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Quantitative analysis of scratch-induced microabrasion on silica glass
Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
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Quantitative analysis of scratch-induced microabrasion on silica glass Elham Moayedi, Lothar Wondraczek⁎ Otto Schott Institute of Materials Research, University of Jena, Fraunhoferstrasse 6, 07743 Jena, Germany
A R T I C L E I N F O
A B S T R A C T
Keywords: Glass Damage resistance Scratch Weibull distribution Silica
We employ instrumented nanoindentation for obtaining quantitative information on the onset of scratch-induced microabrasion on silica glass. For this, in situ evaluation of lateral force and friction coefficient is compared to post mortem optical inspection, following edge-forward scratching with a Berkovich indenter at velocities of 10–500 μm/s under continuously increasing normal load of up to 300 mN. In the two approaches, the onset of microabrasion is identified from the occurrence of pop-ins in the load-displacement curve and phenomenologically determined from the scratch pattern, respectively. Obtained data are analyzed in terms of a Weibull distribution, assuming that microabrasion sets-on as a result of acting stress as well as surface state. Aside of the occurrence of occasional outliers at low load (probably induced through individual surface defects), data indicate two underlying probability functions, i.e., the probability for the propagating scratch to hit a surface flaw and the probability that such an event causes an observable micro-crack. Dominance of the former leads to an exponential function with Weibull modulus ~1, reflecting a purely random distribution with loadindependent probability of failure. This is observed in particular at high scratching velocity after passing a certain normal load. For the latter, the Weibull modulus increases with increasing scratching velocity, that is, from ~1.6 to 4.4, at intermediate load. Here, low Weibull modulus at low load is attributed to the increasing time of local strain, which leads to a reduction of the load-dependence of micro-cracking relative to a fastermoving scratch. In the present case, the critical lateral load for microabrasion of silica (50th percentile) is around 30–40 mN. Within the employed experimental conditions, this value is practically independent of scratching velocity.
1. Introduction As a commodity component in a variety of consumer applications, glass surfaces are frequently subjected to abrasive load and scratching. At the same time, most of these applications rely on the surface quality and visual appearance of the employed glass. Scratch-induced surface flaws may strongly compromise this aspect. In addition, they also act as stress amplifiers and, hence, reduce overall mechanical performance. Understanding abrasive damage and the underlying material properties has therefore been a subject of significant interest. However, present considerations of the scratch and abrasion resistance of glasses are mostly phenomenological [1–5]. In particular, this concerns the established protocols for scratch testing, which provide only qualitative information. In the first steps towards a rigorous and eventually mechanistic description of the scratching process on glass surfaces [1], Le Houérou considered the archetype example of soda lime silicate glass by dynamic micro-indentation. Applying an increasing normal load on a Vickers indenter during linear lateral displacement at constant speed, they found a characteristic pattern in which distinct
⁎
regimes of damage are observed. With increasing normal load, these comprise, in sequence, of plastic deformation, micro-cracking, chipping and micro-abrasion, Fig. 1a–b. According to these early observations, radial (chevron) cracks are the first flaws which appear beyond the ductile regime, at relatively low load. With increasing load, lateral and median cracks reach the surface and form chips. Here, median cracks propagate deeply into the material while lateral cracks appear close to the surface in a depth which lies within the so-called plastic zone [6,1]. A broad variety of parameters determines this phenomenology, including the rate of scratching, the indenter geometry relative to the scratching direction, the applied normal force, glass surface conditions, environmental atmosphere and humidity, and the presence of debris or impurities on the specimen surface. So far, the concrete action of these parameters has received only very limited attention [2,7,8]. This is particularly the case for the technically relevant question of compositional dependence. Here, recent approaches to compositional development rely largely on the assumption that data obtained from normal indentation correlate directly (or even linearly) with damage resistance under lateral contact
Corresponding author. E-mail address: [email protected] (L. Wondraczek).
http://dx.doi.org/10.1016/j.jnoncrysol.2017.05.003 Received 20 March 2017; Received in revised form 25 April 2017; Accepted 10 May 2017 0022-3093/ © 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).
Please cite this article as: Moayedi, E., Journal of Non-Crystalline Solids (2017), http://dx.doi.org/10.1016/j.jnoncrysol.2017.05.003
Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
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Fig. 1. Typical scratch pattern which is observed on silicate glasses during steady scratching with increasing normal load (a). In (b), this phenomenology is shown for the specific case of fused silica at a scratching rate of 50 μm/s and a normal load which increases from zero to 300 mN, using an irregular diamond edge for scratching. (c) is a representation of the corresponding variation in the apparent friction coefficient (see text for details).
control of the normal load LN on a Berkovich tip and recording of the lateral load LL during lateral displacement as illustrated in Fig. 2. The value of LL results from a specific rate of normal loading and lateral displacement. It is determined from the lateral stiffness of the indenter, KL, and its displacement in x- and y-directions, shown schematically in Fig. 2a. The overall observation length (lateral displacement) was kept constant among all samples (1.0 mm). Samples themselves were cylindrical with a diameter of 33 mm and thickness of approximately 3 mm. On the studied surface, they were sequentially polished with dry silicon carbide powder with grain sizes of 70, 40 and 9 μm, and finally with a suspension of diamond powder with a grain size of 1.0 μm, leading to an average roughness of 1.19 μm (mean arithmetic height, taken from confocal microscopy) and subsequently stored in vacuum. Directly before analysis, the samples were cleaned in an ultrasonic bath of pure isopropanol for 5 min at room temperature, and subsequently flushed with ethanol. Tests were conducted by increasing the normal load LN from 0.05 mN to 300 mN during lateral displacement at rates of 10, 50, 100, 150, 300 and 500 μm/s across the overall lateral displacement range of 1.0 mm, at room temperature. This corresponds to normal loading rates between 3 mN/s and 150 mN/s. The employed tip geometry is shown in Fig. 2c. Scanning was conducted in edgeforward configuration (EF, Fig. 2b). For each test, an initial specimen surface profile was obtained before scratching by pre-scanning the sample's surface with the indenter under a load of 50 μN. While testing, both the penetration depth and the value of LL were continuously monitored. After scratching, the surface profile of the sample was scanned again under the same conditions as during the pre-scanning stage. For each loading rate, 20 scratches were performed. Scratch
load. The consensus is that the indentation response of glasses is governed by the interplay of elastic deformation, structural compaction and shear [9]. Relaxation studies can subsequently be used to evaluate individual contributions of the latter two [10–12]. Then, the ability of the considered material to compact depends directly on its free volume, on molecular scale, and correlates with Poisson's ratio [13]. Accordingly, vitreous silica, with exceptionally low Poisson ratio and high free volume, exhibits a degree of structural compressibility which beats that of almost all other glasses. However, it has also become clear that the structural reactions which underlie damage infliction are significantly more complex [14]. In the present letter, we report on lateral force analyses during scratching of vitreous silica in an effort to obtain increasingly quantitative information on the scratch resistance of glasses. For this, we consider the effect of scratching velocity (loading rate) on the onset of micro-cracking and chipping. The correlation of in situ recordings of friction forces with post mortem imaging of the scratch enables the identification of onset points for scratch-induced fracture events and microabrasion. This is subsequently evaluated through Weibull statistics. 2. Experimental 2.1. Scratch testing Instrumented nanoindentation (G200, Agilent) was employed to generate quantitative data on the scratch resistance of commercialgrade vitreous silica (Heraeus Suprasil 1). The experiment comprises 2
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Fig. 2. (a) Schematic of the determination of lateral load LL. (b) Evolution of lateral force during scratching (lateral displacement) while increasing the normal load from 0.05 mN to 300 mN at a scratching velocity of 50 μm/s. The first 200 μm of lateral displacement correspond to the pre-scan area (in which a normal load of 50 μN is applied). The cracking region is highlighted: arrows mark individual cracking (chipping) events; the onset of microabrasion is marked with a dashed line (see text for details). The upper left inset illustrates the experimental definitions of lateral and normal load, and the tip configurations during scanning, edge-forward (EF, applied here) and face-forward (FF). (c) is a 3D representation of the employed tip, obtained by wide-field confocal microscopy. In (d), an example of a scratch at constant normal load, in the plastic regime is shown (label indicates scratching speed and normal load). The highlighted area in (d) represents the work of deformation. The line in (b) is shown as a guide to the eye.
across those pop-ins and taken as the lateral onset load for microabrasion. Besides the onset of microabrasion, further features can be detected in the data shown in Fig. 1b–c. For one, there is the onset of chipping where there appears to be a deviation between the in situ observation of friction (or lateral load) and the post mortem consideration of the scratch pattern. This indicates that similar to normal indentation, the initial radial (chevron) cracks appear during unloading, i.e., after the scratching tip has passed the specific point of occurrence. Such cracking events can therefore not be detected in situ, although they may cause weaker artifact features on the subsequent plot of LL. The concrete verification of the onset point of micro-abrasion was done based on the appearance of pop-ins in the in situ chart as in the example of Fig. 1b, and with the help of microscopic images as in Fig. 1c. In all three methods, an error bar of ± 5 μm was applied on the obtained value of characteristic displacement. Data on the onset of microabrasion were analyzed in the form of a Weibull distribution so as to obtain statistical information on the scratch-induced cracking behavior of the material. The Weibull distribution is based on the weakest link theory according to which the fracture behavior of a material is linked to the most significant defect within the material. The cumulative Weibull probability function is
patterns were observed by optical microscopy, using a standard optical microscope (Leica DM 2500 M), and a wide-field confocal microscope (Zeiss Smartproof 5) for 3-dimensional topographic evaluation. 2.2. Data analysis The apparent coefficient of friction, μ, is approximated from the ratio of lateral and normal load,
μ=
LL LN
(1)
This assumes a fully plastic contact in which the progressing indenter is opposed by the resistance of the material to be removed in its wake (Fig. 2b). As a quantitative measure of scratch resistance, the occurrence of the first instantaneous cracking event during scratching was analyzed. This analysis was performed on recordings of lateral force and apparent friction coefficient versus lateral displacement and indentation depth, respectively. In a typical such scan (Fig. 1b or Fig. 2b), an approximately steady or, in the case of LL analysis, even linear increase is observed in both parameters with increasing normal load during scratching. At a certain stage, this steady evolution is interrupted by sharp pop-ins. These are assigned to fracture events, leading to sudden bursts at the progressing scratch tip. As illustrated in Fig. 1b–c, the occurrence of these bursts correlates with the post mortem scratch pattern, where the onset of microabrasion corresponds to the onset of strong discontinuity in the plot of friction coefficient versus lateral displacement. The corresponding value of LL was then obtained by extrapolation of the initial regime of the plot (plastic regime, Fig. 1b)
⎡ ⎛ σ − σu ⎞ ⎤m Pf = 1 − exp ⎢ −⎜ ⎟⎥ ⎣ ⎝ σθ ⎠ ⎦
(2)
where Pf is the probability of failure at or below a given stress σ, σu is a threshold parameter which represents the minimum stress below which a test specimen will not break, σϴ is the scaling parameter, taken as the characteristic strength and dependent on specimen size and experiment 3
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configuration, and m is the Weibull modulus. Setting σu to zero and taking the double logarithm of the resulting two-parameter Weibull distribution yields
⎡ ⎛ 1 ⎞⎤ ⎟ ⎥ = mlnσ − mlnσθ ln ⎢ln ⎜ ⎢⎣ ⎝ 1 − Pf ⎠ ⎥⎦
ins are not experimental artifacts, this means that the underlying cracks are either too small to be visually resolved, or that they do not occur on the surface instantaneously, e.g., that they form sub-surface and/or during unloading in the wake of the scratching indenter, so that the crack intersection with the scratch groove which as identified post morten does not correspond to the point of in situ observation of the disturbance of the moving indenter. The latter interpretation is supported by the corresponding observation that certain cracks which are visible post mortem do not have a parallel pop-in event in the in situ scans. In the correlation graphs of Fig. 3, such events are the primary reason for the extreme outliers. Direct inspection of in situ recordings of lateral force LL provides a very similar picture (Fig. 2b). Here as well, individual pop-ins are detected across the phenomenological regions of radial cracking and chipping (Fig. 1a). The occurrence of the first pop-in correlates roughly with the transition from the plastic regime to the regime of radial cracking at a displacement of ~ 400 μm (including the pre-scan of 200 μm, Fig. 1b–c and Fig. 2b). The non-linear onset of μ in the first 200 μm of the scratch is caused by non-linear LL. Interestingly, the onset of microabrasion corresponds to the onset of linearity in LL and, consequently, in μ. It remains a question of further study as to how this non-linearity correlates to, e.g., indentation size effects and the strain-rate dependence of indentation response. Since in the present experiment, a linear increase of LN is imposed on the system, information which is provided through in situ determination of μ or LL is physically equivalent. Thus, determination of the onset of microabrasion from scans of μ or LL should provide equivalent results. Individual pop-ins are more clearly visible in the LL scan, especially for lower normal load where they are not smeared-out through mathematical division. Vice versa, the onset of microabrasion is better seen in the μ scan, which also leads to better agreement with optical inspection, Fig. 3a–b. Over a series of experiments with increasing normal load, the scratching distance and onset load of microabrasion are not constant. As an example, such data are provided in Table 1 for a scratching speed of 50 μm/s (corresponding to a normal loading rate of 15 mN/s). This indicates a strong contribution of the material surface condition [16] and/or experimental parameters (such as the proper orientation of the tip in EF configuration, Fig. 2b) to the occurrence of scratch-induced surface cracks, similar as with strength testing or determination of the load of crack initiation through normal micro-indentation [17–19]. In some cases, the responsible surface flaws can readily be detected by optical inspection, e.g., Fig. 4.
(3)
The probability value of Pf is obtained through Benard's median rank approximation,
Pf =
i − 0.3 n+4
(4)
where i is the rank of each data point in order of ascending LL and n is the total number of scratches per experiment [15]. After linearizing Eq. 3, m is obtained from the slope and σϴ from the intercept. 3. Results and discussion 3.1. Phenomenology Optical analyses confirm the general phenomenon of sequential plastic deformation, chipping and micro-abrasion (Fig. 1b) [1]. Beyond the plastic regime, the cracks which occur around the scratch groove are mostly surface chips or lateral cracks. In the given example, the onset of microabrasion is clearly visible at a scratch length of ~450 μm. In the plot of μ versus displacement (Fig. 1c), this corresponds to the onset of frequent pop-ins without recovering continuous friction. The overlap between in situ variations in μ and post mortem optical inspection, for the microabrasive regime, has two consequences. For one, it indicates suitability of the observation of μ for accurately quantifying the onset of microabrasion. Secondly, it indicates that the pop-ins which are observed in the microabrasive regime correspond to practically instantaneous cracking. For broader verification, the characteristic onsets of microabrasion (OM) of all experiments from the present study such as obtained from μ and from optical inspection, respectively, are plotted against each other in Fig. 3. As an example, there is good accordance between the two ways of observing OM, i.e., a linear correlation with slope ~ 1.014 and Pearson product-moment correlation R ~ 0.8717 for the chart of Fig. 3a (the low value of R is a result of two individual extreme outliers). More detailed inspection of Fig. 1c reveals the occurrence of individual pop-ins already before microabrasion, i.e., in the region of chipping. Here, the points of occurrence do not clearly correspond to post mortem optical observations. Assuming that these individual pop-
Fig. 3. Determination of the onset of microabrasion (scratch length in μm) OM through different methods: (a) Post mortem optical microscopy and in situ observation of the apparent coefficient of friction, and (b) optical microscopy and in situ observation of the lateral force. In (c) the determination of lateral force is considered, i.e., as read directly during in situ scans and as determined from the length at which OM was observed through the apparent coefficient of friction, μ, according to (a). The lines represent linear correlation fits with indicated slope and Pearson product-moment correlation R. Data derive from 20 individual experiments for each of the 6 scratching velocities. In (c), the three data points marked with an asterix were excluded from the linear fit. All lines represent linear fits of the data, with fitting parameters given in the respective panel.
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scratching rates (300–500 μm/s, Fig. 5). In this regime, the probability function levels-off to an exponential equation, indicating constant rate of failure. Such independence of mechanical failure on load (random OM) can be interpreted as resulting from high overall surface quality (thus, generally high abrasion resistance) with very occasional (laterally randomly distributed) failure-inducing flaws. This means that a high scratching rate smears-out the occurrence of OM in some specific samples with low surface defect density. Vice versa, it can also be concluded that some flaws are activated only at low scratching rate: at high enough rate, the indenter is simply passing-by some types of defects. For further evaluation, at the moment, only the intermediate regime was considered as marked in Fig. 5. For this regime, the Weibull modulus is found in the range of roughly 1.6–4.4, increasing with increasing scratch velocity and/or increasing loading rate. Hence, the underlying probability of failure exhibits a compressed exponential or even Gaussian distribution which is further compressed with increasing loading rate. Especially at low scratch velocity, the values are somewhat below but still in the range of those which are typically found in macroscopic testing of similarly prepared glass samples, e.g., by ringon-ring cracking [21]. On the one hand, this signifies the much lower tested volume. On the other hand, it also indicates that at high enough scratching rate (and, thus, tested length), scratch-induced microcracking is similarly affected by the presence of surface flaws as is macroscopic cracking (notwithstanding the above arguments regarding the regime of high load/high rate). As noted above, with the exception of the experiment which was conducted at 50 μm/s, the obtained Weibull moduli depend roughly linearly on scratching velocity. Looking at the exact data (Fig. 5), the increase in the value of m originates from an overall compression of the data. That is, the underlying probability function is compressed on the low-load side, leading to postponed activation of certain flaws at higher scratching velocity and/or accumulation in individual cracking events rather than continuous microabrasion. Data then catch-up at higher load, leading to a steeper profile in the Weibull plot. Vice versa, at lower velocity, more time is left for defect activation and growth. Aside of individual outliers (in the low-load failure regime, see above), the onset of microabrasion follows a normal or even compressed exponential distribution. This reflects a situation where the proceeding scratch is intersecting randomly distributed surface defects with a decreasing stress-dependence of their activation to form cracks. A similar conclusion was drawn by for the case of soda lime silicate glasses [22,23]. Also for these, it was found that changing the scratching velocity affects the cracking behavior. This was attributed to extended time interval over which any one surface defect stays in a stressed state at lower scratching velocity, so that its probability of growing into a visible surface crack increases. It remains to be examined in future studies how this is related to subcritical defect growth.
Table 1 Onset of microabrasion (OM) for a series of 20 experiments, scratching vitreous silica at a rate of 50 μm/s with normal load increasing from 0.05 mN at a rate of 15 mN/s. Experimental errors are ± 5 μm on all displacement data, and ± 0.01 mN on all loads. experiment no.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 average
Displacement of OM (μm) Inspection of μ
Optical inspection
Inspection of LL
LN at OM (mN)
193 275 158 643 439 159 731 554 111 779 629 555 430 208 631 449 550 291 530 605 446
206 280 140 660 370 105 746 334 180 720 590 593 440 210 600 500 580 200 580 525 427.9
273 266 190 499 429 130 131 513 128 703 601 560 431 214 617 486 540 209 513 597 401.5
81.9 79.5 56.9 150 128 38.9 39.0 154 38.3 211 180 168 129 64.1 185 145 162 62.6 154 179 162.1
LL at OM (mN)
22.1 19.9 15.7 54.3 32.3 10.8 58.6 39.2 9.5 55.4 47.6 42.7 32.6 15.9 49.5 38.2 43.3 16.7 39.1 47.1 34.5
3.2. Statistical analysis Following the above observations, statistical analyses were performed in order to extract quantitative data on the scratching behavior of vitreous silica. This included analyses of the probability Pf for the occurrence of microabrasion. In Fig. 5, data are provided for LL at the onset of microabrasion (including the data given in Table 1 for the case of scratching at 50 μm/s, 15 mN/s). Clearly, the probability of failure is higher at higher lateral load. A minimum value of LL is required to start any abrasion, consistent with observations [20] on lateral cracking during unloading in quasi-static indentation experiments. Data on Weibull modulus are summarized in Table 2. Roughly, there are three regimes of failure (failure modes): the first failure mode occurs at relatively low load with relatively high slope (best seen in the plots for scratching velocities of 10 μm/s and 100 μm/s, Fig. 5). We attribute this mode to the occurrence of major surface flaws and/or experimental perturbations. In particular, individual outliers at lowest load indicate the occasional presence of a distinct, single disturbance or flaw. They are thus not taken into account in the following quantitative evaluation. A second regime is seen at very high load, visible only for high
Fig. 4. Post mortem optical microscopic image of a scratch generated at a scratching speed of 10 μm/s under increasing normal load (3 mN/s). The onset of microabrasion (marked) was observed at a normal load of 153.3 mN and a lateral load of 42.4 mN. In this example, the initiating surface flaw was a scratch, probably induced during polishing (marked).
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Fig. 5. Statistical analysis of the onset of microabrasion (OM) in vitreous silica during lateral indentation. Depicted data present the probability of the occurrence of microabrasion as a function of acting lateral load LL. They are plotted for varying scratching velocity with gradually increasing normal load (0. mN to 300 mN) as Weibull distribution with the probability term Pf according to Benard's median rank approximation. OM was determined from in situ lateral force measurements (see text for details). Lines represent linear fits of the intermediate failure regime (fit data in Table 2). Lines represent linear fits of the data with fitting parameters given in Table 2. As a guide to the eye, slopes of 1, 2 and 6 are also indicated.
employing the present experimental approach, the critical lateral load for microabrasion (50th percentile) is around 30–40 mN. This value is very probably dependent on extrinsic parameters such as ambient humidity.
Table 2 Weibull parameters for failure modes I and II and varying speed of scratching. Velocity (μm/s)
m
R-value for m
10 50 100 150 300 500
1.61 2.37 1.72 2.04 2.82 4.40
0.973 0.982 0.996 0.974 0.983 0.985
Acknowledgement This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (ERC grant UTOPES, grant agreement no. 681652).
4. Conclusions
References
In summary, instrumented nanoindentation was employed for obtaining quantitative information on the onset of scratch-induced microabrasion on silica glass. For this, in situ evaluation of lateral force and friction coefficient was compared to post mortem optical inspection, following edge-forward scratching with a Berkovich indenter. Statistical analysis indicated two underlying probability functions for the occurrence of microabrasion, i.e., the probability for the propagating scratch to hit a surface flaw and the probability that such an event causes an observable micro-crack. Dominance of the former follows an exponential function, reflecting a purely random distribution with loadindependent probability of failure. It was observed only at high scratching velocity after passing a certain normal load. For the latter, the Weibull modulus was found to increase with increasing scratching velocity, i.e., from ~1.6 to 4.4. Here, low Weibull modulus at low load was attributed to the increasing time of local strain, which leads to a reduction of the load-dependence of micro-cracking. For silica and
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Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/locate/jnoncrysol
Quantitative analysis of scratch-induced microabrasion on silica glass Elham Moayedi, Lothar Wondraczek⁎ Otto Schott Institute of Materials Research, University of Jena, Fraunhoferstrasse 6, 07743 Jena, Germany
A R T I C L E I N F O
A B S T R A C T
Keywords: Glass Damage resistance Scratch Weibull distribution Silica
We employ instrumented nanoindentation for obtaining quantitative information on the onset of scratch-induced microabrasion on silica glass. For this, in situ evaluation of lateral force and friction coefficient is compared to post mortem optical inspection, following edge-forward scratching with a Berkovich indenter at velocities of 10–500 μm/s under continuously increasing normal load of up to 300 mN. In the two approaches, the onset of microabrasion is identified from the occurrence of pop-ins in the load-displacement curve and phenomenologically determined from the scratch pattern, respectively. Obtained data are analyzed in terms of a Weibull distribution, assuming that microabrasion sets-on as a result of acting stress as well as surface state. Aside of the occurrence of occasional outliers at low load (probably induced through individual surface defects), data indicate two underlying probability functions, i.e., the probability for the propagating scratch to hit a surface flaw and the probability that such an event causes an observable micro-crack. Dominance of the former leads to an exponential function with Weibull modulus ~1, reflecting a purely random distribution with loadindependent probability of failure. This is observed in particular at high scratching velocity after passing a certain normal load. For the latter, the Weibull modulus increases with increasing scratching velocity, that is, from ~1.6 to 4.4, at intermediate load. Here, low Weibull modulus at low load is attributed to the increasing time of local strain, which leads to a reduction of the load-dependence of micro-cracking relative to a fastermoving scratch. In the present case, the critical lateral load for microabrasion of silica (50th percentile) is around 30–40 mN. Within the employed experimental conditions, this value is practically independent of scratching velocity.
1. Introduction As a commodity component in a variety of consumer applications, glass surfaces are frequently subjected to abrasive load and scratching. At the same time, most of these applications rely on the surface quality and visual appearance of the employed glass. Scratch-induced surface flaws may strongly compromise this aspect. In addition, they also act as stress amplifiers and, hence, reduce overall mechanical performance. Understanding abrasive damage and the underlying material properties has therefore been a subject of significant interest. However, present considerations of the scratch and abrasion resistance of glasses are mostly phenomenological [1–5]. In particular, this concerns the established protocols for scratch testing, which provide only qualitative information. In the first steps towards a rigorous and eventually mechanistic description of the scratching process on glass surfaces [1], Le Houérou considered the archetype example of soda lime silicate glass by dynamic micro-indentation. Applying an increasing normal load on a Vickers indenter during linear lateral displacement at constant speed, they found a characteristic pattern in which distinct
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regimes of damage are observed. With increasing normal load, these comprise, in sequence, of plastic deformation, micro-cracking, chipping and micro-abrasion, Fig. 1a–b. According to these early observations, radial (chevron) cracks are the first flaws which appear beyond the ductile regime, at relatively low load. With increasing load, lateral and median cracks reach the surface and form chips. Here, median cracks propagate deeply into the material while lateral cracks appear close to the surface in a depth which lies within the so-called plastic zone [6,1]. A broad variety of parameters determines this phenomenology, including the rate of scratching, the indenter geometry relative to the scratching direction, the applied normal force, glass surface conditions, environmental atmosphere and humidity, and the presence of debris or impurities on the specimen surface. So far, the concrete action of these parameters has received only very limited attention [2,7,8]. This is particularly the case for the technically relevant question of compositional dependence. Here, recent approaches to compositional development rely largely on the assumption that data obtained from normal indentation correlate directly (or even linearly) with damage resistance under lateral contact
Corresponding author. E-mail address: [email protected] (L. Wondraczek).
http://dx.doi.org/10.1016/j.jnoncrysol.2017.05.003 Received 20 March 2017; Received in revised form 25 April 2017; Accepted 10 May 2017 0022-3093/ © 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).
Please cite this article as: Moayedi, E., Journal of Non-Crystalline Solids (2017), http://dx.doi.org/10.1016/j.jnoncrysol.2017.05.003
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Fig. 1. Typical scratch pattern which is observed on silicate glasses during steady scratching with increasing normal load (a). In (b), this phenomenology is shown for the specific case of fused silica at a scratching rate of 50 μm/s and a normal load which increases from zero to 300 mN, using an irregular diamond edge for scratching. (c) is a representation of the corresponding variation in the apparent friction coefficient (see text for details).
control of the normal load LN on a Berkovich tip and recording of the lateral load LL during lateral displacement as illustrated in Fig. 2. The value of LL results from a specific rate of normal loading and lateral displacement. It is determined from the lateral stiffness of the indenter, KL, and its displacement in x- and y-directions, shown schematically in Fig. 2a. The overall observation length (lateral displacement) was kept constant among all samples (1.0 mm). Samples themselves were cylindrical with a diameter of 33 mm and thickness of approximately 3 mm. On the studied surface, they were sequentially polished with dry silicon carbide powder with grain sizes of 70, 40 and 9 μm, and finally with a suspension of diamond powder with a grain size of 1.0 μm, leading to an average roughness of 1.19 μm (mean arithmetic height, taken from confocal microscopy) and subsequently stored in vacuum. Directly before analysis, the samples were cleaned in an ultrasonic bath of pure isopropanol for 5 min at room temperature, and subsequently flushed with ethanol. Tests were conducted by increasing the normal load LN from 0.05 mN to 300 mN during lateral displacement at rates of 10, 50, 100, 150, 300 and 500 μm/s across the overall lateral displacement range of 1.0 mm, at room temperature. This corresponds to normal loading rates between 3 mN/s and 150 mN/s. The employed tip geometry is shown in Fig. 2c. Scanning was conducted in edgeforward configuration (EF, Fig. 2b). For each test, an initial specimen surface profile was obtained before scratching by pre-scanning the sample's surface with the indenter under a load of 50 μN. While testing, both the penetration depth and the value of LL were continuously monitored. After scratching, the surface profile of the sample was scanned again under the same conditions as during the pre-scanning stage. For each loading rate, 20 scratches were performed. Scratch
load. The consensus is that the indentation response of glasses is governed by the interplay of elastic deformation, structural compaction and shear [9]. Relaxation studies can subsequently be used to evaluate individual contributions of the latter two [10–12]. Then, the ability of the considered material to compact depends directly on its free volume, on molecular scale, and correlates with Poisson's ratio [13]. Accordingly, vitreous silica, with exceptionally low Poisson ratio and high free volume, exhibits a degree of structural compressibility which beats that of almost all other glasses. However, it has also become clear that the structural reactions which underlie damage infliction are significantly more complex [14]. In the present letter, we report on lateral force analyses during scratching of vitreous silica in an effort to obtain increasingly quantitative information on the scratch resistance of glasses. For this, we consider the effect of scratching velocity (loading rate) on the onset of micro-cracking and chipping. The correlation of in situ recordings of friction forces with post mortem imaging of the scratch enables the identification of onset points for scratch-induced fracture events and microabrasion. This is subsequently evaluated through Weibull statistics. 2. Experimental 2.1. Scratch testing Instrumented nanoindentation (G200, Agilent) was employed to generate quantitative data on the scratch resistance of commercialgrade vitreous silica (Heraeus Suprasil 1). The experiment comprises 2
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Fig. 2. (a) Schematic of the determination of lateral load LL. (b) Evolution of lateral force during scratching (lateral displacement) while increasing the normal load from 0.05 mN to 300 mN at a scratching velocity of 50 μm/s. The first 200 μm of lateral displacement correspond to the pre-scan area (in which a normal load of 50 μN is applied). The cracking region is highlighted: arrows mark individual cracking (chipping) events; the onset of microabrasion is marked with a dashed line (see text for details). The upper left inset illustrates the experimental definitions of lateral and normal load, and the tip configurations during scanning, edge-forward (EF, applied here) and face-forward (FF). (c) is a 3D representation of the employed tip, obtained by wide-field confocal microscopy. In (d), an example of a scratch at constant normal load, in the plastic regime is shown (label indicates scratching speed and normal load). The highlighted area in (d) represents the work of deformation. The line in (b) is shown as a guide to the eye.
across those pop-ins and taken as the lateral onset load for microabrasion. Besides the onset of microabrasion, further features can be detected in the data shown in Fig. 1b–c. For one, there is the onset of chipping where there appears to be a deviation between the in situ observation of friction (or lateral load) and the post mortem consideration of the scratch pattern. This indicates that similar to normal indentation, the initial radial (chevron) cracks appear during unloading, i.e., after the scratching tip has passed the specific point of occurrence. Such cracking events can therefore not be detected in situ, although they may cause weaker artifact features on the subsequent plot of LL. The concrete verification of the onset point of micro-abrasion was done based on the appearance of pop-ins in the in situ chart as in the example of Fig. 1b, and with the help of microscopic images as in Fig. 1c. In all three methods, an error bar of ± 5 μm was applied on the obtained value of characteristic displacement. Data on the onset of microabrasion were analyzed in the form of a Weibull distribution so as to obtain statistical information on the scratch-induced cracking behavior of the material. The Weibull distribution is based on the weakest link theory according to which the fracture behavior of a material is linked to the most significant defect within the material. The cumulative Weibull probability function is
patterns were observed by optical microscopy, using a standard optical microscope (Leica DM 2500 M), and a wide-field confocal microscope (Zeiss Smartproof 5) for 3-dimensional topographic evaluation. 2.2. Data analysis The apparent coefficient of friction, μ, is approximated from the ratio of lateral and normal load,
μ=
LL LN
(1)
This assumes a fully plastic contact in which the progressing indenter is opposed by the resistance of the material to be removed in its wake (Fig. 2b). As a quantitative measure of scratch resistance, the occurrence of the first instantaneous cracking event during scratching was analyzed. This analysis was performed on recordings of lateral force and apparent friction coefficient versus lateral displacement and indentation depth, respectively. In a typical such scan (Fig. 1b or Fig. 2b), an approximately steady or, in the case of LL analysis, even linear increase is observed in both parameters with increasing normal load during scratching. At a certain stage, this steady evolution is interrupted by sharp pop-ins. These are assigned to fracture events, leading to sudden bursts at the progressing scratch tip. As illustrated in Fig. 1b–c, the occurrence of these bursts correlates with the post mortem scratch pattern, where the onset of microabrasion corresponds to the onset of strong discontinuity in the plot of friction coefficient versus lateral displacement. The corresponding value of LL was then obtained by extrapolation of the initial regime of the plot (plastic regime, Fig. 1b)
⎡ ⎛ σ − σu ⎞ ⎤m Pf = 1 − exp ⎢ −⎜ ⎟⎥ ⎣ ⎝ σθ ⎠ ⎦
(2)
where Pf is the probability of failure at or below a given stress σ, σu is a threshold parameter which represents the minimum stress below which a test specimen will not break, σϴ is the scaling parameter, taken as the characteristic strength and dependent on specimen size and experiment 3
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configuration, and m is the Weibull modulus. Setting σu to zero and taking the double logarithm of the resulting two-parameter Weibull distribution yields
⎡ ⎛ 1 ⎞⎤ ⎟ ⎥ = mlnσ − mlnσθ ln ⎢ln ⎜ ⎢⎣ ⎝ 1 − Pf ⎠ ⎥⎦
ins are not experimental artifacts, this means that the underlying cracks are either too small to be visually resolved, or that they do not occur on the surface instantaneously, e.g., that they form sub-surface and/or during unloading in the wake of the scratching indenter, so that the crack intersection with the scratch groove which as identified post morten does not correspond to the point of in situ observation of the disturbance of the moving indenter. The latter interpretation is supported by the corresponding observation that certain cracks which are visible post mortem do not have a parallel pop-in event in the in situ scans. In the correlation graphs of Fig. 3, such events are the primary reason for the extreme outliers. Direct inspection of in situ recordings of lateral force LL provides a very similar picture (Fig. 2b). Here as well, individual pop-ins are detected across the phenomenological regions of radial cracking and chipping (Fig. 1a). The occurrence of the first pop-in correlates roughly with the transition from the plastic regime to the regime of radial cracking at a displacement of ~ 400 μm (including the pre-scan of 200 μm, Fig. 1b–c and Fig. 2b). The non-linear onset of μ in the first 200 μm of the scratch is caused by non-linear LL. Interestingly, the onset of microabrasion corresponds to the onset of linearity in LL and, consequently, in μ. It remains a question of further study as to how this non-linearity correlates to, e.g., indentation size effects and the strain-rate dependence of indentation response. Since in the present experiment, a linear increase of LN is imposed on the system, information which is provided through in situ determination of μ or LL is physically equivalent. Thus, determination of the onset of microabrasion from scans of μ or LL should provide equivalent results. Individual pop-ins are more clearly visible in the LL scan, especially for lower normal load where they are not smeared-out through mathematical division. Vice versa, the onset of microabrasion is better seen in the μ scan, which also leads to better agreement with optical inspection, Fig. 3a–b. Over a series of experiments with increasing normal load, the scratching distance and onset load of microabrasion are not constant. As an example, such data are provided in Table 1 for a scratching speed of 50 μm/s (corresponding to a normal loading rate of 15 mN/s). This indicates a strong contribution of the material surface condition [16] and/or experimental parameters (such as the proper orientation of the tip in EF configuration, Fig. 2b) to the occurrence of scratch-induced surface cracks, similar as with strength testing or determination of the load of crack initiation through normal micro-indentation [17–19]. In some cases, the responsible surface flaws can readily be detected by optical inspection, e.g., Fig. 4.
(3)
The probability value of Pf is obtained through Benard's median rank approximation,
Pf =
i − 0.3 n+4
(4)
where i is the rank of each data point in order of ascending LL and n is the total number of scratches per experiment [15]. After linearizing Eq. 3, m is obtained from the slope and σϴ from the intercept. 3. Results and discussion 3.1. Phenomenology Optical analyses confirm the general phenomenon of sequential plastic deformation, chipping and micro-abrasion (Fig. 1b) [1]. Beyond the plastic regime, the cracks which occur around the scratch groove are mostly surface chips or lateral cracks. In the given example, the onset of microabrasion is clearly visible at a scratch length of ~450 μm. In the plot of μ versus displacement (Fig. 1c), this corresponds to the onset of frequent pop-ins without recovering continuous friction. The overlap between in situ variations in μ and post mortem optical inspection, for the microabrasive regime, has two consequences. For one, it indicates suitability of the observation of μ for accurately quantifying the onset of microabrasion. Secondly, it indicates that the pop-ins which are observed in the microabrasive regime correspond to practically instantaneous cracking. For broader verification, the characteristic onsets of microabrasion (OM) of all experiments from the present study such as obtained from μ and from optical inspection, respectively, are plotted against each other in Fig. 3. As an example, there is good accordance between the two ways of observing OM, i.e., a linear correlation with slope ~ 1.014 and Pearson product-moment correlation R ~ 0.8717 for the chart of Fig. 3a (the low value of R is a result of two individual extreme outliers). More detailed inspection of Fig. 1c reveals the occurrence of individual pop-ins already before microabrasion, i.e., in the region of chipping. Here, the points of occurrence do not clearly correspond to post mortem optical observations. Assuming that these individual pop-
Fig. 3. Determination of the onset of microabrasion (scratch length in μm) OM through different methods: (a) Post mortem optical microscopy and in situ observation of the apparent coefficient of friction, and (b) optical microscopy and in situ observation of the lateral force. In (c) the determination of lateral force is considered, i.e., as read directly during in situ scans and as determined from the length at which OM was observed through the apparent coefficient of friction, μ, according to (a). The lines represent linear correlation fits with indicated slope and Pearson product-moment correlation R. Data derive from 20 individual experiments for each of the 6 scratching velocities. In (c), the three data points marked with an asterix were excluded from the linear fit. All lines represent linear fits of the data, with fitting parameters given in the respective panel.
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scratching rates (300–500 μm/s, Fig. 5). In this regime, the probability function levels-off to an exponential equation, indicating constant rate of failure. Such independence of mechanical failure on load (random OM) can be interpreted as resulting from high overall surface quality (thus, generally high abrasion resistance) with very occasional (laterally randomly distributed) failure-inducing flaws. This means that a high scratching rate smears-out the occurrence of OM in some specific samples with low surface defect density. Vice versa, it can also be concluded that some flaws are activated only at low scratching rate: at high enough rate, the indenter is simply passing-by some types of defects. For further evaluation, at the moment, only the intermediate regime was considered as marked in Fig. 5. For this regime, the Weibull modulus is found in the range of roughly 1.6–4.4, increasing with increasing scratch velocity and/or increasing loading rate. Hence, the underlying probability of failure exhibits a compressed exponential or even Gaussian distribution which is further compressed with increasing loading rate. Especially at low scratch velocity, the values are somewhat below but still in the range of those which are typically found in macroscopic testing of similarly prepared glass samples, e.g., by ringon-ring cracking [21]. On the one hand, this signifies the much lower tested volume. On the other hand, it also indicates that at high enough scratching rate (and, thus, tested length), scratch-induced microcracking is similarly affected by the presence of surface flaws as is macroscopic cracking (notwithstanding the above arguments regarding the regime of high load/high rate). As noted above, with the exception of the experiment which was conducted at 50 μm/s, the obtained Weibull moduli depend roughly linearly on scratching velocity. Looking at the exact data (Fig. 5), the increase in the value of m originates from an overall compression of the data. That is, the underlying probability function is compressed on the low-load side, leading to postponed activation of certain flaws at higher scratching velocity and/or accumulation in individual cracking events rather than continuous microabrasion. Data then catch-up at higher load, leading to a steeper profile in the Weibull plot. Vice versa, at lower velocity, more time is left for defect activation and growth. Aside of individual outliers (in the low-load failure regime, see above), the onset of microabrasion follows a normal or even compressed exponential distribution. This reflects a situation where the proceeding scratch is intersecting randomly distributed surface defects with a decreasing stress-dependence of their activation to form cracks. A similar conclusion was drawn by for the case of soda lime silicate glasses [22,23]. Also for these, it was found that changing the scratching velocity affects the cracking behavior. This was attributed to extended time interval over which any one surface defect stays in a stressed state at lower scratching velocity, so that its probability of growing into a visible surface crack increases. It remains to be examined in future studies how this is related to subcritical defect growth.
Table 1 Onset of microabrasion (OM) for a series of 20 experiments, scratching vitreous silica at a rate of 50 μm/s with normal load increasing from 0.05 mN at a rate of 15 mN/s. Experimental errors are ± 5 μm on all displacement data, and ± 0.01 mN on all loads. experiment no.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 average
Displacement of OM (μm) Inspection of μ
Optical inspection
Inspection of LL
LN at OM (mN)
193 275 158 643 439 159 731 554 111 779 629 555 430 208 631 449 550 291 530 605 446
206 280 140 660 370 105 746 334 180 720 590 593 440 210 600 500 580 200 580 525 427.9
273 266 190 499 429 130 131 513 128 703 601 560 431 214 617 486 540 209 513 597 401.5
81.9 79.5 56.9 150 128 38.9 39.0 154 38.3 211 180 168 129 64.1 185 145 162 62.6 154 179 162.1
LL at OM (mN)
22.1 19.9 15.7 54.3 32.3 10.8 58.6 39.2 9.5 55.4 47.6 42.7 32.6 15.9 49.5 38.2 43.3 16.7 39.1 47.1 34.5
3.2. Statistical analysis Following the above observations, statistical analyses were performed in order to extract quantitative data on the scratching behavior of vitreous silica. This included analyses of the probability Pf for the occurrence of microabrasion. In Fig. 5, data are provided for LL at the onset of microabrasion (including the data given in Table 1 for the case of scratching at 50 μm/s, 15 mN/s). Clearly, the probability of failure is higher at higher lateral load. A minimum value of LL is required to start any abrasion, consistent with observations [20] on lateral cracking during unloading in quasi-static indentation experiments. Data on Weibull modulus are summarized in Table 2. Roughly, there are three regimes of failure (failure modes): the first failure mode occurs at relatively low load with relatively high slope (best seen in the plots for scratching velocities of 10 μm/s and 100 μm/s, Fig. 5). We attribute this mode to the occurrence of major surface flaws and/or experimental perturbations. In particular, individual outliers at lowest load indicate the occasional presence of a distinct, single disturbance or flaw. They are thus not taken into account in the following quantitative evaluation. A second regime is seen at very high load, visible only for high
Fig. 4. Post mortem optical microscopic image of a scratch generated at a scratching speed of 10 μm/s under increasing normal load (3 mN/s). The onset of microabrasion (marked) was observed at a normal load of 153.3 mN and a lateral load of 42.4 mN. In this example, the initiating surface flaw was a scratch, probably induced during polishing (marked).
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Fig. 5. Statistical analysis of the onset of microabrasion (OM) in vitreous silica during lateral indentation. Depicted data present the probability of the occurrence of microabrasion as a function of acting lateral load LL. They are plotted for varying scratching velocity with gradually increasing normal load (0. mN to 300 mN) as Weibull distribution with the probability term Pf according to Benard's median rank approximation. OM was determined from in situ lateral force measurements (see text for details). Lines represent linear fits of the intermediate failure regime (fit data in Table 2). Lines represent linear fits of the data with fitting parameters given in Table 2. As a guide to the eye, slopes of 1, 2 and 6 are also indicated.
employing the present experimental approach, the critical lateral load for microabrasion (50th percentile) is around 30–40 mN. This value is very probably dependent on extrinsic parameters such as ambient humidity.
Table 2 Weibull parameters for failure modes I and II and varying speed of scratching. Velocity (μm/s)
m
R-value for m
10 50 100 150 300 500
1.61 2.37 1.72 2.04 2.82 4.40
0.973 0.982 0.996 0.974 0.983 0.985
Acknowledgement This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (ERC grant UTOPES, grant agreement no. 681652).
4. Conclusions
References
In summary, instrumented nanoindentation was employed for obtaining quantitative information on the onset of scratch-induced microabrasion on silica glass. For this, in situ evaluation of lateral force and friction coefficient was compared to post mortem optical inspection, following edge-forward scratching with a Berkovich indenter. Statistical analysis indicated two underlying probability functions for the occurrence of microabrasion, i.e., the probability for the propagating scratch to hit a surface flaw and the probability that such an event causes an observable micro-crack. Dominance of the former follows an exponential function, reflecting a purely random distribution with loadindependent probability of failure. It was observed only at high scratching velocity after passing a certain normal load. For the latter, the Weibull modulus was found to increase with increasing scratching velocity, i.e., from ~1.6 to 4.4. Here, low Weibull modulus at low load was attributed to the increasing time of local strain, which leads to a reduction of the load-dependence of micro-cracking. For silica and
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