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Elastic modulus, indentation pressure and fracture toughness of hybrid coatings on glass
Thin Solid Films 366 (2000) 139±149 www.elsevier.com/locate/tsf
Elastic modulus, indentation pressure and fracture toughness of hybrid coatings on glass J. Malzbender a,*, G. de With a, J.M.J. den Toonder b a
Laboratory of Solid State and Materials Chemistry, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands b Philips Research Laboratories, Prof. Holstlaan 4, 5656 AA Eindhoven, The Netherlands Received 30 April 1999; received in revised form 13 December 1999; accepted 13 December 1999
Abstract The indentation load-displacement behavior of an organic-inorganic hybrid coating was tested using a Berkovich indenter in an attempt to offer a simple and fast method to analyze the mechanical properties of a coating. The coatings were deposited using a spin-coating technique. The elastic modulus and the indentation pressure as a measure of the hardness were determined on the basis of the load-displacement curve. The effects of the coating thickness and the coating preparation conditions were investigated. Cracks, delamination and chipping were observed and were used to assess the fracture toughness of the coating and the interface. Elastic modulus, indentation pressure and the fracture toughness were dependent on the time elapsed before application of the coating ¯uid and on the curing temperature. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Coatings; Elastic properties; Hardness; Stress
1. Introduction The main reason for applying coatings on glass is to modify the functional behavior of the glass, i.e. to introduce an anti-glare, anti-re¯ex, or anti-static layer or to realize changes in dielectric or transmission properties. A second reason is to strengthen the glass substrate and protect it from environmental in¯uences such as particle impact or moisture [1±3]. For these purposes inorganic or hybrid, i.e. combined inorganic/organic, coatings can be used [4,5]. One method to prepare the coatings is the sol±gel process, which is described elsewhere [6]. The process requires a ®nal curing, which results in shrinkage of the coating and can produce a tensile stress [7]. The probability of cracking in the coating usually increases with thickness and, therefore, non-cracked coatings have a critical thickness [6]. An increase in this critical thickness has been realized by adding silica particles [8]. Whatever the main reason for applying a coating, mechanical aspects are almost always important. Indentation testing is widely used to characterize the mechanical properties of coatings [9,10]. This technique can be used to estimate the indentation pressure and the elastic modulus of * Corresponding author. Tel.: 1 31-40-247-3059; fax: 1 31-40-2445619. E-mail address: [email protected] (J. Malzbender)
a coating [11±15]. Also, by analyzing cracks in the surface resulting from indentations, the fracture toughness of the coating can be estimated [16]. The present paper presents the results of indentation experiments on a hybrid coating. In these experiments the indentation pressure as a measure of the coating hardness, the elastic modulus, the fracture toughness of coating and interface and the residual stress in the coating were estimated and the dependence of these parameters on preparation conditions was studied. The main advantage of the current approach is that three different phenomena, which can be found during one experiment, were used to assess the fracture toughness of the coating and the interface. 2. Experimental The experiments were carried out using ¯oat glass that was coated with an organic-inorganic hybrid coating. The coating ¯uid contained approximately 30% (weight) solid components, being equal weight amounts of methyltrimethoxysilane (MTMS) and colloidal silica (average particle size 20 nm), and 70% solvents (2% water, 32% methanol, 1% propanol, 35% glycol). In order to increase the stiffness of the coating, 1 wt.% tetraethylorthosilicate (TEOS) was added. The coating ¯uid was allowed for to pre-react for a time of 60 or 240 min. Although hydrolysis of
0040-6090/00/$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. PII: S 0040-609 0(00)00656-8
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the solution took place during this period, the term prereaction time will be used in the following sections since an evaporation of solvents might have occurred. The rectangular glass substrates of 100 cm 2 were 0.2 cm thick. The substrates were cleaned by scrubbing for 2 min using an alkaline soap solution. The soap was removed using ¯owing water. The glass substrates were then immersed in demineralized water for 1 h and subsequently dried using nitrogen gas. The coating ¯uid was ®ltered through a 5 mm Millipore q ®lter before it was applied to the substrate to eliminate any dust particles. The coatings were applied by spinning at speeds between 100 and 2500 rev./min in a closed spinner. The closed spinner con®guration allowed more homogeneous coatings to be applied. After spinning, the coatings were dried by heating them on a hot plate at 1008C for 1 min. The coatings were then cured at 250 or 4008C for 18 h. The resulting coating layer thickness was between 3 and 20 mm. The coated glass plates were cut into smaller samples for the experiments. Indentation experiments were carried out at room temperature and ambient atmosphere using a home-built instrument. The minimum load that can be applied is 2 mN and is limited by the background noise level that is related to thermal and electronic drift phenomena. The instrument operates in a displacement-controlled mode. A loading rate of 10 nm/s was used in the experiments. The apparatus permitted up to 25 indentations to be made in one run at loads ranging from 0 to 1000 mN. A Berkovich-type indenter was used. The calibration procedure suggested by Oliver and Pharr [17] was used to correct for the load frame compliance of the apparatus and the imperfect shape of the indenter tip [18]. The area function of this indenter was calibrated using B270 glass, whose elastic modulus was determined independently using the pulse-echo method. The compliance of the system was 300 ^ 10 nm/N and the projected area of the indenter, A, was related to the contact depth, hc, of the indentation by A ahc 2 1 bhc (a 24:5 ^ 0:5 and b 5:71 ^ 0:09 mm). This plastic contact area was calculated using the slope of the unloading curve according to the method suggested by Oliver and Pharr [17]. The area function corresponds to an ideal Berkovich indenter with a tip radius of approximately 0.9 mm. The calibration was performed for a depth range of 0.1 to 2.9 mm, corresponding to a load range of 5 to 1000 mN, where the maximum indentation depth was restricted by the load limitation. The load-displacement curves were analyzed using the method proposed by Oliver and Pharr [17], yielding the elastic moduli and the indentation pressure
3. Results and discussion In this section the results obtained are given, described with reference to models, which are derived in the subse-
quent sections or the relevant literature, and discussed in comparison to observations made elsewhere. 3.1. General observations During the indentation of the coatings, various phenomena were observed, which will be illustrated by means of a typical indentation load-displacement curve, as shown in Fig. 1 along with the optical micrographs of the indentation marks. Changes in the load-displacement curve can be correlated with cracking occurring in the coating and at the coatingsubstrate interface. In the ®rst place a distinct change is observable in the slope of the load-displacement curve at a load of approximately 30 mN (Fig. 1a), which is related to the onset of radial cracking in the coating (Fig. 1a). These radial cracks were found to grow with increasing load (Fig. 1b,c), but this caused no further signi®cant changes in the load-displacement curve. The load at which the radial cracking started turned was found to be independent of the coating thickness. At higher loads the coating fractured between the radial cracks (Fig. 2a,b). The cracks appearing at this point will be referred to as `annular cracks'. At even higher loads delamination at the interface occurred (Fig. 1c). There is no relation between the formation of annular cracks or delamination and features in the loading or unloading curve. A connection with the surface cracks is strongly suggested by the observations that the delaminated areas were limited by the surface cracks and that delamination occasionally occurred only between some of the cracks of a particular indent. Chipping of coating material was observed (Fig. 1d) at higher loads, for this particular example approximately at 200 mN, which resulted in more abrupt changes in the load displacement curve (Fig. 1d). The critical load at which this phenomenon was observed depended on the coating layer thickness. The coating was resistant to extensive plastic ¯ow due to the high H/E- ratio (see Sections 3.2 and 3.3). In situ observation of the crack formation using a microscope positioned directly under a Vickers indenter con®rmed that radial cracks, delamination and chipping formed during the loading. In summary, many different phenomena occurred in our coatings as a result of the indentation: radial cracking, annular cracking, delamination and chipping. In the following we will focus on extracting information on coating properties from the observed phenomena and the indentation loaddisplacement curve. 3.2. Indentation pressure The hardness of the coating was computed on the basis of the measured load-displacement curve according to the method outlined by Oliver and Pharr [17] using the equation H P=A
1
where A is the projected area of contact between the inden-
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141
ter and substrate at load P (see experimental, Section 2). Again, the plastic contact area A was calculated using the slope of the unloading curve according to the method suggested by Oliver and Pharr [17]. In the current investigation the measured effective hardness was in¯uenced by materials inhomogeneities in the form of a surface layer and by cracking of the coating. Since the effective hardness is a measure of the pressure under the indenter, the phrase indentation pressure will be used in the following. Typical results obtained for the indentation pressure as a function of contact indentation depth are shown in Figs. 3 and 4. There are two remarkable effects to be noted in these plots. First, the indentation pressure exhibits a maximum at the surface. At deeper indentation this value decreases to become a constant value referred to as `main' coating indentation pressure, Hf (see Table 1). Second, with increasing penetration depth, the indentation pressure shows no tendency towards the hardness value measured for the glass substrate, for which we independently determined H 6:0 ^ 0:5 GPa. These effects will be discussed below. The hardness of the glass substrate was determined at loads varying from 5 to 1000 mN using the procedure outlined at the beginning of Section 3.2. Since the contact depth was tenth of micrometers or more the effect of adsorbed water on the hardness should be negligible. The `main' coating indentation pressure appeared to increase with the curing temperature for a longer prereacted coating (Table 1). Neither the `main' coating indentation pressure nor the peak in the indentation pressure at the surface showed any dependence on ®lm thickness. A longer pre-reaction time or a lower curing temperature resulted in a larger extent of the pressure peak into the material. It has been suggested that a peak of the hardness near the surface does not necessarily represent a materials property, but is attributable to an `indentation size effect' [19]. Any connection to the indenter shape can be ruled out since, ®rst, the data have been corrected for the imperfect indenter shape (Section 2) and, second, the depth of this maximum depended on the preparation conditions. A more plausible explanation in this experiment appears to be the presence of a top layer of a different nature. This layer might be the result of oxidation or transport of solvents in the ®lm. This explanation is supported by the data presented in Fig. 5, which shows the indentation pressure data measured immediately after preparation and again in the same specimen after 46 days. In the latter case the indentation pressure pro®le is virtually ¯at. Since the crack length at a particular load was not altered, for the aged coating as compared with the fresh coating, a connecFig. 1. Indentations into a 3 mm thick coating cured at 2508C after a prereaction time of 1 h. Shown are the load- displacement curves along with the images observed using optical microscopy at loads of (a) 30 mN (b) 50 mN (c) 100 mN and (d) 250 mN.
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Fig. 3. Indentation pressure versus contact depth of a coating cured at 2508C after a pre-reaction of 3.5 h. The coating was 11.5 mm thick (see Figs. 7 and 8 for the elastic modulus). The line represents a guide for the eye.
Fig. 2. AFM images of indentation at a load of 200 mN into a 4.5 mm thick coating cured at 4008C (pre-reaction time 1 h) showing radial and annular cracking. Deformations inside the radial crack in image (b) are due to closure of the crack after unloading.
tion between indentation pressure maximum or the `main' indentation pressure and cracking of the coating can be ruled out. Furthermore, the decrease of the maximum near the surface in Fig. 3 started at loads at which no crack related features were visible. It is therefore suggested that the initially measured surface indentation pressure is related to a change in the materials properties due to in-diffusion of water. Aged coatings were found to show a higher OH concentration near the surface. The observed increase of the hardness for shallow indentations might be seen in conjunction with calculations performed by Begley and Hutchinson [20] on the mechanics
of size-dependent indentation. According to their calculations the relative plastic zone size is larger for smaller indents as compared to larger indents. This effect should be reduced for harder materials [20]. Thus the calibration of the indenter using glass, which has a signi®cantly larger hardness than the coating, did not show this effect. Especially the coatings cured at a lower temperature, which have a low `main' indentation pressure, possessed a larger relative plastic zone size for shallow indentations than the value determined from the calibration curve. This led to an overestimation of the near surface indentation pressure. The reduction of the surface peak for aged coatings suggests a change in the materials properties. The fact that the indentation pressure does not show the expected trend towards the glass substrate hardness in the case of deeper indentations (Figs. 3 and 4) can be attributed to the in¯uence of coating fracture on the indentation pressure. It was shown in Section 3.1 that the coatings showed radial cracks at an indentation load of approximately 30 mN, which corresponded to a contact depth of 0.7 to 0.9 mm. It is known that cracks in a coating decrease the measured effective hardness [21].
Fig. 4. Indentation pressure versus contact depth measured for a 11 mm thick coating cured at 4008C after a pre-reaction time of 3.5 h. The line represents a guide for the eye.
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Table 1 Indentation pressure parameters, fracture toughness and residual stress
s (Mpa) (^3)
Curing temperature (8C)
Pre-reaction (h)
Hf (GPa) (^0.05)
Fracture toughness determined using Radial Cracks KIC (MPa m 0.5) (^0.05)
Chipping KIC a (MPa m 0.5) (^0.05)
Delamination KIC (MPa m 0.5) (^0.05)
250 250 400 400
1 3.5 1 3.5
1.25 1.2 1.2 1.5
0.23 0.14 0.19 0.16
0.19 ±b 0.21 ±b
0.21 0.14 0.17 0.17
b a
25 12 13 0
Samples were not analyzed using this method. p Measured values were divided by 2.
3.3. Elastic modulus The elastic moduli of the coatings as a function of indentation depth were calculated using the unloading curves, on the basis of the procedure suggested by Oliver and Pharr [17]. Two different equations have been proposed to express the elastic modulus of a coating substrate combination, i.e. the model by Gao et al. [22] and Doerner and Nix [23]. The Gao [22] the Doerner and Nix [23] model considers only elastic deformation. Nevertheless, both models are widely used to deconvolute indentation data. First, Gao et al. [22] used a moduli - perturbation analysis to derive a relationship for the elastic modulus of a coated material which can be simpli®ed for materials with similar Poisson ratios to E Es 1 Ef 2 Es fG
2
where Ef and Es are the elastic moduli of the ®lm and the substrate, respectively, and f G is a weight function expressed by
fG
2 1 1 parctank 2p 1 2 n " ! # 1 1 k2 k 2 £ 1 2 2nkln k2 1 1 k2
1 1 2 n2 1 1 n2i 1 E Ei E*
6
where E and n represent the materials elastic modulus and Poisson's ratio and the suf®x i refers to the parameters of the indenter (diamond: Ei 1140 GPa, ni 0:07 [17]). The elastic modulus of the substrate (approximately 70 GPa) was measured in a separate experiment using uncoated glass and was used as a ®xed parameter in the ®tting process. A typical ®t obtained using the Doerner and Nix's model [23] is shown in Fig. 6. Fig. 7 shows a ®t obtained using the simpli®ed Gao [22] expression (Eq. (3)). The function derived by Gao [22] led to a value of the elastic modulus of approximately 8 GPa as compared to 10 GPa for the Doerner and Nix [23] model. The three parameter function suggested by Doerner and Nix [23] described the nearsurface data of the elastic moduli better than Gao's two parameter model [22]. The former was therefore used to estimate the modulus of the coating. The elastic modulus of the coating was found to be equal to 10 ^ 1 GPa, irrespective of the preparation conditions. It is not surprising that the function derived by Gao [22] led to lower values of
3
where k h=a expresses the ratio of the coating thickness, h, and the contact radius, a, and n is the Poisson's ratio. Second, Doerner and Nix [23] proposed on the basis of experimental results for the composite modulus of a ®lm and its substrate a function of the form 1=E* 1=Ef FDN 1 1=Es 1 2 FDN
4
The parameter F DN is a weight function de®ned as
FDN 1 2 e2bh=x
5
where b is a constant and h/x is the ratio of thickness, h, and contact indentation depth, x, and E* is the reduced elastic modulus, given by
Fig. 5. Comparison of the indentation pressure versus contact depth of a coating cured at 2508C after a pre-reaction time of 1 h. The stars represent the data obtained one week after the preparation; the diamonds represent the measurement after 46 days. The layer was 9.5 mm thick. The lines represent a guide for the eye.
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Fig. 6. Effective elastic modulus of a coating cured at 2508C after a prereaction of 3.5 h. The coating was 11.5 mm thick. The line is a ®t to the Doerner and Nix model [23].
Fig. 8. Pre-exponential factor b for coatings cured at 2508C after 3.5 h prereaction and 4008C after 1 or 3.5 h 0 pre-reaction. The dashed line represents a guide of the eye.
the elastic modulus, since his derivation was based on a ¯at punch. The use of a spherical or conical indenter leads to the measurement of an average modulus, since these styluses measure the unloading compliance at different depths simultaneously. The value of ®tting constant b , on the other hand, seems to depend on the coating thickness. Generally, b was found to be greater for thicker coatings (Fig. 8), suggesting a dependence of the materials properties on the thickness of the coating. The function suggested by Gao [22] showed a similar dependency of the ®tted function on the layer thickness. Calculations indicated that a spin rate effect on the particle distribution can be ruled out in the case of the spin rates used in the experiments (100±2500 rev./min) [20]. It is reasonable to assume that the change in the dependency of the elastic modulus on the coating thickness could be attributed to the inadequacy of the relatively simple ®tting routine suggested by Doerner and Nix [23] or to the increased uncertainty of Gao's [22] function for large differences in coating and substrate moduli and thin coatings. Alternatively, the in¯uence of the cracking and delamination and the increased energy dissipation in these processes for thin coatings might be responsible for the observed behavior.
Gao [22] has shown through ®nite element simulation that interfacial delamination can modify the contact compliance. This was also remarked by Wu et al. [24] for delamination and cracking normal to the interface. The elastic modulus is measured from the start of the unloading curve. At this moment the thickness of the coating is smaller than its original value, since the coating became thinner due to plastic ¯ow during loading and the coating is compressed elastically [25]. This effect will in¯uenced thinner coatings to a much stronger extent than thicker coatings. A combination of the above effects results in the observed dependency of b on the coating layer thickness. In the present experiment, the elastic modulus of the coatings was obtained from the smallest indentation depths, which were not in¯uenced by the cracking of the coating that took place at higher loads. Our samples did not show signs of pile-up after the indentation as observed using AFM, although generally pile-up can be expected for soft ®lms [24]. Annular cracking was observed before pile-up could become signi®cant. Comparison of the elastic modulus with the indentation pressure results shows that the elastic modulus curves do not exhibit any maximum near the surface. Obviously, a thin surface layer of a high indentation pressure has no in¯uence on the unloading compliance, which was used to estimate the elastic modulus [17]. The elastic modulus depends on the response of the indented body as a whole, whereas the indentation pressure depends on the volume of the plastically deformed region [25]. Re-measurement of the elastic modulus after 46 days resulted in values similar to those measured immediately after the curing, in contrast to what was observed in the indentation pressure values. 3.4. Fracture toughness In this section the fracture toughness of the coatings is calculated using radial cracks, chipping phenomena and the load at which initial signs of delamination became visible.
Fig. 7. Effective elastic modulus of a coating cured at 2508C after a prereaction of 3.5 h. The coating was 11.5 mm thick. The line is a ®t to the Gao model [22].
3.4.1. Fracture toughness - radial cracks After the indentation radial cracks were observed in the
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surface. Longer pre-reaction time and higher curing temperature led to shorter cracks at a particular load (Fig. 9). One method for determining the fracture toughness, KIC, and the residual stress at the surface, s , of bulk materials is to measure the length of radial cracks, c, that form during indentation as a function of indentation load, P. The relation that is generally used reads [26]
xr P=c1:5 KIC 2 2s c=p0:5
7
where xr 0:016 E=H0:5 for a Berkovich-type indenter [27]. The model was developed for bulk materials, but has been used successfully to determine the fracture toughness of coatings [27±30]. Furthermore, the hardness to elastic modulus ratio of coating and substrate are similar, implying a stress ®eld similar to that of a bulk material [31]. Delamination or chipping of the coating in¯uences the energy dissipation only at high loads. The indentation results were analyzed according to this method. A fracture toughness of 0.62 MPa m 0.5 was obtained for the glass substrate using the radial cracks that formed during indentation, which is in agreement with value quoted in the literature (0.71 MPa m 0.5 for soda lime glass [32]). The `main' coating indentation pressure as a representation of the hardness (Section 3.2, Table 1) and the ®lm elastic modulus (Section 3.3) determined in previous sections were used in the calculation. Fig. 10 shows a typical graph of x rP/c 1.5 versus 2(c/ p ) 0.5. The intercept with the ordinate axis is KIC, and the slope is equal to the residual stress, with a negative slope implying a tensile stress. Only cracks that were longer than the plastic indentation size were used in the analysis [26]. The length of the radial cracks, and therefore the fracture toughness and residual stress, were found to be independent of the thickness of the coatings. Moreover it is clear from Table 1 that the coatings cured at the lower temperature show a higher (tensile) stress at the same pre-reaction time. Also, a longer pre-reaction time led to a decrease in both KIC and s at the same curing temperature. As far as cracking is concerned, these effects counteract one another: radial cracks will be larger at lower KIC values, but they will be smaller at lower tensile stresses, s . In our case, this had
Fig. 9. Comparison of the surface crack length versus indenter load for coatings cured after 3.5 h at 2508C (dashed) and 4008C (full line). The lines represent a guide for the eye.
Fig. 10. x rP/c 1.5 as a function of 2(c/p ) 0.5 for a coating cured at 4008C after a pre-reaction of 1 h; thickness 5 mm. The line represents a linear ®t.
the effect that, although the fracture toughness was smaller for the higher temperature, the crack length was also smaller due to the diminished tensile stress. This agrees with observations made on the critical thickness of coatings which was smaller for coatings cured at 2508C as compared to a curing temperature of 4008C [33]. Various chemical and physical processes that in¯uence the mechanical properties of the ®nal coating take place upon curing. They include bond scission, an increase in the number of local defects, cross-linking, oxidation, rearrangement of the particles in the coating and thermal degradation. The ratio of cross-linking and scission may vary with the preparation conditions. Possible causes of the observed reduction in the fracture toughness and the residual stress at a higher curing temperature could therefore be a relaxation mechanism on a microscopic scale like bond scission or localized burn-out of CH3 groups in the coating resulting in microscopic defects. A reduction of the residual stress at higher temperatures has also been reported by Syms [34], who found that annealing above a critical temperature reduces the residual stress in thick (10 mm) sol±gel phosphosilicate ®lms and related this observation to a reduction of thermal and intrinsic stresses at higher temperatures. Further support to our observations is given by the observations of the stress in SiO2 ®lms deposited by plasma and ozone TEOS chemical vapor deposition processes [35] where it was found that the intrinsic stress decreased above 4008C. The re-measurement of the fracture toughness 46 days after the curing showed no signi®cant change in the values of the fracture toughness and residual stress with time, which suggests that environmental moisture has a limited relaxation effect on the residual stress. 3.4.2. Fracture toughness - chipping Since the indentation depth corresponding to the observed radial cracks exceeds 10% of the coating thickness, the elastic-plastic zone might extend to the substrate. Therefore, a second method proposed by Li and Bhushan [36] was chosen to estimate the fracture toughness of the
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coating on the basis of the energy dissipated during chipping, U. In Section 3.1 it was shown that the loading curve shows discontinuities at higher loads, which were associated with chipping of the coating (see Fig. 1d). Initially, the coating delaminated. At a certain delamination length the crack proceeds further through the coating and a coating chip is removed. At this point the fracture toughness is determined. The discontinuities in the load displacement curve can be associated with this single event of chipping. The edge of the chipping is far from the indenter and is not in¯uenced by any substrate penetration of the indenter, which overcomes the limitation imposed for the calculation of the fracture toughness on the basis of the radial cracks. In the suggested method [36] the loading curve is extrapolated in a tangential direction from the starting point of the discontinuity to the same indentation depth as at the end of the discontinuity. The difference between the extrapolated and the measured load displacement curve is then a measure of the dissipated energy. The fracture toughness can then be calculated using [36] 0:5 E U 8 KIC h0 N 1 2 n2 2pcd where cd is the diameter of the delamination crack, N is the number of delamination cracks (usually three in our experiments), and h 0 is the effective coating thickness (coating thickness divided by sin(q ), where q is the average angle of the chipping edge, which was 17:5 ^ 28). The average angle of the chipping edge was determined from the distance between the lower and the upper edge of a removed area at a particular coating thickness using an optical microscope. The fracture toughness measured with the aid of this method should not be affected by residual stress, since the energy is released during the formation of the interfacial crack. Hu et al. [37] have shown that the stress intensity of a crack extending perpendicular through a ®lm is a factor of two larger than that of a crack extending parallel along the ®lm. The values of the calculated fracture toughness divided by two are shown in Table 1, along with the results calculated on the basis of the radial cracks, showing that the two sets of data are in good agreement. 3.4.3. Fracture toughness - load of delamination Fig. 11 shows a typical graph of the dependence of the critical load of delamination on the coating layer thickness. Delamination, which occurred during loading, was visible as bright spots occasionally associated with interference fringes. (Fig. 1c). Chipping at larger loads clearly con®rmed that failure occurred at the interface between the coating and the substrate (Fig. 1d). The relationship between load at which delamination became visible, Pc, and the layer thickness, h, could well be described by Pc < h1:5 . In this section it will be attempted to calculate the fracture toughness in a third way, next to the two methods that are based on the radial cracking and the chipping as explained
Fig. 11. Load of initial delamination measured for a sample cured at 4008C after a pre-reaction of 1 h. The line represents a ®t of the function P ah1:5 , where a 18 MN/m 1.5.
in the previous sections. Therefore, it is assumed that the delamination occurs due to cracks that grow perpendicular [38] to the surface during loading, reach the interface and are then de¯ected. These cracks could be either related to a perpendicular extension of the annular or radial cracks observed in the surface of the sample after indentation, or to median cracks that form under the center of the indenter during loading as a part of the `median/radial crack system' [39] (see Section 3.5 for calculations of the interfacial fracture toughness using models for the buckling of soft coatings on hard substrates that relate the stress at the interface to the normal load under the indenter). The fact that the deformation pattern of the radial cracks, which is wider in the center of the indent, con®rms that the cracks are of radial rather than Palmquist like shape. At higher loads a number of parallel annular cracks were observed. The annular cracks were limited in their depth by the indentation stress ®eld [38]. Furthermore, each annular crack leads to a relaxation of tensile stress, which is related to its depth. If the indentation continues, stress will build up after the crack growth stops and will lead to a parallel annular crack. Since annular cracks occur at equal distances, which were found to be smaller than the coating thickness, their depths will always be the same. Considering linear elastic relaxation [33], this depth should be approximately equal to their distance. Therefore, it is unlikely that the annular cracks were responsible for the observed delamination. The condition for the growth of median cracks in bulk material during indentation loading can be described using a relation similar to Eq. (7) [39] crM P=c1:5 KIC 2 2s c=p0:5
9
where the constant x rM differs from x r in Eq. (7) since it takes into consideration the residual component of the stress ®eld on the axis as opposed to Eq. (7) which applies to the surface. Lawn et al. [39] found for glass xrM 0:02 and xrM 0:048, thus a crack will grow more easily sideways than downwards.
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In the present study we have a coating instead of a bulk material. It can be assumed that the median crack growth is governed by a relationship of the form of Eq. (9), but the constant x rM will have a different value than suggested by Lawn [39]. To determine x rM the fracture toughness of the coatings cured at 2508C with the longer pre-reaction time was used (see Section 3.4.1). The value of the residual stress found in Section 3.4.1 was used as a constant in the following calculations. The measured delamination load and the corresponding coating thickness, h, were substituted into Eq. (9) since it is assumed that delamination occurs due to de¯ection of the median cracks, when their length c h. The resulting value of xrM 0:012 was used to calculate the fracture toughness for the coatings cured at the various conditions. The results in Table 1 show good agreement with the values determined using radial cracks and chipping (Sections 3.4.1 and 3.4.2). Lawn [39] found for x r/x rM a ratio of 2.4, whereas we found a ratio of 3.8. The difference between this value and our ®ndings and the results of Lawn [39] is probably related to the modi®cation of the stress ®eld by the substrate material [40]. This is in agreement with the report of Beuth [33], who found a reduction of the stress intensity for a tensile loaded surface crack in the case of a coating on a substrate having a larger elastic modulus as compared to a bulk material. The crack can only reach the interface if some defect is present at the interface since the stress intensity will reduce below KIC before the interface is approached [41]. 3.5. Interfacial fracture toughness In this section, it will be attempted to estimate the fracture toughness of the interface between the glass and the coating from the indentation results. Furthermore, the critical condition for chipping will be estimated on the basis of buckling of the coating. Several existent models will be applied and the results will be compared. As described above, our observations suggest that delamination initiates due to median/radial cracks growing towards and then de¯ecting into the interface. The size delamination cracks increases as the load is increased, leading to buckling of the coating and at a certain load chipping occurs as the interfacial crack de¯ects into the substrate. The whole process takes place during the loading cycle (Sections 3.1 and 3.4.1). In situ observation of the crack formation using a microscope positioned directly under a Vickers indenter revealed that buckling occurred during loading (see Section 3.1). The fracture toughness of the interface was therefore estimated by considering crack de¯ection and chipping (see Section 3.4.2), similar to the energy balance approach to spallation by wedging of coating due to residual stress by Evans [42]. Initially, the coating delaminates at the interface, but at higher loads the coating chips due to the de¯ection of the interfacial delamination crack.
147
As a ®rst method to estimate the range of the interfacial fracture toughness of our coatings, we used the results of He and Hutchinson [43,44], who carried out theoretical studies on the kinking of a crack at [44] and out of the interface [43] between two dissimilar elastic solids. First, the crack will de¯ect into the interface as it approaches the interface from the surface if the ratio of fracture energy of the substrate to interface is less than 0.43 [44] using the Dundurs parameters a 20:75 and b 20:25, that apply to our coating/substrate system. Second, the interfacial crack will de¯ect into the coating if the ratio of the fracture energy of the coating to the fracture energy of the interface is lower than 1.15 [43], for the Dundurs parameters a 0:75, b 0:25 and K II =K I 0:2 (de¯ection angle of approximately 208 [40], see Section 3.4.2). The interfacial fracture toughness is de®ned as K IC GIC Ef , where Ef is the elastic modulus of the coating. This leads to 0:16 # K IC # 0:46 MPa m 0.5. The fact the fracture occurs at the interface suggests that the interfacial fracture toughness is closer to the lower value. There are other approaches for estimating the interfacial fracture energy from the delamination and buckling [45,46] of a coating including systems of soft coatings on glass substrates [47±49]. Two of these models will be applied to our measurements for comparison. The mechanism of crack initiation in these models is not the de¯ection of a crack into the interface, as suggested in our investigation, but it is assumed that delamination initiates at the interface at a position below the edge of the contact and then proceeds until an equilibrium radius is reached. The ®rst model, which is based on the contact radius at the initiation of delamination under the indenter, is by Ritter et al. [47,48], who, following an approach by Matthewson [45], proposed the following expression for the interfacial shear strength between a soft coating and its substrate [47]
tc
0:56Hc 0 K1 fac =h=fK1 fac =h 1 nh=ac f2
10
where the suf®x c refers to the critical point of crack formation, H to the hardness of the coating, K1 is a modi®ed Bessel function of the second kind, K1 0 is the derivative of this function, ac is the contact radius, f 6 1 2 n= 4 1 n1=2 , h is the thickness of the ®lm, and n is the Poisson ratio of the ®lm. Substituting the appropriate values into Eq. (10) leads to an average interfacial shear strength of 0.32 GPa for our coatings. The interfacial shear strength is the controlling factor for crack initiation, rather than propagation. To determine a value of the interfacial fracture toughness, a maximum ¯aw size at the interface of ci 0:2 mm is assumed, which appears to be a reasonable value considering the optical micrographs of the delaminations and the interfaces after chipping. Then, the interfacial fracture toughness can be estimated by K IC tc pci [40] as 0.18 MPa m 0.5. This value is within the range estimated above using the results
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of He and Hutchinson [43,44], and makes it impossible to differentiate between the mechanism suggested above, i.e. the de¯ection of cracks into the interface or the loss of the adhesion due to the shear stress at a pre-existent ¯aw, which is the basis of Eq. (10). Optical micrographs of interfaces after the coatings chipped off suggest that the radial cracks have reached the interface. Another method to calculate the interfacial fracture toughness from indentation experiments in soft coatings is provided by Rosenfeld et al. [49] on the basis of calculations by Thouless [50] on the decohesion of ®lms with axisymmetric geometries. Based on the results of Rosenfeld et al. [49] the interfacial fracture toughness is linked to the size of the delaminated area and the corresponding indentation load as follows KiC
p 0:792H 1 2 n2 h 1 1 n 1 2 1 2 nHc2 =P
11
where c is the radius of the delamination crack, and P the corresponding load. The radius of the delamination crack was determined using an optical microscope after the indentation load had been applied. Calculating the interfacial fracture toughness from the increase of the crack length versus load [45,49] using Eq. (11) leads to values of 0.6 MPa m 0.5 and 0.75 MPa m 0.5 for a curing temperature of 250 and 4008C, respectively, for the 1 h pre-reacted solutions. For the 3.5 h pre-reacted solution the values are 0.9 and 1.1 MPa m 0.5 for a curing temperature of 250 and 4008C, respectively. Thus, the fracture toughness increases by 25% by increasing the curing temperature from 250 to 4008C, whereas it increases by 50% by increasing the pre-reaction time of the coating solution from 1 to 3.5 h. The used model assumes that the pressure at the interface is approximately equal to the hardness, i.e. the indentation pressure in our case. This appears reasonable since the indentation pressure was not modi®ed signi®cantly by the occurrence of interfacial delamination. The values calculated using the model by Rosenfeld et al. [49] are higher than estimated above. This is probably related to the fact that interaction of radial cracks in the surface and interfacial cracks, which reduces the stress at the interface by relaxation, was ignored. Furthermore, the stress intensity for interfacial cracks will be modi®ed by the elastic mismatch between coating and substrate [51]. Rosenfeld [49] considered a clamped circular plate constrained to have zero de¯ection at its center. If we consider that the delamination occurs between the radial cracks as three separate circular clamped plates, but with de¯ection at their center, then the buckling stress and shear stress at the interface will be reduced by a factor of 0.34 [44]. Thus, the average fracture toughness will reduce to 0:28 ^ 0:06 MPa m 0.5, which appears to be in agreement with the values estimated using the results of He and Hutchinson [43,44]. Eqs. (10) and (11) are based on indentation data, i.e. the contact area at initial delamination (determined from the
load-displacement curve following Oliver and Pharr [17]), the radius of delamination, and the indentation load. Hence, the interfacial fracture toughness has indeed been determined on the basis of indentation data. In the case of interfacial delamination, the de¯ection angle will be 908 and the fracture will be limited by the interfacial fracture toughness for mode II, which has been supported by numerical calculations [51]. The chemical bonding via O±Si groups in the coating and at the interface suggest a similar fracture toughness of coating and interface. There are several theories for mixed mode failure based on linear elastic fracture mechanics, which allow a prediction of the ratio of the fracture toughness for pure mode II to pure mode I failure, i.e. KIIC to KIC. This ratio is 0.81 according to the strain energy release rate theory [53], 0.87 according to the maximum hoop stress theory [54] and 1.05 according to the strain energy density theory [55] for bulk materials. Experimentally, ratios between 2 [56] and 1.2 [57] were found. Suresh [58] suggested that the high apparent fracture toughness for mode II arises from crack face friction, which is probably a mechanism leading to a higher apparent interfacial fracture toughness as calculated using Rosenfeld's model [49]. Finally, it was observed that chipping of the coating occurred always at a discrete ratio h/w of coating thickness to half the diameter of delaminated area (h=w 0:18 ^ 0:06 for coatings made from fresh solutions). Evans and Hutchinson [52] investigated the mechanics of delamination and spalling/chipping of an indented ®lm by modeling the ®lm as clamped circular plate under compression. The critical condition for spalling found by Evans and Hutchinson [52] reads 0:5 w E 1:92 f 12 s0 h where Ef is the elastic modulus of the coating and s 0 the biaxial compressive stress induced in the coating. If we consider s 0 to be equivalent to 0.56 times the hardness [41], which is equivalent to the indentation pressure (Section 3.1), Eq. (12) gives a value of h/w of 0.14. This is slightly lower than the measured ratio given above. Eq. (12) allows a prediction of the critical delamination size that leads to spalling of a coating of a particular thickness and can therefore be used as a failure criterion. 4. Conclusions In this paper we have studied the indentation response of organic-inorganic hybrid coatings on glass substrates. It was observed, that many different phenomena occurred in the coatings during indentation. In particular, radial cracking, chipping, and delamination occurred all during one indentation, and could be related to changes in the load-displacement curves. From the measured load-displacement curves,
J. Malzbender et al. / Thin Solid Films 366 (2000) 139±149
the apparent hardness and the elastic modulus were determined. We found that the apparent hardness possessed a peak near the coating surface, which was most probably related to strain hardening of the coating. Also, the cracking in¯uenced the measured hardness at larger indentation depths. Due to these phenomena, the data could not be ®tted to existing models. Existing models could describe the change of the elastic modulus with indentation depth. An estimate of the coating fracture toughness KIC and the residual stress could be obtained by different methods, each making use of a different cracking phenomenon that occurring during the measurement. Hence, we obtained KIC from analysis of radial cracking, chipping, and delamination. Clear in¯uences of preparation conditions were observed. Moreover, there was close resemblance between the values obtained by the different methods, which gives con®dence in the result. Finally, also the interfacial fracture toughness of the coating-substrate interface was estimated using various existing models. The results obtained using different models to determine the elastic modulus and fracture toughness showed good agreement. Acknowledgements The authors would like to acknowledge Dr A.R. Balkenende, Dr T.N.M. Bernards and Dr P.C.P. Bouten (Philips Research Laboratories, Eindhoven, The Netherlands) for their technical support and useful discussions. References [1] A. Paul, Chemistry of Glasses, Chapman and Hall, London, 1990. [2] H. Bach, D. Krause, Thin Films on Glass, Springer-Verlag, Berlin, 1997. [3] G.L. Smay, Glass Technol. 26 (1985) 46. [4] F.H. Wang, X.M. Chen, B. Ellis, R.J. Hand, A.B. Seddon, J. Mater. Sci. Technol. 13 (1997) 163. [5] T.H. Wang, P.F. James, J. Mater. Sci. 26 (1991) 354. [6] H. Schmidt, J. Sol±gel Sci. Technol. 1 (1994) 217. [7] A. Atkinson, R.M. Guppy, J. Mater. Sci. 26 (1991) 3869. [8] R.H. Brzesowsky, G. de With, S. van de Cruijsem, I.J.M. SnijkersHendrickx, W.A.M. Wolter, J.G. van Lierop, J. Non-Cryst. Solids 241 (1998) 27. [9] M.R. McGurk, T.F. Page, J. Mater. Res. 14 (1999) 2283. [10] Y.M. Lim, M.M. Chaudhri, Y. Enomoto, J. Mater. Res. 14 (1999) 2314. [11] Page, T.F., Phar, G.M., Hay, J.C., Oliver, W.C., Lucas, B.N., Herbert, E., Riester, L., Fundamentals of Nanoindentation and Nanotribology. MRS Symp. Proc. 522. 53 1998 [12] M. Sakai, S. Shimizu, T. Ishikawa, J. Mater. Res. 14 (1999) 1471. [13] J.-H. Ahn, D. Kwon, J. Appl. Phys. 82 (1987) 3266. [14] E. Soederlund, D.J. Rowcliffe, J. Hard Mater. 5 (1994) 149.
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[15] A.K. Bhattacharya, W.D. Nix, Int. J. Solids Struct. 24 (1988) 1287. [16] B. Bhushan, Handbook of Micro/Nano Tribology, CRC Press, New York, 1995. [17] W.C. Oliver, G.M. Pharr, J. Mater. Res. 7 (1992) 1564. [18] J. Mencik, M.V. Swain, J. Mater. Res. 10 (1995) 1491. [19] B. Johnsson, S. Hogmark, Thin Solid Films 114 (1984) 257. [20] M.R. Begley, J.W. Hutchinson, J. Mech. Phys. Solids 40 (1998) 2049. [21] A.M. Korsunsky, M.R. McGurk, S.J. Bull, T.F. Page, Surf. Coat. Technol. 99 (1998) 171. [22] H. Gao, C.H. Chiu, J. Lee, Int. J. Solids Struct. 29 (1992) 2471. [23] M.F. Doerner, W.D. Nix, J. Mater. Res. 1 (1986) 6501. [24] T.W. Wu, M. Moshref, P.S. Alexopoulos, Thin Solid Films 187 (1990) 295. [25] J. Menik, D. Munz, E. Quandt, E.R. Weppelmann, M.V. Swain, J. Mater. Res. 12 (1997) 2475. [26] D.B. Marshall, B.R. Lawn, J. Am. Ceram. Soc. 60 (77) 86. [27] G.M. Pharr, D.S. Harding, in: M. Nastasi, D.M. Parkin, H. Gleiter, Mechanical Properties and Deformation Behavior of Materials Having Ultra-Fine Microstructures, Kluwer Academic, Dordrecht, 1993. È cËisik, C. Bindal, Surf. Coat. Technol. 94±95 (1997) 561. [28] A.H. U [29] M.L. Emiliani, J. Mater. Sci. 28 (1993) 5280. [30] P. Kodali, K.C. Walter, N. Nastasi, Tribol. Int. 30 (1997) 591. [31] S.J. Bull, D.S. Rickerby, Surf. Coat. Technol. 42 (1990) 149. [32] P.D. Warren, J. Eur. Ceram. Soc. 15 (1995) 201. [33] J. Malzbender, G. de With, Thin Solid Films 359 (2000) 210. [34] R.R.A. Syms, J. Non-Cryst. Solids 167 (1994) 16. [35] K. Ramkumar, A.N. Saxena, J. Electrochem. Soc. 5 (1992) 1437. [36] X. Li, B. Bhushan, Thin Solid Films 315 (1998) 214. [37] M.S. Hu, M.D. Thouless, A.G. Evans, Acta Met. 36 (1988) 1301. [38] P.D. Warren, D.A. Hills, S.G. Roberts, J. Mater. Res. 9 (1994) 3194. [39] B. Lawn, A.G. Evans, D.B. Marshall, J. Am. Ceram. Soc. 63 (1980) 574. [40] J. Mencik, Mechanics of Components with Treated or Coated Surfaces, Kluwer Academic, Dordrecht, 1996. [41] J.L. Beuth, Int. J. Solids Struct. 29 (1992) 1657. [42] U.R. Evans, An Introduction to Metallic Corrosion, Edwald Arnold, London, 1948. [43] M.Y. He, J.W. Hutchinson, J. Appl. Mech. 56 (1989) 270. [44] M.Y. He, A.G. Evans, J.W. Hutchinson, Int. J. Solids Struct. 313 (1994) 3443. [45] M.J. Matthewson, Appl. Phys. Lett. 49 (1986) 1426. [46] Y. Wei, J.W. Hutchinson, J. Mech. Phys. Solids 45 (1997) 1137. [47] J.E. Ritter, T.J. Lardner, L.G. Rosenfeld, M.R. Lin, J. Appl. Phys. 66 (1989) 3626. [48] J.E. Ritter, L.G. Rosenfeld, J. Adhesion, Sci. Technol. 4 (1990) 551. [49] L.G. Rosenfeld, J.E. Ritter, T.J. Lardner, M.R. Lin, J. Appl. Phys. 67 (1990) 3291. [50] M.D. Thouless, Acta Metall. 36 (1988) 3131. [51] S.A.F. Oliveira, A.F. Bower, Wear 198 (1996) 15. [52] A.G. Evans, J.W. Hutchinson, Int. J. Solids Struct. 20 (1984) 455. [53] K. Palaniswamy, W.G. Knauss, Mechanics Today, Pergamon Press, New York, 1978. [54] F. Ergogan, G.C. Sih, J. Basic Eng. 85 (1963) 519. [55] G.C. Sih, Int. J. Fract. 10 (1974) 305. [56] D. Singh, D.K. Shetty, J. Am. Ceram. Soc. 72 (1989) 78. [57] D.K. Shetty, A.R. Rosenfeld, W.H. Duckworth, J. Am. Ceram. Soc. 26 (1987) 825. [58] S. Suresh, C.F. Shih, A. Morrone, N.P. O'Dowd, J. Am. Ceram. Soc. 73 (1990) 1257.
Elastic modulus, indentation pressure and fracture toughness of hybrid coatings on glass J. Malzbender a,*, G. de With a, J.M.J. den Toonder b a
Laboratory of Solid State and Materials Chemistry, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands b Philips Research Laboratories, Prof. Holstlaan 4, 5656 AA Eindhoven, The Netherlands Received 30 April 1999; received in revised form 13 December 1999; accepted 13 December 1999
Abstract The indentation load-displacement behavior of an organic-inorganic hybrid coating was tested using a Berkovich indenter in an attempt to offer a simple and fast method to analyze the mechanical properties of a coating. The coatings were deposited using a spin-coating technique. The elastic modulus and the indentation pressure as a measure of the hardness were determined on the basis of the load-displacement curve. The effects of the coating thickness and the coating preparation conditions were investigated. Cracks, delamination and chipping were observed and were used to assess the fracture toughness of the coating and the interface. Elastic modulus, indentation pressure and the fracture toughness were dependent on the time elapsed before application of the coating ¯uid and on the curing temperature. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Coatings; Elastic properties; Hardness; Stress
1. Introduction The main reason for applying coatings on glass is to modify the functional behavior of the glass, i.e. to introduce an anti-glare, anti-re¯ex, or anti-static layer or to realize changes in dielectric or transmission properties. A second reason is to strengthen the glass substrate and protect it from environmental in¯uences such as particle impact or moisture [1±3]. For these purposes inorganic or hybrid, i.e. combined inorganic/organic, coatings can be used [4,5]. One method to prepare the coatings is the sol±gel process, which is described elsewhere [6]. The process requires a ®nal curing, which results in shrinkage of the coating and can produce a tensile stress [7]. The probability of cracking in the coating usually increases with thickness and, therefore, non-cracked coatings have a critical thickness [6]. An increase in this critical thickness has been realized by adding silica particles [8]. Whatever the main reason for applying a coating, mechanical aspects are almost always important. Indentation testing is widely used to characterize the mechanical properties of coatings [9,10]. This technique can be used to estimate the indentation pressure and the elastic modulus of * Corresponding author. Tel.: 1 31-40-247-3059; fax: 1 31-40-2445619. E-mail address: [email protected] (J. Malzbender)
a coating [11±15]. Also, by analyzing cracks in the surface resulting from indentations, the fracture toughness of the coating can be estimated [16]. The present paper presents the results of indentation experiments on a hybrid coating. In these experiments the indentation pressure as a measure of the coating hardness, the elastic modulus, the fracture toughness of coating and interface and the residual stress in the coating were estimated and the dependence of these parameters on preparation conditions was studied. The main advantage of the current approach is that three different phenomena, which can be found during one experiment, were used to assess the fracture toughness of the coating and the interface. 2. Experimental The experiments were carried out using ¯oat glass that was coated with an organic-inorganic hybrid coating. The coating ¯uid contained approximately 30% (weight) solid components, being equal weight amounts of methyltrimethoxysilane (MTMS) and colloidal silica (average particle size 20 nm), and 70% solvents (2% water, 32% methanol, 1% propanol, 35% glycol). In order to increase the stiffness of the coating, 1 wt.% tetraethylorthosilicate (TEOS) was added. The coating ¯uid was allowed for to pre-react for a time of 60 or 240 min. Although hydrolysis of
0040-6090/00/$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. PII: S 0040-609 0(00)00656-8
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the solution took place during this period, the term prereaction time will be used in the following sections since an evaporation of solvents might have occurred. The rectangular glass substrates of 100 cm 2 were 0.2 cm thick. The substrates were cleaned by scrubbing for 2 min using an alkaline soap solution. The soap was removed using ¯owing water. The glass substrates were then immersed in demineralized water for 1 h and subsequently dried using nitrogen gas. The coating ¯uid was ®ltered through a 5 mm Millipore q ®lter before it was applied to the substrate to eliminate any dust particles. The coatings were applied by spinning at speeds between 100 and 2500 rev./min in a closed spinner. The closed spinner con®guration allowed more homogeneous coatings to be applied. After spinning, the coatings were dried by heating them on a hot plate at 1008C for 1 min. The coatings were then cured at 250 or 4008C for 18 h. The resulting coating layer thickness was between 3 and 20 mm. The coated glass plates were cut into smaller samples for the experiments. Indentation experiments were carried out at room temperature and ambient atmosphere using a home-built instrument. The minimum load that can be applied is 2 mN and is limited by the background noise level that is related to thermal and electronic drift phenomena. The instrument operates in a displacement-controlled mode. A loading rate of 10 nm/s was used in the experiments. The apparatus permitted up to 25 indentations to be made in one run at loads ranging from 0 to 1000 mN. A Berkovich-type indenter was used. The calibration procedure suggested by Oliver and Pharr [17] was used to correct for the load frame compliance of the apparatus and the imperfect shape of the indenter tip [18]. The area function of this indenter was calibrated using B270 glass, whose elastic modulus was determined independently using the pulse-echo method. The compliance of the system was 300 ^ 10 nm/N and the projected area of the indenter, A, was related to the contact depth, hc, of the indentation by A ahc 2 1 bhc (a 24:5 ^ 0:5 and b 5:71 ^ 0:09 mm). This plastic contact area was calculated using the slope of the unloading curve according to the method suggested by Oliver and Pharr [17]. The area function corresponds to an ideal Berkovich indenter with a tip radius of approximately 0.9 mm. The calibration was performed for a depth range of 0.1 to 2.9 mm, corresponding to a load range of 5 to 1000 mN, where the maximum indentation depth was restricted by the load limitation. The load-displacement curves were analyzed using the method proposed by Oliver and Pharr [17], yielding the elastic moduli and the indentation pressure
3. Results and discussion In this section the results obtained are given, described with reference to models, which are derived in the subse-
quent sections or the relevant literature, and discussed in comparison to observations made elsewhere. 3.1. General observations During the indentation of the coatings, various phenomena were observed, which will be illustrated by means of a typical indentation load-displacement curve, as shown in Fig. 1 along with the optical micrographs of the indentation marks. Changes in the load-displacement curve can be correlated with cracking occurring in the coating and at the coatingsubstrate interface. In the ®rst place a distinct change is observable in the slope of the load-displacement curve at a load of approximately 30 mN (Fig. 1a), which is related to the onset of radial cracking in the coating (Fig. 1a). These radial cracks were found to grow with increasing load (Fig. 1b,c), but this caused no further signi®cant changes in the load-displacement curve. The load at which the radial cracking started turned was found to be independent of the coating thickness. At higher loads the coating fractured between the radial cracks (Fig. 2a,b). The cracks appearing at this point will be referred to as `annular cracks'. At even higher loads delamination at the interface occurred (Fig. 1c). There is no relation between the formation of annular cracks or delamination and features in the loading or unloading curve. A connection with the surface cracks is strongly suggested by the observations that the delaminated areas were limited by the surface cracks and that delamination occasionally occurred only between some of the cracks of a particular indent. Chipping of coating material was observed (Fig. 1d) at higher loads, for this particular example approximately at 200 mN, which resulted in more abrupt changes in the load displacement curve (Fig. 1d). The critical load at which this phenomenon was observed depended on the coating layer thickness. The coating was resistant to extensive plastic ¯ow due to the high H/E- ratio (see Sections 3.2 and 3.3). In situ observation of the crack formation using a microscope positioned directly under a Vickers indenter con®rmed that radial cracks, delamination and chipping formed during the loading. In summary, many different phenomena occurred in our coatings as a result of the indentation: radial cracking, annular cracking, delamination and chipping. In the following we will focus on extracting information on coating properties from the observed phenomena and the indentation loaddisplacement curve. 3.2. Indentation pressure The hardness of the coating was computed on the basis of the measured load-displacement curve according to the method outlined by Oliver and Pharr [17] using the equation H P=A
1
where A is the projected area of contact between the inden-
J. Malzbender et al. / Thin Solid Films 366 (2000) 139±149
141
ter and substrate at load P (see experimental, Section 2). Again, the plastic contact area A was calculated using the slope of the unloading curve according to the method suggested by Oliver and Pharr [17]. In the current investigation the measured effective hardness was in¯uenced by materials inhomogeneities in the form of a surface layer and by cracking of the coating. Since the effective hardness is a measure of the pressure under the indenter, the phrase indentation pressure will be used in the following. Typical results obtained for the indentation pressure as a function of contact indentation depth are shown in Figs. 3 and 4. There are two remarkable effects to be noted in these plots. First, the indentation pressure exhibits a maximum at the surface. At deeper indentation this value decreases to become a constant value referred to as `main' coating indentation pressure, Hf (see Table 1). Second, with increasing penetration depth, the indentation pressure shows no tendency towards the hardness value measured for the glass substrate, for which we independently determined H 6:0 ^ 0:5 GPa. These effects will be discussed below. The hardness of the glass substrate was determined at loads varying from 5 to 1000 mN using the procedure outlined at the beginning of Section 3.2. Since the contact depth was tenth of micrometers or more the effect of adsorbed water on the hardness should be negligible. The `main' coating indentation pressure appeared to increase with the curing temperature for a longer prereacted coating (Table 1). Neither the `main' coating indentation pressure nor the peak in the indentation pressure at the surface showed any dependence on ®lm thickness. A longer pre-reaction time or a lower curing temperature resulted in a larger extent of the pressure peak into the material. It has been suggested that a peak of the hardness near the surface does not necessarily represent a materials property, but is attributable to an `indentation size effect' [19]. Any connection to the indenter shape can be ruled out since, ®rst, the data have been corrected for the imperfect indenter shape (Section 2) and, second, the depth of this maximum depended on the preparation conditions. A more plausible explanation in this experiment appears to be the presence of a top layer of a different nature. This layer might be the result of oxidation or transport of solvents in the ®lm. This explanation is supported by the data presented in Fig. 5, which shows the indentation pressure data measured immediately after preparation and again in the same specimen after 46 days. In the latter case the indentation pressure pro®le is virtually ¯at. Since the crack length at a particular load was not altered, for the aged coating as compared with the fresh coating, a connecFig. 1. Indentations into a 3 mm thick coating cured at 2508C after a prereaction time of 1 h. Shown are the load- displacement curves along with the images observed using optical microscopy at loads of (a) 30 mN (b) 50 mN (c) 100 mN and (d) 250 mN.
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Fig. 3. Indentation pressure versus contact depth of a coating cured at 2508C after a pre-reaction of 3.5 h. The coating was 11.5 mm thick (see Figs. 7 and 8 for the elastic modulus). The line represents a guide for the eye.
Fig. 2. AFM images of indentation at a load of 200 mN into a 4.5 mm thick coating cured at 4008C (pre-reaction time 1 h) showing radial and annular cracking. Deformations inside the radial crack in image (b) are due to closure of the crack after unloading.
tion between indentation pressure maximum or the `main' indentation pressure and cracking of the coating can be ruled out. Furthermore, the decrease of the maximum near the surface in Fig. 3 started at loads at which no crack related features were visible. It is therefore suggested that the initially measured surface indentation pressure is related to a change in the materials properties due to in-diffusion of water. Aged coatings were found to show a higher OH concentration near the surface. The observed increase of the hardness for shallow indentations might be seen in conjunction with calculations performed by Begley and Hutchinson [20] on the mechanics
of size-dependent indentation. According to their calculations the relative plastic zone size is larger for smaller indents as compared to larger indents. This effect should be reduced for harder materials [20]. Thus the calibration of the indenter using glass, which has a signi®cantly larger hardness than the coating, did not show this effect. Especially the coatings cured at a lower temperature, which have a low `main' indentation pressure, possessed a larger relative plastic zone size for shallow indentations than the value determined from the calibration curve. This led to an overestimation of the near surface indentation pressure. The reduction of the surface peak for aged coatings suggests a change in the materials properties. The fact that the indentation pressure does not show the expected trend towards the glass substrate hardness in the case of deeper indentations (Figs. 3 and 4) can be attributed to the in¯uence of coating fracture on the indentation pressure. It was shown in Section 3.1 that the coatings showed radial cracks at an indentation load of approximately 30 mN, which corresponded to a contact depth of 0.7 to 0.9 mm. It is known that cracks in a coating decrease the measured effective hardness [21].
Fig. 4. Indentation pressure versus contact depth measured for a 11 mm thick coating cured at 4008C after a pre-reaction time of 3.5 h. The line represents a guide for the eye.
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Table 1 Indentation pressure parameters, fracture toughness and residual stress
s (Mpa) (^3)
Curing temperature (8C)
Pre-reaction (h)
Hf (GPa) (^0.05)
Fracture toughness determined using Radial Cracks KIC (MPa m 0.5) (^0.05)
Chipping KIC a (MPa m 0.5) (^0.05)
Delamination KIC (MPa m 0.5) (^0.05)
250 250 400 400
1 3.5 1 3.5
1.25 1.2 1.2 1.5
0.23 0.14 0.19 0.16
0.19 ±b 0.21 ±b
0.21 0.14 0.17 0.17
b a
25 12 13 0
Samples were not analyzed using this method. p Measured values were divided by 2.
3.3. Elastic modulus The elastic moduli of the coatings as a function of indentation depth were calculated using the unloading curves, on the basis of the procedure suggested by Oliver and Pharr [17]. Two different equations have been proposed to express the elastic modulus of a coating substrate combination, i.e. the model by Gao et al. [22] and Doerner and Nix [23]. The Gao [22] the Doerner and Nix [23] model considers only elastic deformation. Nevertheless, both models are widely used to deconvolute indentation data. First, Gao et al. [22] used a moduli - perturbation analysis to derive a relationship for the elastic modulus of a coated material which can be simpli®ed for materials with similar Poisson ratios to E Es 1 Ef 2 Es fG
2
where Ef and Es are the elastic moduli of the ®lm and the substrate, respectively, and f G is a weight function expressed by
fG
2 1 1 parctank 2p 1 2 n " ! # 1 1 k2 k 2 £ 1 2 2nkln k2 1 1 k2
1 1 2 n2 1 1 n2i 1 E Ei E*
6
where E and n represent the materials elastic modulus and Poisson's ratio and the suf®x i refers to the parameters of the indenter (diamond: Ei 1140 GPa, ni 0:07 [17]). The elastic modulus of the substrate (approximately 70 GPa) was measured in a separate experiment using uncoated glass and was used as a ®xed parameter in the ®tting process. A typical ®t obtained using the Doerner and Nix's model [23] is shown in Fig. 6. Fig. 7 shows a ®t obtained using the simpli®ed Gao [22] expression (Eq. (3)). The function derived by Gao [22] led to a value of the elastic modulus of approximately 8 GPa as compared to 10 GPa for the Doerner and Nix [23] model. The three parameter function suggested by Doerner and Nix [23] described the nearsurface data of the elastic moduli better than Gao's two parameter model [22]. The former was therefore used to estimate the modulus of the coating. The elastic modulus of the coating was found to be equal to 10 ^ 1 GPa, irrespective of the preparation conditions. It is not surprising that the function derived by Gao [22] led to lower values of
3
where k h=a expresses the ratio of the coating thickness, h, and the contact radius, a, and n is the Poisson's ratio. Second, Doerner and Nix [23] proposed on the basis of experimental results for the composite modulus of a ®lm and its substrate a function of the form 1=E* 1=Ef FDN 1 1=Es 1 2 FDN
4
The parameter F DN is a weight function de®ned as
FDN 1 2 e2bh=x
5
where b is a constant and h/x is the ratio of thickness, h, and contact indentation depth, x, and E* is the reduced elastic modulus, given by
Fig. 5. Comparison of the indentation pressure versus contact depth of a coating cured at 2508C after a pre-reaction time of 1 h. The stars represent the data obtained one week after the preparation; the diamonds represent the measurement after 46 days. The layer was 9.5 mm thick. The lines represent a guide for the eye.
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Fig. 6. Effective elastic modulus of a coating cured at 2508C after a prereaction of 3.5 h. The coating was 11.5 mm thick. The line is a ®t to the Doerner and Nix model [23].
Fig. 8. Pre-exponential factor b for coatings cured at 2508C after 3.5 h prereaction and 4008C after 1 or 3.5 h 0 pre-reaction. The dashed line represents a guide of the eye.
the elastic modulus, since his derivation was based on a ¯at punch. The use of a spherical or conical indenter leads to the measurement of an average modulus, since these styluses measure the unloading compliance at different depths simultaneously. The value of ®tting constant b , on the other hand, seems to depend on the coating thickness. Generally, b was found to be greater for thicker coatings (Fig. 8), suggesting a dependence of the materials properties on the thickness of the coating. The function suggested by Gao [22] showed a similar dependency of the ®tted function on the layer thickness. Calculations indicated that a spin rate effect on the particle distribution can be ruled out in the case of the spin rates used in the experiments (100±2500 rev./min) [20]. It is reasonable to assume that the change in the dependency of the elastic modulus on the coating thickness could be attributed to the inadequacy of the relatively simple ®tting routine suggested by Doerner and Nix [23] or to the increased uncertainty of Gao's [22] function for large differences in coating and substrate moduli and thin coatings. Alternatively, the in¯uence of the cracking and delamination and the increased energy dissipation in these processes for thin coatings might be responsible for the observed behavior.
Gao [22] has shown through ®nite element simulation that interfacial delamination can modify the contact compliance. This was also remarked by Wu et al. [24] for delamination and cracking normal to the interface. The elastic modulus is measured from the start of the unloading curve. At this moment the thickness of the coating is smaller than its original value, since the coating became thinner due to plastic ¯ow during loading and the coating is compressed elastically [25]. This effect will in¯uenced thinner coatings to a much stronger extent than thicker coatings. A combination of the above effects results in the observed dependency of b on the coating layer thickness. In the present experiment, the elastic modulus of the coatings was obtained from the smallest indentation depths, which were not in¯uenced by the cracking of the coating that took place at higher loads. Our samples did not show signs of pile-up after the indentation as observed using AFM, although generally pile-up can be expected for soft ®lms [24]. Annular cracking was observed before pile-up could become signi®cant. Comparison of the elastic modulus with the indentation pressure results shows that the elastic modulus curves do not exhibit any maximum near the surface. Obviously, a thin surface layer of a high indentation pressure has no in¯uence on the unloading compliance, which was used to estimate the elastic modulus [17]. The elastic modulus depends on the response of the indented body as a whole, whereas the indentation pressure depends on the volume of the plastically deformed region [25]. Re-measurement of the elastic modulus after 46 days resulted in values similar to those measured immediately after the curing, in contrast to what was observed in the indentation pressure values. 3.4. Fracture toughness In this section the fracture toughness of the coatings is calculated using radial cracks, chipping phenomena and the load at which initial signs of delamination became visible.
Fig. 7. Effective elastic modulus of a coating cured at 2508C after a prereaction of 3.5 h. The coating was 11.5 mm thick. The line is a ®t to the Gao model [22].
3.4.1. Fracture toughness - radial cracks After the indentation radial cracks were observed in the
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145
surface. Longer pre-reaction time and higher curing temperature led to shorter cracks at a particular load (Fig. 9). One method for determining the fracture toughness, KIC, and the residual stress at the surface, s , of bulk materials is to measure the length of radial cracks, c, that form during indentation as a function of indentation load, P. The relation that is generally used reads [26]
xr P=c1:5 KIC 2 2s c=p0:5
7
where xr 0:016 E=H0:5 for a Berkovich-type indenter [27]. The model was developed for bulk materials, but has been used successfully to determine the fracture toughness of coatings [27±30]. Furthermore, the hardness to elastic modulus ratio of coating and substrate are similar, implying a stress ®eld similar to that of a bulk material [31]. Delamination or chipping of the coating in¯uences the energy dissipation only at high loads. The indentation results were analyzed according to this method. A fracture toughness of 0.62 MPa m 0.5 was obtained for the glass substrate using the radial cracks that formed during indentation, which is in agreement with value quoted in the literature (0.71 MPa m 0.5 for soda lime glass [32]). The `main' coating indentation pressure as a representation of the hardness (Section 3.2, Table 1) and the ®lm elastic modulus (Section 3.3) determined in previous sections were used in the calculation. Fig. 10 shows a typical graph of x rP/c 1.5 versus 2(c/ p ) 0.5. The intercept with the ordinate axis is KIC, and the slope is equal to the residual stress, with a negative slope implying a tensile stress. Only cracks that were longer than the plastic indentation size were used in the analysis [26]. The length of the radial cracks, and therefore the fracture toughness and residual stress, were found to be independent of the thickness of the coatings. Moreover it is clear from Table 1 that the coatings cured at the lower temperature show a higher (tensile) stress at the same pre-reaction time. Also, a longer pre-reaction time led to a decrease in both KIC and s at the same curing temperature. As far as cracking is concerned, these effects counteract one another: radial cracks will be larger at lower KIC values, but they will be smaller at lower tensile stresses, s . In our case, this had
Fig. 9. Comparison of the surface crack length versus indenter load for coatings cured after 3.5 h at 2508C (dashed) and 4008C (full line). The lines represent a guide for the eye.
Fig. 10. x rP/c 1.5 as a function of 2(c/p ) 0.5 for a coating cured at 4008C after a pre-reaction of 1 h; thickness 5 mm. The line represents a linear ®t.
the effect that, although the fracture toughness was smaller for the higher temperature, the crack length was also smaller due to the diminished tensile stress. This agrees with observations made on the critical thickness of coatings which was smaller for coatings cured at 2508C as compared to a curing temperature of 4008C [33]. Various chemical and physical processes that in¯uence the mechanical properties of the ®nal coating take place upon curing. They include bond scission, an increase in the number of local defects, cross-linking, oxidation, rearrangement of the particles in the coating and thermal degradation. The ratio of cross-linking and scission may vary with the preparation conditions. Possible causes of the observed reduction in the fracture toughness and the residual stress at a higher curing temperature could therefore be a relaxation mechanism on a microscopic scale like bond scission or localized burn-out of CH3 groups in the coating resulting in microscopic defects. A reduction of the residual stress at higher temperatures has also been reported by Syms [34], who found that annealing above a critical temperature reduces the residual stress in thick (10 mm) sol±gel phosphosilicate ®lms and related this observation to a reduction of thermal and intrinsic stresses at higher temperatures. Further support to our observations is given by the observations of the stress in SiO2 ®lms deposited by plasma and ozone TEOS chemical vapor deposition processes [35] where it was found that the intrinsic stress decreased above 4008C. The re-measurement of the fracture toughness 46 days after the curing showed no signi®cant change in the values of the fracture toughness and residual stress with time, which suggests that environmental moisture has a limited relaxation effect on the residual stress. 3.4.2. Fracture toughness - chipping Since the indentation depth corresponding to the observed radial cracks exceeds 10% of the coating thickness, the elastic-plastic zone might extend to the substrate. Therefore, a second method proposed by Li and Bhushan [36] was chosen to estimate the fracture toughness of the
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coating on the basis of the energy dissipated during chipping, U. In Section 3.1 it was shown that the loading curve shows discontinuities at higher loads, which were associated with chipping of the coating (see Fig. 1d). Initially, the coating delaminated. At a certain delamination length the crack proceeds further through the coating and a coating chip is removed. At this point the fracture toughness is determined. The discontinuities in the load displacement curve can be associated with this single event of chipping. The edge of the chipping is far from the indenter and is not in¯uenced by any substrate penetration of the indenter, which overcomes the limitation imposed for the calculation of the fracture toughness on the basis of the radial cracks. In the suggested method [36] the loading curve is extrapolated in a tangential direction from the starting point of the discontinuity to the same indentation depth as at the end of the discontinuity. The difference between the extrapolated and the measured load displacement curve is then a measure of the dissipated energy. The fracture toughness can then be calculated using [36] 0:5 E U 8 KIC h0 N 1 2 n2 2pcd where cd is the diameter of the delamination crack, N is the number of delamination cracks (usually three in our experiments), and h 0 is the effective coating thickness (coating thickness divided by sin(q ), where q is the average angle of the chipping edge, which was 17:5 ^ 28). The average angle of the chipping edge was determined from the distance between the lower and the upper edge of a removed area at a particular coating thickness using an optical microscope. The fracture toughness measured with the aid of this method should not be affected by residual stress, since the energy is released during the formation of the interfacial crack. Hu et al. [37] have shown that the stress intensity of a crack extending perpendicular through a ®lm is a factor of two larger than that of a crack extending parallel along the ®lm. The values of the calculated fracture toughness divided by two are shown in Table 1, along with the results calculated on the basis of the radial cracks, showing that the two sets of data are in good agreement. 3.4.3. Fracture toughness - load of delamination Fig. 11 shows a typical graph of the dependence of the critical load of delamination on the coating layer thickness. Delamination, which occurred during loading, was visible as bright spots occasionally associated with interference fringes. (Fig. 1c). Chipping at larger loads clearly con®rmed that failure occurred at the interface between the coating and the substrate (Fig. 1d). The relationship between load at which delamination became visible, Pc, and the layer thickness, h, could well be described by Pc < h1:5 . In this section it will be attempted to calculate the fracture toughness in a third way, next to the two methods that are based on the radial cracking and the chipping as explained
Fig. 11. Load of initial delamination measured for a sample cured at 4008C after a pre-reaction of 1 h. The line represents a ®t of the function P ah1:5 , where a 18 MN/m 1.5.
in the previous sections. Therefore, it is assumed that the delamination occurs due to cracks that grow perpendicular [38] to the surface during loading, reach the interface and are then de¯ected. These cracks could be either related to a perpendicular extension of the annular or radial cracks observed in the surface of the sample after indentation, or to median cracks that form under the center of the indenter during loading as a part of the `median/radial crack system' [39] (see Section 3.5 for calculations of the interfacial fracture toughness using models for the buckling of soft coatings on hard substrates that relate the stress at the interface to the normal load under the indenter). The fact that the deformation pattern of the radial cracks, which is wider in the center of the indent, con®rms that the cracks are of radial rather than Palmquist like shape. At higher loads a number of parallel annular cracks were observed. The annular cracks were limited in their depth by the indentation stress ®eld [38]. Furthermore, each annular crack leads to a relaxation of tensile stress, which is related to its depth. If the indentation continues, stress will build up after the crack growth stops and will lead to a parallel annular crack. Since annular cracks occur at equal distances, which were found to be smaller than the coating thickness, their depths will always be the same. Considering linear elastic relaxation [33], this depth should be approximately equal to their distance. Therefore, it is unlikely that the annular cracks were responsible for the observed delamination. The condition for the growth of median cracks in bulk material during indentation loading can be described using a relation similar to Eq. (7) [39] crM P=c1:5 KIC 2 2s c=p0:5
9
where the constant x rM differs from x r in Eq. (7) since it takes into consideration the residual component of the stress ®eld on the axis as opposed to Eq. (7) which applies to the surface. Lawn et al. [39] found for glass xrM 0:02 and xrM 0:048, thus a crack will grow more easily sideways than downwards.
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In the present study we have a coating instead of a bulk material. It can be assumed that the median crack growth is governed by a relationship of the form of Eq. (9), but the constant x rM will have a different value than suggested by Lawn [39]. To determine x rM the fracture toughness of the coatings cured at 2508C with the longer pre-reaction time was used (see Section 3.4.1). The value of the residual stress found in Section 3.4.1 was used as a constant in the following calculations. The measured delamination load and the corresponding coating thickness, h, were substituted into Eq. (9) since it is assumed that delamination occurs due to de¯ection of the median cracks, when their length c h. The resulting value of xrM 0:012 was used to calculate the fracture toughness for the coatings cured at the various conditions. The results in Table 1 show good agreement with the values determined using radial cracks and chipping (Sections 3.4.1 and 3.4.2). Lawn [39] found for x r/x rM a ratio of 2.4, whereas we found a ratio of 3.8. The difference between this value and our ®ndings and the results of Lawn [39] is probably related to the modi®cation of the stress ®eld by the substrate material [40]. This is in agreement with the report of Beuth [33], who found a reduction of the stress intensity for a tensile loaded surface crack in the case of a coating on a substrate having a larger elastic modulus as compared to a bulk material. The crack can only reach the interface if some defect is present at the interface since the stress intensity will reduce below KIC before the interface is approached [41]. 3.5. Interfacial fracture toughness In this section, it will be attempted to estimate the fracture toughness of the interface between the glass and the coating from the indentation results. Furthermore, the critical condition for chipping will be estimated on the basis of buckling of the coating. Several existent models will be applied and the results will be compared. As described above, our observations suggest that delamination initiates due to median/radial cracks growing towards and then de¯ecting into the interface. The size delamination cracks increases as the load is increased, leading to buckling of the coating and at a certain load chipping occurs as the interfacial crack de¯ects into the substrate. The whole process takes place during the loading cycle (Sections 3.1 and 3.4.1). In situ observation of the crack formation using a microscope positioned directly under a Vickers indenter revealed that buckling occurred during loading (see Section 3.1). The fracture toughness of the interface was therefore estimated by considering crack de¯ection and chipping (see Section 3.4.2), similar to the energy balance approach to spallation by wedging of coating due to residual stress by Evans [42]. Initially, the coating delaminates at the interface, but at higher loads the coating chips due to the de¯ection of the interfacial delamination crack.
147
As a ®rst method to estimate the range of the interfacial fracture toughness of our coatings, we used the results of He and Hutchinson [43,44], who carried out theoretical studies on the kinking of a crack at [44] and out of the interface [43] between two dissimilar elastic solids. First, the crack will de¯ect into the interface as it approaches the interface from the surface if the ratio of fracture energy of the substrate to interface is less than 0.43 [44] using the Dundurs parameters a 20:75 and b 20:25, that apply to our coating/substrate system. Second, the interfacial crack will de¯ect into the coating if the ratio of the fracture energy of the coating to the fracture energy of the interface is lower than 1.15 [43], for the Dundurs parameters a 0:75, b 0:25 and K II =K I 0:2 (de¯ection angle of approximately 208 [40], see Section 3.4.2). The interfacial fracture toughness is de®ned as K IC GIC Ef , where Ef is the elastic modulus of the coating. This leads to 0:16 # K IC # 0:46 MPa m 0.5. The fact the fracture occurs at the interface suggests that the interfacial fracture toughness is closer to the lower value. There are other approaches for estimating the interfacial fracture energy from the delamination and buckling [45,46] of a coating including systems of soft coatings on glass substrates [47±49]. Two of these models will be applied to our measurements for comparison. The mechanism of crack initiation in these models is not the de¯ection of a crack into the interface, as suggested in our investigation, but it is assumed that delamination initiates at the interface at a position below the edge of the contact and then proceeds until an equilibrium radius is reached. The ®rst model, which is based on the contact radius at the initiation of delamination under the indenter, is by Ritter et al. [47,48], who, following an approach by Matthewson [45], proposed the following expression for the interfacial shear strength between a soft coating and its substrate [47]
tc
0:56Hc 0 K1 fac =h=fK1 fac =h 1 nh=ac f2
10
where the suf®x c refers to the critical point of crack formation, H to the hardness of the coating, K1 is a modi®ed Bessel function of the second kind, K1 0 is the derivative of this function, ac is the contact radius, f 6 1 2 n= 4 1 n1=2 , h is the thickness of the ®lm, and n is the Poisson ratio of the ®lm. Substituting the appropriate values into Eq. (10) leads to an average interfacial shear strength of 0.32 GPa for our coatings. The interfacial shear strength is the controlling factor for crack initiation, rather than propagation. To determine a value of the interfacial fracture toughness, a maximum ¯aw size at the interface of ci 0:2 mm is assumed, which appears to be a reasonable value considering the optical micrographs of the delaminations and the interfaces after chipping. Then, the interfacial fracture toughness can be estimated by K IC tc pci [40] as 0.18 MPa m 0.5. This value is within the range estimated above using the results
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J. Malzbender et al. / Thin Solid Films 366 (2000) 139±149
of He and Hutchinson [43,44], and makes it impossible to differentiate between the mechanism suggested above, i.e. the de¯ection of cracks into the interface or the loss of the adhesion due to the shear stress at a pre-existent ¯aw, which is the basis of Eq. (10). Optical micrographs of interfaces after the coatings chipped off suggest that the radial cracks have reached the interface. Another method to calculate the interfacial fracture toughness from indentation experiments in soft coatings is provided by Rosenfeld et al. [49] on the basis of calculations by Thouless [50] on the decohesion of ®lms with axisymmetric geometries. Based on the results of Rosenfeld et al. [49] the interfacial fracture toughness is linked to the size of the delaminated area and the corresponding indentation load as follows KiC
p 0:792H 1 2 n2 h 1 1 n 1 2 1 2 nHc2 =P
11
where c is the radius of the delamination crack, and P the corresponding load. The radius of the delamination crack was determined using an optical microscope after the indentation load had been applied. Calculating the interfacial fracture toughness from the increase of the crack length versus load [45,49] using Eq. (11) leads to values of 0.6 MPa m 0.5 and 0.75 MPa m 0.5 for a curing temperature of 250 and 4008C, respectively, for the 1 h pre-reacted solutions. For the 3.5 h pre-reacted solution the values are 0.9 and 1.1 MPa m 0.5 for a curing temperature of 250 and 4008C, respectively. Thus, the fracture toughness increases by 25% by increasing the curing temperature from 250 to 4008C, whereas it increases by 50% by increasing the pre-reaction time of the coating solution from 1 to 3.5 h. The used model assumes that the pressure at the interface is approximately equal to the hardness, i.e. the indentation pressure in our case. This appears reasonable since the indentation pressure was not modi®ed signi®cantly by the occurrence of interfacial delamination. The values calculated using the model by Rosenfeld et al. [49] are higher than estimated above. This is probably related to the fact that interaction of radial cracks in the surface and interfacial cracks, which reduces the stress at the interface by relaxation, was ignored. Furthermore, the stress intensity for interfacial cracks will be modi®ed by the elastic mismatch between coating and substrate [51]. Rosenfeld [49] considered a clamped circular plate constrained to have zero de¯ection at its center. If we consider that the delamination occurs between the radial cracks as three separate circular clamped plates, but with de¯ection at their center, then the buckling stress and shear stress at the interface will be reduced by a factor of 0.34 [44]. Thus, the average fracture toughness will reduce to 0:28 ^ 0:06 MPa m 0.5, which appears to be in agreement with the values estimated using the results of He and Hutchinson [43,44]. Eqs. (10) and (11) are based on indentation data, i.e. the contact area at initial delamination (determined from the
load-displacement curve following Oliver and Pharr [17]), the radius of delamination, and the indentation load. Hence, the interfacial fracture toughness has indeed been determined on the basis of indentation data. In the case of interfacial delamination, the de¯ection angle will be 908 and the fracture will be limited by the interfacial fracture toughness for mode II, which has been supported by numerical calculations [51]. The chemical bonding via O±Si groups in the coating and at the interface suggest a similar fracture toughness of coating and interface. There are several theories for mixed mode failure based on linear elastic fracture mechanics, which allow a prediction of the ratio of the fracture toughness for pure mode II to pure mode I failure, i.e. KIIC to KIC. This ratio is 0.81 according to the strain energy release rate theory [53], 0.87 according to the maximum hoop stress theory [54] and 1.05 according to the strain energy density theory [55] for bulk materials. Experimentally, ratios between 2 [56] and 1.2 [57] were found. Suresh [58] suggested that the high apparent fracture toughness for mode II arises from crack face friction, which is probably a mechanism leading to a higher apparent interfacial fracture toughness as calculated using Rosenfeld's model [49]. Finally, it was observed that chipping of the coating occurred always at a discrete ratio h/w of coating thickness to half the diameter of delaminated area (h=w 0:18 ^ 0:06 for coatings made from fresh solutions). Evans and Hutchinson [52] investigated the mechanics of delamination and spalling/chipping of an indented ®lm by modeling the ®lm as clamped circular plate under compression. The critical condition for spalling found by Evans and Hutchinson [52] reads 0:5 w E 1:92 f 12 s0 h where Ef is the elastic modulus of the coating and s 0 the biaxial compressive stress induced in the coating. If we consider s 0 to be equivalent to 0.56 times the hardness [41], which is equivalent to the indentation pressure (Section 3.1), Eq. (12) gives a value of h/w of 0.14. This is slightly lower than the measured ratio given above. Eq. (12) allows a prediction of the critical delamination size that leads to spalling of a coating of a particular thickness and can therefore be used as a failure criterion. 4. Conclusions In this paper we have studied the indentation response of organic-inorganic hybrid coatings on glass substrates. It was observed, that many different phenomena occurred in the coatings during indentation. In particular, radial cracking, chipping, and delamination occurred all during one indentation, and could be related to changes in the load-displacement curves. From the measured load-displacement curves,
J. Malzbender et al. / Thin Solid Films 366 (2000) 139±149
the apparent hardness and the elastic modulus were determined. We found that the apparent hardness possessed a peak near the coating surface, which was most probably related to strain hardening of the coating. Also, the cracking in¯uenced the measured hardness at larger indentation depths. Due to these phenomena, the data could not be ®tted to existing models. Existing models could describe the change of the elastic modulus with indentation depth. An estimate of the coating fracture toughness KIC and the residual stress could be obtained by different methods, each making use of a different cracking phenomenon that occurring during the measurement. Hence, we obtained KIC from analysis of radial cracking, chipping, and delamination. Clear in¯uences of preparation conditions were observed. Moreover, there was close resemblance between the values obtained by the different methods, which gives con®dence in the result. Finally, also the interfacial fracture toughness of the coating-substrate interface was estimated using various existing models. The results obtained using different models to determine the elastic modulus and fracture toughness showed good agreement. Acknowledgements The authors would like to acknowledge Dr A.R. Balkenende, Dr T.N.M. Bernards and Dr P.C.P. Bouten (Philips Research Laboratories, Eindhoven, The Netherlands) for their technical support and useful discussions. References [1] A. Paul, Chemistry of Glasses, Chapman and Hall, London, 1990. [2] H. Bach, D. Krause, Thin Films on Glass, Springer-Verlag, Berlin, 1997. [3] G.L. Smay, Glass Technol. 26 (1985) 46. [4] F.H. Wang, X.M. Chen, B. Ellis, R.J. Hand, A.B. Seddon, J. Mater. Sci. Technol. 13 (1997) 163. [5] T.H. Wang, P.F. James, J. Mater. Sci. 26 (1991) 354. [6] H. Schmidt, J. Sol±gel Sci. Technol. 1 (1994) 217. [7] A. Atkinson, R.M. Guppy, J. Mater. Sci. 26 (1991) 3869. [8] R.H. Brzesowsky, G. de With, S. van de Cruijsem, I.J.M. SnijkersHendrickx, W.A.M. Wolter, J.G. van Lierop, J. Non-Cryst. Solids 241 (1998) 27. [9] M.R. McGurk, T.F. Page, J. Mater. Res. 14 (1999) 2283. [10] Y.M. Lim, M.M. Chaudhri, Y. Enomoto, J. Mater. Res. 14 (1999) 2314. [11] Page, T.F., Phar, G.M., Hay, J.C., Oliver, W.C., Lucas, B.N., Herbert, E., Riester, L., Fundamentals of Nanoindentation and Nanotribology. MRS Symp. Proc. 522. 53 1998 [12] M. Sakai, S. Shimizu, T. Ishikawa, J. Mater. Res. 14 (1999) 1471. [13] J.-H. Ahn, D. Kwon, J. Appl. Phys. 82 (1987) 3266. [14] E. Soederlund, D.J. Rowcliffe, J. Hard Mater. 5 (1994) 149.
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