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

Human tooth enamel is a natural nanocomposite with a hierarchical structural architecture that spans from macroscale to nanoscale. us 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 signi�cant. erefore, 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. e nanoindentation experiments were conducted at loading rates in the range of 10 to ∼ 0.3 × 10 μμN ⋅ s at peak load of 10 μμN at room temperature with a Berkovich tip on the longitudinal section from a freshly extracted premolar tooth enamel surface from a 65-year-old Indianmale. �o the best of our knowledge here we report for the �rst 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. e results were explained by considering the microstructural details and the shear stress underneath the nanoindenter.


Introduction
e 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][2][3].e tooth enamel can survive normally up to even a billion contacts between themselves.e tooth enamel has nanohardness () in the range of 3 to 5 GPa [4][5][6][7][8][9][10]. e indenter shape [5], teeth type [6], location [7,8], degree of biomineralization [9,10], and depth of indentation [11] can affect the data.e HAP single crystals have nanohardness higher than that of enamel [12].e 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 signi�cant details [1][2][3][4][5][6][7][8][9][10][11][12].Neither the role of micro-pop-in nor micro-pop-out issues during nanoscale contact events happening under different loading rates in in�uencing the nanoscale contact resistance has been discussed in the available literature on tooth enamel [1][2][3][4][5][6][7][8][9][10][11][12].erefore 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.

Experimental
e polished (  ∼ 0.25 m) longitudinal section from a freshly extracted premolar tooth enamel surface from a 65year-old Indian male individual was the sample.e nanoindentation experiments (Fischerscope H100-XYp; Fischer, Switzerland) were conducted at a constant load of 10 5 N (µN) at room temperature with a Berkovich tip of 150 nm radius.e well-known Oliver and Pharr method [13] was used to evaluate the nanohardness () and Young's modulus () data from the load () versus depth (ℎ) plots.By varying the loading times the loading rates Ṗ were varied in the range of 10 3 to ∼ 0.3×10 6 N ⋅ s −1 .Further details are given elsewhere [14].

Results and Discussions
Figure 1 exhibits the -ℎ plots at various loading rates and the inset their exploded views.e 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][16][17], sapphire [18], GaN [19] and ZnO [20], glass [21,22], and polycrystalline alumina [23,24].e inset of Figure 1 also shows that the load increment (Δ) at which two consecutive "micro-pop-in" events (say, 1, 2) happened during the loading cycle were not the same as the load decrement (−Δ) at which two consecutive "micropop-out" (say, 1, 2) occurred during the unloading cycle.e number of "micro-pop-in" and "micro-pop-out" events occurred much more at 10 3 than at 10 4 N ⋅ s −1 loading rates, Figure 1 (inset).Each discrete jump in the -ℎ plots marks a critical load   and the corresponding depth is a critical depth (ℎ  ) at which the nanoscale plasticity events had just initiated.e data of Figure 2 con�rms that both   and the corresponding maximum shear stresses ( max [25][26][27][28] ∼ 10 − 30 GPa) exhibited positive power law dependencies on the loading rate.
is 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 signi�es the minimum force that is re�uired to just overcome the intrinsic resistance against contact-induced deformation.us, the present data is the very �rst experimental observation that the intrinsic contact deformation resistance of enamel nanocomposites increased with Ṗ.To the best of our knowledge, such observation is the �rst.is aspect shall be discussed in detail later.
e value of  max was much higher than  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).e depth increment (Δℎ = ℎ  1 − ℎ  2 ) (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 (Δ), Figure 4 and also on   (inset, Figure 4).
Similarly ℎ  displayed a positive empirical power law dependence on   of the enamel nanocomposite, Figure 5. e power law dependence of depth (ℎ) on load () during the loading cycle of the nanoindentation experiments can be explained in accordance with two recent models [29,30].e experimental -ℎ data presented in Figure 6 con�rmed the generic nature of such dependencies of ℎ on  for loading rates of 10 3 to 0.3 × 10 6 N ⋅ s −1 .Further, both Δℎ and depth decrement (−Δℎ = ℎ  1 − ℎ  2 ) showed empirical power law dependencies on the loading rate with positive exponents (Figure 7).e empirical power law dependence of Δℎ on Ṗ was in accordance with the theoretical prediction ℎ ∝ Ṗ of a recent model [30] where  was an empirical constant.e model [30] required that at all loading rates ḣ were effectively constant with respect to time.is condition was indeed true (Figure 8) for the present F 6: e experimental data on dependence of the instantaneous nanoindentation depth (ℎ) on the instantaneous nanoindentation load () obtained during the loading cycles at different loading rates of 0.3 × 10 6 , 10 5 , 10 4 , and 10 3 N ⋅ s −1 (inset of Figure 6).e solid lines indicate the corresponding power law �ts.experiments.Similarly, the reduced depth ℎ ′ (= ℎ − ℎ  where ℎ and ℎ  represents the instantaneous and the �nal depth of penetrations obtained from the unloading cycle data) at all loading rates had empirical power law dependencies on the instantaneous nanoindentation load (), Figure 9. e recent model [30] has also shown that if this power law dependence holds good then ℎ ′ is related to Ṗ as: ℎ ′ ∝ Ṗ where  is an empirical constant.us, the power law dependence of (−Δℎ) on Ṗ (Figure 7) can be explained as mentioned above.F 9: e experimental data on dependence of the instantaneous reduced nanoindentation depth ℎ ′ on the instantaneous nanoindentation load () obtained during the unloading cycles at 10 5 N⋅s −1 and 10 3 N⋅s −1 (inset of Figure 9) loading rates employed in the present work.e solid lines indicate the corresponding power law �ts.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-tonanoscale hybrid nanocomposite with a hierarchical architecture [1][2][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].en, 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.erefore, 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 signi�cantly stretch in response to the applied loading rate.But the biopolymers deform viscoelastically which comprises of both the elastic and anelastic components.erefore, 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 con-�guration.is 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.erefore, a smaller critical load (  ) 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 �nal depth of penetration at lower loading rate and lower �nal depth of penetration at higher loading rates.e experimental data (Figure 10) was completely in conformity with this conjecture and indeed showed an inverse power law dependence of the �nal depth of penetration on the loading rate.erefore, it is obvious that at higher loading rates, a higher critical load (  ) will be needed to initiate the nanoscale plasticity events, as was indeed experimentally observed (Figure 2).F 10: e dependence of the �nal depth of penetration (ℎ  ) on the loading rate (dP/dt).e solid line indicates the empirical inverse power law �t.

Conclusions
During nanoindentation experiments in human tooth enamel it was found that the critical load (  ) which signi�es 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 �rst.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.

F 1 :
Load ()-depth (ℎ) plots at different loading rates (inset: exploded views of the loading and unloading parts).

F 2 :F 3 :
Variations of the critical load (  ) and maximum shear stress ( max ) active just underneath the nanoindenter as a function of the loading rates (dP/dt).e solid lines indicate the corresponding power law �ts.1 µm FESEM photomicrograph of shear-induced microfracture (marked by hollow white arrow) at the vicinity of a typical nanoindentation made at 10,000 N ⋅ s −1 loading rate in the tooth enamel.

F 4 :F 5 :
e dependencies of depth increment (Δℎ) and decrement (−Δℎ) on the corresponding load increment (Δ) and decrement (−Δ) at which two consecutive nanoscale plasticity events had occurred during the loading and unloading cycles (inset), respectively.e solid lines indicate the corresponding power law �ts.e dependence of the critical depth (ℎ  ) on the critical load (  ) in tooth enamel.e solid line indicates the corresponding power law �ts.