Micro-Pop-In Issues in Nanoscale Contact Deformation Resistance of Tooth Enamel

Abstract

Human tooth enamel is a natural nanocomposite with a hierarchical structural architecture that spans from macroscale to nanoscale. Thus it offers the unique opportunity to study the physics of deformation at the nanoscale in a controlled manner using the novel nanoindentation technique. In spite of the wealth of literature, however, the information about the effect of loading rate on the nanoindentation behavior of human tooth enamel is far from being significant. Therefore, the major objective of the present work was to study the loading rate effect on nanoindentation behavior of enamel with a view to improve our understanding that could be used for development of better bioinspired synthetic structures for functional as well as biomedical utilities. The nanoindentation experiments were conducted at loading rates in the range of 10³ to ∼0.3×10⁶ 𝜇N⋅s⁻¹ at peak load of 10⁵ 𝜇N at room temperature with a Berkovich tip on the longitudinal section from a freshly extracted premolar tooth enamel surface from a 65-year-old Indian male. To the best of our knowledge here we report for the first time the experimental observation of the increase in intrinsic resistance against contact-induced deformation at the nanoscale with the loading rate applied to the enamel surface. The results were explained by considering the microstructural details and the shear stress underneath the nanoindenter.

1. Introduction

The nanocomposite structure of the human tooth enamel provides a unique opportunity to study the physics of deformation during the nanoscale contact events because it consists of hydroxyapatite (HAP) nanocrystals embedded in an organic-protein matrix with hierarchical structures from macrostructure to microstructure to sub-microstructure to nanostructure to sub-nanostructure [1–3]. The tooth enamel can survive normally up to even a billion contacts between themselves. The tooth enamel has nanohardness (𝐻) in the range of 3 to 5 GPa [4–10]. The indenter shape [5], teeth type [6], location [7, 8], degree of biomineralization [9, 10], and depth of indentation [11] can affect the data. The HAP single crystals have nanohardness higher than that of enamel [12]. The tooth makes various mastications during all oral cavity movements. All these contact-induced events that determine the life of the enamel are the sum total of a multitude of nanoscale contact events under a wide variety of loading rates which have not been studied in significant details [1–12]. Neither the role of micro-pop-in nor micro-pop-out issues during nanoscale contact events happening under different loading rates in influencing the nanoscale contact resistance has been discussed in the available literature on tooth enamel [1–12]. Therefore the major objective of the present work is the study of the loading rate effect on nanoindentation behavior of enamel for further utilization of bioinspired synthetic structures for both biomedical and functional applications.

2. Experimental

The polished (𝑅_𝑎∼0.25 μm) longitudinal section from a freshly extracted premolar tooth enamel surface from a 65-year-old Indian male individual was the sample. The nanoindentation experiments (Fischerscope H100-XYp; Fischer, Switzerland) were conducted at a constant load of 10⁵ μN at room temperature with a Berkovich tip of 150 nm radius. The well-known Oliver and Pharr method [13] was used to evaluate the nanohardness (𝐻) and Young’s modulus (𝐸) data from the load (𝑃) versus depth (ℎ) plots. By varying the loading times the loading rates 𝑃̇ were varied in the range of 10³ to ∼0.3×10⁶ 𝜇N⋅s⁻¹. Further details are given elsewhere [14].

3. Results and Discussions

Figure 1 exhibits the 𝑃-ℎ plots at various loading rates and the inset their exploded views. The prominent signatures of the initiation of nanoscale plasticity events during the nanoindentation experiments are borne by the large number of multiple “micr-pop-in” and “micro-pop-out” events those occurred (inset, Figure 1) during the loading and unloading cycles. Similar pop-in behavior has been observed for bulk metallic glasses [15–17], sapphire [18], GaN [19] and ZnO [20], glass [21, 22], and polycrystalline alumina [23, 24].

Figure 1 

Load (𝑃)-depth (ℎ) plots at different loading rates (inset: exploded views of the loading and unloading parts).

The inset of Figure 1 also shows that the load increment (Δ𝑃) at which two consecutive “micro-pop-in” events (say, 1, 2) happened during the loading cycle were not the same as the load decrement (−Δ𝑃) at which two consecutive “micro-pop-out” (say, 1, 2) occurred during the unloading cycle. The number of “micro-pop-in” and “micro-pop-out” events occurred much more at 10³ than at 10⁴ 𝜇N⋅s⁻¹ loading rates, Figure 1 (inset). Each discrete jump in the 𝑃-ℎ plots marks a critical load 𝑃_𝑐 and the corresponding depth is a critical depth (ℎ_𝑐) at which the nanoscale plasticity events had just initiated. The data of Figure 2 confirms that both 𝑃_𝑐 and the corresponding maximum shear stresses (𝜏_max [25–28] ∼10−30 GPa) exhibited positive power law dependencies on the loading rate.

Figure 2 

Variations of the critical load (𝑃𝑐) and maximum shear stress (𝜏max) active just underneath the nanoindenter as a function of the loading rates (dP/dt). The solid lines indicate the corresponding power law fits.

This data proved beyond doubt that the critical load for initiation of plasticity at the nanoscale of the enamel nanocomposite was actually enhanced with increase in 𝑃̇. For the enamel nanocomposite, the critical load basically signifies the minimum force that is required to just overcome the intrinsic resistance against contact-induced deformation. Thus, the present data is the very first experimental observation that the intrinsic contact deformation resistance of enamel nanocomposites increased with 𝑃̇. To the best of our knowledge, such observation is the first. This aspect shall be discussed in detail later.

The value of 𝜏_max was much higher than 𝜏_theor ∼3−6 GPa which implies that nanoscale plasticity events [27, 28], for example, shear-induced microfracture, were expected in the vicinity of the nanoindented enamel nanocomposite, as was indeed observed (Figure 3). The depth increment (Δℎ=ℎ_𝑐1−ℎ_𝑐2) (at which two consecutive “micro-pop-in events” (say, 1, 2) had happened) exhibited empirical power law dependencies with positive exponents on the corresponding load increment (Δ𝑃), Figure 4 and also on 𝑃_𝑐 (inset, Figure 4).

Figure 3 

FESEM photomicrograph of shear-induced microfracture (marked by hollow white arrow) at the vicinity of a typical nanoindentation made at 10,000 𝜇N⋅s−1 loading rate in the tooth enamel.

Figure 4 

The dependencies of depth increment (Δℎ) and decrement (−Δℎ) on the corresponding load increment (Δ𝑃) and decrement (−Δ𝑃) at which two consecutive nanoscale plasticity events had occurred during the loading and unloading cycles (inset), respectively. The solid lines indicate the corresponding power law fits.

Similarly ℎ_𝑐 displayed a positive empirical power law dependence on 𝑃_𝑐 of the enamel nanocomposite, Figure 5. The power law dependence of depth (ℎ) on load (𝑃) during the loading cycle of the nanoindentation experiments can be explained in accordance with two recent models [29, 30]. The experimental 𝑃- ℎ data presented in Figure 6 confirmed the generic nature of such dependencies of ℎ on 𝑃 for loading rates of 10³ to 0.3 × 10⁶ 𝜇N⋅s⁻¹.

Figure 5 

The dependence of the critical depth (ℎ𝑐) on the critical load (𝑃𝑐) in tooth enamel. The solid line indicates the corresponding power law fits.

Figure 6 

The experimental data on dependence of the instantaneous nanoindentation depth (ℎ) on the instantaneous nanoindentation load (𝑃) obtained during the loading cycles at different loading rates of 0.3×106, 105, 104, and 103 𝜇N⋅s−1 (inset of Figure 6). The solid lines indicate the corresponding power law fits.

Further, both Δℎ and depth decrement (−Δℎ=ℎ_𝑐1−ℎ_𝑐2) showed empirical power law dependencies on the loading rate with positive exponents (Figure 7). The empirical power law dependence of Δℎ on 𝑃̇ was in accordance with the theoretical prediction ℎ∝𝑃̇^𝛼 of a recent model [30] where α was an empirical constant. The model [30] required that at all loading rates ℎ̇ were effectively constant with respect to time. This condition was indeed true (Figure 8) for the present experiments. Similarly, the reduced depth ℎ^′ (=ℎ−ℎ_𝑓 where ℎ and ℎ_𝑓 represents the instantaneous and the final depth of penetrations obtained from the unloading cycle data) at all loading rates had empirical power law dependencies on the instantaneous nanoindentation load (𝑃), Figure 9.

Figure 7 

The dependencies of the depth increment (Δℎ=ℎ𝑐2−ℎ𝑐1) and decrement (−Δℎ=ℎ𝑐1−ℎ𝑐2 inset) at which two consecutive nanoscale plasticity events say, 1 and 2 had occurred on the corresponding loading rates (dP/dt). The solid lines indicate the corresponding power law fits.

Figure 8 

The minimal dependencies of (dh/dt) on time (𝑡) for the nanoindentation experiments conducted on tooth enamel at different loading rates of 105, 104 𝜇N⋅s−1, and 103 𝜇N⋅s−1.

Figure 9 

The experimental data on dependence of the instantaneous reduced nanoindentation depth ℎ′ on the instantaneous nanoindentation load (𝑃) obtained during the unloading cycles at 105𝜇N⋅s−1 and 103 𝜇N⋅s−1 (inset of Figure 9) loading rates employed in the present work. The solid lines indicate the corresponding power law fits.

The recent model [30] has also shown that if this power law dependence holds good then ℎ^′ is related to 𝑃̇ as: ℎ^′∝𝑃̇^𝛽 where 𝛽 is an empirical constant. Thus, the power law dependence of (−Δℎ) on 𝑃̇ (Figure 7) can be explained as mentioned above.

Now, we try to draw a plausible picture of the increase in nanoscale contact resistance with loading rate. Basically, the human tooth enamel can be considered from the deformation physics viewpoint as a macroscale-to-microscale-to-nanoscale hybrid nanocomposite with a hierarchical architecture [1–3] as mentioned earlier. At the microscopic level it comprises of aligned prisms surrounded by an organic sheath. Here, the organic sheath plays the role of a protein matrix that is a biopolymer and hence is expected to deform in a viscoelastic manner [1].

At the nanoscale level, each prism contains numerous HAP crystal rods (Figure 3) of ~50 nm diameter and oriented along the prism axis [3]. A nanometer-thin organic layer separates these rods [2]. Then, in response to the applied loading rate, the biopolymer matrix can shear to various extents to accommodate the strain due to the imposed deformation and in the process can also transfer the load among the adjacent mineral components. Therefore, it follows that at the nanoscale level then a sequential process of (a) repetitive loading, (b) load transfer, (c) unloading, and (d) subsequent loading process will happen during the penetration and withdrawal of the nanoindenter into and out of the enamel microstructure. It is proposed that this characteristic nanoscale deformation process gives rise to the observed pop-in effect in enamel nanoindentation.

In addition, there can be two additional factors which may contribute. For instance these are (i) the extent of local sharing of the total strain in between the protein matrix and the HAP crystal rods [31] and (ii) the process of stretching of individual biomolecules in the protein matrix all of which contribute in an additive fashion locally to the complete stretching of the protein matrix layer. We conjecture that at the lowest loading rate, this is what happens. Since the time of contact is more, the individual biomolecules in the protein matrix may get enough time to significantly stretch in response to the applied loading rate. But the biopolymers deform viscoelastically which comprises of both the elastic and anelastic components. Therefore, as the nanoindenter is withdrawn at the lower loading rates the individual biomolecules in the protein matrix will not get enough time to curl back completely to their original configuration. This is most likely to happen possibly due to the anelastic component of the deformation and more open structure of the biomolecules. As a result of this physical process, the overall elastic recovery becomes much lesser for the nanocomposite. Therefore, a smaller critical load (𝑃_𝑐) is necessary at smaller loading rates to initiate the nanoscale plasticity events. However, at moderate and still higher loading rates (Figure 1) a completely different situation may arise. In such cases the time of contact was very small (e.g., ∼0.4 second). As a consequence, the individual biomolecules in the protein matrix may get just enough time to at least moderately stretch in response to the applied loading rates. Under such situation then it becomes logical only to expect that they curl back to a relatively much higher extent (as compared to the case of lower loading rate) when the nanoindenter is withdrawn very quickly within for example, ∼0.4 s during the unloading cycle.

Such a generic process will lead to a situation such that the overall elastic recovery becomes much higher for the nanocomposite at the higher loading rates. If this picture is correct, the nanoscale deformation of tooth enamel will give higher final depth of penetration at lower loading rate and lower final depth of penetration at higher loading rates. The experimental data (Figure 10) was completely in conformity with this conjecture and indeed showed an inverse power law dependence of the final depth of penetration on the loading rate. Therefore, it is obvious that at higher loading rates, a higher critical load (𝑃_𝑐) will be needed to initiate the nanoscale plasticity events, as was indeed experimentally observed (Figure 2).

Figure 10 

The dependence of the final depth of penetration (ℎ𝑓) on the loading rate (dP/dt). The solid line indicates the empirical inverse power law fit.

4. Conclusions

During nanoindentation experiments in human tooth enamel it was found that the critical load (𝑃_𝑐) which signifies the materials intrinsic resistance against the initiation of incipient plasticity events at the nanoscale apparently increased with the applied loading rate. To the best of our knowledge, such experimental observation is the first. Based on the current experimental data it is suggested that the generic process responsible for such observation is the extent of elastic recovery or the lack of it in the biopolymeric matrix phase of the enamel nanocomposite in response to the lower and higher loading rates applied in the current nanoindentation experiments.

Acknowledgments

The authors are grateful to the Director, CSIR-Central Glass and Ceramic Research Institute (CGCRI), Kolkata for his kind permission to publish this paper. In addition, the authors appreciate the infrastructural supports received from all colleagues and particularly those received from the colleagues of the Mechanical Property Evaluation Section, NOCCD. Finally, the authors gratefully acknowledge the financial supports received from CSIR (Project no. NWP 0027).