NASA Technical Memorandum 4185

Fracture Toughness and Crack Growth of Zerodur

Michael J. Viens

APRIL 1990

,,_ [c f
.... {i

!i!: !iiiiii_4__

L" i I i

ii: _ 7

2

L::::,::....

x

i:t

...... !r,Ti= ?_ Z

i rl it iiii_i--_

ii!!i i!!!!i_i_i i!!_i!i

!ill

.... ii ii

}---.

=

i_Zs--_t--

i

...... #

=

. i_i i __

= :=

X; i :

= ....

ig

=

=

]

_2gl

Zz_: ::

i

} _.: i_

i- 1_: "

==

7_- Z

==

_:_

TE

_Z
NASA Technical Memorandum 4185

Fracture Toughness and

Crack Growth of Zerodur

Michael J. Viens

Goddard Space Flight Center

Greenbelt, Maryland

National Aeronaut,ssand

Space Administration

Office of Management

Scientific and Technical

Information Division

1990

TABLE OF CONTENTS

ABSTRACT ........................................... 1

INTRODUCTION ....................................... I

THEORETICAL BACKGROUND ............................. 2

TEST MATERIAL ....................................... 6

TEST SPECIMENS AND PROCEDURE ......................... 6

RESULTS ............................................ 8

DISCUSSION ......................................... 13

CONCLUSIONS ....................................... 16

REFERENCES ........................................ 17

ADDENDUM ......................................... 19

PRECEDING PAGE BLANK NOT FILMED

iii

FRACTURE TOUGHNESS AND CRACK GROWTH PROPERTIES OF ZERODUR

ABSTRACT

The fracture toughness and crack growth parameters of Zerodurl, a low expansion glass ceramic

material, were determined. The fracture toughness was determined using indentation techniques

and was found to be 0.9 MPa.m 1/2. The crack growth parameters were determined using

indented biaxial specimens subjected to static and dynamic loading in an aqueous environment.

The crack growth parameters n and In(B) were found to be 30.7 and -6.837, respectively. The

crack growth parameters were also determined using indented biaxial specimens subjected to

dynamic loading in an ambient 50% relative humidity environment. The crack growth

parameters n and In(B) at 50% relative humidity were found to be 59.3 and -17.51, respectively.

INTRODUCTION

Zerodurl is an engineered lithium aluminosilicate glass-ceramic material which is ideal for use

as telescope mirrors due to its homogeneity and low coefficient of thermal expansion [1]. The

use of Zerodur is anticipated in the Advanced X-ray Astrophysics Facility (AXAF) and the Far

Ultraviolet Spectroscopic Explorer (FUSE). Zerodur is also, at present, the pre-phase B baseline

mirror material for the Orbiting Solar Laboratory (OSL). In order to conform to fracture control

guidelines [2] the components made from the Zerodur material must be either proof tested and/or

analytically shown to be capable of withstanding the anticipated loading. The work reported

here was initiated to supply the necessary material dependent crack growth data to enable

analytical predictions of component lifetimes to satisfy the safe-life design criteria.

To demonstrate safe-life, the initial flaw size, the flaw growth rate and the critical flaw size must

be known. The initial flaw size is dependent on the manufacturing processes used to produce the

component. The strength controlling flaw could be either a surface flaw created during

machining the component or volume flaws created during manufacturing of the bulk material.

The strength controlling flaws in glass and ceramic components are generally one to two orders

of magnitude smaller in size than those that can be located with conventional non-destructive

inspection techniques. Because the inherent flaw sizes cannot be measured directly, the initial

condition of the component cannot be directly determined (except for very large flaws). The

flaw population must be determined indirectly using test coupons prepared with the same surface

finish(es) as the flight component. A large population of coupons must be tested to accurately

determine the spectrum of flaw sizes created by a given fmisl_ng technique. The flaw size then

used as the initial flaw size of the component is statistically made based on test results and some

acceptable level of probability. The initial flaw size must be determined on a case by case basis

and no inference as to initial flaw size should be drawn from this report.

The crack growth observed in glass and ceramic materials is known to be assisted by the

presence of ambient moisture. To calculate the amount of growth a flaw will under go, the rate

at which the flaw will grow in the service environment and the applied stress levels must be

known.

1 Short Optical Glass Inc., Duryea, PA
Thefracture toughness of the material must also be known to demonstrate safe-life. The fracture

toughness of the material will dictate how much stress a component can withstand for a given

flaw size, or will predict the flaw size that will induce failure for a given stress.

The primary purpose of the testing performed for this report was to determine the crack growth

rate in Zerodur. The fracture toughness has also been determined using indentation techniques.

While specimens were tested in the as-received condition to quantify the initial flaw size

distribution, no attempt should be made to use the strength of the as-received specimens as a

design parameter.

THEORETICAL BACKGROUND

Biaxial Loading

The use of biaxial loading to interrogate glass and ceramic materials has been well documented

in recent years [3-5]. The primary advantage of this technique is the specimen cost. A cylinder

with the desired diameter can be core drilled from bulk material and the disk specimens sliced

off the cylinder. The specimens can then be polished to the desired surface finish. Very little

attention needs to be paid to the specimen edges because the creation of the maximum stress at

the center of the specimen prevents any failures from edge flaws, as is observed in three or four

point bend specimens.

The stress on the tensile surface of the test specimens (_) is given as [3]:

o = 3P[2(l+v)ln(a/b)+(l-v)(a2-b2)/R2)l/4(_)t 2 (1)

where P is the applied load in newtons, v is the Poisson's ratio, t is the specimen thickness, a is

the support ring radius, b is the loading ring radius and R is the specimen radius. The specimen

dimensions are in millimeters.

The strength data at each test condition were fitted to a two parameter Weibull relationship [6]:

In In [1/(I-F)] = m ln[of/Oo] (2)

where the value tyf is used to denote the specimen strength at failure, m and (to are the Weibull

modulus and Weibull scale parameter, respectively. The Weibull parameters are determined by

a least squares linear regression of Eq. (2) where F is the cumulative failure probability def-med

as, F=(i+0.5)/J (i is the speeimen rank and J is the total number of specimens tested). The

Weibull median strength is the fracture strength corresponding to a failure probability of 0.5 and

the Weibull modulus represents the scatter in the specimen strengths.

The strength of large components can be predicted based on small specimen strengths by

accounting for the difference in size or area stressed. The relationship is given as:

O1/_2 =(A2/A 1)l/m (3)
where A is the area being interrogated and m is the Weibull modulus, the subscripts 1 and 2

represent the large component and test specimens, respectively. Equation (3) accounts only for

surface flaws. If volume flaws are the strength controlling defects then the volume and the stress

distribution in that volume must be taken into account.

Indentation Theory

The use of indenters (Knoop and Vickers) to create well deemed flaw systems (Figure 1) in glass

and ceramic components has been well documented [7-14]. The variation in strength of

specimens with indentation flaws is much lower than that of specimens with as-machined

surfaces and is thus ideally suited for the introduction of flaws for crack growth testing. The

flaws created using the indentation technique are on the scale of the as machined flaws.

The response of brittle materials when indented with a Vickers indenter is the creation of a well

defined crack system driven by contact residual stress. The contact residual stress is created by a

strain mismatch between the plastically deformed material adjacent to the indentation site and

the elastically deformed surrounding matrix. During the indentation event two crack systems are

formed; radial and lateral. The radial cracks grow perpendicular to the surface and are the flaws

from which fracture occurs. The lateral flaws form at the base of the plastic zone and grow

parallel to the surface.

2% -I

Figure 1. Idealized model of damage created by indentation with Vickers indenter. The

radial crack length is Co and the lateral crack length is ct.. The darkened area beneath the

indentation represents the plastic zone end <;a.is the far field applied stress (after

reference [91).
Fracture Toughness

Dhect Crack Method

The stress intensity at the tip of the radial crack created during indentation is determined by

modelling the indentation stress field and the radial crack system as a center loaded crack. It can

be shown that the radial crack dimension after indentation (Co) is [l 0]:

Co = [)_rP/KIc]2D (4)

where P is the indenter load, KIc is the critical stress intensity factor (fracture toughness) and Zr

is the residual stress constant that is dependent on indenter geometry and material properties.

The Zr factor has been calibrated using a wide range of ceramic materials and was found to be

equal to 0.016 (E/H) 1/2 where E is the elastic modulus and H is the hardness. Rearranging

equation (4) yields the critical stress intensity as [10]:

KIC = 0.016[E/H 11/2[P/co3/2] (5)

Note that the [P/co3/2] term is a material constant. This value should be constant in the absence

of a far field residual stress in tile material being tested.

Strength Method

The stress intensity at the tip of a radial crack may be found by sununing the stress intensity due

to residual and applied stresses. The post indentation strength is calculated at the point where

crack instability occurs: KI=KIC and dKi/dc>0. At this point the critical stress intensity is found

to be [11]:

KIC = 11 [E/H]I/8 [qfpl/313/4 (6)

where r1 is a calibration constant that also incorporates the flax,,' geometry, assumed to be an ideal

halfpenny shape. The 1I constant has been calibrated to be 0.59 (_+0.12) [11].

Crack Growth Parameters

Static Fatigue

Crack growth of glass and ceramic materials occurs when statically loaded in an aggressive

environment. The crack growth can be expressed as a power function of the stress intensity

factor (KI) and is given as [14-17]:

v = v0 (KI/KIc) n (7)

where v is the crack velocity, and v0 & n are material and environmental crack growth

constants. From the power law relationship an expression for the time to failure (tf) can be

derived in terms of the applied stress ((_a), and is given as:

4
tf = B oi n-2 Oa "n

B = 2/Iv0 y2 (n-2) KIC(-2)]

(8)

(8a)

where oi is the strength in the absence of subcritical crack growth or inert strength and Y is a

flaw geometry factor taken to be x for surface flaws.

The crack growth parameters n and B are found using the median time to failure and

corresponding applied stress. The use of median values are convenient as they represent the thne

to failure at a 50% failure probability. A least squares linear regression analysis is performed on

the natural logs of the median time to failure and the corresponding applied stress. The slope is

the n parameter and the intercept is 03 oin-2].

Dynamic Fatigue

Dynamic fatigue of glass and ceramic materials refers to the decrease in the observed strength as

a function of decreasing stressing rate. The relationship between failure stress (of) and stressing

rate (o) is given as:

of n+l = B (n+l) (5in-2 (5 (9)

The crack growth parameters B and n are determined as described above for static fatigue, using

the median failure stress and the associated stressing rate.

Fatigue of Indentation Flaws

.It has been shown that the fatigue parameters determined using indentation flaws differ from

those determined when the residual stress field associated with the indentation event is removed

by annealing., The relationship between the apparent fatigue exponent (n') and actual fatigue

exponent (n) is given as [17]:

n= 1.31 n' (10)

The primed notation designates the value determined in the presence of the residual stress. The

relationship between the B and B ' values is not as straight forward as that of n. The true value

of the fatigue parameter v0 as a function of indentation load is given as [ 17]:

v o = [2.84 n' 0.462 Om n' Cm]/X,

k' = B' (n' +1) Om (n' -2)

(11)

(lla)

where Om is the inert strength for a given indentation load and em is the corresponding radial

crack size at failure and taken to be 2.5 times larger than Co. The value for Om is taken as the

inert strength in equations (8) and (9). The true B parameter can be determined by substituting

values obtained in equations (I0) and (11) into equation (8a).

5
TEST MATERIAL

Zerodur is an opaque, engineered glass-ceramic material based on a lithium-aluminosilicate

formulation with the crystalline phase consisting of metastable solid solutions of high quartz

structure. Zerodur is 70 to 78% by weight crystalline phase with crystals generally 50 to 55

nanometers in size. The material composition is given in Table 1.

Table 1. Zerodur Composition*

Composition

wt% mol%

SiO2 55.4 63.9

A1203 25.4 17.2

Li20 3.7 8.5

Na20 0.2 0.2

K20 0.6 0.5

MgO 1.0 1.7

ZnO 1.6 1.3

P205 7.2 3.5

TiO2 2.3 2.0

ZrO2 1.8 1.0

AsO3 0.6 0.2

* Ref. [19]

Table 2. Zerodur Mechanical Properties*

Modulus of Elasticity (E,GPa)

Poisson's Ratio (v)

Density (p,g/cm 3)

Hardness, Knoop (H, GPa)

Strength (MPal

91.0

0.24

2.53

6.18

90.0**

* Manufacturers data.

** 0.5 cm2 test area, loaded at 2 MPa/sec, No. 600

loose grain tinish, 5% failure probabifity.

The manufacture of the Zerodur material requires tight control of a nucleation and crystallization

process which creates the material's microstructure. Annealing of sodalime glass specimens

with indentation flaws has been shown to remove the localized residual stress created during the

indentation event [15]. Annealing of the Zerodur specimens to remove the indentation residual

stress field might have altered this microstructure, so was not performed.

Zerodur has very good thermal stability. Various thermal expansion classes are available with

the most stable being expansion class 1 which has a thermal expansion coefficient of 0 +

0.05ppm/K for 0 to 50oC.

Zerodur has good resistance to chemical attack. Zerodur resists attack by most acids (with

exception of hydrofluoric acid), alkalis and salts at room temperature. Sulfuric acid does attack

Zerodur at higher temperatures.

TEST SPECIMENS AND PROCEDURE

Zerodur disks (38.1 nun dia x 1.78 mm) were used in this study. The faces were polished to a

commercial grade finish by the manufacturerl. All spechnens were randomized prior to testing

to avoid any systematic error due to manufacturing processes.

1 Short Optical Glass Inc., Duryea, PA

6
Indentation

A Vickers diamond indenter was used to introduce indentations into the Zerodur specimens at

loads ranging from 300 to 2000 grams. The hardness tester2 used to introduce indentations into

the specimens had a constant loading rate of 6 mm]min and remained in contact for 20 seconds.

Crack lengths were measured one hour after the indentation event on a Nikon Epiphot

microscope at 1000 times magnification.

The indents were placed in the center of the tensile side of the specimens. The center of the

specimen was located by placing the specimen on a template and placing a small fiducial dot

in the center of the compressive face. The dot was a dry transfer lettering bullet. The center of

the specimen was then located directly under the indenter. This fiducial dot also insured that the

center of the specimen, and indentation, were located at the center of the loading ring. The test

specimens were allowed to sit in ambient conditions for one hour prior to strength testing.

Dynamic Testing

A biaxial test fixture mounted on a servo hydraulic test machine3 was used for all dynamic

strength testing. All specimens were tested with a ring on ring loading configuration (Figure 2).

The loading and support rings were 5.8 and 25.4 mm diameter thrust bearings, respectively.

The use of the thrust bearings to support the specimens was preferred over machined rings for

several reasons. The use of thrust bearings was felt to lessen the amount of friction on the

specimen surface, there is a high degree of dimensional consistency between bearings and the

cost of the thrust bearings was much less than the cost of machining several rings The test

f'txtures used were easily retrofitted using the thrust bearing races. The smaller thrust bearings

were used as loading rings to avoid any effect that might arise at the periphery of a ground ball

and to provide dimensional consistency between loading fixtures.

Loading Shaft

I/4" diameter ball

Bearing Race

l_oading Thrust Bearing

Test Specimen

SuppOrt TboJst Bearing

Bearing Race

Cotton Wick

Moisture Reservoir

Plastic Tubing

i

.¢=..

Figure 2. Schematic of test configuration.

Tukon Tester Model FB, Wilson Instruments, Binghamton, NY

Instron 1350, lnstron Corp., Canton, MA

7
The inert strength of the Zerodur specimens was determined for both as-received and indented

specimens. The indentation loads were 300, 500, 1000 and 2000 grams. A minimum of 10

specimens was tested at each condition. The inert strength specimens were tested in air at a

loading rate of 2 millimeters/second which resulted in stressing rates of approximately 2000

MPa/sec. This loading rate was felt to be sufficient to limit the environmentally assisted crack

growth.

The load was recorded using a data acquisition and plotting system4. The load was monitored

with a piezoelectric load cell5 at loading rates greater than 0.2 mm/sec and with a standard strain

gauged load cell at loading rates less than 0.2 mm]sec. The slowest loading rate used was 5

ram/hr.

The dynamic fatigue parameters were determined for a water environment using specimens with

500 and 1000 gram Vickers indentations. The water environment was created by placing a drop

of deionized water over the indentation prior to testing. The dynamic fatigue parameter was also

determined for 50% relative humidity (RH) using specimens with 1000 gram indentations. The

50% RH was provided by the ambient lab enviromnent.

Static Testing

The static fatigue testing reported here used only two fixtures. The f'txtures used for static

fatigue testing were identical to that used for the dynamic fatigue testing but had a weight pan

attached to the loading shaft. It was conf'trmed that the applied stress on the tensile surface

agreed with theory using a strain gauged Zerodur specimen. The agreement with theory was

within 1 percent for both f'txtures.

A target stress was selected and the desired weight calculated using Eq. (1) and the individual

specimen thickness. The load was applied with lead blocks and lead shot. The lead shot was

weighed out to the precise load required to induce the target stress. The load was applied to the

specimen via a weight pan. When specimen failure occurred the weight pan tripped a

microswitch and the failure time was automatically recorded by a personal computer6.

The static fatigue specimens were tested in a deionized water environment. The water was

wicked to the specimen surface from a reservoir located directly beneath the tensile surface. The

reservoir was replenished as required via plastic tubing.

RESULTS

Hardness

The indentation diagonal sizes are presented in Table 3. The hardness, calculated as twice the

applied load divided by the indentation diagonal squared (the factor of two represents the

Vickers indenter geometry), was found to decrease with increasing indenter load. This variation

of hardness with increasing load has been previously noted with sodalime glass [21]. The mean

hardness value was found to be 6.37 GPa. This value agrees with the hardness value provided by

the manufacturer (6.2 GPa).

4

5

6

Hewlett Packard Measurement Plotting System (HP-7090A), Hewlett-Packard Co., Rockville MD

Kistler Instrument Corp., Amherst NY

COMPAQ, COMPAQ Computer Corp.,
Table 3. Indentation Dimensional Measurements

Indentation Indentation Hardness Crack Fracture*

Load Diagonal Length Toughness

(grams) (urn) (GPa) (Co,um) (MPa-m 1/2)

300 29.2(1.1) 6.89 32.1(1.8) 0.941

500 39.2(0.9) 6.39 46.3(1.6) 0.940

1000 56.3( I. 1) 6.20 74.7(3.2) 0.931

2000 80.8(2.9) 6.01 129.4(9.8) 0. 830

* Calculated using equation (5)

Numbers in parenthesis are standard deviations.

Inert Strength

The inert strength data is presented in Table 4. The as-received strength value determined in this

study can be compared to previously reported Zerodur strength (90 MPa, Table 2) by first

calculating the strength at a 5% failure probability using Eq. (2) and then scaling the 5% failure

probability strength to the appropriate test area using Eq. (3). Taking (ro=197.9 MPa and m=3.2

(Table 4) the as-received strength at a 5% failure probability is 78.2 MPa. Then scaling from the

0.264 cm2 area used in this study is to the 0.5cm2 area previously used the strength is 64.1 MPa.

The lower strength determined from this study indicates that the surface finish was slightly better

on the previously tested specimens.

Table 4. Inert Strength

Indent Specimens Median Mean KIC*

Load Tested Strenglh Strength

(grams) (MPa) (MPa) (MPa-m 1/2)

Weibull

Paramete_

(_o m

(MPa)

As-received 18 154.9 175.2(69.) 197.9 3.2

300 10 105.9 107.2(5.6) 1.101 109.9 21.5

500 10 86.6 87.7(2.5) 1.092 89.1 36.2

1000 20 72.0 71.0(5.3) 1.141 73.5 15.6

2000 10 57.8 57.9(2.7) 1.156 59.2 24.3

* Calculated using equation (6)

The numbers in parenthesis represent I standard deviation

The mean and standard deviation data are plotted in Figure 3 on a In-In plot. The line through

the data in Figure 3 has a slope of-1/3 with the [ofpl/3] term taken to be 152.7 MPaNI/3.

Indentation theory predicts that the strength of an indented material, in the absence of any far

field residual stress, will vary as the indentation load to the 1/3 power. The test results are in

good agreement with theory.

9
5.50

el

v

m

Io

(n

o

It.

t_a

5

5.40

5.30

5.20

5.10

5.00

4.90

4.80

4.70

4.60

4.50

4.40-

4.30

4.20

4.10

4.00

3.go

3.80

3.70

3.60

0.00

! I I 1 | I I l I I I I ! I

0.40 0.80 1.20 1.60 2.00 2.40 2.80

[JN[Indontot_onLoad (N)]

Figure 3. Inert specimen strength of the Zerodur as a function of the indentation load.

The shaded area to the left represents the mean and standard deviation of the as-received

specimen strength. The line through the data has a theoretical slope of -I/3 with the

constant (oP I/3) value taken to be 152.7 MpaNt/3.

Fracture Toughness

The fracture toughness determined using the direct crack method and the strength method were

calculated with equations (5) and (6), respectively, and are presented in Tables 3 and 4. The

average fracture toughness determined by the direct crack method was 0.911 MPa-m 1/2 and the

average fracture toughness determined from the strength method was 1.123 MPa-m 1/2. These

fracture toughness values are greater than previously determined using a large crack

measurement technique (0.844 MPa.m 1/2) [22].

Fatigue Testing

The static fatigue median value data and associated standard deviations are plotted in Figure 4.

The fatigue parameters calculated from the median value analysis of the static fatigue data are

listed in Table 5. The data shown in Figure 4 at the 25 MPa applied stress was not used to

calculate the fatigue parameters. Testing at this stress level is, at the time of this writing, still

under way (three specimens failed prior to predicted median time to failure and two, currently

being tested, have exee._ed median time to failure).

10
24.00

@

Q

v

w

s)

..J

0

w

g

5

22.00

20.00

18.00 -

16.01 -

14.00

12.00

10.00 -

8.00

6.00

4.00

2.00 -

i

0.00 i

.3.10

.6

÷

+ i

++IT

I I I I I

3.30 3.50 3.70

LNFAPPUEO LOAD (Mpo)]

Figure 4. Static fatigue data for Zerodur with 9.8 newton indentations in a water

environment. The line through the data was best fit to the median values (triangles). The

error bars represent one standard deviation and the crosses represent individual failures.

The specimens at 25 Mpa were not used in the regression analysis.

The results of dynamic fatigue testing using median value analysis are presented in Figures 5 and

6 and the calculated fatigue parameters are listed in Table 5. The fatigue parameter value listed

for the 1000 gram indentations tested in 50% relative humidity was calculated only from

specimen strengths when the rate of crack growth was dominated by the ambient moisture.

These data are at the four lower stressing rates shown in Figure 6. The crack growth at the three

higher stressing rates in Figure 6 is not completely controlled by ambient moisture.

Table 5. Apparent Fatigue Parameters Determined from Median Values

Indentation Loading Environment Fatigue Parameters

Load ln(B' )

(grams)

n ¢

500 Dynamic Water -2.192 23.6

1000 Dynamic Water -3.631 23.5

1000 Static Water -8.252 30.6

1000 Dynamic 50% RH -13.885 45.2

II
¢-n

o

o.

v

VI

Ul

W

laJ

D

.J

Z

.J

4.60

4.50 1

4.40

4.30

4.20

4.10

4.00

,3.90

3.80

3.70

:3.60

.3,50

-3.00

INDE_TAnON • 4.9 N (n'-23.6) LOAD

• 9.8 N (n'-23.5)

I I I I I I I "T T I

-- 1 .(X3 1.00 3.00 5 O0 7.00

L.N [.STRESSING R.JkTE (Mpa/,ec:)]

Figure 5. Dynamic fatigue data for indented Zerodur specimens in a water envisorurtent.

The lines through the data are best fit to the median values for each indentation load. The

shaded area to the right represent the inert strengths.

o

{1

_E

v

w

w

3

5

! i ! '| 1 I I I 1 1 I

--3.00 -- 1.00 1.00 3.00 5.00 7.00

LN [smr:.SStN_RXrE(u_/,.¢)]

Figure 6. Dynamic fatigue data for Zcrodur specimens with 9.8 newton indentadons at

ambient humidity (50% RH). The line through the data was best fit to the median values

for at the four lower stressing rates where the crack growth is controlled by ambient

moisture. The shaded area to the right represent the inert strengths.

12
DISCUSSION

While the as-received strength of the specimens tested in this study should not be used as the asreceived strength of flight components, it is instructive to observe the strength distribution of the

specimens tested in the as-received condition. The Z,erodur specimens used in this study were

polished to a commercial grade finish. The Weibull plots for the inert strengths are shown in

Figure 7. The distribution of the as-received strengths appears to be that of a bimodal

distribution. Bimodal distributions generally occur when the strength controlling flaws come

from two distinct flaw populations. These populations might be inherent voids or bubbles

created during the pouring of the Zerodur and line or point flaws created by machining or

handling of the specimens. The distinct flaw populations could also arise due to specimen

preparation preformed by different machinists, on different machines or on different days. The

fracture origin could only be located in the weakest of specimens and that defect appears to be a

linear flaw.

2

I

v

t..J

C

r

-1

-2

-3

-4

x

0

[]

0

0

o

3.g 4.1 4.3 4.5 4.7 4.9 5.1

In[FAILURE STRI_'S(Mpa)]

0

n

INDENTATION LOAD

o _-REC (m-_._)

o 2.g N (m-21.5)

Z_ 4.g N (m--36.2)

x g SN (m-lS6)

V 19.6 N (m-24.3)

5.3 5.5 5.7 5.9

Figure 7. WeibuU distribution of inert strength data.

13
The variation of fracture toughness values obtained from different techniques (Table 6)

illustrates the uncertainty in any value obtained using a single technique. As demonstrated by

the fracture toughness values determined for sodalime glass, the indentation strength technique

gives an approximate fracture toughness value but is generally found to overestimate the

generally accepted fracture toughness values for very low KIC glass materials (<lMPa.ml/2).

The over estimation of the fracture toughness of glass materials by the strength method may be

due to the range over which the calibration constant is obtained. The calibration constant for the

strength method is determined using materials ranging from 0.7 MPa.m 1/2 to 10 MPa-m 1/2 [11].

The standard deviation associated with the calibration constant is 20% of the mean value. Due

the consistent overestimation of the fracture toughness of low KIC materials when using the

indentation strength technique, it would be prudent to use a twenty percent lower calibration

constant to calculate the fracture toughness. Using a calibration constant of 0.47 (in place of the

mean value, 0.59) in Eq.(5) the Zerodur fracture toughness determined from the strength

technique is 0.90 MPa-m 112, which is in good agreement with that determined by the direct crack

method.

The fracture toughness calculated using the direct crack method was slightly greater than that

using a large flaw technique. The direct crack method usually is in good agreement with the

large flaw technique. The fracture toughness of sodalime glass determined by the direct crack

method, using the same equipment and procedures as was used to test the Zerodur, was found to

agree with values determined at other laboratories. This discrepancy may be due to the

specimens originating from different material lots. To insure the component design is

conservative the lower toughness value (0.844 MPa.m 1/2) should be used for design purposes.

Table 6. Comparison of Fracture Toughness Values(MPa-m tr2)

Zerodur Soda-Lime Glass

Ref 19 GSFC[23]

Direct Crack 0.911 0.70 0.67

Strength Method 1.123 0.94 0.94

Large Crack Method 0.844[ 19] 0.75

Upon initial examination of the apparent fatigue parameters in Table 5, there appears to be poor

agreement between fatigue parameters determined from static and dynamic testing. The

discrepancy is eliminated when the adjusted dynamic fatigue parameters are compared to the

unadjusted static fatigue parameters (Table 7). The difference observed in the fatigue parameters

may be explained by the relaxation of the localized residual stress field associated with the

indentation event due to the lateral crack growth during the early stages of static loading.

Recent studies have shown that the strength of sodalime glass specimens with indentation flaws

increases with time after the indentation event [24]. It was observed that both the radial and

lateral cracks grew during exposure to aqueous environments, but the strength increase has been

attributed to the lateral crack growth relieving the localized residual stress. While the strength of

the specimens tested in reference [24] did increase, the maximum strengths were less than that of

the indented and annealed specimens. The strength difference between the aged and annealed

specimens is attributed to the growth of the radial cracks during aging.

If it is assumed that the sustained static loading allowed the lateral cracks to grow and that the

localized residual stress was relieved then the fatigue parameters determined from the static

fatigue testing are the true fatigue parameters and do not need to be adjusted. The adjusted

14
parametersfrom the dynamic data agree quite well with the non adjusted parameters determined

from the static fatigue testing (Table 7). The slightly lower B value for the static fatigue data

may be attributed to the slightly different flaw geometry/stress field resulting from the growth of

the lateral flaws; i.e. the determination of the B parameter is dependent on the inert strength

value.

Table 7. Fatigue Parameters in the Absence of Residual Stress

Indentation

Load

(grams)

Loading Environment Fatigue Parameters

In(B)*

500 Dynamic Water -5.347 30.9

1000 Dynamic Water -6.913 30.8

1000 Static** Water -8.252 30.6

I000 Dynamic 50% RH -17.51 59.2

* True B parameter calculated using equations (8) & (11).

** Static parameters not adjusted

It seems justified at this point to draw the conclusion that the results obtained using static and

dynamic testing do agree. The average fatigue parameters for Zerodur in the absence of residual

stresses are n=30.7 and the In(B) = -6.837. For design purposes the B value determined from the

static fatigue testing could be used to insure a conservative design. To further insure that the

design is conservative the fatigue parameters determined in the presence of the indentation

localized residual stress field (Table 5) could be used for life time predictions. The use of the

latter parameters could allow for the presence of residual stresses created during machining of

the component, which would increase the crack growth rate.

While it is necessary to insure the component will survive launch, excessive conservatism will

add undesired weight to the component. The use of crack growth parameters determined in a

water environment to predict component lifetimes adds a greater degree of conservatism. It is

clear from the data presented in Tables 5 and 7 that the rate of crack growth in ambient moisture

is much less than that in an aqueous environment. The values determined for ln(B' ) and n" at

50% RH were -13.89 and 45.2, respectively. When these values are adjusted to reflect the true

values, In(B) and n values are -17.51 and 59.2, respectively. These values are in fair agreement

with values determined in reference [22] which used "...unilaterally toothed, tensile samples

loaded on one axis..." in an ambient environment of 40 to 60% RH. In that reference the In(B)

an n parameters were found to be -11.49 and 51.7, respectively. The difference in fatigue

parameters may again be due to batch to batch material variations.

It is clear from the above results that the actual component environment should be taken in to

account during component design. Figure 8 shows curves generated using equation (8), an

assumed proof stress level of 70 iPa and the parameters listed in Table 7. The initial or inert

strength in equation (8) can be replaced with the proof stress and the time calculated is a

minimum time to failure. The 70 MPa stress was arbitrarily selected and corresponds to a failure

probability during proof stressing of 3.7%. It can be seen in Figure 8 that the variation of the B

parameter does not signifieandy affect the lifetime analysis while the component environment

does severely affect the component lifetime.

15
¢--t

O

hi

¢Y

D

..J

o

Itd

P

t..J

20.0

1g.0

18.0

17.0

16.0

15.0

14.0

13.0

12-0

11.0

10.0

g.O

8.0

7.0

6.0

5.0

4.0

3.0

2-0 4

1.0 5

0.0

3.00

Curve Test Type Flow

1 Dynamic 4.gN Indent

2 Dynamic g.6N Indent

3 StoUc 9.6N Indent

Dynamic Large Flow

D_nam;c g.SN Indent

I I I

.3.20

1 4

Environment

Water

Water

Water

40X-60X RH

50_ RH

! I i

3.40 3.60

LN[APPUEOSTReSS(M_)]

3.80

10 YEARS

1YEAR

1DAY

4.00

Figure 8. Median specimen lifetime calculated using fatigue parameters listed in Table 8

and in reference [22]. Inert strength was assumed to be 70 Mpa.

CONCLUSIONS

The fracture toughness determined from this study was found to be approximately 0.9 MPa-m 1/2.

A previous stud,Yl_219] using a large crack propagation technique found the fracture toughness to be 0.844 MPa-m . It is felt the lesser value should be used to insure a conservative design.

The average true crack growth parameters n and In(B) for Zerodur in 100% relative humidity

were determined to be 30.7 and -6.837, respectively. The true crack growth parameters n and

In(B) for Zerodur in 50% relative humidity were determined to be 59.3 and -17.51, respectively.

In the presence of a residual stress these values are considerably less.

ACKNOWLEDGEMENTS

The author would like to thank the Far Ultraviolet Spectrographic Explorer project for suppling

both the manpower and test s_,cimens which enabled this research to be performed. The author

would like to thank Mr. Heslm for his technical guidance. Implementation of the static fatigue

testing was performed by Glenn Vanlandingham and Julie Brusslan.

16
REFERENCES

.

.

.

.

,

.

+

.

.

10.

11.

12.

13.

14.

H. Scheidler and E. Rodek, "Li2-AI203-SiO 2 Glass-Ceramics," Ceram. Bull., 68 [1 I],

1926-30 (1989).

Fracture Control Requirements for Payloads using the National Transport System, NBH

8071.1 September I, 1988.

D.K. Shetty, et al,"Biaxial Flexure Tests for Ceramics," Ceram. Bull., 59 [12], 1193-97

(1980).

J.B. Watchmann, Jr, W. Capps and J. Mandel, "Biaxial Flexure Tests of Ceramic

Substrates, Journal of Materials,7 [2], 188-94 (1972).

J.E. Ritter, Jr, K. Jakus, A. Batakis and N. Bandyopadhyay, "Appraisal of Biaxial

Strength Testing," Joumal of Non-Crystalline Solids, [38-39], 419-24, (1980).

W. WeibuU, "A Statistical Distribution Function of Wide Applicability," Journal of

Applied Mechanics, [18] 293-97 (1951)

B.R. Lawn, A.G. Evans and D.B. Marshall, "Elastic/Plastic Indentation Damage in

Ceramics: The Median/Radial Crack System," J. Am. Ceram. Soc., 63 [9-10], 554-60

(1980).

D.B. Marshall, B.R. Lawn and A.G. Evans, "Elastic/Plastic Indentation Damage in

Ceramics: The Lateral Crack System," J. Am. Ceram. Soc., 65 [11], 561-66 (1982).

B.R. Lawn and T.R. Wilshaw, "Review Indentation Fracture: Principles and

Applications," J. Mater. Sci. ,10 [6], 1049-81 (1975).

G.R. Anstis, P. Chantikul, B.R. Lawn and D.B. Marshall, "A Critical Evaluation of

Indentation Techniques for Measuring Fracture Toughness: I, Direct Crack

Measurement," J. Am. Ceram. Soc., 64 [9], 533-38 (1981).

P. Chantikul, G.R. Anstis, B.R. Lawn and D.B. Marshall, "A Critical Evaluation of

Indentation Techniques for Measuring Fracture Toughness: I1, Strength Method," J. Am.

Ceram. Soc., 64 [9], 539-43 (1981).

B.R. Lawn, S.w. Friedman T.L. Baker D.D. Cobb and A.C. Gonzalez, "Study of

Microstructural Effects in the Strength Controlled Flaws," J. Am. Ceram. Soc., 67 [4],

C67-69 (1984).

R.F. Cook, B.R. Lawn and CJ. Fairbanks, "Microstmcture-Strength Properties on

Ceramics: I, Effect of Crack Size on Toughness," J. Am. Ceram. Soc., 68 [1 I], 604-15

(1985).

D.B. Marshall and B.R. Lawn, Residual Stress Effects in Sharp Contact Cracking: Part 1,

Indentation Fracaxre Mechanics," J. Mater. Sei., 14, 2001-12 (1979).

17
15.

16.

17.

18.

19.

0,

21

22.

23.

24.

T.M. Heslin, M.B. Magida and K.A. Forrest, "A Method for Developing Design

Diagrams for Ceramic and Glass Materials using Fatigue Data," NASA RP 1174,

September 1986.

D.B. Marshall and B.R. Lawn, "Flaw Characteristics in Dynamic Fatigue: The Influence

of Residual Contact Stress," J. Amer. Ceram. Soc., _63 [9-10], 532-36 (1980).

P. Chantikul, B.R. Lawn, and D.B. Marshall, "Micromechanics of Flaw Growth in Static

Fatigue: Influence of Residual Contact Stress," J. Amer. Ceram. Soc., 64 [6], 322-25

(1981).

B.R. Lawn, D.B. Marshall, G.R. Anstis, and T.P. Dabbs, "Fatigue Analysis of Brittle

Materials using Indentation Flaws," Journal of Materials Science, [ 16] 2846-54 (1981 ).

V. Maier and G.Muller, "Mechanism of Oxide Nucleation in Lithium Aluminosilicate

Glass Ceramics,"J. Am. Ceram. Soc., 70 [8] C176-78 (1987).

K. Jakus, D.C. Coyne,and J.E. Ritter, Jr, "Analysis of Fatigue Data for Life Time

Predictions for Ceramic Materials," Joumal of Materials Science, [13] 2071-80 (1978).

J.E. Ritter, Jr, F.M. Mahoney and K. Jakus, " A Comparison of Vickers and Knoop

Indentations in Soda-Lime Glass," Fracture Mechanics of Ceramics, Vol. 8, Edited by

R.C. Brant, A.G. Evans, D.P.H. Hasselman and F.F. Lange, Plenum Publishing Corp

(1986).

H. Richter and G. Kleer, "Investigations on Characterizhag Stability Behavior of

Zerodur," Frauenhofer Institut Fuer Werkstoffmelhaik, Freiburg, Report V24/83, 1983.

M.J. Viens, "Implementation of Ring on Ring Flexure Testing," internal memorandum,

Goddard Space Flight Center, (October, 1987)

B.R. Lawn, K. Jakus and A.C. Gonzales, "Sharp vs Blunt Crack Hypotheses in the

Strength of Glass: A Critical Study using Indentation Flaws," J. Amer. Ceram. Soc., 68

[I], 25-34 (1985).

18
ADDENDUM

Homologous Ratio Analysis

A material's crack growth constants are generally determined using the median values, since

these values are at equal failure probabilities (0.5). The median values analysis, while easy to

apply, can result in large uncertainties in the B and n values. An altemate method to analyze the

data is based on a homologous stress ratio (oilS), given as [20]:

(SHS = (Ya/(Si (1 1 )

The homologous stress is ranked based on the inert strength ranking and associated with the

correspondingly ranked time to failure for a given applied stress. Equation (8) is rewritten as:

ln(tf_i 2) = InB - n In Oils (12)

The dynamic fatigue can be similarly analyzed by deeming the homologous stress ratio to be:

GrID = G_i (13)

and equation (9) can be rewritten as:

In OHD = (n+l)-l[ln B + ln(n+l) + ln(o/oi3)] (14)

Static Fatigue

The static fatigue data analyzed using the homologous ratio analysis technique are presented in

Figure 9. The fatigue parameters determined at each applied stress and that determined using all

the data are listed in Table 8. When the ranked data had unequal populations, data from the

larger set were randomly selected and removed from the population, the population was then reranked.

The cause for the variation in the fatigue parameters obtained using the homologous ratio to

analyze the static fatigue data is not certain. The homologous static fatigue parameters

determined using all stress levels were close to the parameters calculated using the median

values. Two individual stress levels were in excellent agreement while the other two deviated

somewhat. This technique uses all the data but it is not known if there is a minimum number of

data points required to insure convergence to the correct fatigue parameters.

19
Table 8. Fatigue Parameters Determined from

Homologous Ratio Analysis of Static Fatigue Data

AspPt _ Fatigue Parameters ln(B') n"

(MPa)

28 -10.730 35.1

30 -8.736 30.7

32 -14.190 37.9

36 -7.645 30.9

Combined -8.579 31.5

Dynamic Fatigue

The homologous ratio analysis of the dynamic fatigue data at individual stress rates did not yield

realistic values for the crack growth parameters. The values for the n parameter calculated from

the 500 gram indentation data at individual stressing rates were negative. The n parameter

calculated from the 1000 gram indentation in 100% RH varied from 4 at the 120 MPa/sec

stressing rate to 21 at the 0.15 MPa/sec stressing rate. While the latter n parameter is close to

that determined by the median value technique, the correlation coefficient was 0.56. The n

parameter values for the 50% RH data varied from 15 to 23. These are considerably less than

the value determined by the median value technique.

The regression analysis of dynamic fatigue data from all of the stressing rates, for a given

indentation load and environment, using the homologous ratio gave parameters equivalent to

using the median values technique. The dynamic fatigue homologous ratio data is presented in

Figures 10-12.

The homologous dynamic fatigue parameters determined for individual stressing rates bore no

resemblance to the values determined using the median values. The basic assumption that the

homologous technique hinges on is that the strength distribution of inert specimens and

specimens failing at various stressing rates describe the same flaw population: i.e. the weakest

specimen at a given stressing rate will fail from the same sized initial flaw as that of the weakest

inert specimen. The use of the indentation technique decreases the scatter in both inert and

dynamic fatigue data. The scatter in the static fatigue time to failure is substantial even with the

Vickers indentations. The poor agreement obtained using the homologous ratio analysis of the

dynamic fatigue data may be attributed to the small amount of scatter in both the inert and

dynamic fatigue data sets.

20
tN

(

¢1(3.

0

v

¢¢

(

c.

5

30.0 ]

28.0 -_

26.0 -

24.0

22.0

20.0

18.0

t6.0

14.0

12.0

10.0

8.0

6.0

4.0

2.0

0.0

+___°o 0 O0 O0

x x

+ D

x mlope-31.5g

: D Q _"_X.

APPUEO STRESS

o 28 Mpo

+ 30 MI_

o 32 Mpo

X 36 Mpo

I I I I I

.1 -O.g -0.7

LN [HOMOLOGOUS STRESS (_"o/O'T)]

-0.5

Figure 9. Static fatigue data analyzed using the homologous ratio technique. The line

through the data is a best fit using all results from the four applied stresses.

¢1

D

O

o

o

.J

o

o

5

-0.32

--0.34

--0.38

--0.38

--0.40

--0.42

--0.44

-0.46

--0.48

-0.50

--0.52

-0.54

-O.5e

-0.58

-0.80

-0.62

-0.64

-0.66

-16

0

0

8

o

o

o

o

o

B

_y

%o

o

o

o

I I I I I

--14 -12 -10

UW [_/_'3( 1/(,,,=',_'2)1

Figure 10. Dynamic fatigue data (4.9 N indentation in water) analyzed using

homologous ratio technique.

i

-8

21
--0.20

v

0

0

0

5

-0.30

,-0.40

--0.50

--0.150

0

0

0

c£

B

OlD

"-0.70 i w I _ i l _ i

-16.0 -14.0 -12.0 -10.0 -8.0

[RA'm../O'I-30/(,,<-M_^2)]

-15.0

Figure I I. Dynamic fatigue data (9.8 N indentation in water) analyzed using

homologous ratio technique.

¢!

2:)

O

0

0

5

-0.40 ]

--0.41 -

i

--0.42 -

--0.43 -

--0.44 -

--0.45 -

--0.415

--0.47

-0.48

-0.49

-0.50

--0.51

--0.52

-0.53

--0.54

--0.55

-0.515

--0.57

-0.58

--0.59

-0.60

-115.00

0

0

0

0 0 o

0

0

0

8

0

0

0

0

0

0

0

O0

0

0

0

0 o

0

IO

0

n 0 DO

o cb

0 n

0

0

[]

o

0

I I I 1 I

-16.00 -14.00 --12.00

U_ [ _/_7-3( 1/("_'M_-2)]

Figure 12. Dynamic fatigue data (9.8 N indentation in 50% RH) analyzed using

homologous ratio technique.

22

N_O_I _ao_cs a_l

S_ce AOrrY,_talo_

1. Report No.

NASA TM-4185

Report Documentation Page

2. Government Accession No.

4. Title and Subtitle

Fracture Toughness and Crack Growth of Zerodur

7. Author(s)

Michael J. Viens

9. Perfo_ing Organization Name and Address

National Aeronautics & Space Administration

Goddard Space Flight Center

Greenbelt, MD 20771

12. Spon_ring Agency Name and Address

National Aeronautics & Space Administration

Washington, DC 20546-0001

3. Recipient's Catalog No.

5. Report Date

April 1990

6. Performing Organization Code

90B00097

8. Performing Organization" Report No.

313

10. Work Unit No.

11. Contract or Grant No.

13. Ty_ of Report and Permd Covered

Memorandum Technical

14. Sponsoring Agency Code

I

15. Supplernen_w Notes

M. Viens is affiliated with Goddard Space Flight Center, Greenbelt, PE) 20771

16. Abstract

The fracture toughness and crack growth parameters of Zerodur, a low expansion glass

ceramic material, were determined. The fracture toughness was determined using

indentation techniques and was found to be 0.9 MPa-m ='_, The crack growth parameter

were determined using indented biaxial specimens subjected to static and dynamic

loading in an aqueous environment. The crack growth parameters n and In(B) were

found to be 30.7 and -6.837, respectively. The crack growth parameters were also

determined using indented biaxial specimens subjected to dynamic loading in an

ambient 50% relative humidity environment. The crack growth parameters n and In(B)

at 50% relative humidity were found to be 59.3 and -17.51, respectively.

17. Key Wor_ (Sugared by Author(s))

Zerodur, lithium-aluminosilicate

glass ceramic, crack growth

fracture toughness

18. Distribution Statement

Unclassified - Unlimited

Subject Category 27

19. Security Classif. (of this report)

Unclassified

NASA FORM li!26 OCT 86

20. Security Clauif. (of this page)

Unclassified

21. No. of pages

26

22. Price

A03

NASA-lamgiey, 1990