Dynamic Fatigue of a Lithia-Alumina-Silica Glass-Ceramic

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J Am Cerom Soc 73 181 2528-30 [IPPO)

Dynamic Fatigue of a Lithia-Alumina-Silica Glass-Ceramic Dennis S. Tucker NASA-Marshall Space Flight Center, Huntsville, Alabama

A dynamic fatigue study was performed on a LizO-AI203SiOz glass-ceramic in order to assess its susceptibility to delayed failure. Fracture mechanics techniques were used to analyze the results for the purpose of making lifetime predictions for optical elements made from this material. The material has reasonably good resistance (N = 20) to stress corrosion in ambient conditions. Analysis also indicated the elements should survive applied stresses incurred during grinding and polishing operations. [Key words: glassceramics, fatigue, dynamics, fracture mechanics, stress.]

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constructed using the following expression: lntf = In B

+ ( N - 2/mi){ln In [l/(l - F ) ] + m, In uo,}- N

In

ua

(1) where m i and uoiare the Weibull modulus and scaling parameter, respectively, F is the probability of failure, uais the applied stress, and B and N are fatigue constants. 11. Experimental Methods

I. Introduction

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Samples in disk form were supplied to NASA by the manufacturer. The disks were of 66-mm diameter and approximately 9 mm thick. The disks were prepared for mechanical testing by grinding to a thickness of 6 5 0.3 mm with an automatic grinder using 230 to 270 diamond grit. The 92 samples were separated into lots of 23 specimens each and tested at rates of 0.1, 5.8, 200, and 5.5 X lo5 MPa/s using a concentric ring bend test." The two Iowest stress rates were tested on a standard mechanical test machine,'while the two highest stress rates were tested on a servohydraulic test machine* to take advantage of the faster response times. The stress rate of 5.5 x lo5 MPals was used to determine the inert strength of the glass-ceramic. The samples for inert strength testing were first heated to 500°C for 24 h in a dry nitrogen environment and then stored in a desiccator until testing. A chamber was fabricated to enable the inert testing to be performed in an inert environment. Each sample was exposed to flowing dry nitrogen for 1 min prior to testing. Failure analysis was performed on each sample to determine the origin of failure, using a stereomicroscope at 6 0 ~ magnification or less.

has selected a Li20-Al2O3-SiO2 glass-ceramic* as the material for the grazing incidence mirrors of its Advanced X-ray Astrophysics Facility. The material contains 70% to 78% by weight crystalline phase of high-quartz structure, with a mean crystal size of SO to 55 nm.' The vitreous phase has a positive thermal expansion coefficient which is practically balanced by the negative coefficient of the crystalline phase. This results in a material which can maintain longitudinal stability during thermal cycling much like that expected for an orbiting telescope. The optical elements will consist of two sets of six nested, concentric, cylindrical mirrors. These elements were produced and given a rough surface finish (230 to 270 grit) by the manufacturer before shipment to the United States for final polishing and assembly. Before and during the polishing operation, each element will be subjected to lifting loads as well as loads due to polishing. Analysis has shown that the maximum loads will be incurred during vacuum lifting operations. These loads translate to stresses of approximately 5.5 MPa applied to the areas of vacuum attachment. It is expected that the elements will see these stresses for up to a total of 10 h, 1 h per lift, with a total of 10 lifts during processing. It is important to know if the elements can survive these stresses applied over the duration of the lifting operations. An allowable stress can be calculated for this material based upon modulus of rupture data; however, this does not take into account the problem of delayed failure. It is well-known that many ceramic materials undergo delayed failure, most likely due to stress corrosion, which can significantly shorten lifetime^.^-^ Fortunately, a theory based on fracture mechanics has been developed enabling lifetime predictions to be made for brittle materials susceptible to delayed Knowledge of the factors governing the rate of subcritical flaw growth in a given environment enables the development of relations between lifetime, applied stress, and failure probability for the material under study. Dynamic fatigue testing is one method of obtaining the necessary information to develop these relationships. In this study the dynamic fatigue method was used to construct a time-to-failure diagram for roughground LizO-AI203-Si02 glass-ceramic. The diagram was ASA

111. Results and Discussion

The breaking strength of each sample was calculated from the following equation:

l.08Pb/t2 (2) where (Tb is the breaking stress or modulus of rupture, Pb is the breaking load, and t is the sample thickness. The constant 1.08 takes into account the sample and fixture geometry and Poisson's ratio." The strength data are shown in Fig. 1, where fracture stresses q are plotted as a function of failure probability, F, at each stress rate. Failure probability was calculated from U b

=

F = (n - O.S)/N

(3)

where n is the rank of each stress and N is the total number of stresses in the distribution. Each set of strength values was fitted to a two-parameter Weibull distribution by linear leastsquares regression analysis of In ofon In In [l/(l - F)]." Estimates of the Weibull modulus and scaling parameter go were obtained from the regression analysis and are shown

S. Freiman-contributing editor

'1125, Instron Corp., Canton, MA. '880, MTS Corp., Minneapolis, MN.

Manuscript No. 197705. Received March 21,1990; approved May 17, 1990. 'Zerodur, Schott Glaswerke, Mainz, FRG.

2528

August 1990

2529

Communications of the American Ceramic Society Table I. Results of Dynamic Fatigue Testing of Concentric Ring Bend Specimens* & (MPa/sl

m

In un

R2

0.1 5.8 200 5.5 x lo5

13.81 11.67 19.51 10.10

17.58 17.74 17.95 18.10

0.92 0.89 0.96 0.97

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INERT DATA

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'23 samples.

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with strength data in Table I. Since the correlation coefficients were greater than 0.85, the two-parameter Weibull distribution was concluded to be acceptable and was used in the dynamic fatigue analysis. The distributions in Fig. 1 exhibit deviations from linearity which could indicate a bimodal flaw distribution. However, failure analysis revealed that all specimens failed within the region of highest stress (i.e., within the area bounded by the load ring on the tensile surface). It can also be seen from Fig. 1 that the distributions of the two highest stress rates approach the same lower limit strength. This may indicate an upper limit to the initial flaw size. The distributions also show a wide range of Weibull modulus. This may be due to thickness variations, deviations from the specified flatness tolerance for the specimens, or a combination of these two factors. Both were noted for the specimens used in this study. Median fracture stresses, uf,used in the analysis of the dynamic fatigue results, are plotted in Fig. 2 as a function of stress rate, a. The dependence of median strength on stress rate indicates that subcritical crack growth is taking place prior to failure. A linear regression analysis of In ufon In yielded estimates of the slope and intercept from which the fatigue constants N and B were calculated. The values of N and B were found to be 20 and 7 x 10'' Pa%, respectively. These two values, along with the inert Weibull modulus m , and the inert Weibull scaling factor uo,,were used to construct the time-tofailure diagram shown in Fig. 3, utilizing Eq. (1). The diagram was constructed for probabilities of failure, 0.001, 0.01, and 0.2. Owing to the uncertainty in estimates of N, B, m, and uo,large uncertainties in calculated lifetimes may occur. For example, in the present study, the variances of N and In B

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In 6 (8 in Pals) Fig. 2. Dynamic fatigue data and inert strength data: median strength af (Pa) as a function of stress rate & (Pa/s).

were found to be k2.7 and ?1.2, respectively. These values were determined from equations derived in Ref. 12. Therefore, confidence intervals were calculated using a statistical analysis based on the theory of error pr~pagation.'~ In this instance the error analysis developed by Ritter et al." was used to calculate 90% confidence intervals for the 0.001 failure probability curve, Fig. 4. Thus, for a constant applied stress of 5.5 MPa with 0.001 probability of failure, the lifetime is approximately 737000 years. However, because of the uncertainty in t f , the lifetime would be shortened to approximately 335 years for 90% confidence. Thus, it appears that this stress should not result in failure of the optical elements during lifting operations. This is actually a safe stress for components with stressed areas comparable in size, stress state, and edge and surface finish. The test specimens were given the same surface finish as the optical elements, while the lifting loads will be applied well away from the cylinder edges. The question remains, though, of the effect of increased stressed area on time to failure. Computer

2 applied stress in psi 500 40

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In of ( o f in Pascals) Fig. 1. Strength distributions for dynamic fatigue of LizOAl2O3-SiO2 glass-ceramic.

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In oa ( Q~ in Pascals)

Fig. 3. Time-to-failure diagram for LizO-Al203-SiO~ glassceramic from dynamic fatigue data for values of F indicated.

Communications of the American Ceramic Society

2530 applied stress in psi 500 40

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Vol. 73, No. 8

because of obtaining the needed specimen material and problems with grinding such large specimens to test specifications. Thus, there will be an unidentified uncertainty with the effect of increased stressed area. Fortunately, the polishing operation will commence after the second lift, which means the rough-ground elements will see the 5.5 MPa applied stress for only approximately 2 h. At this time, controlled polishing will begin removing large flaws, which should lead to an increase in the strength of the elements and longer lifetime at a given applied stress.

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Acknowledgments:

The author would like to acknowledge Floyd E. Roberts I11 for testing the samples. The author would also like to thank S.W. Freiman for helpful discussions.

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References

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15

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17

18

In oa ( oa in Pascals)

T i m e - t o - f a i l u r e diagram for Li20-Al2O3-Si02 glassc e r a m i c from d y n a m i c f a t i g u e d a t a ; F = 0.001 w i t h 90% c o n f i d e n c e limits.

Fig. 4.

analysis yielded a value for the ratio of stressed area during lifting to stressed area of the test specimens of approximately 980/1. Normally, the Weibull scaling law would be used to ascertain any difference the increased area would have on the strength by testing specimens with a larger stressed area. If any difference were found to exist, then adjustments could be made to the allowable stress which would reflect the change in strength. In the present case, if the test specimen diameters were double, this would yield an area ratio for the larger specimens to the specimens used in this study of 4/1. It was not felt that using a ratio of 4/1 would be indicative of the much larger ratio of 980/1. Using even larger specimens which would approach the higher ratio would be difficult at best

‘H. Scheidler and E. Rodek, ‘‘Li~0-Al~O3-SiO2 Glass-Ceramics,” Am. Ceram. Soc. Bull., 68 [ll] 1926-30 (1989). 2J. E. Ritter and J. A. Meisel, “Strength and Failure Predictions for Glass and Ceramics,” 1. Am. Ceram. Soc., 59 [ll-121 478-81 (1976). )A.G. Evans and H. Johnson, “Fracture Stress and Its Dependence on Slow Crack Growth,” J. Mater. Sci., 10 [2] 214-22 (1975). 4J. E. Ritter, “Engineering Design and Fatigue Failure of Brittle Materials’’; pp. 667-86 in Fracture Mechanics of Ceramics. Edited by R.C. Bradt, D. P. H. Hasselman, and F. F. Lange. Plenum Press, New York, 1978. SH.C. Chandan, R. C. Bradt, and G. E. Rindone, “Dynamic Fatigue of Float Glass,”I. Am. Ceram. Soc., 61 [5-61 207-10 (1978). 6K.Jakus, D. C. Coyne, and J. E. Ritter, ‘Xnalysis of Fatigue Data for Lifetime Predictions for Ceramic Materials,” J. Muter. Sci., 13 [lo] 2071-80 (1978). ’S. M. Wiederhorn, A. G . Evans, E. R. Fuller, and H. Johnson, ‘Application of Fracture Mechanics to Space-Shuttle Windows,”J. Am. Ceram. Soc., 57 [7] 319-23 (1974). 8K. K. Smyth and M. B. Magida, “Dynamic Fatigue of a Machinable Glass-Ceramic,” J. Am. Ceram. Soc., 66 [7] 500-505 (1982). 9S.W. Freiman, A. C. Gonzalez, and S. M. Wiederhorn, “Lifetime Predictions for Solar Glasses,”Am. Ceram. Soc. Bull., 63 [4] 597-99 (1984). ‘%Standard DIN 52292, Part 1, Testing of Glass And Glass Ceramics; Determination of the Bending Strength, Double-Ring Bending Test on FlatPlate Specimens with Small Test Areas, April 1984. “E.Y. Robinson, “Estimating Weibull Parameters for Materials,” NASA Report No. TM 33-580, Jet Propulsion Laboratory, Pasadena, CA, 1972. I2J. E. Ritter, N. Bandyopadhyay, and K. Janus, “Statistical Reproducibility of the Dynamic and Static Fatigue Experiments,”Am. Ceram. Soc. Bull., 60 [8] 798-806 (1981). l3P,R . Bevington, Data Analysis and Error Reduction in the Physical Sci17 ences; pp. 56-64. McGraw-Hill, New York, 1969.