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Effect of load in scratch experiments on soda lime silica glass
Journal of Non-Crystalline Solids 358 (2012) 1091–1103
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Effect of load in scratch experiments on soda lime silica glass Payel Bandyopadhyay a, Arjun Dey a, c, Sudakshina Roy b, Anoop K. Mukhopadhyay a,⁎ a b c
Mechanical Property Evaluation Section, CSIR-Central Glass and Ceramic Research Institute, Kolkata-700 032, India Electron Microscopy Section, CSIR-Central Glass and Ceramic Research Institute, Kolkata-700 032, India Thermal Systems Group, ISRO Satellite Centre, Vimanapura, Post, Bangalore 560 017, India
a r t i c l e
i n f o
Article history: Received 6 November 2011 Received in revised form 30 January 2012 Available online 2 March 2012 Keywords: Soda–lime–silica glass; Scratch; Tribology; Deformation
a b s t r a c t Today the technological applications of glass span from everyday life to many advanced areas. These advanced applications require very accurate grinding and polishing that involve controlled removal of glass to achieve micron or even sub-micron surface finish. The major bottleneck in this connection is that the material removal mechanisms during such processes are yet to be fully understood. Since grinding involves many single pass scratch processes happening simultaneously, to develop better understanding about the effect of the normal load in affecting the material removal mechanisms; a number of single pass scratch experiments were conducted on a commercially available soda lime silica glass as a function of various normal loads (2–15 N) at a constant scratch speed of 100 μm.s − 1. The results showed that the tribological properties, the severity and the spatial density of damage evolution were sensitive to the applied normal loads and the resultant tensile as well as shear stresses. Extensive optical and scanning electron photomicrography of the surface and sub-surface deformation zones proved the existence of three distinct deformation zones in the immediate vicinity of the scratch grooves and led to the development of a qualitative model of the material removal mechanisms. © 2012 Elsevier B.V. All rights reserved.
1. Introduction The advanced applications of glass cover a truly wide range. It spans from our everyday life to the latest electronic gadgets to biomedical sensor technology to strategic transparent armors to thermal protection system component of space shuttles to space telescope lenses. Very accurate grinding and polishing of glass for fabrication of engineering components having utmost dimensional precision is a fundamental need for all such applications. However, to grind and polish glass with requisite dimensional precision is a big challenge as the characteristic brittleness makes it prone to undergo brittle fracture. That is the reason why the scientific issues behind the material removal mechanisms during the grinding and polishing of brittle materials like glasses as well as ceramics and glass ceramic have been receiving a huge research interest [1–20]. Recent works on alumina [21], C/C composite [22], plasma sprayed ceramic coating [23], titanium oxide thin film on glass [24], ZrB2–SiC composite [25,26], sialon ceramics [27], dental ceramics [28], DLC coatings [29], calcium phosphate coatings [30], and chromium nitride and titanium nitride coatings [31] provide the invaluable importance of scratch testing for understanding the material removal mechanisms as well as coating
⁎ Corresponding author at: Central Glass and Ceramic Research Institute, 196, Raja S.C. Mullick Road, Kolkata-32, India. Tel.: + 91 33 2473 3469/76/77/96; fax: + 91 33 2473 0957. E-mail addresses: [email protected], [email protected] (A.K. Mukhopadhyay). 0022-3093/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2012.02.006
failure mechanisms. There have been traditionally two approaches to further the fundamental understanding about the basic mechanisms of material removal process during grinding of brittle materials. Such experiments are done with single point indentation [2–4] as well as single, double or multiple pass scratch [5–8] tests conducted on glass as well as other brittle ceramics. The occurrence of microfracturing during the scratching of glass was found to be [5] very similar to the one that happens under quasi-static indentation; however the severity of stress field was enhanced due to the additional presence of the tangential load. The friction coefficient and specific energy affect the grindability of brittle solids including glass [9–11]. It was reported further [12] that when a hard sphere slides over the flat surface of glass, the classical Hertzian tensile cracks appear at the rear of the sphere when the load applied (P) exceeds a critical load (Pc) that scales with the square of the ball radius for a coefficient of friction greater than 0.02 [12,13]. Research on a glass scratched by a steel ball [14] of radius larger than the limiting radius supported these observations [12]. Li et al. [15] observed that at a normal load of 10 gf the friction coefficient was independent of scratching speed of ~ 2 to 200 μm.s − 1 but, the crack density decreased with increase in scratching speed. A transition from the deformationcontrolled to fracture-controlled process of damage evolution was identified at P > Pc from multiple scratch test experiments on glass [16]. In the case of optical glass e.g., BK7 the degree of spatial interaction among neighboring scratches [17] played a major role in material removal mechanism. Depending upon the normal load in the incremental scratch test on obsidian, three zones e.g. a micro-ductile
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zone, a micro-cracking zone and a micro-abrasive zone were reported [18]. Scratch behavior of SLS glasses was very sensitive to the loading history, the hygrometry level, the chemical structure and/or composition of the lubricant and the glass composition [19,20]. A survey of the pertinent literature data (Table 1) indeed points out that in spite of the wealth of literature there has not been any systematic study on the scratching behavior of commercially available soda lime silica glass in the intermediate load range of 2 to 15 N at a comparatively lower speed of 100 μm.s − 1. Thus, the major objective of the present work was to evaluate the scratch deformation behavior of a commercially available soda lime silica glass as a function of the applied normal load in the range of 2 to 15 N. The other important objective was to gain a better picture of the damage evolution and/or material removal mechanisms. 2. Materials and methods Commercially available 1.40 mm thick soda lime–silica glass slides (Blue Star Microscopic Cover Slide, Kolkata, India) polished down to 0.25 μm diamond paste grit size (Eastern Diamond Products Pvt. Ltd, Kolkata, India) were used in the present experiments. The glass composition was determined following the ASTM C169-92 standards and is given in Table 2. The amount of silica and calcia in the glass composition was measured by the conventional titration method. The flame photometry technique was utilized to evaluate the amount of Na2O. The inductively coupled plasma-atomic emission spectroscopy (ICPAES, Spectro Flame Modula, Model Q3: STM 08, Spectro Analytical Instruments, Germany) technique was used to determine the trace elements. The scratch tests were conducted on 15× 10× 1.40 mm size samples of the SLS glass with a commercially available scratch tester (Model TR-102-M3, Ducom, Bangalore, India) equipped with a Rockwell C diamond indenter of 200 μm tip radius. The machine comprised of the scratch tester unit along with the controller, the machine control software, the data acquisition system, the image acquisition system, the acoustic emission sensor and the connecting cables etc. A compound force transducer attached to the scratch tester measured both normal load and lateral force of up to 20 N with a load cell that had a resolution of ±0.01 N. The stroke length for all scratches was 3 mm. The scratch offset was set at 0.5 mm for all the scratches. The acoustic emission sensor (VS 150-M, capacity: 100–450 kHz, peak frequency 150 kHz, Vallen Systeme, Schäftlarner Weg 26a 82057 Icking, Germany 08178 9474400) was connected with the transducer near the indenter and had a precision level of ±0.01 dB. Four different constant normal loads (P) of 2, 5, 10 and 15 N and a constant scratch speed of
Table 1 Literature survey on scratch experiments in various glasses.
Table 2 Composition of the SLS glass. Component
Amount (wt.%)
SiO2a Na2Oa CaOa Al2O3 MgO Fe2O3 K2O TiO2
74.36 13.55 6.70 1.14 3.53 0.11 0.20 0.03
a
Principal amount.
100 μm.s − 1 were used in the present experiments. To have a statistically reliable data at least three scratches were made at a given normal load. A profilometer (Form Talysurf 120, Taylor Hobson, UK) was utilized to measure the depth and width data of the scratches. The values of the coefficients of friction (μ) were calculated by dividing the lateral force (F) by the normal load (P) in all the cases. The glass density was measured on powder sample by pycnometry method [19]. The three point bend strength of the SLS glass was measured using a standard universal testing machine (Model No. 5500 R, Instron, UK) at a crosshead speed of 0.5 mm.min − 1. The sample size was (80 mm × 25 mm × 1.40 mm). The span length was kept at 60 mm. Keeping the statistical variability of surface flaw distribution for a brittle material like glass, a total of twenty five samples were used and the average data taken. The Young's modulus and the nanohardness of the SLS glass of size 25 mm × 25 mm × 1.40 mm were measured at 100 mN load using a commercial nanoindenter (Fischerscope, H100XYP, Fischer, Switzerland). The load sensing resolution of the machine was 0.2 μN. The depth sensing resolution was 1 nm. The machine worked according to the DIN 50359-1 standard. The machine was calibrated with nanoindentation based independent evaluation of nanohardness, H ~ 4.14 ± 0.1 GPa and Young's modulus, E ~ 84.6 ± 3.5 GPa of a standard reference block e.g. Schott BK7 Glass (Schott, Germany) provided by the supplier. A nanoindentation matrix of 7 × 7 indents was utilized for the present SLS glass. The loading and unloading times were both kept fixed at 30 s with no hold time at the peak nanoindentation load of 100 mN. The nanohardness and Young's modulus data were measured from the individual load–depth plots following the well known Oliver–Pharr method [32]. Thus, the reported data for average nanohardness and Young's modulus was calculated from 49 individual measurements of the same. The fracture toughness (KIc) of the present SLS glass was measured by the conventional indentation fracture toughness method using a standard Vicker's diamond indenter at a load of 9.81 N using a hardness tester (LV 700, LECO, USA) for five individual SLS glass samples of size 25 mm × 25 mm × 1.40 mm. The fracture toughness was calculated using the following equation [33]:
Indenter type: blunt r* (μm) ~ 1500–9500 76 200
2000
P+ (N) +
P > Pc ~ 392.4–2746.8 0.098–0.49 Up to 100, ramping (single scratch test) 0.1–25 (repeated scratch test) 20
Indenter type: sharp nd 0.25–4 3 0.049–0.25 0.3 μm 0.01–3 nd 0.03–0.3 5 0.1 nd 0–4 nd 0.98
1=2
V# (μm.s− 1)
Type of glass
Ref. no.
660 10 nd
Commercial Soda–lime silica Soda–lime silica
[14] [15] [16]
250
Obsidian
[18]
1000 2–200 0.04–400 10 250 100 50
Soda–lime Soda–lime silica NaCa, SF58 Optical BK7 Obsidian Soda–lime silica Soda lime
[5] [15] [10] [17] [18] [19] [20]
r* — indenter radius, P+ — applied normal load, V# — scratch speed.
KIc ¼ 0:016ðE=HÞ
Pi :c
−3=2
:
ð1Þ
In Eq. (1) Pi is the indentation load (9.81 N), E is Young's modulus of the SLS glass as measured from the nanoindentation technique as described above, H is hardness measured at the same load (Pi), and c is the characteristic crack parameter measured as half of the sum of average indentation diagonal plus the average surface crack length measured from the tip of the indent. For a given sample at least ten indents were made for fracture toughness evaluation. Thus, for each sample the average indentation diagonal was calculated from 20 individual measurements while the average surface crack length was calculated from 40 individual measurements. The typical scatters of all data were represented as ±1 standard deviation. Both optical microscopy (Olympus GX51, Olympus, USA) and Scanning Electron Microscopy (SEM: s430i, Leo, UK) were utilized to understand how the damage evolution processes took place during
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the scratch tests. A 50–70 nm carbon film was deposited on the glass sample by the arc deposition technique to avoid charging; then it was inserted into the sample chamber for SEM.
3. Results The chemical composition of glass is given in Table 2. The data in Table 2 show that the total amount of network modifier was more than 20% in the present glass composition. The density of the SLS glass was 2.42 ± 0.07 g.cc − 1. The three point bend strength, Young's modulus, nanohardness and indentation fracture toughness (KIc) of the SLS glass were respectively ~ 98.1 ± 9.2 MPa, 51.76 ± 0.54 GPa, 3.51 ± 0.04 GPa and 0.72 ± 0.09 MPa.m 0.5. These data matched with those reported by others [19,34].
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3.1. Effect of normal load The experimental results show that for the present SLS glass the lateral force F (Fig. 1a), the coefficient of friction, μ (Fig. 1b), the acoustic emission (Fig. 1c), the width (Fig. 1d) and depth (Fig. 1e) of scratches and the wear volume (Fig. 1f) increased with the applied normal load (P). The solid lines in Fig. 1(a) to (e) are just trend lines for the experimental data points and do not represent any predicted data points. The solid line in Fig. 1(f) represents a power-law fit of the wear volume data to the applied normal load. The values of the maximum tensile stress acting at the wake of the indenter were predicted following [12] for both static (Fig. 2a) and dynamic contacts (Fig. 2b). The solid lines here also just show the trend line through the predicted data points. It may be seen from these trend lines that the data of Fig. 2 showed a trend similar to that of the data of Fig. 1.
Fig. 1. (a–f): Variations in various tribological parameters of soda lime silica (SLS) glass as a function of the applied normal loads, P: (a) lateral force, (b) coefficient of friction, (c) acoustic emission, (d) width of scratch groove, (e) depth of the scratch groove and (f) wear volume.
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3.2. Damage evolution characteristics
Fig. 2. (a–b): Variations in maximum tensile stress as a function of the applied normal load (P) for (a) static and (b) dynamic contact situations in the SLS glass.
Fig. 3(a–d) shows the low magnification optical photomicrographs of the scratch grooves made in the SLS glass at 2 N, 5 N, 10 N and 15 N normal loads, respectively. The insets of each of these photomicrographs show the scratches at the corresponding load at a still lower magnification. The corresponding higher magnification photomicrographs are displayed in Fig. 4(a–d). At a typical low value of normal load e.g. 2 N, both complete and partial Hertzian tensile cracks were adjacent yet separated, thereby limiting the interaction among them (Figs. 3a, 4a). The nomenclature “Hertzian tensile cracks” was coined by the ASTM C1624-05 Standard. Basically it means what other researchers [12] term as “ring cracks” which originate following the Hertzian contact mechanics. In addition, there were very few edge cracks as marked by a small hollow black arrow oriented at an angle of about 30° to the direction of scratch; emanating from the periphery of the Hertzian tensile cracks. At a slightly higher normal load of 5 N, the extent of interaction between the Hertzian tensile cracks increased significantly (Figs. 3b, 4b). Another interesting observation was the presence of much larger “intra-Hertzian tensile crack” cracks of e.g. about 9 μm at 2 N and about 15–20 μm at 5 N at the periphery of the Hertzian tensile cracks and their growth both toward and away from the central region of the Hertzian tensile cracks as shown by the opposite white arrowheads in Fig. 4b. Such features were present throughout the length of the scratch made at 5 N. At a relatively higher normal load of 10 N, the separation between the Hertzian tensile cracks had decreased manifold leading to more interaction among the Hertzian tensile cracks (Figs. 3c, 4c). It was also an important observation that now the consecutive Hertzian tensile cracks were regularly joined and intersected by the edge cracks. At the highest applied normal load of 15 N, the additional cracks which had just appeared at 10 N normal load; were
Fig. 3. (a–d): Optical photomicrographs of the scratch grooves created in the SLS glass at different applied normal loads: (a) 2 N, (b) 5 N, (c) 10 N, and (d) 15 N. The arrowhead in (d) indicates the scratch direction for all the photomicrographs. The insets represent the lower magnification images of the corresponding optical photomicrographs.
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Fig. 4. (a–d): Optical photomicrographs of the scratch grooves created in the SLS glass at different applied normal loads at high magnification: (a) 2 N, (b) 5 N, (c) 10 N, and (d) 15 N. The black arrowhead in (d) indicates the scratch direction for all the optical photomicrographs.
more severely present with a much higher spatial density (Figs. 3d, 4d). The severity of interaction among the consecutive Hertzian tensile cracks had increased so much at 15 N normal load that they almost overlapped and intruded into each other's growth territory (Figs. 3d, 4d). As a consequence of this intense overlapping and interaction possibly a separate series of inclined cracks which we prefer to term as “secondary cracks” evolved nearly parallel to each other behind the trailing edge of the indenter and located at the edge of the scratch groove (Fig. 4d). The angle of orientation of this new set of cracks (e.g. ~8.23° for 10 N and ~ 12.08° for 15 N) was completely different from those (e.g. ~30° for 2 N and ~ 14° for 5 N) of the edge cracks. It is also observed from Fig. 4(a–d) that apparently the extent of the whitish zone, that signifies the presence of sub-surface damages was gradually enlarged as the applied normal load was increased from 2 to 15 N. Subsequently, the evidence of sub-surface damage was obtained by the well established bonded interface technique [35,36] and are illustrated by the optical photomicrographs presented in Figs. 5–8 respectively, for the applied normal loads of 2, 5, 10 and 15 N. At even a comparatively lower normal load of 2 N, a distinct semielliptical sub-surface primary damage zone followed by a secondary damage zone and a tertiary damage zone (marked as “S”) was formed (Fig. 5a) along with the localized presence of extensive shear deformation markings statistically oriented at various angles within the damage zone, Fig. 5(b–d). At the center of the primary damage zone was a portion containing crushed SLS glass. The extent of the semielliptical sub-surface damage zone was definitely increased at 5 N (Fig. 6a) compared to that observed at 2 N (Fig. 5a). Beyond this primary damage zone was the significant presence of what appeared to be a shallow lateral crack [4]. Near the center of this secondary damage zone was a microcracked small chip of glass where the direction of crack was perpendicular to the direction of scratching (Fig. 6b).
This microchipped part of glass appeared to be almost on the verge of getting detached showing again a significant role of the localized microfracture in the material removal mechanism. In addition, even this small chip of glass showed extensive presence of shear deformation lines marked by hollow white arrows (Fig. 6b). Additional shear deformation lines were found around the shallow lateral crack features on both sides of the center of the sub-surface damage zone (Fig. 6c). Further, the closer inspection indicated the presence of orthogonal cracks within the shallow lateral crack zone as marked by the hollow white arrows facing each other in Fig. 6d. The extent of the sub-surface damage zone was increased manifold at 10 N (Fig. 7a). Higher magnification views of the different relevant portions of Fig. 7a are shown respectively in Fig. 7(b–e). Beyond the main sub-surface damage zone that formed just underneath the scratch groove here also present were an extensive secondary damage zone and a tertiary damage zone. Enlarged views of the portions marked as “1” and “2” in Fig. 7(a) are shown respectively in Fig. 7(b) and (c). The higher magnification views of these zones confirmed the presence of extensive shear deformation (Fig. 7b and c). Similarly, enlarged views of the portions marked as “3” and “4” in Fig. 7(a) are shown respectively in Fig. 7(d) and (e). The higher magnification views of both these zones also confirmed the presence of extensive shear deformation (Fig. 7d and e). In addition, Fig. 7(e) depicted a thin layer of glass that was cracked from all sides and was almost on the verge of popping out. This evidence provides a direct mechanism of microchip formation that is an important step toward the material removal process. Fig. 8(a) shows that corresponding to the highest applied normal load of 15 N, a very large sub-surface elliptical damage zone had formed. Beyond this immediate primary damage zone, there was a region of secondary damage formation which had intercepted the surface and chipped out a reasonable amount of material in the
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Fig. 5. (a–d): The optical photomicrographs of the sub-surface deformation zones beneath the scratch grooves created in the SLS glass at an applied normal load of 2 N: (a) at low magnification, (b), (c), and (d) at high magnification.
process. Enlarged view of the portions marked as “1”, “2”, “3” and “4” in Fig. 8(a) is shown respectively, in Fig. 8(b), (c), (d) and (e). All these optical photomicrographs presented in Fig. 8(b) to (e) provided evidence for localized yet extensive shear deformation. As shown in the enlarged view of Fig. 8(b), near the base of the secondary damage zone; there was some amount of comminuted material. This portion was followed by a series of concentric partial arc like features which
were often intercepted by orthogonal shear deformation bands. Such orthogonal deformation bands are also evident from Fig. 8(d) which shows an enlarged view of the portion marked as “3” in Fig. 8(a). Fig. 9 shows a distinct evidence of the mechanism as to how a microchip evolves in the scratched surface of the SLS glass due to the intense interaction between the overlapping Hertzian tensile cracks.
Fig. 6. (a–d): The optical photomicrographs of the sub-surface deformation zones beneath the scratch grooves created in the SLS glass at an applied normal load of 5 N: (a) at low magnification, (b), (c), and (d) at high magnification.
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Fig. 7. (a–d): The optical photomicrographs of the sub-surface deformation zones beneath the scratch grooves created in the SLS glass at an applied normal load of 10 N: (a) the total deformation zone at low magnification, (b), (c), (d), and (e) the marked zones of (a) at higher magnification.
Based on the earlier work reported by other researchers [12,37], the data on predicted values of the critical load (Pc) as a function of the applied normal loads are shown in Fig. 10(a) and (b) respectively for static and dynamic contact situations of relevance to the present experimental conditions. It is obvious from these results that there was a huge reduction in the requirement of critical load for Hertzian tensile crack formation during dynamic contact situation as compared to that of static contact situation in the present SLS glass. Confirmatory evidences of the damage evolution characteristics are presented in the scanning electron microscope (SEM) photomicrographs of the scratch grooves, Fig. 11(a–d). Even at a low normal load of 2 N, the Hertzian tensile cracks were present (Fig. 11a) as mentioned earlier (Figs. 3 and 4). The SEM photomicrograph presented in Fig. 11(b) confirmed that as the applied normal load was increased from a typical low magnitude e.g. 2 N to an intermediate yet a relatively higher magnitude, e.g. 5 N; more Hertzian tensile cracks were formed and their spatial density increased. As a result, the inter-Hertzian tensile crack separation decreased. This leads to more localized interaction zones among the Hertzian tensile cracks, indicated as black dotted circle in Fig. 11(b). Further, the consecutive Hertzian tensile cracks were regularly joined and intersected by the edge cracks as indicated by a white dotted line. At higher normal loads of 10 and 15 N (Fig. 11c and d), the degree of severity of such interactions and micro chip formation leading to evolution of micro wear debris increased manifold. This micro wear debris is marked by the white arrows in Fig. 11(b), (c) and (d). It was found that additional narrow cracks were also formed in the middle of the scratch groove at a higher normal load of 15 N (Fig. 11d). A plot (Fig. 12) of the subsurface crack depth Cdh as measured from the photomicrographs
(Figs. 5 to 8) versus the normal load gave a power law exponent of 0.66 which was comparable to the theoretical value of 0.67 [38]. 4. Discussions 4.1. The tribological behavior of the SLS glass There was an increase of all the tribological characteristic data of the present SLS glass with the applied normal load (Fig. 1). A careful inspection of Fig. 1a revealed that the slopes of the trend line were dF different for different load ranges. The slope dP was 0.09 and 0.27 for the load ranges of 2–5 N and 5–15 N, respectively. Similarly, dμ was dP low at ~0.004 but jumped by about three times to ~0.011 for the load range of 5–15 N (Fig. 1b). The μ values span the range of 0.09 to 0.19 with an average of 0.14 ± 0.05. This average μ data was comparable to dF the reported data of 0.15 ± 0.02 [39]. The change in the slopes dP and dμ possibly indicated a change in damage mechanism of the scratch dP grooves as the load was increased from 2 to 15 N, as also suggested for various glasses [5,18] and alumina [7,8]. For both the lateral force and the coefficient of friction the slopes of the straight lines in the load range of 5–15 N were ~3 times higher than those at the load range of 2–5 N which suggests that the changed mechanism that was operative for lateral force was also influencing the data on the coefficient of friction for the present SLS glass. Ideally, according to the Coulomb law of friction; μ should be independent of normal load. However, the extent of forced interaction between the asperity distributions on the surfaces of the indenter and the glass and the resultant force distribution between the asperities can govern the extent of physical friction which controls the
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Fig. 8. (a–d): The optical photomicrographs of the sub-surface deformation zones beneath the scratch grooves created in the SLS glass at an applied normal load of 15 N: (a) the total deformation zone at low magnification, (b), (c), (d), and (e) the marked zones of (a) at higher magnification.
numerical magnitude of friction coefficient. As the normal load increases the interaction between the Hertzian tensile cracks is enhanced and leads to the formation of micro chips on the soda lime silica glass surface. When such microchips fall in between the sliding indenter and the scratch groove they are further comminuted to form the micro wear debris which get entrapped in between the sliding indenter and the scratch groove, and enhance the coefficient of friction. Further, for conical indenters with a large tip radius e.g. as in the present case (R = 200 μm), that is actually doing the scratching; the force ratio is expected to increase [15] with increase in the applied normal load. The acoustic emission data also increased with the applied normal load (Fig. 1c). The increase in the magnitude of acoustic emission suggested an increase in inelastic and microfracture processes in the immediate vicinity of both the surface and the sub-surface regions of the scratch groove with increase in normal load which was in
Fig. 9. The optical photomicrograph of the scratch groove created in the SLS glass at applied normal load of 15 N at high magnification. The dotted black circle indicates the formation mechanism of a micro-chip of the SLS glass during the scratch experiment.
Fig. 10. Variations of critical load (Pc) for Hertzian tensile crack formation in the SLS glass under different contact situations: (a) static and (b) dynamic.
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tune with the experimental observations (Figs. 5 to 8). Therefore, the higher the applied normal load, the more would be the probability of the occurrence of microfracture events [5] which should increase the magnitude of the acoustic emissions (Fig. 1c) as was also noted by others for alumina, yttria stabilized zirconia, silicon carbide [16] and bulk metallic glasses [34]. There was an increase of scratch width with normal load (P), Fig. 1d. The maximum tensile stress due to static contacts ( σ sm ) under an applied normal load P in the present experiments were calculated using the following equation [12,37]: s
σm ¼
ð1−2νs ÞP : 2πa2s
ð2Þ
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scratch groove with enhancement of the applied normal load. Eq. (3) predicts that with the increase in normal load (P) the contact radius and hence, the scratch width should increase, Fig. 1(d). From the experimental data of the scratch width (Fig. 1d) and depth (Fig. 1e), the wear volume was calculated as the length of the groove (3 mm) times the area of the groove which had an approximately triangular cross section. The solid line in Fig. 1f actually represents an empirical power law fit of the experimental wear volume data (shown as individual points) to the applied normal load as noted by others also [6,40]. Further, the maximum tensile stress due to dynamic contact (σ dm ) between the glass surface and the sliding indenter during the scratch experiments were obtained from the following equation [12]: d
s
The quantity as in Eq. (2) denotes the static contact radius given by [12],
σ m ¼ ð1 þ 15:5μ Þσ m
1=3 3 2 2 Es 1−νs þ 1−νi : PrEs as ¼ 4 Ei
where μ is the coefficient of friction between the glass sample and the sliding indenter. Thus, the maximum tensile stress values were calculated from Eqs. (2), (3) and (4) for both static and dynamic contact cases using the following values of the physical properties e.g. νs = 0.25, νi = 0.07, Es = 51.76 GPa, Ei = 1141 GPa [32] and the results are given in Fig. 2(a–b) as mentioned earlier. The tensile stress of ~0.5–1 GPa (Fig. 2a) developed during the static contact at the rear and periphery of the contact circle, was itself much greater than the experimentally measured fracture strength (98 MPa) of the SLS
ð3Þ
In Eq. (3), Es and νs are the Young's modulus and Poisson's ratio of the glass, νi and Ei are the Poisson's ratio and the Young's modulus of the indenter and r is the radius of the indenter (200 μm). There was a huge increase in contact pressure with increase in the applied normal load which is possibly reflected as increase in depth (Fig. 1e) of the
ð4Þ
Fig. 11. SEM photomicrographs of the scratch grooves created in the SLS glass at different applied normal loads: (a) 2 N, (b) 5 N, (c) 10 N, and (d) 15 N. The black downward arrowheads indicate the scratch direction for all the photomicrographs.
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glass and was capable to initiate microfracture even on static contact. In the dynamic experiments, the tensile stress jumps abruptly to ~ 1– 4 GPa (Fig. 2b) which was conducive for more microfracture initiation thereby causing an increase in lateral force (Fig. 1a), coefficient of friction (Fig. 1b) and acoustic emission (Fig. 1c).
as partial cone cracks [12] because each individual crack leaves behind an incomplete arcuate trace on the glass surface. The incomplete surface traces of these partial cone cracks on the glass surface are termed as Hertzian tensile cracks [12] which are nearly equi-spaced. The critical load (Pc) for cone crack initiation is given by [12]:
4.2. The damage evolution processes in the SLS glass −3
At low load e.g. 2 N (Fig. 4a) there were only few Hertzian tensile cracks and even fewer interactions. However, the scenario changed at intermediate loads e.g. 5 N as shown in Fig. 4b. The opposite growths of the two edge cracks toward each other would facilitate the possibility of their interaction further. It is suggested that the cracks which grow toward the central region from the periphery of the Hertzian tensile cracks might have been formed during unloading rather than during loading. It is suggested further that at a relative higher applied normal load of 10 N as indicated by the dotted lines in Fig. 4(c), the regular interaction between the Hertzian tensile cracks themselves and their intersection by the edge cracks provided an intermediate step of “multiple micro-chip evolution” and consequently formation of micro wear debris facilitating a means of material removal. This conjecture was subsequently confirmed from scanning electron microscopic observations as would be discussed later. The angle of the tangents to the Hertzian tensile cracks with respect to the scratching direction varied in the range of about 120° to 134° (Fig. 4). This information would suggest that possibly some different stress components were responsible for their genesis. The slightly uplifted appearances of the edge cracks in Fig. 4(c) and (d) indicate that their genesis could be linked to the combined presence of strong tensile and shear stress components in the vicinity of and at the wake of the indenter. There was an increase in the extent of whitish zone of Fig. 4(a–d) with the applied normal load. This observation suggests that the extent of subsurface deformation increased with the applied normal load. Further confirmatory evidence of subsurface deformation emerges from Fig. 5(a–d) which were obtained by the well known bonded interface technique, as mentioned earlier. The presence of a crushed primary zone just below the indenter in the scratch groove created even at a low applied normal load of 2 N (Fig. 5a) indicates the important role played by the localized microfracture followed by the microcomminution processes in evolution of the material removal mechanism. Fig. 5d also presents a distinct evidence of formation of orthogonal cracks in between consecutive Hertzian tensile cracks which should also play an important role in the material removal process. The profuse presence of shear deformation bands at an intermediate load of 5 N, Fig. 6(a–d), as well as at a relatively higher load of 10 N, Fig. 7(a–d) strongly suggested again that shear stress played a major role in the damage evolution process of the scratched SLS glass. The extent of highly localized shear deformation increased manifold at the highest applied normal load of 15 N, Fig. 8(a–d). As the cracks formed, extended and joined all around a very thin layer of glass (Fig. 9), it appears to be on the verge of being chipped out. When such multiple micro-chip formation occurs, the detached thin layers contribute to the genesis of the micro wear debris. In general, the sub-surface damage zones in the present SLS glass almost characteristically contained a primary damage zone followed by a distinct secondary damage zone and in some cases, even a tertiary damage zone. It follows logically that the secondary damage zones are prospective candidate zones to play a major role in material removal process during repeated scratch experiments. In the present experiments, the Hertzian tensile cracks formed at all loads ≥2 N (Fig. 3a–d). It is well known that for all applied normal load P > Pc (the critical load for crack initiation) a cone shaped fracture is initiated [12,37] because now σ sm will be greater than the fracture strength σ f of glass. The frustum of this fracture cone intersects the glass surface close to the circle of contact of radius as , which now becomes the critical contact radius ac . These cracks are termed
Pc ¼ 6:7 10
9 16
h n oi 1=2 2 2 γs 1−νs þ 1−νi EEs Es i 1 r s P:
1=2 ð1 þ 15:5μ Þ3 I3f c3=2 1−νs 2 ð1−2νs Þ f
ð5Þ Taking the values of fracture energy of glass γs ~ 5 J m − 2 from [41], critical flaw size (cf) ~ 1 μm, If3 = 1/2 from [12], E = 51.76 GPa and r = 200 μm from the present experimental data, we get from Eq. (5) above; Pc ¼
0:03P : ð1 þ 15:5μ Þ3
ð6Þ
Corresponding to the applied normal loads of 2 to 15 N, Pc was about 0.05 to 0.45 N, Fig. 10a. However, for dynamic contact situations Pc decreased by almost an order of magnitude to about 0.005 to 0.08 N for applied normal loads of 2, 5, 10 and 15 N respectively, Fig. 10b. Thus the additional presence of the traction force made it even easier for the Hertzian tensile cracks to form as the sliding indenter scratches the soda lime silica glass. As the applied normal load P was already greater than the critical load Pc for Hertzian tensile crack formation, the Hertzian tensile cracks formed at all loads ≥2 N (Fig. 3a–d) in the present experiments. The photomicrographic evidence (Fig. 11) obtained by scanning electron microscopy presented confirmatory support to the suggestion made earlier in the present work that interaction between the Hertzian tensile cracks and “intra-Hertzian tensile cracks” crack formation provides an intermediate step which acted as a more plausible means of micro-chip evolution and consequently formation of micro wear debris thereby facilitating a means of material removal. Such intense interaction indeed leads to genesis of the microfracture events followed by micro chipping (mc) as indicated in Fig. 11(b) as a white dotted circle. The occurrence of the additional narrow cracks in the center of the scratch groove produced at the highest applied normal load of 15 N (Fig. 11d) was most likely due to the presence of a huge tensile stress component at the trailing edge of the indenter. Based on the crack depth (Cdh ) data measured from the photomicrographs of the sub-surface damage presented in Figs. 5–8, the fracture toughness ( KIc ) was evaluated using the following relation [42,43]; −1:5 d KIc ¼ χh Peff ch
ð7Þ
h
where, χh is a parameter that depends on the Poisson's ratio [31] and Peff is given by the following relation [42,43]: 2 0:5 : Peff ¼ P 1 þ μ
ð8Þ
The quantity Peff represents the effective force on the SLS glass under dynamic contact situation. It is nothing but the resultant magnitude of the vector sum of the applied normal force (e.g. load) P and the lateral force μP that acts in a direction perpendicular to that of P. The evaluated values of KIc varied in the range of 0.55 to 0.80 MPa.m 0.5 as the applied normal load was increased from 2 to 15 N. Thus, for the sub-surface cracks the average fracture toughness was ~0.71 ± 0.11 MPa.m 0.5 which was comparable to the independently measured fracture toughness (KIc) value of 0.72 ± 0.09 MPa.m0.5 evaluated by the conventional indentation fracture toughness method as mentioned earlier.
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Further, the experimental evidences presented in the photomicrographs of Figs. 5–8 also confirmed the significant presence of shear induced deformation. The maximum shear stress underneath the indenter was theoretically predicted using the following equation [44,45]: 16Peff E2r 9π2 r2
τmax ¼ 0:445
!1=3 ð9Þ
where Er is the reduced modulus given by the following relation [12]: Er ¼
hn
2
1−νs
. o n . oi−1 2 : Es þ 1−νi Ei
ð10Þ
A plot of τmax as a function of the effective applied normal force, Peff (Fig. 13) shows that the shear stress generated just underneath the indenter enhanced from ~ 10 to 20 GPa as the effective normal force increased from about 2.01 to 15.3 N corresponding to the applied normal loads of 2 to 15 N. The experimentally measured shear modulus of soda–lime–silica glass is ~ 30 GPa [46,47]. Thus, the theoretical shear strength (τtheor) for the soda–lime–silica glass is ~3–6 GPa (e.g. τtheor ~ G/5–G/10 [47]). Therefore, as τmax » τtheor of glass [46,47] shear induced flow and/or deformation was expected (Figs. 5–8). 4.3. The material removal mechanisms in the SLS glass Based on the present experimental evidences, Figs. 14 and 15 represent respectively the schematic pictures of both surface and subsurface deformations and damages for the scratch grooves formed at various applied normal loads. At a typical low load (e.g.2 N, Fig. 14a) few Hertzian tensile cracks and very few edge cracks are present on the surface of the SLS glass. At an intermediate normal load (e.g. 5 N, Fig. 14b) the Hertzian tensile cracks started to interact among themselves and form the micro-chips which create micro wear debris in the scratch tracks, also the number of edge cracks increased. As expected, the severity of total damage increased with the applied normal load. The number of Hertzian tensile cracks and the interactions among themselves were more in the scratch track for a relatively higher load (e.g. 10 N, Fig. 14c) leading to more micro-chip formations which enhanced the number of micro wear debris. At still higher normal load (e.g. 15 N, Fig. 14d), an additional set of cracks generated at an angle (0° b θ b 90°) with the scratch direction and lied nearly parallel to each other in the scratch track that was partially and/or totally crushed. In the schematic figures representing sub-surface deformations, the direction of the scratch was perpendicular to the plane of paper and goes inward as indicated by the cross sign. Fig. 15a revealed that the there were three successive damage zones in the sub-
Fig. 12. Variation of crack depths with the applied normal loads in the SLS glass.
Fig. 13. Variation of shear stress underneath the indenter with the effective normal loads in the SLS glass.
surface deformation region for an applied low load of 2 N. These were the “primary damage zone” that was just underneath the scratch groove, the “secondary damage zone” comprising of partially and/or fully crushed material, and finally a “tertiary damage zone” full of shear markings. These primary, secondary and tertiary damage zones are indicated in Fig. 15a respectively by a gray shade, a textured shade and black markings. Fig. 15b showed that at an intermediate load (e.g. 5 N) in addition to the three distinct damage zones, the shallow lateral cracks in the sub-surface damage zone joined and created a “now-loosened” portion of glass just beneath the scratch groove which was about to chip out (i.e. ca. Fig. 6c,d). At higher applied normal load (e.g. 10 N) a large number of shear bands oriented either perpendicular or at random to each other were also present in the cross section of the scratch groove in addition to the three damage zones and the formation of microchips, (i.e. ca. Figs. 15c and 7). Thus, at P > 5 N there was a distinct change of damage evolution mechanism as reflected also in the tribological characteristic data (Fig. 1). At still higher loads e.g. 15 N the spatial extent of damage zone increased so much substantially, (i.e. ca. Figs. 15d and 8) that the primary and secondary damage zones merged and thereby making it impossible to point out their separate existence. A large number of shear bands in various orientations are clearly visible as τmax » τtheor of glass [46,47].
5. Conclusions The major conclusions from the present work were: (a) The tribological parameters e.g. the lateral force, the coefficient of friction, the acoustic emission, the width and depth of the scratch groove and the wear volume all increased in the present soda lime silica glass with the applied normal loads in the range of 2 to 15 N due to the presence of a very large (e.g., up to 5 GPa) tensile stress component active at the wake of the sliding indenter. It is also suggested that the shear stress played a major role in causing the sub-surface damage evolutions beneath the scratch grooves. (b) Extensive optical and scanning electron photomicrographs provided evidence that the spatial extent and number of damages in the scratch grooves of the SLS glass increased with the applied normal loads (2–15 N). As the applied normal load was enhanced in the current scratch tests, the major material removal mechanism in the present SLS glass appeared mainly to involve the “enhanced degree of interaction” among Hertzian tensile cracks. This process leads to microfracture. The microfracture caused micro-chip formation. Finally, when these microchips got detached from the scratch grooves, the micro-wear debris was generated.
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Fig. 14. The schematic representation of the surface damages in the scratch grooves created in the SLS glass at different normal loads: (a) 2 N, (b) 5 N, (c) 10 N, and (d) 15 N. The arrowhead in (a) indicates the direction of the movement of the sliding indenter for the cases (b), (c), and (d) also. The dotted black circle indicates the interaction among Hertzian tensile cracks and formation mechanism of micro-chip of the SLS glass during the scratch experiment.
Fig. 15. The schematic representation of the sub-surface damages in the scratch grooves created in the SLS glass at different normal loads: (a) 2 N, (b) 5 N, (c) 10 N, and (d) 15 N.
(c) Extensive optical photomicrography confirmed that nearly elliptical subsurface deformation zones were formed beneath the scratch grooves made at 2–15 N normal loads in the present SLS glass. There were in general three distinct subsurface damage zones e.g., (i) an almost fully crushed “primary damage zone” just underneath the scratch groove, (ii) a “secondary damage zone” characterized mainly by extensive microfracture as well as shear deformations lines, and (iii) a “tertiary damage zone” mainly characterized by occurrences of lateral cracks and shear deformation bands. It is suggested that these secondary and tertiary damage zones may play an important role in material removal process of the SLS glass under repeated single pass contacts e.g. as in a grinding process.
CSIR (Project No. NWP 0027). The author AD also acknowledges the constant encouragement from the Director, ISAC, Bangalore.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
Acknowledgments The authors are grateful to the Director, CSIR-Central Glass and Ceramic Research Institute (CGCRI), Kolkata for his kind permission to publish this paper. In addition, the authors appreciate the infrastructural supports received from all colleagues and particularly those received from the colleagues of the Mechanical Property Evaluation Section, NOCCD. The experimental assistance of Mrs. R. Chakraborty, S. Sarkar and D. Das of CSIR-CGCRI are gratefully acknowledged. Finally, the authors gratefully acknowledge the financial supports received from
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Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/ locate/ jnoncrysol
Effect of load in scratch experiments on soda lime silica glass Payel Bandyopadhyay a, Arjun Dey a, c, Sudakshina Roy b, Anoop K. Mukhopadhyay a,⁎ a b c
Mechanical Property Evaluation Section, CSIR-Central Glass and Ceramic Research Institute, Kolkata-700 032, India Electron Microscopy Section, CSIR-Central Glass and Ceramic Research Institute, Kolkata-700 032, India Thermal Systems Group, ISRO Satellite Centre, Vimanapura, Post, Bangalore 560 017, India
a r t i c l e
i n f o
Article history: Received 6 November 2011 Received in revised form 30 January 2012 Available online 2 March 2012 Keywords: Soda–lime–silica glass; Scratch; Tribology; Deformation
a b s t r a c t Today the technological applications of glass span from everyday life to many advanced areas. These advanced applications require very accurate grinding and polishing that involve controlled removal of glass to achieve micron or even sub-micron surface finish. The major bottleneck in this connection is that the material removal mechanisms during such processes are yet to be fully understood. Since grinding involves many single pass scratch processes happening simultaneously, to develop better understanding about the effect of the normal load in affecting the material removal mechanisms; a number of single pass scratch experiments were conducted on a commercially available soda lime silica glass as a function of various normal loads (2–15 N) at a constant scratch speed of 100 μm.s − 1. The results showed that the tribological properties, the severity and the spatial density of damage evolution were sensitive to the applied normal loads and the resultant tensile as well as shear stresses. Extensive optical and scanning electron photomicrography of the surface and sub-surface deformation zones proved the existence of three distinct deformation zones in the immediate vicinity of the scratch grooves and led to the development of a qualitative model of the material removal mechanisms. © 2012 Elsevier B.V. All rights reserved.
1. Introduction The advanced applications of glass cover a truly wide range. It spans from our everyday life to the latest electronic gadgets to biomedical sensor technology to strategic transparent armors to thermal protection system component of space shuttles to space telescope lenses. Very accurate grinding and polishing of glass for fabrication of engineering components having utmost dimensional precision is a fundamental need for all such applications. However, to grind and polish glass with requisite dimensional precision is a big challenge as the characteristic brittleness makes it prone to undergo brittle fracture. That is the reason why the scientific issues behind the material removal mechanisms during the grinding and polishing of brittle materials like glasses as well as ceramics and glass ceramic have been receiving a huge research interest [1–20]. Recent works on alumina [21], C/C composite [22], plasma sprayed ceramic coating [23], titanium oxide thin film on glass [24], ZrB2–SiC composite [25,26], sialon ceramics [27], dental ceramics [28], DLC coatings [29], calcium phosphate coatings [30], and chromium nitride and titanium nitride coatings [31] provide the invaluable importance of scratch testing for understanding the material removal mechanisms as well as coating
⁎ Corresponding author at: Central Glass and Ceramic Research Institute, 196, Raja S.C. Mullick Road, Kolkata-32, India. Tel.: + 91 33 2473 3469/76/77/96; fax: + 91 33 2473 0957. E-mail addresses: [email protected], [email protected] (A.K. Mukhopadhyay). 0022-3093/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2012.02.006
failure mechanisms. There have been traditionally two approaches to further the fundamental understanding about the basic mechanisms of material removal process during grinding of brittle materials. Such experiments are done with single point indentation [2–4] as well as single, double or multiple pass scratch [5–8] tests conducted on glass as well as other brittle ceramics. The occurrence of microfracturing during the scratching of glass was found to be [5] very similar to the one that happens under quasi-static indentation; however the severity of stress field was enhanced due to the additional presence of the tangential load. The friction coefficient and specific energy affect the grindability of brittle solids including glass [9–11]. It was reported further [12] that when a hard sphere slides over the flat surface of glass, the classical Hertzian tensile cracks appear at the rear of the sphere when the load applied (P) exceeds a critical load (Pc) that scales with the square of the ball radius for a coefficient of friction greater than 0.02 [12,13]. Research on a glass scratched by a steel ball [14] of radius larger than the limiting radius supported these observations [12]. Li et al. [15] observed that at a normal load of 10 gf the friction coefficient was independent of scratching speed of ~ 2 to 200 μm.s − 1 but, the crack density decreased with increase in scratching speed. A transition from the deformationcontrolled to fracture-controlled process of damage evolution was identified at P > Pc from multiple scratch test experiments on glass [16]. In the case of optical glass e.g., BK7 the degree of spatial interaction among neighboring scratches [17] played a major role in material removal mechanism. Depending upon the normal load in the incremental scratch test on obsidian, three zones e.g. a micro-ductile
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zone, a micro-cracking zone and a micro-abrasive zone were reported [18]. Scratch behavior of SLS glasses was very sensitive to the loading history, the hygrometry level, the chemical structure and/or composition of the lubricant and the glass composition [19,20]. A survey of the pertinent literature data (Table 1) indeed points out that in spite of the wealth of literature there has not been any systematic study on the scratching behavior of commercially available soda lime silica glass in the intermediate load range of 2 to 15 N at a comparatively lower speed of 100 μm.s − 1. Thus, the major objective of the present work was to evaluate the scratch deformation behavior of a commercially available soda lime silica glass as a function of the applied normal load in the range of 2 to 15 N. The other important objective was to gain a better picture of the damage evolution and/or material removal mechanisms. 2. Materials and methods Commercially available 1.40 mm thick soda lime–silica glass slides (Blue Star Microscopic Cover Slide, Kolkata, India) polished down to 0.25 μm diamond paste grit size (Eastern Diamond Products Pvt. Ltd, Kolkata, India) were used in the present experiments. The glass composition was determined following the ASTM C169-92 standards and is given in Table 2. The amount of silica and calcia in the glass composition was measured by the conventional titration method. The flame photometry technique was utilized to evaluate the amount of Na2O. The inductively coupled plasma-atomic emission spectroscopy (ICPAES, Spectro Flame Modula, Model Q3: STM 08, Spectro Analytical Instruments, Germany) technique was used to determine the trace elements. The scratch tests were conducted on 15× 10× 1.40 mm size samples of the SLS glass with a commercially available scratch tester (Model TR-102-M3, Ducom, Bangalore, India) equipped with a Rockwell C diamond indenter of 200 μm tip radius. The machine comprised of the scratch tester unit along with the controller, the machine control software, the data acquisition system, the image acquisition system, the acoustic emission sensor and the connecting cables etc. A compound force transducer attached to the scratch tester measured both normal load and lateral force of up to 20 N with a load cell that had a resolution of ±0.01 N. The stroke length for all scratches was 3 mm. The scratch offset was set at 0.5 mm for all the scratches. The acoustic emission sensor (VS 150-M, capacity: 100–450 kHz, peak frequency 150 kHz, Vallen Systeme, Schäftlarner Weg 26a 82057 Icking, Germany 08178 9474400) was connected with the transducer near the indenter and had a precision level of ±0.01 dB. Four different constant normal loads (P) of 2, 5, 10 and 15 N and a constant scratch speed of
Table 1 Literature survey on scratch experiments in various glasses.
Table 2 Composition of the SLS glass. Component
Amount (wt.%)
SiO2a Na2Oa CaOa Al2O3 MgO Fe2O3 K2O TiO2
74.36 13.55 6.70 1.14 3.53 0.11 0.20 0.03
a
Principal amount.
100 μm.s − 1 were used in the present experiments. To have a statistically reliable data at least three scratches were made at a given normal load. A profilometer (Form Talysurf 120, Taylor Hobson, UK) was utilized to measure the depth and width data of the scratches. The values of the coefficients of friction (μ) were calculated by dividing the lateral force (F) by the normal load (P) in all the cases. The glass density was measured on powder sample by pycnometry method [19]. The three point bend strength of the SLS glass was measured using a standard universal testing machine (Model No. 5500 R, Instron, UK) at a crosshead speed of 0.5 mm.min − 1. The sample size was (80 mm × 25 mm × 1.40 mm). The span length was kept at 60 mm. Keeping the statistical variability of surface flaw distribution for a brittle material like glass, a total of twenty five samples were used and the average data taken. The Young's modulus and the nanohardness of the SLS glass of size 25 mm × 25 mm × 1.40 mm were measured at 100 mN load using a commercial nanoindenter (Fischerscope, H100XYP, Fischer, Switzerland). The load sensing resolution of the machine was 0.2 μN. The depth sensing resolution was 1 nm. The machine worked according to the DIN 50359-1 standard. The machine was calibrated with nanoindentation based independent evaluation of nanohardness, H ~ 4.14 ± 0.1 GPa and Young's modulus, E ~ 84.6 ± 3.5 GPa of a standard reference block e.g. Schott BK7 Glass (Schott, Germany) provided by the supplier. A nanoindentation matrix of 7 × 7 indents was utilized for the present SLS glass. The loading and unloading times were both kept fixed at 30 s with no hold time at the peak nanoindentation load of 100 mN. The nanohardness and Young's modulus data were measured from the individual load–depth plots following the well known Oliver–Pharr method [32]. Thus, the reported data for average nanohardness and Young's modulus was calculated from 49 individual measurements of the same. The fracture toughness (KIc) of the present SLS glass was measured by the conventional indentation fracture toughness method using a standard Vicker's diamond indenter at a load of 9.81 N using a hardness tester (LV 700, LECO, USA) for five individual SLS glass samples of size 25 mm × 25 mm × 1.40 mm. The fracture toughness was calculated using the following equation [33]:
Indenter type: blunt r* (μm) ~ 1500–9500 76 200
2000
P+ (N) +
P > Pc ~ 392.4–2746.8 0.098–0.49 Up to 100, ramping (single scratch test) 0.1–25 (repeated scratch test) 20
Indenter type: sharp nd 0.25–4 3 0.049–0.25 0.3 μm 0.01–3 nd 0.03–0.3 5 0.1 nd 0–4 nd 0.98
1=2
V# (μm.s− 1)
Type of glass
Ref. no.
660 10 nd
Commercial Soda–lime silica Soda–lime silica
[14] [15] [16]
250
Obsidian
[18]
1000 2–200 0.04–400 10 250 100 50
Soda–lime Soda–lime silica NaCa, SF58 Optical BK7 Obsidian Soda–lime silica Soda lime
[5] [15] [10] [17] [18] [19] [20]
r* — indenter radius, P+ — applied normal load, V# — scratch speed.
KIc ¼ 0:016ðE=HÞ
Pi :c
−3=2
:
ð1Þ
In Eq. (1) Pi is the indentation load (9.81 N), E is Young's modulus of the SLS glass as measured from the nanoindentation technique as described above, H is hardness measured at the same load (Pi), and c is the characteristic crack parameter measured as half of the sum of average indentation diagonal plus the average surface crack length measured from the tip of the indent. For a given sample at least ten indents were made for fracture toughness evaluation. Thus, for each sample the average indentation diagonal was calculated from 20 individual measurements while the average surface crack length was calculated from 40 individual measurements. The typical scatters of all data were represented as ±1 standard deviation. Both optical microscopy (Olympus GX51, Olympus, USA) and Scanning Electron Microscopy (SEM: s430i, Leo, UK) were utilized to understand how the damage evolution processes took place during
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the scratch tests. A 50–70 nm carbon film was deposited on the glass sample by the arc deposition technique to avoid charging; then it was inserted into the sample chamber for SEM.
3. Results The chemical composition of glass is given in Table 2. The data in Table 2 show that the total amount of network modifier was more than 20% in the present glass composition. The density of the SLS glass was 2.42 ± 0.07 g.cc − 1. The three point bend strength, Young's modulus, nanohardness and indentation fracture toughness (KIc) of the SLS glass were respectively ~ 98.1 ± 9.2 MPa, 51.76 ± 0.54 GPa, 3.51 ± 0.04 GPa and 0.72 ± 0.09 MPa.m 0.5. These data matched with those reported by others [19,34].
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3.1. Effect of normal load The experimental results show that for the present SLS glass the lateral force F (Fig. 1a), the coefficient of friction, μ (Fig. 1b), the acoustic emission (Fig. 1c), the width (Fig. 1d) and depth (Fig. 1e) of scratches and the wear volume (Fig. 1f) increased with the applied normal load (P). The solid lines in Fig. 1(a) to (e) are just trend lines for the experimental data points and do not represent any predicted data points. The solid line in Fig. 1(f) represents a power-law fit of the wear volume data to the applied normal load. The values of the maximum tensile stress acting at the wake of the indenter were predicted following [12] for both static (Fig. 2a) and dynamic contacts (Fig. 2b). The solid lines here also just show the trend line through the predicted data points. It may be seen from these trend lines that the data of Fig. 2 showed a trend similar to that of the data of Fig. 1.
Fig. 1. (a–f): Variations in various tribological parameters of soda lime silica (SLS) glass as a function of the applied normal loads, P: (a) lateral force, (b) coefficient of friction, (c) acoustic emission, (d) width of scratch groove, (e) depth of the scratch groove and (f) wear volume.
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3.2. Damage evolution characteristics
Fig. 2. (a–b): Variations in maximum tensile stress as a function of the applied normal load (P) for (a) static and (b) dynamic contact situations in the SLS glass.
Fig. 3(a–d) shows the low magnification optical photomicrographs of the scratch grooves made in the SLS glass at 2 N, 5 N, 10 N and 15 N normal loads, respectively. The insets of each of these photomicrographs show the scratches at the corresponding load at a still lower magnification. The corresponding higher magnification photomicrographs are displayed in Fig. 4(a–d). At a typical low value of normal load e.g. 2 N, both complete and partial Hertzian tensile cracks were adjacent yet separated, thereby limiting the interaction among them (Figs. 3a, 4a). The nomenclature “Hertzian tensile cracks” was coined by the ASTM C1624-05 Standard. Basically it means what other researchers [12] term as “ring cracks” which originate following the Hertzian contact mechanics. In addition, there were very few edge cracks as marked by a small hollow black arrow oriented at an angle of about 30° to the direction of scratch; emanating from the periphery of the Hertzian tensile cracks. At a slightly higher normal load of 5 N, the extent of interaction between the Hertzian tensile cracks increased significantly (Figs. 3b, 4b). Another interesting observation was the presence of much larger “intra-Hertzian tensile crack” cracks of e.g. about 9 μm at 2 N and about 15–20 μm at 5 N at the periphery of the Hertzian tensile cracks and their growth both toward and away from the central region of the Hertzian tensile cracks as shown by the opposite white arrowheads in Fig. 4b. Such features were present throughout the length of the scratch made at 5 N. At a relatively higher normal load of 10 N, the separation between the Hertzian tensile cracks had decreased manifold leading to more interaction among the Hertzian tensile cracks (Figs. 3c, 4c). It was also an important observation that now the consecutive Hertzian tensile cracks were regularly joined and intersected by the edge cracks. At the highest applied normal load of 15 N, the additional cracks which had just appeared at 10 N normal load; were
Fig. 3. (a–d): Optical photomicrographs of the scratch grooves created in the SLS glass at different applied normal loads: (a) 2 N, (b) 5 N, (c) 10 N, and (d) 15 N. The arrowhead in (d) indicates the scratch direction for all the photomicrographs. The insets represent the lower magnification images of the corresponding optical photomicrographs.
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Fig. 4. (a–d): Optical photomicrographs of the scratch grooves created in the SLS glass at different applied normal loads at high magnification: (a) 2 N, (b) 5 N, (c) 10 N, and (d) 15 N. The black arrowhead in (d) indicates the scratch direction for all the optical photomicrographs.
more severely present with a much higher spatial density (Figs. 3d, 4d). The severity of interaction among the consecutive Hertzian tensile cracks had increased so much at 15 N normal load that they almost overlapped and intruded into each other's growth territory (Figs. 3d, 4d). As a consequence of this intense overlapping and interaction possibly a separate series of inclined cracks which we prefer to term as “secondary cracks” evolved nearly parallel to each other behind the trailing edge of the indenter and located at the edge of the scratch groove (Fig. 4d). The angle of orientation of this new set of cracks (e.g. ~8.23° for 10 N and ~ 12.08° for 15 N) was completely different from those (e.g. ~30° for 2 N and ~ 14° for 5 N) of the edge cracks. It is also observed from Fig. 4(a–d) that apparently the extent of the whitish zone, that signifies the presence of sub-surface damages was gradually enlarged as the applied normal load was increased from 2 to 15 N. Subsequently, the evidence of sub-surface damage was obtained by the well established bonded interface technique [35,36] and are illustrated by the optical photomicrographs presented in Figs. 5–8 respectively, for the applied normal loads of 2, 5, 10 and 15 N. At even a comparatively lower normal load of 2 N, a distinct semielliptical sub-surface primary damage zone followed by a secondary damage zone and a tertiary damage zone (marked as “S”) was formed (Fig. 5a) along with the localized presence of extensive shear deformation markings statistically oriented at various angles within the damage zone, Fig. 5(b–d). At the center of the primary damage zone was a portion containing crushed SLS glass. The extent of the semielliptical sub-surface damage zone was definitely increased at 5 N (Fig. 6a) compared to that observed at 2 N (Fig. 5a). Beyond this primary damage zone was the significant presence of what appeared to be a shallow lateral crack [4]. Near the center of this secondary damage zone was a microcracked small chip of glass where the direction of crack was perpendicular to the direction of scratching (Fig. 6b).
This microchipped part of glass appeared to be almost on the verge of getting detached showing again a significant role of the localized microfracture in the material removal mechanism. In addition, even this small chip of glass showed extensive presence of shear deformation lines marked by hollow white arrows (Fig. 6b). Additional shear deformation lines were found around the shallow lateral crack features on both sides of the center of the sub-surface damage zone (Fig. 6c). Further, the closer inspection indicated the presence of orthogonal cracks within the shallow lateral crack zone as marked by the hollow white arrows facing each other in Fig. 6d. The extent of the sub-surface damage zone was increased manifold at 10 N (Fig. 7a). Higher magnification views of the different relevant portions of Fig. 7a are shown respectively in Fig. 7(b–e). Beyond the main sub-surface damage zone that formed just underneath the scratch groove here also present were an extensive secondary damage zone and a tertiary damage zone. Enlarged views of the portions marked as “1” and “2” in Fig. 7(a) are shown respectively in Fig. 7(b) and (c). The higher magnification views of these zones confirmed the presence of extensive shear deformation (Fig. 7b and c). Similarly, enlarged views of the portions marked as “3” and “4” in Fig. 7(a) are shown respectively in Fig. 7(d) and (e). The higher magnification views of both these zones also confirmed the presence of extensive shear deformation (Fig. 7d and e). In addition, Fig. 7(e) depicted a thin layer of glass that was cracked from all sides and was almost on the verge of popping out. This evidence provides a direct mechanism of microchip formation that is an important step toward the material removal process. Fig. 8(a) shows that corresponding to the highest applied normal load of 15 N, a very large sub-surface elliptical damage zone had formed. Beyond this immediate primary damage zone, there was a region of secondary damage formation which had intercepted the surface and chipped out a reasonable amount of material in the
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Fig. 5. (a–d): The optical photomicrographs of the sub-surface deformation zones beneath the scratch grooves created in the SLS glass at an applied normal load of 2 N: (a) at low magnification, (b), (c), and (d) at high magnification.
process. Enlarged view of the portions marked as “1”, “2”, “3” and “4” in Fig. 8(a) is shown respectively, in Fig. 8(b), (c), (d) and (e). All these optical photomicrographs presented in Fig. 8(b) to (e) provided evidence for localized yet extensive shear deformation. As shown in the enlarged view of Fig. 8(b), near the base of the secondary damage zone; there was some amount of comminuted material. This portion was followed by a series of concentric partial arc like features which
were often intercepted by orthogonal shear deformation bands. Such orthogonal deformation bands are also evident from Fig. 8(d) which shows an enlarged view of the portion marked as “3” in Fig. 8(a). Fig. 9 shows a distinct evidence of the mechanism as to how a microchip evolves in the scratched surface of the SLS glass due to the intense interaction between the overlapping Hertzian tensile cracks.
Fig. 6. (a–d): The optical photomicrographs of the sub-surface deformation zones beneath the scratch grooves created in the SLS glass at an applied normal load of 5 N: (a) at low magnification, (b), (c), and (d) at high magnification.
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Fig. 7. (a–d): The optical photomicrographs of the sub-surface deformation zones beneath the scratch grooves created in the SLS glass at an applied normal load of 10 N: (a) the total deformation zone at low magnification, (b), (c), (d), and (e) the marked zones of (a) at higher magnification.
Based on the earlier work reported by other researchers [12,37], the data on predicted values of the critical load (Pc) as a function of the applied normal loads are shown in Fig. 10(a) and (b) respectively for static and dynamic contact situations of relevance to the present experimental conditions. It is obvious from these results that there was a huge reduction in the requirement of critical load for Hertzian tensile crack formation during dynamic contact situation as compared to that of static contact situation in the present SLS glass. Confirmatory evidences of the damage evolution characteristics are presented in the scanning electron microscope (SEM) photomicrographs of the scratch grooves, Fig. 11(a–d). Even at a low normal load of 2 N, the Hertzian tensile cracks were present (Fig. 11a) as mentioned earlier (Figs. 3 and 4). The SEM photomicrograph presented in Fig. 11(b) confirmed that as the applied normal load was increased from a typical low magnitude e.g. 2 N to an intermediate yet a relatively higher magnitude, e.g. 5 N; more Hertzian tensile cracks were formed and their spatial density increased. As a result, the inter-Hertzian tensile crack separation decreased. This leads to more localized interaction zones among the Hertzian tensile cracks, indicated as black dotted circle in Fig. 11(b). Further, the consecutive Hertzian tensile cracks were regularly joined and intersected by the edge cracks as indicated by a white dotted line. At higher normal loads of 10 and 15 N (Fig. 11c and d), the degree of severity of such interactions and micro chip formation leading to evolution of micro wear debris increased manifold. This micro wear debris is marked by the white arrows in Fig. 11(b), (c) and (d). It was found that additional narrow cracks were also formed in the middle of the scratch groove at a higher normal load of 15 N (Fig. 11d). A plot (Fig. 12) of the subsurface crack depth Cdh as measured from the photomicrographs
(Figs. 5 to 8) versus the normal load gave a power law exponent of 0.66 which was comparable to the theoretical value of 0.67 [38]. 4. Discussions 4.1. The tribological behavior of the SLS glass There was an increase of all the tribological characteristic data of the present SLS glass with the applied normal load (Fig. 1). A careful inspection of Fig. 1a revealed that the slopes of the trend line were dF different for different load ranges. The slope dP was 0.09 and 0.27 for the load ranges of 2–5 N and 5–15 N, respectively. Similarly, dμ was dP low at ~0.004 but jumped by about three times to ~0.011 for the load range of 5–15 N (Fig. 1b). The μ values span the range of 0.09 to 0.19 with an average of 0.14 ± 0.05. This average μ data was comparable to dF the reported data of 0.15 ± 0.02 [39]. The change in the slopes dP and dμ possibly indicated a change in damage mechanism of the scratch dP grooves as the load was increased from 2 to 15 N, as also suggested for various glasses [5,18] and alumina [7,8]. For both the lateral force and the coefficient of friction the slopes of the straight lines in the load range of 5–15 N were ~3 times higher than those at the load range of 2–5 N which suggests that the changed mechanism that was operative for lateral force was also influencing the data on the coefficient of friction for the present SLS glass. Ideally, according to the Coulomb law of friction; μ should be independent of normal load. However, the extent of forced interaction between the asperity distributions on the surfaces of the indenter and the glass and the resultant force distribution between the asperities can govern the extent of physical friction which controls the
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Fig. 8. (a–d): The optical photomicrographs of the sub-surface deformation zones beneath the scratch grooves created in the SLS glass at an applied normal load of 15 N: (a) the total deformation zone at low magnification, (b), (c), (d), and (e) the marked zones of (a) at higher magnification.
numerical magnitude of friction coefficient. As the normal load increases the interaction between the Hertzian tensile cracks is enhanced and leads to the formation of micro chips on the soda lime silica glass surface. When such microchips fall in between the sliding indenter and the scratch groove they are further comminuted to form the micro wear debris which get entrapped in between the sliding indenter and the scratch groove, and enhance the coefficient of friction. Further, for conical indenters with a large tip radius e.g. as in the present case (R = 200 μm), that is actually doing the scratching; the force ratio is expected to increase [15] with increase in the applied normal load. The acoustic emission data also increased with the applied normal load (Fig. 1c). The increase in the magnitude of acoustic emission suggested an increase in inelastic and microfracture processes in the immediate vicinity of both the surface and the sub-surface regions of the scratch groove with increase in normal load which was in
Fig. 9. The optical photomicrograph of the scratch groove created in the SLS glass at applied normal load of 15 N at high magnification. The dotted black circle indicates the formation mechanism of a micro-chip of the SLS glass during the scratch experiment.
Fig. 10. Variations of critical load (Pc) for Hertzian tensile crack formation in the SLS glass under different contact situations: (a) static and (b) dynamic.
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tune with the experimental observations (Figs. 5 to 8). Therefore, the higher the applied normal load, the more would be the probability of the occurrence of microfracture events [5] which should increase the magnitude of the acoustic emissions (Fig. 1c) as was also noted by others for alumina, yttria stabilized zirconia, silicon carbide [16] and bulk metallic glasses [34]. There was an increase of scratch width with normal load (P), Fig. 1d. The maximum tensile stress due to static contacts ( σ sm ) under an applied normal load P in the present experiments were calculated using the following equation [12,37]: s
σm ¼
ð1−2νs ÞP : 2πa2s
ð2Þ
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scratch groove with enhancement of the applied normal load. Eq. (3) predicts that with the increase in normal load (P) the contact radius and hence, the scratch width should increase, Fig. 1(d). From the experimental data of the scratch width (Fig. 1d) and depth (Fig. 1e), the wear volume was calculated as the length of the groove (3 mm) times the area of the groove which had an approximately triangular cross section. The solid line in Fig. 1f actually represents an empirical power law fit of the experimental wear volume data (shown as individual points) to the applied normal load as noted by others also [6,40]. Further, the maximum tensile stress due to dynamic contact (σ dm ) between the glass surface and the sliding indenter during the scratch experiments were obtained from the following equation [12]: d
s
The quantity as in Eq. (2) denotes the static contact radius given by [12],
σ m ¼ ð1 þ 15:5μ Þσ m
1=3 3 2 2 Es 1−νs þ 1−νi : PrEs as ¼ 4 Ei
where μ is the coefficient of friction between the glass sample and the sliding indenter. Thus, the maximum tensile stress values were calculated from Eqs. (2), (3) and (4) for both static and dynamic contact cases using the following values of the physical properties e.g. νs = 0.25, νi = 0.07, Es = 51.76 GPa, Ei = 1141 GPa [32] and the results are given in Fig. 2(a–b) as mentioned earlier. The tensile stress of ~0.5–1 GPa (Fig. 2a) developed during the static contact at the rear and periphery of the contact circle, was itself much greater than the experimentally measured fracture strength (98 MPa) of the SLS
ð3Þ
In Eq. (3), Es and νs are the Young's modulus and Poisson's ratio of the glass, νi and Ei are the Poisson's ratio and the Young's modulus of the indenter and r is the radius of the indenter (200 μm). There was a huge increase in contact pressure with increase in the applied normal load which is possibly reflected as increase in depth (Fig. 1e) of the
ð4Þ
Fig. 11. SEM photomicrographs of the scratch grooves created in the SLS glass at different applied normal loads: (a) 2 N, (b) 5 N, (c) 10 N, and (d) 15 N. The black downward arrowheads indicate the scratch direction for all the photomicrographs.
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glass and was capable to initiate microfracture even on static contact. In the dynamic experiments, the tensile stress jumps abruptly to ~ 1– 4 GPa (Fig. 2b) which was conducive for more microfracture initiation thereby causing an increase in lateral force (Fig. 1a), coefficient of friction (Fig. 1b) and acoustic emission (Fig. 1c).
as partial cone cracks [12] because each individual crack leaves behind an incomplete arcuate trace on the glass surface. The incomplete surface traces of these partial cone cracks on the glass surface are termed as Hertzian tensile cracks [12] which are nearly equi-spaced. The critical load (Pc) for cone crack initiation is given by [12]:
4.2. The damage evolution processes in the SLS glass −3
At low load e.g. 2 N (Fig. 4a) there were only few Hertzian tensile cracks and even fewer interactions. However, the scenario changed at intermediate loads e.g. 5 N as shown in Fig. 4b. The opposite growths of the two edge cracks toward each other would facilitate the possibility of their interaction further. It is suggested that the cracks which grow toward the central region from the periphery of the Hertzian tensile cracks might have been formed during unloading rather than during loading. It is suggested further that at a relative higher applied normal load of 10 N as indicated by the dotted lines in Fig. 4(c), the regular interaction between the Hertzian tensile cracks themselves and their intersection by the edge cracks provided an intermediate step of “multiple micro-chip evolution” and consequently formation of micro wear debris facilitating a means of material removal. This conjecture was subsequently confirmed from scanning electron microscopic observations as would be discussed later. The angle of the tangents to the Hertzian tensile cracks with respect to the scratching direction varied in the range of about 120° to 134° (Fig. 4). This information would suggest that possibly some different stress components were responsible for their genesis. The slightly uplifted appearances of the edge cracks in Fig. 4(c) and (d) indicate that their genesis could be linked to the combined presence of strong tensile and shear stress components in the vicinity of and at the wake of the indenter. There was an increase in the extent of whitish zone of Fig. 4(a–d) with the applied normal load. This observation suggests that the extent of subsurface deformation increased with the applied normal load. Further confirmatory evidence of subsurface deformation emerges from Fig. 5(a–d) which were obtained by the well known bonded interface technique, as mentioned earlier. The presence of a crushed primary zone just below the indenter in the scratch groove created even at a low applied normal load of 2 N (Fig. 5a) indicates the important role played by the localized microfracture followed by the microcomminution processes in evolution of the material removal mechanism. Fig. 5d also presents a distinct evidence of formation of orthogonal cracks in between consecutive Hertzian tensile cracks which should also play an important role in the material removal process. The profuse presence of shear deformation bands at an intermediate load of 5 N, Fig. 6(a–d), as well as at a relatively higher load of 10 N, Fig. 7(a–d) strongly suggested again that shear stress played a major role in the damage evolution process of the scratched SLS glass. The extent of highly localized shear deformation increased manifold at the highest applied normal load of 15 N, Fig. 8(a–d). As the cracks formed, extended and joined all around a very thin layer of glass (Fig. 9), it appears to be on the verge of being chipped out. When such multiple micro-chip formation occurs, the detached thin layers contribute to the genesis of the micro wear debris. In general, the sub-surface damage zones in the present SLS glass almost characteristically contained a primary damage zone followed by a distinct secondary damage zone and in some cases, even a tertiary damage zone. It follows logically that the secondary damage zones are prospective candidate zones to play a major role in material removal process during repeated scratch experiments. In the present experiments, the Hertzian tensile cracks formed at all loads ≥2 N (Fig. 3a–d). It is well known that for all applied normal load P > Pc (the critical load for crack initiation) a cone shaped fracture is initiated [12,37] because now σ sm will be greater than the fracture strength σ f of glass. The frustum of this fracture cone intersects the glass surface close to the circle of contact of radius as , which now becomes the critical contact radius ac . These cracks are termed
Pc ¼ 6:7 10
9 16
h n oi 1=2 2 2 γs 1−νs þ 1−νi EEs Es i 1 r s P:
1=2 ð1 þ 15:5μ Þ3 I3f c3=2 1−νs 2 ð1−2νs Þ f
ð5Þ Taking the values of fracture energy of glass γs ~ 5 J m − 2 from [41], critical flaw size (cf) ~ 1 μm, If3 = 1/2 from [12], E = 51.76 GPa and r = 200 μm from the present experimental data, we get from Eq. (5) above; Pc ¼
0:03P : ð1 þ 15:5μ Þ3
ð6Þ
Corresponding to the applied normal loads of 2 to 15 N, Pc was about 0.05 to 0.45 N, Fig. 10a. However, for dynamic contact situations Pc decreased by almost an order of magnitude to about 0.005 to 0.08 N for applied normal loads of 2, 5, 10 and 15 N respectively, Fig. 10b. Thus the additional presence of the traction force made it even easier for the Hertzian tensile cracks to form as the sliding indenter scratches the soda lime silica glass. As the applied normal load P was already greater than the critical load Pc for Hertzian tensile crack formation, the Hertzian tensile cracks formed at all loads ≥2 N (Fig. 3a–d) in the present experiments. The photomicrographic evidence (Fig. 11) obtained by scanning electron microscopy presented confirmatory support to the suggestion made earlier in the present work that interaction between the Hertzian tensile cracks and “intra-Hertzian tensile cracks” crack formation provides an intermediate step which acted as a more plausible means of micro-chip evolution and consequently formation of micro wear debris thereby facilitating a means of material removal. Such intense interaction indeed leads to genesis of the microfracture events followed by micro chipping (mc) as indicated in Fig. 11(b) as a white dotted circle. The occurrence of the additional narrow cracks in the center of the scratch groove produced at the highest applied normal load of 15 N (Fig. 11d) was most likely due to the presence of a huge tensile stress component at the trailing edge of the indenter. Based on the crack depth (Cdh ) data measured from the photomicrographs of the sub-surface damage presented in Figs. 5–8, the fracture toughness ( KIc ) was evaluated using the following relation [42,43]; −1:5 d KIc ¼ χh Peff ch
ð7Þ
h
where, χh is a parameter that depends on the Poisson's ratio [31] and Peff is given by the following relation [42,43]: 2 0:5 : Peff ¼ P 1 þ μ
ð8Þ
The quantity Peff represents the effective force on the SLS glass under dynamic contact situation. It is nothing but the resultant magnitude of the vector sum of the applied normal force (e.g. load) P and the lateral force μP that acts in a direction perpendicular to that of P. The evaluated values of KIc varied in the range of 0.55 to 0.80 MPa.m 0.5 as the applied normal load was increased from 2 to 15 N. Thus, for the sub-surface cracks the average fracture toughness was ~0.71 ± 0.11 MPa.m 0.5 which was comparable to the independently measured fracture toughness (KIc) value of 0.72 ± 0.09 MPa.m0.5 evaluated by the conventional indentation fracture toughness method as mentioned earlier.
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Further, the experimental evidences presented in the photomicrographs of Figs. 5–8 also confirmed the significant presence of shear induced deformation. The maximum shear stress underneath the indenter was theoretically predicted using the following equation [44,45]: 16Peff E2r 9π2 r2
τmax ¼ 0:445
!1=3 ð9Þ
where Er is the reduced modulus given by the following relation [12]: Er ¼
hn
2
1−νs
. o n . oi−1 2 : Es þ 1−νi Ei
ð10Þ
A plot of τmax as a function of the effective applied normal force, Peff (Fig. 13) shows that the shear stress generated just underneath the indenter enhanced from ~ 10 to 20 GPa as the effective normal force increased from about 2.01 to 15.3 N corresponding to the applied normal loads of 2 to 15 N. The experimentally measured shear modulus of soda–lime–silica glass is ~ 30 GPa [46,47]. Thus, the theoretical shear strength (τtheor) for the soda–lime–silica glass is ~3–6 GPa (e.g. τtheor ~ G/5–G/10 [47]). Therefore, as τmax » τtheor of glass [46,47] shear induced flow and/or deformation was expected (Figs. 5–8). 4.3. The material removal mechanisms in the SLS glass Based on the present experimental evidences, Figs. 14 and 15 represent respectively the schematic pictures of both surface and subsurface deformations and damages for the scratch grooves formed at various applied normal loads. At a typical low load (e.g.2 N, Fig. 14a) few Hertzian tensile cracks and very few edge cracks are present on the surface of the SLS glass. At an intermediate normal load (e.g. 5 N, Fig. 14b) the Hertzian tensile cracks started to interact among themselves and form the micro-chips which create micro wear debris in the scratch tracks, also the number of edge cracks increased. As expected, the severity of total damage increased with the applied normal load. The number of Hertzian tensile cracks and the interactions among themselves were more in the scratch track for a relatively higher load (e.g. 10 N, Fig. 14c) leading to more micro-chip formations which enhanced the number of micro wear debris. At still higher normal load (e.g. 15 N, Fig. 14d), an additional set of cracks generated at an angle (0° b θ b 90°) with the scratch direction and lied nearly parallel to each other in the scratch track that was partially and/or totally crushed. In the schematic figures representing sub-surface deformations, the direction of the scratch was perpendicular to the plane of paper and goes inward as indicated by the cross sign. Fig. 15a revealed that the there were three successive damage zones in the sub-
Fig. 12. Variation of crack depths with the applied normal loads in the SLS glass.
Fig. 13. Variation of shear stress underneath the indenter with the effective normal loads in the SLS glass.
surface deformation region for an applied low load of 2 N. These were the “primary damage zone” that was just underneath the scratch groove, the “secondary damage zone” comprising of partially and/or fully crushed material, and finally a “tertiary damage zone” full of shear markings. These primary, secondary and tertiary damage zones are indicated in Fig. 15a respectively by a gray shade, a textured shade and black markings. Fig. 15b showed that at an intermediate load (e.g. 5 N) in addition to the three distinct damage zones, the shallow lateral cracks in the sub-surface damage zone joined and created a “now-loosened” portion of glass just beneath the scratch groove which was about to chip out (i.e. ca. Fig. 6c,d). At higher applied normal load (e.g. 10 N) a large number of shear bands oriented either perpendicular or at random to each other were also present in the cross section of the scratch groove in addition to the three damage zones and the formation of microchips, (i.e. ca. Figs. 15c and 7). Thus, at P > 5 N there was a distinct change of damage evolution mechanism as reflected also in the tribological characteristic data (Fig. 1). At still higher loads e.g. 15 N the spatial extent of damage zone increased so much substantially, (i.e. ca. Figs. 15d and 8) that the primary and secondary damage zones merged and thereby making it impossible to point out their separate existence. A large number of shear bands in various orientations are clearly visible as τmax » τtheor of glass [46,47].
5. Conclusions The major conclusions from the present work were: (a) The tribological parameters e.g. the lateral force, the coefficient of friction, the acoustic emission, the width and depth of the scratch groove and the wear volume all increased in the present soda lime silica glass with the applied normal loads in the range of 2 to 15 N due to the presence of a very large (e.g., up to 5 GPa) tensile stress component active at the wake of the sliding indenter. It is also suggested that the shear stress played a major role in causing the sub-surface damage evolutions beneath the scratch grooves. (b) Extensive optical and scanning electron photomicrographs provided evidence that the spatial extent and number of damages in the scratch grooves of the SLS glass increased with the applied normal loads (2–15 N). As the applied normal load was enhanced in the current scratch tests, the major material removal mechanism in the present SLS glass appeared mainly to involve the “enhanced degree of interaction” among Hertzian tensile cracks. This process leads to microfracture. The microfracture caused micro-chip formation. Finally, when these microchips got detached from the scratch grooves, the micro-wear debris was generated.
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Fig. 14. The schematic representation of the surface damages in the scratch grooves created in the SLS glass at different normal loads: (a) 2 N, (b) 5 N, (c) 10 N, and (d) 15 N. The arrowhead in (a) indicates the direction of the movement of the sliding indenter for the cases (b), (c), and (d) also. The dotted black circle indicates the interaction among Hertzian tensile cracks and formation mechanism of micro-chip of the SLS glass during the scratch experiment.
Fig. 15. The schematic representation of the sub-surface damages in the scratch grooves created in the SLS glass at different normal loads: (a) 2 N, (b) 5 N, (c) 10 N, and (d) 15 N.
(c) Extensive optical photomicrography confirmed that nearly elliptical subsurface deformation zones were formed beneath the scratch grooves made at 2–15 N normal loads in the present SLS glass. There were in general three distinct subsurface damage zones e.g., (i) an almost fully crushed “primary damage zone” just underneath the scratch groove, (ii) a “secondary damage zone” characterized mainly by extensive microfracture as well as shear deformations lines, and (iii) a “tertiary damage zone” mainly characterized by occurrences of lateral cracks and shear deformation bands. It is suggested that these secondary and tertiary damage zones may play an important role in material removal process of the SLS glass under repeated single pass contacts e.g. as in a grinding process.
CSIR (Project No. NWP 0027). The author AD also acknowledges the constant encouragement from the Director, ISAC, Bangalore.
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Acknowledgments The authors are grateful to the Director, CSIR-Central Glass and Ceramic Research Institute (CGCRI), Kolkata for his kind permission to publish this paper. In addition, the authors appreciate the infrastructural supports received from all colleagues and particularly those received from the colleagues of the Mechanical Property Evaluation Section, NOCCD. The experimental assistance of Mrs. R. Chakraborty, S. Sarkar and D. Das of CSIR-CGCRI are gratefully acknowledged. Finally, the authors gratefully acknowledge the financial supports received from
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