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Densification and flow phenomena of glass in indentation experiments
JOURNAL OF NON-CRYSTALLINESOLIDS 5 (1970) 103--115 © North-Holland Publishing Co.
D E N S I F I C A T I O N AND F L O W P H E N O M E N A OF GLASS IN I N D E N T A T I O N E X P E R I M E N T S
K. W. PETER Physical Laboratory Mosbaek, Karlsruke University, Karlsruhe, Germany Received 13 May 1970 Flow of glass may occur during indentations. Remarkable accordance with conclusions from the theory of plasticity was found on micrographs. Simultaneously densification beneath the indentation must be noticed to be a more general property of glasses, whereas flow at room temperature seems to require a minimum percentage of network modifiers.
1. Generation of high pressure by indentation Examination of high pressure properties of almost all glasses performed by piston-cylinder or anvil apparatus yields permanent densification at room temperature beyond a threshold of pressure. The considerable scattering of the results of quantitative densification may be explained regarding the correct state of stress in the sample, especially the influence of shear. More densification after the same outer pressure should be achieved at less degree of hydrostatic states of stressesi-S). Besides expensive high pressure devices also relatively simple indentation experiments are suitable to subject glasses to extreme stresses and strains within certain limits. Neglecting the possible influences of surface layers, an equilibrium exists in such " p o i n t " loading corresponding to a constant maximum pressure on the sample, which depends on the material and cannot be varied. The sapphire or diamond indenters are considered to be perfectly rigid. This kind of loading causes a complicated inhomogeneous state of stress in the interior of the sample. But it is well-known in the case of elastic deformations with great symmetry4). Using indenters with small radii of curvature, however, the indentations on glass then imply inelastic effects 5) calculable only by approximations.
2. Densification caused by indentations The transparency of glass permits microscopical observations during and after application of load showing a local increase of the refractive index and 103
104
K.W.PETER
consequently of the density 5, 6). By means of an interferometric technique, a minimum depth of the densified zone is estimated to be about one fourth of the indentation diameter T). These observations, and particularly recovery effectsS), make it most improbable that any flow must be assumed during indentation on fused silica. Rather it is densification that occurs, a process leading to a more close-packed arrangement without breaking molecular bonds, which has been shown by IR-spectra 9). Densification may be defined as a "disappeared" volume A V/V measurable after indentation by direct microscopical observation (fig. 1). To this end,
!!!i~!i i!! !
Fig. 1. Profile of a ball indentation on plate glass. Radius of curvature of the indenter p = 20 pm; load L = 100 g. Light microscope, top illumination. the indentation must be set just at the tip of a prepared assisting crack. After that, it is caused to move through the specimen, thus revealing the indentation's profile. This procedure was proved not to disturb seriously the original formation. Beneath the remaining small depression (depth 7"1 from the surface) one perceives a zone according in size and shape with observations made by reason of the changed refractive index. The image contrast of this area arises because some stressed material has been displaced into the gap, forming a slight convexity on the surface of the assisting crack which is sufficient to become visible in the light - or scanning microscope (fig. 2). This zone (depth 7"2 from the surface) is regarded as the volume V in which the material is mainly compacted. Its expansion is quite similar to the region of triaxial compressive stresses in the Hertzian field of elastic deformationsl°). If the volumes A V and V are calculated as volumes of revolution around the axis of indentation then AV/V ~ T,/T2 (1) provided that 7"1 ~ T2.
DENSIFICATION AND FLOW PHENOMENA OF GLASS IN INDENTATION EXPERIMENTS
Fig. 2.
105
S u r f a c e a n d profile o f fig. 1. S c a n n i n g e l e c t r o n m i c r o s c o p e , S E M .
An average pressure p = 6 . 5 x l01° dyn/cm 2 on the area of contact is available by ball indentations on commercial plate glass with an indenter radius p = 20 = pm (curvature) (figs. 1 and 2). The depths T1 = 0.48 lam and T2 = 6.7 gm remain after application of the load L = 100 g; therefore A 1,1/V= 0.07. On similar experimental conditions AV/V=O.13 in the case of fused silica (Homosil) where crack formation is inevitable11). These AV/V values do not actually correspond to a uniform state of stress. But they are reasonable compared with data from high pressure experiments1). The shape of the indenter is not very critical in experiments like fig. 1. Similar pictures are available with pyramid indenters.
3. Flow during indentation 3.1. INTRODUCTIONOF A YIELD POINT There are phenomena of deformation of glass at room temperature which cannot be described in terms of densification: Scratching produces curls like the treatment of metalsle,13). In an early stage particles close to the scratch have been identified which have not been separated from the bulk by the usual crack processes14). Even during single indentations when performed with very tapered pyramids plate glass is piled up by a lateral displacement
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K.W.PETER
process15,16), hardly imaginable without flow. For some glasses at least a flow criterion should exist as assumed in refs. 17 and 18. Subsequently, certain principal statements of the theory of plastic homogeneous and isotropic bodies 19,2°) are compared with the behavior of four silicate glasses. In this theory equilibria between outer loads and internal stresses are computed on condition that flow begins at defined states of stresses. A frequently suggested simple strength criterion demands a constant maximum shear stress Zmax = k = const.
(2)
The equilibrium state for this "St. Venant b o d y " can be calculated in the two-dimensional case of an angular or circular punch penetrating into a body of half-infinite extent. The results should be regarded as an approach to pyramid and ball indentation in default of an exact solution of the three-dimensional problem. 3.2.
PRESSURE ON THE AREA OF INDENTATION
If the "area of indentation" A is the projection of the area of contact on the plane surface and L is the load, then
(3)
p = L / A = p (~, ~)
is a function 19) of ~ and c5, where y is an angle describing geometrical relations of the indentation (fig. 3). Tentatively frictional forces between the indenter and the glass are assumed to be t = k sin 26, i.e. an elementary part of the area of contact having an inclination greater than 6 to the plane surface of the sample will overcome the force of friction. As long as y < 55 ° there is only a weak dependence p = p (y, 6) in the theory and it becomes still weaker with greater 6. The application of different indenters (pyramides wi the, = 15-55 ° and balls up to 7 = 3 0 °) in the present investigation did not yield any
o.) Fig. 3.
b)
Definition of y in indention processes. (a) Angular indenter, (b) circular indenter.
DENSIFICATIONAND FLOWPHENOMENAOF GLASSIN INDENTATIONEXPERIMENTS
107
significant t e n d e n c y for p, so t h a t p ~ const. (p = 6.5 × 10 l° d y n / c m 2 for plate glass a n d p = 11.3 x 10 l° d y n / c m 2 for fused silica) is stated within the limit o f 5 ~ . I f 6 > 10 ° then the accuracy o f p m e a s u r e m e n t s has to be essentially better t h a n 5~o to ascertain a n y d e p e n d e n c y in the available 7 range. N o serious d e p e n d e n c e p = p (7) m a y indicate t h a t friction has t a k e n part, a n d therefore the e x p e r i m e n t a l result p = c o n s t . on the a b o v e - m e n t i o n e d conditions is in a c c o r d a n c e with the t h e o r y o f plasticity. 3.3. REPRODUCTION OF SURFACE STRUCTURES OF THE INDENTER There is a m o r e direct effect to be i n t e r p r e t e d by friction d u r i n g the indentation. In the zone o f c o n t a c t o f ball i n d e n t a t i o n s no slip processes are allowed for 7 < 6 , whereas slipping occurs 20) for 7 > 6 . C o r r e s p o n d i n g l y , fig. 2 and some replica m i c r o g r a p h s in ref. 5 have a r a t h e r u n d i s t u r b e d central a r e a o f contact, m o r e a n d m o r e r o u g h in the direction o f the p e r i p h e r y ; a l t h o u g h no difference in roughness is detected on the i n d e n t e r (fig. 4). W i t h some c a u t i o n an angle o f friction 6 ~ 12 ° m a y be evaluated f r o m this pictures. In such distinct m a n n e r this p h e n o m e n o n is restricted to plate glass a n d related glasses. O n fused silica the " r e p l i c a " o f the i n d e n t e r is f o u n d to be m u c h w e a k e r a n d m o r e u n i f o r m all over the area, b u t there is always a c o r r e l a t i o n between i n d e n t e r a n d i n d e n t a t i o n structures.
Fig. 4. Tip of a sapphire indenter. SEM.
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K.W. PETER
3.4. SLIP LINES
Indentations on St. Venant bodies (and also on such bodies with a more complicated flow criterion) should produce a piling-up o f material on the surrounding surface. This could be shown using very tapered indenters16). Again there are differences in the behavior o f glasses. N o piling-up but intensive formation of cracks can be seen in the case o f fused silica and a binary soda-silicate glass (fig. 5) opposite plate glass (fig. 6), where also slight elevations in the neighborhood o f ball indentations are observable by means o f surface interference technique.
Fig. 5. Indentation on a binary glass (15 ~ Na20) with a 70 ° pyramid (angle between opposite areas of the pyramid is 70 °). SEM.
Fig. 6. Indentation on plate glass with a 70 ° pyramid. SEM.
D E N S I F I C A T I O N A N D F L O W P H E N O M E N A OF G L A S S I N I N D E N T A T I O N E X P E R I M E N T S
109
Fig. 7. Ball indentation with p 80 !urn on plate glass; L -- I100 g. Observation during indentation parallel to the surface and perpendicular to the applied outer force; the doubling of the line system is produced by total reflection on the surface. Light microscope. J
,
t,,L
.....
/
/
\
Fig. 8. Slip line system (rmax = const.) around a circular cylindric tube inside a plastic body caused by normal pressure on the wall [from Sokolowskij19)].
S t r o n g e r s y m p t o m s for plastic b e h a v i o r o f plate glass are detectable below the surface: W i t h g r a d u a l increase o f l o a d a system o f curved lines is develo p e d d u r i n g the last stage o f the f o r m a t i o n o f the densified region (fig. 7). It suggests the " r o s e t t e " p a t t e r n on the surface in refs. 15 a n d 16, see fig. 6. This is very m u c h like "slip l i n e " systems occurring in theoretically wellk n o w n p r o b l e m s o f plasticity (fig. 8), usually observed in the case o f p u n c h
110
K.W. PETER
Fig. 9. Surface, etched with 1 ~ HF, of plate glass with ball indentation, p -- 17 Bin, L -32 g. T h e line p a t t e r n o f fig. 7 appears in a nearly concentric a r r a n g e m e n t within the indentation area. T h e widely etched radial cracks are without a n y i m p o r t a n c e in this case. Electron microscopical replica.
Fig. 10.
Detail of the peripheral area of a n indentation like fig. 9. Electron microscopical replica.
DENSIFICATION AND FLOW PHENOMENA OF GLASS IN INDENTATION EXPERIMENTS
Fig. 11.
1l 1
Detail o f a Vickers i n d e n t a t i o n (136 ° pyramid) on plate glass after etching. Electron microscopical replica.
Fig. 12.
G r o u n d surface of plate glass after etching s h o w s "slip lines". Electron microscopical replica.
112
K.W. PETER
loaded metals. The lines in question appear also after etching away a layer of 0.2 lam thickness from the surface of the sample. They may be clearly recognized in figs. 9 and 10 on the typically etched surface within ball the indentation. With some reserve one can speak o f 'flaws caused by shear stresses". They seem to represent a kind of loosening bonds where etching with H F most probably does not cause an increase o f the distance of edges of "fract u r e " as k n o w n for c o m m o n cracks. Similar "slip lines" as in fig. 9 are likewise to be found below the surface of pyramid indentations and scratches on plate glass (figs. 11 and 12); here they include angles different from 90 °. That means in terms o f the theory o f plasticity the existence o f a flow criterion not so simple as supposed in eq. (2). The examination o f the convergent cone fracture 5) besides the Hertzian crack in ball indentations showed this p h e n o m e n o n to be the first stage o f "slip line" formation. 4. Review of some deformation properties o f glasses
The p h e n o m e n a discussed in the preceding sections are listed in table 1. The + or - signs stand for the occurrence or non-occurrence of the event under consideration. Silicate glasses with different portions o f network TABLE 1 ~
~
Phenomenon ~
Glass
Plate glass
SiO2 76 % NazO 14% CaO 10 %
SiO~ 85 % Na20 15%
SiO2 100 % (Homosil; Fa. Heraeus)
÷ -]-
+ ÷
-+--
+
+
+
(-)
+ ÷
+ +
~
Densification (figs. 1,2) Pressure on the area of indentation p = const. Increased structures near the rim of the indentations (fig. 2) Piling-up (figs. 5, 6) "Slip lines" below the indentation (figs. 7, 9-12)
+
n
modifiers have been examined. The hygroscopity o f the binary glass made it sometimes difficult to decide whether it occurred or not (for that reason the brackets were added in the third column). To sum up the results o f the indentation experiments according to table 1 : - all glasses can be c o m p a c t e d ;
DENSIFICATION AND FLOW PHENOMENA OF GLASS IN INDENTATION EXPERIMENTS
] 13
the pressure on the area of indentation is constant within a wide range; apparently the flow properties are correlated to a minimum percentage of network modifiers. The binary glass and fused silica do not behave in any way that could be qualified as plastic. Observing p = const, within a limit of a few percent and regarding friction may at most be a necessary condition for plastic behavior but no sufficient one. The ternary and the plate glass show properties explicable with inferences from the theory of plasticity. Perfect accordance cannot be expected because this theory neglects compression of material. Probably this is the reason to explain the dependence of the lateral piling-up of plate glass from the geometrical shape of the indenter16). The blunter the indenter, the more deformation occurs as densification, and the less as plastic deformation. A further lack concerning quantitative conclusions is the comparison of the available two-dimensional model with the three-dimensional reality. There are references to the insufficiency of a simply flow criterion. A more general theory states the dependence of the maximum permissible shear stress from the principal stresses 20, 21). Perhaps this would lead to an explanation for that it seems to make a difference if shear is produced by tensile or by pressure loading experiments with glass. Obviously shear does not play an important role in testing tensile strength where the greatest principal stress is the main aspect.
-
5.
Structural
interpretation
of flow
It is difficult to understand any plastic deformation in glasses in the sense of volume-conserving flow, because there is no dislocation model working like in crystals. Attempts based on this conception did not succeed up to now17, z2). Another interpretation was proposed, looking at the influence of shear on viscositylS): In a rate process potential barriers are reduced in the direction of the effective shear stress, facilitating transitions of an atom to a neighboring potential well in this direction 23). Recently these rheological considerations have been continued for glasses 24), where in the presence of network modifiers potential barriers of various height occur. It follows that groups of atoms start moving. The atoms are strongly bound to each other within the group, but only loosely bound to their surroundings with the exception of one atom. At this site a local stress concentration is generated at last providing the energy for the motion. From this model the Bingham flow equation has been deducedZ4). Its essential characteristic is the existence of a yield point, which cannot be concluded in the case of the uniform bonds in SiO2 or B203 glass. This was experimentally
114
K.W. PETER
confirmed c o m p a r i n g the viscous flow o f B 2 0 3 glass a n d alkali b o r a t e glasses 25) a n d c o r r e s p o n d s to the results o f this paper. However, it is still impossible to c o m p u t e satisfactory q u a n t i t a t i v e values o f flow b e h a v i o r at r o o m t e m p e r a t u r e . R a t h e r a r b i t r a r y a s s u m p t i o n s can be m a d e concerning the size o f the m o v i n g groups in viscous flow. It is j u s t this p o i n t which influences very sensitively the decrease o f viscosity by shearl4,17,1s). 6. S u m m a r y H i g h pressure investigations within certain limits m a y be carried o u t by i n d e n t a t i o n experiments. A l k a l i silicate glasses in the range from plate glass to fused silica show r e m a i n i n g densification at r o o m t e m p e r a t u r e . This can be directly m e a s u r e d in microscopes. In plate glass a n d in a t e r n a r y glass, deform a t i o n s are o b t a i n e d which m a y be a p p r o x i m a t e l y described in terms o f the t h e o r y o f plasticity with a flow criterion Zmax= const. There are references to the insufficiency o f such a simple c o n d i t i o n . T h e n o n - p l a s t i c b e h a v i o r o f fused silica a n d a b i n a r y glass with relatively low percentage o f n e t w o r k modifiers is r e d u c e d to the impossibility in d e d u c i n g a yield p o i n t f r o m rate process c o n s i d e r a t i o n s in the case o f p r e d o m i n a n t u n i f o r m b o n d s in glasses.
Acknowledgement
The a u t h o r is grateful to the G e r m a n F e d e r a l M i n i s t r y for E c o n o m i c Affairs for the s u p p o r t o f this research under c o n t r a c t No. 1628 (V 135/70). References
1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17)
S. Sakka and J. D. Mackenzie, J. Non-Crystalline Solids 1 (1968-69) 107. J. D. Mackenzie and R. P. Laforce, Nature (London) 197 (1963)481. W. Poch, Phys. Chem. Glasses 8 (1967) 129. S. Timoshenko and J. N. Goodier, Theory of Elasticity (McGraw-Hill, New York, 1951). K. Peter, Glastechn. Bet. 37 (1964) 333. M. Evers, Glastechn. Ber. 40 (1967) 41. F. M. Ernsberger, J. Am. Ceram. Soc. 51 (1968) 545. W. B. Hillig, in: Advances in Glass Technology, Vol. II (Plenum Press, New York, 1963) p. 52. J. D. Mackenzie, J. Am. Ceram. Soc. 46 (1963) 461. H. Hertz, Gesammelte Werke, Vol. I (Barth, Leipzig, 1895) p. 155. K. Peter, Glastechn. Ber. 43 (1970) 277. E. Ryschkewitsch, Glastechn. Ber. 20 (1942) 166. W. Klemm, Fachausschussvortrag [ref. Glastechn. Ber. 27(1954) 140]. K. Peter and E. Dick, Glastechn. Ber. 40 (1967) 470. E. Dick, Naturwissenschaften 56 (1969) 367. E. Dick, Glastechn. Bet, 43 (1970) 16. D. M. Marsh, Proc. Roy. Soc. (London) A 282 (1964) 33.
DENSIFICATION AND FLOW PHENOMENAOF GLASSIN INDENTATION EXPERIMENTS 18) 19) 20) 21) 22) 23) 24) 25)
1 15
R. W. Douglas, J. Soc. Glass Technol. 42 (1958) 145T. V. V. Sokolowskij, Theorie der Plastizitiit (Technik, Berlin, 1955) (from the Russian). L. Prandtl, Nachr. K6nigl. Ges. Wiss. GOttingen, Math-Phys. Klasse 1 (1920) 74. M. Reiner, in: Handbueh der Physik, Vol. 6, Ed. S. FliJgge (Springer, Berlin, 1958) p. 434. W. C. Levengood, Intern. J. Fracture Mech. 2 (1966) 400. S. N. Gladstone, K. Laidler and H. Eyring, The Theory o f Rate Processes (McGrawHill, New York, 1941). H. N. Stein, C. W. Cornelisse and J. M. Stevels, J. Non-Crystalline Solids 1 (1968-69) 143. C. W. Cornelisse, T. J. M. Visser, H. N. Stein and J. M. Stevels, J. Non-Crystalline Solids 1 (1968-69) 150.
D E N S I F I C A T I O N AND F L O W P H E N O M E N A OF GLASS IN I N D E N T A T I O N E X P E R I M E N T S
K. W. PETER Physical Laboratory Mosbaek, Karlsruke University, Karlsruhe, Germany Received 13 May 1970 Flow of glass may occur during indentations. Remarkable accordance with conclusions from the theory of plasticity was found on micrographs. Simultaneously densification beneath the indentation must be noticed to be a more general property of glasses, whereas flow at room temperature seems to require a minimum percentage of network modifiers.
1. Generation of high pressure by indentation Examination of high pressure properties of almost all glasses performed by piston-cylinder or anvil apparatus yields permanent densification at room temperature beyond a threshold of pressure. The considerable scattering of the results of quantitative densification may be explained regarding the correct state of stress in the sample, especially the influence of shear. More densification after the same outer pressure should be achieved at less degree of hydrostatic states of stressesi-S). Besides expensive high pressure devices also relatively simple indentation experiments are suitable to subject glasses to extreme stresses and strains within certain limits. Neglecting the possible influences of surface layers, an equilibrium exists in such " p o i n t " loading corresponding to a constant maximum pressure on the sample, which depends on the material and cannot be varied. The sapphire or diamond indenters are considered to be perfectly rigid. This kind of loading causes a complicated inhomogeneous state of stress in the interior of the sample. But it is well-known in the case of elastic deformations with great symmetry4). Using indenters with small radii of curvature, however, the indentations on glass then imply inelastic effects 5) calculable only by approximations.
2. Densification caused by indentations The transparency of glass permits microscopical observations during and after application of load showing a local increase of the refractive index and 103
104
K.W.PETER
consequently of the density 5, 6). By means of an interferometric technique, a minimum depth of the densified zone is estimated to be about one fourth of the indentation diameter T). These observations, and particularly recovery effectsS), make it most improbable that any flow must be assumed during indentation on fused silica. Rather it is densification that occurs, a process leading to a more close-packed arrangement without breaking molecular bonds, which has been shown by IR-spectra 9). Densification may be defined as a "disappeared" volume A V/V measurable after indentation by direct microscopical observation (fig. 1). To this end,
!!!i~!i i!! !
Fig. 1. Profile of a ball indentation on plate glass. Radius of curvature of the indenter p = 20 pm; load L = 100 g. Light microscope, top illumination. the indentation must be set just at the tip of a prepared assisting crack. After that, it is caused to move through the specimen, thus revealing the indentation's profile. This procedure was proved not to disturb seriously the original formation. Beneath the remaining small depression (depth 7"1 from the surface) one perceives a zone according in size and shape with observations made by reason of the changed refractive index. The image contrast of this area arises because some stressed material has been displaced into the gap, forming a slight convexity on the surface of the assisting crack which is sufficient to become visible in the light - or scanning microscope (fig. 2). This zone (depth 7"2 from the surface) is regarded as the volume V in which the material is mainly compacted. Its expansion is quite similar to the region of triaxial compressive stresses in the Hertzian field of elastic deformationsl°). If the volumes A V and V are calculated as volumes of revolution around the axis of indentation then AV/V ~ T,/T2 (1) provided that 7"1 ~ T2.
DENSIFICATION AND FLOW PHENOMENA OF GLASS IN INDENTATION EXPERIMENTS
Fig. 2.
105
S u r f a c e a n d profile o f fig. 1. S c a n n i n g e l e c t r o n m i c r o s c o p e , S E M .
An average pressure p = 6 . 5 x l01° dyn/cm 2 on the area of contact is available by ball indentations on commercial plate glass with an indenter radius p = 20 = pm (curvature) (figs. 1 and 2). The depths T1 = 0.48 lam and T2 = 6.7 gm remain after application of the load L = 100 g; therefore A 1,1/V= 0.07. On similar experimental conditions AV/V=O.13 in the case of fused silica (Homosil) where crack formation is inevitable11). These AV/V values do not actually correspond to a uniform state of stress. But they are reasonable compared with data from high pressure experiments1). The shape of the indenter is not very critical in experiments like fig. 1. Similar pictures are available with pyramid indenters.
3. Flow during indentation 3.1. INTRODUCTIONOF A YIELD POINT There are phenomena of deformation of glass at room temperature which cannot be described in terms of densification: Scratching produces curls like the treatment of metalsle,13). In an early stage particles close to the scratch have been identified which have not been separated from the bulk by the usual crack processes14). Even during single indentations when performed with very tapered pyramids plate glass is piled up by a lateral displacement
106
K.W.PETER
process15,16), hardly imaginable without flow. For some glasses at least a flow criterion should exist as assumed in refs. 17 and 18. Subsequently, certain principal statements of the theory of plastic homogeneous and isotropic bodies 19,2°) are compared with the behavior of four silicate glasses. In this theory equilibria between outer loads and internal stresses are computed on condition that flow begins at defined states of stresses. A frequently suggested simple strength criterion demands a constant maximum shear stress Zmax = k = const.
(2)
The equilibrium state for this "St. Venant b o d y " can be calculated in the two-dimensional case of an angular or circular punch penetrating into a body of half-infinite extent. The results should be regarded as an approach to pyramid and ball indentation in default of an exact solution of the three-dimensional problem. 3.2.
PRESSURE ON THE AREA OF INDENTATION
If the "area of indentation" A is the projection of the area of contact on the plane surface and L is the load, then
(3)
p = L / A = p (~, ~)
is a function 19) of ~ and c5, where y is an angle describing geometrical relations of the indentation (fig. 3). Tentatively frictional forces between the indenter and the glass are assumed to be t = k sin 26, i.e. an elementary part of the area of contact having an inclination greater than 6 to the plane surface of the sample will overcome the force of friction. As long as y < 55 ° there is only a weak dependence p = p (y, 6) in the theory and it becomes still weaker with greater 6. The application of different indenters (pyramides wi the, = 15-55 ° and balls up to 7 = 3 0 °) in the present investigation did not yield any
o.) Fig. 3.
b)
Definition of y in indention processes. (a) Angular indenter, (b) circular indenter.
DENSIFICATIONAND FLOWPHENOMENAOF GLASSIN INDENTATIONEXPERIMENTS
107
significant t e n d e n c y for p, so t h a t p ~ const. (p = 6.5 × 10 l° d y n / c m 2 for plate glass a n d p = 11.3 x 10 l° d y n / c m 2 for fused silica) is stated within the limit o f 5 ~ . I f 6 > 10 ° then the accuracy o f p m e a s u r e m e n t s has to be essentially better t h a n 5~o to ascertain a n y d e p e n d e n c y in the available 7 range. N o serious d e p e n d e n c e p = p (7) m a y indicate t h a t friction has t a k e n part, a n d therefore the e x p e r i m e n t a l result p = c o n s t . on the a b o v e - m e n t i o n e d conditions is in a c c o r d a n c e with the t h e o r y o f plasticity. 3.3. REPRODUCTION OF SURFACE STRUCTURES OF THE INDENTER There is a m o r e direct effect to be i n t e r p r e t e d by friction d u r i n g the indentation. In the zone o f c o n t a c t o f ball i n d e n t a t i o n s no slip processes are allowed for 7 < 6 , whereas slipping occurs 20) for 7 > 6 . C o r r e s p o n d i n g l y , fig. 2 and some replica m i c r o g r a p h s in ref. 5 have a r a t h e r u n d i s t u r b e d central a r e a o f contact, m o r e a n d m o r e r o u g h in the direction o f the p e r i p h e r y ; a l t h o u g h no difference in roughness is detected on the i n d e n t e r (fig. 4). W i t h some c a u t i o n an angle o f friction 6 ~ 12 ° m a y be evaluated f r o m this pictures. In such distinct m a n n e r this p h e n o m e n o n is restricted to plate glass a n d related glasses. O n fused silica the " r e p l i c a " o f the i n d e n t e r is f o u n d to be m u c h w e a k e r a n d m o r e u n i f o r m all over the area, b u t there is always a c o r r e l a t i o n between i n d e n t e r a n d i n d e n t a t i o n structures.
Fig. 4. Tip of a sapphire indenter. SEM.
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K.W. PETER
3.4. SLIP LINES
Indentations on St. Venant bodies (and also on such bodies with a more complicated flow criterion) should produce a piling-up o f material on the surrounding surface. This could be shown using very tapered indenters16). Again there are differences in the behavior o f glasses. N o piling-up but intensive formation of cracks can be seen in the case o f fused silica and a binary soda-silicate glass (fig. 5) opposite plate glass (fig. 6), where also slight elevations in the neighborhood o f ball indentations are observable by means o f surface interference technique.
Fig. 5. Indentation on a binary glass (15 ~ Na20) with a 70 ° pyramid (angle between opposite areas of the pyramid is 70 °). SEM.
Fig. 6. Indentation on plate glass with a 70 ° pyramid. SEM.
D E N S I F I C A T I O N A N D F L O W P H E N O M E N A OF G L A S S I N I N D E N T A T I O N E X P E R I M E N T S
109
Fig. 7. Ball indentation with p 80 !urn on plate glass; L -- I100 g. Observation during indentation parallel to the surface and perpendicular to the applied outer force; the doubling of the line system is produced by total reflection on the surface. Light microscope. J
,
t,,L
.....
/
/
\
Fig. 8. Slip line system (rmax = const.) around a circular cylindric tube inside a plastic body caused by normal pressure on the wall [from Sokolowskij19)].
S t r o n g e r s y m p t o m s for plastic b e h a v i o r o f plate glass are detectable below the surface: W i t h g r a d u a l increase o f l o a d a system o f curved lines is develo p e d d u r i n g the last stage o f the f o r m a t i o n o f the densified region (fig. 7). It suggests the " r o s e t t e " p a t t e r n on the surface in refs. 15 a n d 16, see fig. 6. This is very m u c h like "slip l i n e " systems occurring in theoretically wellk n o w n p r o b l e m s o f plasticity (fig. 8), usually observed in the case o f p u n c h
110
K.W. PETER
Fig. 9. Surface, etched with 1 ~ HF, of plate glass with ball indentation, p -- 17 Bin, L -32 g. T h e line p a t t e r n o f fig. 7 appears in a nearly concentric a r r a n g e m e n t within the indentation area. T h e widely etched radial cracks are without a n y i m p o r t a n c e in this case. Electron microscopical replica.
Fig. 10.
Detail of the peripheral area of a n indentation like fig. 9. Electron microscopical replica.
DENSIFICATION AND FLOW PHENOMENA OF GLASS IN INDENTATION EXPERIMENTS
Fig. 11.
1l 1
Detail o f a Vickers i n d e n t a t i o n (136 ° pyramid) on plate glass after etching. Electron microscopical replica.
Fig. 12.
G r o u n d surface of plate glass after etching s h o w s "slip lines". Electron microscopical replica.
112
K.W. PETER
loaded metals. The lines in question appear also after etching away a layer of 0.2 lam thickness from the surface of the sample. They may be clearly recognized in figs. 9 and 10 on the typically etched surface within ball the indentation. With some reserve one can speak o f 'flaws caused by shear stresses". They seem to represent a kind of loosening bonds where etching with H F most probably does not cause an increase o f the distance of edges of "fract u r e " as k n o w n for c o m m o n cracks. Similar "slip lines" as in fig. 9 are likewise to be found below the surface of pyramid indentations and scratches on plate glass (figs. 11 and 12); here they include angles different from 90 °. That means in terms o f the theory o f plasticity the existence o f a flow criterion not so simple as supposed in eq. (2). The examination o f the convergent cone fracture 5) besides the Hertzian crack in ball indentations showed this p h e n o m e n o n to be the first stage o f "slip line" formation. 4. Review of some deformation properties o f glasses
The p h e n o m e n a discussed in the preceding sections are listed in table 1. The + or - signs stand for the occurrence or non-occurrence of the event under consideration. Silicate glasses with different portions o f network TABLE 1 ~
~
Phenomenon ~
Glass
Plate glass
SiO2 76 % NazO 14% CaO 10 %
SiO~ 85 % Na20 15%
SiO2 100 % (Homosil; Fa. Heraeus)
÷ -]-
+ ÷
-+--
+
+
+
(-)
+ ÷
+ +
~
Densification (figs. 1,2) Pressure on the area of indentation p = const. Increased structures near the rim of the indentations (fig. 2) Piling-up (figs. 5, 6) "Slip lines" below the indentation (figs. 7, 9-12)
+
n
modifiers have been examined. The hygroscopity o f the binary glass made it sometimes difficult to decide whether it occurred or not (for that reason the brackets were added in the third column). To sum up the results o f the indentation experiments according to table 1 : - all glasses can be c o m p a c t e d ;
DENSIFICATION AND FLOW PHENOMENA OF GLASS IN INDENTATION EXPERIMENTS
] 13
the pressure on the area of indentation is constant within a wide range; apparently the flow properties are correlated to a minimum percentage of network modifiers. The binary glass and fused silica do not behave in any way that could be qualified as plastic. Observing p = const, within a limit of a few percent and regarding friction may at most be a necessary condition for plastic behavior but no sufficient one. The ternary and the plate glass show properties explicable with inferences from the theory of plasticity. Perfect accordance cannot be expected because this theory neglects compression of material. Probably this is the reason to explain the dependence of the lateral piling-up of plate glass from the geometrical shape of the indenter16). The blunter the indenter, the more deformation occurs as densification, and the less as plastic deformation. A further lack concerning quantitative conclusions is the comparison of the available two-dimensional model with the three-dimensional reality. There are references to the insufficiency of a simply flow criterion. A more general theory states the dependence of the maximum permissible shear stress from the principal stresses 20, 21). Perhaps this would lead to an explanation for that it seems to make a difference if shear is produced by tensile or by pressure loading experiments with glass. Obviously shear does not play an important role in testing tensile strength where the greatest principal stress is the main aspect.
-
5.
Structural
interpretation
of flow
It is difficult to understand any plastic deformation in glasses in the sense of volume-conserving flow, because there is no dislocation model working like in crystals. Attempts based on this conception did not succeed up to now17, z2). Another interpretation was proposed, looking at the influence of shear on viscositylS): In a rate process potential barriers are reduced in the direction of the effective shear stress, facilitating transitions of an atom to a neighboring potential well in this direction 23). Recently these rheological considerations have been continued for glasses 24), where in the presence of network modifiers potential barriers of various height occur. It follows that groups of atoms start moving. The atoms are strongly bound to each other within the group, but only loosely bound to their surroundings with the exception of one atom. At this site a local stress concentration is generated at last providing the energy for the motion. From this model the Bingham flow equation has been deducedZ4). Its essential characteristic is the existence of a yield point, which cannot be concluded in the case of the uniform bonds in SiO2 or B203 glass. This was experimentally
114
K.W. PETER
confirmed c o m p a r i n g the viscous flow o f B 2 0 3 glass a n d alkali b o r a t e glasses 25) a n d c o r r e s p o n d s to the results o f this paper. However, it is still impossible to c o m p u t e satisfactory q u a n t i t a t i v e values o f flow b e h a v i o r at r o o m t e m p e r a t u r e . R a t h e r a r b i t r a r y a s s u m p t i o n s can be m a d e concerning the size o f the m o v i n g groups in viscous flow. It is j u s t this p o i n t which influences very sensitively the decrease o f viscosity by shearl4,17,1s). 6. S u m m a r y H i g h pressure investigations within certain limits m a y be carried o u t by i n d e n t a t i o n experiments. A l k a l i silicate glasses in the range from plate glass to fused silica show r e m a i n i n g densification at r o o m t e m p e r a t u r e . This can be directly m e a s u r e d in microscopes. In plate glass a n d in a t e r n a r y glass, deform a t i o n s are o b t a i n e d which m a y be a p p r o x i m a t e l y described in terms o f the t h e o r y o f plasticity with a flow criterion Zmax= const. There are references to the insufficiency o f such a simple c o n d i t i o n . T h e n o n - p l a s t i c b e h a v i o r o f fused silica a n d a b i n a r y glass with relatively low percentage o f n e t w o r k modifiers is r e d u c e d to the impossibility in d e d u c i n g a yield p o i n t f r o m rate process c o n s i d e r a t i o n s in the case o f p r e d o m i n a n t u n i f o r m b o n d s in glasses.
Acknowledgement
The a u t h o r is grateful to the G e r m a n F e d e r a l M i n i s t r y for E c o n o m i c Affairs for the s u p p o r t o f this research under c o n t r a c t No. 1628 (V 135/70). References
1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17)
S. Sakka and J. D. Mackenzie, J. Non-Crystalline Solids 1 (1968-69) 107. J. D. Mackenzie and R. P. Laforce, Nature (London) 197 (1963)481. W. Poch, Phys. Chem. Glasses 8 (1967) 129. S. Timoshenko and J. N. Goodier, Theory of Elasticity (McGraw-Hill, New York, 1951). K. Peter, Glastechn. Bet. 37 (1964) 333. M. Evers, Glastechn. Ber. 40 (1967) 41. F. M. Ernsberger, J. Am. Ceram. Soc. 51 (1968) 545. W. B. Hillig, in: Advances in Glass Technology, Vol. II (Plenum Press, New York, 1963) p. 52. J. D. Mackenzie, J. Am. Ceram. Soc. 46 (1963) 461. H. Hertz, Gesammelte Werke, Vol. I (Barth, Leipzig, 1895) p. 155. K. Peter, Glastechn. Ber. 43 (1970) 277. E. Ryschkewitsch, Glastechn. Ber. 20 (1942) 166. W. Klemm, Fachausschussvortrag [ref. Glastechn. Ber. 27(1954) 140]. K. Peter and E. Dick, Glastechn. Ber. 40 (1967) 470. E. Dick, Naturwissenschaften 56 (1969) 367. E. Dick, Glastechn. Bet, 43 (1970) 16. D. M. Marsh, Proc. Roy. Soc. (London) A 282 (1964) 33.
DENSIFICATION AND FLOW PHENOMENAOF GLASSIN INDENTATION EXPERIMENTS 18) 19) 20) 21) 22) 23) 24) 25)
1 15
R. W. Douglas, J. Soc. Glass Technol. 42 (1958) 145T. V. V. Sokolowskij, Theorie der Plastizitiit (Technik, Berlin, 1955) (from the Russian). L. Prandtl, Nachr. K6nigl. Ges. Wiss. GOttingen, Math-Phys. Klasse 1 (1920) 74. M. Reiner, in: Handbueh der Physik, Vol. 6, Ed. S. FliJgge (Springer, Berlin, 1958) p. 434. W. C. Levengood, Intern. J. Fracture Mech. 2 (1966) 400. S. N. Gladstone, K. Laidler and H. Eyring, The Theory o f Rate Processes (McGrawHill, New York, 1941). H. N. Stein, C. W. Cornelisse and J. M. Stevels, J. Non-Crystalline Solids 1 (1968-69) 143. C. W. Cornelisse, T. J. M. Visser, H. N. Stein and J. M. Stevels, J. Non-Crystalline Solids 1 (1968-69) 150.