The inherent brittleness of glass invariably leads to a large variability in strength data and a time dependence in strength. Leading rate plays a large role in strength values. Glass is found to be weaker when supporting loads over long periods of time as compared to glass which undergoes rapid leading. These properties complicate the structural design allowables for the utilization of glass components in an application such as Advanced X-ray Astrophysics Facility (AXAF). The test methodology to obtain parameters which can be used to predict the reliability and life time of Zerodur glass-ceramic which is to be used for the mirrors in the AXAF is described

Tucker, Dennis S.

English

NASA Technical Reports Server

! 
N09 - 21 7 5  3 
1988 
NASA/ASEE SUMMER FACULTY FELLOWSHIP PROGRAM 
MARSHALL SPACE FLIGHT CENTER 
THE UNIVERSITY OF ALABAMA 
DYNAMIC FATIGUE TESTING OF ZERODUR GLASS-CERAMIC 
Prepared by: 
Academic Rank: 
University and Department: 
0 
NASA/MSFC : 
Division : 
Branch : 
NASA Colleague: 
Contract No.: 
Laboratory: 
XXVII 
Dennis S. Tucker 
Assistant Professor 
Georgia Tech 
Materials and Processes 
Non-Metallic Materials 
Ceramics and Coatings 
Ron L. Nichols 
NGT-01-002-009 
The University of Alabama 
https://ntrs.nasa.gov/search.jsp?R=19890012382 2020-03-20T02:22:37+00:00Z
ABSTRACT 
The inherent brittleness of glass invariably leads to a 
large variability in strength data and a time dependence in 
strength. Loading rate plays a large role in strength values. 
Glass is found to be weaker when supporting loads over long 
periods of time as compared to glass which undergoes rapid 
loading. These properties complicate the structural design 
allowables for the utilization of glass components in an 
application such as the AXAF. 
This report describes the test methodology to obtain 
parameters which can be used to predict the reliability and 
lifetimes of Zerodur glass-ceramic which is to be used for the 
mirrors in the AXAF. 
X W I I - i  
ACKNOWLEDGEMENT 
The author wishes to acknowledgement the NASA/ASEE Summer 
Faculty Fellowship Program along with Mike Freeman, the 
University of Alabama director. 
To NASA counterpart Ronald L. Nichols of the Ceramics and 
Coatings Branch, Non-Metallic Materials Division, gratitude is 
offered. 
XxvII-ii 
List of Figures 
Figure No. 
1 
2 
3 
Caption 
Double Ring Fixture 
Design Diagram f o r  Polished 
ULE Glass 
Design Diagram f o r  Unpolished 
ULE Glass 
XWII-i i i 
INTRODUCTION 
The aim of this study is to provide the necessary data to 
predict the reliability and lifetime of Zerodur Glass-Ceramic 
which will be utilized as the material for the grazing incidence 
mirrors in the Advanced X-ray Astrophysics Facility (AXAF). 
Zerodur is a alumino-silica glass-ceramic containing 70 to 
7 8 %  by weight of high-temperature quartz as the crystalline 
material. The mean crystal size of the crystals is in the region 
of 50 to 55 NM. The crystalline phase has a negative expansion 
coefficient, while the vitreous phase has a positive expansion 
coefficient. This pratically balances out linear thermal 
expansion leading to long term stability even with temperature 
fluctuations. Zerodur, is therefore an ideal candidate for AXAFS 
and other applications such as mirror substrates mounts where 
changes in the material due to temperature variations could 
impair the quality of observations. The composition and 
mechanical, thermal and optical properties have been reported by 
Schott Glass Technologies, producers of Zerodur. However, the 
question of subcritical crack growth in this material has not 
been explored in detail. 
The design of the stresses in the AXAF mirrors is dictated 
by the ultimate strength of the material and a nominal value of 
1450 psi (MOR) is recommended by the manufacturer. This is a 
minimum value or worst case value. In glassy materials, the 
modulus of rupture depends upon primarily the surface condition 
of the material. In other words, a surface with a large number 
of flaws will have a lower strength than one with few on no 
flaws. The reduction in strength is caused by surface flaws 
which concentrate applied stresses leading to failure at much 
lower than theoretical applied loads. These flaws can be 
introduced by machining or normal handling. Thus one method to 
increase strength is to polish the surface thereby removing 
surface flaws. Schott Glass reports an MOR of approximately 
11,000 psi with a failure probability of 0.5% when the surface is 
polished with 600 grit polishing paper. Even higher strengths 
could be expected with a finer polishing medium. Even if one 
were to accept a value in the range of 11,000 psi one must 
consider the effects of delayed failure under constant applied 
loads. Uner these loads, even if small, failure can occur after 
a given period of time has passed. This has been attributed to 
the mechanism of stress corrosion whereby water molecules from a 
humid environment enhance crack growth. Cracks continue to grow 
over a period of time until catastrophic failure occurs. 
j) 
XXVII-1 
Therefore one needs a reliable method of predicting life 
times under applied loads. The fatigue parameters for making 
lifetime predictions must be obtained under the service 
environment, if at all possible and can be obtained from one of 
three types of experiments: crack velocity, static fatigue and 
dynamic fatigue. 
Crack velocity can be measured directly as a function of the 
stress intensity factor on speci ens specifically designed for 
fracture mechanics experiments? These speicmens contain a 
macroscopic crack which allows accurate measurenent of crack 
velocity and stress intensity factor. For purposes of failure 
prediciton crack velocity data is not as reliable as that from 
static or dynamic fatigue strength experiments because data from 
large, preformed cracks is not necessarily relevent to th 
propagation of microscopic cracks present in brittle materials. 5 
Static fatiue data is generally obtained by measuring the 
time to failure 08 a large number of samples at several constant 
applied stresses. 
Dynamic fatigue is generated by measuring fracture strength 
as a function of stress rate.3 For this study dynamic fatigue 
was chosen to develop the time-to-failure equation necessary to a 
design diagram. This concept will be developed fully in the 
Technical Discussion section. 
Due to problems in obtaining samples in time to perform the 
actual experiments no data will be presented in the report. 
Instead attention will be paid to theoretical development of the 
design diagram and the proposed experimental procedure to obtain 
the necessary data for the diagram. 
Technical Discussion 
Initial Strength 
Modulus of Rupture (MOR) will be determined using the double 
ring bending strength test meth~d.~ Figure 1 is a graphical 
representation of this technique. In this case a disc shaped 
specimen is loaded between two concentric rings. For limited 
forces, a tensile stress field will be set up in the central 
region of the convexly bent speicmen surface. Outside the load 
ring the radial and tangential stresses in the specimen decrease 
toward the edge, so that the possibility of fracture there is 
small. By increasing the force the tensile stress in the 
specimen center is increased at a constant rate until fracture 
occurs, with the expectation that the fracture is initiated in 
the region of the surface subjected to the maximum stress, 
underneath the load ring. 
XXVII-2 
The major advantage of this technique, as compared to techniques 
such as 3 and 4 point bending, is the elimination of edge 
effects. 
To calculate the rate of increase of the bending stress in 
circular specimens the following is applicable: 
Where: 
A F = Increase of test force, measured in the time interval 
near the fracture initiation 
A S = Specimen thickness 
1.08 = Numerical constant related to the load ring and 
.. 
specimen support ring diameters and Poisson's Ratio 
The bending strength (as ) belonging to the maximum force 
(Fmax) from equation (1) is: 0 
Gz = 1.08 Fmax 
S2 
Where : 
%8 = bending strength 
Fmax = greatest force 
S = specimen thickness 
Weibull Statistics 
In order to determine the distributions of strength Weibull- 
plots will be utilized. Fracture of brittle materials can be 
regarded as a statistical process, since the material has a 
distribution of flaw sizes. Weibull' described the mathematics 
for this process in terms of probability functions. His 
equations can take forms: 
XXVII-3 
or 
F = l - e x p  (4) 
V O  
where: 
F = probability that the material will fail at stress 
ru,ro = constants which describe the distribution 
= constant (Weibull modulus) 
Equation ( 3 )  is the two-parameter model and represents an 
unbounded distribution. Equation ( 4 )  is the three-parameter 
model and represents a lower bounded distribution. 
A number of dynamic fatigue studies of glass and glass- 
ceramics have shown the two-parameters model to be acceptable in 
describi g the flaw population and it's relation to material 
failure. 7 1  Therefore, in this study equation ( 3 )  will be a 
ut il i zed. 
One can rearrange equation ( 3 )  to obtain a more workable 
equation. Starting with equation ( 3 )  
F = 1 - exp (-5 J" 
1 - F = exp ( -5  )* 
or 
Taking In of both sides of 
( 5 )  
(5) 
XXVII-4 
In I+l=f q d- )” 
and taking In again; 
Where : 
Q - =  
And : 
F =  
Where : 
/n= 
A J =  
Thus a 
of m 
Failure stress (MOR) 
Rank of sample in terms of strength 
Number of samples tested 
plot of In ( In 1 ) versus 1 n T  will yield a slope 
1-F . The slope indicates the distribution of strengths. As 
he slope (h) increases the distribution narrows, i.e. there is 
less scatter in the results. 
Lifetime Prediciton Equation 
Weibull statistics can be combined with data on static or 
dynamic fatigue to yield predictions of the lifetime of rittle 
materials under various environmental conditions. ’ The 
derivation of this equation combines elements of fracture 
mechanics theory and Weibull statistics. 
The rate of crackgrowth in a material can be expressed as a 
power law funciton: 
V = = AKI 
& Where: 
a = crack length 
KI = stress intensity factor 
A, N = constant for a given material and environmental 
XXVII-5 
The stress intensity factor can be expressed as: 
K I =  VY\ra (9) 
Where: 
a = crack length 
v = applied stress 
Y = crack geometry parameter which is constant for a 
given material 
Combining equations ( 8 )  and (9) to eliminate KI yields: 
A =  A T N y N a %  (10) 7
For the case of constant applied stress ( rb- ) :
or 
T o  obtain the material lifetime, this expression is 
integrated over the initial-to-final crack length and from the 
time the stress was applied ( # = o )  tothe time of fracture 
XXVII-6 
which yields: 
Rearranging equation (9): 
and substituting into equation (13): 
The stress intensity factor when fracture occurs, KIc, and 
the fracture stress v& is the stress at which fracture would 
occur in an inert enviornment unaffected by subcritical crack 
growth ( Ti 1 
XXVII-7 
Substituting into equation (14): 
Therefore one can write: 
05) 
Solving for 2&: 
Where: 
B =  2 
Taking /Iv of of both sides of equation 
Rearrangement of Equation (7) yields: 
or 
XWII-8 
In an enviornment where no subcritical flaw grow occurs 
prior to fracture one can write equation (19) in terms of inert 
strength ( ) i.e. 
Substitution of equation (20) into equation (18) for 1/LI Vi 
yields : 
Where: 
&& represents the time required for a flaw to grow from an initial subcritical s i z e  to dimensions critical for catastrophic 
crack propagation leading to material failure. 
And : 
B and N are constants which characterize the subcritical flaw 
growth. 
Determination of B and N 
Evans 10 derived an expression relating the strength of a 
material (r ) to the stressing rate ( &  ) at constant 
temperature for the case of subcritical flaw growth as follows: 
XXVII-9 
Dividing by/& i 
* , =  +~r & 
Since = V (crack velocity) : 
Av = v 
Now, we know that, 
Therefore we can write: 
AK; 
We also know: 
or 
K< = y d v d a q a  
Substituting this expression into equaiton (26) gives: 
XXVII-10 
Integrating over the extent of crack growth from an intial stress 
of zero to a final failure stress or obtains: 
which yields: 
the former can be dropped leading to: 
The intial flaw size can be taken as: 
or 
Substituting equation (31) into (30) for a; yields: 
XXVII-11 
Can rewrite equation (32) as: 
where: 
Taking In of both sides of equation (33): 
I (N + 1) 1 N Y  = 1 ~ b  (N + 1) + (N - 2 ) S g  + l ~ e  
or 
I (34) = 1N L B  (N + 1) + (N - 2)CJ + l N +  
/v-f / 
I Rewriting Equation (34) : 
lN[B (N + l u  + (N - 2) + 1MV- (35) 
N4 I 
1~Gj  = 
where: 
a, = y 
N + l  
XXVII-12 
Thus, to obtain values for B and N, one fits fracture stress 
and stress rate data for samples tested in humid enviornment to a 
straight line g iven by equation (36), that is a plot versus 
l ~ +  . To ensure that the values of B and N are reliable one 
needs to test over a wide range of stress rates (i.e. over 
several orders of magnitude). The inert strength ( V# ) should 
be obtained at high enough stress rates to insure that crack 
growth is independent of environmental (Le. no stress corrosion 
at the crack tip is occurring). 
Design Diagrams 
Once the values of the constants B and N are determined, the 
time-to-failure for various values of failure probability (F) and 
applied stress (Ta) can be computed. Figure 2 shows an exmaple 
of a design diagram for polished ULE glass at F = 0.001, 0.01 and 
0.20. Comparing this to a diagram for unpolished ULE glass 
(Figure 3 )  one can note decrease in strength at a given time 
period (Ex. 10 yrs.) as compared to polished glass. This infers 
that at a given probability of failure the polished glass should 
withstand an applied stress for a longer period of t me. For 
examples at F = 0.01 and an applied stress of 24 x 10' MPa the 
polished material will fail in one hour whereas the Gnpolished 
fails in one second. a - 
Experimental Approach 
The investigation will be carried out in three phases. 
Phase I- Residual Stress Investigation 
In order to determine the effects of residual stresses on 
the modulus of rupture of Zerodur, 10 samples with ground surfae 
finish will be annealed and compared with 10 duplicate unannealed 
samples using the double ring bend test method. All tests will 
be performed at a stress rate of 290 psi/sec, which is in 
accordance with test standard DIN 52292. 
Phase I1 - Generation of Design Diagram 
Weibull plots [ l ~  ( 1 r J h  ) vs. 1~ Q'& 3 will be sade in order 
to determine the strength distributions for three types of sample 
preparation (AS cut, ground, and ground with acid etch). The 
etching technique is to be supplied by Schott Glass Co. MOR data 
will be obtained at four different stress rates, 3.5 x 
MPa/s, 2.7 x 10 -2 MPa/s, 2 MPa/s and 200 MPa/s. Thirty five 
samples will be tested. The final stress at each stress rate 
will be used to determine the inert strength. In this instanc 
samples will be heated at 15OoC for 24 hours in a dry N 
environment and put in a vacuum dessicator before testing. 
8 
0 
XXVII-13 
Each sample will be exposed to flowing dry initrogen for fifteen 
minutes before testing, in a plexiglass chamber Pitted to the 
testing machine. To insure that this stress rate leads to crack 
growth independent of environment, t.en samples will be placed in 
distilled water for 2 4  hours and then tested at 200 MPa/s. The 
sample to be tested at the three lower stress rates will be 
stored at ambient conditions (T = 25OC, R.H. = 50%) for at least 
one week before testing. 
Using the time-to-failure equation developed in this paper, 
a time-to-failure diagram will bc developed for each sample 
preparation. That is a separate diagram for the as cut, ground, 
and ground and acid etched samples. 
Phase 111- Verficiation of Diagrams 
In order to verify the three time-to-failure diagrams, 
applied stress values which intersect the F = 0.005 probability 
curve corresponding to time-to-failures of 1 minute, 1 hour, and 
1 day will be selected and used to test 10 specimens each using 
the double ring test method. 
XXVII-14 
Bibliography 
1. S. M. Wiederhorn, "Subcr i t ica l  Crack Growth i n  C e r a m i c s , I l  pp 
613-46 i n  Frac ture  Mechanics of C e r a m i c s , V o l .  2, ed. by R. 
C. Brandt ,  D. P. H. Hasselman, and F. F. Lange, Plenum 
Press, New York (1974). 
2. J. E. R i t t e r ,  Jr., IIEngineering Design and F a t i g u e  F a i l u r e  
of B r i t t l e  Materials,n pp. 667-686 i n  Frac ture  Mechanics of 
-------, C e r m a i c s  V o l .  4, Ed. by R. C. B rad t ,  D. P. H . Hasselman, 
and F. F. Lange, Plenum Press, New York (1978). 
3 .  J. E. R i t t e r ,  Jr. and C. L. Sherburne ,  IIDynamic and S t a t i c  
Fat igue of Sil icate Glasses," J. of Am. C e r a m .  SOC., 54 601- 
05, (1971). 
4. " T e s t i n g  of G l a s s  and G l a s s  Ceramics;  D e t e r m i n a t i o n  of  
Bending Strengths ,"  German Standard DK 66.151: 650.174, D I N  
52292 P a r t  1 Apri l  1984. 
5. W. W e i b u l l ,  "A S t a t i s t i c a l  Theory  of  t h e  S t r e n g t h  o f  
Mater ia ls ,"  Roy. Swed. Acad. of Eng. S c i .  Proc.  151, 1-45 
(1939). 
------- ----- - 
0 6. R. J. Char l e s .  IIDynamic F a t i g u e  of  G l a s s , I l  J. of Appl. Phys. 
29 [12] 1657-62, (1958). -
7. K. K. Smyth  and  M .  B. Magida ,  IIDynamic F a t i g u e  of  a 
Machinable  Glass-Ceramic,It J. Am. C e r a m .  SOC. 66 [7], 500- 
505 (1983). - 
8. D. C. C r a m n e r  and  D. J. Speece, I I D y n a m i c  F a t i g u e  of  
Ultralow-Expansion G l a s s  f o r  Space Mirrors,I@ Report SD-TR- 
86-49, Space D i v . ,  Airforce Systems Command, Aug. 
S. M. Wiederhorn, ---------- F r a c t u r e  1977 Ed. D. M. R. T a p l i n ,  Vo1.3, 
pp. 893-901, Waterloo Univ. Press, Waterloo, Can. (1977). 
1986. 
9. 
1 0 .  Evans, A. G . ,  I n t .  J. Fract. 1 0  251-259 (1974). -
XXVII-15 
. .  
Figure 1 
ORlGlNAL PAGE IS 
OF POOR QUALITY 
XXVII-16 
ORIGINAL PAGE IS 
OF POOR QUALITY 
I n  ua (applied slress. MPa) 
Figure 2 
IO year 
1 year 
I day 
1 hr 
I min 
I sec 
i i  
X X V I  I - 17 
- 10 
10 
ORIGINAL PAGE IS 
OF POOR QUALITY 
\\\! 
1 I I .  I 
9 3 MPa ( 1  3 ksi) 
5 8 MPa (0 8 ksi) 
4.2 MPa (0 6 ksi) 
" I 
! 
I 
I 
\ \ I \ ;  I 
I 
Oyear 
year 
day 
hr 
min 
sec 
(n ua (applied stress. MPa) 
F i g u r e  3 
X X V I  1-18 


Dynamic fatigue testing of Zerodur glass-ceramic

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