Abstract
Objectives
The small volume of human dentin available for sample preparation and the local variations in its microstructure present a real challenge in the determination of their mechanical properties. The main purpose of the present study was to develop a new procedure for the preparation and mechanical testing of small-scale specimens of biomaterials such as dentin, so as to probe local mechanical properties as a function of microstructure.
Methods
Ultra short laser pulses were used to mill a block of dentin into an array of 16 μm size dentin pillars. These could then be individually tested in compression with an instrumented nanoindenter fitted with a 30 μm wide flat punch.
Results
The laser-based pillar preparation procedure proved effective and reliable. Data was produced for the mechanical properties of a first set of dry dentin micro-pillars.
Significance
This novel experimental approach enables the preparation and compression of micron-scale samples with well-defined microstructure. For dentin, this means samples containing a relatively small number of well-defined parallel tubules, with a distinct orientation relative to the applied load. The ability to isolate the separate effects of microstructural parameters on the mechanical properties is of major significance for future substantiation of theoretical models.
1
Introduction
Understanding the relation between tooth structure and its mechanical properties is of interest from the mechanical, biological and medical points of view. Studies of dentin biomechanics date back to the end of the nineteenth century when G.V. Black tested dentin cubes (with cross-sectional area of the order of 0.08 in. 2 , or 51.6 mm 2 ) under compression and produced the first data on dentin’s mechanical properties . Since then, many studies have used a similar experimental methodology, with comparable specimen dimensions (in the ∼mm × mm range), yielding modulus of elasticity values of 5.5–16 GPa . Due to experimental impediments, there are practically no studies dealing with the relationship between mechanical properties and microstructure at smaller (micron) scale. Recent measurements of Young’s modulus of dentin clearly contradict each other. Vickers microhardness measurements show – perhaps unexpectedly – a minimum value in the tubule direction and a maximum in the direction perpendicular to it . However, Kinney et al. , using resonant ultrasound spectroscopy (RUS), found no significant dependence of Young’s modulus on tubule direction, whereas this parameter is claimed by Lees and Rollins to be higher in the tubule direction (as quoted in ). Other mechanical properties using mm-size specimens were measured as a function of orientation , again with rather conflicting results.
It seems that one of the inherent problems in obtaining more reliable experimental answers lies in the technical difficulty to prepare specimens exhibiting well-defined tubular orientation and tubular geometry and density, partly due to the relatively large size of the specimen compared to the tubule size. Ideally, one would need to prepare very small-scale specimens, in the micron range, with a limited number of quasi-parallel tubules. These would be structurally better defined compared to the usual millimeter range specimens in which tens of thousands of tubules are present and show lengthwise diversity in size and density, and more random tubular orientation. Such small-scale specimens would represent ideal models (“basic structural units”) of dentin viewed as a composite and would therefore provide much needed basic understanding of the correlation between local structure and overall material properties. Preparing such specimens is the main motivating thrust of the present communication, which also offers preliminary results of the effect of tubule direction on the compressive modulus of elasticity and strength of micron-size dry coronal dentin specimens with well-defined tubular orientation. The experimental method is general and could in principle be applied to study any biocomposite material with tubular or elongated filler. Note however that if the preparation of a biological sample is always problematic to some extent, as one would like its in vivo properties to be measured, it is an even bigger challenge for preparation, and mechanical measurements, at the micron scale. It should be stated, too, that the preparation and testing of small-scale specimens is becoming increasingly popular in materials science research to investigate the size dependence of materials.
2
Materials and methods
2.1
Dentin slicing
A carious-free human molar, recently extracted from a young adult for therapeutic purposes, was washed with tap water, cleaned of all debris with a curette immediately after extraction and stored in Hank’s balanced salt solution (HBSS) containing 1% penicillin solution of 10,000 units/μL. A water-cooled diamond cutting-disk (Minitom ® Struers, Copenhagen, Denmark) was used to remove the root and coronal enamel before grinding. The remaining coronal dentin slice was cut in two halves in the mid sagittal plane, then metallographically ground and successively polished with a series of SiC abrasive papers (up to 4000 mesh) on a water-irrigated grinding wheel and with a 1.0 μm particle size diamond suspension on soft polishing cloths (LaboForce-3 ® & LaboPol-2 ® , Struers ® , Copenhagen, Denmark). A plano-parallel lapping device (AccuStop 30 ® , Struers ® , Ballerup, Denmark) was used to obtain uniform specimen thickness. Copious water rinsing followed by ultrasonic cleaning was performed after each polishing step. Between each preparation step the specimen was kept in a closed container under 100% relative humidity conditions.
2.2
Laser drilling of micro-pillar arrays
Micron-sized dentin pillars were cut by ablation using ultra short laser pulses generated by a Ti:Sapphire chirped Pulse Amplifier System (Tsunami ® and Spitfire ® , Spectra Physics Lasers ® , USA). The laser parameters were 15 μJ/pulse, 100 fs pulse regime, centered at a wavelength λ = 800 nm, at 1 KHz repetition rate. The specimen was mounted on a motorized translation stage positioned perpendicular to the direction of the laser beam. The beam was focused through a 10× magnification lens to a full width at half maximum ∼5–10 μm Gaussian spot size. A total of 32 micro-pillars were milled in two 4 × 4 arrays. The area selected was above the ascending part of the pulp horn at a distance of ∼800 μm from the pulp chamber (see Fig. 1 ). The pillar arrays were imaged with an inverted optical microscope (Axiovert 200 MAT, Zeiss ® , Germany) (see Figs. 2 and 3 ). The pillar dimensions and the orientation (inclination, °) of the tubules relative to the direction of the applied load were measured from calibrated microscope images using a digital image analysis program (ImageJ, NIH, Bethesda, MD, USA, ). Due to technical limitations, the tubule orientation was measured from the first row only and the angle of the next (hidden) 4 pillars was assumed to be equal to that of the first row, in view of their relative proximity. The pillar top was examined (and photographed if necessary) from the occlusal view, whereas the side (height) of the pillar was examined from the sagittal view. The mean value of three areas within each pillar (Upper to lower third) was measured and adopted as the representative value ( Fig. 3 ). The tapering angle of the pillars was small (4.5–5°).
2.3
Micro-pillar compression tests
The micro-pillars were tested in compression by means of a nanoindenter (Nano Indenter XP, Agilent Technologies, USA), using a 30 μm flat punch tip (Micro Star technologies ® , USA). The integrated optical system (10× magnification) was used to locate and select the micro-pillars prior to testing. Before each set of experiments the indenter head was calibrated to ensure stage movement accuracy and the precise placement of the indenter tip above the pillar. The compression tests were performed at a constant strain rate of 0.1 s −1 under displacement control, with a maximum preset displacement of about 30% of the pillar height. Under these conditions, the entire loading cycle was completed within less than 1 min of establishing contact with the pillar top. All experiments were performed in air. In some of the tests several small failures appeared in the specimens before final failure and these experiments were discarded. Young’s modulus was determined from the straight portion of the slope of load vs. displacement curves, and the strength was obtained from the maximum recorded load. Typical load–displacement curves recorded by the nanoindenter are shown in Fig. 4 . The compressive Young’s modulus ( E ) and strength ( σ max ) of each pillar were determined from the load–displacement curves as follows:
E = σ ε = ( Δ P / A ) ( Δ ℓ / ℓ ) = Δ P Δ ℓ ℓ w t
σ max = P max A = P max w t
where σ is the stress (in Pa), ε is the strain (no dimensions), Δ P is the compressive load (in N), Δ ℓ is the displacement (in m), A is the pillar cross-section (in m 2 ), with A = width ( <SPAN role=presentation tabIndex=0 id=MathJax-Element-3-Frame class=MathJax style="POSITION: relative" data-mathml='w’>ww
w
) × thickness ( t ), both taken here as the free end (top) of the pillar, and ℓ is the pillar length (or height). P max and σ max are the maximum compressive load and stress, respectively. The micro-pillar experiments are run under displacement control: the punch pushes on the surface for a preset distance after making contact. Since the nanoindenter controls distance under feedback control using the force transducer, applied force does not fall upon failure, rather, the distance increases to maximal extension while load remains unchanged. Young’s modulus was corrected to account for the fact that the pillar is sitting on a substrate of the same material (thus, with the same mechanical properties), which thus makes the pillar look more compliant under compression . The correcting factor used here was 1.26 (see Fig. 3a in reference ), which accounts for a pillar aspect ratio (=length/diameter) of ∼100/5 = 5, and a tapering angle of ∼5°.
2
Materials and methods
2.1
Dentin slicing
A carious-free human molar, recently extracted from a young adult for therapeutic purposes, was washed with tap water, cleaned of all debris with a curette immediately after extraction and stored in Hank’s balanced salt solution (HBSS) containing 1% penicillin solution of 10,000 units/μL. A water-cooled diamond cutting-disk (Minitom ® Struers, Copenhagen, Denmark) was used to remove the root and coronal enamel before grinding. The remaining coronal dentin slice was cut in two halves in the mid sagittal plane, then metallographically ground and successively polished with a series of SiC abrasive papers (up to 4000 mesh) on a water-irrigated grinding wheel and with a 1.0 μm particle size diamond suspension on soft polishing cloths (LaboForce-3 ® & LaboPol-2 ® , Struers ® , Copenhagen, Denmark). A plano-parallel lapping device (AccuStop 30 ® , Struers ® , Ballerup, Denmark) was used to obtain uniform specimen thickness. Copious water rinsing followed by ultrasonic cleaning was performed after each polishing step. Between each preparation step the specimen was kept in a closed container under 100% relative humidity conditions.
2.2
Laser drilling of micro-pillar arrays
Micron-sized dentin pillars were cut by ablation using ultra short laser pulses generated by a Ti:Sapphire chirped Pulse Amplifier System (Tsunami ® and Spitfire ® , Spectra Physics Lasers ® , USA). The laser parameters were 15 μJ/pulse, 100 fs pulse regime, centered at a wavelength λ = 800 nm, at 1 KHz repetition rate. The specimen was mounted on a motorized translation stage positioned perpendicular to the direction of the laser beam. The beam was focused through a 10× magnification lens to a full width at half maximum ∼5–10 μm Gaussian spot size. A total of 32 micro-pillars were milled in two 4 × 4 arrays. The area selected was above the ascending part of the pulp horn at a distance of ∼800 μm from the pulp chamber (see Fig. 1 ). The pillar arrays were imaged with an inverted optical microscope (Axiovert 200 MAT, Zeiss ® , Germany) (see Figs. 2 and 3 ). The pillar dimensions and the orientation (inclination, °) of the tubules relative to the direction of the applied load were measured from calibrated microscope images using a digital image analysis program (ImageJ, NIH, Bethesda, MD, USA, ). Due to technical limitations, the tubule orientation was measured from the first row only and the angle of the next (hidden) 4 pillars was assumed to be equal to that of the first row, in view of their relative proximity. The pillar top was examined (and photographed if necessary) from the occlusal view, whereas the side (height) of the pillar was examined from the sagittal view. The mean value of three areas within each pillar (Upper to lower third) was measured and adopted as the representative value ( Fig. 3 ). The tapering angle of the pillars was small (4.5–5°).
2.3
Micro-pillar compression tests
The micro-pillars were tested in compression by means of a nanoindenter (Nano Indenter XP, Agilent Technologies, USA), using a 30 μm flat punch tip (Micro Star technologies ® , USA). The integrated optical system (10× magnification) was used to locate and select the micro-pillars prior to testing. Before each set of experiments the indenter head was calibrated to ensure stage movement accuracy and the precise placement of the indenter tip above the pillar. The compression tests were performed at a constant strain rate of 0.1 s −1 under displacement control, with a maximum preset displacement of about 30% of the pillar height. Under these conditions, the entire loading cycle was completed within less than 1 min of establishing contact with the pillar top. All experiments were performed in air. In some of the tests several small failures appeared in the specimens before final failure and these experiments were discarded. Young’s modulus was determined from the straight portion of the slope of load vs. displacement curves, and the strength was obtained from the maximum recorded load. Typical load–displacement curves recorded by the nanoindenter are shown in Fig. 4 . The compressive Young’s modulus ( E ) and strength ( σ max ) of each pillar were determined from the load–displacement curves as follows:
E = σ ε = ( Δ P / A ) ( Δ ℓ / ℓ ) = Δ P Δ ℓ ℓ w t
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