AN APPLICATION OF MICROSCOPIC DIGITAL IMAGE CORRELATION TO
DENTAL MATERIALS
Dwayne Arola, Ahmad Nazari
Department of Mechanical Engineering, University of Maryland Baltimore County,
Baltimore, MD 21250
darola@umbc.edu
anazari1@umbc.edu
Miao Luo, ♣Dongsheng Zhang
Department of Mechanics, Shanghai University,
Shanghai, 200444, PR China
luomiao82@hotmail.com
donzhang@staff.shu.edu.cn
ABSTRACT
An understanding of the fatigue and fracture behavior of dental materials is critical to the maintenance of physical and oral
health. Recent studies suggest that there are a number of mechanisms contributing to crack extension and crack arrest in these
materials, and that they appear to be a function of moisture and age of the tissue. An understanding of these processes can
provide new ideas that are relevant to the design of multi-functional engineering materials. As a result, we have adopted the use
of microscopic Digital Image Correlation (DIC) to examine the mechanisms of crack growth resistance and near-tip
displacement distribution for cracks in human dentin that are subjected to opening mode loads. In this paper we describe
application of these experimental methods and present some recent results concerning fatigue crack growth and stable crack
extension in dentin.
Introduction
The mechanical properties of the human tooth have been of interest for many decades. While the strength and elastic modulus
of these tissues have been examined in detail, comparatively few studies have evaluated their fatigue and fracture behavior [1].
An understanding of crack initiation and growth in hard tissues of the human body is essential for the successful development of
medical and dental treatments aimed at maintaining a high quality of life [2,3]. While there are many existing questions, studies
conducted over the past decade have provided a foundation for further understanding.
Recent investigations of dentin indicate that the fracture toughness ranges from 1 to 2 MPa•m0.5 [4,5] and that the lowest
toughness is exhibited for cracks extending perpendicular to the dentin tubules. Dentin exhibits an increase in toughness with
crack extension, which is at least partially attributed to bridging forces resulting from collagen fibrils and ligaments of dentin
tissue spanning the crack [6,7]. Energy dissipation is also believed to occur through inelastic deformation adjacent to the crack
tip, a process that is not currently well understood [8]. Tubule orientation and hydration have been shown to play an important
role on the crack growth resistance of dentin through differences in the contribution of toughening mechanisms.
While fracture is a relevant concern, the initiation and growth of cracks due to fatigue are potentially of greater importance.
Studies on fatigue crack growth in human dentin [6,7] have shown that cyclic crack growth can be modeled using the Paris Law
0.5
and occurs over a stress intensity range from approximately 0.7 to 2 MPa•m . Complementary studies in this area have shown
that the rate of crack growth is dependent on the tubule orientation [8], increases with mean stress [9] and increases with a
reduction in loading frequency [10]. Also, recent results have shown that structural changes that occur in dentin with aging
appear to contribute to a reduction in the resistance to crack initiation [11] and facilitate an increase in the fatigue crack growth
rate [7]. Paris law exponents for cyclic crack growth reportedly range between 8 and 13 for the dentin of comparatively young
patients (18≤age≤35), whereas the value increases to over 20 for dentin of more senior patients (age≥50).
In this paper we describe some novel experimental techniques that have been adopted/developed for examining the fatigue and
fracture behavior of hard tissues. The overall objectives of the manuscript are to present the methodology, validate their
application, and to convey their value in studying fracture processes in hard tissues, particularly in instances where the size of
tissue available is limited and standardized methods are not sufficient. The methods of evaluation are described in detail and
♣
Corrsponding Author
representative results are presented and discussed.
Materials and methods
In the following studies the dentin of human teeth were examined. To support these efforts, second and third molars were
acquired from participating dental practices in Maryland according to an approved protocol by the Institutional Review Board of
the University of Maryland Baltimore County. All teeth were stored immediately after extraction in a bath of Hanks Balanced Salt
Solution (HBSS) at 2°C, and maintained in hydration during all aspects of specimen preparation. Overall, the experimental
methods used in evaluating these tissues were comprised of developing specimens of selected tissue and application of an
optical approach for both characterizing and quantifying crack extension. In addition, microscopic digital image correlation was
adopted to evaluate the mechanics of fracture and identify mechanisms contributing to crack growth resistance.
Specimen Preparation
The experimental evaluation was conducted using CT specimens. A CT specimen comprised completely of dentin (Fig. 1) can
generally be obtained from the crown of an unrestored molar. In the present study, sections of dentin were obtained from the
crown using diamond impregnated slicing equipment and continuous hydration. The methods and equipment used for
sectioning have been described in detail elsewhere [8].
B*
1
4
a
W
2
B
6
Figure 1 schematic diagram of the “standard” dentin CT specimen
The dentin CT specimens were gently sanded on both sides using #220 mesh SiC paper to obtain a uniform cross-section. A
channel was also introduced on the back of all specimens to guide the direction of crack extension using diamond impregnated
slicing wheels (of #320 mesh particles) and a programmable slicer/grinder. Two holes were drilled for application of the opening
mode loads (Fig. 1) and counter-bored to a depth equivalent to that of the channel. Counter-boring insured that the resolved
opening loads were located centrally about the reduced specimen thickness (B*) adjacent to the channel. Lastly, a notch was
machined (Fig. 1) using a diamond impregnated slicing wheel and the tip was sharpened using a razor blade and diamond
paste (1 or 8 µm particles) to facilitate crack initiation.
Equipment and Procedures
The CT specimens were subjected to either quasi-static or cyclic Mode I loads for different aspects of evaluation. All specimens
were subjected to cyclic loading at first to initiate a crack from the sharpened notch. Cyclic loading was performed using an
Enduratec Model 3200 universal testing system with the specimens immersed in a hydration bath (22°C). Crack initiation was
achieved using a stress ratio (R) of 0.5 and frequency of 5 Hz with maximum load of approximately 5 Newtons. Cyclic loading of
the specimens was continued using R=0.1, with maximum load of between 8 to 12 Newtons, until the crack was extended a
length of approximately 0.5 mm past the notch. The extension was used to reduce notch effects during further cyclic or
quasi-static loading.
The dentin and inset CT specimens was performed using a specially designed universal testing system, complemented with
microscopic imaging equipment comprised of a specially designed miniature universal loading frame, a stereomicroscope and a
control computer (Fig. 2). The loading frame is fully automated, enables load or displacement control actuation and has a load
range of 100 Newtons with precision of 0.05%. In addition, the system utilizes a central lead screw with both left- and right-hand
lead, which results in simultaneous actuation of both grips in opposite directions. As a result, the system minimizes changes in
the field of view that are typical with single lead systems. The microscopic imaging system consists of a stereo light microscope
(Nikon SMZ-1000) with optical output for a camera, a progressive scan CCD camera (JAI CV-A1 CCD camera) and an imaging
board. With a fixed zoom ratio of 10:1, a 1X objective lens and a 1X step-up ring at the output of the microscope, the optical
system allows up to 200X magnification using the aforementioned camera and microscope. A single computer is used with
dedicated software to control the load frame, sample the load and displacement data, as well as acquire and synchronize the
digital images with the load/displacement response. The load, load-line displacement responses and crack length
measurements were used with results of a numerical model for estimating the apparent toughness.
Figure 2 Experimental arrangement
The microscopic system was adjusted to capture images from the specimen’s surface over a field of view of approximately 3x4
mm, with a resolution of 1376X1035 pixels and in grayscale mode. Opening mode loads were applied in increments of 0.5 to 1
Newton, until the onset of cracking was identified from reduction in the apparent stiffness. Loading was then continued in
displacement control in increments of approximately 0.5 Newton and lower, followed by a dwell at each load increment (typically
of 2 min), and then followed by partial unloading and reloading. The dwell-time was utilized to examine time-dependent changes
in crack extension under constant load line displacement. Digital images were acquired at the onset of loading, at the peak load,
and after the dwell time to document the crack growth process. These procedures were followed through progressive
increments of crack extension until the onset of instability. Images of a glass plate with precision cross-grating and fixed spatial
frequency were acquired after the experiment and used to convert the documented field of view into physical dimensions and to
correct for potential errors caused by lens aberration [12].
Micro Digital Image Correlation
Digital image correlation has found a tremendous number of applications in quantifying displacement and strain distributions
within the field of experimental mechanics [13]. Despite some difficulties, applications within the field of biomechanics are
becoming more common [e.g. 14-17]. In the present study, DIC was employed to quantify the full-field displacement distribution
that resulted from crack extension. Briefly, digital images of the specimen’s surface in the plane of loading were acquired at an
initial (before loading) and deformed condition (under load). The displacement at each location within the field of view was
determined from a correlation of the grayscale distribution of the deformed and reference images. A cross correlation algorithm
was employed to compare subsets of the images according to
(1)
< F1 ⋅ F2 > − < F1 > ⋅ < F2 >
C=
1
[< ( F1 − < F1 > ) 2 > ⋅ < ( F2 − < F2 >) 2 >] 2
where F1 and F2 are grayscale matrices of subsets of pixels in the initial and deformed images, respectively. The symbol <>
in Eqn. (1) represents the mean value of the elements in the matrix.
Lens aberration can cause distortion between the image plane and the object plane. As the main distortions are radial and
perspective related, the lens distortion distribution of light microscopes can be presented as the warping function having
first-order and second-order terms, defined as follows,
⎧⎪δ x ( xi , yi ) = a0 + a1 xi + a 2 yi + a3 xi 2 + a 4 xi yi + a5 yi 2 + a6 xi 3 + a7 xi 2 yi + a8 xi yi 2 + a9 yi 3
⎨
2
2
3
2
2
3
⎪⎩ δ y ( xi , yi ) = b0 + b1 xi + b2 yi + b3 xi + b4 xi yi + b5 yi + b6 xi + b7 xi yi + b8 xi yi + b9 yi
where
(2)
xi and yi are coordinate locations in the image plane, and ai and bi (i = 0L9) are coefficients to be determined.
Aberration errors ( δ x and
δ y ) in this paper were assessed by using a precise cross-grating plate with fixed spatial frequency
as a standard. Images of the grating were acquired with the same microscopic imaging system. Two independent equations
represented the aberration distributions are generated according to eqn. 2 by all of the cross-grating nodes[12].
Numerical Methods
According to the unique geometry of the dentin CT specimens (Fig. 1), the stress intensity distribution with crack growth could
not be estimated using relationships provided by ASTM standards E399 [37] or E647 [38]. The stress intensity distribution was
evaluated across the specimen thickness, and as a function of the crack length. The distribution in KI with crack extension for
the standard CT specimens as described in Figure 1(a) is given by
1
⎛ B* +1 ⎞ 2
KI =
⎜
⎟ (0.131 + 0.320α + 0.211α 2 ) [MPa•m0.5]
B* W ⎝ B+1 ⎠
P
(1.4≤a≤3.0)
(3)
where P is the opening load (in Newtons), is the ratio of a to W (Fig. 1) and the quantities B* and B are the ligament thickness
(within the region of the channel) and nominal specimen thickness, respectively. All parameters of geometry in Eqn. 3 are to be
introduced in millimeters.
RESULTS
The opening mode load was applied in displacement control to achieve stable crack extension from the fatigue crack.
Incremental loading of the specimens was then continued to achieve sub-critical crack growth until reaching a critical length. A
representative image of the full field opening mode displacement (v) associated with crack growth is shown in Figure 3(a).
Displacement distributions were determined from digital images taken after each increment of crack extension. These were
used to identify the incremental crack tip location, as evident from the v-distribution (where v=0), and in determining the COD
distribution. Typical COD profiles are shown in Figure 3(b) that were obtained immediately following crack arrest (time=0 min),
and after a 2 minute dwell from crack extension (time=2 min), in which the load-line displacement was held constant.
10
COD/2 (µm)
8
6
4
2
0
0.0
time = 0 min
time = 2 min
0.2
0.4
0.6
0.8
1.0
1.2
Distance from Crack tip (mm)
(a) displacement field near the crack tip
(b) COD profile at crack tip
Figure 3 Analysis of the mechanics of fracture associated with crack extension in human dentin
The load history and crack length measurements were used in evaluating the crack growth resistance of human dentin with
crack extension (∆a). Two specimens were obtained from a young (age=18) and more senior (age=55) patient. To aid in
characterization, the initiation toughness (Ko) has been defined at the inception of crack extension, a growth toughness (Kg)
used to quantify the increase in toughness with crack extension, and a critical stress intensity (i.e. fracture toughness; Kc)
defined at either the plateau or maximum toughness. The Ko for the young and old specimen is 1.2 and 1.1 MPa•m0.5,
respectively, and the growth toughness for both specimens is approximately 1.1 MPa•m0.5/mm. The Kc for the young dentin
was found to be 1.65 MPa•m0.5, in comparison to 1.30 MPa•m0.5 for that of the senior patient (more than 20% lower). Both
responses show rising toughness with crack extension. The toughening in these responses is commonly observed and
expected to at least partially result from the development of ligaments that are regularly identified behind the crack.
DISCUSSION
Through application of DIC, the opening mode displacement distribution was obtained about the crack tip during stable crack
extension in CT specimens of human dentin. Using these distributions, representative COD profiles were presented for stable
cracks immediately after extension, and after a 2 minute period of relaxation under constant load-line displacement. While
optical observations of crack-tip blunting have been reported for crack growth in hydrated elephant dentin [10], the contribution
of this mechanism to crack growth resistance in human dentin has not been previously reported. One benefit of adopting
microscopic DIC for studying the fracture process in hard tissues is the ability to observe and quantify the near tip mechanics
that contribute to the apparent toughness. Mechanisms potentially contributing to the non-linearity and time dependence
include the movement of bound water and hydraulic processes, microcracking adjacent to the crack tip, and/or the non-linear
extension of the collagen fibrils. Further research is underway to identify the specific mechanisms responsible and the
significance of their contribution to crack arrest.
There are many obstacles to evaluating the fatigue and fracture properties of hard tissues and obtaining reliable results. Firstly,
the standardized methods of characterization cannot often be applied due to the restricted volume of tissue available. Some
would argue that indentation fracture provides an alternative to the techniques presented, and eliminates the size constraints.
However, a recent review has addressed the shortcomings of indentation fracture tests, particularly in regards to the load
dependence [19]. Toughness estimates from indentation fracture may be 50 to 100 % in error. The need to maintain hydration of
the tissue and inherent moisture poses further difficulties, particularly with application of optical methods for documenting the
fracture process. Interferometric methods, which have been commonly employed for quantifying fracture processes in
engineering materials, are not as robust when applied to moist substrates. Yet, an optical examination of the fracture process is
invaluable in this area due to the opportunity for identifying important mechanisms contributing to the quantitative
measurements. Post-process evaluations of the fracture surfaces (using fractography) can be of equal value in examining
fracture in hard tissues [20]. Through microscopic digital imaging and use of DIC, both qualitative and quantitative information
can be obtained with a displacement resolution that fully supports the comparatively large range in displacements associated
with fracture in hydrated hard tissues. By combining the benefits of microscopic DIC with unique approaches for preparing and
loading specimens, a detailed and reliable understanding of fatigue and fracture within hard tissues is possible. It is hoped that
the techniques described herein will enable many future studies of hard tissues that are otherwise considered impossible.
SUMMARY
Some novel experimental approaches were presented for examining the mechanisms of crack growth resistance and near-tip
displacement distribution associated with sub-critical crack growth in hard tissues. Successful application of microscopic DIC in
examination of crack growth in dentin of human teeth shows that it is a suitable non-contact optical method for evaluating the
mechanics of fracture in hard tissues. New results on the crack opening displacement (COD) distribution of human dentin were
obtained. While applications were limited to the human tooth, the methods introduced in this study would serve equally well for
examining crack extension in other hydrated tissue or for material systems where there are geometric constraints. The methods
should support future studies aimed at development of new knowledge on the mechanics of fatigue and fracture in selected
hard tissues.
ACKNOWLEDGEMENT
This research was supported in part by the National Science Foundation (BES 0238237) and the American Association of
Endodontists Foundation. The author A. Nazari also wishes to acknowledge support from a GAANN Fellowship. The authors
would also thank the support of the National Science Foundation of China under Grand # 30672348 and Shanghai Pujiang
program.
REFERENCES
Kinney JH, Marshall SJ, Marshall GW. The mechanical properties of human dentin: a critical review and re-evaluation of
the dental literature. Crit Rev Oral Biol Med. 2003;14:13-29.
2. Xu HH, 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):472-480.
3. Hassan R, Caputo AA, Bunshah RF. Fracture toughness of human enamel. J Dent Res. 1981;60(4):820-827.
4. Imbeni V, Nalla RK, Bosi C, Kinney JH, Ritchie RO. In vitro fracture toughness of human dentin. J Biomed Mater Res A.
2003;66(1):1-9.
5. Iwamoto N, Ruse ND. Fracture toughness of human dentin. J Biomed Mater Res A. 2003;66(3):507-512.
6. Nalla RK, Imbeni V, Kinney JH, Staninec M, Marshall SJ, Ritchie RO. In vitro fatigue behavior of human dentin with
implications for life prediction. J Biomed Mater Res A. 2003;66(1):10-20.
7. Bajaj D, Sundaram N, Nazari A, Arola D. Age, dehydration and fatigue crack growth in dentin. Biomaterials.
2006;27(11):2507-2517.
8. Arola D, Rouland JA. The effects of tubule orientation on fatigue crack growth in dentin. J Biomed Mater Res A.
2003;67(1):78-86.
9. Arola D, Zheng W, Sundaram N, Rouland JA. Stress ratio contributes to fatigue crack growth in dentin. J Biomed Mater Res
A. 2005;73(2):201-212.
10. Kruzic JJ, Nalla RK, Kinney JH, Ritchie RO. Mechanistic aspects of in vitro fatigue-crack growth in dentin. Biomaterials.
2005;26(10):1195-1204.
11. Arola D, Reprogel RK. Effects of aging on the mechanical behavior of human dentin. Biomaterials. 2005;26(18):4051-4061
12. Zhang D, Luo M, and Arola D. Displacement/strain measurement under optical microscope with digital image correlation.
Opt Engr 2006 45(3):1-9.
13. Chu TC, Ranson WF, Sutton MA and Peters WH. Applications of digital-image-correlation techniques to experimental
mechanics. Exp Mech 1985;25(3):232-244.
14. Zhang D and Arola D. Application of digital image correlation to biological tissues. J Biomed Opt. 2004;9(4):691-699.
15. Sachs C, Fabritius H, Raabe D. Experimental investigation of the elastic-plastic deformation of mineralized lobster cuticle
by digital image correlation. J Struct Biol. 2006 (in press).
16. Zhang J, Jin GC, Meng LB, Jian LH, Wang AY, Lu SB. Strain and mechanical behavior measurements of soft tissues with
digital speckle method. J Biomed Opt. 2005 May-Jun;10(3):034021.
17. Zhang D, Arola D, Reprogel R, Zheng W, Tasch U and Dyer RM. A Method for Characterizing the Mechanical Behaviour of
Hoof Horn. J Mat Sci. 2006 (in press).
18. Imbeni V, Kruzic JJ, Marshall GW, Marshall SJ, Ritchie RO. The dentin-enamel junction and the fracture of human teeth. Nat
Mater. 2005;4(3):229-232.
19. Quinn GD "Fracture toughness of ceramics by the Vickers indentation crack length method; A critical review" Ceramic
Engineering and Science Proceedings, 2006 (in press), and Proceedings of the 30th International Conference on
Advanced Ceramics and Composites, Cocoa Beach Fl, January, 2006.
20. Yan J, Clifton KB Reep RL and Mecholsky JJ. Application of fracture mechanics to failure in manatee rib bone. J Biomech.
Eng, 2006;128(3):281-289.
1.