NBSIR 74-485

Strength of Glass--A Fracture

Mechanics Approach

S. M. Wiederhorn

Inorganic Materials Division

Institute for Materials Research

National Bureau of Standards

Washington, D.C. 20234

May 1974

Interim Report for Period July I, 1973 through June 30, 1974

Prepared for

Department of the Navy

Office of Naval Research

Arlington, Virginia 22217

NBSIR 74-485

STRENGTH OF GLASS-- A FRACTURE

MECHANICS APPROACH

S. M. Wiederhorn

Inorganic Materials Division

Institute for Materials Research

National Bureau of Standards

Washington, D.C. 20234

May 1974

Interim Report for Period July 1, 1973 through June 30, 1974

To be published in Proceedings of Tenth International

Congress on Glass, Kyoto, Japan, July 8-13, 1974

Prepared for Department of the Navy

Office of Naval Research

Arlington, Virginia 22217

U. S. DEPARTMENT OF COMMERCE, Frederick B. Dent. Secretary

NATIONAL BUREAU OF STANDARDS. Richard W. Roberts. Director

ABSTRACT

After a brief review of those factors that determine the

strength of glass (brittleness , surface flaws, susceptibility

to stress corrosion cracking) , a discussion will be given of

how fracture mechanics techniques can be used to understand the

physics and chemistry of glass strength. In this paper we as- sume that the strength of glass is limited by the growth of

cracks that are always present in normal glass surfaces. Fracture mechanics techniques can be used to characterize the crack

growth and to relate the growth to experimental parameters such

as temperature, environment and glass composition. Crack growth

data obtained in this manner can be used to develop a deeper

understanding of fracture mechanisms, and to develop charts that

can be used for the design of glass structural components.

Examples of both applications are given in this paper.

i

INTRODUCTION

In this paper fracture mechanics is discussed: as a method of understanding the strength of glass, and as a method of providing data that can

be used to assure the structural reliability of glass. A review is first

presented of the main factors that control the strength of glass (temperature, environment, surface condition, etc.). Then fracture mechanics

techniques are described, and the available fracture mechanics data are reviewed. Finally, the use of fracture mechanics for failure prediction is

discussed.

REVIEW OF THE LITERATURE ON THE STRENGTH OF GLASS

The two main characteristics that determine the strength of glass are brittle behavior and static fatigue. Glass is one of the most brittle

materials known because at low temperatures deformation is almost completely

elastic. This elasticity has been demonstrated on silica rods and fibers

by Hillig (Ref. 1) and by Mallinder and Proctor (Ref. 2) to loads as high

2 6 1.1 GN/m (1.6 X 10 psi) , and on soda lime silicate glass fibers by Mallinder

and Proctor (Ref. 2) to 0.4 GN/m (0.6 x 10 psi). The stresses were so high in these experiments that non-linear elastic behavior was observed;

nowever, the deformation completely disappeared when the load was released.

Interestingly, the Youngs modulus for the silica glass increased during

these experiments, while that for soda lime silicate glass decreased.

Permanent deformation can occur in glass under certain circumstances.

Permanent densifica tion has been observed by Bridgeman (Ref. 3) and by

Cohen and Roy (Ref. 4) on glasses that have been subjected to pressures of

2 6 7 GN/m (10 psi). During hardness indentation tests, plastic flow and

densif ication occurs because of the high compressive and shear stresses

2

('^ 10 GN/m ) near the indenter (Ref. 5,6). Permanent deformation has also

been observed in compressive tests conducted by Ernsberger (Ref. 7) on glass rods that contained oblate bubbles. In these experiments densif ication was observed in Pyrex and silica glass at stresses of approximately

2

7 GN/m . In all of the above cases, high compressive loads were necessary

for the occurrence of plastic deformation. To date, there have been no unequivocal reports of plastic deformation of glass that has been subjected

to tensile loads.

1
The low strength of glass is a direct result of this brittle behavior.

When glass is polished and ground, small cracks are left in the glass

p surface. These cracks act as stress concentrators so that the crack tip

stress is considerably higher than the average applied stress. Since

plastic deformation does not occur to relieve these crack tip stresses, the

surface cracks propagate when a critical stress is reached at the crack

tip. The critical stress required for crack motion is determined in part

by the glass composition, and in part by the environment at the crack tip.

The environmental contribution to crack motion results in a time dependence

of strength known as static fatigue.

Static fatigue of glass was observed first by Grenet (Ref. 9) who

noted a time dependence of strength for both static and dynamic loading

conditions. For a constant loading rate, the strength depended on the rate

of loading, increasing as the rate increased; whereas for constant load,

failure occurred after a period of time at load. The phenomenon of static

fatigue at constant load is illustrated in figure 1.

The failure time depends on the

load applied to the glass; large loads can only be supported for short periods

of time. If the load is small enough,

a fatigue limit occurs; fracture does

16

t CT|2

C

"~O

OQ — o

o

u>

1 III .- 1 III 1 III 1 III 1 . 1 II 1111 1 1 II \ \0*

Duration of Load (sec)

10*

Fig. 1 Static fatigue of sodalime silicate glass (Ref. 10)

not occur regardless of the time for

which the load is applied. r Static fatigue can be explained

by the growth of cracks caused by a stress enhanced chemical reaction

between water and glass. Static

fatigue occurs only in the presence of

water which reacts chemically with the

strained bonds at the crack tip causing

bond rupture. The rate of crack

growth is determined by the rate of

the chemical reaction, and the time to

failure is determined by the time

required for the crack to grow from a subcritical to a critical size, at

which point, failure is instantaneous.

Before the advent of fracture mechanics concepts, strength measurements were used to study static fatigue. The strength was measured in

three or four point loading as a function of loading rate, or the time to

failure was measured as a function of applied load. Using these techniques

the following observations were made:

2
o static fatigue occurred only in the presence of water (Ref. 11-

14) . o Static fatigue could be detected for load times as short as 10~

second (Ref. 14)

o Static fatigue did not occur in a vacuum or at very low tempera

tures (-196»C) (Ref. 12, 13, 15).

o Static fatigue was an activated process, fracture becoming

easier at higher temperatures (Ref. 16, 17).

o Static fatigue was the result of a single process that did

not depend on the surface flaw size (Ref. 18)

o The static fatigue limit occurs at approximately 20-30

percent of the environment-free strength (Ref. 10, 19).

While strength studies provided considerable information on the

strength of glass and the occurrence of static fatigue, fracture

mechanics techniques added to this body of knowledge, providing a deeper insight into the fracture process.

FRACTURE MECHANICS TECHNIQUES

Fracture mechanics techniques are all based on Griffith's original

studies of the fracture of brittle materials (Ref. 21) . One conclusion

of Griffith's work is that the strength of brittle materials depends

on the presence of cracks in these materials. The strength, S, was related to the crack length by the following formula (derived for an elliptical through crack of length 2a)

S = (2EY/7Ta)^ (1)

where y is the fracture surface energy of the material and E is Young's

modulus. Griffith showed that the fracture behavior of glass containing

macroscopic cracks obeyed the above equation.

The theory developed by Griffith was generalized by Irwin (Ref.

21) who established fracture mechanics as a practical science which

could be used to assure the reliability of structural materials. In

Irwin's analysis the condition for failure could be expressed in the

following general form for plane stress deformation: *

= 2Ey (2)

Where is known as the stress intensity factor for opening mode

loading.

The stress intensity factor, K^ , occupies a central position in

the science of brittle fracture because it is proportional to the
stress near the crack tip. In fact at any point near the crack tip the

stress, Oj^j, is related to the stress intensity factor by the following

equation (Ref . 22)

where r is the distance from the crack tip and f^^ (6) is a function of the

angle 9 from the fracture plane. Eqn. (3) applies to the region near the

crack tip for any crack shape, provided the crack is subjected to opening

mode loading (all loads are perpendicular to the crack plane) . For any

particular crack can be related to the applied load by a stress analysis

of the crack geometry. Therefore, the applied load can be related to the

stresses near the crack tip. For th^is reason, is the main mechanical

parameter that controls the fracture of brittle materials.

The relation between and the applied load has been determined for

many different crack configurations (Ref. 23, 24). For a Griffith crack K^. = S/rra, which is obtained by comparing Eqn. (1) and (2). While the

« Griffith configuration could be used to obtain fracture information, other

crack configurations are easier to use. Two crack configurations that have

been used most frequently to obtain fracture mechanics data on glass are

the double cantilever beam configuration (Ref. 24, 25) and the double

torsion configuration (Ref. 26). Either of these techniques can be used

conveniently to obtain fracture mechanics data on glass (Ref. 27, 28).

FRACTURE MECHANICS DATA ON GLASS

a. . = (KV/r) f . . (6) 13 I' 13(3)

studies, conducted in nitrogen gas

containing various amounts of water

vapor (Ref. 29), showed that glass

fracture was no simple process.

Fracture appeared to occur by several

mechanisms as indicated by the trimodal curves shown in Fig. 2. Three

characteristic regions of crack growth

were observed. At low values of K^,

region I, the crack velocity, v, depended exponentially on K^, and

also on the parital pressure of

Crack Growth Data

The earliest fracture mechanics

Fig. 2 Effect of water vapor

(% R.H.) on crack propagation

(Ref. 29)

water in the environment.

4
At higher values ot K^, region II, the crack velocity depended on the

partial pressure of water in the environment, but was nearly independent of

K^. Finally at the highest values of K^., region III, crack growth again

depended exponentially on K^., but now did not depend on water in the

environment. In region I and II crack growth was attributed to a chemical

reaction between water in the environment and the stressed glass at the

crack tip. In region I crack motion was reaction rate limited while in

region II crack motion was transport rate limited depending on concentration

differences between the crack tip and the bulk environment. In region III

crack motion was independent of environment and fracture was due to some process that depends only on the glass structure. More recent studies of

fracture in vacuum (see below) indicate that region III does not occur for

all glasses.

Crack propagation in region I has been shown to depend on temperature,

glass composition' and environment. For constant K^, the crack velocity in

water increases as the temperature is increased suggesting that crack

growth is an activated process (Ref. 30). A least squares fit of crack

growth data for a number of glasses to an Arhenius type equation yields a zero-stress activation energy that ranges from 20 to 30 Kcal/ mol. This

range of activation energies is consistent with that expected from a chemical reaction, and is, therefore, consistent with the mechanism proposed

by Charles and Hillig for the static fatigue of glass (Ref- 31, 32) . In

other aqueous environments (acids, bases and various salt solutions) crack

propagation has been shown to depend on the pH of the test solution (Ref.

33) , Fig. 3. For example, in silica glass crack

propagation curves obtained in high pH

solutions have about twice the slope of

those obtained in low pH solutions.

This change of slope with pH can be used

to explain similar slope changes observed

for other glasses that were tested in

water (Ref. 30). In general, high

alkali containing glasses have slopes

that are more shallow than the low

alkali containing glasses. This difference in slope has been attributed to

a difference in pH at the crack tip,

the pH being determined by a

icr»

lorio

3 4 5 6 STRESS INTENSITY FACTOR, Kj.x 10"*Nm"2''2 Fig. 3 Effect of pH on crack propagation (Ref. 33)

5
1

i

0.4 0.5 0.6

Stress Intensity Factor, Kj_, MN/n

0.7

3/2

Fig- 4 Crack propagation

in Butyl alcohol (Ref. 35)

chemical reaction between the glass

and the crack tip solution. The

high alkali containing glasses

react to form a basic crack tip

environment while glasses containing

little or no basic constituents

react to form an acidic environment.

Region I crack growth has also

been investigated in normal alcohols

by Freiman (Ref. 34) and by Evans

and Wiederhorn (Ref. 35) . Trimodal curves were obtained (Fig. 4)

indicating that crack growth behavior

in these environments was similar

to that in nitrogen gas containing

water vapor. At a given value of •

, Kj, the crack velocity was proportional to the concentration of the

water in the alcohol, suggesting

that crack propagation is mainly

due to the water in the alcohol and not to the alcohol itself. However, in

region III the alcohol chain length does have a small effect in the position

of the crack velocity curve. Information on the mechanism of fracture in region III has been

obtained recently by Wiederhorn et. al (Ref. 36) from crack propagation

studies in vacuum. In these studies, it was observed that the crack growth

depended on the composition of the

glass. For some glass compositions crack

growth in region III depended on temperature in an Arhenian manner (Fig. 5).

For other glass compositions slow crack

growth did not occur; instead glass

fractured abruptly at a critical value

of Kj.. These differences in behavior

apparently depend on the elastic properties of the glass. Crack growth in

vacuum occurred for glasses exhibiting

normal elastic behavior (the bulk modulus

decreasing with increasing temperatures

but increasing with increasing pressure)

By contrast crack growth did not occur

^ io-»

0.6 0.7 ITRCSS INTENSITY f»CTOR. UH/m" Fig. 5 Crack propagation

in vacuum (Ref. 36)

6
for glasses that exhibited anomolous elastic behavior (the bulk modulus

increasing with increasing temperatures, but decreasing with increasing

pressure). Wiederhorn et al (Ref. 36) suggested that this difference in

behavior could be related to the glass structure near the crack tip.

Thomson's theory of "lattice trapping" which relates structure to fracture

behavior may explain the fracture behavior of glass in vacuum (Ref. 37,

38) . The reader is referred to the original article by Wiederhorn et al^ (Ref. 36) for a futher discussion of this point.

CRITICAL STRESS INTENSITY FACTOR DATA

In addition to crack propagation studies, fracture mechanics techniques can be used to measure the critical stress intensity factor for

abrupt fracture, K^^. Because is related to the stresses and strains

near the crack tip, K^^ gives a measurement of the maximum stresses or strains that a material can withstand prior to failure. K^^ is commonly

defined as the value of that is required for crack growth in a inert

environment. K-j.^^ is a well defined parameter for materials that fail

abruptly because of rapid crack acceleration at a well defined value of K^.

However, for materials that exhibit slow crack growth in an inert environment, is not so easily defined because the lower limit of for the

initiation of crack motion is not easily measure. For these materials we have defined K^^ as the value of (measured experimentally) required for

a crack to move at a velocity '^^10~'m/s . Using this definition, values of

have been reported for a number of different glass compositions (Ref*.

39, 40). The values of K for glass depend on composition and range from

0.6 to 0.9 MN/m^ . The values of for glass can be used to demonstrate the extreme

brittleness of glass. Dugdale (Ref. 41) and McClintock and Irwin (Ref. 42)

"have shown that a good estimate of the plastic zone size, R, near a crack

tip can be obtained from the following equation:

R = (tt/8) (Kj(./a^)^ (4)

where a is the yield stress of the glass. Applying this equation

y 3/2 to silica glass (K ^

= 0.79 MN/m '

) and soda lime silicate glass

3/2

(K,.-, = 0.75 MN/m ) for which a has been estimated from hardness IC ' y 2 indentation studies (Ref. 43) to be 19.5 and 10 GN/m respectively,

the sizes of the plastic zones at the crack tip calculated from

eqn. 4 are 6.4 x 10 "'"^m for silica glass and 26 x 10 '''^m for soda

lime silicate glass. The fact that the plastic zone sizes for

-4 -4 -4

metals and plastics (1.4 x 10 - 14 x 10 m for PMMA and 7.1 x 10 m

7
for 4340 steel} (R@f. 44) are so much larger emphasizes the extremely

brittle nature of glass. Plastic flow at crack tips in glass does not

significantly reduce the stress concentrating effect of surface microcracks.

Comparison of Crack Propagation Data with Strength Data

Crack growth data are of value for engineering purposes only if the

data are consistent with strength data obtained at constant load or at

constant loading rate. The easiest experimental comparison is between the

crack propagation data and the loading rate data.

For most glasses the crack velocity can be expressed as a power

function of K^, v = AK^, where A and n are experimentally determined crack

propagation parameters. Using this expression, Evans showed that the

loading rate, 6, was related to the strength, o, by the following equation

(Ref. 45):

a = 2(n + 1)6 o^^ /Ay K^^ (n - 2) (5)

where a^^ is the median strength of the glass measured in an inert environment (vacuum or super dry nitrogen) , and Y is the factor that depends on

the crack geometry. Using this equation, a comparison between crack propagation data and strain rate data was made for two glasses: a soda lime

silicate glass (Ref. 47) and an ultralow expansion silica glass containing

7.5 percent Ti02 (Ref. 48). Results for

th? silica glass tested in water (Fig.

6) show excellent agreement between

strength measurement and crack propagation data suggesting that failure

was primarily by crack propagation. A

similar comparison for soda lime silicate

glass tested in nitrogen, one percent

R.H., also gives excellent agreement

between the crack propagation data and

the strength data.

Other less complete comparisons

between strength and crack propagation

data have been made. In a recent studies

on a variety of glasses, Ritter (Ref.

48) reports good agreement for n obtained

10 10"' I 10 10* LoodingRote, log o/o^

Fig. 6 A comparison of

strength and crack propagation data (Ref. 48)

8
from loading rate and crack propagation

studies. Slopes determined from

constant load studies on silica and

i,oda lime silicate glass in water are also in good agreement with slopes

determined from crack propagation

* studies (Ref . 30) . However, constant

load studies on abraded silica glass

and on Pyrex glass (abraded and chemically

polished) do not agree with crack

propagation studies CRef. 49, 50). This

difference in behavior has been attributed to differences in crack tip

chemistry for the two types of studies

(Ref. 33). Thus, if the pH at the crack

tip differed for the two types of studies

then differences in slope would be

expected. Because the failure time can be estimated from crack growth information, it is of practical importance

to resolve these differences in behavior.

. STRESS INTENSITY FACTOR, Kj, MN/m^"

Fig. 7 Crack propagation

air (50% R.H.): A silica

glass; pytex; o sodalime (Ref. 51)

The Static Fatigue Limit in Glass

Fracture mechanics techniques can be used to investigate the static

fatigue limit in glass. This limit, which for a given component is the load

below which fracture will not occur regardless of how long the component is

subjected to load, has been estimated by various authors as 20 to 30

percent of the short term strength (presumably ^jq) (Ref. 10, 19). Fracture

mechanics data can also be used to estimate the value of the static fatigue

limit in glass. The fatigue limit is determined by the value of at

which crack motion stops. Recent studies by Wiederhorn and Johnson (Ref.

51) at crack velocities as low as 10 ^^m/s gave no indication of a static

fatigue limit for Pyrex or silica glass tested in air (50 percent R.H.).

The crack velocity data for these glasses approximate a straight line on a logarithmic plot over the entire range of parameters (Fig. 7) . The lowest

* In these studies the crack velocity was expressed as an exponential

function of K^, v = v^ exp BK^, and the strength as '^/'^jq = 0.5 - (l/BK^.^)

In (t/t^ ^), where tQ ^ is the time to failure at a load Termed

the universal fatigue curve, this type of strength plot was suggested

first by Mould (Ref. 18) . For glass, - v data are represented equally

well by an exponential or power function of K .

9
values of Kj measured for these glasses suggest that the fatigue limit is

less than '\'44 percent of the short term strength for both Pyrex and silica

glass. By contrast, the curve for soda lime silicate glass does exhibit

severe bending at low velocities suggesting a fatigue limit 0.3

MN/m"^^^, which is '^>40 percent of the short term strength. (Defined here as Kj/Kj^). This value is slightly higher than those reported in the literature. If Pyrex is tested in an acid environment (pH < 1.7) one observes a 3/2 fatigue limit of '^' 0.41 MN/m ^ which is '^^53 percent of the short term

strength (Ref . 34) . This limit results from an aggressive attack of the

acid on the glass which causes crack tip rounding.

FRACTURE MECHANICS FOR FAILURE PREDICTION

The excellent agreement between crack propagation data and

strength data (Ref. 46, 47) supports the argument that failure in these

glasses is by crack growth, and suggests that crack growth data can be used

for failure prediction purposes- This use of crack growth data depends on

a complete characterization of crack growth for a given application. Once

the crack growth has been characterized then the time-to-failure can be

calculated provided the size of the critical flaw can be determined . The

key to this application of fracture mechanics is in fact the determination

of the initial flaw size. Recent work by Evans and Wiederhorn (Ref. 52,

53) suggest that for practical purposes the initial flaw size can be estimated

by overload proof testing.

Proof testing is used in structural design to break weak components

before they can be placed into service. By so doing we assure the structural

integrity of components that are placed in service. In a proof test, a proof test load, a , which is larger than the service load, a , is applied

p a to the components in an inert environment. This procedure guarantees that

components passing the proof test have flaws smaller than the critical size

that would have resulted in failure during service. In fracture mechanics

terms, the stress intensity factor at the crack tip of the most serious

flaw, has to be less than K^^ if the component is not to break during

the proof test. Thus, for a component to pass the proof test,

^IC > Kp = °p Y (6)

where Y is a geometric factor and a^ is the crack length of the most

serious flaw in the component.

10
When a component has passed the proof test and is placed into service

the stress intensity factor at the most serious flaw is given by:

K. = a^Y/a. (7)

where a is the service load,

a By dividing Eqn. (6) into Egn. (7), the following equation is obtained

for the stress intensity factor at the beginning of service:

^i < ^IC ''a/^ . Thus by proof testing a component prior to service, an estimate of the

maximum stress intensity factor at the beginning of service may be obtained.

In service, the component will be gradually weakened by crack growth

until failure occurs. The time to failure can be estimated from the definition of crack velocity, v = da/dt, and the relation between K^, a, and a: (Kj = aY/a) . For a constant load

V = (2Kj/Y^a^^) dKj/dt (9)

This equation can be solved to give the following expression for the

failure time:

t = (2/Y^a^^) (Kj/v) dK^ (10) , K.

1 This equation can be evaluated either numerically or analytically if a relationship between and v is available. For v = Ak", a minimum timeto-failure, t . , is obtained by substituting K. from equation 8 into the mm ^ 1

^ -ower integration limits of Eqn. (10).

t . = 2a"^ (K^^ a /a ) ^""/AY^ (n-2) (11) min a IC a p

^

Note that all the variables in the right hand side of this equation can be

determined experimentally.

The main features of Eqn. (11) is that the minimum time to failure

^min' ^^^^^ ^ proof test is inversely proportional to the service stress

squared and directly proportional to a function of the proof test ratio,

a /a . In functional form the equation may be expressed as follows:

P °-

t . = a"^ . f(o /a ) (12) min a p' a

11
The function of proportionality, f (o /o ), is determined from measurements

P ^ of and from crack growth data. Thus, all the necessary information for

failure prediction can be obtained by fracture mechanics techniques.

The relationship given by Eqn. (12) can be presented graphically in

the form of a proof test diagram that can be used for design purposes. A

diagram of this type is given in Fig. 8 for a low expansion silica glass

containing 7.5 percent Ti02. The

diagram gives a plot of the minimum

time to failure versus the service

stress. Each of the lines on this

diagram represents the relationship between t . and a for a ^ mm a given proof test ratio, a /a . p a The diagram is used to selecc an appropriate proof test ratio for a specific application. The silica

glass represented by this diagram

was considered for use as windows

in the Space Shuttle, for which the

glass was required to sustain a load of 3 MN/m^ (^A,000 psi)

Assuming that for safe operation

the load would have to be supported

for one year, a proof test ratio of

approximately 2.6 is obtained from

the diagram. Thus reliable performance

of the space craft windows would require proof testing to a stress of 12

MN/m^ ('^^10,000 psi) . The above example of proof testing illustrates the basic procedure

that should be followed to assure the reliability of (J'lass for structural

application. However, certain precautions are necessary to assure the

validity of the method. These precautions are concerned with the accuracy

and applicability of the proof test data, the design .of a proper proof test

procedure and the possibility of strength degradation after the proof test

has been completed. These precautions are necessary since an incorrect

assessment of any one of them could invalidate the proof test and result in

premature component failure. The interested reader is referred to references

52-56 for a more complete discussion of the method and its application to

structural design. Despite these precautions, proof testing is a promising

method of using fracture mechanics data to assure the reliability of glass

structures.

1 — 1

Ultnj-low Eipansion Gl05»

i;;JO0 years

;

-10 yeori - year

— doy

1 1 1 1 t.o 10.0

2 Service Stress, c; , MN/m

Fig.

(Ref

,

! Proof test diagram

47)

12
SUMMARY

This paper has summarized the strength and fracture data on glass,

emphasizing the phenomenon of static fatigue. In summarizing the strength

of glass, it was noted that glass is characterized by extreme brittle

behavior. The practical strength is much less than the theoretical strength

because of the presence of cracks in the glass surface. The growth of

these cracks caused by water in the environment leads to the phenomenon of

static fatigue, which is characterized by delayed failure under constant

load, or a loading rate dependence of strength.

Static fatigue can be studied by the techniques of fracture mechanics

which use specimens that contain large artificially introduced cracks. The

key variable that can be measured by fracture mechanics techniques is the

stress intensity factor, K^, which is proportional to the stresses near the

crack tip. By relating to the crack velocity, temperature, environment

and glass composition it has been demonstrated that the fracture of glass

is a complex phenomenon that is controlled by a number of different mechanisms

involving chemical reactions, diffusion and glass structure. In cases where a direct comparison has been made between crack growth data and

strength data, good agreement is obtained suggesting that crack growth data

can be used for design purposes. A method of using fracture mechanics data

to obtain proof test diagrams is outlined. These diagrams can be used to

select the proof test load that will assure the lifetime of a structural

component for a particular application.

ACKNOWLEDGEMENT

The author greatfully acknowledges the support of the office of Naval

Research, Contract NAonr 5-73, NR032-535.

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les moyens de I'ameliorer, Union Scientifique Continentale du Verre,

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(11) Milligan, L. H. , J. Soc. Glass Technol., 13, 341T (1929).

13
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(23) Brown, W. F. and Srawley, J. E., ASTM Special Technical Publication

No. 410

(24) Srawley, J. E. and Gross, B., Mater, Res. Stand. 7, 155 (1967).

(25) Wiederhorn, S. M. , Shorb, A. M. and Moses, R. L. , J. Appl. Phys. 39_,

1569 (1968). -

(26) Evans, A. G., J. Mater. Sci. 7, 1137 (1972).

(27) Evans, A. G., Fracture Mechanics of Ceramics, Plenum Press, New York

(1974) . (28) Wiederhorn, S. M. , ibid.

(29) Wiederhorn, S. M., J. Am. Ceram. Soc. 59^, 407 (1967).

(30) Wiederhorn, S. M. and Bolz, L. H. , J. Am. Ceram. Soc. 53^, 543 (1970).

(31) Charles, R. J. and Hillig, W. B., C. R. Symposium sur la resistance

mecanique du verre et les moyens de I'ameliorer, Union Scientifique

Continentale du Verre, Charleroi (1962)

(32) Hillig, W. B. and Charles, R. J., High Strength Materials, John Wiley

and Sons, New York (1965).

(33) Wiederhorn, S. M and Johnson, H., J. Am. Ceram. Soc. 56^, 192 (1973).

(34) Freiman, S. W. , J. Am. Ceram. Soc, August (1974).

(35) Evans, A. G. and Wiederhorn, S. M. , J. Am, Ceram. Soc, To be published.

(36) Wiederhorn, S. M. , Johnson, H. , Diness, A. M. and Heuer, A. H. , J. Am.

Ceram. Soc, July (1974).

(37) Thomson, R. , Hsieh, C. and Rana, R. , J. Appl. Phys. 42^, 3154 (1971).

(38) Hsieh, C. and Thomson, R. , J. Appl. Phys. 4_4, 2051 (1973).

(39) Wiederhorn, S. M., J. Am, Ceram. Soc 5_2, 99 (1969).

(40) Wiederhorn, S, M, Evans, A. G. and Roberts, D, E, , Fracture Mechanics

of Ceramics, Plenum Press, New York (1974).

14
(41) Dugdale, D. S., J. Mech. Phys. Solids 8, 100 (1960).

(42) McClintock, F. A. and Irwin, G. R. , ASTM Special Technical Publication,

No. 381.

(43) Marsh, D. M. , Proc. Ray. Soc. A279 , 420 (1964).

(44) McClintock, F. A. and Argon, A. S., Mechanical Behavior of Materials,

Addison-Wesley Publication Co., Inc., Reading, Mass. (1966).

(45) Evans, A. G., Int. J. Fract. Mech., To be published.

(46) Evans, A. G. and Johnson, H., J. Mat. Sci, . To be published.

(47) Wiederhorn, S. M., Evans, A. G., Fuller, E. R. , and Johnson, H.

,

J. Am. Ceram. Soc, August (1974).

(48) Ritter, J. E. and Sherburne, C. L. , J. Am. Ceram. Soc, 5£, 601 (1971).

(49) Ritter, J. E. and Manthuruthil , J., Glass Tech. 14_, 60 (1973).

(50) Doremus, R. H.., Corrosion Fatigue: Chemistry Mechanics and Microstructure, Nat. Ass. Corrosion Engr. (1972).

(51) Wiederhorn, S. M and Johnson, H., unpublished data.

(52) Evans, A. G. and Wiederhorn, S. M. , Int. J. Fract. Mech. (1974), NBS

Report No. NBSIR 73-147.

(53) Wiederhorn, S. M. , J. Am. Ceram. Soc. 56, 27 (1973).

(54) Evans, A. G. and Fuller, E. R. , Met. Trans. 5^, 27 (1974).

(55) Evans, A. G. and Fuller, E. R. , J. Mech. Phys. Solids, To be published.

(56) Wiederhorn, S. M., To be published in Proceedings of Ceramics for High

Performance Application, Hyannis, Nov. 13-16 (1973).

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NBS-1 UA (RKV ;. /.o

U S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. rimi.K A rioN or !<! i'ok i no. IIBSIR 74-4852, ( lOV 'l A( ( I- S S 1 III! 3. l<( 1 ipii III s Ai <. ( s.siiin Nil.

4. I I 1 AND .sun in

Strength of Glass—A Fracture Mechanics Approach

5. 1 'iilij K ai lull 1 I6. I'crforiiiing Organization < ode

7. Airi HOKiS'l S. M. Wiederhorn

8. 1 Vrforniiiig Organ. Rc-porl No. NBSIR 74-485

9. PKRFORMINC. OR(i AN I/.A'I'ION NAMH ANll AIMIR l-.SS NATIONAL BUREAU OF STANDARDS

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16. Al^STRAC'T (A 200-word or less factual summary of most si^ificant information. If document includes a significant

bibliography or literature survey, mention it here.) After a brief review of those factors that determine the strength of glass (brittleness , surface flaws, susceptibility to stress corrosion cracking), a discussion will

be given of how fracture mechanics techniques can be used to understand the physics

and chemistry of glass strength. In this paper we assume that the strength of glass

is limited by the growth of cracks that are always present in normal glass surfaces.

Fracture mechanics techniques can be used to characterize the crack growth and to

relate the growth to experimental parameters such as temperature, environment and

glass composition. Crack growth data obtained in this manner can be used to develop

a deeper understanding of fracture mechanisms, and to develop charts that can be used

for the design of glass structural components. Examples of both applications are given in the paper.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons

)

Crack growth: fracture; glass; static fatigue; strength.

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