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Influence of surface treatments on the dynamic fatigue of soda-lime glass with indentation flaws
Materials Science and Engineering, 85 (1987) L25-L29
L25
Letter
Influence of surface treatments on the dynamic fatigue of soda-lime glass with indentation flaws
G. SORARI) and R. DAL MASCHIO Istituto di Chimica Industriale, Universit~ di Padova, via Marzolo 9, 35100 Padua (Italy) (Received July 18, 1986; in revised form October 3, 1986)
ABSTRACT The dynamic fatigue behaviour involving both post-threshold and subthreshold Vickers' indentation flaws of a soda-lime glass in water was investigated in samples subjected to two different surface treatments. The apparent fatigue susceptibility o f the subthreshold flaws was found to be strongly dependent on the treatments performed.
1. INTRODUCTION Indentation techniques have recently become one of the most powerful methods for the study of fracture mechanisms of brittle materials [ 1-3 ]. A proper account of the residual contact stress field has allowed the response of well-developed radial and median cracks (hereafter referred to simply as radial cracks) to applied stresses to be described, thereby providing a means of determining the intrinsic fracture properties, e.g. the toughness [4] and the fatigue parameters [5, 6]. Also the behaviour of subthreshold flaws subjected to an applied stress is now being studied [7, 8]. The analysis of dynamic fatigue data of soda-lime glass in water obtained with post-threshold and subthreshold indentation flaws has shown (a) that the strengths obtained with subthreshold flaws are substantially higher and (b) that their apparent fatigue susceptibility, the slope 0025-5416/87/$3.50
of logarithmic fatigue curves, is greater than that of well-developed flaws [ 7 , 8 ] . Recently the high susceptibility of the threshold load for Vickers' indentations to surface treatments of a soda-lime glass has been demonstrated. For instance the same sample showed a different susceptibility to radial crack nucleation when etched with HF solution to that when soaked in boiling water; the threshold load was higher with the latter treatment [9]. The aim of this letter is to verify whether the dynamic fatigue behaviour involving both post-threshold and subthreshold Vickers' indentation flaws in a soda-lime glass is also influenced by surface treatment. In particular, two types of surface treatment were compared: (1) etching in HF solution and (2) etching in HF solution followed by soaking in boiling water. It should be pointed out that the dynamic fatigue tests with indentation flaws quoted in the literature have been performed on samples treated in the former manner. In fact, it is necessary to etch the samples with an HF solution to reduce the severity of the preexisting surface flaws before indenting and strength testing. In the present work, these experiments were repeated for two main reasons: (a) the acid etching is different from those quoted in the literature in composition, time and temperature; (b) owing to the large data scatter in the strength tests with subthreshold flaws, it was preferred to compare results obtained under the same experimental conditions.
2.
EXPERIMENTAL DETAILS
Rod specimens of soda-lime silicate glass (AR Schott-Ruhrglas GmbH) were cut from rods 7 mm in diameter into 100 mm lengths. They were annealed at 520 °C for 24 h to relieve any residual stresses. The samples were then etched for 10 min in a solution of 20% HF kept at a constant temperature of 35 °C, which removed about 100 pm in thickness. Q Elsevier Sequoia/Printed in The Netherlands
L26 After this treatment, some specimens were soaked in distilled boiling water for 1 h. All the rods were indented and tested immediately after the treatments. The dynamic fatigue behaviour in water was measured by the threepoint bending method with both post-threshold and subthreshold Vickers' indentation flaws. Each rod was indented with a standard Vickers' indenter in air (constant contact duration, 15 s) with a working load range of 0.2-10 N. Special care was taken to align the indenting pyramid symmetrically with respect to the rod such that the impression diagonals were oriented perpendicular and parallel to the rod axis. A methodology, similar to that suggested b y Dabbs e t al. [6] but with small modifications due to the use of three-point bending, was used to ensure that the indentation flaws were always located at the maxim u m tensile surface and midway along the rod length in the bending rig. The crack environment was controlled by covering the indentations with a drop of distilled water. Immediately prior to bending, a transparent tape was wound round them to avoid shattering the rods at higher strengths. It allowed for determination of the failure origin and thus for confirmation or otherwise of the indentation as the dominant flaw. After preliminary tests, since the threshold load of the samples subjected to only etching in HF solution was about 0.25 N, a load of 0.2 N was chosen to make the dominant flaw in the subthreshold range. Higher loads caused a large number of tests to be rejected, owing to the pop-in of radial cracks before bending. By contrast, lower loads did not ensure that the indentation provided the dominant flaw, thereby causing breakage away from the indentations, most commonly in the vicinity of the supports. In an analogous manner, for the specimens etched in HF solution and subsequently soaked in boiling water, a load of 0.75 N was chosen on similar considerations. The samples were broken b y three-point bending with a span of 50 mm and constant stress rates in the range 0.5-100 MPa s -1. The diameter of every rod was measured before testing at the ends with a micrometer. A b o u t 20 samples were broken for each value of the indentation load and stress rate. Dynamic fatigue data (the median values for each test) were elaborated according to the following fracture mechanics analysis. The
subcritical growth of well-developed cracks in glass is generally described by a power law function [10] v = v0
K
(1)
where v0 and n are empirical fatigue parameters typical of any given material-environment system and K¢ is the critical stress intensity factor. For an indentation radial crack subjected to an applied tensile stress, the stress intensity factor K is the sum of two components [11]: x~P g = c3]2 -[- o(Tf09c) 112
(2)
where ×7 is a dimensionless constant related to the indentation residual stress field, P the indentation load, a the applied stress, co a crack shape parameter and c the characteristic crack size. The first term in the right-hand side of eqn. (2) is associated with the residual contact stress field whereas the second term represents the contribution of the external applied stress to the total stress intensity factor. Under dynamic fatigue conditions, o = dt where 0 is a constant applied stress rate. Lawn and coworkers [ 5, 6 ] numerically integrated eqn. (1), combining it with eqn. (2), and found that aP 113 = (h'6P)l/(n'+ 1)
(3)
where X' and n' are apparent fatigue parameters. They are called apparent parameters because eqn. (3) includes the residual stress term. The true crack velocity exponent n is obtained b y an empirical analysis of numerical fits (in particular, n = 1.31n') whereas from X', with appropriate inert strength determinations, it is possible to obtain v0 [6]. Thus, plotting fatigue data, fitted by a least-squares method, as log(aP l/s) vs. log(~P), allows universal fatigue curves to be obtained, as shown in Fig.. 1. The slope of these curves, which is equal to 1/(n' + 1), corresponds to the apparent fatigue susceptibility of the material-environment system considered. Although eqn. (3) has no strict justification for application to the dynamic fatigue of subthreshold flaws as it applies to well-developed cracks, it is a convenient means of com-
L27 samples with subthreshold flaws than for samples with post-threshold flaws. (2) The straight lines 1 and 3, which both refer to samples with well-developed flaws but are for samples treated in a different way, almost coincide. This means that the soaking in boiling water does not change (with respect to the samples subjected to only etching in HF solution) either the strengths or the fatigue behaviour for this type of defect. (3) Samples with subthreshold flaws are greatly influenced by the different treatments. In particular, samples which had been etched in HF solution and subsequently soaked in boiling water show higher strengths and lower apparent susceptibilities to fatigue (i.e. higher n') than samples subjected to only etching in HF solution. To explain these experimental results, it is necessary to analyse the surface modifications caused by the treatment with boiling water. It is reasonable to think that for a soda-lime glass soaked in boiling water a surface layer, rich in Si--OH groups, forms because of ionic exchange between Na ÷ ions in the glass and H ÷ ions in the water. The extent of this phenomenon has been shown by measurements of the surface concentration profile of hydrogen made by means of nuclear techniques [12, 13]. These measurements were performed on polished slices which had been treated in the same way as the samples for the fatigue tests. The results are reported in Fig. 2. The depth of the hydrogen-enriched layer is 1500 A at the most. From a mechanical point of view, this surface layer, rich in Si--OH groups, yields plastically more easily [ 14] and has lower elastic properties [ 15]. This higher ~lasticity was confirmed by microhardness tests on both samples with loads decreasing from 5 to 0.25 N (Fig. 3). It is possible to see that with low loads the two
paring subthreshold with post-threshold fatigue data. 3. RESULTS AND DISCUSSION In Fig. 1 the straight lines 1 and 2 refer to samples subjected to only etching in HF solution; line 1 is for samples with post-threshold indentation flaws, and line 2 for samples with subthreshold indentation flaws. The straight lines 3 and 4 represent samples etched in HF solution and subsequently soaked in boiling water for 1 h; in an analogous manner, line 3 is for samples with post-threshold indentation flaws, and line 4 for samples with subthreshold indentation flaws. The measured apparent fatigue parameters n' are given in Table 1. By analysing the data in Fig. 1 and Table 1, the following facts emerge. (1) As reported in the literature [7, 8], the scatter in strength data is much larger for
T
rT
LI ....
i
I
! J
:
i • . .i~.,.i
. .,I..,.I
. ..i.,..I
,
.
i....l
,
.
,I.,.,I ?
Fig. 1. Dynamic fatigue plots for subthreshold (lines 2 and 4) and post-threshold (lines 1 and 3) indentation flaws. Lines 1 and 2 refer to samples which had been subjected to only etching in HF solution; lines 3 and 4 refer to samples which had been etched in HF solution and subsequently soaked in boiling water. Error bars represent one standard deviation.
TABLE 1 Apparent fatigue parameters n', together with the corresponding values in parentheses from the literature [6, 7 ] Surface treatment
n' Subthreshold flaws
20% HF solution 20% HF solution + soaking in boiling H20
7.2 + 0.9 (9.0 + 0.8) 30.7 -+ 12
Post-threshold flaws
13.9 + 0.9 14.4 -+2.1
(14.0
+ 0.3)
L28
\ G_ (D v
0 ×
E u
6'
o c
5
]:
0
A
2oo
eoo
,obo
~,~oo
rsbo ' 2 2 ~ b
Depth ( ~, )
Fig. 2. Surface hydrogen concentration profiles: *, glass etched in 20% HF solution followed by soaking in boiling water; A, glass etched in 20% HF solution.
samples have different microhardness values. This difference disappears with increasing load because the indentation depth increases and therefore the influence o f the modified layer decreases. With a load of 0.25 N, when the thickness of the modified layer is n o t a negligible part of the indentation depth, the samples etched in HF solution and subsequently soaked in boiling water have a lower hardness. The lack of influence of the modified surface layer on dynamic fatigue tests on samples with well-developed indentation flaws may be due to the large difference between the layer thickness and the length of the radial cracks. In particular, for the lowest loads, this length is about 5-10 pm, i.e. about 50 times the thickness of the modified layer. By contrast the surface modification induced by soaking in boiling water influences the response to dynamic fatigue with subthreshold flaws. The failure due to these defects has to take into account the radial crack pop-in [8]. Since crack nucleation seems to be a surface phenomenon [9, 16], it is reasonable that a modified surface layer, even if very thin, may influence the crack nucleation. The major point that emerges from this study is that the response to dynamic fatigue tests on samples with subthreshold flaws strongly depends on the surface properties. Thus the apparent fatigue susceptibility of this type of defect may be higher or lower
|
f
!
I
!
I
2
3 P(N)
4
5
'
Fig. 3. Vickers' microhardness values vs. indentation loads: ~., glass etched in 20% HF solution followed by soaking in boiling water; A, glass etched in 20% HF solution.
than that of post-threshold flaws depending on the surface treatments.
ACKNOWLEDGMENTS
The authors are grateful to the Consiglio Nazionale delle Ricerche for economical support and to Dr. C. Rizzi for experimental help.
REFERENCES 1 B. R. Lawn and T. R. Wilshaw, J. Mater. ScL, 10 (1975) 1049. 2 A. G. Evans and E. A. Charles, J. Am . Ceram. S o a , 59 (1976) 371. 3 J.J. Petrovic and M. G. Mendiratta, J. Am. Ceram. Soc., 59 (1976) 163. 4 P. Chantikul, G. R. Anstis, B. R. Lawn and D. B. Marshall, J. Am . Ceram. Soc., 64 (1981) 539. 5 B. R. Lawn, D. B. Marshall, G. R. Anstis and T. P. Dabbs, J. Mater. ScL, 16 (1981) 2846. 6 T. P. Dabbs, B. R. Lawn and P. L. Kelly, Phys. Chem. Glasses, 23 (1982) 58. 7 T. P. Dabbs and B. R. Lawn, Phys. Chem. Glasses, 23 (1982) 93. 8 J. E. Ritter, C. A. Ray and K. Jakus, Proc. 14th Int. Congr. on Glass, New Delhi, 1986, Vol. 2, Special Publication of the Indian Ceramic Society, Central Glass and Ceramic Research Institute, Calcutta, 1986, p. 12. 9 G. Sorar~, R. Dal Maschio and G. Della Mea, Glass TechnoL, 27 (1986) 69. 10 S.M. Wiederhorn and J. E. Ritter, in S. W. Freiman (ed.), Fracture Mechanics Applied to Brittle Materials, Proc. 11th Natl. Symp. on Fracture Mechanics, in A S T M Spea Tech. PubL 678, 1979, p. 202. 11 D. B. Marshall and B. R. Lawn, J. Mater. ScL, 14
L29 (1979) 2001. 12 W. A. Lanford, Nucl. Instrum. Methods, 149 (1978) 1. 13 G. Della Mea, J. C. Dran, J. C. Petit, G. Bezzon and C. Rossi Alvarez, Nucl. Instrum. Methods, 218 (1983) 493.
14 S. P. Gunasekera and D. G. Holloway,Phys. Chem. Glasses, 14 (1973) 45. 15 V. Schmidt and J. Hopfe, J. Mater. Sci. Lett., 13 (1979) 1599. 16 B.R. Lawn, T. P. Dabbs and C. J. Fairbanks, J. Mater. ScL, 18 (1983) 2785.
L25
Letter
Influence of surface treatments on the dynamic fatigue of soda-lime glass with indentation flaws
G. SORARI) and R. DAL MASCHIO Istituto di Chimica Industriale, Universit~ di Padova, via Marzolo 9, 35100 Padua (Italy) (Received July 18, 1986; in revised form October 3, 1986)
ABSTRACT The dynamic fatigue behaviour involving both post-threshold and subthreshold Vickers' indentation flaws of a soda-lime glass in water was investigated in samples subjected to two different surface treatments. The apparent fatigue susceptibility o f the subthreshold flaws was found to be strongly dependent on the treatments performed.
1. INTRODUCTION Indentation techniques have recently become one of the most powerful methods for the study of fracture mechanisms of brittle materials [ 1-3 ]. A proper account of the residual contact stress field has allowed the response of well-developed radial and median cracks (hereafter referred to simply as radial cracks) to applied stresses to be described, thereby providing a means of determining the intrinsic fracture properties, e.g. the toughness [4] and the fatigue parameters [5, 6]. Also the behaviour of subthreshold flaws subjected to an applied stress is now being studied [7, 8]. The analysis of dynamic fatigue data of soda-lime glass in water obtained with post-threshold and subthreshold indentation flaws has shown (a) that the strengths obtained with subthreshold flaws are substantially higher and (b) that their apparent fatigue susceptibility, the slope 0025-5416/87/$3.50
of logarithmic fatigue curves, is greater than that of well-developed flaws [ 7 , 8 ] . Recently the high susceptibility of the threshold load for Vickers' indentations to surface treatments of a soda-lime glass has been demonstrated. For instance the same sample showed a different susceptibility to radial crack nucleation when etched with HF solution to that when soaked in boiling water; the threshold load was higher with the latter treatment [9]. The aim of this letter is to verify whether the dynamic fatigue behaviour involving both post-threshold and subthreshold Vickers' indentation flaws in a soda-lime glass is also influenced by surface treatment. In particular, two types of surface treatment were compared: (1) etching in HF solution and (2) etching in HF solution followed by soaking in boiling water. It should be pointed out that the dynamic fatigue tests with indentation flaws quoted in the literature have been performed on samples treated in the former manner. In fact, it is necessary to etch the samples with an HF solution to reduce the severity of the preexisting surface flaws before indenting and strength testing. In the present work, these experiments were repeated for two main reasons: (a) the acid etching is different from those quoted in the literature in composition, time and temperature; (b) owing to the large data scatter in the strength tests with subthreshold flaws, it was preferred to compare results obtained under the same experimental conditions.
2.
EXPERIMENTAL DETAILS
Rod specimens of soda-lime silicate glass (AR Schott-Ruhrglas GmbH) were cut from rods 7 mm in diameter into 100 mm lengths. They were annealed at 520 °C for 24 h to relieve any residual stresses. The samples were then etched for 10 min in a solution of 20% HF kept at a constant temperature of 35 °C, which removed about 100 pm in thickness. Q Elsevier Sequoia/Printed in The Netherlands
L26 After this treatment, some specimens were soaked in distilled boiling water for 1 h. All the rods were indented and tested immediately after the treatments. The dynamic fatigue behaviour in water was measured by the threepoint bending method with both post-threshold and subthreshold Vickers' indentation flaws. Each rod was indented with a standard Vickers' indenter in air (constant contact duration, 15 s) with a working load range of 0.2-10 N. Special care was taken to align the indenting pyramid symmetrically with respect to the rod such that the impression diagonals were oriented perpendicular and parallel to the rod axis. A methodology, similar to that suggested b y Dabbs e t al. [6] but with small modifications due to the use of three-point bending, was used to ensure that the indentation flaws were always located at the maxim u m tensile surface and midway along the rod length in the bending rig. The crack environment was controlled by covering the indentations with a drop of distilled water. Immediately prior to bending, a transparent tape was wound round them to avoid shattering the rods at higher strengths. It allowed for determination of the failure origin and thus for confirmation or otherwise of the indentation as the dominant flaw. After preliminary tests, since the threshold load of the samples subjected to only etching in HF solution was about 0.25 N, a load of 0.2 N was chosen to make the dominant flaw in the subthreshold range. Higher loads caused a large number of tests to be rejected, owing to the pop-in of radial cracks before bending. By contrast, lower loads did not ensure that the indentation provided the dominant flaw, thereby causing breakage away from the indentations, most commonly in the vicinity of the supports. In an analogous manner, for the specimens etched in HF solution and subsequently soaked in boiling water, a load of 0.75 N was chosen on similar considerations. The samples were broken b y three-point bending with a span of 50 mm and constant stress rates in the range 0.5-100 MPa s -1. The diameter of every rod was measured before testing at the ends with a micrometer. A b o u t 20 samples were broken for each value of the indentation load and stress rate. Dynamic fatigue data (the median values for each test) were elaborated according to the following fracture mechanics analysis. The
subcritical growth of well-developed cracks in glass is generally described by a power law function [10] v = v0
K
(1)
where v0 and n are empirical fatigue parameters typical of any given material-environment system and K¢ is the critical stress intensity factor. For an indentation radial crack subjected to an applied tensile stress, the stress intensity factor K is the sum of two components [11]: x~P g = c3]2 -[- o(Tf09c) 112
(2)
where ×7 is a dimensionless constant related to the indentation residual stress field, P the indentation load, a the applied stress, co a crack shape parameter and c the characteristic crack size. The first term in the right-hand side of eqn. (2) is associated with the residual contact stress field whereas the second term represents the contribution of the external applied stress to the total stress intensity factor. Under dynamic fatigue conditions, o = dt where 0 is a constant applied stress rate. Lawn and coworkers [ 5, 6 ] numerically integrated eqn. (1), combining it with eqn. (2), and found that aP 113 = (h'6P)l/(n'+ 1)
(3)
where X' and n' are apparent fatigue parameters. They are called apparent parameters because eqn. (3) includes the residual stress term. The true crack velocity exponent n is obtained b y an empirical analysis of numerical fits (in particular, n = 1.31n') whereas from X', with appropriate inert strength determinations, it is possible to obtain v0 [6]. Thus, plotting fatigue data, fitted by a least-squares method, as log(aP l/s) vs. log(~P), allows universal fatigue curves to be obtained, as shown in Fig.. 1. The slope of these curves, which is equal to 1/(n' + 1), corresponds to the apparent fatigue susceptibility of the material-environment system considered. Although eqn. (3) has no strict justification for application to the dynamic fatigue of subthreshold flaws as it applies to well-developed cracks, it is a convenient means of com-
L27 samples with subthreshold flaws than for samples with post-threshold flaws. (2) The straight lines 1 and 3, which both refer to samples with well-developed flaws but are for samples treated in a different way, almost coincide. This means that the soaking in boiling water does not change (with respect to the samples subjected to only etching in HF solution) either the strengths or the fatigue behaviour for this type of defect. (3) Samples with subthreshold flaws are greatly influenced by the different treatments. In particular, samples which had been etched in HF solution and subsequently soaked in boiling water show higher strengths and lower apparent susceptibilities to fatigue (i.e. higher n') than samples subjected to only etching in HF solution. To explain these experimental results, it is necessary to analyse the surface modifications caused by the treatment with boiling water. It is reasonable to think that for a soda-lime glass soaked in boiling water a surface layer, rich in Si--OH groups, forms because of ionic exchange between Na ÷ ions in the glass and H ÷ ions in the water. The extent of this phenomenon has been shown by measurements of the surface concentration profile of hydrogen made by means of nuclear techniques [12, 13]. These measurements were performed on polished slices which had been treated in the same way as the samples for the fatigue tests. The results are reported in Fig. 2. The depth of the hydrogen-enriched layer is 1500 A at the most. From a mechanical point of view, this surface layer, rich in Si--OH groups, yields plastically more easily [ 14] and has lower elastic properties [ 15]. This higher ~lasticity was confirmed by microhardness tests on both samples with loads decreasing from 5 to 0.25 N (Fig. 3). It is possible to see that with low loads the two
paring subthreshold with post-threshold fatigue data. 3. RESULTS AND DISCUSSION In Fig. 1 the straight lines 1 and 2 refer to samples subjected to only etching in HF solution; line 1 is for samples with post-threshold indentation flaws, and line 2 for samples with subthreshold indentation flaws. The straight lines 3 and 4 represent samples etched in HF solution and subsequently soaked in boiling water for 1 h; in an analogous manner, line 3 is for samples with post-threshold indentation flaws, and line 4 for samples with subthreshold indentation flaws. The measured apparent fatigue parameters n' are given in Table 1. By analysing the data in Fig. 1 and Table 1, the following facts emerge. (1) As reported in the literature [7, 8], the scatter in strength data is much larger for
T
rT
LI ....
i
I
! J
:
i • . .i~.,.i
. .,I..,.I
. ..i.,..I
,
.
i....l
,
.
,I.,.,I ?
Fig. 1. Dynamic fatigue plots for subthreshold (lines 2 and 4) and post-threshold (lines 1 and 3) indentation flaws. Lines 1 and 2 refer to samples which had been subjected to only etching in HF solution; lines 3 and 4 refer to samples which had been etched in HF solution and subsequently soaked in boiling water. Error bars represent one standard deviation.
TABLE 1 Apparent fatigue parameters n', together with the corresponding values in parentheses from the literature [6, 7 ] Surface treatment
n' Subthreshold flaws
20% HF solution 20% HF solution + soaking in boiling H20
7.2 + 0.9 (9.0 + 0.8) 30.7 -+ 12
Post-threshold flaws
13.9 + 0.9 14.4 -+2.1
(14.0
+ 0.3)
L28
\ G_ (D v
0 ×
E u
6'
o c
5
]:
0
A
2oo
eoo
,obo
~,~oo
rsbo ' 2 2 ~ b
Depth ( ~, )
Fig. 2. Surface hydrogen concentration profiles: *, glass etched in 20% HF solution followed by soaking in boiling water; A, glass etched in 20% HF solution.
samples have different microhardness values. This difference disappears with increasing load because the indentation depth increases and therefore the influence o f the modified layer decreases. With a load of 0.25 N, when the thickness of the modified layer is n o t a negligible part of the indentation depth, the samples etched in HF solution and subsequently soaked in boiling water have a lower hardness. The lack of influence of the modified surface layer on dynamic fatigue tests on samples with well-developed indentation flaws may be due to the large difference between the layer thickness and the length of the radial cracks. In particular, for the lowest loads, this length is about 5-10 pm, i.e. about 50 times the thickness of the modified layer. By contrast the surface modification induced by soaking in boiling water influences the response to dynamic fatigue with subthreshold flaws. The failure due to these defects has to take into account the radial crack pop-in [8]. Since crack nucleation seems to be a surface phenomenon [9, 16], it is reasonable that a modified surface layer, even if very thin, may influence the crack nucleation. The major point that emerges from this study is that the response to dynamic fatigue tests on samples with subthreshold flaws strongly depends on the surface properties. Thus the apparent fatigue susceptibility of this type of defect may be higher or lower
|
f
!
I
!
I
2
3 P(N)
4
5
'
Fig. 3. Vickers' microhardness values vs. indentation loads: ~., glass etched in 20% HF solution followed by soaking in boiling water; A, glass etched in 20% HF solution.
than that of post-threshold flaws depending on the surface treatments.
ACKNOWLEDGMENTS
The authors are grateful to the Consiglio Nazionale delle Ricerche for economical support and to Dr. C. Rizzi for experimental help.
REFERENCES 1 B. R. Lawn and T. R. Wilshaw, J. Mater. ScL, 10 (1975) 1049. 2 A. G. Evans and E. A. Charles, J. Am . Ceram. S o a , 59 (1976) 371. 3 J.J. Petrovic and M. G. Mendiratta, J. Am. Ceram. Soc., 59 (1976) 163. 4 P. Chantikul, G. R. Anstis, B. R. Lawn and D. B. Marshall, J. Am . Ceram. Soc., 64 (1981) 539. 5 B. R. Lawn, D. B. Marshall, G. R. Anstis and T. P. Dabbs, J. Mater. ScL, 16 (1981) 2846. 6 T. P. Dabbs, B. R. Lawn and P. L. Kelly, Phys. Chem. Glasses, 23 (1982) 58. 7 T. P. Dabbs and B. R. Lawn, Phys. Chem. Glasses, 23 (1982) 93. 8 J. E. Ritter, C. A. Ray and K. Jakus, Proc. 14th Int. Congr. on Glass, New Delhi, 1986, Vol. 2, Special Publication of the Indian Ceramic Society, Central Glass and Ceramic Research Institute, Calcutta, 1986, p. 12. 9 G. Sorar~, R. Dal Maschio and G. Della Mea, Glass TechnoL, 27 (1986) 69. 10 S.M. Wiederhorn and J. E. Ritter, in S. W. Freiman (ed.), Fracture Mechanics Applied to Brittle Materials, Proc. 11th Natl. Symp. on Fracture Mechanics, in A S T M Spea Tech. PubL 678, 1979, p. 202. 11 D. B. Marshall and B. R. Lawn, J. Mater. ScL, 14
L29 (1979) 2001. 12 W. A. Lanford, Nucl. Instrum. Methods, 149 (1978) 1. 13 G. Della Mea, J. C. Dran, J. C. Petit, G. Bezzon and C. Rossi Alvarez, Nucl. Instrum. Methods, 218 (1983) 493.
14 S. P. Gunasekera and D. G. Holloway,Phys. Chem. Glasses, 14 (1973) 45. 15 V. Schmidt and J. Hopfe, J. Mater. Sci. Lett., 13 (1979) 1599. 16 B.R. Lawn, T. P. Dabbs and C. J. Fairbanks, J. Mater. ScL, 18 (1983) 2785.