filler size, filler volume fraction as well as the resin system.

82

5.2.2 Materials and Methods

The five selected materials included a microfill composite (A110), two minifill

composites (Z100 and Z250), a polyacid-modified composite (F2000) and a

flowable composite (Filtek Flow). All materials were from the same manufacturer

and of the A2 shade.

Flexural test specimens (25 mm length x 2 mm breath x 2 mm height) of

the various restoratives were fabricated according ISO 4049 specifications in

customized stainless steel molds. The restoratives were placed into the mold,

which was positioned on top of a glass slide. A second glass slide was then

placed on top of the mold and gentle pressure was applied to extrude excess

material. The top and bottom surfaces were then light polymerized in 3

overlapping irradiation steps of 20 to 40 seconds each (depending on

manufacturer's recommendations) using a curing light (Spectrum; Dentsply Caulk,

Milford, DE 19963) with an exit window of 13 mm and an output intensity ≥ 420

mW/cm2. Values were measured with a curing radiometer (Cure Rite, EFOS Inc.,

Ontario, Canada). The centre sections of the specimens were cured first. After

light polymerization, the assembly was placed in a water bath for 15 minutes. The

flash was then removed and the test specimens were separated from their molds

and stored in distilled water at 37 ± 1°C. Fourteen specimens of each composite

were fabricated. Half of the specimens were tested after 1 week and the

remaining half were tested after 1 month of conditioning in water.

At the end of each conditioning period, the flexural properties of the

composites were assessed. The specimens were first blotted dry, sized with

83

sandpaper, and measured using a digital veneer calipers (Mitutoyo Corporation,

Tokyo, Japan). Measurements were taken in two locations for length, breath and

height, and the average of the two values was taken to calculate the flexural

strength and modulus. The specimens were subsequently transferred to a three-

point bending flexural testing apparatus mounted on an Instron Universal testing

machine (Instron model 4502, Canton, MA 02021). The water surrounding the

apparatus and specimens was maintained at 37 ± 1°C and specimens were allowed

to stabilize for 10 minutes prior to testing. A crosshead speed of 0.75 mm/min

was used and the maximum loads exerted on the specimens prior to fracture were

recorded. Flexural strength (σf) and flexural modulus (Ef), in megapascals (MPa)

were calculated using the following equations (ISO 4049):

2max

23

WtLF

f =σ …….. (5.1)

= 3

3

4WtL

DFE f …….. (5.2)

Where

Fmax is the maximum load prior to fracture, in newtons;

L is the distance, in millimeters, between the supports (20 mm);

F /D is the slope of the load-displacement graph, in newtons/millimeters;

W is the width, in millimeters, of the specimen measured prior to testing;

t is the thickness, in millimeters, of the specimens measure prior to testing.

Flexural modulus in MPa was subsequently converted to GPa. The

statistical analysis was conducted at significance level 0.05. Inter-material

modulus was compared using one-way ANOVA/post-hoc Scheffe’s test and the

84

effects of conditioning period on flexural strength and modulus were assessed

using Independent Sample's T-test.

5.2.3 Results and Discussion

The mean flexural strength and modulus of the various materials is shown in

Table 5.1. Results of statistical analysis are shown in Table 5.2. Mean flexural

strength ranged from 66.61 to 147.21 MPa and 67.12 to 151.65 MPa, at 1 week

and 1 month respectively. Mean flexural modulus at 1 week and 1 month ranged

from 3.45 to 11.30 and 4.86 to 13.02 GPa respectively. The load-displacement

curves of all materials are depicted in Fig. 5.1.

Table 5.1 Mean flexural strength and modulus of the composite materials after the two conditioning periods. Materials Flexural Strength (MPa) Flexural Modulus (GPa)

7 days 30 days 7 days 30 days

A110 71.27 (3.64) 76.69 (5.25) 4.85 (0.26) 4.86 (0.29)

Z100 147.21 (1.45) 151.65 (3.88) 11.30 (0.58) 12.29 (0.81)

Z250 130.18 (5.82) 133.62 (5.32) 6.94 (0.65) 7.98 (0.35)

F2000 66.61 (5.09) 67.12 (4.78) 11.03 (0.42) 13.02 (0.47)

Filtek Flow 80.00 (6.55) 81.19 (5.30) 3.45 (0.41) 4.26 (0.44)

Standard deviations in parenthesis.

Table 5.2 Comparison of flexural strength and modulus between materials. Flexural Property Storage Time Differences

Strength 1 week Z100 > Z250 > A110, F2000 & FF

FF > A110 & F2000

1 month Z100 > Z250 > A110, F2000 & FF FF > F2000

85

Modulus

1 week

All other composites > Filtek Flow

Z100, Z250, F2000 > A110

Z100, F2000 > Z250

1 month Z100, Z250, F2000 > A110, Filtek Flow

Z100, F2000 > Z250

Results of one-way ANOVA/Scheffe's test at significance level 0.05. > indicates statistically significant difference in flexural properties.

Baseline testing was delayed for at least 1 week to allow for elution of all

leachable unreacted components and composite post-cure (Ferracane and Condon,

1990; Watts et al., 1987). The latter refers to the progressive cross-linking

reactions in composites after light curing (Yap et al., 2002). Ferracane and others

(1995) studied the effects of normal-cured and heat-cured composites after aging

in water for 1 to 180 days. By 30 days, the aging had little effects in mechanical

properties including flexural modulus for both types of composites. The Ef of the

five selected materials were determined at both conditioning period of 7 and 30

days. This was to allow the subsequent correlation studies between the Ef and Ein

being conducted independently of the conditioning period.

86

Fig. 5.1 Load-displacement curves of various materials when tested under ISO 4049 three-point bending test.

In the load-displacement curves (Fig. 5.1), it was observed that all

materials underwent a brittle failure in the three-point bending test. Noticeably,

the load-deflection curves obtained were not as linear and suggested that the

material underwent some degree of yielding before the brittle failure. The flexural

strength of all composites evaluated fulfilled the minimum requirement specified

in ISO 4049 (flexural strength > 50 MPa). In both conditioning periods, the

flexural strength of Z100 was significantly higher than all other composites

evaluated. The flexural strength of Z250 was significantly higher than A110,

F2000 and FF, and FF was significantly stronger than A110 and F2000. The

results can be explained by the differences in filler content of the composites.

0.00

0.01

0.02

0.03

0.04

0.05

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40

Deflection (mm)

Load

(kN)

⊕ Yield Point

⊕

⊕

⊕

⊕

⊕

87

Studies (Braem et al., 1989; Chung and Greener, 1990; Kim et al., 1994) have

reported a positive correlation between mechanical properties and volume fraction

of fillers. Composites with higher filler volumes such as Z100 and Z250 are

expected to be stronger than those with lower filler volumes. The significantly

lower flexural strength observed with F2000, in spite of its high filler content,

may be attributed to the use of fluoroaluminosilicate glass fillers and/or the

CDMA oligomer. The latter is a methacrylated polycarboxylic acid. Most of the

composites evaluated were based on zirconia silica fillers and BisGMA resin.

Fluoroaluminosilicate glass fillers (the basic glass in glass ionomer cements) were

incorporated into F2000 for fluoride release. Due to their relatively large particle

sizes (3 to 10 µm), the total filler loading by volume is substantially increased. As

both major constituents of F2000 are relatively weak, its flexural strength is

expected to be lower that the other composites evaluated. The low flexural

strength of A110 could be attributed to its low filler (colloidal silica) content and

the fact that the pre-polymerized resin fillers are not well bonded to the polymer

matrix. The resin fillers are heat-cured and do not form covalent chemical bonds

with the polymerizing matrix, due to the lack of available methacrylate groups on

their surfaces. Therefore, they become debonded and dislodged under high

stresses. The higher incidence of clinical fractures observed with microfill

composites as compared to more heavily filled materials might be attributed in

part to their low flexural strengths (Tyas and Wassenaar, 1991). Due to their

lower flexural strengths, F2000, A110 and FF are not indicated for stress-bearing

restorations.

88

The ranking of flexural modulus at 1 week was: Filtek Flow < A110 <

Z250 < F2000 < Z100. Ranking of flexural modulus at 1 month was similar with

exception of the change in ranking between F2000 and Z100 (i.e. Z100 < F2000).

At both time intervals, Z100, Z250 and F2000 were significantly stiffer than A110

and Filtek Flow. In addition, the modulus of Z100 and F2000 were significantly

lower than Z250. The results can be attributed by the differences in filler content

as discussed previously.

For all composites, an increase in Ef was observed with aging. The

increase in stiffness, which can be attributed to post-cure, was significant for all

composites except A110. A substantial proportion of the resin in A110 is in the

form of pre-polymerized resin fillers. As the resin in these fillers is heated-cured,

there is greater conversion of monomer to polymer and minimal additional cross-

linking after light curing (Yap et al., 2002).

5.3 Determination of Micro-hardness and Elastic modulus of Dental Composites using Depth-sensing Indentation Method 5.3.1 Introduction

In this Section, the elastic modulus and hardness of the dental composite materials

were determined using the depth-sensing indentation test as introduced previously.

Correlation studies were performed between the flexural and indentation modulus

values to study the potential of indentation test method as an alternative to the ISO

4049 for the mechanical characterization of dental composite materials.

89


The five similar materials from 3M with the same batch number were used in this

part of investigation. In the micro-indentation test, seven specimens (n = 7) of

size 2mm thick x 3mm width x 3mm long for each material were prepared using

the same method as described previously in Section 4.4. The specimens were

polished progressively using the 3 µm diamond suspension as a final polishing

media or Method D in the specimen surface preparation protocol that was

established in Chapter 4. The indentation modulus was determined after 1 week

and 1 month conditioning in distilled water at 37±1 °C. The same instrumentation

set-up (Fig. 4.1) was used to perform the depth-sensing indentation test. Vickers

indenter, a four-sided square pyramidal diamond indenter with known geometry,

was used. To avoid the indenter tip offset error, the Vickers indenter was

inspected under the microscope to ensure there was no tip blunting before taking

actual measurement.

With the results obtained from Section 4.5, the specimens were indented at

the rate of 0.5 µm/s until a maximum load of 10 N was attained. The maximum

load was held constant for a period of 10 seconds to allow time dependent effects

to diminish. It was then unloaded fully at a rate of 0.2 µm/s. The loading curve

was first fitted with Kick’s law equation (P=Ch2, where C is the loading

curvature) and the initial depth of penetration (hi) was determined from the y-

interception in the plotted graph of h against P1/2. The initial contact may be due

to the surface imperfections or contamination. In the analysis, power-law curve as

described in Section 4.4 was fitted to the unloading data which lied between 50%

to 90% of Pmax (Doerner and Nix, 1986; Oliver and Pharr, 1992). Following the

90

developed analytical solutions as described previously, equations (4.1) to (4.4)

were used to estimate the hardness and elastic modulus from the unloading curve.

The flexural modulus of the materials obtained previously was then

compared with the indentation modulus (Ein). The results were analyzed using

statistical software, SPSS (V11.5, SPSS Inc., USA). Inter-material comparisons

were conducted using one-way analysis of variance (ANOVA)/post-hoc Scheffé’s

test at significance level 0.05. Pearson’s correlation coefficient was computed at

significance level 0.01 to investigate the correlation between the indentation

modulus and the flexural modulus.


The mean hardness, indentation and flexural modulus for the various composites

are tabulated in Table 5.3. The P-h curves for the different composites obtained in

the micro-indentation test are depicted in Fig. 5.2. The photographs of the indent

impressions, which were captured using the digital imaging system, for various

dental composite restoratives are shown in Fig. 5.3. The mean micro-hardness (n

= 7) ranged from 34.15 to 96.28 HV and 31.56 to 90.53 HV at 7 days and 30 days

respectively. The mean indentation modulus (n = 7) ranged from 5.80 to 15.64

GPa and 5.71 to 15.35 GPa at 7 days and 30 days respectively. The mean flexural

modulus (n = 7) ranged from 3.45 to 11.30 GPa and 4.26 to 13.02 GPa at 7 days

and 30 days respectively (Yap et al., 2002).

91

Fig. 5.2 Load-displacement (P-h) curves of various materials obtained in the depth-sensing micro-indentation test.

Table 5.3 Mean hardness, indentation and flexural modulus of the various composites after 7 days and 30 days of conditioning.

Materials (n = 7)

7 Days 30 Days

Indentation Modulus, Ein (GPa)

Flexural Modulus, Ef (GPa)

C1 (Ein/Ef)

Vickers Hardnes*

HV

Indentation Modulus, Ein (GPa)

Flexural Modulus, Ef (GPa)

C2 (Ein/Ef)

Vickers Hardness*

HV

A110 5.80 (0.09)

4.85 (0.29) 1.20 40.16

(1.43) 5.77

(0.16) 4.86

(0.29) 1.19 40.13 (2.60)

Z100 15.64 (0.64)

11.30 (0.58) 1.38 96.28

(3.38) 15.35 (0.35)

12.29 (0.81) 1.25 90.53

(1.14)

Z250 12.52 (0.65)

6.94 (0.65) 1.80 71.70

(3.56) 12.48 (0.47)

7.98 (0.35) 1.56 69.59

(4.42)

F2000 14.58 (0.78)

11.03 (0.42) 1.32 68.66

(2.52) 14.37 (0.77)

13.02 ( 0.47) 1.10 65.95

(1.67)

FF 6.08 (0.32)

3.45 (0.41) 1.76 34.15

(1.66) 5.71

(0.40) 4.26

(0.44) 1.34 31.56 (1.86)

Pearson Correlation Coefficient

0.93 # 0.94 #

Standard deviation in parenthesis # Correlation is significant at the 0.01 level * To convert the Vickers Hardness (HV) to GPa, multiply it by 0.009807

92

Fig. 5.3 Photographs of the indent impressions (Pmax = 10 N) for various dental composite restoratives.

The elastic modulus of all the materials obtained by the micro-indentation

method was higher than those obtained by ISO 4049 test method. C1 and C2 are

the correction factor, which equal to the ratio of Ein over Ef, for the 7 days and 30

days modulus results respectively. A significant, strong and positive correlation

was found between the indentation and flexural modulus (Pearson’s correlation

coefficient = 0.93 and 0.94 at 7 days and 30 days respectively). The result of one-

way ANOVA/Scheffé’s test at 0.05 level of significance is summarized in Table

5.4. For both conditioning periods, the hardness of Z100 was significantly higher

than all other materials. Z250 and F2000 were significantly harder than A110 and

FF while FF had the lowest resistance to plastic deformation. The micro-

indentation test also revealed that the indentation modulus of Z100 was the

highest among all materials investigated. F2000 was significantly higher than

Z250, which was stiffer than A110 and FF. The ranking agreed well with the ISO

flexural test.

Filtek A110 Z250 Z100 Filtek Flow [FF] F2000

93

Table 5.4 Comparison of hardness, indentation and flexural modulus. Conditioning

Period Parameters Significance

7 days

Hardness (H) Z100 > Z250, F2000 > A110 > FF

Ein Z100 > F2000 > Z250 > A110, FF

Ef Z100, F2000 > Z250 > A110 > FF

30 days

Hardness (H) Z100 > Z250, F2000 > A110 > FF

Ein Z100 > F2000 > Z250 > A110, FF

Ef Z100, F2000 > Z250 > A110, FF > indicates statistically difference in hardness and elastic modulus

In this Section, the elastic moduli of five dental composites were

determined by micro-indentation and the results were compared with those

obtained by the ISO 4049 test method. Apart from utilising smaller specimen, the

other apparent advantage of indentation test over the flexural test was its semi-

destructive nature. Only a tiny indent impression was created on the specimen

surface due to localised plastic deformation. Hence, it allowed indentation

modulus to be determined from the same specimen repeatedly. This can be

particularly useful in the investigation of aging and food-simulating effects where

readings could be taken on the same specimen to avoid variations across

specimens. The surface area of the specimen used in the current indentation test

was 3 mm x 3 mm. At indentation peak load of 10 N, the measured diagonal of

the indent was only about 0.1 mm for dental composite restoratives as shown in

Fig. 5.3. This indicated that at least nine indents could be done on the same

specimen based on a separation of five diagonal lengths between each indents.

Specimen size of 3 mm x 3 mm x 2 mm was used so that minimal material was

required and the composite resin could be cured in a single irradiation to avoid

inhomogeneity.

94

In general, the indentation modulus was higher than the flexural modulus.

The discrepancy was attributed to two factors. Firstly, the higher indentation

modulus value obtained could be due to the different stresses being developed

within the materials when subjected to different loading mode. In the three-point

bending test, the measured flexural modulus was primarily due to both bending

moment and shear deformation. While in micro-indentation test, the deformation

around the indenter was far more complex with the resulting deformation stress

field comprised that of compressive, tensile and shear. In the bending test, the 20

mm support span permitted for greater flexibility and deflection upon loading,

giving a lower stiffness. Lastly, the flexural test was susceptible to compliance

errors due to the frame, load cell as well as the contact deformation between the

anvils and specimen. The stiffness of the Instron load cell used in the flexural test

was typically 3600 N/mm. For the five materials tested, the deflection during the

bending test was ranged from 0.4 to 1.3 mm at load level between 25 to 50 N.

This resulted in an error of between 0.5 to 3.9%. On the other hand, surface

referencing technique was employed in the current indentation test set-up in which

the penetration depth was measured directly with corresponding to the applied

load using a LVDT (Fig. 4.1), hence eliminating the load-frame compliance

issues.

The Pearson’s correlation coefficient revealed a positive, significant and

strong correlation between the elastic modulus determined via the micro-

indentation and ISO 4049 test methods. This indicated a strong linear relationship

between the two test methods, despite the fact that the value of indentation

modulus is consistently higher than the flexural modulus. In a comparative study

95

in which the material ranking is more important, the absolute value obtained using

different test methods should not be a major concern. Since ISO 4049 is the only

test standard available for the resin-based dental composite materials, the strong

correlation would imply that the indentation test is potential to be an alternative

test method for dental composite materials. To quantify the difference between

the indentation and flexural modulus value, a correction factor was introduced into

the current analysis. The correction factor is computed as the ratio of Ein over Ef,

and their values are tabulated in Table 5.3. The mean values of C1 and C2, which

correspond to the correction factor at 7 and 30 days, were found to be 1.49 and

1.29 respectively. Within the limitation of this study, it can be deduced that the

indentation modulus is about 30% to 50% higher than the flexural modulus.

In comparing the indentation modulus of the five composites, similar

observations were drawn from both the 7 and 30 days results. It was found that

Z100 had the highest modulus value. The modulus of F2000 was significantly

higher than Z250, which was significantly stiffer than A110 and FF. The

variation in stiffness was attributed to the volume fraction of the reinforced filler

particles which provided the necessary strength to the composite structure. It had

been found previously that a positive correlation existed between stiffness and

filler content of dental composites (Braem et al., 1989; Chung, 1990). The

correlation plot (r = 0.90 to 0.97) between the modulus and the filler volume

content for dental composites under current investigation is presented in Fig. 5.4.

96

Fig. 5.4 Correlation between the modulus and filler volume content of dental composite restoratives.

Composite Z100 and Compomer F2000, which had a higher indentation

modulus, also had a higher filler volume (66% and 67% respectively). Similarly,

the less stiff composites, A110 and FF had a lower filler composition (40% and

47% respectively). Comparison of stiffness by flexural modulus gave similar

results, with the exception of A110 to be significantly stiffer than FF when tested

at 7 days. Generally, the results for inter-material comparison by indentation and

flexural modulus methods were in good agreement. The low standard deviation

obtained in the indentation test suggested that this test method was highly

reproducible. The strong correlation demonstrated that the micro-indentation test

method could be used as an alternate test method for the mechanical

characterization of resin-based dental composites.

R2 (Ein, 1-week) = 0.95

R2 (Ef, 1-month) = 0.87

R2 (Ein, 1-month) = 0.81

R2 (Ef, 1-week) = 0.95

0

2

4

6

8

10

12

14

16

0 20 40 60 80 100Filler volume content / %

Elas

tic M

odul

us E

/ G

PaEin, 1-weekEin, 1-monthEf, 1-weekEf, 1-month

97

Although the micro-indentation test has many advantages as stated earlier,

it also possesses several limitations. Firstly, the resulting stress field developed

under the indenter’s tip is rather complex. Although the test is compressive in

nature, the compressive loads resolve as shear and tensile stresses within the

restoration material. Secondly, the indentation test does not produce a direct

measurement of strength. Thirdly, this test may be limited to only homogenously

dispersed particulate reinforced polymer matrix composites which are assumed to

be isotropic. Non-homogenous or anisotropic composite materials such as fiber

reinforced composite materials would present a problem for this testing method.

Last but not least, the depth-sensing micro-indentation test involves a complex

and expensive test set-up which may not be readily accessible by others. This is a

major shortcoming associated with this test method.

5.4 Determination of Yield Strength of Dental Composites 5.4.1 Introduction

In this Section, the yield strength of the dental composite materials was attempted

to estimate from the indentation P-h data using an empirical method which

described in Section 2.2. Although brittle failure was generally being observed

during the flexural test, it was within the current research’s interest to examine the

yield strength of these polymeric composite materials. All the developed

numerical solutions for sharp indentation indicated that the loading curve follows

the relationship of P = Ch2. Dental composites differ greatly from metals and

ceramics in which many of these studies are based upon. Hence, it is important to

98

first evaluate the discrepancy between the experimental and theoretical results in

adopting the empirical equation to derive the yield strength. In the current

investigation, the yield strength was derived using different curve fitting methods

and the validity of the proposed empirical method as well as the underlying

assumptions on dental composite materials will be assessed. In order to better

understand the strength properties of dental composite materials, the yield strength

results were compared to the values obtained from both flexural and compressive

test.


The load-displacement (P-h) data obtained from the previous indentation test

conducted on the five dental materials from 3M were used in this part of

investigation. The yield strength of the materials was determined using the

empirical method proposed by Zeng and Chiu (2001). This method was chosen as

it purports not to assume a known elastic-plastic behaviour and has been found to

be effective for a diverse range of materials, from ductile materials such as

aluminium and 301 stainless steel to brittle materials like fused silica, zirconia and

even a plastic, polycarbonate. The method being semi-empirical based, does

make assumptions but generalises the behaviour of the material as having some

mixed elastic-plastic response. Dental materials from the flexural tests

demonstrates characteristics of having a brittle behaviour with a indistinct yield

point. At first cut, the method therefore held promise for this material. The

alternate method by Giannakopoulos and Suresh (1999) presumes a strain

hardening elastic-plastic behaviour.

99

With known Poisson’s ratio, the effect of the Poisson’s ratio on elastic

indentation f(ν) were computed for various materials tested. The pure elastic

curve boundary of P = f(ν)Eh2 was first plotted on the load-displacement graph.

To establish the elastic perfect-plastic boundary, a line was drawn to fit the first

three points of the unloading curve as suggested by Zeng and Chiu (2001). The

weight ratio (θ) was estimated graphically at 50% of Pmax as shown in Fig. 2.2.

This was consistent with the Oliver & Pharr’s curve fitting method presented

earlier and other studies (Doerner and Nix, 1986; Zeng and Chiu, 2001) which

demonstrated that Eqn. (2.17) only fitted well to the upper portion of the

unloading curves.

The loading curve was first fitted with the power law relation, P = C’hn to

determine the exponent n for various tested dental composite materials. With

known C’ and using Eqn. (2.14), the yield strength (σy) was extracted from below

Eqn. (5.3).

yy

EC σσθ

°+

+

°=

322tanln111

)22(tan273.1' 2 ........ (5.3)

In the second part of the analysis, the loading curve was fitted with

polynomial equation, P = C”h2+y. The “y” constant reflects the fact that the

curve fitting for P = C”h2, was not followed for the initial part of the plot. Figure

5.5 illustrates this clearly when the load P is plotted against h2. In most cases, the

deviation from the h2 linear relationship occurred around 2 to 3N although some

showed strong linearity from the start while others as high as 4N. For some cases

100

the correlation for linearity remained around 0.95 all the way. All these various

forms of result occurred between indents for the same test specimen.

From the C”, the yield strength was determined using the above equation

5.3. For yield strength values obtained using both curve fitting methods, inter-

material comparisons were conducted using one-way analysis of variance

(ANOVA)/post-hoc Scheffé’s test at significance level of 0.05.

Fig. 5.5 Load to h2 relationship of a typical indent. The lower portion of the plot deviates from linearity.


The yield strength values computed using both power law and h2 curve fitting

methods are tabulated in Table 5.5. In the analysis where the loading curve is

fitted with power law curve, the mean exponent (n) was ranged from 1.50 to 1.65.

The weight ratio (θ) was ranged between 0.114 and 0.210. The mean value of C’

and yield strength ranged from 2378 to 6493 and 5.81 to 21.20 MPa respectively.

101

The standard deviation for both the indentation loading curvature C’ and yield

strength was exceptionally high. For the yield strength of Z100, the coefficient of

variation (ratio of standard deviation over mean) was found to be as high as 95%.

The result of the one-way ANOVA/Scheffé’s test at 0.05 level of significance is

summarized in Table 5.6. Clearly, the attempt to use the entire P-h curve to

analyze the result is subject to too high a degree of experimental error to yield any

meaningful result.

Table 5.5 Mean yield strength of various composites determined using power and polynomial curve fitting method.

Standard deviation in parenthesis

Table 5.6 Comparison of yield strength of various dental composites.

Curve fitting method Significance

Loading Curve, P=C’hn N.A.

Loading Curve, P=C"h2+y Z100 > A110, Z250 & F2000 > FF

> indicates statistically difference in yield strength

Loading Curve,

P=C’hn Loading Curve,

P=C"h2+y Material

(n=7) θ C’ n σy (MPa) θ C" y σy

(MPa)

A110 0.210 (0.022)

2567 (892)

1.62 (0.10)

11.34 (5.23)

0.210 (0.022)

9714 (602)

0.601 (0.296)

63.91 (9.361)

Z100 0.156 (0.030)

6493 (4414)

1.63 (0.18)

21.20 (20.21)

0.156 (0.030)

22805 (2095)

0.850 (0.371)

101.75 (26.87)

Z250 0.151 (0.026)

6014 (4390)

1.65 (0.21)

19.28 (16.60)

0.151 (0.026)

16671 (1513)

0.946 (0.591)

71.47 (18.47)

F2000 0.114 (0.029)

3029 (1629)

1.50 (0.16)

5.81 (3.84)

0.114 (0.029)

18558 (2518)

0.738 (0.426)

55.10 (20.20)

FF 0.139 (0.021)

2378 (714)

1.62 (0.11)

6.34 (1.82)

0.139 (0.021)

8813 (307)

0.483 (0.392)

34.18 (7.111)

102

The use of the P=C"h2+y relationship as recommended by Zeng and Chiu

(2001), showed a fairly reproducible yield result. The exception was F2000 where

the standard deviation was largest with a 36.6% deviation. The other results had a

deviation of less than 20% which is more typical of strength tests. The result of

the one-way ANOVA/Scheffé’s test at 0.05 level of significance summarized in

Table 5.6 indicates that the same.

Comparing the methods of analysis, it is clear that the use of the power

law curve fitting method using P=C’hn, is not good. There is a clear lack of

consistency in the results with the resultant yield strength obtained highly variable

even for the same sample indented more than once. In contrast, the assumption of

a P=C"h2 behavior based on the response under higher loads demonstrated

promise in giving a more consistent result. Figure 5.6 shows the C”h2 fit to the

data of a typical indentation. It affirms the observation that the initial portion of

the loading curve is highly irregular and experimentally difficult to control. This

is perhaps unsurprising if the composite nature of these dental materials is

recognised. These dental resins are highly filled and the initial indent contact will

result in possibly the indenter interacting with one or a few hard particles which

are typically around 5 to 10um in size. It is therefore likely that only after the

indenter has penetrated an area large enough to reflect the average composite

material, do we obtain the expected h2 response. The value of “y”, the constant in

the h2 equation, is highly variable, typically showing a 43 to 81% deviation. This

reflects the indeterminate nature of where the indent is being made. However, the

consistency in the value of C” for each type of dental resin supports the view that

the gross material behaviour under the indent is reflective of the material yield

103

response. The improved consistency of this result allows therefore the conclusion

that this analysis has avoided major sources of experimental variability and

therefore of potential as a measure of yield strength.

This then raises the question of the significance of this yield result. It

should be recognised that this is a complex question. Yielding as a phenomenon

is a function of the stress state in the specimen. Indentation induces a complex

stress state in the material. What defines the point of yielding therefore depends

on how the stress is made manifest by the test method. For example, with a

flexural test, given that the specimens failed predominantly in a brittle manner via

a single dominant crack, suggests that the flexural test on these resins will yield a

result that reflects a tensile type of load. The brittleness of the failure also raises

question on its sensitivity to cracks and other defects. A quick comparison against

flexural strength shows some correlation as seen in Figure 5.7. This less than

convincing correlation suggests therefore that the indentation yielding process is

different to the tensile dominated flexural test but, there is nonetheless correlation

that a stronger flexural strength does relate to a higher indentation yield strength.

104

Fig. 5.6 Curve fitting for F2000 using P=C”h2+y.

Fig. 5.7 Correlation between flexural strength and indentation yield strength.

105

It might be speculated that there may be better correlation between the

indentation process to a compression test process. Some compression testing were

carried out in the course of this research. The compression tests were an initial

pilot study and it was carried out on just three of the five materials. In this testing,

the specimen test size used was 2mm by 2mm by 10 mm. The compression test

was performed between two flat anvils mounted onto a universal tester, with a

crosshead speed of 0.5 mm/min. The stress-strain curve is shown in Fig. 5.8(a).

and the comparison chart to the indentation yield and flexural strength of various

materials in Fig. 5.8(b).

(a)

106

(b)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Indentation Yield Strength

Flexural Strength

Compression strength

KIC (SENB) KIC (Indentation)

Nor

mal

ised

Res

ult Z100

A110

F2000

FF

Z250

(c)

Fig 5.8 (a) Compressive stress-strain curves, (b) Comparison of flexural, yield and compressive strength of dental composites, (c) Normalised strength plots.

107

From the compressive stress-strain curves shown in Fig. 5.8(a), it could be

observed that the materials do not have a distinct yield point before fracture.

Extrapolations might suggest a yield point of around 80 to 90MPa in the case of

A110 which is a resin rich material. For Z100 and F2000, such a point is difficult

to define. It is also noted the flexural and yield strength were consistently lower

than the compressive strength values. This was consistent with the literature

findings (Hasegawa et al., 1999) in which compressive strength of brittle dental

materials was found to be higher than both the diametric tensile and flexural

strength values.

It is interesting to note also that these resin rich system had the lowest

scatter of 14.65% for indentation yield strength though this is not reflected in the

flexural strength data. The next lowest scatter is for FF with 20.81% which also

corresponded to the specimens with the highest flexural strain. This observation

supports the observation that these materials would have the more distinct yield

point. This supports the thesis that the indentation yield strength is a material

characteristic. The more brittle materials with a less distinct yield point would

result in a higher data scatter.

The materials ranking was in good agreement for all materials

investigated. The difference in strength values was due to the different loading

condition resulting in the different stress distribution being generated within the

composite structure. It is also interesting to note from Fig. 5.8(c), the normalised

strength comparison that the strength ratios for the indentation yield strength is

108

between the flexural and compression results although the yield values are

typically lower than might be expected from inspection of the compression curve.

However, comparing with the flexural plots, the very brittle failure modes

of A110 and F2000 suggest that the yield point is indeed close to the flexural

strength. But, for the more ductile systems Z100, Z250 and FF, it is not

unreasonable to suggest that there is yielding occurring before fracture and this is

reflected in proportionally lower indentation yield strength. Marking the relevant

points of the indentation yield point on the graph Fig 5.1, it can be observed that

the indicated yield point is not unreasonable for each plot. Consequently, it would

be inappropriate to directly relate the flexural strength to the indentation yield

strength since the failure during a flexural test is affected not just by the material’s

ultimate strength, but also by its fracture toughness. In other words, a ductile

material would indicate a low indentation yield strength with respect to its

ultimate flexural strength, while a brittle material would indicate a high

indentation strength with respect to its flexural strength. Indeed the results as

summarised in Fig 5.8(c) show that the 2 toughest materials by its KIC value are

FF and Z250 as determined by the KIC SENB test or by indentation fracture test.

Correspondingly, these two materials show the lowest ratio of indentation yield

strength to flexural strength: 0.427 and 0.549 respectively.

Strength, which measures the stress at failure, is a common mechanical

parameter used in evaluating the structural performance of brittle dental materials.

However it is more of a “conditional” than an inherent material property. Its

values are dependent on the testing methodology, material microstructure and

109

associated failure mechanism (Kelly, 1995). This was evident in the current

comparative studies among the indentation yield, flexural and compressive

strength of dental composite materials. However, the methodology of indentation

yield strength using the analysis of Zeng and Chiu (2001) has been shown useful

as a measure of the incipient point of yielding in these dental materials. It is

clearly not directly correlated the failure strength of materials but is nonetheless a

useful indicator of the material characteristic and adds to the toolbox of the

materials scientist in comparing properties of materials.

In the next chapter, the fracture toughness of the dental composites will be

determined using both the conventional bending test method on single edge notch

beam specimens and the indentation fracture method. Correlation studies will

then be performed on the fracture toughness values obtained to determine the

suitability of indentation fracture test on dental composite restorative materials.

110

Chapter 6 6. Indentation Fracture of Dental Composite Restoratives 6.1 Introduction

As mentioned previously, fracture remains one of the main clinical failures

associated with dental restorative materials (Roulet, 1988; Brackett et al., 2007).

In view of the brittle nature of dental composite restoratives, the analysis and

understanding of the fracture toughness is of primary importance. In this part of

the PhD thesis, fracture toughness was determined using both three-point bend test

with single-edge notched beam (SENB) specimens and the indentation fracture

method. Following this, correlation studies were performed on the KIC values

obtained between these two test methods. The advantages and limitations of these

two test methods were discussed, and suitability of the indentation fracture

method was assessed.

6.2 Determination of KIC of Dental Composites by Three-point Bend test

6.2.1 Introduction

The bending test employing SENB specimens has been routinely used in

determining the fracture properties of dental materials. This method offers an

advantage as it can be applied on most of the material testing systems with a three

or four-point bending test fixture. In this part of the research project, the plane-

strain fracture toughness of the selected dental composite materials will be

111

determined using the established ASTM E399 and ASTM D5045 test standards.

The validity of the obtained KIC will be investigated and to be used as reference

values for subsequent comparative studies with the indentation fracture test.


The experiment was done in accordance to the test protocol for the single edge

notched test as documented in ASTM Standards E399 (1997) and D5045 (1996).

The same five dental materials were used in the experiment and their technical

specifications are tabulated in Table 4.1. Fifteen specimens of 25 mm length x 2

mm width x 2 mm thick for each material were prepared using the similar method

as previously described in Section 5.2.

Prior to the test, the width (W) and thickness (t) of the specimens were

measured using a digital vernier caliper with an accuracy of 0.01 mm and

recorded. To create the chevron notch, the middle of the specimen was first

initiated using a 0.3 mm diamond wafering blade (BUEHLER Series 15C

Diamond 7.6cm x 0.15mm) mounted on a Struers Minitom cutter after which a

sharp razor blade was run through the notch to create a nearly sharp V-shaped

notch. This was done in accordance to the specimen preparation protocol as

specified in ASTM D5045 (1996).

Specimens were then placed under a microscope to measure the crack

length (a) of the notch which was a crucial variable in the calculation of KIC. The

micrograph of the crack was taken and measured against a calibrated scale bar.

112

Specimens which did not conform to the crack length requirement of

0.45<a/W<0.55 were being discarded. Remaining samples were then conditioned

in distilled water at 37°C for a period of 7 days for the polymerization process to

be fully settled down. After the conditioning period, the specimens were removed

and subjected to a three-point bend test using a customized fixture mounted onto

the Instron microtester (Instron 5848, Instron Corporation, Canton, USA) as

shown in Fig. 6.1.

Fig. 6.1 Three-point bending test set-up for determining the KIC.

The crosshead speed used was 0.5 mm/min and the maximum load

required to fracture the specimen was recorded. Throughout the test, specimens

were conditioned in a chamber filled with distilled water, which was maintained at

37°C. The environmental chamber as incorporated into the custom designed

three-point bending fixture (Fig. 6.1). The test was carried out with a support

113

span of 20 mm and the radius of both support and loading shaft was 1.0 mm. The

fracture toughness, KIC was then calculated using equation 6.1 (ASTM E399).

Cracks of fractured specimens are then observed under the microscope to see if

the cracks propagated were single or multiple as this can affect the readings. The

specimens with crack not initiated from the tip were being discarded from the

analysis. Inter-material fracture toughness was compared using one-way

ANOVA/post-hoc Scheffe’s test at significance level 0.05.

)/(2/3 WaftW

PLKIC = …….. (6.1)

Where

P is the load,

t and W is the thickness and width of the specimen respectively,

L is the span distance between the two supports which equals to 20mm,

a is the crack length, and

f(a/W) is the function of a/W. For bend specimen where x = a/W and 0 < x < 1,

2/3

22/1

)1)(21(2)]7.293.315.2)(1(99.1[3)(

xxxxxxxxf

−++−−−

= ........ (6.2)

In order to ensure that the obtained KIC results to be considered valid

according to this test method, the size criteria as stated in equation 6.3 needs to be

satisfied.

t, a, (W – a) > 2.5(KQ/σy)2 …….. (6.3)

Where

KQ is the trial KIC value,

114

σy is the yield strength of the material. For brittle dental materials, it is approximated by the flexural strength values obtained in Section 5.2.


The specimen size, crack length and their corresponding KIC values for the

composite materials are tabulated in Table 6.1. The ratio of the crack length (a)

over the width (W) was approximately half and was within the range of 0.45 to

0.55 for all specimens. The fracture toughness for the composites ranged from

1.01 to 1.91 MPa.m0.5 with Z250 being the highest. The KIC of Z250 was

significant higher than all materials investigated. FF was significantly tougher

than Z100, A110 and F2000, and the compomer F2000 had the lowest resistance

to fracture or crack propagation. The validity test results are presented in Table

6.2. The results showed that the measured KIC values were valid as they satisfied

all the size criterion equations in ensuring plane-strain measurement. The KIC

values of various materials obtained from this part of the experiment will be used

in the subsequent correlation study.

Table 6.1 Mean KIC of the composite materials determined by three-point bending test method. Material (n=7) a (mm) t (mm) W (mm) KIC (MPa.m0.5) A110 1.09 (0.13) 1.99 (0.03) 2.08 (0.02) 1.29 (0.10) Z100 1.11 (0.15) 2.04 (0.05) 2.03 (0.02) 1.25 (0.12) Z250 1.03 (0.12) 2.01 (0.04) 2.03 (0.03) 1.91 (0.12) F2000 1.00 (0.15) 2.00 (0.03) 2.05 (0.02) 1.01 (0.09) FF 0.95 (0.13) 1.98 (0.04) 1.99 (0.02) 1.40 (0.15) Significance Z250 > FF> A110 & Z100 > F2000 Standard deviations in parenthesis, > indicates statistically difference (p < 0.05)

115

Table 6.2 Validity test of the KIC values determined by three-point bending test method. Material σf (MPa) 2.5[KQ/σf]2 (mm) W - a (mm) 2.5(KQ/σf)2<t, a, (W – a) A110 71.27 0.82 0.99 Yes Z100 147.21 0.18 0.92 Yes Z250 130.18 0.54 1.00 Yes F2000 66.61 0.58 1.05 Yes FF 80.00 0.77 1.04 Yes

The value of KIC of resin-based dental composite is highly dependent on

the volume fraction and the size of the filler particles (Higo et al., 1991). In a

notched specimen, the crack propagates through the matrix resin and the presence

of filler particles will inhibit crack propagation increasing the fracture toughness

of the material. As cracks cannot form across filler particles, they have to move

along the perimeter of the particle. For composite with larger filler particles and

filler content such as Z250, the crack has to form across a larger distance thus

increasing the energy required for formation of the crack. Although the

compomer F2000 had both large filler size and content, its fracture toughness

values were the lowest among all materials investigated. This may attribute to its

CDMA/GDMA resin matrix which resulted in low fracture resistance of the

composite structure. With referring to the material profile shown in Table 4.1, it

was observed that only composite F2000 had this distinct resin matrix as

compared to other tested materials. Based on the above, the compomer F2000 is

not recommended for posterior restorations which are subjected to high loads. It

was noted that composite FF had high fracture toughness though its filler content

was relatively low at 47%. Among all materials tested, the FF composite has the

widest range of filler particle sizes ranging from 0.01 to 6 μm that are randomly

116

arranged in the composite structure. It is anticipated that these irregularities have

inhibited the crack growth path to a large extent and dissipated the energy during

the propagation, efficiently into its rich resin matrix. However, the low hardness

and modulus values (Table 5.3) of FF do not favour its usage in high-stress

bearing area.

In the validity test as tabulated in Table 6.2, the values of 2.5[KQ/σy]2 was

found to range between 0.54 to 0.82 mm. These values were lower than the

corresponding thickness (t), crack length (a), and the difference between the width

(W) and the crack length for all materials. Basically, this satisfied the required

size criteria in the adopted test standards implying that the specimen was of

adequate size to give linear elastic behaviour. Hence, the measured KIC in the

current SENB test was valid. The above validation is critical as the scheme used

in the test standards assumed linear elastic behaviour of the crack specimens, such

that the state of stress near the crack tip approaches plain strain, and the crack-tip

plastic zone must be relatively small as compared with the crack size and

specimen dimensions in the constraint direction (ASTM D5045, 1996).

In the above evaluation, the flexural strength was used in the computation

instead of the yield strength. There are two reasons for assuming this. Firstly, the

dental composite materials were observed to fail predominantly in brittle manner

during the flexural test (Fig. 5.1) and it had been shown previously in Section 5.4

that the yield point was closed to flexural strength for most brittle dental

composite materials. Secondly, the yield strength values obtained from the

indentation test data was not directly correlated the failure strength of materials.

117

The three-point bend test used in determining the KIC of materials offered

great advantage of being simple in terms of the test itself and also the required test

set-up. Although the three-point bend test was easy to conduct but the specimens

were technically difficult to prepare especially for dental composite materials.

During preparations, approximately half of the specimens had to be discarded due

to the failure to achieve the crack length criteria as specified by ASTM E399.

Upon inspecting the crack morphology after the bending test, the crack formed on

few specimens was not initiated from the crack tip and were being excluded in the

analysis. In view of the above, only 7 to 8 specimens out of 15 were used for the

analysis. Besides this, the utilization of large beam specimens required much

material, time and cost for the fabrication of dental composite specimens. The

three-point bend test method was also very susceptible to various specimen and

experimental related variables. Among them, the impossibility to create an

infinite sharp tip as required by the fracture equation. This was due to the

thickness of the blade which was used to initiate the crack on the beam specimens.

Moulding the materials around the razor blade is another possible method to

create sharp notch, however this may not work for dental composite materials. In

view of its constituents, resin rich layers are highly possible to be formed near the

razor blade when the dental composite were pushed around it. This would

certainly affect the homogeneity of the materials and hence the test accuracy.

Lastly, the compliance of the test fixture and possible slippage between the

specimen and the supports could further contribute to the measurement errors. In

view of the above drawbacks associated with the three-point bend test method, it

is of the current research interest to explore the potential of the indentation

118

fracture method to determine the fracture property of the dental composite

materials.

6.3 Determination of KIC of dental composites by indentation

fracture test 6.3.1 Introduction

The indentation method will be used to determine the fracture toughness of dental

composite materials in this section. In the indentation fracture mechanics as

presented in section 2.2.5, the empirical constant, ξ is a function of the indenter

geometry and is always regarded as non material dependent. Its value for various

type of indenter has been calibrated experimentally and well established for a

variety of pure glass as well as ceramic materials (Lawn et al., 1980; Anstis et al.,

1981). In the current research, the dental composite materials are of complex

structure with glass filler particles reinforced in resin-based matrix. Hence, the

use of the calibrated value of ξ on dental composite materials involves some

degree of uncertainty. In this research, indentation fracture toughness of various

dental composite materials was first determined using a calibrated value of ξ from

the literature. A correlation study was then performed on the fracture toughness

values obtained through both bending and indentation fracture test. To evaluate

the validity of ξ on dental composite restoratives, both the LEM model and the

Lankford’s equation for the half-penny crack were used with fracture toughness

values from the SENB test as a reference. The obtained values were then

compared with the experimentally value.

119


The same five 3M materials were used in this part of the investigation. In the

indentation fracture test, seven specimens (n = 7) of size 2mm thick x 3mm width

x 3mm long for each material were prepared using the same method as described

previously. The specimens were polished progressively using Method D with

diamond suspension of 3 µm as the final polishing media, as previously described

in Section 4.4.

The indentation fracture test was determined using the same

instrumentation set-up (Fig. 4.1) after 7 days conditioning the specimens in

distilled water at 37±1 °C. Corner cube indenter (apical face angle 35.3°), a three-

sided pyramidal diamond indenter was used to induce crack on dental composite

materials. The indenter was inspected under the microscope to ensure there was

no tip blunting before taking the measurement. In view of its larger face angle,

the corner cube indenter was employed so as to induce crack at loads of smaller

order. The indentation head was fitted with a static loadcell (Instron Corp., CA,

USA) of 1kN capacity. Prior to the actual experiment, a pilot test was conducted

to determine the load level in which pop-in cracks were initiated in various dental

composite materials.

In the experiment, the specimen was loaded at a rate of 0.5 µm/s until the

desired load, P to induce cracks had been attained. The specimen was then

unloaded fully at the same rate and the image of the residual impression was

captured immediately using the optical imaging system that incorporated into the

indentation head. With reference to the calibration data, the half-length of the

120

half-penny cracks, c was measured from the centre of the indent origin to the end

of the crack as illustrated in Fig. 6.2. The indentation fracture toughness of the

materials was evaluated and compared using the two established equations from

the indentation fracture mechanics as below.

5.1

5.0

, cP

HEK LEMIC

=ξ …….. (6.6)

56.1

5.1

5/2

,

=− c

aaP

HEK PennyHalfIC ξ …….. (6.7)

Fig 6.2 Residual impression of corner cube indentation fracture showing characteristics dimensions c and a of radial-median crack. The crack length, l is computed as the difference between c and a.

The modulus (E) and hardness (H) values were to be obtained from the

previous depth-sensing indentation experiment as presented in section 5.3. The

indentation fracture toughness was first determined using the experimentally

calibrated value of ξ which was equal to 0.036 for corner cube indenter (Harding

et al., 1995). The results were then compared and correlated with the KIC values

121

obtained previously from the three-point bending test in Section 6.2. As a

validation test, the empirical constant ξ was subsequently determined for various

composite materials by substituting the KIC values obtained from the SENB

bending test, at equilibrium.

Results were analyzed using statistical software, SPSS (V11.5, SPSS Inc.,

USA). Inter-material comparisons were conducted using one-way analysis of

variance (ANOVA)/post-hoc Scheffé’s test at significance level 0.05. Pearson’s

correlation coefficient was computed at significance level 0.01 to investigate the

correlation between the fracture toughness values obtained through different

methods.


In the pilot experiment, the dental composite materials under were found to

require load level of between 100N to 200N in order to induce a crack formation

with l/a of at least 0.5. The composite FF required the highest load of at least

200N for a crack to form. The indentation fracture load for initiating the crack

was rather inconsistent for some materials. It was found that the resulting crack

morphology was rather complex with substantial lateral cracks extend from the

deformation zone to the subsurface being observed for most of the materials (Fig.

6.2). This was due to the response of the dental composite structure under the

high tensile stresses during the crack initiation. These “clouds” of lateral cracks

had led to difficulty in measuring the characteristics crack lengths in some

materials. For statistical significance and better accuracy, additional test

122

specimens were fabricated and tested with achieving the sample size of at least

seven (n = 7) in the analysis. To avoid complication in the current analysis, the

indentation fracture toughness was evaluated with using only the LEM model and

improved equation for the half-penny crack morphology which was well

developed for the current group of materials under study.

It was important to note that the indentation fracture models as shown in

Eqn. (2.18) to (2.20) were based on the assumption that there were no pre-existing

surface stresses. Therefore in the current experiment, all the specimen surfaces

were polished using the established polishing protocol to avoid any influence on

the elastic-plastic stress field due to the existence of any surface flaws. After the

polishing, the specimens were conditioned in distilled water for 7 days prior to the

fracture test. This conditioning period was just an estimate which it should be

long enough to alleviate any residual stresses that could be induced on the

specimen surfaces during the polishing.

The results of the indentation fracture toughness determined based on ξ =

0.036 are presented in Table 6.3 and Fig. 6.3. The results of the statistical analysis

are shown in Table 6.4. The KIC in the LEM model was found to range between

1.43 to 2.38 MPa.m0.5. When computed using the improved half-penny equation,

the indentation fracture toughness values were found to be lower with ranging

from 1.05 to 1.79 MPa.m0.5. In the statistical analysis, similar rankings were

found for both the KIC,LEM and KIC,Half-Penny. The indentation fracture toughness of

Z250 and FF were significantly higher (p<0.05) than F2000, and both composites

A110 and Z100 had significantly lower toughness than F2000. As observed in the

123

normalized plot (Fig. 6.3b), the KIC,LEM and KIC,Half-Penny of compomer F2000 and

flowable composite FF were not in good agreement with the fracture toughness

obtained in the SENB test .

Table 6.3 Mean KIC of the composite materials determined by three-point bending test and indentation fracture method.

Material Bending Test Indentation Test

KIC,SENB (MPa.m0.5) KIC,LEM (MPa.m0.5) KIC,Half-Penny(MPa.m0.5) A110 1.29 (0.10) 1.44 (0.05) 1.08 (0.04) Z100 1.25 (0.12) 1.43 (0.23) 1.05 (0.18) Z250 1.91 (0.12) 2.41 (0.25) 1.79 (0.19) F2000 1.01 (0.09) 1.79 (0.30) 1.29 (0.22) FF 1.40 (0.15) 2.38 (0.08) 1.76 (0.06) Pearson Correlation Coefficient 0.36# 0.39# Standard deviations in parenthesis # Correlation is not significant at the 0.01 level Table 6.4 Comparison of KIC between materials obtained from different methods. Significance KIC,SENB Z250 > FF> A110 & Z100 > F2000 KIC,LEM Z250 & FF > F2000 > A110 & Z100 KIC,Half-Penny Z250 & FF > F2000 > A110 & Z100 Results of one-way ANOVA/Scheffe's test at significance level 0.05. > indicates statistically significant difference in flexural properties.

124

(a)

(b) Fig. 6.3 (a) KIC of dental composite restoratives obtained from different methods and (b) its normalized plot.

In the literature (Ponton and Rawlings, 1989a), it was noted that the SENB

test gives a fast fracture toughness value (KIC) that tends to overestimate the

fracture toughness associated with an atomically sharp crack. This was due to the

absolute bluntness of the notch. Technically, it is impossible to create an infinite

125

sharp crack tip in the SENB test which forms a limitation of this test method.

From the current indentation fracture experiment, the KIC value computed using

the LEM model was found to be even higher than results from the previous SENB

test. This was not in good agreement with the literature. The inconsistency was

probably due to the formulation of the LEM equation which was mainly based on

glass and ceramics. On the other hand, the improved indentation fracture equation

for half-penny crack (Eqn. 6.7) was found to have a lower value (in a magnitude

of not more than 30%) when compared to the KIC obtained from SENB test.

Within the limitations of this study, it can be concluded that the indentation

fracture equation developed by Lankford (1982) better represents the crack system

developed in resin-based dental composite restoratives when compared with the

LEM model.

In the correlation analysis (Table 6.3), no significant (p>0.01) nor positive

correlation was found in the fracture toughness between the SENB and the

indentation fracture test methods. The Pearson correlation coefficient was found

to be 0.36 and 0.39 when comparing KIC,SENB to KIC,LEM and KIC,Half-penny,

respectively. The weak correlation in the current analysis was due to the non-

linear elastic behaviour of the materials and disagreement in the KIC values for

both F2000 and FF, as evidenced in the normalized plot (Fig. 6.3b). From the

materials profile as tabulated in Table 4.1, it was observed that the compomer

F2000 has a distinct resin matrix when compared to the other dental composite

materials investigated. In addition, it was reinforced with larger filler particle

ranging between 3 to 10 μm. These large filler particles may have inhibited the

crack growth path and increased the resistant to fracture. Similarly, the composite

126

FF has filler particles size of up to 6 μm in its structure. These two composite

materials contained larger fillers than the other materials under current

investigation. Based on the above, it was hypothesized that different group of

dental composites with distinct materials composition would require a different

treatment in the indentation fracture test equations. To evaluate this, the

correlation plot was done with F2000 and FF being separated from the remaining

micro and minifilled composites. From Fig. 6.4, it was observed that there were

indeed correlations between the SENB and indentation fracture tests for different

groups of dental composites. In view of the limited types of dental composite

material being tested, it may be too weak to make further conclusive statement

based on this observation and it warrants further research works. However, we

could conclude that the resin and filler types of dental composite restoratives have

effects on the indentation fracture test results.

Fig. 6.4 KIC correlation plot for different groups of dental composites.

127

The above analysis implies that is no one single indentation fracture

equation can be used to determine the fracture toughness accurately for the entire

spectrum of dental composite materials. Instead, the use of the indentation

fracture equations on different “groups” of dental bio-composites would require a

careful and separate treatment. In the literature (Harding et al., 1995), the

empirical constant ξ has been found to be geometry dependent for pure glass and

ceramic materials. In the indentation fracture test for dental composite materials,

the constant ξ could have some interaction effects with the type and/or size of its

constituents as evidenced from the current analysis. This is going to be an

interesting but yet a very complex problem which may require both experimental

and finite element analysis to address.

As mentioned previously, both the theoretical and empirical indentation

equations derived in the literature were mainly based on pure glass and ceramic

materials with uniform material composition which conformed to the law of linear

elasticity. Hence, their direct application on complex dental composite

restoratives was definitely questionable in terms of their validity. Although it has

been discussed previously that the constant ξ may have some implications on the

dental composite materials, it would be interesting as an attempt to determine its

values for the various materials obtained from the LEM model and improved

equation for half-penny crack configuration. The results are summarized in Table

6.5. In the LEM model, the value ξ was found to range from 0.021 to 0.032.

When determined using Lankford’s equation, the value of ξ was found to be

higher and ranged from 0.029 to 0.044 with an average of 0.037. By observation,

the difference in ξ from the two equations was in the same order of magnitude.

128

With comparing to the experimentally calibrated value of 0.036 for corner cube

indenter (Harding et al., 1995), the improved half-penny crack equation

employing the term (E/H)2/5 appeared to give the closest agreement between the

stress intensity values at equilibrium (K = KIC). This was in good agreement with

the studies conducted by Ponton and Rawlings (1989b).

Table 6.5 Determination of the empirical constant (ξ) using different indentation fracture mechanics equations.

Material Reference Value Empirical Constant, ξ

KIC,SENB (MPa.m0.5) LEM (Eqn. 6.2) Half-Penny (Eqn. 6.6) A110 1.29 0.032 (0.001) 0.043 (0.002) Z100 1.25 0.032 (0.005) 0.044 (0.008) Z250 1.91 0.029 (0.003) 0.039 (0.004) F2000 1.01 0.021 (0.004) 0.029 (0.006) FF 1.40 0.021 (0.001) 0.029 (0.001)

Overall Average 0.027 (0.006) 0.037 (0.008) Standard deviations in parenthesis

From Table 6.5, it was obvious that the value of ξ for both F2000 and FF

were lower than all other materials tested. This was consistent with the

observation made earlier. The empirical constant, ξ is not only geometry

dependent, but also material dependent for dental composite restoratives. The ξ

for the micro and minifilled dental composites (A110, Z100 and Z250) were fairly

constant with an average value of 0.042 for the modified half-penny equation.

With reference to the calibrated value of 0.036 for ξ, equation 6.7 can be modified

to deduce the indentation fracture toughness of micro and minifilled dental

composites by introducing a correction factor which is given by

56.1

5.1

5/2

=

ca

aP

HEkKIC ξ …….. (6.8)

where k = 1.167.

129

Overall, the indentation fracture test was technically difficult to be

conducted on polymeric dental composite materials. Cracks were not consistently

formed within the same material when subjected to the same indentation load

level. The validity of the various developed indentation fracture equations on

dental composite materials remained an issue which requires more works to fully

address. The current research work was rather superficial and there was a need to

study the indentation fracture mechanics in greater depth before applying it to

determine the fracture toughness of the complex polymeric dental composites.

Within the limitation of this study, it was found that the improved half–penny

indentation fracture equation with the (E/H)2/5 term better described current dental

composite materials. This was consistent with the literature in which the half-

penny equation had been verified on a wider spectrum of glass ceramic materials.

For dental composite restoratives, the term ξ in the indentation fracture equations

was material dependent. The ξ of conventional micro and minifilled dental

composites was found to be different from that of flowable composites and

compomers. In view of the complexity of dental composite structures, this has to

be further verified by using a wider spectrum of materials with varying

composition. In conclusion, the application of indentation fracture test on the

dental composite materials is still valid and it has shown to yield some useful test

results. However it has to be used with extreme care and would require

understanding on the effects of different material composition in reacting to the

indentation fracture equations used. In the current state of development, it is not

recommended to use the indentation fracture technique on dental composite

materials if the absolute accuracy is important.

130

Chapter 7 7. Conclusions and Recommendations 7.1 Conclusions

7.1.1 Depth-sensing micro-indentation methodology

Depth-sensing micro-indentation test method was successfully developed for

resin-based dental composite restoratives. The test specimen dimensions were

optimized (3x3x2 mm) towards a clinically relevant size and it allowed the

composite materials to be cured in a single irradiation. In the micro-indentation

test, the customized indentation head was capable of measuring the load and the

corresponding penetration depth with high accuracy. A test loading/unloading

profile for measuring the H and Ein was developed: Test specimen was loaded at

0.5 µm/s until Pmax of 10 N was attained and then held for a period of 10 seconds,

it was then unloaded fully at a rate of 0.2 µm/s. With this profile, the entire

loading/unloading cycle took about 30 seconds. It was concluded that the depth-

sensing micro-indentation test is a reliable method which is suitable for

determining the elasto-plastic properties of resin-based dental composite

restoratives.

7.1.2 Experimental and specimen-related variables

The effects of specimen surface roughness, peak indentation load,

loading/unloading rate, and load holding period on the indentation hardness and

modulus were successfully investigated. It was found that indentation modulus

131

and hardness of dental composite restoratives were independent of the surface

finish provided that the indenter penetration was sufficiently deep. A highly

reproducible and user-friendly polishing protocol (Method D, see chapter 4) was

established as a surface preparation technique for the indentation test of dental

composite restoratives. The hardness values were higher at shorter holding time

which was due to the creep effects of the material. The loading and unloading rate

has no effects on Ein and H of all materials investigated. Due to the indentation

size effect, Ein and H decreased with increasing indentation load. The Ein was not

sensitive to the load holding time. In conclusion, dental composite materials have

negligible effects on the measured Ein provided that the load holding period is

sufficiently long (~ 10 seconds) to diminish the creep effects.

7.1.3 Elasto-plastic properties

Although the ISO 4049 flexural test method is well established and its test results

are highly reproducible, the fabrication and utilization of large beam specimen is a

drawback associated with this test method especially in the context of dental

composite restoratives. In the correlation study, significant and strong correlation

(0.94 at p<0.01) was found between the flexural and indentation modulus. The

depth-sensing micro-indentation test is therefore a good alternative test method for

the mechanical characterization of resin-based dental restorative materials. When

applied to dental composite restoratives, the micro-indentation method has several

advantages over the ISO 4049 test standard as follows:

1. It can be performed on small volumes of material and hence it is more

cost and time effective.

132

2. It is non-destructive in nature allowing for multiple indents to be made

on the same specimen surface. This allows for the study of time-

dependent behaviours and environmental interactions using the same

specimen.

3. The test results are highly reproducible.

On the other hand, there are several limitations associated with the micro-

indentation test method as compared to the ISO 4049 as follows:

1. The experimental set-up and instrumentation are far more complex

than the conventional three-point bending test, and hence it is costly.

2. In view of the high cost, it may not accessible to many educational

institutions and commercial entities in order to perform comparative

studies on the materials.

3. The indentation test does not provide a direct measurement of strength.

7.1.4 Indentation fracture

The indentation fracture test was attempted to determine the fracture toughness of

various dental composite materials. Using the corner cube indenter, load levels of

between 100 to 200 N were required for crack initiation in the dental composites.

It was observed that the modified Lankford’s equation for half-penny crack

system better estimated the indentation fracture toughness of dental composite

restoratives. No significant correlation was found between the indentation

fracture toughness and the KIC obtained from the SENB test. Agreement between

the two methods improved when the dental composites were separated into

133

different groups according to their types and being analyzed separately. This

observation suggests the need for different empirical constant (ξ) for different

types of composite materials. Using KIC,SENB as referenced values, the

experimentally determined ξ in Lankford’s equation ranged between 0.029 to

0.043, and was material dependent. Within the limitations of current experiment,

ξ of conventional micro and minifilled dental composites was found to be

different from that of flowable composites and compomers. The use of

indentation fracture test on dental composite materials would require extreme care

and understanding of the materials. This warrants further research work.

7.2 Recommendations

7.2.1 Direct Amax measurement

In deriving the elastic modulus from the unloading portion of the indentation P-h

curve, all developed analytical (Doerner and Nix, 1986; Oliver and Pharr, 1992)

and numerical (Dao et al., 2001) solutions involved the estimation of the

maximum projected contact area, Amax. With underlying assumptions, the

solutions were often being developed for certain class of materials which have

distinctive deformation behavior under indentation loading. Hence the developed

solutions cannot be generalized for all materials. As far as estimation is

concerned, there is always a certain degree of error associated with the Amax value

being derived. The above can be circumvented if the projected contacted area can

be measured directly and in real-time while the indenter is still in contact with the

specimen. This type of analysis is possible if appropriate mechanical and optical

134

arrangement is applied to the current setup. Such a system would allow

performing an absolute measurement of Amax.

7.2.2 Indentation fracture equation for resin-based dental restoratives

Most of the indentation fracture equations found in the literature was derived

empirically based on glass ceramic materials. Hence, its validity on dental

composite restoratives remained a practical question. Dental composite is a

complex structure consisting of organic resin-based polymer and inorganic fillers

of varying size as reinforcement. In the indentation fracture test, the elastic-

plastic stress field being generated in the composite structure is complex and

requires specific analysis. This problem is further enhanced due to the clinical

application of different types of composite materials (varying resin and filler

properties). Hence, with the increasing demands for dental composite

restoratives, the development of an empirical indentation fracture equation is

essential for the fracture characterization of these materials. This involves

evaluation of physico-mechanical properties of the individual constituents and

their effects on indentation fracture toughness of the composite structure as a

whole.

135

Bibliography 1. Anstis GR, Chantikul P, Lawn BR, Marshall DB. A critical evaluation of

indentation technique for measuring fracture toughness: I, direct crack measurements. J Am Ceram Soc 1981;64(9):533-8.

2. Anusavice KJ. Physical properties of dental materials. Phillip's Science of Dental Materials 1996, 10th edition Philadelphia: Saunders WB Company:33-74.

3. ASTM Designation: E399-90. Standard test method for plane-strain fracture toughness of metallic materials. ASTM 1997, PA, USA.

4. ASTM Designation: D5045-96. Standard test method for plane-strain fracture toughness and strain energy release rate of plastic materials. ASTM 1996, PA, USA.

5. Barber JR, Ciavarella M. Contact mechanics. Int J Solids Struct, 2000; 37(1-2):29-43.

6. Bec S, Tonck A, Georges JM, Georges E, Loubet JL. Improvements in the indentation method with a surface force apparatus. Phil Mag A, 1996; 74(5):1061-72.

7. Bobji MS, Biswas SK. Deconvolution of hardness from data obtained from nanoindentation of rough surfaces. J Mater Res, 1999; 14(6):2259-68.

8. Bonilla ED, Mardirossian G, Caputo AA. Fracture toughness of posterior resin composites. Dent Mater 2001;32(3):206-10.

9. Bonilla ED, Yashar M, Caputo AA. Fracture toughness of nine flowable resin composites. J Prosthet Dent 2003;89:261-7.

10. Bowen RL. Use of epoxy resins in restorative materials. J Dent Res 1956;35(3):360-9.

11. Brackett WW, Browning WD, Brackett MG, Callan RS, Blalock JS. Effect of restoration size on the clinical performance of posterior "packable" resin composites over 18 months. Oper Dent 2007;32(3):212-6.

12. Braem M, Finger WJ, Van Doren VE, Lambrechts P, Vanherle G. Mechanical properties and filler fraction of dental composite. Dent Mater 1989;5:346-9.

13. Braem M, Van Doren VE, Lambrechts, Vanherle G. Determination of Young's modulus of dental composites: a phenomenological model. J Mater Sci 1987;22:2037-42.

http://www.ncbi.nlm.nih.gov/sites/entrez?Db=pubmed&Cmd=Search&Term=%22Brackett%20WW%22%5BAuthor%5D&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_DiscoveryPanel.Pubmed_RVAbstractPlus�

http://www.ncbi.nlm.nih.gov/sites/entrez?Db=pubmed&Cmd=Search&Term=%22Browning%20WD%22%5BAuthor%5D&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_DiscoveryPanel.Pubmed_RVAbstractPlus�

http://www.ncbi.nlm.nih.gov/sites/entrez?Db=pubmed&Cmd=Search&Term=%22Brackett%20MG%22%5BAuthor%5D&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_DiscoveryPanel.Pubmed_RVAbstractPlus�

http://www.ncbi.nlm.nih.gov/sites/entrez?Db=pubmed&Cmd=Search&Term=%22Callan%20RS%22%5BAuthor%5D&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_DiscoveryPanel.Pubmed_RVAbstractPlus�

http://www.ncbi.nlm.nih.gov/sites/entrez?Db=pubmed&Cmd=Search&Term=%22Blalock%20JS%22%5BAuthor%5D&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_DiscoveryPanel.Pubmed_RVAbstractPlus�

http://80-www.sciencedirect.com.libproxy1.nus.edu.sg/#hit2�

136

14. Bryant RW, Hodge KL. A clinical evaluation of posterior composite resin restorations. Aust Dent J 1994;39(2):77-81.

15. Bulychev SI, Alekhin VP, Shorshorov MKh and Ternovskii AP and Shnyrev GD. Determining Young's modulus from the indentor penetration diagram. Industrial Laboratory 1975;41(9):1137-40.

16. Bulychev SI, Alekhin VP, Shorshorov MKh and Ternovskii AP. Mechanical properties of materials studied from kinetic diagrams of load versus depth of impression during microimpression. Strength of Materials 1976;8(9):79-83.

17. Chabrier F, Lloyd CH, Scrimgeour SN. Measurement at low strain rates of the elastic properties of dental polymeric materials. Dent Mater 1999;15:33-8.

18. Chudoba T, Schwarzer N and Richter F. Determination of elastic properties of thin films by indentation measurements with a spherical indenter. Surface and Coatings Technology 2000;127:9-17.

19. Chudoba T, Richter E. Investigation of creep behaviour under load during indentation experiments and its influence on hardness and modulus results Surface & Coatings Technology, 2001;148(2-3):191-8.

20. Chung K, Greener EH. Correlation between degree of conversion, filler concentration and mechanical properties of composite resins. Journal of Oral Rehabilitation 1990;17(5) 487-94.

21. Chung KH. The relationship between composition and properties of posterior resin composites. J Dent Res 1990;69:852-6.

22. Chung SM, Yap AUJ, Koh WK, Tsai KT , Lim CT. Measurement of Poisson's ratio of dental composite restorative materials. Biomaterials 2004;25(13):2455-60.

23. Condon JR, Ferracane JL. In vitro wear of composite with varied cure, filler level, and filler treatment. J Dent Res 1997;76(7):1405-11.

24. Craig RG. Restorative dental materials. Mosby Year Book Inc. 1993:54-105.

25. Dao M, Chollacoop N, Van Vliet KJ, Venkatesh TA, Suresh S. Computational modeling of the forward and reverse problems in instrumented sharp indentation. Acta Mater 2001;49(19):3899-918.

26. Della Bona A, Benetti P, Borba M, Cecchetti D. Flexural and diametral tensile strength of composite resins. Braz Oral Res 2008;22(1):84-9.

27. Doerner MF, Nix WD. A method for interpreting the data from depth-sensing indentation instruments. J Mater Res 1986;1(4):601-9.

28. Evans AG and Charles EA. Fracture toughness determination by indentation. Journal of the American Ceramic Society 1976;59:371-2.

http://www.ncbi.nlm.nih.gov/sites/entrez?Db=pubmed&Cmd=Search&Term=%22Della%20Bona%20A%22%5BAuthor%5D&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_DiscoveryPanel.Pubmed_RVAbstractPlus�

http://www.ncbi.nlm.nih.gov/sites/entrez?Db=pubmed&Cmd=Search&Term=%22Benetti%20P%22%5BAuthor%5D&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_DiscoveryPanel.Pubmed_RVAbstractPlus�

http://www.ncbi.nlm.nih.gov/sites/entrez?Db=pubmed&Cmd=Search&Term=%22Borba%20M%22%5BAuthor%5D&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_DiscoveryPanel.Pubmed_RVAbstractPlus�

http://www.ncbi.nlm.nih.gov/sites/entrez?Db=pubmed&Cmd=Search&Term=%22Cecchetti%20D%22%5BAuthor%5D&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_DiscoveryPanel.Pubmed_RVAbstractPlus�

137

29. Ferracane JL. Current trends in dental composites Critical Review of Oral Biology and Medicine 1995;6(4):302-18.

30. Ferracane JL, Condon JR. Rate of elution of leachable components from composite. Dent Mater 1990;6(4):282-7.

31. Ferracane JL, Condon JR. In vitro evaluation of the marginal degradation of dental composites under simulated occlusal loading. Dent Mater 1999;15(4):262-7.

32. Ferracane JL, Antonio RS, Matsumoto H. Variables affecting the fracture toughness of dental composites. J Dent Res 1987;66(6) 1140-5.

33. Ferracane JL, Hopkin JK, Condon JR. Properties of heat-treated composites after aging in water. Dent Mater 1995;11(6):354-8.

34. Ferracane JL, Mitchem JC, Condon JR, Todd R. Wear and marginal breakdown of composites with various degrees of cure. J Dent Res 1997;76(8):1508-16.

35. Fischer H, Marx R. Fracture toughness of dental ceramics: comparison of bending and indentation method. Dent Mater 2002;18:12-19.

36. Flores A, Bayer RK, Krawietz K, Calleja FJB. Elastoplastic properties of starch-based materials as revealed by microindentation measurements. Journal of Macromolecular Science – Physics 2000;39B(5-6):749-59.

37. Gao,YX, Fan H. A micro-mechanism based analysis for size-dependent indentation hardness. J Mater Sci 2002;37:4493-98.

38. Giannakopoulos AE, Larsson PL, Vestergaard R. Analysis of Vickers indentation. Int J Solids Structures 1994;33(19):2679-708.

39. Giannakopoulos AE, Suresh S. Indentation of solids with gradient in elastic properties: Part I. Point force. Int J Solids Structures 1997;34(19):2357-92.

40. Giannakopoulos AE, Suresh S. Determination of elastoplastic properties by instrumented sharp indentation. Scripta Mater 1999;40(10):1191-8.

41. Gong JH. Determining indentation toughness by incorporating true hardness into fracture mechanics equations. J Am Ceram Soc 1999;19:1582-92.

42. Guo S, Kagawa Y. Effect of loading rate and holding time on hardness and Young's modulus of EB-PVD thermal barrier coating. Surface & Coatings Technology 2004;182(1):92-100.

43. Halitim F, Ikhlef N, Boudoukha L, Fantozzi G. Microhardness, Young's modulus and fracture toughness of alumina implanted with Zr, Cr, Ti and Ni. The effect of the residual stresses. Journal of Physics D: Applied Physics 1997;30(3):330-337.

138

44. Harding DS, Oliver WC, Pharr GM. Evolution of thin film and surface structure and morphology. Mater Res Soc Proc 355 1995, Pittsburgh, 663.

45. Hasegawa T, Itoh K, Koike T, Yukitani W, Hisamitsu H, Wakumoto S, Fujishima A. Effect of mechanical properties of resin composites on the efficacy of the dentin bonding system. Oper Dent 1999;24:323-30.

46. Heymann Ho, Sturdevant JR, Bayne S, Wilder AD, Sluder TB, Brunson WD. Examining tooth flexure effects on cervical restorations: a two-year clinical study. J am Dent Assoc 1991;122(5):41-7.

47. Higo Y, Damri D, Nunomura. The fracture toughness characteristics of three dental composite resins. Bio-Medical Materials and Engineering 1991;1:223-31.

48. ISO Designation ISO 4049. Dentistry-Resin based dental fillings. International Organization for Standardization 2002, Geneve, Switzerland.

49. Jacobsen PH, Darr AH. Static and dynamic moduli of composite restorative materials. J Oral Rehabil 1997;24:265–73.

50. Jones DW, Rizkalla AS. Characterization of experimental composite materials. J Biomed Mater Res1996;33(2):89-100.

51. Joslin DL and Oliver WC. New method for analyzing data from continuos depth-sensing microindentation tests. Journal of Materials Research 1990; 5(1):123-126.

52. Kelly JR. Perspectives on strength. Dent Mater 1995;11:103-10.

53. Kim KH, Park JH, Imai Y & Kishi T. Microfracture mechanisms of dental resin composites containing spherically-shaped filler particles. J Dent Res 1994;73(2):499-504.

54. King RB. Elastic analysis of some punch problems for a layered medium. Int J Solids Structures 1987;23(12):1657-64.

55. Kishen A, Ramamurty U, Asundi A. Experimental studies on the nature of property gradients in the human dentine. J Biomed Mater Res 2000;51(4):650-9.

56. Kvam K. Fracture toughness determination of ceramic and resin-based dental composites. Biomaterials 1992;13(2):101-4.

57. Lambrechts P, Braem M, Vanherle G. Evaluation of clinical performance of posterior composite resins and dentin adhesives. Oper Dent 1987;12(2):53-78.

58. Lankford J. Indentation microfracture in the Palmqvist crack regime: implications for fracture toughness evaluation by the indentation method. J Mater Sci Lett 1982;1:493-5.

https://www.researchgate.net/author/D+W+Jones�

https://www.researchgate.net/author/A+S+Rizkalla�

139

59. Larsson PE, Giannakopoulos AE, Söderlund E, Rowcliffe DJ, Vestergaard R. A critical investigation of the unloading behavior of sharp indentation. Int. J. Solids Struct. 1996;33(2):221-36.

60. Lawn BR, Wilshaw TR. Indentation fracture: Principles and applications. J Mater Sci 1975;10(6):1049-81.

61. Lawn BR, Evans AG. A model for crack initiation in elastic/plastic indentation fields. J Mater Sci 1977;12(11):2195-99.

62. Lawn BR, Marshall DB. Hardness, toughness, and brittleness: An indentation analysis. J Am Ceram Soc 1979;62(7-8):347-50.

63. Lawn BR, Evans AG , Marshall DB. Elastic/Plastic indentation damage in ceramics: The median/radial crack system. Am Ceram Soc 1980;63(9-10):574-81.

64. Lawn BR. Fracture of brittle solids. Cambridge University Press 1993: 249-306.

65. Leinfelder KF. Composite resins in posterior teeth. Dent Clin North Am 1981;25:357-64.

66. Lu H, Lee YK, Oguri M, Powers JM. Properties of a dental resin composite with a spherical inorganic filler. Oper Dent 2006;31(6):734-40.

67. Low D, Swain MV. Mechanical properties of dental investment materials. J Mater Sci - Mater Med 2000;11(7):399-405.

68. Maehara S, Fujishima A, Hotta Y, Miyazaki T. Fracture toughness measurement of dental ceramics using the indentation fracture method with different formulas. Dent Mater 2005;24(3):328-34.

69. Marshall DB, Lawn BR. Indentation of brittle materials. Microindentation Techniques in Materials Science and Engineering. ASTM STP 889 1986:26-46.

70. Marshall GW, Balooch M, Gallagher RR, Gansky SA, Marshall SJ. Mechanical properties of the dentinoenamel junction: AFM studies of nanohardness, elastic modulus, and fracture. J Biomed Mater Res 2001;54(1):87-95.

71. Matsumoto RLK. Evaluation of fracture toughness determination method as applied to ceria-stabilized tetragonal zirconia polycrystal. J Am Ceram Soc 1987;70:C366-8.

72. McCabe JF. Requirements of direct filling materials. Applied Dental Materials 1994. 7th edition Oxford: Blackwell Scientific Publications:130-1.

73. McKinney JE, Antonucci JM, Rupp NW. Wear and microhardness of glass ionomer cements. J Dent Res 1987;66(6):1134-1139.

http://www.ncbi.nlm.nih.gov/sites/entrez?Db=pubmed&Cmd=Search&Term=%22Maehara%20S%22%5BAuthor%5D&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVAbstractPlus�

http://www.ncbi.nlm.nih.gov/sites/entrez?Db=pubmed&Cmd=Search&Term=%22Fujishima%20A%22%5BAuthor%5D&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVAbstractPlus�

http://www.ncbi.nlm.nih.gov/sites/entrez?Db=pubmed&Cmd=Search&Term=%22Hotta%20Y%22%5BAuthor%5D&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVAbstractPlus�

http://www.ncbi.nlm.nih.gov/sites/entrez?Db=pubmed&Cmd=Search&Term=%22Miyazaki%20T%22%5BAuthor%5D&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVAbstractPlus�

140

74. Menčik J, Swain MV. Errors associated with depth-sensing micro-indentation tests. J Mater Res, 1995; 10(6):1491-1501.

75. Meredith N, Sherriff M, Setchell DJ, Swanson SAV. Measurement of the microhardness and Young's modulus of human enamel and dentine using an indentation technique. Archives of Oral Biology 1996;41(6):539-45.

76. Mohamed-Tahir MA, Tan HY, Woo AA, Yap AU. Effects of pH on the micro hardness of resin-based restorative materials. Oper Dent 2005;30(5):661-6.

77. Nakayama WT, Hall DR, Grenoble DE and Katz JL. Elastic properties of dental resin restorative materials. J Dent Res 1974;53:1121-1126.

78. Nihara K, Morena R, Hasselman DPH. Evaluation of KIC of brittle solids by indentation method with low crack-to-indent ratios. J Mater Sci Lett 1982;1:13-6.

79. Oliver WC, Hutchings R and Pathica JB. Measurement of hardness at indentation depths as low as 20 nanometers. ASTM Special Technical Publication 889: Microindentation Techniques in Materials Science and Engineering 1984, Edited by Blau PJ and Lawn BR, Philadelphia, 90-108.

80. Oliver WC, Pharr GM. An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J Mater Res 1992;7(6):1564-83.

81. Palmqvist S. Occurrence of crack formation during Vickers indentation as a measure of the toughness of hard metals. Arch. Eisenhuettenwes 1962;33(9): 629-633.

82. Peggs GN and Leigh IC. Recommended procedures for micro-indentation Vickers hardness test. Report No.: MOM 62. England: National Physical Laboratory, 1983.

83. Pharr GM, Oliver WC, Brotzen FR. On the generality of the relationship among contact stiffness, contact area, and elastic modulus during indentation. J Mater Res 1992;7(3):613-7.

84. Ponton CB, Rawlings RD. Vickers indentation fracture toughness test: Part 1, Review of literature and formulation of standardized indentation toughness equations. Mater Sci Technol 1989a;5:865-72.

85. Ponton CB, Rawlings RD. Vickers indentation fracture toughness test: Part 2, application and critical evaluation of standardized indentation toughness equations. Mater Sci Technol 1989b;5:961-76.

86. Poolthong S, Mori T, Swain MV. Determination of elastic modulus of dentin by small spherical diamond indenters. Dent Mater 2001;20(3):227-36.

87. Roulet JF. A material scientist’s view: Assessment of wear and marginal integrity. Quintessence Int 1987;18:543-52.

http://www.ncbi.nlm.nih.gov/sites/entrez?Db=pubmed&Cmd=Search&Term=%22Mohamed-Tahir%20MA%22%5BAuthor%5D&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVAbstractPlus�

http://www.ncbi.nlm.nih.gov/sites/entrez?Db=pubmed&Cmd=Search&Term=%22Tan%20HY%22%5BAuthor%5D&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVAbstractPlus�

http://www.ncbi.nlm.nih.gov/sites/entrez?Db=pubmed&Cmd=Search&Term=%22Woo%20AA%22%5BAuthor%5D&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVAbstractPlus�

http://www.ncbi.nlm.nih.gov/sites/entrez?Db=pubmed&Cmd=Search&Term=%22Yap%20AU%22%5BAuthor%5D&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVAbstractPlus�

141

88. Roulet JF. The problems associated with substituting composite resins for amalgam. J Dent 1988;16(3):101-13.

89. Samuels LE. Microindentation in metals. ASTM Special Technical Publication 889: Microindentation Techniques in Materials Science and Engineering 1984, Edited by Blau PJ and Lawn BR, Philadelphia, 5-24.

90. Silva CM, Dias KR. Compressive strength of esthetic restorative materials polymerized with quartz-tungsten-halogen light and blue LED. Braz Dent J 2009;20(1):54-7.

91. Simmons G, Wang H. Single crystal elastic constants and calculated aggregate properties: A handbook, 2nd Ed., MIT Press, Cambridge, MA, 1971.

92. Simoes MI, Fernandes JV, Cavaleiro A. The influence of experimental parameters on hardness and Young's modulus determination using depth-sensing testing. Philosophical Magazine A: Physics of Condensed Matter, Structure, Defects and Mechanical Properties, 2002;82(10):1911-1919.

93. Sneddon IN. The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile. International Journal of Engineering Science 1965;3:47-57.

94. Soares CJ, Pizi EC, Fonseca RB, Martins LR. Mechanical properties of light-cured composites polymerized with several additional post-curing methods. Oper Dent 2005;30(3):389-94.

95. Spinner S, Tefft WE. A method for determining mechanical resonance frequencies and for calculating elastic moduli from these frequencies. Proceedings ASTM 1961:1221-38.

96. Stilwell NA and Tabor D. Elastic recovery of conical indentations. Proceedings Of The Physical Society Of London 1961;78:169-179.

97. Suresh S, Alcala J and Giannakopoulos AE. MIT Case No. 7280, 1996. Patent.

98. Tabor D. A Simple Theory of Static and Dynamic Hardness. Proceedings of the Royal Society of London Series A 1948;192:247-74.

99. Tabor D. The hardness of metals. New York: Oxford University Press Inc, 2000.

100. Trindade AC, Cavaleiro A and Fernandes JV. Estimation of Young's modulus and of hardness by ultra-low load hardness tests with a Vickers indenter. Journal of Testing & Evaluation 1994;22(4):365-9.

101. Tyas MJ and Wassenaar P. Clinical evaluation of four composite resins in posterior teeth. Five-year results. Aust Dent J 1991;36(5):369-73.

http://www.ncbi.nlm.nih.gov/sites/entrez?Db=pubmed&Cmd=Search&Term=%22Silva%20CM%22%5BAuthor%5D&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_DiscoveryPanel.Pubmed_RVAbstractPlus�

http://www.ncbi.nlm.nih.gov/sites/entrez?Db=pubmed&Cmd=Search&Term=%22Dias%20KR%22%5BAuthor%5D&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_DiscoveryPanel.Pubmed_RVAbstractPlus�

http://www.ncbi.nlm.nih.gov/sites/entrez?Db=pubmed&Cmd=Search&Term=%22Soares%20CJ%22%5BAuthor%5D&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_DiscoveryPanel.Pubmed_RVAbstractPlus�

http://www.ncbi.nlm.nih.gov/sites/entrez?Db=pubmed&Cmd=Search&Term=%22Pizi%20EC%22%5BAuthor%5D&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_DiscoveryPanel.Pubmed_RVAbstractPlus�

http://www.ncbi.nlm.nih.gov/sites/entrez?Db=pubmed&Cmd=Search&Term=%22Fonseca%20RB%22%5BAuthor%5D&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_DiscoveryPanel.Pubmed_RVAbstractPlus�

http://www.ncbi.nlm.nih.gov/sites/entrez?Db=pubmed&Cmd=Search&Term=%22Martins%20LR%22%5BAuthor%5D&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_DiscoveryPanel.Pubmed_RVAbstractPlus�

142

102. van Dijken JW, Wing KR, Ruyter IE. An evaluation of the radiopacity of composite restorative materials used in Class I and Class II cavities. Acta Odontol Scand 1989;47(6):401-7.

103. Venkatesh TA, Van Vliet KJ, Giannakopoulos AE and Suresh S. Determination of elasto-plastic properties by instrumented sharp indentation: guidelines for property extraction. Scripta Materialia 2000;42(9),:833-9.

104. Wang YL, Lin Z, Lin, JP, Peng JH, Chen GL. Influence of sample surface condition on nano indentation experiment. Rare Metals, 2002; 21(2):131-132.

105. Watanabe H, Khera SC, Vargas MA, Qian F. Fracture toughness comparison of six resin composites. Dent Mater 2007;11.

106. Watts DC, Amer OM & Combe RC. Surface hardness development in light-cured composites. Dent Mater 1987;3(5):265-9.

107. Wei Wu, Sadeghipour K, Boberick K and Baran G. Predictive modeling of elastic properties of particulate-reinforced composites. Materials Science & Engineering A (Structural Materials: Properties, Microstructure and Processing) 2002;332:362-70.

108. Whiting R and Jacobsen PH. A non-destructive method of evaluating the elastic properties of anterior restorative materials. Journal of Dental Research 1980;59:1978-84.

109. Wilson NH, Dunne SM, Gainsford ID. Current materials and techniques for direct restorations in posterior teeth. Part 2: Resin composite systems. Int Dent J 1997;47(4):185-93.

110. Wilson TW, Turner DT. Characterization of polydimethacrylates and their composites by dynamic mechanical analysis. J Dent Res 1987;66(5):1032-5.

111. Wolf B. Inference of mechanical properties from instrumented depth sensing indentation at tiny loads and indentation depths. Crystal Research and Technology 2000;35:377-99.

112. Xu HHK , Quinn JB, Smith DT, Antonucci JM, Schumacher GE, Eichmiller

FC. Dental resin composites containing silica-fused whiskers - effects of whisker-to-silica ratio on fracture toughness and indentation properties. Biomaterials 2002;23(3):735-42.

113. Xu HHK, Smith DT, Schumacher GE, Eichmiller FC, Antonucci JM (2000) Indentation modulus and hardness of whisker-reinforced heat-cured dental resin composites Dental Materials 2000;16(4):258-254.

114. Xu HHK, Smith DT, Jahanmir S, Romberg E, Kelly JR, Thompson VP, Rekow ED. Indentation damage and mechanical properties of human enamel and dentin. J Dent Res 1998;77(3):472-80.

http://www.ncbi.nlm.nih.gov/sites/entrez?Db=pubmed&Cmd=Search&Term=%22Watanabe%20H%22%5BAuthor%5D&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVAbstractPlus�

http://www.ncbi.nlm.nih.gov/sites/entrez?Db=pubmed&Cmd=Search&Term=%22Khera%20SC%22%5BAuthor%5D&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVAbstractPlus�

http://www.ncbi.nlm.nih.gov/sites/entrez?Db=pubmed&Cmd=Search&Term=%22Vargas%20MA%22%5BAuthor%5D&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVAbstractPlus�

http://www.ncbi.nlm.nih.gov/sites/entrez?Db=pubmed&Cmd=Search&Term=%22Qian%20F%22%5BAuthor%5D&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVAbstractPlus�

http://www.ncbi.nlm.nih.gov/pubmed/9532458?ordinalpos=3&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_DefaultReportPanel.Pubmed_RVDocSum�






http://80-www.sciencedirect.com.libproxy1.nus.edu.sg/#hit2�

143

115. Yap AUJ, Chandra SP, Chung SM, Lim CT. Changes in flexural properties of composite restoratives after aging in water. Oper Dent 2002;27:468-74.

116. Yüzügüllü B, Ciftçi Y, Saygili G, Canay S. Diametral tensile and compressive strengths of several types of core materials. J Prosthodont 2008;17(2):102-7.

117. Zeng K and Chiu CH. An analysis of load-penetration curves from instrumented indentation. Acta Materialia 2001;49:3539-51

118. Zhao D, Botsis J, Drummond JL. Fracture studies of selected dental restorative composites. Dent Mater 1997;13(3):198-207.

http://www.ncbi.nlm.nih.gov/sites/entrez?Db=pubmed&Cmd=Search&Term=%22Zhao%20D%22%5BAuthor%5D&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVAbstractPlus�

http://www.ncbi.nlm.nih.gov/sites/entrez?Db=pubmed&Cmd=Search&Term=%22Botsis%20J%22%5BAuthor%5D&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVAbstractPlus�

http://www.ncbi.nlm.nih.gov/sites/entrez?Db=pubmed&Cmd=Search&Term=%22Drummond%20JL%22%5BAuthor%5D&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVAbstractPlus�

core.ac.uk · Acknowledgements . I am greatly indebted to my supervisor, A/Prof. Adrian Yap U Jin,...

Documents

Transcript of core.ac.uk · Acknowledgements . I am greatly indebted to my supervisor, A/Prof. Adrian Yap U Jin,...