Experimental Mechanics DOI 10.1007/s11340-006-9024-6

Methods for Examining the Fatigue and Fracture Behavior of Hard Tissues D. Zhang & A. Nazari & M. Soappman & D. Bajaj & D. Arola

Received: 29 June 2006 / Accepted: 27 November 2006 # Society for Experimental Mechanics 2007

Abstract An understanding of the fatigue and fracture behavior of hard tissues (e.g., bone and tissues of the human tooth) 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. We have also developed a special compact tension (CT) specimen that permits evaluation of crack extension within small portions of tissue under both quasi-static and fatigue loads. The specimen embodies a selected portion of hard tissue within a resin composite restorative and enables an examination of diseased tissue, or portion with specific physiology, that

D. Zhang Department of Mechanics, Shanghai University, 99 Shangda Rd, Shanghai 200444, People’s Republic of China A. Nazari : M. Soappman : D. Bajaj : D. Arola (*, SEM member) Department of Mechanical Engineering, University of Maryland Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250, USA e-mail: [email protected] D. Arola Department of Endodontics, Prosthodontics, and Operative Dentistry, Baltimore College of Dental Surgery, University of Maryland, Baltimore, MD 21201, USA

would otherwise be impossible to evaluate. 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 and across the dentinenamel-junction (DEJ) of human teeth. Keywords Crack growth . Dentin . Enamel . Fracture . Microscopic digital image correlation

Introduction The mechanical properties of bone and hard tissues 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. While there are many existing questions, studies conducted over the past decade have provided a foundation for further understanding. Fatigue and fracture of the tooth may involve either the enamel or the dentin or both. Enamel serves as the hard, wear-resistant, outermost shell [Fig. 1(a)] and is comprised of carbonated hydroxyapatite crystallites arranged in a framework of prisms that are oriented essentially perpendicular to the Dentin–Enamel Junction (DEJ). Located beneath the enamel, dentin comprises the majority of the human tooth and is approximately 45% inorganic, 30% organic and 25% water by volume [2]. The organic and inorganic components consist of a collagen fibril network and apatite based crystallites, respectively. Dentin is traversed by a network of tubules that extend outward between the pulp and DEJ.

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Fig. 1 Primary tissues of the human tooth and cracks evident in the enamel of a restored tooth. (a) a sectioned molar with distinction of the primary tissues and the Dentin-Enamel Junction (DEJ); (b) top view of a premolar with amalgam restoration. A crack is evident in the enamel as highlighted by the black arrows. Cracks of this type are not uncommon, but seldom extend beyond the DEJ and into the underlying dentin

The tubule lumens have internal diameter of between 1 to 2 μm. Each lumen is surrounded by a cylindrical shell of hypermineralized tissue and referred to as peritubular dentin. Additional details concerning the structure of dentin and enamel are available elsewhere [2]. In accordance with their unique structure, there are some differences in the fracture behavior between human enamel and dentin. The fracture toughness of human enamel has been primarily characterized using indentation methods, and reportedly ranges between 0.5 to 1.3 MPa m0.5 [3, 4]. The lowest toughness corresponds to conditions where crack extension occurred parallel to the enamel prism (and perpendicular to the DEJ). Recent investigations of dentin indicate that the fracture toughness ranges from 1 to 2 MPa m0.5 [5, 6] and that the lowest toughness is exhibited for cracks extending perpendicular to the dentin tubules. Interestingly, this orientation is essentially parallel to the DEJ and perpendicular to the direction of lowest fracture toughness of enamel. Dentin exhibits an increase in toughness with crack extension (i.e., R-Curve behavior), which is at least partially attributed to bridging forces resulting from collagen fibrils and ligaments of dentin tissue spanning the crack [7, 8]. Energy dissipation is also

believed to occur through inelastic deformation adjacent to the crack tip, a process that is not currently well understood [9]. 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 [10, 11] have shown that cyclic crack growth can be modeled using the Paris Law and occurs over a stress intensity range from approximately 0.7 to 2 MPa m0.5. Complementary studies in this area have shown that the rate of crack growth is dependent on the tubule orientation [12] and increases with mean stress [13] and reduction in loading frequency [14]. 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 [15] and facilitate an increase in the fatigue crack growth rate [11]. 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). The DEJ [Fig. 1(a)] represents a natural functionallygraded interfacial region between the dentin and enamel, which exhibit substantially different hardness and elastic modulus [16, 17]. Though cracks are frequently evident in the outermost enamel of teeth e.g., [Fig 1(b)], they seldom extend across the DEJ and into the underlying dentin. Earlier observations [18] suggested that cracks were arrested at the DEJ due to a larger toughness, which is attributed to the orientation and density of collagen fibril bundles at the interface. However, recent evaluations suggest that crack arrest is achieved by crack-tip shielding that originates from ligaments of dentin spanning the crack as it enters the mantle dentin [19], and a combination of inelastic deformation of the DEJ and a dispersion of damage within enamel closest to the DEJ [20]. An evaluation of fatigue crack growth about the DEJ has suggested that crack deflection promotes growth parallel to the DEJ and also contributes to the toughening mechanisms about this interfacial region [21]. Dentin and cortical bone possess similar chemistry and primary structure (i.e., integration of apatite crystals and type I collagen fibrils). Yet cortical bone exhibits larger fracture toughness than dentin with reported measures ranging between 2 and 8 MPa m0.5 [e.g., 22–25]. Studies in this area have shown that osteon orientation, hydration and age are important factors to the fracture behavior. Consistent with dentin, bone exhibits a rising toughness with crack extension [e.g., 26–29], which has been attributed to a combination of microcracking and crack

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bridging that results from ligaments of tissue that span the supposed traction free crack faces. A full description of the fatigue and fracture properties of bone, and the contributing toughening mechanisms are far beyond the scope of the present investigation. However, it is important to highlight that the majority of reported evaluations on both dentin and bone are quite similar; nearly all have been performed on healthy tissue, and/or have incorporated tissue of animals that permit use of large specimens and standardized methods of evaluation. Limitations posed by the small volume of available tissue, and consequent difficulties in applying standardized techniques to potentially hydrated and very small specimens (of a few millimeters) are wellrecognized obstacles. 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 representative results are presented and discussed.

Materials and Methods In the following studies the dentin, enamel and the DEJ 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 particular, a unique compact tension (CT) specimen was developed for achieving crack extension in small portions of tissue under both quasi-static and cyclic loads. 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 of two different configurations. A CT specimen comprised completely of dentin [Fig. 2(a)] can generally be

obtained from the crown of an unrestored molar. For a smaller volume of available tissue (e.g., fractured teeth, sections from the root, etc), a special CT specimen was designed [Fig. 2(b)] that consists of a small piece of tissue inset (or molded) within a polymeric boundary. In the present study, sections of dentin or sections of dentin and enamel (embodying the DEJ) 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 [9, 12]. For the “inset” CT specimens, sections with geometry of roughly 2×2×2 mm3 were obtained. Surfaces of the inset spanning the thickness (i.e., the bonding surfaces) were etched using 35% phosphoric acid for 15 s, rinsed with water, and then lightly dried. A total-etch adhesive resin system1 commonly used in dentistry for bonding resin composites to dentin was applied to the etched surfaces according to the manufacturers instructions. The adhesive resin was then cured for 10 s using a curing light2 placed directly over the surface. These sections were then placed in a mold cavity of approximately 6×6×2 mm, such that the inset was positioned centrally, along the path of projected crack growth [Fig. 2(b)], and 1 mm from the free edge. Placement of the inset was selected according to a finite element analysis aimed at minimizing interfacial stresses at the bonding surfaces and also achieving the smallest increase in stress intensity over the inset length. A commercial resin composite3 used in restorative dentistry was then packed into the mold about the inset tissue and cured for 30 s. All specimens were prepared with the dentin tubules oriented perpendicular to the plane of crack growth, unless otherwise specified. The standard dentin and molded inset CT specimens were lightly sanded on both sides using no. 220 mesh SiC paper to obtain a uniform cross-section. A channel was also introduced on the back of all specimens using diamond impregnated slicing wheels (of no.320 mesh particles) and a programmable slicer/grinder to guide the direction of crack extension. Two holes were drilled for application of the opening mode loads [Fig. 2(b)] 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. 2) 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. 1 Optibond® Solo Plus resin adhesive, Kerr, Orange, CA (Lot #410833). 2 Ultra-Lume® LED 5 curing light; Ultradent Products, Inc, Provo, Utah. 3 Vit-l-escence resin composite; Ultradent, Provo, Utah (Lot #A0403).

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Fig. 2 Details of the compact tension (CT) specimen geometry used in evaluating the fatigue and fracture behavior. (a) schematic diagram of the “standard” dentin CT specimen (b) schematic diagram of the inset CT specimen. The inset tissue is approximately 2×2×2 mm3 and is highlighted for clarity. The tissue is embodied within a dental composite resin

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 N. Cyclic loading of the specimens was continued using R=0.1, with maximum load of between 8 to 12 N, 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 quasistatic loading. For specimens prepared to study the fatigue behavior, cyclic loading was continued at R=0.1, maximum load between 8 to 12 N, and frequency of 5 Hz. An inspection of the crack length was conducted using an optical microscope (×100) with scaled reticule and the measurements were conducted after specific intervals of fatigue loading until the specimen fractured. Details of the fatigue loading arrangement and method of crack length measurement have been described elsewhere [11]. In general, the number of cycles between measurements typically ranged between 5 and 50 kcycles and the average increment of extension was between 100 to 300 μm. Generally between three and eight increments of crack extension were achieved with the inset CT specimens. Measurements of crack extension (Δa) over the increment of growth (ΔN) were used in quantifying the fatigue crack growth rate (da/dN). The steady state (Region II) response was quantified using the Paris Law according to da ¼ C ð$K Þm dN

ð1Þ

where ΔK is the stress intensity range, and C and m are the fatigue crack growth coefficient and exponent, respectively. Quasi-static loading of selected dentin and inset CT specimens was performed using a specially designed universal testing system, complemented with microscopic imaging equipment. The system is comprised of a specially designed miniature universal loading frame, a stereomicroscope and a control computer (Fig. 3). The loading frame is fully automated, enables load or displacement control actuation and has a load range of 100 N 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 microscope4 with optical output for a camera, a progressive scan CCD camera5 and an imaging board. With a fixed zoom ratio of 6.3:1, a ×1 objective lens and a ×1 step-up ring at the output of the microscope, the optical system allows up to ×180 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. Due to the influence of moisture in biological tissues, there are obvious obstacles to application of interferemetric optical methods for examining the displacement distribution resulting from loading. Debonding of the grating in Moire interferometry, and decorrelation errors caused by 4 5

SMZ-800 Steromicroscope; Nikon, Tokyo, Japan. CV-A1 CCD camera; JAI America Inc., Laguna Hills, CA.

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2 min), and then followed by partial unloading and reloading. The dwell-time was utilized to examine timedependent 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 [30]. Micro Digital Image Correlation

Fig. 3 Experimental arrangement for examining stable crack growth using the stereomicroscope and universal testing frame

evaporation of moisture in Electronic Speckle Pattern Interferometry (ESPI) are critical concerns. As a result, Digital Image Correlation (DIC) was adopted for evaluation of crack extension in the CT specimens using the acquired digital images. As dentin exhibits a nearly uniform yellow color, a surface preparation was required for application of DIC to the hydrated tissue. A mixture of toner powder and diluted correction fluid was prepared to coat the specimens with a very thin layer (approximately 5 μm). The coating provided an adequate distribution of fine black speckles on a white background. Hydration of the samples during loading was achieved through a saturated cotton swab “cradle” that was nestled beneath the specimen and maintained moist with an eyedropper of HBSS. The microscopic system was adjusted to capture images from the specimen’s surface over a field of view of approximately 3×4 mm, with a resolution of 1,376×1,035 pixels and in grayscale mode (256 range). Opening mode loads were applied in increments of 0.5 to 1 N, 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 N and lower, followed by a dwell at each load increment (typically of

Digital image correlation has found a number of applications in quantifying displacement and strain distributions within the field of experimental mechanics [31]. Despite some difficulties, applications within the field of biomechanics are becoming more common [e.g., 32–35]. 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 using the optical system 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 < F1  F2 >  < F1 >  < F2 > C¼h i 12 < ðF1  < F1 >Þ2 >  < ðF2  < F2 >Þ2 >

ð2Þ

where F1 and F2 are grayscale matrices of subsets of pixels in the initial and deformed images, respectively. The symbol <> in equation (2) represents the mean value of the elements in the matrix. In the present study, DIC was adopted to determine the full-field displacement distribution of the CT specimens at particular crack lengths and loading conditions, and to identify the crack tip. In general, subsets of 15×15 pixels were used in determining displacements with respect to the undeformed image. However, small subsets (e.g., 5×5 pixels) were chosen at the crack boundaries to avoid decorrelation. A Fast-Search Strategy (FSS) was adopted in searching for the locations with maximum correlation, which combines a multiple search step approach and maximum coefficient gradient finder [36]. Using the FSS with the digital microscopic images provided a displacement resolution of approximately 0.03 μm. In application to the CT specimens subjected to quasi-static loading, sequential images were acquired as a function of the opening

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mode load and increment of crack extension. Evaluation of the images using the FSS provided the full-field displacement distribution, which were then used to identify the crack tip and crack opening displacement (COD) profile. Numerical Methods According to the unique geometry of the dentin and inset CT specimens (Fig. 2), the stress intensity distribution with crack growth could not be estimated using relationships provided by ASTM standards E399 [37] or E647 [38]. Therefore, numerical models were developed to determine the stress intensity distribution as a function of crack length, opening load and specimen geometry. Commercially available software6 was used in constructing 3-D finite element models for both the standard [Fig. 2(a)] and inset [Fig. 2(b)] CT specimens. Briefly, the models consisted of over 10,000 20-noded second order brick elements. A refined mesh was used near the crack tip and the crack tip was modeled using a ring of second order brick elements with collapsed face, and biased node placement towards the crack tip. Elastic properties of the tissues were used for modeling. A review of dentin has reported that the elastic properties are isotropic [1]. Similarly, while human enamel is structurally anisotropic, the ratio of elastic modulii parallel and perpendicular to the enamel prism is approximately 1.2 [39]. Based on these reports, all materials were treated as linear elastic and isotropic in the numerical models as an approximation. For dentin, an elastic modulus and Poisson’s ratio of 19 GPa and 0.3 were used, respectively. In the models including enamel, an elastic modulus and Poisson’s ratio of 70 GPa and 0.3 were used, respectively; the modulus is most reflective of that closest to the DEJ [40]. The restorative resin used for the inset specimens had an elastic modulus and Poisson’s ratio of 15 GPa and 0.3, respectively, and was estimated using nanoindentation. The stress intensity distribution was estimated in terms of the energy release rate with crack extension. The energy release rate and corresponding stress intensity were determined from the average of a minimum of five contour integrals defined about the crack tip. Details of the approach have been presented elsewhere [11]. Note that counterboring of the holes to a depth equivalent to the channel depth [Fig. 2(b)] resulted in symmetric load distribution about the ligament centerline and maintained Mode I loading. However, a stress concentration is posed by the back channel geometry, which promotes an increase in the opening mode stress near the channel root. To insure that the geometric changes of the dentin CT specimens did not cause mixed mode loading, all three components of the 6

ABAQUS Version 6.5; ABAQUS Inc., Providence. RI.

stress intensity were quantified. Results of the numerical models for both CT specimens indicated that the in-plane and out-of-plane shearing components (KII and KIII) were at least two orders of magnitude lower than Mode I [11]. 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 Fig. 2(a) is given by  1  P B * þ 1 2 pffiffiffiffiffi KI ¼ 0:131 þ 0:320α þ 0:211α2 Bþ1 B* W   MPam0:5

ð1:4  a  3:0Þ ð3Þ

where P is the opening load (Newtons), α is the ratio of a to W [Fig. 2(b)] 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 equation (3) are to be introduced in millimeters; the unit conversion from millimeter to meter is conducted in the constants. Note that the distribution in KI described by equation (3) provides the average stress intensity across the specimen’s thickness. An identical evaluation was performed for the inset CT specimens comprised of dentin. The distribution in KI with crack extension for the inset CT specimens comprised of dentin (with E=19 GPa) is given by KI ¼

 1 P B* þ 1 2 pffiffiffiffiffi ð2:906 þ 15:178α B* W B þ 1    21:464α2 þ 2:645α3 þ 11:442α4 Þ MPam0:5 ð4Þ

where P, α, a and W are consistent with the definitions used in equation (3), and 2.75≤a≤4.0 mm. Equations (3) and (4) were used with the load and crack length measurements to quantify the stress intensity distribution with crack length and to construct the crack growth resistance curves. Experiments have also been conducted using the new inset CT specimen and microscopic DIC to evaluate crack growth across the Dentin–Enamel Junction (DEJ). For these specimens a separate numerical model was developed due to unique placement and shape of the DEJ. Results A representative load vs. load-line displacement response for a dentin CT specimen subjected to quasi-static Mode I loading is shown in Fig. 4(a). 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

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Fig. 4 Analysis of the near-tip displacement field resulting for crack growth in human coronal dentin. The specimen was obtained from the third molar of a 40-year old male patient. (a) typical load, load-line displacement response (b) an example of the full field opening-mode displacement distribution; (c) example of the COD at selected increments of the crack extension and time. The COD was documented at two instances of time, i.e., immediately after crack extension (time=0 min) and after a period of constant opening mode displacement (time=2 min)

growth until reaching a critical length. A representative image of the full field opening mode displacement (v) associated with crack growth in the specimen of Fig. 4(a) is shown in Fig. 4(b). Displacement distributions were deter-

mined 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 Fig. 4(c) that were obtained immediately following crack arrest (time=0 min), and after a 2 min dwell from crack extension (time=2 min), in which the load-line displacement was held constant. The load history and crack length measurements were used in evaluating the crack growth resistance of human dentin with crack extension (Δa). Representative crack growth resistance curves (R-curves) from experiments with CT specimens of coronal dentin obtained from two different patients are presented in Fig. 5(a). These 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. Examples are shown in Fig. 5(b) and appeared to be less common in the older tissue. In addition to adopting microscopic DIC for evaluating crack growth in hard tissues, an inset CT specimen was developed to enable a characterization of small portions of tissue under both quasi-static and cyclic loading. An example of the fatigue crack growth responses for coronal dentin with dentin tubules aligned perpendicular to the plane of the crack are shown in Fig. 6. Responses for the inset specimens are compared with earlier results [11] obtained using the standard dentin CT specimen geometry. The average Paris Law exponent for the inset dentin specimens tested thus far (N=4) is 13.8±7.6. While the variation in m for the inset specimens is relatively large, the average exponent compares well with that of the standard CT specimen ðm ¼ 13:3  1:1Þ. The new inset specimen was also used to examine the mechanics of crack extension across the DEJ. Selected digital images documenting stable crack extension in a representative specimen from human enamel, across the DEJ and into the underlying dentin are shown in Fig. 7(a) through (c). The grayscale images on the bottom of each presentation correspond to the v-field displacement distri-

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bution (opening mode displacement) that was obtained using DIC. The crack in this inset specimen was a natural crack in the enamel of an unrestored tooth that is oriented

da/dN (mm/cycle)

10-3

10-4

10-5 inset CT standard CT

10-6 0.1

1.0

10.0

∆K (MPa*m ) 0.5

Fig. 6 A comparison of fatigue crack growth in human dentin from the standard CT specimen and the new “inset” CT specimen. The dentin in all of these examinations was obtained from unrestored third molars of patients of age between 18 and 25 years

along the enamel prism and perpendicular to the DEJ. Decorrelation errors are evident at the crack surfaces of the displacement fields and result from the relatively large crack opening displacement. Using crack length measurements from the processed displacement fields and the documented opening mode load, estimates for the fracture toughness of the enamel and DEJ were obtained. The critical stress intensity for crack growth in enamel was approximately 1.0 MPa m0.5, and there was no distinct evidence of an R-curve response. The driving force required for crack extension increased at the DEJ, resulting in an apparent toughness of 2.45 MPa m0.5. Interestingly, the toughness decreased as the crack progressed within 200 μm from the DEJ into the adjacent dentin to 2.2 MPa m0.5, and unstable fracture occurred with additional extension.

Discussion

Fig. 5 Representative results for quasi-static crack extension experiments in human dentin. (a) effective stress intensity distribution with crack extension within two different dentin CT specimens. The responses are characterized in terms of an initiation toughness (Ko), a growth toughness (Kg) and an apparent critical stress intensity (Kc) defined at instability. (b) a micrograph of ligaments evident spanning the crack in a CT specimen of human dentin. The tissue is from a male patient 19 years old

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 min period of relaxation under constant load-line displacement. As evident from Fig. 4(c), there appears to be an increase in the COD distributions with time, and particularly near the crack tip, which suggests that crack-tip blunting occurs in human dentin through localized nonlinear deformation. While optical observations of crack-tip

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Fig. 7 Selected microscopic images of crack extension across the DEJ (top) and the corresponding displacement distributions (bottom) identified using DIC. Note that the outlined box is the dentin/enamel inset within the CT specimen and is 2 mm2. The crack begins in enamel (E) in (a), progresses and is arrested at the DEJ (b), and then continues into the underlying dentin (D) in (c). (a) crack in enamel (b) crack at the DEJ (c) crack in dentin

blunting have been reported for crack growth in hydrated elephant dentin [8, 14], 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. The representative crack growth resistance curves in Fig. 5(a) exhibited toughening with crack extension, which was quantified in terms of the growth toughness. For both specimens, the Kg was approximately 1.1 MPa m0.5/mm. Recent results obtained for hydrated elephant dentin reported a Kg of 0.54±0.16 MPa m0.5/mm [8], only half that found for human dentin. The fracture toughness estimated for the young dentin (Kc =1.65 MPa m0.5) agrees with results of previous studies on human dentin with dentin tubules oriented perpendicular to the plane of crack

growth; in [5] Kc ¼ 1:79  0:05 MPa  m0:5 and in [6], Kc ¼ 1:13  0:36 MPa  m0:5 . Also, a recent study of transparent dentin (i.e., sclerotic dentin of senior patients) reported a mean Kc of 1.46±0.11 MPa m0.5 [41]. Results from the present study appear to confirm that there is a reduction in the fracture toughness of human dentin with aging, but also suggest that the reduction in toughness is not limited to tissue that has undergone sclerosis (i.e., complete occlusion of the dentin tubules). The crack growth resistance curves presented in Fig. 5(a) are representative of the responses for dentin samples with comparative ages. While these results are limited to the dentin of two different patients, no study has shown the Rcurve response for human dentin and potential differences in the toughening behavior related to aging. The rise in crack growth resistance with crack extension in dentin has been attributed to ligaments of the tissue that span the supposed traction free faces of the crack, thereby shielding the crack tip through development of posterior bridging stresses. Ligaments of this type were documented during the experiments using the microscopic system [Fig. 5(b)]. Of relevance here, recent studies have shown that there is a significant decrease in strength and strain to fracture of dentin with patient age [15]. Therefore, the extent of toughening with

Exp Mech Fig. 8 Evaluation of the mechanisms of crack growth retardation at the DEJ of a human tooth. (a) the COD distribution for a crack at the DEJ and comparison to that for crack extension in dentin from Fig. 4(c) with time=0.0 seconds. (b) bridging in human enamel. Individual “ligaments” spanning the crack are highlighted by the arrows

crack extension in dentin would be expected to decrease with patient age due to a reduction in ligament strength and the subsequent reduction in bridging forces acting behind the crack tip. Neither of the R-curves in Fig. 5(a) develops a clear toughness plateau. One of the clear drawbacks of using small specimens for characterization of fracture behavior is the gradient in stress intensity with crack growth and difficulty in maintaining crack stability. Additional experiments are required to make more substantial statements regarding the specific changes in toughening mechanisms in young and old dentin. There were many early complications in application of the new inset CT specimen to study fatigue crack growth in dentin. Many of the specimens failed due to fatigue along the interface between the resin composite and dentin. These failures appeared to have occurred due to voids in the adhesive resin [42] and were minimized through careful control of the methods of preparation (i.e., etching time, moisture, adhesive thickness and curing time). Overall, fatigue crack growth rates obtained with the dentin inset specimens ranged from 2.0E-6 to approximately 5.0E-3 mm/cycle, which are consistent with those obtained in previous investigations using the standard CT specimen [11]. The average fatigue crack growth exponents obtained using the standard and inset specimens were also in agreement. While these results provide some confidence, additional results are needed using the inset specimen to achieve a rigorous validation. Additional work is underway using this specimen to study fatigue crack growth in selected tissues that are otherwise considered impossible to examine. The inset CT specimen was also used to examine the mechanics of fracture associated with crack extension across DEJ. COD distribution for the crack at the DEJ from Fig. 7(b) is shown in Fig. 8(a), and compared to the average COD for the cracks in dentin of Fig. 4(c). The COD distribution at the DEJ exhibits a large degree of near-tip blunting. Non-linear and inelastic deformation at the DEJ

has been identified in previous evaluations [20]. Application of microscopic DIC in the present evaluation provides further evidence of this mechanism of toughening and potential crack arrest. Interestingly, a closer examination of the crack in Fig. 7 shows that bridging of tissue also contributes to the fracture process in human enamel. Examples of ligaments of enamel spanning the crack surface are shown at greater magnification in Fig. 8(b). Bridging ligaments in dentin have been suggested to arise from microcracks that develop in front of the crack tip, and potentially initiate at the tubule lumens as a result of the effective stress concentration [41]. Enamel does not exhibit prominent tubules like dentin. The ligaments could develop from microcracking at intrinsic defects, or within near-field interprismatic enamel (i.e., the cement lines). Nevertheless, the identification of bridging ligaments in enamel reveals that it also develops some of the similar mechanisms of toughening as that of dentin and bone. The estimates for fracture toughness of the enamel and dentin are consistent with reported measures for these two materials [3–6]. According to results of previous studies [e.g., 17], the largest apparent toughness was expected to occur at the DEJ. However, recent microscopic observations of crack extension across the DEJ initiated from indents in enamel [19] showed that cracks penetrated the DEJ and were arrested in the nearby (10 μm) mantle dentin. While the maximum toughness in the present evaluation was observed to occur as the crack reached the DEJ, the actual crack tip location was unknown, (i.e., whether distinctly at the DEJ, or within the mantle dentin). There are other concerns. Clearly the near-tip nonlinearity in Fig. 8(a), and within the COD response for dentin in Fig. 4(c), strongly suggests that inelastic deformation contributes to the fracture process in dentin. However, both the enamel and dentin were treated as linear elastic materials in the numerical models and the apparent toughness was estimated in terms of the strain energy release rate. While consistent with the treatments in prior studies, the

Exp Mech

estimated toughness for enamel, dentin and DEJ presented herein should be considered approximations. Future evaluations of fracture and the mechanisms of toughening in these materials should account for the contributions of inelastic deformations. 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 [43]. Toughness estimates from indentation fracture may be 50–100% in error, and further difficulties arise for materials exhibiting R-curve behavior. 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 [44]. 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 subcritical crack growth in hard tissues. Successful application of microscopic DIC in examination of crack growth in dentin, enamel and the DEJ 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 growth resistance (R-curves) and crack opening

displacement (COD) distribution of human dentin were obtained. Furthermore, a special compact tension (CT) specimen was introduced for evaluating crack growth in relatively small portions of hard tissue under both quasistatic and fatigue loads. The COD distribution for a crack arrested at the DEJ was determined using this new specimen, and a new estimate for the DEJ toughness was obtained (Kc =2.45 MPa m0.5). 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 tissues, 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 wishes to acknowledge support from a GAANN Fellowship and the lead author would like to thank the Education Committee of Shanghai and Pujiang Project for partial support (Grant no. 04AB59).

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