Loading rate effect on the mechanical behavior of

Materials Science & Engineering A 619 (2014) 247–255

Contents lists available at ScienceDirect

Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea

Loading rate effect on the mechanical behavior of zirconia in nanoindentation Abdur-Rasheed Alao, Ling Yin n Matter and Materials, College of Science, Technology and Engineering, James Cook University, Townsville, QLD 4811, Australia

art ic l e i nf o

a b s t r a c t

Article history: Received 14 August 2014 Received in revised form 15 September 2014 Accepted 26 September 2014 Available online 2 October 2014

This paper reports the loading rate effect on the mechanical behavior of zirconia using nanoindentation and in situ scanning probe imaging techniques. Nanoindentation tests were performed at a peak load of 10 mN and 0.1–2 mN/s loading rates. The results show that the contact hardness increased by 31% with the loading rate while the Young's modulus was loading rate independent (ANOVA, p 40.05). A strain rate sensitivity model was applied to determine the strain rate sensitivity and the intrinsic contact hardness. A pressure-sensitive idealized yield criterion model was applied to analyze the pressure hardening coefficient and the intrinsic compressive yield stress. Extensive discontinuities and largest maximum and contact depths were also observed on the force–displacement curves at the lowest loading rate. These phenomena corresponded to nanoindentation-induced strain softening. The in situ scanning probe images of indentation imprints showed plastic deformation without fracture at all loading rates and dislocation-induced pileups around indentation imprints at the low loading rate. The amount of pileups decreased with increase in loading rate. Finally, these results provide scientific insight into the submicron material removal mechanisms for zirconia during sharp abrasive machining. & 2014 Elsevier B.V. All rights reserved.

Keywords: Zirconia Loading rate Mechanical behavior Nanoindentation In situ scanning probe imaging

1. Introduction Zirconia has high strength, high fracture toughness, low thermal conductivity, high ionic conductivity and biocompatibility. It is widely used in load-bearing and wear-resistant structures in engineering and medicine/dentistry as thermal barrier coatings, fuel cell electrolytes, pump components, valve seals, bushings/ bearings, body implants, dental restorations, etc. [1–6]. The high fracture toughness of zirconia is associated with the tetragonal-tomonoclinic phase transformation [7–9] or ferroelastic domain switching [10,11], resulting in a high damage tolerance [12]. Zirconia structures are usually shaped by abrasive grinding and polishing. In dentistry, sandblasting with alumina abrasives is also used to treat zirconia cementation surfaces for improved adhesion [2,13,14]. These abrasive processes can trigger the tetragonal-tomonoclinic phase transformation in zirconia which can enhance its strength [15,16]. However, the tensile stresses generated by abrasive machining can also induce surface and subsurface damage in zirconia that change its surface properties and deteriorate its structural integrity and material reliability [17,18]. To improve zirconia's mechanical performance, machining-induced damage in

n

Corresponding author. Tel.: þ 61 7 4781 6254. E-mail address: [email protected] (L. Yin).

http://dx.doi.org/10.1016/j.msea.2014.09.101 0921-5093/& 2014 Elsevier B.V. All rights reserved.

the material must be minimized by applying ductile mode grinding conditions [19,20]. Understanding the mechanical behavior of zirconia can provide scientific insights into ductile regime machining mechanisms for the material, which can be simulated by indentation mechanics [21,22]. The mechanical contact conditions in indentation are geometrically similar to the conditions in abrasive machining. Machining forces, cutting speed and abrasive geometries can be simplified by indentation loads, loading rates, and indenter geometries, respectively. Thus, indentation features reflect the essential abrasive machining mechanics. Indentation techniques have been used to characterize the mechanical behavior of zirconia. In particular, Hertzian indentation was performed to study the deformation and fracture of zirconia [23–25], which is ideal to measure the elastic properties and the elastic–plastic transitions [26]. In general, sharper indenters, such as Vickers, can induce larger stresses and strains sufficient to displace large material volumes and impose large amounts of shear stresses allowing easy plastic deformation [26,27]. Thus, Vickers indentations were used to study the plastic behavior of zirconia [28–31]. Those microscale indentation studies also demonstrated fracture mechanisms for zirconia in which critical load thresholds for median/radial crack formation were exceeded. As the scale of deformation becomes small in the sub-threshold region, materials can be removed from zirconia by plastic flow

248

A.-R. Alao, L. Yin / Materials Science & Engineering A 619 (2014) 247–255

leaving a crack-free surface [32]. Nanoindentation can be used to characterize such scale deformation events, including probing the contact hardness, Hc, and Young's modulus, E, based on the Oliver and Pharr method [33,34]. Combining with in situ scanning probe imaging, nanoindentation can also discern various material deformation behaviors underneath the indenter [35]. Several nanomechanical studies were conducted on the zirconia behavior influenced by grain size [36,37], ageing [38–40], indentation size effect [41] and crystallographic orientation [42]. However, those studies were conducted at constant loading rates which assumed equilibrium deformation conditions. In fact, loading rates can affect the material hardness [27], which is an important material design consideration where hardness is taken as a basis for predicting strength, machinability, wear and erosion characteristics. At the microscale, loading rate effects on the mechanical behavior of alumina, alumina oxynitride, silicon nitride, silicon carbide, zirconia and Pyrex glass have been investigated in postthreshold indentations in which fractures occurred [29,30,43]. It was also found that loading rates influenced the behavior and properties of bulk metallic glasses in nanoindentation [44–48]. However, the loading rate effect on the mechanical behavior of zirconia is not studied at the submicron scale, which is vital in the understanding of removal mechanisms in ductile regime machining for the material. This paper aimed to study the loading rate effect on the mechanical behavior of zirconia using nanoindentation and in situ scanning probe imaging. The contact hardness, Hc, and Young's modulus, E, were measured as a function of loading rate in the range 0.1–2 mN/s at the peak load of 10 mN. Nanoindentationinduced discontinuities in zirconia were markedly manifested in loading–unloading curves at the lowest loading rate whereas they tended to be imperceptible at the highest loading rate. These loading rate-dependent mechanical responses of zirconia to different phenomena were analyzed. Finally, the linkage between the nanoindentation responses and the modes of material removal of zirconia was established.

2. Experimental procedures 2.1. Materials Cylindrical blocks of pre-sintered zirconia (IPS e.max ZirCAD, Ivoclar Vivadent) were selected in this study, which are commonly processed in chair-side dental CAD/CAM systems for crowns and bridges. This material consisted of 87–95 wt% ZrO2, 4–6 wt% Y2O3, 1–5 wt% HfO2, 0.1–1 wt% Al2O3, 97% tetragonal and 3% monoclinic phases [4,49,50]. Indentation samples with dimension of 15 mm 15 mm 2 mm were obtained using the procedures described by Alao and Yin [49]. Briefly, they were metallographically ground and polished using successively finer diamond paste to obtain mirror surfaces. The root-mean-squared surface roughness, Rq, was approximately 72.3 nm from the scan area of 50 μm 50 μm [49] using scanning probe imaging (NT-MDT NTEGRA, Hysitron, USA). After polishing, those samples were sintered in a furnace (MTI GSL1500X) to 1300 1C for 2 h at 10 1C/ min heating rate and then naturally cooled to room temperature. These sintering conditions agree with the specifications for clinical zirconia restorations [51]. Sintered zirconia samples were rescanned using the scanning probe imaging. Fig. 1(a) shows a scanned sintered zirconia surface on which the root-mean-squared surface roughness, Rq, was 102 nm from the same scan area of 50 μm 50 μm for presintered samples. This indicates that sintered zirconia surfaces became rough due to sintering-induced grain coarsening,

Fig. 1. 2D scanning probe images of zirconia surfaces (a) after sintering and (b) after repolishing.

shrinkage, residual stresses and monoclinic to tetragonal phase transformation. To meet the sample roughness requirement for nanoindentation, sintered samples were repolished using the same metallographic process for pre-sintered zirconia. After repolishing, zirconia surfaces were scanned using the scanning probe imaging. Fig. 1(b) shows a scanned repolished sintered zirconia surface, obtaining the root-mean-squared surface roughness, Rq, of approximately 7.7 nm in a scan area of 50 μm 50 μm and an average zirconia grain size of 500 nm. 2.2. Nanoindentation tests Nanoindentation tests were conducted using a Hysitron Triboscope (Hysitron, USA), which has load and depth sensing resolutions of 1 nN and 0.0002 nm respectively. A Berkovich diamond indenter of approximately 150 nm tip radius was applied. Prior to


the nanoindentation test, the system was calibrated using a fused silica standard. Thermal drift corrections were made to obtain the maximum drift rate which was 0.05 nm/s. Nanoindentation testing was performed on zirconia in a load-control mode at 10 mN peak load. Loading and unloading rates of 0.1 mN/s, 0.5 mN/s, 1 mN/s and 2 mN/s were used, which corresponded to 100, 20, 10 and 5 s loading and unloading times, respectively. The contact hardness, Hc, is defined as the ratio of the peak load, Pmax, to the residual or projected area, A [33]. The projected area, A, is a shape function of the contact depth, hc, described by [33,34] 2

1

1=2

A ¼ 24:5hc þ C 1 hc þ C 2 hc

1=4

þ C 3 hc

1=128

þ ::: þ C 8 hc

ð1Þ

where C1…C8 are constants determined through curve-fitting procedures. The contact depth, hc, in Eq. (1) is given by [33,34] hc ¼ hmax 0:75

P max S

ð2Þ

where hmax is the maximum penetration depth and S is the contact stiffness determined from the unloading curve. The unloading curve is best described by the following power law relation [33]: m ð3Þ P ¼ k2 h hf where k2 and m are the unloading constant and exponent respectively and are empirically determined by curve-fitting procedures, h is an instantaneous indentation displacement and hf is the final depth. The slope of the unloading curve during the initial stages of unloading is the contact stiffness, S, which is described by [33] pffiffiffi m 1 dP 2 S¼ ð4Þ ¼ mk2 hmax hf ¼ pffiffiffiffiEr A dh h ¼ hmax β π where β is a correction factor which was established as 17 0.05 [34], Er is the reduced modulus between the specimen and the indenter. The specimen's Young's modulus, E, can be determined using [33] " # 1 1 1 ν2i 2 ð5Þ E ¼ 1ν Er Ei where v is the specimen's Poisson's ratio, and Ei and vi represent the indenter's Young's modulus and Poisson's ratios, respectively. For a diamond indenter, Ei and vi are 1141 GPa and 0.07, respectively [33]. For zirconia, v is 0.3 [52]. The contact depth, hc, the final contact depth, hf, the maximum penetration depth, hmax, the contact stiffness, S, the contact hardness, Hc, and Young's modulus, E, were determined as a function of a loading rate. Six indentations at different locations were performed on zirconia at each loading rate to determine the mean values and standard deviations of the properties. Singlefactor analysis of variance (ANOVA) was applied at a 5% confidence interval to examine significant effects of loading rate on properties. Prior to and after indentation, the indented areas were scanned to obtain the surface and indentation patterns using the in situ scanning probe imaging. For each indentation imprint, a depth cross-sectional analysis was conducted to investigate the material response underneath the indenter.

3. Results 3.1. Force–displacement curves Fig. 2 shows the force–displacement curves for six indentations at loading rates of 0.1 mN/s, 0.5 mN/s, 1 mN/s and 2 mN/s. At 0.1 mN/s loading rate in Fig. 2(a), frequent pop-in events were observed on the loading and unloading curves. At 0.5 mN/s

249

loading rate in Fig. 2(b), fewer discontinuities were observed on the loading and unloading curves. In contrast, at 1 mN/s and 2 mN/s loading rates, no evidence of pop-ins in the loading and unloading curves (Fig. 2(c) and (d)). Pop-in phenomena on loading and unloading curves can reflect different physical events beneath the indenter tip. Fig. 2 indicates that slow indentation rates promoted extensive discontinuities while rapid indentation rates suppressed the discontinuities. In addition, the largest dispersion is also observed on the force–displacement curves at the lowest loading rate in Fig. 2(a). As the loading rate was increased, the dispersion on the force–displacement curves is reduced as shown in Fig. 2(b)–(d). Fig. 3 shows the final penetration depths, hf, the contact penetration depths, hc, and the maximum penetration depths, hmax, versus loading rate. Both contact and maximum penetration depths decreased with increase in loading rate with the largest contact and maximum penetration depths occurring at the lowest loading rate of 0.1 mN/s. In comparison, final depths increased as the loading rate was increased to 1 mN/s but decreased when the loading rate increased from 1 mN/s to 2 mN/s. 3.2. Mechanical properties Fig. 4 shows the contact stiffness, S, versus loading rate. The contact stiffness decreased as the loading rate was increased from 0.1 mN/s to 1 mN/s and remained constant when the loading rate increased from 1 mN/s to 2 mN/s. At the lowest loading rate of 0.1 mN/s, the standard deviation for the contact stiffness was very large. Fig. 5 shows the indentation contact hardness, Hc, versus loading rate. The contact hardness increased with the loading rate. The measured means and standard deviations for contact hardness at 0.1 mN/s, 0.5 mN/s, 1 mN/s and 2 mN/s loading rate are 7.61 7 2.96 GPa, 9.097 1.16 GPa, 9.33 71.02 GPa, and 9.97 70.92 GPa, respectively. Thus, by increasing the loading rate from 0.1 mN/s to 2 mN/s, the mean contact hardness increased by 31%. In addition, the standard deviations decreased with the loading rate. This is in line with the dispersions associated with the force–displacement curves in Fig. 2. Fig. 6 shows Young's modulus, E, versus loading rate. The measured Young's modulus means and standard deviations at 0.1 mN/s, 0.5 mN/s, 1 mN/s and 2 mN/s loading rates are 158.4 757.13 GPa, 189.55 714.28 GPa, 157.50 711.31 GPa, and 167.32 79.06 GPa, respectively. The standard deviations of Young's moduli decreased with the loading rate, which followed the dispersion trend in the force–displacement curves in Fig. 2. Single factor ANOVA shows the insignificant loading rate effect on Young's modulus (p 4 0.05).

3.3. Indentation morphologies Fig. 7 shows 3D scanning probe images of the indented morphologies at 0.1 mN/s, 0.5 mN/s, 1 mN/s and 2 mN/s loading rates. Plastic deformation was observed on all indented areas and no radial cracks along the corners where highest stresses are usually concentrated were found. Fig. 8 shows 2D scanning probe images of the indented morphologies and their depth cross-sectional profiles at 0.1 mN/s, 0.5 mN/s, 1 mN/s and 2 mN/s loading rates. Significant pileups in Fig. 8(a), (b) and (c) were observed around the indentations at 0.1 mN/s, 0.5 mN/s and 1 mN/s loading rates, corresponding to surface deformation displacements of 25 nm, 10 nm and 9 nm, respectively. However, there was no evidence of pileup around the indenter at 2 mN/s loading rate in Fig. 8(d). These indicate that the occurrence of the pileup phenomenon for sintered zirconia was

250


Fig. 2. Force–displacement curves for six indentations at 10 mN peak load with loading rates of (a) 0.1 mN/s, (b) 0.5 mN/s, (c) 1 mN/s and (d) 2 mN/s.

400

Indentation displacement (nm)

hf hc

280

hmax 210

140

70

Contact stiffness, S (μN/nm)

350

300

200

100

0 0

0.5

1

1.5

2

Loading rate (mN/s)

0 0

0.5 1 1.5 Loading rate (mN/s)

2

Fig. 3. Final depth (hf), contact depth (hc) and maximum penetration depth (hmax) versus loading rate. Each data point is the mean value of the six repeated indentations; each error bar corresponds to 7 1 standard deviation for the six repeated indentations.

Fig. 4. Contact stiffness (S) versus loading rate. Each data point is the mean value for the six repeated indentations; each error bars corresponds to 71 standard deviation for the six repeated indentations.

dependent on the loading rate. It may be taken that the critical loading rate at which pileup events cannot occur in this zirconia investigated was 1–2 mN/s.


Therefore, it is important to determine the accuracy of the measured properties with the Oliver–Pharr method. The conditions nullifying the Oliver–Pharr method for indentations with significant pileups are that the ratios of the final depths, hf, to the maximum depths, hmax, must be greater than 0.7 [54]. The calculated means and standard deviations of hf/hmax ratios at 0.1 mN/s, 0.5 mN/s, 1 mN/s and 2 mN/s loading rates in Fig. 2 are 0.4570.28, 0.6370.10, 0.6370.08, and 0.670.03, respectively, which are smaller than the threshold of 0.7. Therefore, it is confident that the pileups in the nanoindentation patterns studied (Figs. 7 and 8) were not a significant factor. In this study, strain hardening may have occurred, which can be measured by the material's sensitivity to strain hardening using a strain rate sensitivity model. This model relates the contact hardness, Hc, to the effective strain rate, ε_ , as follows [55]:

Contact hardness, Hc (GPa)

18 15 12 9 6 3

H c ¼ H o ε_ n

0 0

0.5 1 1.5 Loading rate (mN/s)

2

Fig. 5. Contact hardness (Hc) versus loading rate. Each data point is the mean value for the six repeated indentations; each error bar corresponds to 7 1 standard deviation for the six repeated indentations.

ð6Þ

where n is the strain rate sensitivity and Ho is the intrinsic contact hardness free from strain rate sensitivity. For strain-hardening materials, n is greater than 0. By taking the logarithm of both sides of Eq. (6), we obtain Log ðH c Þ ¼ n Log ðε_ Þ þ Log H o

ð7Þ

The effective strain rate, ε_ , can be related to a constant loading _ as follows [56]: rate, P,

350

ε_ ¼ Young's modulus, E (GPa)

251

280

1 P_ 2 P max

ð8Þ

where Pmax is the peak load. Thus, corresponding to 0.1 mN/s, 0.5 mN/s, 1 mN/s and 2 mN/s loading rates and 10 mN peak load, the constant strain rates are 0.005 s 1, 0.025 s 1, 0.05 s 1 and 0.1 s 1, respectively. Fig. 9 reveals Log(Hc) versus Log(ε_ ) in which the corresponding linear equation with a coefficient of determination, R2, of 97% is expressed as

210

140

Log ðH c Þ ¼ 0:113 Log ðε_ Þ þ 1:1189 70

0 0

0.5

1

1.5

2

Loading rate (mN/s) Fig. 6. Young's modulus (E) versus loading rate. Each data point is the mean value for the six repeated indentations; each error bar corresponds to 7 1 standard deviation for the six repeated indentations.

4. Discussion This work demonstrates for the first time that the loading rate has a significant influence on the mechanical behavior of sintered zirconia in nanoindentation. The lowest loading rate resulted in the largest maximum penetration and contact depths (Fig. 3). This indicates that contact areas between the indenter and the material were most enhanced at this loading rate. Increasing the loading rate, contact areas reduced, corresponding to the reduction in contact depths (Fig. 3). Thus, the decrease in contact area with increase in loading rate led to higher contact hardness (Fig. 5). This loading rate-dependent contact hardness of zirconia at the submicron scale has enhanced our understanding of the similar behavior of silicon carbide, zirconia and alumina at the microscale [29,30,53]. However, the measured contact hardness (Fig. 5) and Young's moduli (Fig. 6) can be overestimated when pileup is significant. This is because the Oliver–Pharr method does not account for the pileup phenomenon around the contact boundary which often leads to underestimating the true contact area [54]. Evidence of the occurrence of pileup events is manifest in Figs. 7(a)–(c) and 8(a)–(c).

ð9Þ

where n ¼0.113 and Log(Ho)¼1.1189. This indicates that zirconia was sensitive to strain hardening at a moderate level. Thus, when hf/hmax o0.7, or materials that moderately work harden, the Oliver–Pharr method gives acceptable results of the contact hardness and Young's moduli in this study [54]. In addition, the pileup absence in Fig. 8(d) cannot be attributed to the sinking-in effect. The sinking-in phenomenon can predominate in materials which strain hardening sensitivity, n, must be greater than 0.2 [57]. Given that n was less than 0.2 for the zirconia studied, it was unlikely for the sinking-in effect to occur at 2 mN/s loading rate. As this material was moderately sensitive to strain hardening, its loading rate-independent or intrinsic contact hardness free from strain rate sensitivity, Ho, is determined to be 13.15 GPa from Eq. (9). This value is consistent with microhardness values (13–15 GPa) for zirconia ceramics [4,57,58]. This indicates that the strain rate sensitivity model is valid to determine the material intrinsic contact hardness as well as the surface contact hardness at any loading rates. The loading-rate dependent contact hardness in zirconia (Fig. 5) may also be attributed to pressure hardening, which can be measured by the material's pressure-hardening sensitivity using a pressure-sensitive idealized yield criterion model [59]. This ideal elastic–plastic yield criterion is given as [59]

σ Y ¼ αP þ σ o

ð10Þ

where σo is the compressive yield stress at zero pressure, α is the pressure hardening coefficient, P is the confining internal pressure and σY is the compressive yield stress due to internal pressures. The higher the value of α, the greater the material sensitivity to pressure hardening. For materials of an ideal elastic–plastic yielding behavior like zirconia, a relationship between the contact hardness, Hc, and the compressive yield stress, σY, has been

252


Fig. 7. 3D scanning probe images of the nanoindentation impressions at 10 mN peak load and loading rates of (a) 0.1 mN/s, (b) 0.5 mN/s, (c) 1 mN/s and (d) 2 mN/s, showing permanent plastic deformation with the absence of radial cracks in the tensile regions around indent corners.

established [60] Hc ¼ C σ Y

ð11Þ

where C is a constraint factor approximately equal to 3 [60]. Thus, the means and standard deviations of compressive yield stresses at 0.1 mN/s, 0.5 mN/s, 1 mN/s and 2 mN/s loading rates are estimated to be 2.54 70.99 GPa, 3.03 70.39 GPa, 3.11 70.34 GPa, and 3.32 70.31 GPa, respectively. Fig. 10 demonstrates compressive _ in which a linear relation with yield stress versus loading rate,P, a coefficient of determination, R2, of 78% was established as

σ y ¼ 0:356P_ þ 2:68

ð12Þ

At the zero loading rate in Fig. 10, the zero pressure, σo, is estimated to be 2.68 GPa. For pressure-sensitive materials, the intrinsic contact hardness, Ho, can also be estimated using the following equation [59]: H o ¼ ð3 þ 2αÞσ o

ð13Þ

where Ho ¼13.15 GPa and σo ¼ 2.68 GPa. Upon substituting these values, the coefficient of pressure hardening, α, is 0.953.

A comparison between α and n shows that α is about 8.5 times higher than n. This indicates that the zirconia was more sensitive to pressure hardening than strain hardening. Further, by replacing, Hc in Eq. (11) with Ho ¼13.15 GPa, the loading rate-independent or intrinsic compressive yield stress, σY, is 4.38 GPa. This value agrees with the yield strength (4.36 7 0.13 GPa) determined for zirconia by Zeng and Chiu [61] using a different method. This reconfirms the validation of our applied method and authenticates its results. Substituting, the values of σY ¼ 4.38 GPa, σo ¼2.68 GPa, and α ¼0.953 in Eq. (10), the confining pressure, P, is 1.79 GPa. Unlike the contact hardness, Young's moduli for zirconia (Fig. 6) were independent of the loading rate. The reason for this is that Young's modulus is dependent on both the contact stiffness and the contact area (Eq. (4)). Even though the contact area decreased with the loading rate (Fig. 3), this effect did not affect Young's modulus because the contact stiffness depends, in a complex manner, on the maximum and final depths and the unloading exponent. As shown in Fig. 3, the final depth had a complex relationship with the loading rate and this also influenced the contact stiffness in Fig. 4. In addition, Fig. 7 has shown that the


253

Fig. 8. 2D scanning probe images of the nanoindentaiton impressions and their corresponding depth cross-sectional profiles at 10 mN and loading rates of (a) 0.1 mN/s, (b) 0.5 mN/s, (c) 1 mN/s, (d) 2 mN/s, showing that pileups and surface deformation displacements were 25 nm, 10 nm, 9 nm and invisible, respectively.

254


Contact hardness, Hc (GPa)

100

n = 0.113 10

1 0.001

0.01

0.1

1

Strain rate (s-1) Fig. 9. Contact hardness (Hc) versus strain rate (_ε). Each data point is the mean value for six repeated indentations; each error bar corresponds to 7 1 standard deviation for the six repeated indentations. The linear graph is described by Log ðHc Þ ¼ 0:113 Log ðε_ Þ þ 1:1189 and the slope of the graph gives the strain-rate sensitivity, n¼ 0.113.

Compressive yield stress, σY (GPa)

5

4

3

2

1

0 0

0.5

1

1.5

2

Loading rate (mN/s) Fig. 10. Compressive yield stress (σy) versus loading rate. Each data point is the mean value for the six repeated indentations; each error bar corresponds to 7 1 standard deviation for the six repeated indentations. The linear graph is described by σ y ¼ 0:356P_ þ 2:68 and the intercept on the y-axis gives the zero loading rate compressive yield stress, σo ¼2.68 GPa.

indentation patterns at all loading rates deformed plastically and did not fracture. The material stiffness was unchanged because plastic deformation involved extremely small defects [26]. These loading rate-independent Young's moduli buttress the point that sinking-in process did not occur at the highest loading rate (Fig. 8(d)) because the material would have become stiffer at 2 mN/s loading rates if sinking-in had occurred [57]. Therefore, the mean and standard deviation of the measured Young's modulus at all loading rates from 24 indentations were 168.197 31.20 GPa. This value is consistent with Young's modulus extracted for Y-TZP by Alcalá [28] with Vickers indenter under varying applied loads. Another remarkable indentation distinction observed by changing the loading rate is the dependence of the pop-in formation on the loading rate (Fig. 2). These pop-ins were most markedly manifested in the loading–unloading curves at the lowest loading rate. With increase in loading rate, their number decreased and was almost imperceptible at the highest loading rate. The mechanisms of the pop-ins may be associated with fracture, phase transformation, shear bands or dislocation

networks [35]. These pop-ins are not due to fracture because there were no radial cracks in the tensile regions around the indent corners in Figs. 7 and 8. Further, the tetragonal-monoclinic phase transformation may not be responsible for the pop-ins since a critical contact pressure (13.3 GPa) is required to transform tetragonal to monoclinic in polycrystalline zirconia with a Berkovich indenter [42]. The contact hardness at any loading rate in Fig. 5 is lower than this critical contact pressure for the occurrence of the martensitic tetragonalmonoclinic transformation. If the tetragonal-monoclinic phase transformation might have occurred, the contact pressure would have decreased rather than increased with the loading rate because this phase transformation is associated with a volume increase [38,62]. The densities of tetragonal zirconia and monoclinic zirconia are 6.09 g/cm3 and 5.68 g/cm3, respectively. The increase in volume could lower the atomic density, resulting in a decrease in contact hardness [38,62]. In addition, shear bands cannot be responsible for the pop-ins because shear bands occur in amorphous materials where no dislocations or strain hardening occurs [35]. In this study, the sintered zirconia is polycrystalline containing grain boundaries and impurities where dislocation motion and interaction can prevail. Also, strainhardening occurred as evident in Fig. 9. Therefore, the observed popins in Fig. 2 are due to dislocation nucleation and interactions. The surface relief in Fig. 7 was due to the motion of dislocations (slip lines) or ductile streaks associated with the polishing process prior to nanoindentation. These dislocation networks were also responsible for plastic deformation in the form of material pileups materials around the indenter's contact boundaries (Figs. 7 and 8). Dislocation gliding (slip lines) was not observed using scanning probe imaging in this study. However, a similar observation was reported by Gaillard et al. [42] who used a Berkovich indenter to indent a polycrystalline zirconia. They observed dislocation gliding on the material when a cube corner indenter was used to induce larger stresses which favored dislocation motions on respective glide systems of the material [42]. This shows that dislocations were confined around the pileup areas. Each observed pop-in in Fig. 2, therefore, represents the activation of a dislocation network. When a pressure-sensitive material is indented at a low loading rate, a higher internal pressure is required to sustain the impression due to the pressure hardening near the impression [59]. In this case, elastic–plastic indentation boundaries were further pushed outward, resulting in material pileups. This process could also lead to surface strain softening of the material, yielding lower contact hardness. As the loading rate was raised, the induced compressive stress increased deforming larger material volume and broadening the plastic zone size (Fig. 8(d)). This rationalizes why surface deformation displacements in Fig. 8 decreased with the loading rate. Consequently, pressure hardening raised the compressive yield stress (Fig. 10) and the contact hardness (Fig. 5) as the loading rate increased. The responses of zirconia to a sharp indenter at different loading rates provide valuable insights into mechanisms of material removal for the material. When zirconia is machined with diamond abrasives of sharp cutting edges, the material removal is distributed over many abrasives. Thus, the contribution of each abrasive to the induced normal machining force can be very low, in the range of the peak load used in this study. Since this peak load is at the mili-Newton scale, plastic deformation can thus be formed at all loading rates. This indicates that ductile regime machining is possible for zirconia. However, as indicated in Figs. 7 and 8, material pileups were also formed around the indenter at low loading rates. This means that plastically deformed material would flow on the machined surface during slow abrasive machining. Since the cutting force performs a secondary role of extruding chips from a plastic zone that has been fully developed


by the normal force [63], it is easier to extrude large volume of material from the deformed material at low cutting speed [63]. Discrete slip events in Fig. 2(a) also indicate that serrated or discontinuous chips may occur while machining at a low speed. Further, a discontinuous chip from one abrasive can be ground by the next abrasive, increasing the surface roughness. Therefore, slow deformation rates may favor rough machining for zirconia. Continuous chips may be removed when machining zirconia at a high cutting speed due to the suppression of serrated flow (Fig. 2(d)). Therefore, this study predicts that high deformation rates may favor small- or submicron-scale material removal processes like ductile machining, fine finishing and polishing for zirconia. This assertion may contribute to the realization of ductile machining of zirconia at high cutting speeds [64,65]. 5. Conclusions This work revealed the loading-rate dependent mechanical behavior of zirconia in nanoindentation. Contact hardness showed an increased trend with the loading rate while the intrinsic hardness of 13.15 GPa for zirconia was obtained based on a strain rate sensitivity model, which was in the range of the published micro-hardness values. Young's modulus of 168.19 731.20 GPa revealed insignificantly loading-rate dependent. Serrated pop-ins on the force–displacement curves at lower loading rates were attributed to inhomogeneous dislocation networks and indentation-induced microstructural pileups. The suppression of the pop-ins at high loading rates on the force–displacement curves was ascribed to moderate strain hardening and pressure hardening. The results also indicated that plastic feature of zirconia at the tested peak load and all loading rates. The mechanical behavior of zirconia in nanoindentation might reflect material removal mechanisms in small volume abrasive machining using diamond abrasives. Finally, it is suggested that high deformation rates may favor small-scale material removal processes while low deformation rates may produce rough surfaces due to increased pileups. Acknowledgments The authors would like to thank Dr. Shane Askew of the Advanced Analytical Center at James Cook University (JCU) for experimental assistance; Dr. Rosalind Gummow of JCU for sintering the zirconia samples and Mr. Phillip Mcguire of Northern Petrographics Pty Ltd. for sample preparation. A.-R.A acknowledges the JCU PhD (JCU IPRS) scholarship. The work was supported by the JCU Collaboration Grants Scheme (2013-14) awarded to L.Y. References [1] J. Chevalier, L. Gremillard, A.V. Virkar, D.R. Clarke, J. Am. Ceram. Soc. 92 (2009) 1901–1920. [2] T. Miyazaki, T. Nakamura, H. Matsumura, S. Ban, T. Kobayashi, J. Prosthodont. Res. 57 (2013) 236–261. [3] C. Piconi, G. Maccauro, Biomaterials 20 (1999) 1–25. [4] C. Ritzberger, E. Apel, W. Höland, A. Peschke, V.M. Rheinberger, Materials 3 (2010) 3700–3713. [5] M.V. Swain, Acta Metall. 33 (1985) 2083–2091. [6] M.V. Swain, Acta Biomater. 5 (2009) 1668–1677. [7] R.C. Garvin, R.H. Hannink, R.T. Pascoe, Nature 258 (1975) 703–704. [8] R.H.J. Hannink, M.V. Swain, Annu. Rev. Mater. Sci. 24 (1994) 359–408.

[9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65]

255

R.H.J. Hannink, P.M. Kelly, B.C. Muddle, J. Am. Ceram. Soc. 83 (2000) 461–487. M.G. Cain, M.H. Lewis, Mater. Lett. 9 (1990) 309–312. A.V. Virkar, R.L.K. Matsumoto, J. Am. Ceram. Soc. 69 (1986) C224–C226. J.R. Kelly, I. Denry, Dent. Mater. 24 (2008) 289–298. P.C. Guess, Y. Zhang, J.-W. Kim, E.D. Rekow, V.P. Thompson, J. Dent. Res. 89 (2010) 592–596. Y. Zhang, B.R. Lawn, E.D. Rekow, V.P. Thompson, J. Biomed. Mater. Res. Part B: Appl. Biomater. 71B (2004) 381–386. M. Guazzato, L. Quach, M. Albakry, M.V. Swain, J. Dent. 33 (2005) 9–18. T. Kosmač, C. Oblak, P. Jevnikar, N. Funduk, L. Marion, Dent. Mater. 15 (1999) 426–433. R.G. Luthardt, M. Holzhüter, O. Sandkuhl, V. Herold, J.D. Schnapp, E. Kuhlisch, M. Walter, J. Dent. Res. 81 (2002) 487–491. H.H.K. Xu, S. Jahanmir, L.K. Lewis, Mach. Sci. Technol. 1 (1997) 49–66. K. Li, W. Liao, J. Mater. Process. Technol. 57 (1996) 207–220. L. Yin, X.F. Song, Y.L. Song, T. Huang, J. Li, Int. J. Mach. Tools Manuf. 46 (2006) 1013–1026. R. Komanduri, D.A. Lucca, Y. Tani, CIRP Ann.—Manuf. Technol. 46 (1997) 545–596. S. Malkin, T.W. Hwang, CIRP Ann.—Manuf. Technol. 45 (1996) 569–580. B.R. Lawn, Y. Deng, P. Miranda, A. Pajares, H. Chai, D.K. Kim, J. Mater. Res. 17 (2002) 3019–3036. S.K. Lee, R. Tandon, M.J. Readey, B.R. Lawn, J. Am. Ceram. Soc. 83 (2000) 1428–1432. I.M. Peterson, A. Pajares, B.R. Lawn, V.P. Thompson, E.D. Rekow, J. Dent. Res. 77 (1998) 589–602. M.L. Oyen, R.F. Cook, J. Mech. Behav. Biomed. Mater. 2 (2009) 396–407. B.R. Lawn, R.F. Cook, J. Mater. Sci. 47 (2012) 1–22. J. Alcalá, J. Am. Ceram. Soc. 83 (2000) 1977–1984. R.J. Anton, G. Subhash, Wear 239 (2000) 27–35. M.A. Klecka, G. Subhash, J. Am. Ceram. Soc. 93 (2010) 2377–2383. J.A. Munoz-Tabares, E. Jiménez-Piqué, J. Reyes-Gasga, M. Anglada, J. Eur. Ceram. Soc. 32 (2012) 3919–3927. T.G. Bifano, T.A. Dow, R.O. Scattergood, J. Eng. Ind. Trans. ASME 113 (1991) 184–189. W.C. Oliver, G.M. Pharr, J. Mater. Res. 7 (1992) 1564–1583. W.C. Oliver, G.M. Pharr, J. Mater. Res. 19 (2004) 3–20. C.A. Schuh, Mater. Today 9 (2006) 32–40. S. Guicciardi, T. Shimozono, G. Pezzotti, Adv. Eng. Mater. 8 (2006) 994–997. J. Lian, J.E. Garay, J. Wang, Scr. Mater. 56 (2007) 1095–1098. S.A. Catledge, M. Cook, Y.K. Vohra, E.M. Santos, M.D. Mcclenny, K.D. Moore, J. Mater. Sci.—Mater. Med. 14 (2003) 863–867. Y. Gaillard, E. Jiménez-Piqué, F. Soldera, F. Mücklich, M. Anglada, Acta Mater. 56 (2008) 4206–4216. S. Guicciardi, T. Shimozono, G. Pezzotti, J. Mater. Sci. 42 (2007) 718–722. L. Shao, D. Jiang, J.H. Gong, Adv. Eng. Mater. 15 (2013) 704–707. Y. Gaillard, M. Anglada, E. Jiménez-Piqué, J. Mater. Res. 24 (2009) 719–727. G.D. Quinn, P.J. Patel, I. Lloyd, J. Res. Natl. Inst. Stand. 107 (2002) 299–306. T. Burgess, K.J. Laws, M. Ferry, Acta Mater. 56 (2008) 4829–4835. A. Concustell, J. Sort, G. Alcalá, S. Mato, A. Gebert, J. Eckert, M.D. Baró, J. Mater. Res. 20 (2005) 2719–2725. A.L. Greer, A. Castellero, S.V. Madge, I.T. Walker, J.R. Wilde, Mater. Sci. Eng. A— Struct. 375–377 (2004) 1182–1185. W.H. Li, T.H. Zhang, D.M. Xing, B.C. Wei, Y.R. Wang, Y.D. Dong, J. Mater. Res. 21 (2006) 75–81. C.A. Schuh, T.G. Nieh, Acta Mater. 51 (2003) 87–99. A.-R. Alao, L. Yin, J. Mech. Behav. Biomed. Mater. 36 (2014) 21–31. C. Monaco, A. Tucci, L. Esposito, R. Scotti, J. Dent. 41 (2013) 121–126. I. Denry, J.A. Holloway, Materials 3 (2010) 351–368. N. Ereifej, F.P. Rodrigues, N. Silikas, D.C. Watts, Dent. Mater. 27 (2011) 590–597. M. Bhattacharya, R. Chakraborty, A. Dey, A.K. Mandal, A.K. Mukhopadhyay, Appl. Phys. A—Mater. 107 (2012) 783–788. A. Bolshakov, G.M. Pharr, J. Mater. Res. 13 (1998) 1049–1058. D. Peykov, E. Martin, R.R. Chromik, R. Gauvin, M. Trudeau, J. Mater. Sci. 47 (2012) 7189–7200. B.N. Lucas, W.C. Oliver, Metall. Mater. Trans. A 30A (1999) 601–610. J. Alcalá, A.C. Barone, M. Anglada, Acta Mater. 48 (2000) 3451–3464. C. Santos, L.H.P. Teixeira, J.K.M.F. Daguano, S.O. Rogero, K. Strecker, C.N. Elias, Ceram. Int. 35 (2009) 709–718. I.-W. Chen, J. Am. Ceram. Soc. 69 (1986) 189–194. D. Tabor, The Hardness of Metals, first ed., Oxford University Press, London, 1951. K. Zeng, C.-H. Chiu, Acta Mater. 49 (2001) 3539–3551. M. Cattani-Lorente, S.S. Scherrer, P. Ammann, M. Jobin, H.W.A. Wiskott, Acta Biomater. 7 (2011) 858–865. M.C. Shaw, CIRP Ann.—Manuf. Technol. 44 (1995) 343–348. L. Yin, H. Huang, Mach. Sci. Technol. 8 (2004) 21–37. L. Yin, S. Jahanmir, L.K. Ives, Wear 255 (2003) 975–989.