Materials Science and Engineering C 55 (2015) 448–456

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Materials Science and Engineering C journal homepage: www.elsevier.com/locate/msec

Viscoplastic response of tooth enamel under cyclic microindentation Yunfei Jia a, Fu-Zhen Xuan a,⁎, Fuqian Yang b,⁎ a b

Key Laboratory of Pressure System and Safety, MOE, School of Mechanical and Power Engineering, East China University of Science and Technology, Shanghai 200237, People's Republic of China Materials Program, Department of Chemical and Materials Engineering, University of Kentucky, Lexington, KY 40506, USA

a r t i c l e

i n f o

Article history: Received 29 September 2014 Received in revised form 8 May 2015 Accepted 28 May 2015 Available online 1 June 2015 Keywords: Cyclic microindentation Tooth enamel Anisotropy Energy dissipation

a b s t r a c t Cyclic microindentations were performed on the occlusal surface and axial section of tooth enamel, using the Berkovich indenter. Under the action of a cyclic indentation load, the indenter continuously penetrated into the tooth enamel and reached a quasi-steady state at which the penetration depth per cycle was a constant. At the quasi-steady state, both the amplitude of the indentation depth and the penetration depth per cycle for the cyclic indentation of the axial section are larger than those for the indentation of the occlusal section under the same loading condition. The energy dissipation per cycle consists of two contributions; one is the plastic energy dissipated per cycle due to the propagation of the plastic zone underneath the indentation and the other is the energy dissipation due to the viscous flow during the cyclic indentation. Both the penetration depth and the plastic energy dissipated per cycle at the quasi-steady state are independent of the maximum applied load and increase with increasing the amplitude of the cyclic indentation load. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Human enamel is composed of numerous rods with the diameter of 5–6 μm, which are surrounded by the protein-rich sheath of ~1 μm thickness [1,2]. The constituents of the enamel are approximately 92–96% inorganic crystals, 1–2% organic proteins, and 3–4% water by weight [3]. As a typical hierarchical structure of biomaterials [4], the enamel rod consists of bundles of hydroxyapatite (HAP) crystallites of ~50 nm in diameter, which are joined by protein layers of approximately 1 nm thickness [5]. The crystallites align parallel to the longitudinal direction of the enamel rod around the central region [6]. The highly oriented microstructure introduces anisotropic characteristics of the mechanical properties of the enamel, which determines its biofunctionality. It is very difficult to use conventional mechanical testing techniques to measure the mechanical properties of the enamel due to its small size. Indentation [7] has become one of the major techniques used to characterize the mechanical properties of the enamel [8–10]. The enamel can be considered as viscous-elastic–plastic according to the indentation creep tests [11–13] and the indentation load–displacement curves [9,14]. The elastic modulus and the indentation hardness in the direction parallel to the axis of the enamel rods have been found to be larger than those in the direction perpendicular to the axis of the rods, which is likely associated with the arrangement of the apatite crystals and the composite feature of rods [15]. Xu et al. [16] observed that the indentation-induced cracks in the direction parallel to the occlusal surface are significantly shorter than that in the direction perpendicular to the axial section. Moreover, the occlusal surface also has a larger ⁎ Corresponding authors. E-mail addresses: [email protected] (F.-Z. Xuan), [email protected] (F. Yang).

http://dx.doi.org/10.1016/j.msec.2015.05.074 0928-4931/© 2015 Elsevier B.V. All rights reserved.

resistance to wear than the axial section from the macro-level to the nano-level [17,18]. Currently, most studies have been focused on single indentation of the enamel. It is known that the tooth enamel experiences repetitive contact deformation during daily chewing [19]; the dynamic behavior and cyclic deformation of human enamel should be explored to examine the effect of repetitive contact on its biofunctionality. Cyclic indentation has been used to investigate the dynamic behavior of materials [20–23]. The numerical and experimental studies of cyclic indentation on homogeneous materials have been performed [23–25]. Xu and Yue [26] observed the ratcheting behavior for the cyclic indentation of copper by a cylindrical indenter of flat end. Xu et al. [24] suggested that the indentation penetration could be phenomenally related to the propagation of a fatigue crack. Yang et al. [23] used the cyclic indentation to evaluate the dynamic response of aluminum, and they observed that the penetration rate reached a constant with increasing the cycles. Shen et al. [27] simulated the cyclic indentation of the metal/ceramic nanolayered composites and showed that the ductile layers deformed plastically during the unloading phase. Jia and Xuan [28] studied the single- and multi-nanoindentation of the occlusal surface and axial section of tooth enamel under the same loading conditions and observed the difference in the load-depth curves. They suggested the presence of anisotropic damage in the tooth enamel underneath the indentation. However, they did not study the cyclic indentation deformation of the tooth enamel, and there is little study on the “dynamic behavior” of tooth enamel. In this work, the cyclic indentation of the tooth enamel has been performed to evaluate the nature of the mechanical deformation of the tooth enamel under the action of cyclic indentation loading. This work focuses on the dependence of the dynamic deformation of the tooth enamel on

Y. Jia et al. / Materials Science and Engineering C 55 (2015) 448–456

the loading conditions, including the dependence of the steady state penetration depth (per cycle) on the maximum indentation load and the amplitude of the cyclic indentation load. The energy dissipation per cycle is also discussed. 2. Experimental detail

449

with a constant loading rate was used instead of a constant frequency. Due to the anisotropic characteristic of the axial section, 6 cyclic indentations were performed on the occlusal surface of the enamel and 12 cyclic indentations were performed on the axial section from the outer enamel surface to the dentino-enamel junction of the enamel for each loading condition. The distance between adjacent indentations was set to be ten times the imprint size.

2.1. Sample preparation 3. Results and discussion A healthy third molar tooth from an adult between 20 and 30 years old was collected from the orthodontics after obtaining patient's consent. The tooth was first preserved in a Hank's balanced salt solution (HBSS) at 4 °C [1]. The tooth for the indentation tests was embedded in a plastic mold with cold-curing resin before grinding and polishing. The enamel was grounded on the occlusal surface at the cusp and on the axial section (as shown in Fig. 1), using sequential SiC papers from 400 to 2000 grit, and then polished by diamond paste until the enamel rods were observable under an optical microscope. For the detailed information, see the work by Jia and Xuan [17]. Zheng et al. [29] pointed out that the mechanical behavior of the enamel surface does not change after 4 hours drying in a vacuum chamber. Considering that the total experimental time for the indentations of the enamel were over one month, dehydrated enamel was used here to eliminate the possible contribution of aqueous liquid in the enamel. Thus, the tooth was dried in air for 10 days to approximately reach stable structure. No visible cracks on the enamel surface were found after dehydration. 2.2. Cyclic microindentation Agilent Nano Indenter G200 (Agilent Technologies Inc., Santa Clara) with a Berkovich indenter of the tip radius less than 40 nm was used to perform the cyclic microindentation tests on the occlusal surface and the axial section of the enamel. Cyclic microindentation in a triangular wave form, as shown in Fig. 2a, was used. During the test, the indenter was pushed onto the sample to the maximum indentation load of Pmax, and then was withdrawn to the minimum load of Pmin. The loading/ unloading process was repeated for 300 times, i.e. the cyclic indentation. The effects of the loading parameters of Pmax and ΔP (=Pmax − Pmin) on the cyclic indentation of the two enamel sections were studied. The maximum indentation load was in the range of 160 to 300 mN for the load amplitude of 150 mN, and the load amplitude was in the range of 20 to 170 mN for the maximum indentation load of 200 mN. The loading/ unloading rates for all tests were 40 mN/s. Zhou and Hsiung [13] suggested that there exists the rate-dependent deformation of the enamel during indentation due to the flow of proteins. Considering the viscous characteristics of enamel, indentation

Fig. 1. (a) Schematic of the occlusal surface and the axial section of tooth enamel, and (b) schematic of the locations of the cyclic indentation on surface of the tooth enamel.

During the cyclic indentation, the indentation depth was recorded as a function of time. Fig. 2b shows the variation of the indentation depth, h, with time for the indentation of the axial section under the loading conditions of Pmax = 200 mN and ΔP = 150 mN. The indentation depth oscillated between the maximum indentation depth of himax and the minimum indentation depth of himin. Here, the superscript i is the cycle number. The indenter continuously penetrated onto the enamel with increasing the number of cycles, similar to the observation by Yang et al. [23] for the cyclic indentation of aluminum and by Xu et al. [21] for the cyclic indentation of copper. Note that, for the cyclic indentation of brittle materials, e.g. ceramics, most studies have been focused on the fatigue damage accumulation [30,31], the strength degradation [32], and the crack evolution in contact area [33]. Few studies have reported the h–t curves. In addition, the measured surface roughness of the enamel is less than 100 nm, which is much smaller than the indentation depth in this study. The effect of the surface roughness of the sample on the indentation behavior is negligible. From Fig. 2, one can find that there exists two states for the cyclic indentation; one is transient state and the other is quasi-steady state. In the transient state, the increasing rate of the maximum indentation depth, dhimax/dt, decreases with increasing the number of cycles, while dhimax/ dt remains constant in the quasi-steady state. The continuous penetration of the indenter onto the enamel under the cyclic loading suggests that there exists the propagation of the plastic deformation zone underneath the indenter and the penetration rate likely is associated with the propagation rate of the plastic zone. Small cyclic loading superposed on a large, constant indentation load can create local inelastic deformation around the indenter and lead to the continuous penetration of the indenter. Such behavior is similar to the fatigue deformation of ductile materials. It is worth pointing out that the quasi-steady state was reached in 300 cycles. The cyclic deformation behavior of the enamel sample under the indenter is unknown after 300 cycles. In general, the indentation deformation of enamel consists of elastic, plastic, and viscous deformation. The continuous penetration of the indenter onto the enamel under cyclic indentation is associated with the propagation of the plastic deformation zone. The mechanism of plastic deformation likely involves local densification associated with the rearrangement and plastic deformation of the slender hydroxyapatite crystals. The rearrangement of the slender hydroxyapatite crystals is related to the densification, and the plastic deformation of the slender hydroxyapatite crystals is related to the shearing of slip planes. The shear deformation of the protein layer likely is associated with viscous flow. Large indentation loads likely introduced microcracking on the surface of the enamel. Fig. 3a shows the indentation depth-time curves for the cyclic indentation of the axial section under the action of two indentation loads of Pmax = 160 mN and 250 mN with the load amplitude of ΔP = 150 mN. After a short transient state, the cyclic indentation reaches the quasi-steady state. The indentation depth for both cases oscillates in their respective ranges. For the first loading phase, the maximum indentation depth for Pmax = 160 mN is less than that for Pmax = 250 mN, as expected. The penetration rate in the quasi-steady state is approximately independent of the maximum indentation load of Pmax. Fig. 3b shows the indentation depth-time curves for the cyclic indentation of the occlusal surface and the axial section under the loading conditions of Pmax = 200 mN and ΔP = 30 mN. For the first loading

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Y. Jia et al. / Materials Science and Engineering C 55 (2015) 448–456

3500

Pmax

3000

Load: P (mN)

Depth: h (nm)

Pmax-Pmin= P

Pmin 0

T

hS

2500 Transient state 2000

Quasi-steady state

himin

1500 1000

Axial section

500 0

0

dhSmax/dt

himax

Pmax=200mN, P=150mN 0

500

1000 1500 2000 2500 3000

Time: t (s)

Time: t (s)

(a)

(b)

Fig. 2. (a) Schematic of the cyclic indentation loading, and (b) variation of the indentation depth, h, with time for the cyclic indentation of the axial section (Pmax = 200 mN and ΔP = 150 mN).

phase, the maximum indentation depth for the axial section is much larger than that for the occlusal surface. Both the penetration rate of dhSmax/dt and the depth amplitude of ΔhS in the quasi-steady state for the axial section are larger than those for the occlusal surface. These results suggest the anisotropic characteristics of the tooth enamel with the axial section being more compliant than the occlusal surface. Generally, one can use the maximum indentation depth for the first loading phase, h1max, to represent the penetration resistance of a material. Fig. 4 depicts the dependence of the maximum indentation depth of h1max on the maximum indentation load for the first loading phase for both the occlusal surface and the axial section. The magnitude of h1max for the indentation of the axial section is larger than that for the indentation of the occlusal surface under the same indentation load. The occlusal surface has a larger penetration resistance, which is likely due to its higher hardness and elastic modulus than the axial section [15,34]. For homogeneous materials, the relationship between the indentation load and the maximum indentation depth for a single quasi-static indentation can be described by the following equation [35] n

ð1Þ

F ¼ Kmh

where Km is a constant related to the deformation behavior of the material, and n is an exponential index. Using Eq. (1) to curve-fit the experimental data shown in Fig. 4, one obtains Km = 6.95 × 10−4 mN · nm−1.7 and n = 1.7 for the occlusal surface and Km = 1.21 × 10−3 mN · nm−1.6 and n = 1.6 for the axial section. Both the exponent indexes are different from 2 as obtained from dimensional analysis for a geometrically similar indenter [36]. The dimensional analysis, which is simply based on the

4000

Axial section

2400

2500 2000 1500

Pmax=160mN

1000

P=150mN

500 0

500

1000

Pmax=200mN, P=30mN

2200

Pmax=250mN

3000

1500

2000

2500

Depth: h (nm)

Depth: h (nm)

3500

0

von-Mises flow rule for the indentation of microstructure-less materials, is inapplicable for the description of the indentation deformation in tooth enamel. One needs to be cautious in using the dimensional analysis to analyze the indentation deformation of materials, since both the flow behavior and the microstructures of materials play important roles in local deformation. During individual unloading phases for the cyclic indentation, the enamel experienced elastic recovery, which led to the residual indentation depth at the minimum indentation load less than the indentation depth at the maximum indentation load. Fig. 5a shows the variation of the amplitude of the indentation depth per cycle, Δhi(himax − himin), with the indentation cycle for the cyclic indentation on the occlusal surface under the loading condition of Pmax = 200 mN and ΔP = 150 mN. The value of Δhi is about 353 nm for the first indentation cycle, then decreases with the increase of the number of the indentation cycles, and approaches a plateau value of 344 nm, resembling the fatigue test of materials with an endurance limit. Using the results given in Fig. 5a, one obtains that Δhi/Δhmax approaches 0.95 with i ≥ 200. This results indicates that the variation of Δhi is relatively independent of the number of the indentation cycles and the indentation recovery approximately remains unchanged. +1 (= Fig. 5b shows the increment of the indentation depth of Δhimax i+1 i hmax − hmax) as a function of the number of the indentation cycles for the same indentation conditions as in Fig. 5a. The maximum value of +1 +1 is 22 nm at i = 1. The magnitude of Δhimax decreases significantΔhimax ly with the increase of the number of the indentation cycles and approaches a plateau value of 1.7 nm. Fast propagation of the plastic deformation zone during the cyclic indentation occurs at the first

Axial section

2000 1800 1600

Occlusal surface 1400 1200

0

100

200

300

400

Time: t (s)

Time: t (s)

(a)

(b)

500

600

700

Fig. 3. (a) Two cyclic indentation depth-time curves for the cyclic indentation of the axial section (Pmax = 160 mN and 250 mN with ΔP = 150 mN), and (b) two cyclic indentation depthtime curves for the cyclic indentation of the occlusal surface and the axial section, respectively (Pmax = 200 mN and ΔP = 30 mN).

Y. Jia et al. / Materials Science and Engineering C 55 (2015) 448–456

300

Load: P (mN)

the unloading being pure elastic [37,38]. There exists hysteresis loops for the cyclic loading of viscoelastic materials, and the area enclosed by the reloading curve and the previous unloading curve could be regarded as the viscous energy dissipation for the cyclic deformation [28,38]. Thus, the area enclosed by the hysteresis loop of individual cycles could be approximated as the viscous energy dissipation of Eiv. Define the total energy dissipation at the ith cycle as Eit, which is calculated from the enclosed area between the ith loading–unloading curve as

Occlusal surface Axial section Fitting curve for occlusal surface Fitting curve for axial section

250 200 150

1st loading

100 50 0

500

1000

1500

2000

Fig. 4. Load–displacement curves of the first loading phase for the cyclic indentation of the occlusal surface and the axial section.

several cyclic indentations, and slow propagation of the plastic deformation zone takes place for the subsequent cyclic indentation, which is in accord with the presence of the transient and quasi-steady states during cyclic indentation. Such behavior is likely associated with local densification during the cyclic indentation. The indentation-induced local densification increases the resistance to local deformation and leads to the decrease of the indentation depth for the same indentation load. For the indentation of elastoplastic materials, the energy dissipation occurs during a loading/unloading cycle owing to the propagation of the plastic zone under the indentation [23]. For viscoelastic-plastic materials, the total energy dissipation during a loading/unloading cycle consists of the viscous energy dissipation for viscous flow and the plastic energy dissipation for the propagation of the plastic deformation zone. Comparing the indentation force-time curves with the corresponding indentation depth-time curves of both the two enamel sections, one observes that there is a phase shift. This result confirms the viscous characteristic of tooth enamel, as observed in the indentation creep of tooth enamel [11,12], which likely plays an important role in the energy absorption during cyclic loading. Fig. 6a shows the second loading/unloading curve, the third reloading curve, the 106th loading/unloading curve, and the 107th reloading curve for the cyclic indentation on the occlusal surface with the loading conditions of Pmax = 200 mN and ΔP = 150 mN. There exists a hysteresis loop between the unloading and reloading curve, the loading curve and the unloading curve do not overlap for the following indentation cycle. It is known that the reloading curve will overlap with the unloading curve for materials without viscous characteristics and

1.10

Occlusal surface

356

hmax

352

hi/ hmax

1.05 1.00 0.95 0.90

Pmax=200mN, P=150mN

0.85 0.80 0

348

50

100

150 200

250 300

Cycles (i) 344 Quasi-steady state

0

50

unload

   Fdh 

iþ1 −Eiunload Eiv ¼ Eload

  i  iþ1   Z Z    ¼  Pdh−    load

unload

   Pdh: 

Eit ¼ Eiv þ Eip

ð4Þ

in which the graphical method used to calculate the plastic energy dissipation of Eip is shown in Fig. 6a. From Fig. 6a, one can note that at the 106th cycle is much less the plastic energy dissipation of E106 p than that of E2p at the 2nd cycle, suggesting that the plastic energy dissipation decreases significantly with the number of the indentation cycles. Such behavior represents the ratcheting behavior of the indentation deformation of the tooth enamel. In general, the elastic energy stored in a material during the loading would be released during the unloading [39]. When the indenter withdraws during the unloading of each cycle, the energy released can be considered as the elastic recovery energy Eie [40], which can be calculated as the area under the unloading curve as

Eie

 i  Z  ¼  

unload

   Fdh: 

ð5Þ

Fig. 6b, c, and d depict the variation of the elastic recovery energy, the viscous energy dissipation, and the plastic energy dissipation with

1.0

20

h2max

15

Transient state

5 0

0.6

0.2 100 150 200 250 300

Cycles (i)

Quasi-steady state

(b)

250

300

50

50

(a)

200

0

Pmax=200mN, P=150mN

0.4

0.0 0

10

Occlusal surface

0.8

100 150 200 Cycles (i)

150

ð3Þ

The total energy dissipation at the ith cycle for the indentation of viscoelastic–plastic materials consists of the contribution of the viscous energy dissipation, Eiv, and the plastic energy dissipation, Eip, i.e.

Cycles (i)

100

ð2Þ

where Eiload and Eiunload are calculated from the area under the loading curve and the unloading curve of the ith cycle, respectively. The viscous energy dissipation for the ith cycle is calculated as

25

360

hi =himax-himin (nm)

  i  i   Z Z     ¼ Fdh−    load

Depth: h (nm)

340

¼

Eiload −Eiunload

2500

i+1 i hi+1 max= hmax- hmax (nm)

0

Eit

2 hi+1 max/ hmax

350

451

250

300

+1 Fig. 5. (a) Variation of the amplitude of the indentation depth, Δhi, with the number of the indentation cycles, and (b) variation of the increment of the indentation depth per cycle, Δhimax , with the number of the indentation cycles for the cyclic indentation of the occlusal surface (Pmax = 200 mN and ΔP = 150 mN).

Y. Jia et al. / Materials Science and Engineering C 55 (2015) 448–456

i Eit = Ep

Eiv

+

1.10

50000

1.05

120

48000

42000

1.00 0.95

46000

0.90

44000

Emax e

80 40 0 1200

106th loading 106th unloading 107th loading

2nd loading 2nd unloading 3rd loading

1400

1600

1800

2000

Occlusal surface

Eie/Emax e

160

52000 Occlusal surface

(mN.nm)

Load: P (mN)

200 Pmax=200mN, P=150mN

Eie

452

Pmax=200mN, P=150mN

0.85 0.80 0

50

Cycles (i)

40000 38000

0

50

100

150

(a)

3000

1.00

Pmax=200mN, P=150mN

0.95 0.90 0.85 0.80 0

50

100 150 200 250 300

Cycles (i)

2900 2800

3000

Occlusal surface

1.05

Quasi-steady state

0

50

100

150

200

250

Emax p

300

Eip/Emax p

Eiv /Emax v

3100

3500

1.10

2500 2000 1500

300

Occlusal surface

0.8 0.6

Pmax=200mN, P=150mN

0.4 0.2

Transient state

500 0

1.0

0.0 0

1000

Eip

Eiv

(mN.nm)

3200

250

(b)

(mN.nm)

Emax v

200

Cycles (i)

Depth: h (nm)

3300

100 150 200 250 300

0

50

50

100 150 200 250 300

Cycles (i) Quasi-steady state

100

150

200

Cycles (i)

Cycles (i)

(c)

(d)

250

300

Fig. 6. (a) Load-depth curves for the second loading/unloading and third loading phases, and the 106th loading/unloading and 107th loading phases, (b) variation of the elastic energy of Eie with the number of the indentation cycles, (c) variation of the viscous energy dissipation of Eiv with the number of the indentation cycles, and (d) variation of the plastic energy dissipation of Eip with the number of the indentation cycles (cyclic indentation of the occlusal surface with Pmax = 200 mN and ΔP = 150 mN).

the indentation cycles for the cyclic indentation on the occlusal surface under the loading conditions of Pmax = 200 mN and ΔP = 150 mN. All the three normalized energies at each cycle by their respective maxi, Eiv/Emax and Eip/Emax ) are embedmum values of the first cycle (Eie/Emax e v p ded in the corresponding figure. According to Fig. 6b, c, and d, the magnitude of the elastic recovery energy is much larger than the other two energies; only small portion of the indentation energy is dissipated through the viscous energy dissipation and the plastic energy dissipation for each indentation cycle. The normalized elastic recov, decreases from 1 to 0.95 for the indentation cycle ery energy, Eie/Emax e to 275, revealing that the elastic recovery energy does not vary significantly with the number of the indentation cycles. The viscous energy dissipation decreases with the increase of the number of the indentation cycles and reach a plateau value around the 125th indentation cycle. The dissipation of the viscous energy also does not decrease significantly. It is noted that, from Fig. 6c, the normalized decreases from 1 to 0.9 with inviscous energy dissipation of Eiv/Emax v creasing the number of the indentation cycles, which suggests that the energy dissipation during the cyclic indentation of the enamel is controlled by the viscous flow. For the indentation of elastoplastic materials, the unloading is mainly controlled by the elastic recovery. For the indentation of viscoelastic– plastic materials, the unloading behavior is a function of elastic and viscous deformation of the materials, depending on the unloading rate. From Figs. 5a, 6b, and c, one notes that the trend of the variation of the normalized amplitude of the indentation depth per cycle with the number of the indentation cycles is similar to that of the normalized elastic energy and the viscous energy dissipation. This result supports that the cyclic deformation of the tooth enamel is mainly controlled

by viscoelastic deformation. However, the magnitude of the elastic recovery energy for individual indentation cycles is 10 times more than the corresponding viscous energy dissipation. The viscous flow only plays a limited role in the cyclic deformation of the tooth enamel, and the amplitude of the indentation depth per cycle is limited by the elastic properties of the tooth enamel. As shown in Fig. 6d, the plastic energy dissipation decreases significantly with the increase of the number of the indentation cycles. There exist a transient state and a quasi-steady state. The variation of the plastic energy dissipation with the number of the indentation cycles is very similar to the increment of the indentation depth per cycle, as shown in Fig. 5b, which suggests that the increment of the indentation depth per cycle is associated with the propagation of the plastic zone underneath the indentation. Fig. 7a shows the dependence of the amplitude of the indentation depth per cycle at the quasi-steady state, ΔhS, on the amplitude of the cyclic indentation load, ΔP, for the indentation on the occlusal surface and the axial section at the maximum indentation load of Pmax = 200 mN. The magnitude of ΔhS increases with increasing the magnitude of ΔP. Large amplitude of the cyclic indentation load will produce large amplitude of the indentation depth. Fig. 7b shows the variation of ΔhS with Pmax at ΔP = 150 mN for the indentation on the occlusal surface and the axial section. The magnitude of ΔhS decreases linearly with increasing the magnitude of Pmax, and the decreasing rate of the axial section is larger than that of the occlusal surface. Note that, for the same amplitude of the cyclic indentation load, larger amplitude of the indentation depth was produced on the axial section than on the occusal surface. This result suggests that there exists less elastic recovery of the occlusal surface than that of the axial section

Y. Jia et al. / Materials Science and Engineering C 55 (2015) 448–456

hS =hSmax-hSmin (nm)

500 400

500

Occlusal surface Axial section Fitting curve :y=0.5x1.3 Fitting curve :y=1.55x1.1

hS =hSmax-hSmin (nm)

600

300 200 100

Pmax=200 mN

0

-100

0

40

80

120

453

160

P=150mN 450 400 350 300 250 120

200

Occlusal surface Axial section Fitting line for occlusal surface Fitting line for axial section

160

P (mN)

200

240

Pmax

(mN)

(a)

280

320

(b)

Fig. 7. Variation of the amplitude of the indentation depth at the quasi-steady state, ΔhS, with (a) the amplitude of the indentation load, ΔP, (Pmax = 200 mN), and (b) the maximum indentation load of Pmax (ΔP = 150 mN) for the cyclic indentation of the occlusal surface and the axial section.

S

Δhmax ¼ BΔP m

ð6Þ

hSmax=(dhSmax/dt)T (nm)

where B and m are constants. Using the best curve-fitting to fit the curve in Fig. 8a, one obtains m = 2.42 and 2.27 for the occlusal surface and the axial section, respectively. The power indexes for the cyclic indentation of the occlusal surface and the axial section are approximately the same, while they are significantly different from 0.59 and 0.63 for the single indentation of the occlusal surface and the axial section, respectively, as determined from Eq. (1). Such a difference in the power indexes

10

1

0.1

Occlusal surface Fitting curve for occlusal surface Axial section Fitting curve for axial section

Pmax=200 mN

0.01 10

100

P (mN)

(a)

indicates that the quasi-static mechanical behavior of the tooth enamel is different from the dynamic behavior. One needs to be cautious in using the quasi-static mechanical properties of biomaterials to analyze their dynamic behavior. Fig. 8b shows the dependence of the penetration depth per cycle at the quasi-steady state on the maximum indentation load under the action of the constant load amplitude of 150 mN for the occlusal surface and the axial section. The penetration depth per cycle at the quasisteady state is independent of the maximum indentation load under the experimental conditions for both the occlusal surface and the axial section. As shown in Fig. 8a and b, the cyclic indentation of the axial section produces larger penetration depth per cycle than the cyclic indentation of the occlusal section under the same load function. The occlusal surface has larger resistance to the propagation of the plastic zone than the axial section under the same cyclic loading, the same as the quasistatic indentation. For a linear viscoelastic material subjected to the stress-controlled cyclic loading, the viscous energy dissipation over a cycle can be expressed as W = πσ20G2, where G2 is the loss compliance of the viscoelastic material, and σ0 is the stress amplitude [41]. From Fig. 7a, one notes that the amplitude of the indentation depth per cycle at the quasi-steady state, ΔhS, is nearly a linear function of the amplitude of the cyclic indentation load, and the viscous energy dissipation is much larger than the plastic energy dissipation, as shown in Fig. 6c and d. One expects that the viscous energy dissipation is proportional to the square of the amplitude of the cyclic indentation loads. Fig. 9a shows

hSmax=(dhSmax/dt)T (nm)

under the same load function, which could be due to lower elastic modulus of axial section than that of the occlusal surface [15]. Generally, the residual indentation depth for a single loading– unloading indentation is associated with the size of the plastic zone underneath the indentation [35]. One expects that the penetration depth per cycle at the quasi-steady state, ΔhSmax (=(dhSmax/dt)T), can be used to represent the propagation behavior of the plastic zone. Fig. 8a shows the variation of the penetration depth per cycle at the quasisteady state with the amplitude of the cyclic indentation load for the cyclic indentation of the occlusal surface and the axial section with Pmax = 200 mN. Large load amplitude produces large penetration depth per cycle, as expected. The cyclic indentation by an indentation load of large amplitude accelerates the propagation of the plastic zone underneath the indentation. Assume that the dependence of ΔhSmax on ΔP for the cyclic indentation of both the occlusal surface and the axial section can be described as

10

P=150mN

Occlusal surface Axial section

1

120

160

200

240

280

320

Pmax (mN)

(b)

Fig. 8. Variation of the penetration depth per cycle at the quasi-steady state, ΔhSmax, with (a) ΔP (Pmax = 200 mN), and (b) Pmax (ΔP = 150 mN) for the cyclic indentation of the occlusal surface and the axial section.

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the variation of the viscous energy dissipation at the quasi-steady state, ESv, with the amplitude of the cyclic indentation load, ΔP, for the cyclic indentation of the occlusal surface and the axial section under the loading condition of Pmax = 200 mN. Obviously, the viscous energy dissipation at the quasi-steady state, ESv, for the load-controlled cyclic indentation of the tooth enamel is a parabolic function of the loading amplitude, ΔP, as ESv ¼ CΔP 2

ð7Þ

where C is a fitting constant, which depends on the viscoelastic property of the enamel. Using the best curve-fitting to fit the results in Fig. 9a, one obtains C = 0.15 and 0.19 for the occlusal surface and the axial section, respectively. This result suggests that the tooth enamel can be approximated as linearly viscoelastic for the experimental condition used in this work. Fig. 9b depicts the variation of the viscous energy dissipation at the quasi-steady state, ESv, with the maximum indentation load, Pmax, for the cyclic indentation of the occlusal surface and the axial section under the loading condition of ΔP = 150 mN. The viscous energy dissipation decreases linearly with increasing the maximum indentation load due to the increase in the energy dissipation through plastic deformation, i.e. the increase of the size of the plastic deformation zone underneath the indentation. The magnitude of the viscous energy dissipation for the cyclic indentation of the axial section is larger than that for the cyclic indentation of the occlusal surface. The axial section of the tooth enamel can absorb more energy during surface contact. The viscous characteristic of tooth enamel is due to the presence of protein [12], which has the special function of dissipating mechanical energy to resist failure during cyclic loading. During loading and unloading, the protein between mineral crystals experiences stretch/relaxation deformation. During the stretch, the recoverable folded peptide chain domain bond, i.e. sacrificial bond, in the protein molecule unfolds [42], while the sacrificial bond refolds during the relaxation. However, due to the hysteresis effect, only a fraction of the domain bonds could refold after the extension of the protein molecules [43]. During the cyclic indentation, the unfolding and the partial refolding of the sacrificial bonds occur repeatedly, which results in the hysteresis loops. Furthermore, viscous flow and the viscous energy dissipation take place during the cyclic indentation, which would have an effect on the amplitude of the indentation depth and the penetration depth per cycle. The viscous energy dissipation absorbs the mechanical energy and protects the enamel from the impact damage under dynamic loading. Fig. 10a and b show the variation of the plastic energy dissipation at the quasi-steady state with the amplitude of the cyclic indentation load and the maximum indentation load, respectively, for the cyclic indentation of the occlusal surface and the axial section. The plastic

energy dissipation of ESp at the quasi-steady state increases with the increase of the amplitude of the cyclic indentation load, ΔP, and is a power function the amplitude of the cyclic indentation load. The power indexes for the cyclic indentation of the occlusal surface and the axial section are 3.33 and 3.04, respectively, while the plastic energy dissipation at the quasi-steady state is independent of the maximum indentation load. Comparing Fig. 8a with Fig. 10a, the variation of the penetration depth per cycle at the quasi-steady state, ΔhSmax, with the amplitude of the cyclic indentation load is analogous to that of the plastic energy dissipation of ESp, and both the values of ΔhSmax and ESp are independent of Pmax (as shown in Figs. 8b and 10b). The similar trend of the penetration depth per cycle and the plastic energy dissipation at the quasi-steady state suggests that the concept of the plastic energy dissipation and the calculation of the plastic energy dissipation are reasonable in describing the dynamic behavior of the tooth enamel. As shown in Fig. 10, the axial section dissipates more plastic energy at the quasi-steady state than the occlusal surface under the same loading conditions, in accord with that the penetration depth per cycle for the cyclic indentation of the axial section is larger than that of the occlusal surface, as shown in Fig. 8. The plastic deformation occurs during single indentation of human enamel [2,44,45], and the enamel exhibits the metallic-like mechanical behavior as comparing with ceramics and metals [46,47]. It is well known that enamel experiences millions of repetitive contact loading over the whole life without catastrophic failure. The dissipation of mechanical energy plays an important role in protecting the enamel by mitigating catastrophic failure. Moreover, the presence of proteins of small volumes endows the enamel with high capability of viscous flow [46,47]. Under the same cyclic loading, the axial section experiences larger propagation of plastic zone and has more dissipations of mechanical energy than the occlusal surface. Although the metallic-like mechanical behavior of enamel has been proposed, the fracture and cracks of enamel are also common under the action of a large load or an impact load. It was reported that one in twenty people fractures a tooth each year [48,49]. The fracture toughness of the enamel, being treated as a brittle material, was measured by the indentation crack length method, using Vickers indenter [16,50]. It was observed that an indentation load of 2 N generated cracks in enamel at the corner of a Vickers indenter [16]. For the indentations of brittle polycrystalline alumina and ductile annealed copper, radial cracks could be produced in alumina at an indentation load of 1 N [51], while no cracks was observed on the annealed copper even for the indentation load being larger than 800 N [52]. Thus, the enamel generally behaves metallic-like; however the enamel also shows some brittle characteristics under some loading conditions. Fig. 11 shows the two typical SEM images of the impressions at the end of the 300 cycles on the enamel. Local cracks were observed at

6000 Occlusal surface Axial section

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5000

(mN.nm)

Fitting curve :y=0.15x2 Fitting curve :y=0.19x2

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ESv

ESv

(mN.nm)

8000

0

40

80

120

P (mN)

(a)

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200

P=150mN

4000 3000 2000 1000 120

Occlusal surface Axial section Fitting line for occlusal surface Fitting line for axial section

160

200

240

280

320

Pmax (mN)

(b)

Fig. 9. Variation of the viscous energy dissipation at the quasi-steady state, ESv, with (a) ΔP (Pmax = 200 mN), and (b) Pmax (ΔP = 150 mN) for the occlusal surface and the axial section.

100 10 1 10

Pmax=200 mN 100

P (mN)

800 700 600 500 400

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Occlusal surface Axial section

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P=150mN

ESp

ESp

(mN.nm)

1000

Axial section Occlusal surface Fitting curve for occlusal surface Fitting curve for axial section

(mN.nm)

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100 120

160

200

240

280

320

Pmax (mN)

(a)

(b)

Fig. 10. The plastic energy dissipation at the quasi-steady state of ESp as a function of (a) ΔP under Pmax = 200 mN and of (b) Pmax under ΔP = 150 mN for the cyclic indentation of the occlusal surface and the axial section.

the corner of the indentation, which likely were due to the damage accumulation during the cyclic indentation at the loading rate of 40 mN/s. Note that the load for the crack initiation during the cyclic indentations of brittle materials can likely be detected from the jump in the plot of hysteresis loop versus the load, as demonstrated by Chen and Bull [53] in the multi-cycling nanoindentation study of thin optical coatings on glass and supported by the in-situ AFM imaging. Such an approach may also be used to reveal the crack initiation in enamel since viscoelastic deformation will not introduce the discontinuity in the curve of hysteresis loop versus the load. The anisotropic characteristics of viscoplastic deformation during the cyclic indentation are controlled by the microstructures of the enamel. When indenting on the occlusal surface, the loading direction is parallel to the direction of the slender crystals. The contact stress during cycling is not sufficient to induce fracture or plastic deformation of the mineral crystals [42,54]. The dissipation of mechanical energy is mainly due to the shear deformation of proteins between the mineral crystals [54]. When indenting on the axial section, the loading direction is approximately perpendicular to the direction of the mineral crystals. The bending deformation of the slender crystals contributes to the increase in the penetration resistance to the indentation deformation [28]. The results of the cyclic indentation on enamel presented in this study can provide the guidance for the design and selection of the novel dental materials. The penetration depth and plastic energy dissipation per cycle at the quasi-steady state can be used as the parameters for evaluating the cyclic deformation response of the dental materials

under the condition of the contact. These parameters can be contained for the optimal design of the novel dental materials. 4. Conclusions The load-controlled cyclic microindentation of tooth enamel was carried out on two perpendicular sections, i.e. the occlusal surface and the axial section, using the Berkovich indenter. The effects of two loading parameters, i.e. the maximum indentation load and the load amplitude, on the cyclic response of the enamel were characterized. The following is the summary of the main results. (1) The cyclic indentation of the enamel consisted of a transient state and a quasi-steady state. (2) At the quasi-steady state, both the penetration depth per cycle and the plastic energy dissipation increase with the increase of the amplitude of the cyclic indentation load. The viscous energy dissipation is a parabolic function of the amplitude of the cyclic indentation load, revealing the linear viscous characteristic of the enamel. (3) At the quasi-steady state, both the penetration depth per cycle and the plastic energy dissipation are independent of the maximum indentation load for the experimental conditions. The amplitude of the indentation depth and the viscous energy dissipation decrease linearly with increasing the maximum indentation load.

Fig. 11. Two typical SEM images of the impressions on the enamel.

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(4) The amplitude of the indentation depth, the penetration depth per cycle, and the energy dissipation for the cyclic indentation of the axial section are larger than those of the occlusal surface, which likely are due to the highly-oriented microstructures of the enamel. (5) The penetration depth per cycle can be used to represent the propagation of the plastic zone underneath the indentation, which has similar change trend to the plastic energy dissipation.

Acknowledgment FZX is grateful for the support provided by the National Natural Science Foundation of China (51325504). YFJ is grateful for the support from China Scholarship Council (201306740020) and the Fundamental Research Funds for the Central Universities (22A201514024). References [1] S. Habelitz, G.W. Marshall, M. Balooch, S.J. Marshall, J. Biomech. 35 (2002) 995–998. [2] S.F. Ang, E.L. Bortel, M.V. Swain, A. Klocke, G.A. Schneider, Biomaterials 31 (2010) 1955–1963. [3] J. Zheng, F. Xiao, L.M. Qian, Z.R. Zhou, Tribol. Int. 42 (2009) 1558–1564. [4] Z.H. Xie, M. Swain, P. Munroe, M. Hoffman, Biomaterials 29 (2008) 2697–2703. [5] S. Bechtle, S. Habelitz, A. Klocke, T. Fett, G.A. Schneider, Biomaterials 31 (2010) 375–384. [6] L.H. He, M.V. Swain, J. Mech. Behav. Biomed. Mater. 1 (2008) 18–29. [7] S. Suresh, A.E. Giannakopoulos, Acta Mater. 46 (1998) 5755–5767. [8] A. Braly, L.A. Darnell, A.B. Mann, M.F. Teaford, T.P. Weihs, Arch. Oral Biol. 52 (2007) 856–860. [9] L.H. He, M.V. Swain, Dent. Mater. 23 (2007) 814–821. [10] J. Zhou, L.L. Hsiung, J. Biomed. Mater. Res. A 81 (2007) 66–74. [11] S.F. Ang, M. Saadatmand, M.V. Swain, A. Klocke, G.A. Schneider, J. Mater. Res. 27 (2012) 448–456. [12] L.H. He, M.V. Swain, J. Biomed. Mater. Res. A 91 (2009) 352–359. [13] J.K. Zhou, L.L. Hsiung, Appl. Phys. Lett. 89 (2006) 051904. [14] Y. Jia, F.-Z. Xuan, F. Yang, J. Mech. Behav. Biomed. Mater. 25 (2013) 33–40. [15] S. Habelitz, S.J. Marshall, G.W. Marshall, M. Balooch, Arch. Oral Biol. 46 (2001) 173–183. [16] H.H.K. Xu, D.H. Smith, S. Jahanmir, E. Romberg, J.R. Kelly, V.P. Thompson, E.D. Rekow, J. Dent. Res. 77 (1998) 472–480. [17] Y.F. Jia, F.Z. Xuan, Wear 290 (2012) 124–132.

[18] J. Zheng, Z.R. Zhou, J. Zhang, H. Li, H.Y. Yu, Wear 255 (2003) 967–974. [19] H. Chai, J.J.W. Lee, P.J. Constantino, P.W. Lucas, B.R. Lawn, Proc. Natl. Acad. Sci. U. S. A. 106 (2009) 7289–7293. [20] S.N.G. Chu, J.C.M. Li, J. Eng. Mater. Technol. 102 (1980) 337–340. [21] B.X. Xu, Z.F. Yue, J. Wang, Mech. Mater. 39 (2007) 1066–1080. [22] F.Q. Yang, J.C.M. Li, Mater. Sci. Eng. R 74 (2013) 233–253. [23] F.Q. Yang, L. Peng, K. Okazaki, J. Mater. Sci. 42 (2007) 4513–4520. [24] B.X. Xu, Z.F. Yue, X. Chen, Scripta Mater. 60 (2009) 854–857. [25] F.Q. Yang, A. Saran, J. Mater. Sci. 41 (2006) 6077–6080. [26] B. Xu, Z.F. Yue, J. Mater. Res. 21 (2006) 1793–1797. [27] Y.L. Shen, C. Blada, J. Williams, N. Chawla, Mater. Sci. Eng. A 557 (2012) 119–125. [28] Y.-F. Jia, F.-Z. Xuan, J. Mech. Behav. Biomed. Mater. 16 (2012) 163–168. [29] J. Zheng, L.Q. Weng, M.Y. Shi, J. Zhou, L.C. Hua, L.M. Qian, Z.R. Zhou, Wear 301 (2013) 316–323. [30] F. Guiberteau, N.P. Padture, H. Cai, B.R. Lawn, Philos. Mag. A 68 (1993) 1003–1016. [31] M. Matsuzawa, N. Yajima, S. Horibe, J. Mater. Sci. 34 (1999) 5199–5204. [32] Y.G. Jung, I.M. Peterson, D.K. Kim, B.R. Lawn, J. Dent. Res. 79 (2000) 722–731. [33] D.K. Kim, Y.G. Jung, I.M. Peterson, B.R. Lawn, Acta Mater. 47 (1999) 4711–4725. [34] Y.-R. Jeng, T.-T. Lin, H.-M. Hsu, H.-J. Chang, D.-B. Shieh, J. Mech. Behav. Biomed. Mater. 4 (2011) 515–522. [35] F.Q. Yang, L. Peng, K. Okazaki, Metall. Mater. Trans. A 35 (2004) 3323–3328. [36] Y.-T. Cheng, Int. J. Solids Struct. 36 (1999) 1231–1243. [37] A. Richter, H. Gojzewski, J.J. Belbruno, Int. J. Mater. Res. 98 (2007) 414–423. [38] A. Richter, M. Gruner, J.J. BelBruno, U.J. Gibson, M. Nowicki, Colloids Surf. A 284 (2006) 401–408. [39] R.S. Lakes, Viscoelastic Materials, Cambridge University Press, New York, 2009. [40] F.Q. Yang, J.C.M. Li, Micro and Nano Mechanical Testing of Materials and Devices, Springer Verlag, 2008. [41] G. Zhou, X. Liu, Theory of Viscoelasticity (Chinese), University of Science and Technology of China Press, Hefei, China, 1996. [42] L.H. He, M.V. Swain, Appl. Phys. Lett. 90 (2007) 171916. [43] M. Rief, M. Gautel, F. Oesterhelt, J.M. Fernandez, H.E. Gaub, Science 276 (1997) 1109–1112. [44] S.F. Ang, T. Scholz, A. Klocke, G.A. Schneider, Dent. Mater. 25 (2009) 1403–1410. [45] L.H. He, N. Fujisawa, M.V. Swain, Biomaterials 27 (2006) 4388–4398. [46] K. Bai, T.H. Zhang, Z.Y. Yang, F. Song, X.D. Yang, K. Wang, Chin. Sci. Bull. 52 (2007) 2310–2315. [47] L.H. He, M.V. Swain, J. Dent. 35 (2007) 431–437. [48] P. Abbott, N. Leow, Aust. Dent. J. 54 (2009) 306–315. [49] J.D. Bader, J.A. Martin, D.A. Shugars, J. Am. Dent. Assoc. 126 (1995) 1650–1654. [50] R. Hassan, A.A. Caputo, R.F. Bunshah, J. Dent. Res. 60 (1981) 820–827. [51] J. Lankford, J. Mater. Sci. 16 (1981) 1567–1578. [52] M.M. Chaudhri, Acta Mater. 46 (1998) 3047–3056. [53] J. Chen, S.J. Bull, J. Phys. D Appl. Phys. 41 (2008) 074009. [54] L.H. He, M.V. Swain, J. Biomed. Mater. Res. A 81 (2007) 484–492.