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Indentation-induced microhardness changes in glasses: Possible fictive temperature increase caused by plastic deformation
Journal of Non-Crystalline Solids 354 (2008) 4056–4062
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Indentation-induced microhardness changes in glasses: Possible fictive temperature increase caused by plastic deformation T.M. Gross, M. Tomozawa * Department of Materials Science and Engineering, School of Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, United States
a r t i c l e
i n f o
Article history: Received 16 November 2007 Received in revised form 16 April 2008 Available online 4 July 2008 PACS: 81.70.Bt 81.05.Kf 62.20.Qp 62.20.Fe 62.20.Mk
a b s t r a c t The microhardness around a large indentation was measured for different types of glasses. In soda-lime silicate glass, a typical normal glass, the region in the immediate vicinity of the indentation was found to exhibit a lower hardness than the region far removed from the indentation. In silica glass, a typical anomalous glass, the region in the immediate vicinity of a large indentation was found to exhibit a higher hardness than the region far removed from the indentation. Asahi less brittle glass, an intermediate glass between normal and anomalous glasses, was found to exhibit little change in hardness in the vicinity of the large indentation. These findings can be explained by a deformation-induced fictive temperature increase leading to a lower hardness for soda-lime silicate glass and a higher hardness for silica glass. Ó 2008 Elsevier B.V. All rights reserved.
Keywords: Hardness Silica Silicates Soda-lime-silica
1. Introduction Permanent deformation can be produced on a glass during microhardness testing by a Vickers indenter. The deformation of glass is attributed to plastic deformation and/or densification [1,2]. A possible structural change associated with the permanent deformation, however, is rarely considered. Recently, it has been shown by Koike and Tomozawa using Fourier Transform Infrared Spectroscopy (FTIR) that the region surrounding an indentation in soda-lime silicate glass undergoes a plastic deformation-induced fictive temperature increase [3]. This region with a different fictive temperature is expected to have a corresponding different density from that of the bulk of the glass as each fictive temperature has an associated unique density value. The soda-lime silicate glass undergoing the fictive temperature increase may be experiencing a plastic dilatation around shear bands as seen in metallic and polymeric glasses [4–7]. This appears to be the case in normal glasses, i.e. those exhibiting decreasing density and hardness with increasing fictive temperature. Anomalous glasses, such as silica glass, i.e. those exhibiting increasing density and hardness with increasing fictive temperature, should exhibit deformation-in* Corresponding author. Tel.: +1 518 276 6659; fax: +1 518 276 8554. E-mail address: [email protected] (M. Tomozawa). 0022-3093/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2008.05.042
duced densification. The dilatation or densification expected to occur in normal and anomalous glasses, respectively, was investigated using microhardness measurements in the plastically deformed region surrounding an indentation formed under a high load. Asahi less brittle glass, an intermediate glass between normal and anomalous glass, was also investigated for comparison. The plastically deformed region is defined by Hill as the hemisphere surrounding a Vickers indentation with a diameter equal to three times the major diagonal of the indentation as shown schematically in Fig. 1. The majority of plastic deformation, however, occurs within the hemispherical region with a diameter equal to the length of the major diagonal of the indentation, l [8]. Similar phenomena have been reported in polymeric glasses. The terminology in polymer science is different from that of glass science, but the mechanism appears to be equivalent. The inherent energy of the structure of polymers can decrease with time during the process of physical aging [9,10]. In glass science the terms ‘inherent energy of structure’ and ‘physical aging’ can be replaced with ‘fictive temperature’ and ‘structural relaxation,’ respectively. When a shear stress is applied to a polymeric glass that has undergone physical aging, the inherent energy can be increased to that of the original state in a process termed ‘mechanical rejuvenation’ [9,10]. If inorganic glasses follow the same trend it is then expected that the deformed material surrounding an indentation will exhibit
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610
2
Hardness (kgf/mm )
590 570 550 530 510 490
In Nitogen In Air
470 450 0
20
40
60
80
100
Time (sec) Fig. 2. Hardness as a function of loading time for 50 gf indentations taken for sodalime silicate glass in a dry nitrogen environment and in an atmospheric air environment. Dotted lines are a guide to the eyes.
Fig. 1. Schematic of plastically deformed zone, radius = 3l, according to Hill [8].
an increase in fictive temperature, just as polymers exhibit an increase in the inherent energy of structure under shear stress. It is then expected that normal glasses will have a plastically deformed region of lower density as well as lower hardness while anomalous glasses will have a deformed region of higher density as well as higher hardness. It is the purpose of the present work to demonstrate the expected hardness change in the deformed zone created by indentation. 2. Experimental Samples of soda-lime silicate glass, silica glass, and less brittle glass were obtained from Asahi Glass Company, Ltd. of Japan. Asahi less brittle glass consists of 13% Na2O, 1% K2O, 4% MgO, 1% CaO, 2% Al2O3 and 79% SiO2 (all in mole percents) [11–13]. Samples of each type of glass were cut to approximate dimensions of 5 mm 5 mm 1 mm. The soda-lime silicate glass was manufactured by the float process and the side of the as-received glass that did not contact tin was used. The samples were polished using a series of 240, 400, and 600 grit SiC polishing paper followed by a final polish in a 1 lm cerium oxide slurry to obtain an optical finish. The change in hardness in the region surrounding a large indentation was studied for these glasses. Samples of Asahi less brittle glass, Asahi soda-lime silicate glass, and Asahi silica glass were each heated at their respective glass transition temperatures, 515, 550, and 1200 °C, for 4 h in nitrogen. The samples were then furnace cooled at a rate of approximately 5 °C/min to eliminate residual stresses on the glass surface. The absence of residual stress was confirmed by polariscope. Vickers hardness was measured using a Leco M-400 microhardness tester. The hardness can vary with time when measured in air, due to the presence of water vapor [14], while the value measured in a dry nitrogen atmosphere is constant with time as shown in Fig. 2 where the hardness values of soda-lime silicate glass obtained under 50 g force (gf) are plotted against the loading time. The data obtained in a nitrogen atmosphere will primarily be reported here. The hardness tester was enclosed in a ‘glove bag’ and hardness testing was performed under dry nitrogen. The ‘glove bag’ was evacuated and filled with nitrogen then re-evacuated and re-filled with dry nitrogen to ensure that air was removed from the bag prior to hardness testing. The glass samples were placed into
the bag immersed in dry toluene prior to filling the bag with dry nitrogen to ensure that water is not present on the glass surface and the glass was removed from the toluene in the dry nitrogen environment and wiped dry. Toluene is a non-polar liquid with low water solubility [14]. A large one kilogram force (kgf) Vickers indentation was made for 15 s and then 50 gf indentations were made for 15 s outside the large indentation at various distances from the edges of the larger indentation. These smaller indentations were made at an approximately 45° angle from the corners of the large 1 kgf indentation. Indentations made with a load of 50 gf are small enough to analyze the hardness of the deformed zone. The distance from the center of the 1 kgf indentation to the edge of each of the 50 gf indentations was measured and used to define the location of the probe indentation. For each type of glass a plot of hardness vs. distance from the larger indentation is then made. For each type of glass the density and hardness were also measured as a function of fictive temperature for four different temperatures. Table 1 shows the fictive temperatures studied for each glass with the heat-treatment time in parentheses. The density was measured as a function of fictive temperature using a sink-float density measurement technique [15,16]. The sink-float density measurement was conducted by making a solution of 1bromonaphthalene and 1,1,2,2 tetrabromoethane in which the glass sample just floats at room temperature. The solution was then heated at 0.1 °C/min until the glass sample begins to sink and the temperature is recorded. The density of the liquid at selected temperatures was determined using a Bingham pycnometer. The resulting density vs. temperature curve can then be used to determine the liquid density at the temperature at which the sample sank. This liquid density at this temperature is then equal to the sample density. Hardness was also measured as a function of fictive temperature using a Vickers indenter with a 50 gf load for 15 s. Fifteen
Table 1 Glass transition temperatures of the samples used in the present work and heattreatment conditions to prepare samples with various fictive temperatures Type of glass Asahi Less Brittle Glass Asahi Soda-Lime Silicate Glass Asahi Silica Glass
Glass transition temperature (°C)
Fictive temperatures (°C) (Heat treatment time (h))
515
450 (48), 500 (24), 550 (4), 600 (2)
550
500 (24), 550 (4), 600 (2), 650 (2)
1200
1050 (280), 1100 (160), 1150 (50), 1200 (4)
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indentations were made at each fictive temperature studied for each glass under a dry nitrogen atmosphere and the mean hardness was calculated. 3. Results Fig. 3 shows the fictive temperature dependence of density for the three glasses investigated here. Soda-lime silicate glass, a normal glass, shows decreasing density with increasing fictive temperature while silica glass, an anomalous glass, shows increasing density with increasing fictive temperature. The slopes for sodalime silicate glass and silica glass are 2 10 4 (g/(cm3 °C)) and 9 10 6 (g/(cm3 °C)), respectively. Less brittle glass, can be considered intermediate between normal and anomalous glass although its overall behavior is that of a normal glass, with its density decreasing with fictive temperature with a slope of 9 10 5 (g/ (cm3 °C)). Photomicrographs showing a large 1 kgf indentation and 50 gf indentations at varying distances from the large indentation for each of these glasses are shown in Fig. 4. It should be noted that the large indentation shows normal cracking behavior for sodalime silicate glass in that median cracks propagate from the corners of the indentation. For both silica glass and less brittle glass, the cracking behavior around the large indentations show median cracking behavior and some anomalous, conical cracking behavior. Plots showing the hardness as a function of distance from the center of the large indentation for the three glasses are shown in Fig. 5. Here, data from several separate indentations of the same glass are plotted together. The vertical dotted lines represent the
2.55
soda-lime silicate glass less brittle glass
2.5
ρ = -0.0002TF + 2.58
silica glass
3
Density (g/cm )
2.45 2.4
ρ = -9E-05TF + 2.4414
2.35 2.3 2.25
ρ = 9E-06TF + 2.1898
2.2 2.15 400
600
800
1000
1200
o
Fictive Temperature ( C) Fig. 3. Density vs. fictive temperature for soda-lime glass, less brittle glass, and silica glass.
positions at which the edges of the 1 kgf indentations come in contact with the edges of the 50 gf indentations. It can be seen from the plot that the region close to the 1 kgf indentation gives lower hardness values than at larger distances for soda-lime silicate glass (Fig. 5(a)). From the plot it can be seen that the hardness is lower in the region within 10 lm from the edge of the large indentation. This length is approximately equal to the length of the region between the indentation edge and the circle with the diameter equal to the indentation length as shown schematically in Fig. 6. This region will be defined as the shear deformation zone. This is the region in which volume change primarily takes place. The average hardness at a distance beyond the shear deformation zone is 583 ± 19 kg/mm2 for soda-lime silicate glass. The average value of the hardness within the shear deformation zone is 550 ± 31 kgf/mm2. The plot of the hardness vs. distance from the large 1 kgf indentation is shown in Fig. 5(b) for silica glass. Unlike soda-lime silicate glass, the hardness is very high in the region immediately surrounding the indentation and decreases to a constant value at larger distances. The increase in hardness appears to occur within 5 lm of the edge of the large indentation. We will define this region as the compacted zone. The average hardness outside the compacted zone is 748 ± 18 kgf/mm2. The average hardness within the compacted zone is 803 ± 37 kgf/mm2. In Fig. 5(c) it is shown that the hardness does not exhibit a noticeable change in the region immediately surrounding the large 1 kgf indentation in less brittle glass. The hardness from the edge of the indentation extending to the non-deformed portion of the glass stays at a steady value of 492 ± 25 kgf/mm2. The experiment was repeated in an air atmosphere for all three glasses using a loading time of 15 s. No time dependent hardness is expected to occur as shown in Fig. 2. The results were nearly identical to those obtained in dry nitrogen atmosphere. Fig. 7 shows hardness vs. fictive temperature for the three glasses as determined with a 50 gf load for 15 s in a dry N2 atmosphere. It is shown that soda-lime silicate glass shows normal glass behavior, decreasing in hardness with increasing fictive temperature with a slope equal to 0.6081 (kgf/(mm2 °C)). Silica glass exhibits anomalous behavior, increasing in hardness with increasing fictive temperature with a slope equal to 0.3773 (kgf/ (mm2 °C)). The hardness variation with fictive temperature is also shown for Asahi less brittle glass. This glass shows normal behavior with a slope of 0.2810 (kgf/(mm2 °C)), much smaller magnitude than those of soda-lime silicate glass and silica glass. For soda-lime silicate glass, the hardness value outside the shear deformation zone was 583 ± 19 kgf/mm2. From Figs. 3 and 7 this corresponds to a fictive temperature of 543 ± 32 °C and a density of 2.4714 ± 0.0064 g/cm3. The shear deformation zone had a hardness of 550 ± 31 kgf/mm2, which corresponds to a fictive temperature of 597 ± 51 °C and a density of 2.4606 ± 0.0102 g/cm3. It can be seen that there is a marked increase in fictive temperature and a decrease in density in the shear deformation zone when
Fig. 4. Indentation patterns for (a) soda-lime silicate glass, (b) silica glass, (c) less brittle glass.
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Hardness (kgf/mm2)
610 590 570 550 Distance from center of 1 kgf indentation to its edge
530 510 490 470 450 0
20
40
60
80
100
Distance from center of 1 kgf indentation (μm)
Fig. 6. Schematic of the 1 kgf Vickers indentation and the surrounding shear deformation for soda-lime silicate glass.
900 850
2
Vickers Hardness (kgf/mm )
800
2
Hardness (kgf/mm )
850
800 Distance from center of 1 kgf indentation to its edge
750
700
650
750
silica glass soda-lime silicate glass less brittle glass
H = 0.3773TF + 313.05
700 650 600 550
H = -0.6081TF + 913.11 500
H = -0.281TF + 637.53
450
600 0
10
20
30
40
50
60
70
80 400 400
Distance from center of 1 kgf indentation (μm)
500
600
700
800
900
1000
1100
1200
1300
Fictive Temperature (oC) 650
Fig. 7. Hardness vs. fictive temperature for silica glass, soda-lime silicate glass, and less brittle glass under a 50 gf load for 15 s in dry N2 atmosphere.
2
Hardness (kgf/mm )
600
ness is 492 ± 25 kgf/mm2 and from Figs. 3 and 7 the fictive temperature and density are determined to be 518 ± 89 °C and 2.3948 ± 0.008 g/cm3. Even if a hardness change occurred in this glass, since the slope dH/dTf is small it is difficult to observe. Within the error bar the hardness near the indentation may be as low as 467 kgf/mm2 which corresponds to a possible fictive temperature increase up to 607 °C near the indentation edge.
550 Distance from center of 1 kgf indentation to its edge
500
450
400
4. Discussion
350 0
10
20
30
40
50
60
70
80
Distance from 1 kgf indentation (μm) Fig. 5. Hardness (50 gf) vs. distance from 1 kgf indentation for (a) soda-lime silicate glass, (b) silica glass, (c) less brittle glass. Curved and horizontal dotted lines are guides to eyes.
compared to the region outside of this zone for soda-lime silicate glass. For silica glass the hardness value outside of the compacted zone was 748 ± 18 kgf/mm2. From Figs. 3 and 7, the fictive temperature and density are determined to be 1152 ± 49 °C and 2.2002 ± 0.0004 g/cm3, respectively. Within the compacted zone the hardness is 803 ± 37 kgf/mm2 which corresponds to a fictive temperature of 1298 ± 98 °C and a density of 2.2015 ± 0.0008 g/ cm3. It can be seen that the fictive temperature and density are both higher in the compacted region when compared to the noncompacted region. In the case of Asahi less brittle glass, hardness does not seem to change with distance from the indentation edge. The average hard-
It is known that there is residual stress around an indentation [17–22]. Furthermore, Kese et al. [17] attributed the observed hardness and modulus decrease around a large Vickers indentation of soda-lime glass to the residual stress. It is important, therefore, to learn the possible effect of residual stress on the indentation hardness in order to interpret the present experimental observation correctly. The residual stress distribution around a large 45 N indentation in soda-lime silicate glass has been estimated by Zeng and Rowcliffe [21] by measuring the crack lengths around smaller, 2.94 N (300 gf) load Vickers indentations at various angles from a median crack of the larger indentation. These crack lengths around the small indentation were measured as a function of distance from the larger indentation. The cracks extending in the radial direction became longer when a larger residual tensile stress existed tangentially to the large indentation edge. The cracks extending in the tangential direction became shorter when a larger residual compressive stress existed radially from the indentation edge. The procedure is schematically shown in Fig. 8. From this
T.M. Gross, M. Tomozawa / Journal of Non-Crystalline Solids 354 (2008) 4056–4062
Fig. 8. Schematic showing the orientation of 100 gf indentations made in the residual stress field of a 1 kgf Vickers indentation to measure the residual tensile stress.
measurement, Zeng and Rowcliffe [21] obtained the residual stress profiles consisting of tangential tensile stress and radial compressive stress. The magnitude of the residual stress decreased with increasing distance from the main indentation and at a given distance from the main indentation, the magnitude of the radial compressive stress was much larger than that of the tangential tensile stress. For example, in the 45° direction from the main crack, a maximum tensile stress of 32.5 MPa in the tangential direction and a maximum compressive stress of 185 MPa in the radial direction were observed at the closest point to the large indentation. The residual stress was found to decrease with increasing distance, r, from the large indentation by (1/r)3 [23]. Another important effect of indentation on glasses is densification. Yoshida et al. [24] as well as Ji et al. [25] showed that glasses exhibit densification under Vickers indenter, the magnitude of densification becoming greater for glasses with smaller Poisson’s ratio. They found that more than 60% of the indentation volume was due to densification for soda-lime silicate glasses and even the pile-up region exhibited densification [25]. Thus, there are three possible effects which can affect hardness of glasses near a large Vickers indentation: fictive temperature change, residual stress and densification. In this Discussion, an attempt will be made to differentiate these three effects by using their different relaxation times upon heat-treatment of soda-lime silicate glass. The change of fictive temperature by heat-treatment involves structural relaxation, while the change of residual stress by heat-treatment is dictated by stress relaxation time, sstress, which is usually shorter than the structural relaxation time, sstruct, by a factor of 10. [26]. The densification relaxation time, sdens, by heat-treatment appears to be shorter than the stress relaxation time, being accomplished by the heat-treatment at 0.9 Tg (K) for 2 h [24,25]. Namely, the following relation holds. sstruct, > sstress, > sdens. Soda-lime silicate glass with a 1 kgf Vickers indentation was heat-treated at 495 °C for 2 h in dry N2 atmosphere. This temperature corresponds to 0.933 Tg(K), which is higher than the heattreatment temperature, 0.9 Tg(K) employed by Yoshida et al. [24] to remove the densification. Thus densification introduced by Vickers indentation is considered to have disappeared by this heat-treatment. The residual stress before and after the heat-treatment was also measured using the same technique employed by Zeng and Rowcliffe [21]. Specifically, 100 gf indentations were made in air at 45° to the corners in the perpendicular direction to the large indentation edges as a function of distance from the
large indentation. These smaller indentations were aligned so that one median/radial crack was perpendicular to the large indentation edge as shown in Fig. 8. The lengths of the cracks that were on the side away from the large indentation were measured to determine the relative amount of residual stress. The length of the crack in an annealed soda-lime silicate glass was also measured for comparison. The lengths of the cracks in the radial direction were shorter after the heat-treatment, compared with those of sample without the heat-treatment, by a factor of 2–3 at 13–20 lm distance from the edge of the large indentation. This reduction of the crack length corresponds, according to the equation employed by Zeng and Rowcliffe [21], to the reduction of the tangential tensile stress by approximately 20%. Also present in several of the indentations of the heat-treated sample were cracks in the tangential direction. This indicates that residual radial compressive stress is also relieved by this heat-treatment. The hardness distribution around a pre-existing 1 kgf indentation was determined by probing with 50 gf indentations after the heat-treatment as shown in Fig. 9. The results are virtually identical to those in Fig. 5(a). This experiment shows that the residual stress has no measurable influence on the indentation hardness. The densification of this glass also appears to have little influence since the densification in the pile-up region is expected to disappear by the heat-treatment employed. Kese et al. [17] and Erikkson [20] have previously shown that hardness and elastic modulus decrease in the region surrounding a 45 N indentation in soda-lime silicate glass and have attributed this to residual stress. Furthermore, Kese et al. [17] showed that both elastic modulus and hardness change with applied bending stress, increasing with uniaxial compressive stress and decreasing with uniaxial tensile stress. Comparison of our Figs. 3 and 7 show that with a given glass, increasing density is accompanied by increasing hardness. The effect of applied bending stress on hardness obtained by Kese et al [17] exhibits the similar trend: uniaxial tensile stress which is expected to increase the glass volume produces a lower hardness while uniaxial compressive stress which decreases glass volume produces a higher hardness for soda-lime glass. The residual stress around Vickers indentation, according to Zeng and Rowcliffe [21] measurement, exhibit biaxial stress with the radial compressive stress having five times greater magnitude compared with the magnitude of tangential tensile stress. Thus, the volume of the soda-lime silicate glass in the vicinity of Vickers indentation is expected to decrease by the residual stress. Therefore, the residual stress is expected to increase the hardness of soda-lime silicate glass. Thus, it appears unreasonable to attribute the observed lower hardness of soda-lime silicate glass near
600 590
Hardness (kgf/mm2)
4060
580 570 Distance from center of 1 kgf indentation to its edge
560 550 540 530 520 510 0
10
20
30
40
50
60
70
80
Distance from center of 1 kgf indentation (μm) Fig. 9. Hardness vs. distance from 1 kgf indentation after annealing at 495 °C for 2 h.
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a large Vickers indentation to the residual stress. Furthermore, the observed lower hardness is confined to the immediate vicinity of the large Vickers indentation while the residual stress is known to spread more widely, decreasing with the distance, r, as (1/r)3 [23]. Erikson et al. [20] found the lower hardness even in the center of a large Vickers indentation, after a partial polishing, by probing with a smaller indenter. Their analysis of the observation using finite element analysis based upon the residual stress could not give a satisfactory explanation of the experimental observation. Kese et al. [18] attempted to use the lower elastic modulus around a large Vickers indentation to probe the residual stress, assuming the observed elastic constant distribution is caused by the residual stress. Their finding that the residual stress could not be eliminated even by the heat-treatment at 540 °C for 24 h is in contrast to earlier direct observation that the residual stress disappearing easily by the heat-treatment at similar or even lower temperatures [27–29]. This discrepancy indicates that the assumption of lower hardness and elastic modulus around a large Vickers indentation of soda-lime silicate glass originating from the residual stress is not valid. On the other hand, lower hardness and higher hardness in the deformed region immediately surrounding the 1 kgf indentation in soda-lime silicate glass and silica glass, respectively shown in Fig. 5(a) and (b) correspond to a higher fictive temperature as shown in Fig. 7. This is consistent with the observation made by Kioke and Tomozawa, using infrared spectroscopy, that the plastically deformed region experiences a fictive temperature increase at least in the case of soda-lime silicate glass [3]. Earlier, Tomozawa et al. [30,31] showed from the peak shift of IR silica structural bands that silica glass with higher density having higher fictive temperature has a smaller Si–O–Si bond angle. Similarly, Si–O–Si bond angle of silica glass increases under tensile stress which increases the glass volume and decreases hardness [30]. These results, combined with the present result, indicate that the volume change of a glass, whether it is produced by permanent deformation or elastic deformation, is accompanied by the similar Si–O– Si bond angle change and similar hardness change. Again, the net compressive residual stress should have a hardening effect on soda-lime silicate glass.
4061
In order to find the structural origin of the lower hardness near the large Vickers indentation of soda-lime silicate glass, cross-sectional observation of the region underneath 1 kgf indentations in soda-lime glass was made following the method described by Hagan [32]. Fig. 10(a) shows the cross-section of an indentation in which one major diagonal is aligned with the sectioning crack. In this image it appears that all of the shear bands are contained beneath the indentation and do not extend beyond the indentation corners. Fig. 10(b) shows a cross-section of the same glass, but this time the sectioning intersects the middle of two opposite edges. In this orientation, the shear bands appear to extend beyond the edges. The shear deformation zone may, in fact, be comprised of a hemisphere with a diameter equal to the indentation major diagonal. A similar result was obtained earlier for a metallic glass [33]. This is the region in which the measured hardness is found to be different in the glasses studied here. These observations clearly indicate that the observed lower hardness in the vicinity of a large Vickers indentation is closely related to the structural change of the glass. The magnitude of the hardness increase in the plastically deformed zone immediately surrounding the 1 kgf indentation in silica glass shown in Fig. 5(b) is also consistent with the increase of fictive temperature caused by plastic deformation. The increase in hardness and the corresponding density increase may be due partly to other factors besides the increase in fictive temperature. A recoverable densification on indentation has been shown to exist [2,24,25,34,35], which may or may not be a different mechanism than the densification expected to occur during the plastic deformation-induced fictive temperature increase. Ernsberger [2] and MacKenzie [34] have shown experimentally that a densification occurs in silica glass under indentation pressure. MacKenzie [34] claimed that compression in conjunction with shear stress produces an interlocking of two parts of the network. The interlocking results in incomplete volume recovery when the pressure is removed. Neely and MacKenzie [35] and later Yoshida et al. [24] showed that this densification was recoverable at temperatures below the glass transition temperature. These authors claim that recoverable densification should be treated separately from irreversible plastic flow. In the case of silica glass, the effect of recoverable densification and plastic deformation-induced fictive
Fig. 10. Cross-sectional view of Vickers indentation (a) Orientation of Vickers indentation with one major diagonal aligned with the cross-section and the resulting shear bands. Shear bands do not appear to be outside of the indentation in this orientation. (b) Orientation of Vickers indentation with the cross-section intersecting the major diagonals and the resulting shear bands. Shear bands now appear to be outside of the indentation in this orientation.
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temperature increase leading to densification may be superimposed. Yoshida et al. showed that a portion of the recoverable densification extended outside of the boundaries of the indentation at the surface [24] in the same region where the present hardness measurements were taken. The hardness profile in the immediate vicinity of the 1 kgf large indentation for less brittle glass exhibited practically no noticeable difference from the region far removed from the indentation. This glass is intermediate between a normal and anomalous glass, although the overall behavior is similar to a normal glass. From Fig. 7 it is seen that hardness varies the least among the three glasses with changes in fictive temperature, which is consistent with the lack of an observed hardness change in the plastically deformed region. The hardness dependence on fictive temperature for less brittle glass is considerably less than that of both soda-lime silicate and silica glasses. This glass also shows a much lower density dependence on fictive temperature than soda-lime silicate glass. Thus, indentation hardness in the plastically deformed region of the three glasses investigated exhibited changes in hardness consistent with a plastic deformation-induced increase of fictive temperature. This increase in Tf may not be aided by heating since Yoshioka and Yoshioka [36] detected negligible heating during indentation. Another example of a fictive temperature increase without any heating of a glass sample was shown by Devine for glass exposed to neutron radiation [37]. These examples show that a fictive temperature increase in a glass may not necessarily require heating. The lack of an observed hardness change in the plastically deformed zone in the less brittle glass may give an important clue as to why this glass exhibits less brittle behavior or greater crack initiation load under indentation. When a glass is indented or scratched a plastic deformation can occur. If the region close to a large indentation with a different fictive temperature has a different density or different mechanical properties from the rest of the glass, strain mismatches can be generated that could lead to cracking. On the other hand, if this plastic deformation zone has the same density or same mechanical properties as the undeformed glass, the glass will be less likely to fracture. 5. Conclusion Soda-lime silicate glass, a normal glass, has been shown to exhibit volume dilatation in the immediate vicinity of an indentation through microhardness measurements. Silica glass, an anomalous glass, shows the opposite behavior in that a densification occurs
in the immediate vicinity of an indentation. Less brittle glass, showing somewhat intermediate behavior, does not exhibit either of these trends. These features are consistent with fictive temperature increase or rejuvenation by plastic deformation. Acknowledgement This research was supported by an NSF grant under DMR0352773. The authors thank Asahi Glass Co. Ltd. for providing the glass samples used in the present work. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37]
D.M. Marsh, Proc. Roy. Soc. London A279 (1964) 420. F.M. Ernsberger, J. Am. Ceram. Soc. 51 (1968) 545. A. Koike, M. Tomozawa, J. Non-Cryst. Solids 353 (2007) 2318. P.E. Donovan, W.M. Stobbs, Phil. Mag. A 47 (1983) 537. Y. Zhang, A.L. Greer, App. Phys. Lett. 89 (2006) 071907-1. R. Bhowmick, R. Raghavan, K. Chattopadhyay, U. Ramamurty, Acta Mater. 54 (2006) 4221. M. Utz, Q. Peng, M. Nandagopal, J. Polym. Sci.: Part B: Polym. Phys. 42 (2004) 2057. R. Hill, in: The Mathematical Theory of Plasticity, Oxford, Great Britain, 1950. L.C.E. Struik, Polymer 38 (1997) 4053. M. Utz, P.G. Debenedetti, F.H. Stillinger, Phys. Rev. Lett. 84 (2000) 1471. J. Sehgal, S. Ito, J. Am. Ceram. Soc. 81 (1998) 2485. J. Sehgal, S. Ito, Reports Res. Lab. Asahi Glass Co., Ltd. 50 (2000) 1. S. Ito, J. Am. Ceram. Soc. Japan 112 (2004) 477. K. Hirao, M. Tomozawa, J. Am. Ceram. Soc. 7 (1987) 497. ASTM Standard C 729-75, Ann. Book of ASTM Standards, vol. 15.02: Glass; Ceramic Whitewares, ASTM International (2007). ASTM Standard D1217-93, Ann. Book of ASTM Standards, vol. 05.01: Petroluem Products and Lubricants, ASTM International (2007). K.O. Kese, Z.C. Li, B. Bergman, J. Mater. Res. 19 (2004) 3109. K. Kese, M. Tehler, B. Bergman, J. Euro. Ceram. Soc. 26 (2006) 1003. K.O. Kese, Z.C. Li, B. Bergman, J. Euro. Ceram. Soc. 26 (2006) 1013. C.L. Eriksson, P.L. Larsson, D.J. Rowcliffe, Mat. Sci. Eng. A340 (2003) 193. K. Zeng, D.J. Rowcliffe, Acta Metall. Mater. 43 (1995) 1935. K. Zeng, D. Rowcliffe, J. Am. Ceram. Soc. 77 (1994) 524. Z. Burghard, A. Zimmerman, J. Rodel, F. Aldinger, B. Lawn, Acta Mater. 52 (2004) 293. S. Yoshida, J.C. Sangleboeuf, T. Rouxel, J. Mater. Res. 20 (2005) 3404. H. Ji, V. Keryvin, T. Rouxel, T. Hammouda, Script Materialia 55 (2006) 1159. C.T. Moynihan, p.32 in ASTM STP 1249. In: R.J. Seyler (Ed.), ASTM, Phila PA, 1994. D.B. Marshall, B.R. Lawn, J. Am. Ceram. Soc. 63 (1980) 532. P. Chantikul, B.R. Lawn, D.B. Marshall, J. Am. Ceram. Soc. 64 (1981) 322. D.H. Roach, A.R. Cooper, J. Am. Ceram. Soc. 68 (1985) 632. M. Tomozwaa, J.-W. Hong, R.W. Hepburn, Glass Sci. Technol. 75 C1 (2002) 262. M. Tomozawa, J.-W. Hong, S.-R. Ryu, J. Non-Cryst. Solids 351 (2005) 1054. J.T. Hagan, J. Mater. Sci. 15 (1980) 1417. H. Zhang, X. Jing, G. Subhash, L.J. Kecskes, R.J. Dowding, Acta Mater. 53 (2005) 3849. J.D. MacKenzie, J. Am. Ceram. Soc. 46 (1964) 461. J.E. Neely, J.D. MacKenzie, J. Mat. Sci. 3 (1968) 603. N. Yoshioka, M. Yoshioka, Phil. Mag. A 74 (1996) 1273. R.A.B. Devine, J. Non-Cryst. Solids 152 (1993) 50.
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Indentation-induced microhardness changes in glasses: Possible fictive temperature increase caused by plastic deformation T.M. Gross, M. Tomozawa * Department of Materials Science and Engineering, School of Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, United States
a r t i c l e
i n f o
Article history: Received 16 November 2007 Received in revised form 16 April 2008 Available online 4 July 2008 PACS: 81.70.Bt 81.05.Kf 62.20.Qp 62.20.Fe 62.20.Mk
a b s t r a c t The microhardness around a large indentation was measured for different types of glasses. In soda-lime silicate glass, a typical normal glass, the region in the immediate vicinity of the indentation was found to exhibit a lower hardness than the region far removed from the indentation. In silica glass, a typical anomalous glass, the region in the immediate vicinity of a large indentation was found to exhibit a higher hardness than the region far removed from the indentation. Asahi less brittle glass, an intermediate glass between normal and anomalous glasses, was found to exhibit little change in hardness in the vicinity of the large indentation. These findings can be explained by a deformation-induced fictive temperature increase leading to a lower hardness for soda-lime silicate glass and a higher hardness for silica glass. Ó 2008 Elsevier B.V. All rights reserved.
Keywords: Hardness Silica Silicates Soda-lime-silica
1. Introduction Permanent deformation can be produced on a glass during microhardness testing by a Vickers indenter. The deformation of glass is attributed to plastic deformation and/or densification [1,2]. A possible structural change associated with the permanent deformation, however, is rarely considered. Recently, it has been shown by Koike and Tomozawa using Fourier Transform Infrared Spectroscopy (FTIR) that the region surrounding an indentation in soda-lime silicate glass undergoes a plastic deformation-induced fictive temperature increase [3]. This region with a different fictive temperature is expected to have a corresponding different density from that of the bulk of the glass as each fictive temperature has an associated unique density value. The soda-lime silicate glass undergoing the fictive temperature increase may be experiencing a plastic dilatation around shear bands as seen in metallic and polymeric glasses [4–7]. This appears to be the case in normal glasses, i.e. those exhibiting decreasing density and hardness with increasing fictive temperature. Anomalous glasses, such as silica glass, i.e. those exhibiting increasing density and hardness with increasing fictive temperature, should exhibit deformation-in* Corresponding author. Tel.: +1 518 276 6659; fax: +1 518 276 8554. E-mail address: [email protected] (M. Tomozawa). 0022-3093/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2008.05.042
duced densification. The dilatation or densification expected to occur in normal and anomalous glasses, respectively, was investigated using microhardness measurements in the plastically deformed region surrounding an indentation formed under a high load. Asahi less brittle glass, an intermediate glass between normal and anomalous glass, was also investigated for comparison. The plastically deformed region is defined by Hill as the hemisphere surrounding a Vickers indentation with a diameter equal to three times the major diagonal of the indentation as shown schematically in Fig. 1. The majority of plastic deformation, however, occurs within the hemispherical region with a diameter equal to the length of the major diagonal of the indentation, l [8]. Similar phenomena have been reported in polymeric glasses. The terminology in polymer science is different from that of glass science, but the mechanism appears to be equivalent. The inherent energy of the structure of polymers can decrease with time during the process of physical aging [9,10]. In glass science the terms ‘inherent energy of structure’ and ‘physical aging’ can be replaced with ‘fictive temperature’ and ‘structural relaxation,’ respectively. When a shear stress is applied to a polymeric glass that has undergone physical aging, the inherent energy can be increased to that of the original state in a process termed ‘mechanical rejuvenation’ [9,10]. If inorganic glasses follow the same trend it is then expected that the deformed material surrounding an indentation will exhibit
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610
2
Hardness (kgf/mm )
590 570 550 530 510 490
In Nitogen In Air
470 450 0
20
40
60
80
100
Time (sec) Fig. 2. Hardness as a function of loading time for 50 gf indentations taken for sodalime silicate glass in a dry nitrogen environment and in an atmospheric air environment. Dotted lines are a guide to the eyes.
Fig. 1. Schematic of plastically deformed zone, radius = 3l, according to Hill [8].
an increase in fictive temperature, just as polymers exhibit an increase in the inherent energy of structure under shear stress. It is then expected that normal glasses will have a plastically deformed region of lower density as well as lower hardness while anomalous glasses will have a deformed region of higher density as well as higher hardness. It is the purpose of the present work to demonstrate the expected hardness change in the deformed zone created by indentation. 2. Experimental Samples of soda-lime silicate glass, silica glass, and less brittle glass were obtained from Asahi Glass Company, Ltd. of Japan. Asahi less brittle glass consists of 13% Na2O, 1% K2O, 4% MgO, 1% CaO, 2% Al2O3 and 79% SiO2 (all in mole percents) [11–13]. Samples of each type of glass were cut to approximate dimensions of 5 mm 5 mm 1 mm. The soda-lime silicate glass was manufactured by the float process and the side of the as-received glass that did not contact tin was used. The samples were polished using a series of 240, 400, and 600 grit SiC polishing paper followed by a final polish in a 1 lm cerium oxide slurry to obtain an optical finish. The change in hardness in the region surrounding a large indentation was studied for these glasses. Samples of Asahi less brittle glass, Asahi soda-lime silicate glass, and Asahi silica glass were each heated at their respective glass transition temperatures, 515, 550, and 1200 °C, for 4 h in nitrogen. The samples were then furnace cooled at a rate of approximately 5 °C/min to eliminate residual stresses on the glass surface. The absence of residual stress was confirmed by polariscope. Vickers hardness was measured using a Leco M-400 microhardness tester. The hardness can vary with time when measured in air, due to the presence of water vapor [14], while the value measured in a dry nitrogen atmosphere is constant with time as shown in Fig. 2 where the hardness values of soda-lime silicate glass obtained under 50 g force (gf) are plotted against the loading time. The data obtained in a nitrogen atmosphere will primarily be reported here. The hardness tester was enclosed in a ‘glove bag’ and hardness testing was performed under dry nitrogen. The ‘glove bag’ was evacuated and filled with nitrogen then re-evacuated and re-filled with dry nitrogen to ensure that air was removed from the bag prior to hardness testing. The glass samples were placed into
the bag immersed in dry toluene prior to filling the bag with dry nitrogen to ensure that water is not present on the glass surface and the glass was removed from the toluene in the dry nitrogen environment and wiped dry. Toluene is a non-polar liquid with low water solubility [14]. A large one kilogram force (kgf) Vickers indentation was made for 15 s and then 50 gf indentations were made for 15 s outside the large indentation at various distances from the edges of the larger indentation. These smaller indentations were made at an approximately 45° angle from the corners of the large 1 kgf indentation. Indentations made with a load of 50 gf are small enough to analyze the hardness of the deformed zone. The distance from the center of the 1 kgf indentation to the edge of each of the 50 gf indentations was measured and used to define the location of the probe indentation. For each type of glass a plot of hardness vs. distance from the larger indentation is then made. For each type of glass the density and hardness were also measured as a function of fictive temperature for four different temperatures. Table 1 shows the fictive temperatures studied for each glass with the heat-treatment time in parentheses. The density was measured as a function of fictive temperature using a sink-float density measurement technique [15,16]. The sink-float density measurement was conducted by making a solution of 1bromonaphthalene and 1,1,2,2 tetrabromoethane in which the glass sample just floats at room temperature. The solution was then heated at 0.1 °C/min until the glass sample begins to sink and the temperature is recorded. The density of the liquid at selected temperatures was determined using a Bingham pycnometer. The resulting density vs. temperature curve can then be used to determine the liquid density at the temperature at which the sample sank. This liquid density at this temperature is then equal to the sample density. Hardness was also measured as a function of fictive temperature using a Vickers indenter with a 50 gf load for 15 s. Fifteen
Table 1 Glass transition temperatures of the samples used in the present work and heattreatment conditions to prepare samples with various fictive temperatures Type of glass Asahi Less Brittle Glass Asahi Soda-Lime Silicate Glass Asahi Silica Glass
Glass transition temperature (°C)
Fictive temperatures (°C) (Heat treatment time (h))
515
450 (48), 500 (24), 550 (4), 600 (2)
550
500 (24), 550 (4), 600 (2), 650 (2)
1200
1050 (280), 1100 (160), 1150 (50), 1200 (4)
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indentations were made at each fictive temperature studied for each glass under a dry nitrogen atmosphere and the mean hardness was calculated. 3. Results Fig. 3 shows the fictive temperature dependence of density for the three glasses investigated here. Soda-lime silicate glass, a normal glass, shows decreasing density with increasing fictive temperature while silica glass, an anomalous glass, shows increasing density with increasing fictive temperature. The slopes for sodalime silicate glass and silica glass are 2 10 4 (g/(cm3 °C)) and 9 10 6 (g/(cm3 °C)), respectively. Less brittle glass, can be considered intermediate between normal and anomalous glass although its overall behavior is that of a normal glass, with its density decreasing with fictive temperature with a slope of 9 10 5 (g/ (cm3 °C)). Photomicrographs showing a large 1 kgf indentation and 50 gf indentations at varying distances from the large indentation for each of these glasses are shown in Fig. 4. It should be noted that the large indentation shows normal cracking behavior for sodalime silicate glass in that median cracks propagate from the corners of the indentation. For both silica glass and less brittle glass, the cracking behavior around the large indentations show median cracking behavior and some anomalous, conical cracking behavior. Plots showing the hardness as a function of distance from the center of the large indentation for the three glasses are shown in Fig. 5. Here, data from several separate indentations of the same glass are plotted together. The vertical dotted lines represent the
2.55
soda-lime silicate glass less brittle glass
2.5
ρ = -0.0002TF + 2.58
silica glass
3
Density (g/cm )
2.45 2.4
ρ = -9E-05TF + 2.4414
2.35 2.3 2.25
ρ = 9E-06TF + 2.1898
2.2 2.15 400
600
800
1000
1200
o
Fictive Temperature ( C) Fig. 3. Density vs. fictive temperature for soda-lime glass, less brittle glass, and silica glass.
positions at which the edges of the 1 kgf indentations come in contact with the edges of the 50 gf indentations. It can be seen from the plot that the region close to the 1 kgf indentation gives lower hardness values than at larger distances for soda-lime silicate glass (Fig. 5(a)). From the plot it can be seen that the hardness is lower in the region within 10 lm from the edge of the large indentation. This length is approximately equal to the length of the region between the indentation edge and the circle with the diameter equal to the indentation length as shown schematically in Fig. 6. This region will be defined as the shear deformation zone. This is the region in which volume change primarily takes place. The average hardness at a distance beyond the shear deformation zone is 583 ± 19 kg/mm2 for soda-lime silicate glass. The average value of the hardness within the shear deformation zone is 550 ± 31 kgf/mm2. The plot of the hardness vs. distance from the large 1 kgf indentation is shown in Fig. 5(b) for silica glass. Unlike soda-lime silicate glass, the hardness is very high in the region immediately surrounding the indentation and decreases to a constant value at larger distances. The increase in hardness appears to occur within 5 lm of the edge of the large indentation. We will define this region as the compacted zone. The average hardness outside the compacted zone is 748 ± 18 kgf/mm2. The average hardness within the compacted zone is 803 ± 37 kgf/mm2. In Fig. 5(c) it is shown that the hardness does not exhibit a noticeable change in the region immediately surrounding the large 1 kgf indentation in less brittle glass. The hardness from the edge of the indentation extending to the non-deformed portion of the glass stays at a steady value of 492 ± 25 kgf/mm2. The experiment was repeated in an air atmosphere for all three glasses using a loading time of 15 s. No time dependent hardness is expected to occur as shown in Fig. 2. The results were nearly identical to those obtained in dry nitrogen atmosphere. Fig. 7 shows hardness vs. fictive temperature for the three glasses as determined with a 50 gf load for 15 s in a dry N2 atmosphere. It is shown that soda-lime silicate glass shows normal glass behavior, decreasing in hardness with increasing fictive temperature with a slope equal to 0.6081 (kgf/(mm2 °C)). Silica glass exhibits anomalous behavior, increasing in hardness with increasing fictive temperature with a slope equal to 0.3773 (kgf/ (mm2 °C)). The hardness variation with fictive temperature is also shown for Asahi less brittle glass. This glass shows normal behavior with a slope of 0.2810 (kgf/(mm2 °C)), much smaller magnitude than those of soda-lime silicate glass and silica glass. For soda-lime silicate glass, the hardness value outside the shear deformation zone was 583 ± 19 kgf/mm2. From Figs. 3 and 7 this corresponds to a fictive temperature of 543 ± 32 °C and a density of 2.4714 ± 0.0064 g/cm3. The shear deformation zone had a hardness of 550 ± 31 kgf/mm2, which corresponds to a fictive temperature of 597 ± 51 °C and a density of 2.4606 ± 0.0102 g/cm3. It can be seen that there is a marked increase in fictive temperature and a decrease in density in the shear deformation zone when
Fig. 4. Indentation patterns for (a) soda-lime silicate glass, (b) silica glass, (c) less brittle glass.
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Hardness (kgf/mm2)
610 590 570 550 Distance from center of 1 kgf indentation to its edge
530 510 490 470 450 0
20
40
60
80
100
Distance from center of 1 kgf indentation (μm)
Fig. 6. Schematic of the 1 kgf Vickers indentation and the surrounding shear deformation for soda-lime silicate glass.
900 850
2
Vickers Hardness (kgf/mm )
800
2
Hardness (kgf/mm )
850
800 Distance from center of 1 kgf indentation to its edge
750
700
650
750
silica glass soda-lime silicate glass less brittle glass
H = 0.3773TF + 313.05
700 650 600 550
H = -0.6081TF + 913.11 500
H = -0.281TF + 637.53
450
600 0
10
20
30
40
50
60
70
80 400 400
Distance from center of 1 kgf indentation (μm)
500
600
700
800
900
1000
1100
1200
1300
Fictive Temperature (oC) 650
Fig. 7. Hardness vs. fictive temperature for silica glass, soda-lime silicate glass, and less brittle glass under a 50 gf load for 15 s in dry N2 atmosphere.
2
Hardness (kgf/mm )
600
ness is 492 ± 25 kgf/mm2 and from Figs. 3 and 7 the fictive temperature and density are determined to be 518 ± 89 °C and 2.3948 ± 0.008 g/cm3. Even if a hardness change occurred in this glass, since the slope dH/dTf is small it is difficult to observe. Within the error bar the hardness near the indentation may be as low as 467 kgf/mm2 which corresponds to a possible fictive temperature increase up to 607 °C near the indentation edge.
550 Distance from center of 1 kgf indentation to its edge
500
450
400
4. Discussion
350 0
10
20
30
40
50
60
70
80
Distance from 1 kgf indentation (μm) Fig. 5. Hardness (50 gf) vs. distance from 1 kgf indentation for (a) soda-lime silicate glass, (b) silica glass, (c) less brittle glass. Curved and horizontal dotted lines are guides to eyes.
compared to the region outside of this zone for soda-lime silicate glass. For silica glass the hardness value outside of the compacted zone was 748 ± 18 kgf/mm2. From Figs. 3 and 7, the fictive temperature and density are determined to be 1152 ± 49 °C and 2.2002 ± 0.0004 g/cm3, respectively. Within the compacted zone the hardness is 803 ± 37 kgf/mm2 which corresponds to a fictive temperature of 1298 ± 98 °C and a density of 2.2015 ± 0.0008 g/ cm3. It can be seen that the fictive temperature and density are both higher in the compacted region when compared to the noncompacted region. In the case of Asahi less brittle glass, hardness does not seem to change with distance from the indentation edge. The average hard-
It is known that there is residual stress around an indentation [17–22]. Furthermore, Kese et al. [17] attributed the observed hardness and modulus decrease around a large Vickers indentation of soda-lime glass to the residual stress. It is important, therefore, to learn the possible effect of residual stress on the indentation hardness in order to interpret the present experimental observation correctly. The residual stress distribution around a large 45 N indentation in soda-lime silicate glass has been estimated by Zeng and Rowcliffe [21] by measuring the crack lengths around smaller, 2.94 N (300 gf) load Vickers indentations at various angles from a median crack of the larger indentation. These crack lengths around the small indentation were measured as a function of distance from the larger indentation. The cracks extending in the radial direction became longer when a larger residual tensile stress existed tangentially to the large indentation edge. The cracks extending in the tangential direction became shorter when a larger residual compressive stress existed radially from the indentation edge. The procedure is schematically shown in Fig. 8. From this
T.M. Gross, M. Tomozawa / Journal of Non-Crystalline Solids 354 (2008) 4056–4062
Fig. 8. Schematic showing the orientation of 100 gf indentations made in the residual stress field of a 1 kgf Vickers indentation to measure the residual tensile stress.
measurement, Zeng and Rowcliffe [21] obtained the residual stress profiles consisting of tangential tensile stress and radial compressive stress. The magnitude of the residual stress decreased with increasing distance from the main indentation and at a given distance from the main indentation, the magnitude of the radial compressive stress was much larger than that of the tangential tensile stress. For example, in the 45° direction from the main crack, a maximum tensile stress of 32.5 MPa in the tangential direction and a maximum compressive stress of 185 MPa in the radial direction were observed at the closest point to the large indentation. The residual stress was found to decrease with increasing distance, r, from the large indentation by (1/r)3 [23]. Another important effect of indentation on glasses is densification. Yoshida et al. [24] as well as Ji et al. [25] showed that glasses exhibit densification under Vickers indenter, the magnitude of densification becoming greater for glasses with smaller Poisson’s ratio. They found that more than 60% of the indentation volume was due to densification for soda-lime silicate glasses and even the pile-up region exhibited densification [25]. Thus, there are three possible effects which can affect hardness of glasses near a large Vickers indentation: fictive temperature change, residual stress and densification. In this Discussion, an attempt will be made to differentiate these three effects by using their different relaxation times upon heat-treatment of soda-lime silicate glass. The change of fictive temperature by heat-treatment involves structural relaxation, while the change of residual stress by heat-treatment is dictated by stress relaxation time, sstress, which is usually shorter than the structural relaxation time, sstruct, by a factor of 10. [26]. The densification relaxation time, sdens, by heat-treatment appears to be shorter than the stress relaxation time, being accomplished by the heat-treatment at 0.9 Tg (K) for 2 h [24,25]. Namely, the following relation holds. sstruct, > sstress, > sdens. Soda-lime silicate glass with a 1 kgf Vickers indentation was heat-treated at 495 °C for 2 h in dry N2 atmosphere. This temperature corresponds to 0.933 Tg(K), which is higher than the heattreatment temperature, 0.9 Tg(K) employed by Yoshida et al. [24] to remove the densification. Thus densification introduced by Vickers indentation is considered to have disappeared by this heat-treatment. The residual stress before and after the heat-treatment was also measured using the same technique employed by Zeng and Rowcliffe [21]. Specifically, 100 gf indentations were made in air at 45° to the corners in the perpendicular direction to the large indentation edges as a function of distance from the
large indentation. These smaller indentations were aligned so that one median/radial crack was perpendicular to the large indentation edge as shown in Fig. 8. The lengths of the cracks that were on the side away from the large indentation were measured to determine the relative amount of residual stress. The length of the crack in an annealed soda-lime silicate glass was also measured for comparison. The lengths of the cracks in the radial direction were shorter after the heat-treatment, compared with those of sample without the heat-treatment, by a factor of 2–3 at 13–20 lm distance from the edge of the large indentation. This reduction of the crack length corresponds, according to the equation employed by Zeng and Rowcliffe [21], to the reduction of the tangential tensile stress by approximately 20%. Also present in several of the indentations of the heat-treated sample were cracks in the tangential direction. This indicates that residual radial compressive stress is also relieved by this heat-treatment. The hardness distribution around a pre-existing 1 kgf indentation was determined by probing with 50 gf indentations after the heat-treatment as shown in Fig. 9. The results are virtually identical to those in Fig. 5(a). This experiment shows that the residual stress has no measurable influence on the indentation hardness. The densification of this glass also appears to have little influence since the densification in the pile-up region is expected to disappear by the heat-treatment employed. Kese et al. [17] and Erikkson [20] have previously shown that hardness and elastic modulus decrease in the region surrounding a 45 N indentation in soda-lime silicate glass and have attributed this to residual stress. Furthermore, Kese et al. [17] showed that both elastic modulus and hardness change with applied bending stress, increasing with uniaxial compressive stress and decreasing with uniaxial tensile stress. Comparison of our Figs. 3 and 7 show that with a given glass, increasing density is accompanied by increasing hardness. The effect of applied bending stress on hardness obtained by Kese et al [17] exhibits the similar trend: uniaxial tensile stress which is expected to increase the glass volume produces a lower hardness while uniaxial compressive stress which decreases glass volume produces a higher hardness for soda-lime glass. The residual stress around Vickers indentation, according to Zeng and Rowcliffe [21] measurement, exhibit biaxial stress with the radial compressive stress having five times greater magnitude compared with the magnitude of tangential tensile stress. Thus, the volume of the soda-lime silicate glass in the vicinity of Vickers indentation is expected to decrease by the residual stress. Therefore, the residual stress is expected to increase the hardness of soda-lime silicate glass. Thus, it appears unreasonable to attribute the observed lower hardness of soda-lime silicate glass near
600 590
Hardness (kgf/mm2)
4060
580 570 Distance from center of 1 kgf indentation to its edge
560 550 540 530 520 510 0
10
20
30
40
50
60
70
80
Distance from center of 1 kgf indentation (μm) Fig. 9. Hardness vs. distance from 1 kgf indentation after annealing at 495 °C for 2 h.
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a large Vickers indentation to the residual stress. Furthermore, the observed lower hardness is confined to the immediate vicinity of the large Vickers indentation while the residual stress is known to spread more widely, decreasing with the distance, r, as (1/r)3 [23]. Erikson et al. [20] found the lower hardness even in the center of a large Vickers indentation, after a partial polishing, by probing with a smaller indenter. Their analysis of the observation using finite element analysis based upon the residual stress could not give a satisfactory explanation of the experimental observation. Kese et al. [18] attempted to use the lower elastic modulus around a large Vickers indentation to probe the residual stress, assuming the observed elastic constant distribution is caused by the residual stress. Their finding that the residual stress could not be eliminated even by the heat-treatment at 540 °C for 24 h is in contrast to earlier direct observation that the residual stress disappearing easily by the heat-treatment at similar or even lower temperatures [27–29]. This discrepancy indicates that the assumption of lower hardness and elastic modulus around a large Vickers indentation of soda-lime silicate glass originating from the residual stress is not valid. On the other hand, lower hardness and higher hardness in the deformed region immediately surrounding the 1 kgf indentation in soda-lime silicate glass and silica glass, respectively shown in Fig. 5(a) and (b) correspond to a higher fictive temperature as shown in Fig. 7. This is consistent with the observation made by Kioke and Tomozawa, using infrared spectroscopy, that the plastically deformed region experiences a fictive temperature increase at least in the case of soda-lime silicate glass [3]. Earlier, Tomozawa et al. [30,31] showed from the peak shift of IR silica structural bands that silica glass with higher density having higher fictive temperature has a smaller Si–O–Si bond angle. Similarly, Si–O–Si bond angle of silica glass increases under tensile stress which increases the glass volume and decreases hardness [30]. These results, combined with the present result, indicate that the volume change of a glass, whether it is produced by permanent deformation or elastic deformation, is accompanied by the similar Si–O– Si bond angle change and similar hardness change. Again, the net compressive residual stress should have a hardening effect on soda-lime silicate glass.
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In order to find the structural origin of the lower hardness near the large Vickers indentation of soda-lime silicate glass, cross-sectional observation of the region underneath 1 kgf indentations in soda-lime glass was made following the method described by Hagan [32]. Fig. 10(a) shows the cross-section of an indentation in which one major diagonal is aligned with the sectioning crack. In this image it appears that all of the shear bands are contained beneath the indentation and do not extend beyond the indentation corners. Fig. 10(b) shows a cross-section of the same glass, but this time the sectioning intersects the middle of two opposite edges. In this orientation, the shear bands appear to extend beyond the edges. The shear deformation zone may, in fact, be comprised of a hemisphere with a diameter equal to the indentation major diagonal. A similar result was obtained earlier for a metallic glass [33]. This is the region in which the measured hardness is found to be different in the glasses studied here. These observations clearly indicate that the observed lower hardness in the vicinity of a large Vickers indentation is closely related to the structural change of the glass. The magnitude of the hardness increase in the plastically deformed zone immediately surrounding the 1 kgf indentation in silica glass shown in Fig. 5(b) is also consistent with the increase of fictive temperature caused by plastic deformation. The increase in hardness and the corresponding density increase may be due partly to other factors besides the increase in fictive temperature. A recoverable densification on indentation has been shown to exist [2,24,25,34,35], which may or may not be a different mechanism than the densification expected to occur during the plastic deformation-induced fictive temperature increase. Ernsberger [2] and MacKenzie [34] have shown experimentally that a densification occurs in silica glass under indentation pressure. MacKenzie [34] claimed that compression in conjunction with shear stress produces an interlocking of two parts of the network. The interlocking results in incomplete volume recovery when the pressure is removed. Neely and MacKenzie [35] and later Yoshida et al. [24] showed that this densification was recoverable at temperatures below the glass transition temperature. These authors claim that recoverable densification should be treated separately from irreversible plastic flow. In the case of silica glass, the effect of recoverable densification and plastic deformation-induced fictive
Fig. 10. Cross-sectional view of Vickers indentation (a) Orientation of Vickers indentation with one major diagonal aligned with the cross-section and the resulting shear bands. Shear bands do not appear to be outside of the indentation in this orientation. (b) Orientation of Vickers indentation with the cross-section intersecting the major diagonals and the resulting shear bands. Shear bands now appear to be outside of the indentation in this orientation.
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temperature increase leading to densification may be superimposed. Yoshida et al. showed that a portion of the recoverable densification extended outside of the boundaries of the indentation at the surface [24] in the same region where the present hardness measurements were taken. The hardness profile in the immediate vicinity of the 1 kgf large indentation for less brittle glass exhibited practically no noticeable difference from the region far removed from the indentation. This glass is intermediate between a normal and anomalous glass, although the overall behavior is similar to a normal glass. From Fig. 7 it is seen that hardness varies the least among the three glasses with changes in fictive temperature, which is consistent with the lack of an observed hardness change in the plastically deformed region. The hardness dependence on fictive temperature for less brittle glass is considerably less than that of both soda-lime silicate and silica glasses. This glass also shows a much lower density dependence on fictive temperature than soda-lime silicate glass. Thus, indentation hardness in the plastically deformed region of the three glasses investigated exhibited changes in hardness consistent with a plastic deformation-induced increase of fictive temperature. This increase in Tf may not be aided by heating since Yoshioka and Yoshioka [36] detected negligible heating during indentation. Another example of a fictive temperature increase without any heating of a glass sample was shown by Devine for glass exposed to neutron radiation [37]. These examples show that a fictive temperature increase in a glass may not necessarily require heating. The lack of an observed hardness change in the plastically deformed zone in the less brittle glass may give an important clue as to why this glass exhibits less brittle behavior or greater crack initiation load under indentation. When a glass is indented or scratched a plastic deformation can occur. If the region close to a large indentation with a different fictive temperature has a different density or different mechanical properties from the rest of the glass, strain mismatches can be generated that could lead to cracking. On the other hand, if this plastic deformation zone has the same density or same mechanical properties as the undeformed glass, the glass will be less likely to fracture. 5. Conclusion Soda-lime silicate glass, a normal glass, has been shown to exhibit volume dilatation in the immediate vicinity of an indentation through microhardness measurements. Silica glass, an anomalous glass, shows the opposite behavior in that a densification occurs
in the immediate vicinity of an indentation. Less brittle glass, showing somewhat intermediate behavior, does not exhibit either of these trends. These features are consistent with fictive temperature increase or rejuvenation by plastic deformation. Acknowledgement This research was supported by an NSF grant under DMR0352773. The authors thank Asahi Glass Co. Ltd. for providing the glass samples used in the present work. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37]
D.M. Marsh, Proc. Roy. Soc. London A279 (1964) 420. F.M. Ernsberger, J. Am. Ceram. Soc. 51 (1968) 545. A. Koike, M. Tomozawa, J. Non-Cryst. Solids 353 (2007) 2318. P.E. Donovan, W.M. Stobbs, Phil. Mag. A 47 (1983) 537. Y. Zhang, A.L. Greer, App. Phys. Lett. 89 (2006) 071907-1. R. Bhowmick, R. Raghavan, K. Chattopadhyay, U. Ramamurty, Acta Mater. 54 (2006) 4221. M. Utz, Q. Peng, M. Nandagopal, J. Polym. Sci.: Part B: Polym. Phys. 42 (2004) 2057. R. Hill, in: The Mathematical Theory of Plasticity, Oxford, Great Britain, 1950. L.C.E. Struik, Polymer 38 (1997) 4053. M. Utz, P.G. Debenedetti, F.H. Stillinger, Phys. Rev. Lett. 84 (2000) 1471. J. Sehgal, S. Ito, J. Am. Ceram. Soc. 81 (1998) 2485. J. Sehgal, S. Ito, Reports Res. Lab. Asahi Glass Co., Ltd. 50 (2000) 1. S. Ito, J. Am. Ceram. Soc. Japan 112 (2004) 477. K. Hirao, M. Tomozawa, J. Am. Ceram. Soc. 7 (1987) 497. ASTM Standard C 729-75, Ann. Book of ASTM Standards, vol. 15.02: Glass; Ceramic Whitewares, ASTM International (2007). ASTM Standard D1217-93, Ann. Book of ASTM Standards, vol. 05.01: Petroluem Products and Lubricants, ASTM International (2007). K.O. Kese, Z.C. Li, B. Bergman, J. Mater. Res. 19 (2004) 3109. K. Kese, M. Tehler, B. Bergman, J. Euro. Ceram. Soc. 26 (2006) 1003. K.O. Kese, Z.C. Li, B. Bergman, J. Euro. Ceram. Soc. 26 (2006) 1013. C.L. Eriksson, P.L. Larsson, D.J. Rowcliffe, Mat. Sci. Eng. A340 (2003) 193. K. Zeng, D.J. Rowcliffe, Acta Metall. Mater. 43 (1995) 1935. K. Zeng, D. Rowcliffe, J. Am. Ceram. Soc. 77 (1994) 524. Z. Burghard, A. Zimmerman, J. Rodel, F. Aldinger, B. Lawn, Acta Mater. 52 (2004) 293. S. Yoshida, J.C. Sangleboeuf, T. Rouxel, J. Mater. Res. 20 (2005) 3404. H. Ji, V. Keryvin, T. Rouxel, T. Hammouda, Script Materialia 55 (2006) 1159. C.T. Moynihan, p.32 in ASTM STP 1249. In: R.J. Seyler (Ed.), ASTM, Phila PA, 1994. D.B. Marshall, B.R. Lawn, J. Am. Ceram. Soc. 63 (1980) 532. P. Chantikul, B.R. Lawn, D.B. Marshall, J. Am. Ceram. Soc. 64 (1981) 322. D.H. Roach, A.R. Cooper, J. Am. Ceram. Soc. 68 (1985) 632. M. Tomozwaa, J.-W. Hong, R.W. Hepburn, Glass Sci. Technol. 75 C1 (2002) 262. M. Tomozawa, J.-W. Hong, S.-R. Ryu, J. Non-Cryst. Solids 351 (2005) 1054. J.T. Hagan, J. Mater. Sci. 15 (1980) 1417. H. Zhang, X. Jing, G. Subhash, L.J. Kecskes, R.J. Dowding, Acta Mater. 53 (2005) 3849. J.D. MacKenzie, J. Am. Ceram. Soc. 46 (1964) 461. J.E. Neely, J.D. MacKenzie, J. Mat. Sci. 3 (1968) 603. N. Yoshioka, M. Yoshioka, Phil. Mag. A 74 (1996) 1273. R.A.B. Devine, J. Non-Cryst. Solids 152 (1993) 50.