Influence of indentation crack configuration on strength and fatigue behaviour of soda-lime silicate glass

Acta metall, mater. Vol. 43, No. 3, pp. 965 972, 1995

~

Pergamon

0956-7151(94)00335-1

Copyright ~5 1995 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0956-7151/95 $9.50 + 0.00

I N F L U E N C E OF I N D E N T A T I O N CRACK C O N F I G U R A T I O N ON S T R E N G T H A N D F A T I G U E B E H A V I O U R OF SODA-LIME SILICATE GLASS V. M. SGLAVO and D. J. GREEN';" Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA 16802, U.S.A. (Received 23 June 1994)

Abstract--Depending on the conditions under which an indentation is performed or indented specimen stored, different crack configurations can be obtained. In this work, the influence b f these different configurations on the failure process, strength and fatigue behaviour of soda-lime silicate glass, was investigated. To obtain the different crack geometries, indentations were performed in moist air and deionized water with two different dwell times. In this way, typical "half-penny" and deeper "circular" cracks were obtained. Both as-indented and annealed samples were studied. An extensive fractographical analysis revealed a strong "pinning" effect of lateral cracks on the radial crack propagation for indentations obtained in air with short dwell times. Strength measured both in inert and active environments was shown to be lower for indentations obtained in water with longer dwell times. An analogous trend was observed for the lifetime results obtained in static fatigue. Some discrepancies were observed in time-to-failure predictions for "half-penny" indentation cracks and these were related to the interaction between the lateral and radial cracks. R6sum~-Differ6ntes configurations de fissures peuvent atre obtenues, selon les conditions dans lesquelles une indentation est effectu6e et l'6chantillon indent6 est conserv6. Dans ce travail, l'influence de ces differ6ntes configurations sur le proc6de de rupture, la resistance et le comportement en fatigue de verres silicates soda-calciques, a 6t6 6tudi6. Pour obtenir differdntes geometries de fissures, les indentations ont 6t6 effectu6es en atmosphere humide et en pr6sence d'eau deionis6e avec deux temps de residence. De cette faqon, des fissures typiques "half-penny" ont 6t6 obtenu6s ainsi que des fissures circulaires plus en profondeur. Des echantillons juste indent6s mais aussi recuits ont 6t6 6tudies. U n e analyse fractographique detaill6e a revel6 un fort effet de "pinning" des fissures laterales sur la propagation des fissures radiales pour des indentations effectufes fi l'air avec des courts temps de residence. La resistance mesur6e a la fois en environnements inertes ou actifs, s'est revelde 6tre plus faible dans le cas d'indentations realis6es dans l'eau avec des temps de residence plus longs. Des resultats analogues ont 6t6 obtenus pour la dur6e de vie mesur6s en conditions de fatigue statique. Quelques differences ont 6t6 observ6es dans le cas des predictions de dur6es de vie pour les fissures en "half-penny" et ont ~t6 reli6es aux interactions entre fissures laterales et radiales. Zusammenfassung--Abh/ingig von den Bedingungen, unter denen ein Eindrucksversuch vorgenommen wird oder eine eingedrickte Probe aufbewahrt wird, k6nnen verschiedene Riggestaltungen erzeugt werded. In dieser Arbeit wurde der Einflul3 dieser verschiedenen Riggestaltungen a u f den VersagensprozeB, die Festigkeit und das Ermiidungsverhalten von Soda-Kalk-Glas untersucht. U m die verschiedenen RiBgestaltungen zu erhalten, wurden Eindrucksversuche in feuchter Luft und deionisiertem Wasser mit zwei verschiedenen Haltezeiten durchgefiihrt. A u f diese Weise wurden typische "half-penny" und tiefere "runde" Risse erzeugt. Sowohl lediglich eingedrfickte als auch getemperte Proben wurden untersucht. Eine umfassende Analyse der Bruchfl/iche zeigte einen starken "pinning" Effekt der seitlichen Risse an der Ausbreitung der radialen Risse ffir Eindr/icke, welche in Luft mit kurzen Haltenzeiten erhalten wurden. Sowohl in tr/iger als auch in aktiver U m g e b u n g war die Festigkeit geringer ffir Eindrficke, die in wasser mit lfingeren Haltenzeiten erzeugt wurden. Ein entsprechender Trend wurde f/it die in statischer Ermfidung erhaltenenen Lebenszeitergebnisse beobachtet. Einige Abweichungen wurden in Lebenszeitvorhersagen ffir "half-penny" Eindrucksrisse beobachtet. Diese Abweichungen standen in Beziehung mit der Wechselwirkung der seitlichen und der radialen Risse.

1.

INTRODUCTION

o f t h e f r a c t u r e p r o c e s s e s a n d p r o p e r t i e s o f brittle m a t e r i a l s . F o r i n s t a n c e , f r a c t u r e t o u g h n e s s is curr e n t l y o f t e n d e t e r m i n e d by m e a s u r e m e n t o f t h e l e n g t h o f t h e c r a c k s o r i g i n a t i n g f r o m a Vickers i n d e n t a t i o n or f r o m t h e s t r e n g t h o f i n d e n t e d flexural test specim e n s [1-6]. A m o n g t h e a d v a n t a g e s o f s u c h m e a s u r e -

I n d e n t a t i o n c r a c k s h a v e b e e n e x t e n s i v e l y s t u d i e d in t h e last t w o d e c a d e s as a p o w e r f u l tool in t h e a n a l y s i s t T o w h o m all correspondence should be addressed. 965

966

SGLAVO and GREEN:

STRENGTH AND FATIGUE OF SILICATE GLASS

ments are rapid test procedures, low cost and ease of testing. Most of the indentation fracture mechanics theory has been developed on the basis of the experimental evidence obtained on soda-lime silicate glass, due to its properties of brittleness, homogeneity, isotropy, transparency and susceptibility to subcritical crack growth at room temperature [7 15]. Nevertheless, even in soda-lime glass, some inconsistent results and discrepancies in toughness determination have been obtained [14]. Different sets of crack geometries are generated during the indentation of a brittle material but usually the attention is focused on the cracks which depart from the corners of the indentation site [2,9, 13]. These "median/radial" cracks are often considered to be semicircular (Palmqvist crack geometry is only rarely considered [4~6, 14]), centered on the contact site and invariant in shape during the propagation process. The stress intensity factor for the median/radial cracks is generally defined as proportional to the ratio P/c t~, where P is the maximum indentation load and c the crack length. The proportionality constant, Z, is termed the residual stress factor [2, 7, 9, 14]. When an external stress field a is applied to an indented specimen, it is responsible for a second component of the stress intensity factor, represented by the product a~b ,/c, where t) is defined as the crack shape factor [3, 8, 14, 16]. Both t) and Z are usually considered to be constants during the crack propagation process. In some studies, however, the requirements just summarized and encountered in the conventional indentation fracture mechanics are not fulfilled. Depending on the conditions under which the indentation is performed and stored, cracks shape and growth can be complicated by several factors. First of all, the indentation load plays an important role in defining crack dimension and shape. For example, indentation flaws are often subdivided, as a function of P, into sub-threshold and post-threshold cracks, and these cracks exhibit different behaviour during strength and fatigue tests [17 22]. In addition, environmental effects both during and after the indentation can lead to different crack configurations and residual stress factors. We have shown in a previous paper that indentation median cracks in soda-lime glass undergo subcritical growth during indentation, resulting in deeper cracks with a circular shape [15]. Environmental effects prior to the strength testing have also been shown to affect indentation-induced fracture in soda-lime glass [21-24], silicon [25] and in fused silica [26]. Due to the presence of the residual indentation stress field, both median/radial and lateral cracks can grow sub-critically in non-inert environments. The first consequence of this process is that the residual stress field is partially relieved. In this way, Z decreases whilc the strength of indented samples increases [3, 27 31]. The limit of this process, corresponding to Z = 0, can be achieved by removing the indentation stress field with an annealing treat-

mcnt. A second effect is that the shape of the original semicircular median/radial crack changes into a semielliptical geometry, whose major axis lies on the surface of the sample [14, 32]. Finally, some complications occur during the propagation of the median/radial crack when an external stress is applied. In fact, the crack geometry, even for initial semicircular defects, evolves into various semielliptical shapes [14, 33, 34] with a consequent variation in the shape factor ~. The crack shape can be further complicated when radial and lateral cracks interact [14, 32]. Moreover, it is becoming evident that all these complexities can be observed even in the model "brittle" material, soda-lime-silica glass. In this work, the influence of a different indentation crack configurations on the strength and the fatigue behaviour of soda-lime silicate glass is considered. Two distinct crack geometries are analyzed both in the as-indented (Z > 0) and annealed (7. = 0) situation. The fracture process upon the application of a bending stress is studied in detail. Finally, the strength and static fatigue behaviour are discussed on the basis of the conventional indentation fracture mechanics, which allows important features regarding the shape and residual stress factors and the interaction between lateral and radial cracks to be discussed. 2. EXPERIMENTAL P R O C E D U R E

Soda-lime silicate (wt% composition 72 SiO2, 13 Na20, 1 A1203, 9 CaO, 4 MgO, 1 other) glass from a commercial source was used in this work. Glass bars, nominally 6.4 x 63.5 × 2.4 ram, were annealed in air at 520C for 48h in order to remove any residual stress. Heating and cooling rates less than l°C/min were used.

2.1. Indentation procedure Indentation tests were conducted either in laboratory air (relative humidity ~45%, T = 2 5 ° C ) , in deionized water or in silicone oil. Water was used as reactive environment while silicone oil represented an "inert" environment, by minimizing moisture access to cracks. The surface of every sample was cleaned with acetone prior to the indentation procedure. For indentations in oil, samples were stored in a furnace at 120-130~C for 30 rain and immediately immersed in an oil bath; some more droplets of oil were also placed on sample surface before indentation. For indentations in water, a droplet of water was simply placed onto the contact site before indentation. Indentations in oil using loads of 39.2-58.9 N and measurement of surface trace of the median-radial cracks allowed fracture toughness determination by using the relationship proposed by Evans and Charles [1,41.

2.2. Strength and dynamic Jatigue tests Some bars were indented for inert strength and dynamic fatigue measurements. A fixed indentation

SGLAVO and GREEN:

STRENGTH AND FATIGUE OF SILICATE GLASS

load of 9.8 N was chosen for these tests. All samples were prepared with three indentations spaced 3 mm apart along the longitudinal center line, in order to obtain information regarding the failure instability conditions. One set of samples were indented in air using dwell times of 10 s and these have been labeled as set A. The other set of samples were indented in water using dwell time of 1 min (samples W). Both A and W sample sets were stored in a deionized water bath for 1 week prior to testing. This amount of time was sufficient for allowing indentation cracks to grow sub-critically and reach a "stable" configuration [11, 27]. In order to remove indentation residual stress field, a certain number of the samples were annealed in the same manner as previously defined. In this way, sample sets Aa and Wa were obtained from the A and W sets, respectively. Strength values for samples A, W, Aa and Wa were obtained by four-point bending tests, using inner and outer span of 12.7 and 38.1 mm, respectively. Great care was taken in order to center and align indentations inside the inner span. Twenty bars were used for each experimental condition. Inert conditions were obtained by covering the indentation sites with silicone oil [27, 32, 35]. Samples were stored in a furnace at 120-130°C for 30 rain and immediately immersed in an oil bath; some more droplets of oil were also placed on the sample surface before testing. Failure times were kept below 5 s by using a cross-head speed of 1 mm/min, this being the highest cross-head speed compatible with load cell and geometrical features of the test. Dynamic fatigue tests were performed on A and W samples in water in order to determine the sub-critical crack growth parameters. The loading fixture was the same as that used for the inert strength measurements. Cross-head speeds ranging from 1 #m/rain to 1 m m / m i n were used. The corresponding extremes in the stressing rates are 9.82 kPa/s and 9.82 MPa/s. Five bars were tested at each stressing rate and some droplets of water were placed onto the indentation sites before testing. The water drops were sufficient to guarantee a water-environment around cracks during the strength testing. For samples used in the inert strength determination and for those loaded in the water environment, fracture surfaces were observed by optical microscopy. This procedure was used to confirm that failure initiated at the indentation site and to gain evidence about the initial crack shape and dimensions. The two indentations on each specimen which did not fail upon bending were manually broken and all fracture surfaces were observed under an optical microscope. In this way, the crack shape evolution upon loading could be determined from the markings on the fracture surface.

2.3. Static fittigue tests by bending Static fatigue tests were performed in water on the A, Aa, W and Wa samples. The time-to-failure was AM 43i3

H

967

measured as a function of the applied stress but otherwise the experimental conditions were the same as the dynamic fatigue tests. Samples were loaded to the desired stress level using a cross-head speed of 0.5 mm/min; they were then kept at the same load until failure occurred. Stress levels were selected to obtain failure times ranging from ~ 10 to ~ 30,000 s.

3. RESULTS AND DISCUSSION

3. I. Crack shape and failure process Typical fracture surfaces for sample sets A and W loaded in oil are shown in Fig. 1. The presented micrographs correspond to ones obtained fiom the " d u m m y " indentations, which show the crack evolution process up to failure. The shape and dimensions of the indentation cracks can be usually measured at various stages of their evolution, by observing the surface markings caused by crack arrest and coalescence or by variations in the topography of propagation plane. Figure 2 gives schematic illustration of the crack evolution process for the two sample sets. Crack dimensions corresponding to Fig. 2 are shown in Table 1. For the sample set A [Figs l(a) and 2(a)], the median/radial crack is usually semicircular oi slightly semielliptical, centered on the initial contact point (surface crack length, co). In many cases formation of a median crack and its upward propagation into a

Fig. 1. Sub-surface view of "dummy" indentation cracks obtained in air with a dwell time of 10 s (sample set A) (a) and in deionized water with a dwell time of 60 s isample set W) (b). Both samples were loaded in silicone oil.

968 (a)

SGLAVO and GREEN: subcrific~I growth

\

I--,~-- -- -- -- ~cm

~

..-

p astic zone

\

STRENGTH AND FATIGUE OF SILICATE GLASS

X

~_o

--~,-

~

c0

I

Table 2. Inert strength a~ and surface crack length c m at the instability point

, I

I

.... T_

lateral crack

/ ~ median/radial crack I

(b)

s~bcri.e~ growth

.~,,q

\

cm co

,-- . . . .

lateral crack ~

~radial

~J

!

crack

IP

,, median c

T_ r~ -

d

a i (MPa)

c~ ( ~ m )

A Aa W Wa

6 5 . 2 + 1.7 76.6_+ 1.5 58.6-+3.7 73.6 _+ 3.1

151+11 139 + 9 133-+5 126 _+ 7

1

~

plastic zone - -

Sample set

--~1

Fig. 2. Schematic of indentation cracks corresponding to sample sets A (a) and W (b).

radial one is also evident [Fig. l(a)]. Lateral cracks develop beneath the plastic zone and propagate nearly parallel to the surface. After the indentation process both the median/radial and lateral cracks undergo sub-critical growth. The median/radial cracks propagate primarily along the surface, assuming an almost oblong shape. After this process the surface trace dimension (c6) is ahnost twice the length of the initial crack (Table 1). During the sub-critical growth process, the median/radial and lateral crack fronts always appear to intersect each other, with evidence of some interaction during this stage of propagation. Aged radial cracks undergo stable propagation upon the application of the bending stress until the critical crack length (Cm) is reached. The surface crack lengths at the instability points are given in Table 2. In order to verify that stable growth occurred effectively under inert conditions, some tests were conducted using nominal stressing rates up to 600 MPa/s. The crack extension was the same as that observed on samples loaded using stressing rates of 9.82 MPa/s (Table 2) and confirmed the inert strength values reported in Table 2. As evident in Figs l(a) and 2(a), the critical crack shape is strongly influenced by interaction of radial with lateral cracks. It appears the radial crack is being "pinned" by the lateral cracks. Similar behavior has been described by Smith and Scattergood [14] but, in our case, the experimental

Table 1. Crack dimensions (in microns) corresponding to sample sets A and W, as represented in Fig. 2 Sample set A c~ c~ 66+6 124±7

p 64_+5

l 107+7

p~ 40_+7

Sample set W co c(~ 60_+8 118+5

p 110~7

d 144_+6

l 103±13

Pl 25+15

procedure gave a crack shape at instability that is not semi-elliptical but is a more complicated shape. Observation of the fracture surfaces in the annealed (Aa) samples showed the crack propagation prior to loading was similar to the as-indented (A) samples. Surprisingly, significant stable extension upon loading, in a similar fashion to that shown in Fig. 2(a), was also evident in these samples, though the critical crack lengths were smaller than the A samples (Table 2). It is concluded that stable growth can occur for indentation cracks even in the absence of the localized residual stress and is a result of radial/lateral crack interaction process. Similar behaviour has been observed by Smith and Scattergood [32]. A schematic of the indentation fracture pattern for samples W and Wa is shown in Fig. 2(b). It must be pointed out that, in some cases, the crack shape in sample sets W and Wa were similar to that shown in Fig. l(a) [15]. Samples like these were rejected and the test was run again as the primary aim of the study was to determine the effect of the crack configuration on the strength behaviour. Indentation cracks in samples W [Fig. l(b)] show an unusual almost-circular shape. As explained in a previous paper, these "circular" cracks are a result of the sub-critical growth of the median crack during indentation [15]. Upon unloading the indenter, these circular cracks propagate towards the surface to form the radial surface traces. Their length, co, is slightly smaller than found in the A sample set (Table 1). Lateral cracks are also generated in this case, emanating from the bottom of the plastic zone, and these were more shallow than those observed in the A sample set (Table 1). In some samples more than one lateral crack appeared at the indentation and, in these cases, their lengths were significantly smaller than the case when there is the single lateral crack. For sample set W, sub-critical growth was observed both for the radial and lateral cracks but the aged crack length (c6) was slightly smaller than that measured in sample set A (Table 1). Stable crack growth was usually observed both in the as-indented and annealed materials (W and Wa) and the critical crack sizes, Cm, was smaller than in sample sets A and Aa (Table 2). In addition, stable growth of radial cracks in W/Wa samples occurred in regions closer to the surface of the sample than in sample sets A and Aa [Fig. l(b)] and seemed to be less constrained by lateral cracks. Figure l(b) shows also that further propagation of radial cracks beyond the instability point is substantially not affected by any pinning

SGLAVO and GREEN: ,,.i

........

t

........

i

STRENGTH AND FATIGUE OF SILICATE GLASS

........

i

field cr is the sum of the indentation residual stress and external stress components. The net stress intensity factor is usually defined as [3, 8, 14]

6O

50

P K = Z757+ c@v/7

4o 3O ,r,,I

........

I

10 .2

........

I

10 q

........

10 ° ~

I

,

10 ~

(MPa/s)

Fig. 3. Dynamic fatigue plot of the strength err as a function of the stressing rate da for sample sets A and W. Open and solid symbols correspond to strength measured in silicone oil and deionized water, respectively. Fitted lines are calculated according to equation (5). effects and the crack front is almost semielliptical even in regions close to the indentation site. An accurate fractographical analysis revealed that the Wa samples, in which more than one shorter lateral crack was present, did not show any stable growth upon bending. In addition, the extent of the stable growth was generally less with the shallow lateral cracks in the W and Wa systems. Thus, it is again concluded that interaction between the lateral and radial cracks can also stabilize crack growth in these other systems but the interaction is not so strong as in the samples indented in air.

3.2. Inert strength and dynamic Jatigue results Inert strength (cri) data for the various specimen sets are shown in Table 2. The results of the dynamic fatigue tests in term of strength af as a function of stressing rate 6- are plotted in Fig. 3, together with inert strength values. It is clear that the difference in indentation procedure and radial crack configuration leads to a significant difference in strength. Removal of the indentation residual stress by annealing leads to an increase in inert strength. This is about 12% for A and Aa samples while it is smaller ( ~ 5 % ) for W and Wa samples, furnishing important information about the relative intensity of indentation residual stress fields for the two batches. Moreover, as indicated in the previous section, there is a stable growth for all the sample sets (Table 2). For the annealed samples this is a result of interaction between the radial and lateral cracks. It is useful to analyze these results by means of the conventional indentation fracture mechanics [3, 8, 14]. The stress intensity factor corresponding to an indentation crack subjected to an external stress Table

3.

Residual crack

Sample A

stress

shape

factor

factor

set

7. a n d

~,

/.

~,

0.034

0.67

Aa

--

0.80

W

0.028

0.80

Wa

-

0.87

969

(1)

where P is the maximum indentation load, e the crack size, X the residual indentation stress field factor and ~b the shape factor. Under inert conditions, cracks propagate when K = K~. Depending on the sign of the derivative dK/de, growth can occur in a stable fashion or be catastrophical. It has been demonstrated that, due to the particular form of equation (1) and for Z > 0, indentation cracks should undergo some stable growth before the final unstable failure [3, 8]. If ~ and are constant, as usually assumed in indentation fracture mechanics, the crack length at instability point is given by [3, 8]

em

\ K~ /

(2)

while the corresponding strength is

3& - ~ . O'm

(3)

41/j N / Cm

The strength defined in equation (3) corresponds to the strength measured under inert conditions cq, thus O-m ~

Oi.

By using equation (2), Z/Kc ratio can be evaluated from data in Table 2. Values of 47.3 #tnJSN and 39.1 #m]SN were obtained for sample sets A and W, respectively. Measurement of the surface trace of median-radial cracks obtained in oil environment allowed a value of 0.72 _+ 0.07 MPax/~mmto be determined for K~. By inserting this value into equation (2), X values of 0.034 and 0.028 were obtained for sample sets A and W, respectively These results collected in Table 3, point out that the residual stress term in equation (1) is greater for the A sample set. Both the larger extension of median cracks, in analogy to the sub-critical growth of lateral cracks [3, 27 30], and "softening" processes acting during the indentation cycle in the presence of water [3640] could account for the lower X value for sample set W. Nevertheless, it is clear that the differences in inert strength given in Table 2 cannot be explained simply by differences in Cm and )~ and one must consider differences in the crack shape factor ¢,. This factor can be calculated by using equation (3). By inserting values of tr~ and Cm given in Table 2, values of = 0.67, for sample set A, and ~ = 0.80, for sample W, were obtained (Table 3). The crack shape factor can also be calculated for annealed samples at instability point by the equation

K~ - criX~mm"

(4)

The values obtained were 0.80 and 0.87 for Aa and Wa sample set, respectively (Table 3).

970

SGLAVO and GREEN:

STRENGTH AND FATIGUE OF SILICATE GLASS In static fatigue (G = constant), the time-to-failure for Z = 0 and ~, = c o n s t a n t can be expressed as [10,42]

T a b l e 4. F a t i g u e p a r a m e t e r s c a l c u l a t e d by e q u a t i o n (5) for s a m p l e sets A a n d W S a m p l e set

n

vo ( m m / s )

A W

18.8 18.7

14.3 11.7

Tr = - The crack shape factor accounts for ellipticity, free-surface effects and crack interactions [3]. Thus, crack shape and interaction between radial and lateral cracks in sample sets A, Aa, W and Wa should be a primary factor in accounting for the strength differences in Table 2. As can be seen in equations (2) and (3), the shape factor ~ plays a more predominant role than Z Let us now analyze strength results presented in Fig. 3 to obtain information regarding the sub-critical crack growth characteristics for this glass in a water environment. Presumably, if the analysis is performed correctly, the same values of v0 and n will be obtained regardless of the initial crack configuration. It has been shown that the strength of indented brittle materials, under conditions of dynamic fatigue, provided ~ and Z are constant, can be expressed as [41, 42] O-r =

~ aI,~,, + ~/ ~O"

(5)

where =

( 2"5 In'° 462°-'£Cm) ''' + ~

(5a)

[:0

n ' = 0.763n

(6)

with 2

/K

\" 1

~

,~

~= n~_2~ 2~ ) ~(C~o'- ,).,_c~ 2

,).,2)

(6a)

where c 0 and cf represent the initial and critical crack lengths, respectively. When the residual stress term is not zero, numerical procedures are required. The failure times can generally be calculated by solving the integral T,

1 i "f

K~ dc

v~ d,o (o'~6 x,/7 + zP/c 's)

(7)

where, in this case, Cr is the crack size corresponding to the boundary condition at failure (7 a ~'

V / ct~.+ z P - Kc.

(7a)

Equations (6) and (7) were used to calculate Tr for the samples investigated in this work. Values of 7, and ~, were obtained from Table 3, n and v0 from Table 4. The initial crack size co was assumed to be equal to c~, given in Table 1. The theoretical predictions, shown in Fig. 4, seem to be in better agreement for W and Wa samples than for A and Aa samples.

(5b) 70

where 6-~ is the applied stressing rate and Cm and a m are the crack length and the inert strength, respectively, as defined in equations (2) and (3) Linear regression analysis of loger against log 6was performed on strength data obtained in water, as shown in Fig. 3 All original strength data were considered in the regression analysis. By using equations (5a) and (5b), the slope of the fitted line can be used to calculate the value ofn. On the other hand, values of Cm and r~ (Table 2) can be inserted into equation (5a) to obtain v0 from the intercept. The results are shown in Table 4 and show excellent agreement for the two crack configurations. The values also agree well with data presented in literature for soda-lime silica glass [16, 35] It would appear that the theoretical approach is robust enough to deal with the complex crack shapes and interaction seen in this study [41].

60 50 40

30

20 I0 °

102

104

Tf

I0 s

(S)

60 .............................................. 50 ~ ~

ib')i

40

3.3. Static Jatigue behavior Static fatigue tests results are shown in Fig. 4 in terms of time-to-failure Tf as function of the applied stress. Similar to the strength results (Table 2 and Fig. 3), T r is longer for annealed than as-indented samples. Moreover, there is a decrease in the lifetime for the samples containing the deeper "circular" cracks (W and Wa).

1(

........ i 10 °

........ I ........ i 102 T t

........ i ........ i 104

..... 10s

(s)

Fig. 4. Static fatigue plot of the time-to-failure Tf as a function of the applied stress o-a for sample sets A/Aa (a) and W/Wa (b). Lines represent theoretical predictions according to equations (6) and (7).

SGLAVO and GREEN:

STRENGTH AND FATIGUE OF SILICATE GLASS

Table 5. Fatigue parameters calculated by, equatiom (8) for annealed sample sets A a and W a Sample set

n

v0 (mm/s)

Aa Wa

16.1 18.2

1.56 9.50

This discrepancy can also be seen for the annealed specimens by using the static fatigue data to calculate the fatigue parameters. For Z = 0, in the approximation ~ = constant, one can write log or, : 1 log c." - 1_ log Tf. n

(8)

/7

Linear regression of log a a vs log Tf data for the annealed samples furnished values of n and v0 shown in Table 5. Results for the Wa samples are in good agreement with previous measurements by dynamic fatigue tests (Table 4) whereas there is a slight discrepancy for the Aa samples. At this point it must be recalled that theoretical values have been calculated by assuming that X and ~9 remain constant during crack propagation; this hypothesis can be easily refuted [14]. In addition, during static fatigue tests, a crack spends most of its time in the vicinity of the initial flaw [42]. This means that, during a greater proportion of its evolution, a radial crack is subjected to stronger interaction with the lateral cracks. This effect was considered by Yoda and Yoshikawa [43, 44] in order to explain anomalous crack velocity results obtained from Vickers and K n o o p indentation cracks. The differences in radial crack velocity as a function of the applied stress intensity factor between the two different indentations were attributed to the obstruction produced by the lateral cracks on the radial crack propagation. This effect was also used to account for a decrease in the net stress intensity factor during the crack propagation process [43, 44]. For the annealed samples Aa considered in this study, theoretical predictions underestimate the timeto-failure. In analogy with the arguments proposed by Yoda and Yoshikawa [43, 44], this difference can be correlated to the pinning effect of lateral cracks on radial cracks which forces these latter to assume some unnatural shapes [45-47]. A possible consequence of this process is that the crack shape factor reduces with increasing crack size, accounting for the longer lifetime values. Further experimental studies are required for the quantification of the lateral/radial cracks interaction and, for instance, it would be useful to quantify the variation in of Z and tp with crack size. 4. CONCLUSIONS Conditions under which indentations are performed were shown to have an important influence on the failure processes, strength and fatigue behaviour of soda-lime silicate glass. Typical half-penny

971

cracks were obtained by indentation in air with dwell time of 10s while deeper "circular" cracks were obtained by indentations in water with dwell time of 60s. Fractographical analysis showed that radial crack propagation during bending is strongly influenced by interaction with lateral cracks. Strength measured both in inert environment and in water were lower for the indentation performed in water with the longer dwell time. This strength was correlated primarily to different crack shape factor values for the two initial configurations. In spite of the different initial crack configuration, similar fatigue parameters were calculated from dynamic fatigue results. Lifetime results showed the same trend as strength, being longer for initial half-penny crack configuration, but some differences between the theoretical predictions and experimental data were observed for these cracks. The discrepancies between the theoretical and experimental static fatigue results were correlated to the obstruction by the lateral cracks on radial crack propagation.

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