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Strain rate sensitivity of hydroxyapatite coatings
Thin Solid Films 520 (2011) 1516–1519
Contents lists available at ScienceDirect
Thin Solid Films j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / t s f
Strain rate sensitivity of hydroxyapatite coatings H.S. Tanvir Ahmed, Alan F. Jankowski ⁎ Texas Tech University, Mechanical Engineering, Box 41021, Lubbock, TX 79409 USA
a r t i c l e
i n f o
Available online 13 June 2011 Keywords: Hydroxyapatite Coatings Strain rate sensitivity Scratch hardness
a b s t r a c t The strain-rate sensitivity of strength is a significant factor to evaluate the deformation mode of crystalline materials. The strain rate sensitivity of hardness is experimentally investigated here for hydroxyapatite coatings that are sputter deposited onto titanium-coated silicon wafers. These biocompatible HA coatings can provide a strong, dense interface between metal alloy implants and porous hydroxyapatite that can help ingrowth of tissue. The interface to the metal alloy implant is important to transfer stress during loading. So, it is very important to know the behavior of the coating under different conditions of loading. Our dynamic test procedure now takes advantage of nanoscratch testing to measure the change in scratch hardness of the coating over a strain rate range that may well simulate the mechanical loading conditions found at the interface between implants and hydroxyapatite coatings. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Hydroxyapatite Ca10((PO)4)6(OH)2 coatings are widely used on both bone and tooth implants due to its similar chemical composition to natural bone. Orthopedic and dental implants are mostly bio-inert metal alloys and do not offer a good chemical bond to bone as hydroxyapatite (HA) does [1]. Also, porous HA coatings are known to promote bone regeneration [2]. The ideal Ca/P ratio in the HA structure is reported to be 1.67, with a density of the structure being 3.219 g/cm 3 [3]. A hexagonal crystal for HA is reported [4] with lattice parameters a equal to 0.9432 nm and c equal to 0.6881 nm. Today, commercial methods that are used to deposit HA on metal implants include electrophoretic deposition [2,4–6], vapor deposition [7], magnetron sputtering [8–12], dip coating [13], spin coating and plasma spray [14,15]. In these approaches, fabrication of the HA coating with desirable functional properties is challenging [16]. For this purpose, it is necessary to measure the properties of the coatings with techniques that involve fewer underlying assumptions and that reliably reproduce experimental results. Dynamic nanoindentation, i.e. triboindentation, or nanoscratch techniques have evolved as a suitable method of mechanical property measurement of thin coatings as shown by many researchers [17–20]. By varying the scratch velocity, the material surface can be subjected to different strain rates that can simulate the loading rate behavior of the coating as subjected to real-life situations as, e.g., walking to jumping. The strength behavior at different loading rates, i.e. the strain rate sensitivity of strength, is a key parameter to understand the deformation mechanism to the onset and extent of plastic deforma-
⁎ Corresponding author. Tel.: + 1 806 742 3563; fax: + 1 806 742 3540. E-mail address: [email protected] (A.F. Jankowski). 0040-6090/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2011.06.004
tion. It is widely reported [21] that some materials strengthen with increasing strain rate. For example, an increase in strain-rate sensitivity exponent (m) that is measured for several face-centercubic (fcc) metals (as the grain size decreases from the macro- to micro- to nano- scale) provides detail to interpret the mode of mechanical deformation. In this study, time dependent nanoscratch technique has been employed to extract the strain rate sensitivity of strength of the HA coating which would provide important insight to the mechanical responses of such coatings.
2. Experimental methods 2.1. Sample preparation The concept of a graded HA coating is reported [9] in the literature where the coating is: fully dense at the implant-coating interface; and has a gradually increasing porosity towards a value of ~ 50% at the muscle-coating surface. In this study, the coating investigated represents the fully dense structure at the implant-coating interface. These HA coatings were prepared by sputter deposition using planar magnetrons operated in the radio frequency (rf) mode as described [9] elsewhere. The HA target used in the sputter deposition process was produced by hot-pressing HA powders prepared into a right circular cylindrical disk. The powders were prepared by a precipitation [22] method in air at high temperature of 1300 °C. The fine grain structure of the HA target is reported [9] as 99.7% dense with small pores distributed primarily along grain boundaries and triple junctions. The target-material two-phase structure [9,22] contains less than 5% of tri-calcium phosphate in addition to HA as would be expected since apatite is essentially a line compound, and is very difficult to obtain in the pure form.
H.S.T. Ahmed, A.F. Jankowski / Thin Solid Films 520 (2011) 1516–1519
The substrates for the HA deposition are polished, single crystal Si (111) wafers. In some samples, the silicon wafers are first pre-coated with a 1.0 μm thick layer of 99.94% pure titanium (Ti). The 0.65 μm thick HA coatings are sputter deposited [9] onto the Ti-coated Si wafers at a forward power of 75 W using a 1.3 Pa working gas pressure of argon at a 40 cm 3-min −1 flow rate. In preliminary characterization of the coating structure, transmission electron microscopy images reveal [9] the cross-section of the coating to be fully dense. A Rigaku Miniflex II X-ray diffractometer operated in the θ/2θ mode with 30 kV–15 mA Cu kα radiation will be used to assess the crystalline structure of the coating. 2.2. Mechanical testing The nanoscratch test method utilizes a diamond stylus to scratch the coating surface. The resulting scratch width is used to determine the scratch hardness (Hs). A NanoAnalyzer test module is mounted into a CETR (Center for Tribology Inc., Campbell, CA USA) universal mechanical tester (UMT) platform. Scratches on the HA surface are made using a cantilever mounted stylus that is a Berkovitch diamondindenter tip. Also, this same probe is used to scan the surface for imaging the scratch width and depth. Typical values for the scratches are 2 · 10 2–1 · 10 3 nm in width and 10 1 nm in depth. The well-known expression [e.g. 23] for scratch hardness (Hs) as a function of the scratch width (w) and the indent load (N) is given as 2
Hs = c·N = w :
ð1Þ
The geometric constant (c) is specific to the indenter tip shape. For example, if the indentation scratch does not extend beyond the initial hemispherical regime of the indenter tip, then the constant c equals 8/π. This value is readily derived for a projection of the leading half of the hemispherical tip. Therefore, the scratch loads are selected to produce scratches that will not extend in width beyond ~5 · 10 2 nm, i.e. an approximate equivalent to the hemispherical projection of the indenter tip. The actual scratch-load can be measured using a realtime force feedback transducer. The strain-rate (έ) is varied by changing the nanoscratch velocity (v) where the empirical formula [23] for έ as a function of v and the scratch width (w) is given as
έ = v·w
−1
:
ð2Þ
A nominal indent load (N) of 1.0 mN is applied for the nanoscratch hardness testing where the scratch velocity (v) is varied from 10 1 to 10 4 nm sec -1. At least three different scratches are made at each velocity.
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m for strength is determined from the slope to a linear fit for the log–log scale plot of strength (σ) versus strain rate (έ), as m = δ lnðσ Þ = δ lnðέÞ:
ð4Þ
For the scratch test method [23], the scratch hardness (Hs) can be substituted into Eq. (4) in place of the strength (σ) as m = δ lnðHs Þ = δ lnðέÞ:
ð5Þ
The onset of plastic flow that occurs during scratch hardness testing provides a measurement to quantify strength where the strength is approximately [24] one-third the hardness. Therefore, the slope of the log–log scale variation of strain rate (έ) versus scratch hardness (Hs) can be used to measure the strain-rate exponent (m). 3. Results and analysis The X-ray diffraction spectra of the target material and a sputter deposited HA coating are shown in Fig. 1. The Miller indices of the major Bragg reflections for the HA target material are labeled that correspond with the standard peak positions reported [4,16,25] for HA. The relative intensity of the Bragg peaks, i.e. texture, for the target pattern is a good match with results recently reported [16] for microwave sintered material. Additional unlabeled peaks for the target scan as, e.g., the 2θ reflection at 37.80° are likely to correspond with the aforementioned second phase(s) such as tri-calcium phosphate (or, perhaps, calcium oxide). The HA coatings (on the silicon wafers for mechanical property assessment) may be amorphous since no distinct Bragg reflections are seen in the Fig. 1 X-ray diffraction scan. Cross-section traces of the nanoscratches are measured with the NanoAnalyzer operated in its scanning probe microscopy (SPM) mode. Each scratch is measured at five (or more) different locations to achieve a high statistical average of the scratch width (w). Threedimensional SPM images of three parallel nanoscratches that were made using a 1 mN indenter load at a 1000 nm sec −1 scratch velocity are shown in Fig. 2. The profiles of several linear traces across nanoscratches made at 50, 100, and 1000 nm sec −1 scratch velocities are shown in Fig. 3. In all, nanoscratches made using the various indenter tip velocities (v) at 1 mN load produce a range of scratch width that varies from 580 to 830 nm, which is less than the ~ 1 μm indenter tip diameter. The scratch hardness (Hs) of the HA coating is plotted in Fig. 4 as a function of the strain rate. The value of Hs is computed from Eq. (1) using the nominal 1 mN load value, and έ is computed using Eq. (2)
2.3. Analysis method The strain-rate sensitivity exponent (m) of strength (σ) provides information about the mode of deformation as seen in the onset of plasticity and/or the initiation of a flow stress. The exponent m is mathematically obtained from the power-law relationship of strength with strain rate (έ) as given by the Dorn equation (where β is a constant) as m
σ = β·έ :
ð3Þ
The effect of strain hardening is not generally considered [21] for ultra-fine grain nanocrystalline or amorphous solids since these materials do not show any evidence of dislocation generation and storage under plastic deformation. The strain-rate sensitivity exponent
Fig. 1. X-ray diffraction spectra of the sputter target material and a hydroxyapatite coating are shown as taken with Cu kα radiation in the θ/2θ mode.
1518
H.S.T. Ahmed, A.F. Jankowski / Thin Solid Films 520 (2011) 1516–1519
Fig. 2. A set of nanoscratches made with 1 mN normal load (P) at 1000 nm·sec−1 velocity (v) is imaged using the scanning probe mode of the NanoAnalyzer where the image field is 26 μm wide ∗ 6 μm deep ∗ 26 nm high.
with the measured w value as shown in Fig. 3. The nominal 1 mN load is used in the scratch analysis to avoid complications observed using the force feedback loop wherein tip chattering is occasionally seen during testing. The Fig. 4 data is plotted independent of the scratch width since strain hardening effects are not anticipated for the following reasons. The scratch test effectively shears the coating material at its surface. For normal indentation tests, progression of the indenter tip could produce an increase in the hardness for materials that do work harden, which would suggest that the rate sensitivity effect should then be considered for measurements made using similar amounts of deformation. For this situation, similar scratch widths would then be considered in the exponent analysis. However, since the HA coating structure is an ultra-fine grain nanocrystalline or amorphous solid (i.e. without a defined crystalline structure or a dislocation structure), the effects of work hardening on strength are not considered in the present analysis. Also, it is previously reported [9] that a near constant hardness is measured as a function of increasing indentation depth which suggests that the HA coating does not strain harden with increasing load. Thus, the strain rate sensitivity exponent of HA found when varying the speed of scratch testing in this experiment should not be subject to possible strain hardening effects. A fit of the Fig. 4 data using Eq. (5) shows that the strain-rate sensitivity exponent (m) of the HA coating is 0.199 with a high correlation coefficient (R2) of 0.9 for the 10−4–10−1 sec−1 έ range. This έ range spans the deformation region wherein solid solution and dislocation based processes are typical in crystalline solids. The hardness increases three-fold over this strain-rate range to values exceeding 8 GPa. Similar upper bound hardness values of 6–8 GPa were reported [9] for triboindentation tests. In general, similar values for m are reported [26] for fine-grain ceramic materials where the tensile elongation is shown to increase as a strong function of decreasing flow stress. The strain-rate-sensitivity exponent m is greater than 0.3 as the major deformation mechanism in tensile tests for creep fracture and ductility is associated with grain boundary sliding. Strain rate experiments conducted on human and bovine bones show [27] that
Fig. 3. Profiles are shown of nanoscratches made at 50, 100, and 1000 nm·sec−1 scratch velocities (v).
Fig. 4. The strain-rate sensitivity of scratch hardness (Hs) is plotted for the sputterdeposited hydroxyapatite coating as tested at various strain rates (έ).
the compressive strength was proportional to the square of apparent density and to the strain rate raised to the power (m) of 0.06. The compressive strength [25] of optimally sintered freeze-cast HA constructs was measured for constructs with 52% porosity as prepared from aqueous suspensions of 10–20 vol.% HA particles using a waterdioxane solvent. The strain rate sensitivity exponent m was 0.18–0.21 for testing parallel to the freezing direction for a strain rate range of 5.2 · 10 −5 to 5.2 · 10−3 sec−1. For έ N10−1 sec−1, there is an apparent change in the behavior of the HA coating where the value of m decreases to zero. The linear interpolation of the data in this έ range of Fig. 4 indicates a m value of −0.058 with a R2 of only 0.25. At these higher scratch strain rates, it appears that the HA-coating scratch hardness has reached a plateau value and then decreases, perhaps, to values of 6 GPa or less. There is generally a small amount of plastic deformation anticipated for ceramic materials at room temperature due to their intrinsic crystalline structure and chemical bonding. It appears that the change in m indicates a change in the deformation mechanism wherein the hardness becomes independent of strain rate. 4. Discussion The exponent (m) for the strain-rate sensitivity of strength is introduced in Section 2.3 with a standard mathematical representation in Eqs. (3) and (4). The exponent m is most often used to assess the potential for a “hard to machine” material [28] to undergo superplastic deformation as the strain rate increases. The analysis as presented in Section 2.3 assumes that the strain hardening effect on strength is minimal, i.e. a flow stress is manifest. Larger values for m are usually associated with delay to the onset of localized necking, hence, the potential for an increase of plastic deformation. For nanocrystalline ceramics with a limited number of available slip systems as tested at elevated temperatures, the introduction of grain boundary (sliding and rotation) deformation mechanisms should increase the amount of plastic deformation, hence, an increased value for the exponent m. For higher disordered structures, with a cellular structure, such as the “amorphous” HA coatings of this study, the deformation mechanism is not a dislocation dependent in the usual way. As tested at room temperature, the effect of strain rate on and the deformation of higher disordered structures with a cellular structure (as the “amorphous” HA coating) are not well understood with limited data available for analysis. Measurement of the strain-rate sensitivity of ceramic coatings is a challenging task. Complications arise with conventional tensile measurements, for example, when attempting to apply strain rates above ~ 10 −3 sec −1, even when tested at elevated temperature to ensure a ductile failure with some measure of plastic deformation.
H.S.T. Ahmed, A.F. Jankowski / Thin Solid Films 520 (2011) 1516–1519
Therefore, most testing for strain-rate sensitivity effects on strength in ceramic materials is usually conducted under compression at elevated temperatures. This test condition introduces the likelihood of dynamic recrystallization effects [28,29] at higher strain rates that lower the sensitivity to strength. The value of the present measurements is seen in several aspects. First, mechanical test measurements were obtained using a somewhat novel measurement approach in application, i.e. nano-scratch testing of ceramics to strain rates of 10 + 1 sec −1. Second, data was obtained for a ceramic material processed in a form (i.e. as a nanocrystalline or amorphous coating) suitable for use as a robust barrier in medical implants, with the needed highdimensional tolerances and acceptable mechanical properties. Also, the hardness of hydroxyapatite coatings above strain rates of 10−1 sec−1 is measured, perhaps, for the first time. Typical triboindentation effort techniques do not explore the high strain rates N10−2 sec −1 that are important for coating use in knee and hip joint replacement under dynamic (i.e. impact) loading conditions. Lastly, the leveling (or softening) of the hardness at strain rates above 10−1 sec −1 is a new result for hydroxyapatite (HA) coatings, as is the actual measurement of the strain-rate sensitivity exponent (m) to this transition point in strain-rate/deformation mechanism. The present measurement of an exponent of +0.199 for to strain rates up to 10−1 sec −1 is similar to the findings for other ceramic materials, thereby providing a satisfactory internal check for use of the nano-scratch method. The precise change in the deformation mechanism from below to above a strain rate of 10 −1 sec −1 is unknown. First, it appears that the “amorphous” HA coating tested at room temperature and lower strain rates behaves similar to crystalline ceramic counterparts (as tested at elevated temperatures) wherein the material demonstrates high strain rate sensitivity. This is likely due to the nature of the chemical bonding in the HA coating as opposed to details of crystalline structure, i.e. the lack of long-range order. For many ceramic systems, as is sometimes seen in metallic materials, the loss of superplasticity at high strain rates and elevated temperatures is attributed to dynamic recrystallization [28,29]. However, strain-rate induced crystallization of the amorphous hydroxyapatite coating to create a nanocrystalline structure would likely increase its hardness. However, micro-cracking through the micro-plasticity mechanism is suggested for loss in strength (and failure) in crystalline ceramics shock tested at high strain rates under compressive loading [30]. This mechanism produces a “morphological evolution of the plastic region with applied load that results in a highly nonlinear macroscopic response” with “plastic deformation at isolated locations” that can result in the decrease of spall strength with increased strain rate. 5. Conclusion Hydroxyapatite (HA) coatings were magnetron sputter deposited onto titanium-coated silicon wafers. Nanoscratch testing of a 0.65 μm
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thick HA coating was conducted to measure the scratch hardness (Hs). A variation in the scratch velocity induced a strain rate effect. The strain-rate sensitivity exponent (m) of Hs for the HA coating is found to be 0.199 for strain rates (έ) less than 10 −1 sec −1, which is consistent with the behavior of many other fine-grain ceramic materials. The strain rate sensitivity exponent drops to zero (or may become negative) for strain rates above 10 −1 sec −1 indicating an unresolved change in the deformation mechanism.
Acknowledgments This work was supported by a Terry and Linda Fuller TTU Foundation grant, and the J.W. Wright Endowment for Mechanical Engineering at Texas Tech University (TTU).
References [1] C.S. Chai, B. Ben-Nissan, J. Mater. Sci. Mater. Med. 10 (1999) 465. [2] M. Wei, A.J. Ruys, B.K. Milthorpe, C.C. Sorrell, J. Biomed. Res. 45 (1999) 11. [3] D. McConnell, Apatite: Its Crystal Chemistry, Mineralogy, Utilization and Biologic Occurrence, Springer-Verlag, Berlin, 1973. [4] A.S. Posner, A. Perloff, A.F. Diorio, Acta Cryst. 11 (1958) 308. [5] X.F. Xiao, R.F. Liu, Mater. Lett. 21–22 (2006) 2617. [6] H. Dasarathy, C. Riley, H. Coble, W. Lacefield, G. Maybee, J. Biomed. Mater. Res. 31 (1996) 81. [7] M. Hamdi, S. Hakamata, A.M. Ektessabi, Thin Solid Films 377–378 (2000) 484. [8] G.J. Cheng, D. Pirzada, M. Cai, P. Mohanty, A. Bandyopadhyay, Mater. Sci. Eng. C 25 (2005) 541. [9] T.G. Nieh, A.F. Jankowski, J. Koike, J. Mater. Res. 16 (2001) 3238. [10] J.G.C. Wolke, K. van Dijk, H.G. Schaeken, K. de Groot, J.A. Jensen, J. Biomed. Mater. Res. 28 (1994) 1477. [11] K. van Dijk, H.G. Schaeken, C.H.M. Maree, J. Verhoeven, J.G.C. Wolke, F.H.P.M. Habraken, J.A. Jensen, Surf. Coat. Technol. 76–77 (1995) 206. [12] K. van Dijk, H.G. Schaeken, J. Wolke, J.A. Jensen, Biomaterials 17 (1996) 405. [13] W. Weng, J.L. Baptista, J. Mater. Sci. Mater. Med. 9 (1998) 159. [14] D.M. Liu, H.M. Chaou, J.D. Wu, J. Mater. Sci. Mater. Med. 5 (1994) 147. [15] L. Sun, C.C. Berndt, K.A. Gross, A. Kucuk, J. Biomed. Mater. Res. 58 (2001) 570. [16] H. Liu, W. Jiang, A. Malshe, J. Met. Bull. 61 (9) (2009) 67. [17] K.M. Lee, C.-D. Yeo, A.A. Polycarpou, Exp. Mech. 47 (2007) 107. [18] N. Tayebi, T.F. Conry, A.A. Polycarpou, J. Mater. Res. 19 (2004) 3316. [19] N. Tayebi, A.A. Polycarpou, T.F. Conry, J. Mater. Res. 19 (2004) 1791. [20] N. Tayebi, T.F. Conry, A.A. Polycarpou, J. Mater. Res. 18 (2003) 2150. [21] M. Dao, L. Lu, R.J. Asaro, J.T.M. De Hosson, E. Ma, Acta Mater. 55 (2007) 4041. [22] P. Luo, T.G. Nieh, Biomaterials 17 (1996) 1959. [23] L.O. Nyakiti, A.F. Jankowski, Metall. Mater. Trans. 41A (2010) 838. [24] J.T. Burwell, C.D. Strang, Proc. R. Soc. Lond. A Math. Phys. Sci. 212 (1952) 470. [25] Q. Fu, M.N. Rahaman, F. Dogan, B.S. Bal, J. Biomed. Mater. Res. B Appl. Biomater. 86 (2008) 514. [26] W.-J. Kim, Met. Mater. 1 (2) (1995) 117. [27] D.R. Carter, W.C. Hayes, Science 194 (1976) 1174. [28] T.R. Bieler, R.S. Mishra, A.K. Mukherjee, Ann. Rev. Mater. Sci. 26 (1996) 75. [29] G.-D. Zhan, J.D. Kuntz, J. Wan, A.K. Mukherjee, Mater. Res. Soc. Symp. Proc. 740 (2003) 41. [30] K.S. Zhang, M.S. Wu, R. Feng, Int. J. Plast. 21 (2005) 801.
Contents lists available at ScienceDirect
Thin Solid Films j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / t s f
Strain rate sensitivity of hydroxyapatite coatings H.S. Tanvir Ahmed, Alan F. Jankowski ⁎ Texas Tech University, Mechanical Engineering, Box 41021, Lubbock, TX 79409 USA
a r t i c l e
i n f o
Available online 13 June 2011 Keywords: Hydroxyapatite Coatings Strain rate sensitivity Scratch hardness
a b s t r a c t The strain-rate sensitivity of strength is a significant factor to evaluate the deformation mode of crystalline materials. The strain rate sensitivity of hardness is experimentally investigated here for hydroxyapatite coatings that are sputter deposited onto titanium-coated silicon wafers. These biocompatible HA coatings can provide a strong, dense interface between metal alloy implants and porous hydroxyapatite that can help ingrowth of tissue. The interface to the metal alloy implant is important to transfer stress during loading. So, it is very important to know the behavior of the coating under different conditions of loading. Our dynamic test procedure now takes advantage of nanoscratch testing to measure the change in scratch hardness of the coating over a strain rate range that may well simulate the mechanical loading conditions found at the interface between implants and hydroxyapatite coatings. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Hydroxyapatite Ca10((PO)4)6(OH)2 coatings are widely used on both bone and tooth implants due to its similar chemical composition to natural bone. Orthopedic and dental implants are mostly bio-inert metal alloys and do not offer a good chemical bond to bone as hydroxyapatite (HA) does [1]. Also, porous HA coatings are known to promote bone regeneration [2]. The ideal Ca/P ratio in the HA structure is reported to be 1.67, with a density of the structure being 3.219 g/cm 3 [3]. A hexagonal crystal for HA is reported [4] with lattice parameters a equal to 0.9432 nm and c equal to 0.6881 nm. Today, commercial methods that are used to deposit HA on metal implants include electrophoretic deposition [2,4–6], vapor deposition [7], magnetron sputtering [8–12], dip coating [13], spin coating and plasma spray [14,15]. In these approaches, fabrication of the HA coating with desirable functional properties is challenging [16]. For this purpose, it is necessary to measure the properties of the coatings with techniques that involve fewer underlying assumptions and that reliably reproduce experimental results. Dynamic nanoindentation, i.e. triboindentation, or nanoscratch techniques have evolved as a suitable method of mechanical property measurement of thin coatings as shown by many researchers [17–20]. By varying the scratch velocity, the material surface can be subjected to different strain rates that can simulate the loading rate behavior of the coating as subjected to real-life situations as, e.g., walking to jumping. The strength behavior at different loading rates, i.e. the strain rate sensitivity of strength, is a key parameter to understand the deformation mechanism to the onset and extent of plastic deforma-
⁎ Corresponding author. Tel.: + 1 806 742 3563; fax: + 1 806 742 3540. E-mail address: [email protected] (A.F. Jankowski). 0040-6090/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2011.06.004
tion. It is widely reported [21] that some materials strengthen with increasing strain rate. For example, an increase in strain-rate sensitivity exponent (m) that is measured for several face-centercubic (fcc) metals (as the grain size decreases from the macro- to micro- to nano- scale) provides detail to interpret the mode of mechanical deformation. In this study, time dependent nanoscratch technique has been employed to extract the strain rate sensitivity of strength of the HA coating which would provide important insight to the mechanical responses of such coatings.
2. Experimental methods 2.1. Sample preparation The concept of a graded HA coating is reported [9] in the literature where the coating is: fully dense at the implant-coating interface; and has a gradually increasing porosity towards a value of ~ 50% at the muscle-coating surface. In this study, the coating investigated represents the fully dense structure at the implant-coating interface. These HA coatings were prepared by sputter deposition using planar magnetrons operated in the radio frequency (rf) mode as described [9] elsewhere. The HA target used in the sputter deposition process was produced by hot-pressing HA powders prepared into a right circular cylindrical disk. The powders were prepared by a precipitation [22] method in air at high temperature of 1300 °C. The fine grain structure of the HA target is reported [9] as 99.7% dense with small pores distributed primarily along grain boundaries and triple junctions. The target-material two-phase structure [9,22] contains less than 5% of tri-calcium phosphate in addition to HA as would be expected since apatite is essentially a line compound, and is very difficult to obtain in the pure form.
H.S.T. Ahmed, A.F. Jankowski / Thin Solid Films 520 (2011) 1516–1519
The substrates for the HA deposition are polished, single crystal Si (111) wafers. In some samples, the silicon wafers are first pre-coated with a 1.0 μm thick layer of 99.94% pure titanium (Ti). The 0.65 μm thick HA coatings are sputter deposited [9] onto the Ti-coated Si wafers at a forward power of 75 W using a 1.3 Pa working gas pressure of argon at a 40 cm 3-min −1 flow rate. In preliminary characterization of the coating structure, transmission electron microscopy images reveal [9] the cross-section of the coating to be fully dense. A Rigaku Miniflex II X-ray diffractometer operated in the θ/2θ mode with 30 kV–15 mA Cu kα radiation will be used to assess the crystalline structure of the coating. 2.2. Mechanical testing The nanoscratch test method utilizes a diamond stylus to scratch the coating surface. The resulting scratch width is used to determine the scratch hardness (Hs). A NanoAnalyzer test module is mounted into a CETR (Center for Tribology Inc., Campbell, CA USA) universal mechanical tester (UMT) platform. Scratches on the HA surface are made using a cantilever mounted stylus that is a Berkovitch diamondindenter tip. Also, this same probe is used to scan the surface for imaging the scratch width and depth. Typical values for the scratches are 2 · 10 2–1 · 10 3 nm in width and 10 1 nm in depth. The well-known expression [e.g. 23] for scratch hardness (Hs) as a function of the scratch width (w) and the indent load (N) is given as 2
Hs = c·N = w :
ð1Þ
The geometric constant (c) is specific to the indenter tip shape. For example, if the indentation scratch does not extend beyond the initial hemispherical regime of the indenter tip, then the constant c equals 8/π. This value is readily derived for a projection of the leading half of the hemispherical tip. Therefore, the scratch loads are selected to produce scratches that will not extend in width beyond ~5 · 10 2 nm, i.e. an approximate equivalent to the hemispherical projection of the indenter tip. The actual scratch-load can be measured using a realtime force feedback transducer. The strain-rate (έ) is varied by changing the nanoscratch velocity (v) where the empirical formula [23] for έ as a function of v and the scratch width (w) is given as
έ = v·w
−1
:
ð2Þ
A nominal indent load (N) of 1.0 mN is applied for the nanoscratch hardness testing where the scratch velocity (v) is varied from 10 1 to 10 4 nm sec -1. At least three different scratches are made at each velocity.
1517
m for strength is determined from the slope to a linear fit for the log–log scale plot of strength (σ) versus strain rate (έ), as m = δ lnðσ Þ = δ lnðέÞ:
ð4Þ
For the scratch test method [23], the scratch hardness (Hs) can be substituted into Eq. (4) in place of the strength (σ) as m = δ lnðHs Þ = δ lnðέÞ:
ð5Þ
The onset of plastic flow that occurs during scratch hardness testing provides a measurement to quantify strength where the strength is approximately [24] one-third the hardness. Therefore, the slope of the log–log scale variation of strain rate (έ) versus scratch hardness (Hs) can be used to measure the strain-rate exponent (m). 3. Results and analysis The X-ray diffraction spectra of the target material and a sputter deposited HA coating are shown in Fig. 1. The Miller indices of the major Bragg reflections for the HA target material are labeled that correspond with the standard peak positions reported [4,16,25] for HA. The relative intensity of the Bragg peaks, i.e. texture, for the target pattern is a good match with results recently reported [16] for microwave sintered material. Additional unlabeled peaks for the target scan as, e.g., the 2θ reflection at 37.80° are likely to correspond with the aforementioned second phase(s) such as tri-calcium phosphate (or, perhaps, calcium oxide). The HA coatings (on the silicon wafers for mechanical property assessment) may be amorphous since no distinct Bragg reflections are seen in the Fig. 1 X-ray diffraction scan. Cross-section traces of the nanoscratches are measured with the NanoAnalyzer operated in its scanning probe microscopy (SPM) mode. Each scratch is measured at five (or more) different locations to achieve a high statistical average of the scratch width (w). Threedimensional SPM images of three parallel nanoscratches that were made using a 1 mN indenter load at a 1000 nm sec −1 scratch velocity are shown in Fig. 2. The profiles of several linear traces across nanoscratches made at 50, 100, and 1000 nm sec −1 scratch velocities are shown in Fig. 3. In all, nanoscratches made using the various indenter tip velocities (v) at 1 mN load produce a range of scratch width that varies from 580 to 830 nm, which is less than the ~ 1 μm indenter tip diameter. The scratch hardness (Hs) of the HA coating is plotted in Fig. 4 as a function of the strain rate. The value of Hs is computed from Eq. (1) using the nominal 1 mN load value, and έ is computed using Eq. (2)
2.3. Analysis method The strain-rate sensitivity exponent (m) of strength (σ) provides information about the mode of deformation as seen in the onset of plasticity and/or the initiation of a flow stress. The exponent m is mathematically obtained from the power-law relationship of strength with strain rate (έ) as given by the Dorn equation (where β is a constant) as m
σ = β·έ :
ð3Þ
The effect of strain hardening is not generally considered [21] for ultra-fine grain nanocrystalline or amorphous solids since these materials do not show any evidence of dislocation generation and storage under plastic deformation. The strain-rate sensitivity exponent
Fig. 1. X-ray diffraction spectra of the sputter target material and a hydroxyapatite coating are shown as taken with Cu kα radiation in the θ/2θ mode.
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Fig. 2. A set of nanoscratches made with 1 mN normal load (P) at 1000 nm·sec−1 velocity (v) is imaged using the scanning probe mode of the NanoAnalyzer where the image field is 26 μm wide ∗ 6 μm deep ∗ 26 nm high.
with the measured w value as shown in Fig. 3. The nominal 1 mN load is used in the scratch analysis to avoid complications observed using the force feedback loop wherein tip chattering is occasionally seen during testing. The Fig. 4 data is plotted independent of the scratch width since strain hardening effects are not anticipated for the following reasons. The scratch test effectively shears the coating material at its surface. For normal indentation tests, progression of the indenter tip could produce an increase in the hardness for materials that do work harden, which would suggest that the rate sensitivity effect should then be considered for measurements made using similar amounts of deformation. For this situation, similar scratch widths would then be considered in the exponent analysis. However, since the HA coating structure is an ultra-fine grain nanocrystalline or amorphous solid (i.e. without a defined crystalline structure or a dislocation structure), the effects of work hardening on strength are not considered in the present analysis. Also, it is previously reported [9] that a near constant hardness is measured as a function of increasing indentation depth which suggests that the HA coating does not strain harden with increasing load. Thus, the strain rate sensitivity exponent of HA found when varying the speed of scratch testing in this experiment should not be subject to possible strain hardening effects. A fit of the Fig. 4 data using Eq. (5) shows that the strain-rate sensitivity exponent (m) of the HA coating is 0.199 with a high correlation coefficient (R2) of 0.9 for the 10−4–10−1 sec−1 έ range. This έ range spans the deformation region wherein solid solution and dislocation based processes are typical in crystalline solids. The hardness increases three-fold over this strain-rate range to values exceeding 8 GPa. Similar upper bound hardness values of 6–8 GPa were reported [9] for triboindentation tests. In general, similar values for m are reported [26] for fine-grain ceramic materials where the tensile elongation is shown to increase as a strong function of decreasing flow stress. The strain-rate-sensitivity exponent m is greater than 0.3 as the major deformation mechanism in tensile tests for creep fracture and ductility is associated with grain boundary sliding. Strain rate experiments conducted on human and bovine bones show [27] that
Fig. 3. Profiles are shown of nanoscratches made at 50, 100, and 1000 nm·sec−1 scratch velocities (v).
Fig. 4. The strain-rate sensitivity of scratch hardness (Hs) is plotted for the sputterdeposited hydroxyapatite coating as tested at various strain rates (έ).
the compressive strength was proportional to the square of apparent density and to the strain rate raised to the power (m) of 0.06. The compressive strength [25] of optimally sintered freeze-cast HA constructs was measured for constructs with 52% porosity as prepared from aqueous suspensions of 10–20 vol.% HA particles using a waterdioxane solvent. The strain rate sensitivity exponent m was 0.18–0.21 for testing parallel to the freezing direction for a strain rate range of 5.2 · 10 −5 to 5.2 · 10−3 sec−1. For έ N10−1 sec−1, there is an apparent change in the behavior of the HA coating where the value of m decreases to zero. The linear interpolation of the data in this έ range of Fig. 4 indicates a m value of −0.058 with a R2 of only 0.25. At these higher scratch strain rates, it appears that the HA-coating scratch hardness has reached a plateau value and then decreases, perhaps, to values of 6 GPa or less. There is generally a small amount of plastic deformation anticipated for ceramic materials at room temperature due to their intrinsic crystalline structure and chemical bonding. It appears that the change in m indicates a change in the deformation mechanism wherein the hardness becomes independent of strain rate. 4. Discussion The exponent (m) for the strain-rate sensitivity of strength is introduced in Section 2.3 with a standard mathematical representation in Eqs. (3) and (4). The exponent m is most often used to assess the potential for a “hard to machine” material [28] to undergo superplastic deformation as the strain rate increases. The analysis as presented in Section 2.3 assumes that the strain hardening effect on strength is minimal, i.e. a flow stress is manifest. Larger values for m are usually associated with delay to the onset of localized necking, hence, the potential for an increase of plastic deformation. For nanocrystalline ceramics with a limited number of available slip systems as tested at elevated temperatures, the introduction of grain boundary (sliding and rotation) deformation mechanisms should increase the amount of plastic deformation, hence, an increased value for the exponent m. For higher disordered structures, with a cellular structure, such as the “amorphous” HA coatings of this study, the deformation mechanism is not a dislocation dependent in the usual way. As tested at room temperature, the effect of strain rate on and the deformation of higher disordered structures with a cellular structure (as the “amorphous” HA coating) are not well understood with limited data available for analysis. Measurement of the strain-rate sensitivity of ceramic coatings is a challenging task. Complications arise with conventional tensile measurements, for example, when attempting to apply strain rates above ~ 10 −3 sec −1, even when tested at elevated temperature to ensure a ductile failure with some measure of plastic deformation.
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Therefore, most testing for strain-rate sensitivity effects on strength in ceramic materials is usually conducted under compression at elevated temperatures. This test condition introduces the likelihood of dynamic recrystallization effects [28,29] at higher strain rates that lower the sensitivity to strength. The value of the present measurements is seen in several aspects. First, mechanical test measurements were obtained using a somewhat novel measurement approach in application, i.e. nano-scratch testing of ceramics to strain rates of 10 + 1 sec −1. Second, data was obtained for a ceramic material processed in a form (i.e. as a nanocrystalline or amorphous coating) suitable for use as a robust barrier in medical implants, with the needed highdimensional tolerances and acceptable mechanical properties. Also, the hardness of hydroxyapatite coatings above strain rates of 10−1 sec−1 is measured, perhaps, for the first time. Typical triboindentation effort techniques do not explore the high strain rates N10−2 sec −1 that are important for coating use in knee and hip joint replacement under dynamic (i.e. impact) loading conditions. Lastly, the leveling (or softening) of the hardness at strain rates above 10−1 sec −1 is a new result for hydroxyapatite (HA) coatings, as is the actual measurement of the strain-rate sensitivity exponent (m) to this transition point in strain-rate/deformation mechanism. The present measurement of an exponent of +0.199 for to strain rates up to 10−1 sec −1 is similar to the findings for other ceramic materials, thereby providing a satisfactory internal check for use of the nano-scratch method. The precise change in the deformation mechanism from below to above a strain rate of 10 −1 sec −1 is unknown. First, it appears that the “amorphous” HA coating tested at room temperature and lower strain rates behaves similar to crystalline ceramic counterparts (as tested at elevated temperatures) wherein the material demonstrates high strain rate sensitivity. This is likely due to the nature of the chemical bonding in the HA coating as opposed to details of crystalline structure, i.e. the lack of long-range order. For many ceramic systems, as is sometimes seen in metallic materials, the loss of superplasticity at high strain rates and elevated temperatures is attributed to dynamic recrystallization [28,29]. However, strain-rate induced crystallization of the amorphous hydroxyapatite coating to create a nanocrystalline structure would likely increase its hardness. However, micro-cracking through the micro-plasticity mechanism is suggested for loss in strength (and failure) in crystalline ceramics shock tested at high strain rates under compressive loading [30]. This mechanism produces a “morphological evolution of the plastic region with applied load that results in a highly nonlinear macroscopic response” with “plastic deformation at isolated locations” that can result in the decrease of spall strength with increased strain rate. 5. Conclusion Hydroxyapatite (HA) coatings were magnetron sputter deposited onto titanium-coated silicon wafers. Nanoscratch testing of a 0.65 μm
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thick HA coating was conducted to measure the scratch hardness (Hs). A variation in the scratch velocity induced a strain rate effect. The strain-rate sensitivity exponent (m) of Hs for the HA coating is found to be 0.199 for strain rates (έ) less than 10 −1 sec −1, which is consistent with the behavior of many other fine-grain ceramic materials. The strain rate sensitivity exponent drops to zero (or may become negative) for strain rates above 10 −1 sec −1 indicating an unresolved change in the deformation mechanism.
Acknowledgments This work was supported by a Terry and Linda Fuller TTU Foundation grant, and the J.W. Wright Endowment for Mechanical Engineering at Texas Tech University (TTU).
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