NBSIR 76-996

Testing for the Impact

Resistance of Ophthalmic

Lenses

Robert E. Berger

Center for Consumer Product Technology

Institute for Applied Technology

National Bureau of Standards

Washington, D. C. 20234

March 1976

Final

Prepared for

Optical Manufacturers Association

1730 N. Lynn Street

Arlington, Va. 22209

NBSIR 76-996

TESTING FOR THE IMPACT

RESISTANCE OF OPHTHALMIC

LENSES

Robert E. Berger

Center for Consumer Product Technology

Institute for Applied Technology

National Bureau of Standards

Washington, D. C. 20234

March 1 976

Prepared for

Optical Manufacturers Association

1730 N. Lynn Street

Arlington, Va. 22209

U.S. DEPARTMENT OF COMMERCE, Elliot L. Richardson, S»ef0t»ry

James A. Baker, III, Undsr Secntary

Dr. Betsy Ancker-Johnson. Assistant Secretary for Science and Technplogy

NATIONAL BUREAU OF STANDARDS. Ernest Ambler, Acting Director

Final

Introduction

The Optical Manufacturers Association's Research Associate Program

began at the National Bureau of Standards In February 1974. The object

of this program was to develop a mechanical testing procedure for

verifying the Impact resistance of ophthalmic lenses 1^1 . The research

effort was guided by the following specific objectives which were outlined at the onset of the program:

1. Collection and analysis of all available Information

regarding the FDA drop ball test Tj for eyeglass lenses.

2. Identification of the limitations of the present procedure

and the definition of the basic criteria for a proper test.

3. Experimental and analytical efforts to establish a procedure

for a new test.

Throughout the Investigation, a fundamental approach has been maintained

so that specific problems concerning Impact resistant lenses could be

viewed In terms of the broader perspectives of fracture mechanics and

statistics of fracture. Four research papers have been written.

The purpose of this report Is to review, for the sponsor, the

principal findings of the program, to discuss the possible alternatives

to the drop ball test, and to suggest a reasonable direction for continuing the effort. First, some preliminary remarks must be made

regarding impact, fracture, test methods, and damage to lenses.
- 2 -

Surfaces and edges of eyeglass lenses (as with all glass surfaces)

contain many small microcracks or, as they are commonly called, flaws.

The presence of such flaws is unavoidable and is a natural result of

the finishing and edging processes. The number, severity (for now,

severe flaws can be regarded as relatively deep cracks) , and location

of these flaws is random. For an individual lens , techniques do not

exist for describing this random distribution. However, for a group of

identical lenses, there are methods by which this flaw distribution can

be related to the amount of breakage when lenses are subjected to

increasing stress levels in a particular loading configuration.

The flaw distributions for surface flaws and edge flaws must be

described separately. This is because different procedures are used in

surfacing and edging and the nature of the resulting flaws reflects

these differences. An estimate of the depth of surface flaws is

about 1 micrometer. Edge flaws are at least an order of magnitude more

severe (the edge is ground but not polished)

When a lens is impacted, tensile stresses build up in regions of

both surfaces* and also on the edge. Fracture occurs when the stress

in the vicinity of a flaw is sufficiently large to cause that flaw to

grow catastrophically . As the number and severity of the flaws on a

lens increases, the likelihood for fracture also increases. The flaw

distributions on the surface and edge are then most important in

describing the impact resistance of a group of eyeglass lenses.

*In the drop ball test, the most likely surface for fracture initiation

is the concave surface where stresses arise from the flexure of the lens

during impact. Brandt _3/ discusses the relationship between the impact

parameters and the possible sites for fracture initiation.
- 3 -

The net flaw distribution on a group of finished lenses also depends

upon the type and quality of the strengthening technique (in the case

of glass lenses). The net effect of either heat treating or chemical

tempering is the existence of a surface compression region in which

both surface and edge flaws are embedded. For a given flaw, more

tensile stress is required to initiate fracture because the compression in the surface region must be overcome. Effectively, the severity

of the flaw has been reduced. For a group of lenses, the net flaw

distribution will depend upon the strengthening quality.

There are two general methods which can be used in testing for the

impact resistance of the finished product; the first is a proof test.

Each specimen is thoroughly inspected so that any lens containing flaws

in the worst end of the distribution are rejected. Traditionally,

proof tests are the safest and most expensive. A lens which passes

can be guaranteed to have no flaws more severe than some specified

level. Equivalently , it can be guaranteed to withstand a certain level

of impact.

The other alternative is to test for the overall quality of many

lenses. Essentially, one verifies that good machine shop practices are

in effect. No statement is made about an individual lens. Rather,

the percentage of lenses containing severe flaws is kept at some minimum level. Often this is accomplished by statistical sampling procedures.

If either of these methods involves mechanical testing (especially

the proof test), the question of damage to lenses must be resolved.

Damage occurs when the severity of a flaw increases by the process of

slow crack growth (when the applied stress is not large enough to cause
- 4 -

catastrophic failure). The amount of growth depends upon the magnitude

of the applied stress, the length of time over which the stress Is

applied, and the original size of the flaw. In Appendix 1, some limited

experimental data are presented on the subject of crack growth In optical

glass. Also, an equation Is derived In order to compute an appropriate

estimate of damage.

The Drop Ball Test

The drop ball test Is purported to be a proof test; I.e., all lenses

which pass the test may be sold. However, It was found that, during

the drop ball test, both surfaces of the lens are subjected to extremely localized tensile stresses kj ; I.e., the magnitude of the stress

drops off very sharply with distance from the Impact point. Therefore,

a lens which has potentially hazardous flaws will be Identified (by

fracturing In the drop ball test) only If one of these flaws happens

to be relatively near the Impact point. When Individual lenses are

repeatedly subjected to the drop ball test, they typically sustain

many impacts before fracturing _5/. This led to the formulation of the

"search theory" of Impact testing - the ball is searching for a weak

spot on the lens (where there exists a sufficiently severe surface flaw).

The same difficulty arises in the ability of the drop ball test to

detect potentially hazardous edge flaws. For round lenses subjected to

slightly off-center Impacts, the tensile stress at the edge differs,

from one point to another, by about thirty percent. This difference

is large enough to make the search theory applicable for the

failures as well 6^/. For lenses with asymmetrical shapes, differences

in the edge stress as large as 250% have been observed.
- 5 -

According to the FDA regulation 2^/, all lenses must be capable of

passing the drop ball test. However, it is now clear that impact resistance

cannot be verified on the basis of a single impact. Essentially, only a

small area of each lens is sampled in the drop ball test. The absence of

potentially hazardous flaws is verified for only this small area.

The implication that the drop ball test can be interpreted as a

sampling test that insures a minimum level of overall quality must be

resisted. This is because no limits are set for the tolerable amount

of breakage*. For example, a laboratory which breaks five percent of

its lenses (in the drop ball test) produces lenses with an overall

quality (in terms of the number of "bad" flaws) which is five times

worse than the laboratory which only breaks one percent. As any lens

which does not break can be sold, no minimum level of quality can be

attributed to it.

A further difficulty with the drop ball test is that the magnitude

of the peak surface stresses is very high. Often, relatively innocuous

flaws will initiate fracture Ij . Therefore, not all broken lenses were

necessarily bad.

The usefulness of the drop ball test is that a laboratory is likely

to take measures to minimize the amount of broken lenses. However, the

difficulty with enforcing the regulation has led to the suspicion that

laboratories with large amounts of breakage may often just suspend the

test.

*It has been shown that the percentage of broken lenses, for a group of

identical lenses, is nearly proportional to the number of "bad" flaws

per lens l_l , Therefore, the percent of broken lenses could be taken as

a measure of the overall quality of the lenses in the group (see section

on Sampling Tests in this report).
- 6 -

The possibility that the drop ball test causes damage to lenses

must also be investigated. A parameter which measures degradation in

drop ball testing is derived in Appendix 1. For surface flaws, the

strength degradation is on the order of 1% beneath the impact point.

Because the stress drops off so sharply with distance, the average

degradation over the entire lens' surface is several orders of magnitude

less. Further, it is unlikely that a second impact will coincide with

the first; therefore, in terms of a decreased ability to withstand a

second impact, degradation is negligible. For edge flaws, degradations

are on the order of 0.1% or less.

Often, when high power, thick lenses are drop ball tested, small

ring-type fractures can be observed on the impacting surface. As these

do not cause catastrophic failure of the lens, the lens has technically

passed the test, However, the lens is no longer suitable for sale.

Thus, many laboratories insert the lens in a plastic bag before administering the test. It has been suggested that this practice may

denigrate the intended purpose of the test 8^/. However, we have found

that there is a negligible decrease in the ability to detect lenses with

"bad" flaws when the plastic bag is used Ij \ i.e., the presence of the

plastic bag does not change the fact that very few of the bad lenses are

detected. On the other hand, the percentage of broken lenses does, of

course, decrease. If the drop ball test were to be used as a measure

of overall quality, the effect of the plastic bag would have to be taken

into account.
- 7 -

Alternative Proof Tests

One means of eliminating the deficiencies in the drop ball test is

to find a method by which any lens containing a potentially hazardous

flaw can be identified. This would involve inspecting the entire lens.

Early in the program, we investigated the feasibility of nondestructive

inspection techniques in which no stress (or a very low level stress) was

applied to the lens. None of the standard NDT procedures (e.g., acoustic

emission, dye penetrant, ultrasonics, x-ray diffraction) appeared to be

suitable for our purposes.

The remaining alternative is to develop a procedure in which nearly

uniform tensile stresses can be applied to large amounts of the surface

and edges. Two possibilities were investigated: (1) a static load test,

and (2) a thermal shock test. Both will be discussed in turn.

In a static load test, a loading configuration is designed for the

purpose of producing uniform stresses over a large surface area, and

the load is slowly applied to the lens. One restriction is that the

stress at the edge must also be relatively uniform and at a lower

level than the surface stress (because the edge flaws are so much more

severe). The ease with which the load can be applied must also be

considered. The resulting stresses from several types of loading

configurations were calculated with the aid of a finite element computer

analysis*. '

*This computer study, sponsored by the Optical Manufacturers' Association,

was performed by R.A. Mitchell, R.M. Wooley and S. Baker of the Engineering

Mechanics Section at NBS . The finished product of this investigation, a computer code which evaluates the stress and displacement distribution at

all points of a statically loaded lens, was presented to the sponsor.
- 8

-

Concentric ring loading, which had been used successfully for

circular disks 9/ , proved to be the most promising configuration*.

For a fixed support radius, an increase in the load radius (to increase

the stressed area) leads to a decrease in the uniformity of the stress

distribution and an increase in the edge- to-center stress ratio.. For

the load radius fixed, an increase in the support radius does not

seriously affect the uniformity, but does lead to some decrease in the

edge-to-center stress ratio. The values 7 mm and 13 mm, for the load

and support radii, respectively, proved to be a reasonable compromise

among the constraints. This configuration was tested in the laboratory,

with lenses which were instrumented with strain gages, and the agreement

with the analytical model was satisfactory.

There are several difficulties associated with the use of a

concentric ring apparatus as a proof test for ophthalmic lenses:

1. While the uniformly stressed area in this test is large

compared to the drop ball test, it is still small compared

to the total surface area of the lens.

*Other configurations were also investigated: a uniform pressure drop

across the lens did not produce as uniform a stress distribution; a second loading ring improved the uniformity of the stress distribution,

but the experimental duplication of this configuration was extremely

difficult; this was also the problem when the lens was ring loaded

while resting on an elastic foundation.
- 9 -

2. The solutions are only valid for axisymmetric lens geometries.

Lenses having non-round shapes, or lenses with multifocal

segments or cylinders, would not exhibit the same uniformity

in the stress distribution.

3. The required load levels are very high (on the order of several

thousand newtons) and would vary significantly from one lens

power to another (even for symmetric shapes).

4. The high load levels and the necessity for accurate

positioning of the lens make this a very difficult test to

administer at the optical shop level.

Thermal shock tests have been in widespread use as a tool in crack

growth studies of glass specimens. In this procedure, a lens is first

heated and then rapidly immersed in a cold bath. Tensile stresses, which

are roughly proportional to the temperature difference, build up

quickly at all points on the surface and edge. To optimize heat transfer rates, water has been used as the cold bath fluid 10/ . This

method has already been used successfully with ophthalmic lenses in a

study of edge quality; groups of lenses were ranked by comparing the

amounts of breakage as a function of the temperature drop 16/

However, in using the thermal shock method as a test for surface

quality, precautions must be taken to insulate the edge. Otherwise,

as the most severe flaws are at the edge, all fractures will initiate

there. We have built and tested such an apparatus (sketched in

figure 1), but its use as a proof test would introduce several difficulties:
-loci) it requires modification when the lens geometry is changed, (2) it

reduces the tested area, and (3) a separate thermal shock test would be

required for the edge.

Other difficulties with thermal shock testing are: (1) some

evidence of warping was noted in cases where no fracture was observed,

and (2) care must be exercised in maintaining oven and water bath

temperatures at the proper levels.

The most serious objection to both of the above proof tests is that

the amount of lens damage is significantly greater than in the drop ball

test. This is partly because the time duration for applying the load is

much longer. Concerning surface degradation, a case can be made for

testing at a lower stress level than the maximum in the drop ball test;

this can compensate for the increase in the time duration. However, the

edge stresses in the drop ball test are already so low that no further

decrease seems advisable. Even if the stresses could be applied in .02

seconds*, the strength degradation for edge flaws, in the concentric

ring proof test, would be nearly one hundred percent (see Appendix 1).

This amount of degradation cannot be tolerated.

*It is doubtful that the stresses could be applied so quickly in a static

load test without a significant increase in cost. Times of this duration

may not be inconceivable if thermal shock methods are used. However,

because the stresses are applied in a water environment, crack propagation velocities (and hence the degradation) are an order of magnitude

higher 11/.
- 11 -

Sampling Tests

As proof testing does not appear to be an entirely satisfactory

alternative to the drop ball test, we turn our attention to the remaining

alternative: a sampling test to insure that at least the overall quality

of lens production is above some minimum level.

The term "overall quality" must first be defined with respect to

impact resistance. A list of parameters that affect impact resistance

is presented in Table 1. The likelihood of fracture depends upon both

the flaw distribution and the applied stresses. An optical laboratory

has little or no control over the second set of parameters in Table 1

(lens geometry), which are usually determined by the customer. "Overall

quality" is thus determined by how well a particular laboratory can

control those parameters which affect the flaw distribution.

Consider a hypothetical case where a laboratory produces lenses of

only one geometry. That is, the variables affecting the stress distribution are fixed. The amount of breakage (measured by the percent of

lenses broken) in the drop ball test (or any stress test) can be related

to the flaw distribution Jj > The flaw distribution can be identified by

the number of "bad" flaws per lens _7 / . The overall quality is then

maintained by keeping the number of bad flaws per lens to a minimum.

In terms of lens breakage, the percentage broken should not exceed some

fixed level.

However, each laboratory produces many different lens geometries,

and this introduces an entirely new set of variables. That is, there is

a distribution of lens geometries, and it is likely that this distribution
- 12 -

varies among laboratories. There exists the possibility that the

effect of this lens geometry distribution may conceal (or greatly distort) the relationship between the percentage broken and the flaw

distribution*. This Is the major difficulty with using the present

drop ball procedure as a test for overall quality (say, by merely

imposing a limit on the percentage broken)

To eliminate these deficiencies, we consider the possibility of

sampling with "coupon" lenses. Coupon lenses have fixed geometries of

some convenient configuration. As the geometries are fixed, the stress

distribution can be estimated and a relationship between the percentage

broken and the number of bad flaws per lens (for both edge and surface

flaws) can be established. The overall quality of lenses from different

laboratories can then be compared.

The obvious objection to such a procedure is that the lenses which

constitute the sample are different from those which are being produced

for sale. Typical sampling procedures 12/&13/ assume that the products

being inspected are nominally identical. The sample is then chosen

randomly from the finished products. This procedure is certainly not

applicable to the production of ophthalmic lenses, where each finished

product is different. |

Consider the case of a one-man laboratory with only one piece of i

equipment for each of the processes discussed in Table 1 (i.e., one grinder,

one polisher, one edger, one strengthening unit). As discussed earlier, the

Introduction of flaws into the surface or edge appears to be a random process

Because the equipment is fixed, we assume that the number of surface flaws

*For example, the amount of breakage for typical -2 diopter lenses is

over twice as great as for typical +2 diopter lenses when the flaw distribution is assumed fixed. This is one of the results of the finite
- 13 -

introduced should depend only on the amount of surface area processed.

Similarly, the number of edge flaws introduced should depend only on

the amount of edge length processed. We assume that these flaw distributions can be satisfactorily described after some finite amounts of

surface area and edge length have been processed, regardless of what

lens geometries are being produced. Therefore, a batch should not be

defined in terms of a number of finished lenses but in terms of the

amounts of surface area and edge length processed.

For large laboratories, batches must be defined separately for

each combination of the parameters that affect the flaw distribution

(Table 1) . The coupon lenses are processed at predetermined intervals

during the production of each batch. Each coupon lens then comprises a

sample of surface area and edge length. Tests are conducted on them to

assess the overall quality of the entire batch.

The establishment of criteria for determining the amounts of

surface area and edge length which constitute a batch is outside the

scope of this report. However, a general guideline can be suggested:

the surface area and edge length of a batch should be large compared to

sizes required to describe the flaw distribution, but not so large

that significant changes in the equipment have taken place.

An Example

In this section, an example is presented on the use of coupon

lenses in a sampling test for the overall quality of a batch of ophthalmic lenses. In order to make the results quantitative, particular

safety criteria and coupon lens geometry are considered. It should be

understood that this example is for illustrative purposes and that

analogous procedures can be used Cor any safety criteria and coupoii

lens geometry.

\
- 14 -

To set safety criteria for ophthalmic lenses, one must first

choose bad flaw levels for surface and edge flaws. We have already

discussed the idea of categorizing flaws by the critical tensile stress

required for fracture initiation _7 / . At the bad flaw level, s*, all fl

with critical tensile stresses less than or equal to s'"'^ are considered

bad. For edge flaws, we will designate the bad flaw level by s *.

For a given flaw distribution, the number of bad surface flaws

per lens* can be represented by the function F(s*) _7 / ; for edge flaws,

F (s *) 6^/. The overall quality of a group of lenses is considered

acceptable if the number of bad flaws per lens is less than or equal to

some designated amount:

surface: F(s*)<_ N

(1)

edge: ^^(V^ - ^E

In this example, we will use the following values:

s* = 138 MN/m^ (20000 psi)

s^* = 89 MN/m^ (13000 psi) (2)

N = = 0.05 bad flaws per lens

E

The value for s* was used for illustrative purposes in a previous

paper ]_/ . This level was considered to be sufficiently high to insure

that lenses will be properly strengthened. The value chosen for s * is

hi

also arbitrary. It happens to be the highest edge stress which was

measured in some earlier experiments 6^/.

'^Actually, as discussed in the previous section, the number of bad

flaws per unit area would be a more appropriate parameter. However,

as the coupon lenses all have the same geometry, the area per lens is

fixed, and the two quantities differ by a constant factor.
- 15 -

For coupon lenses, we will use round, piano lenses, 48 mm in

diameter, with center thickness, 2.2 mm. These lenses were chosen

because the resulting stress distribution during impact has been

experimentally obtained . Any lens configuration will do, as long

as the stress distribution is known.

The relationship between the expected percentage of broken coupon

lenses in the drop ball test and the number of bad surface flaws per

lens is as follows Ij

1

^ (k+l)F(s*) k+1 f

, k+1 P^W^ (s* - s^)k+l ^DBT /

" ^o^

^'^^^^^

Zo

where s and k are parameters of the flaw distribution function, s^„„

o ' DBT

2

is the maximum stress in the drop ball test (s = 350 MN/m , 50000

Ud 1

psi), and Z

^ = ^o^^DBT* ^ "'"^ ^ function that depends only on

the stress distribution and is considered fixed for a given geometry

of the coupon lens IJ . Substituting the maximum allowable number of

bad surface flaws, N, for F(s*)» we obtain the maximum allowable value

for the expected percentage of broken lenses, P(s|^g^). More breakage

than this indicates that the number of bad flaws per lens in the batch

is too high.

Before a numerical value can be obtained for P(s_,„^) , values must

be chosen for the flaw distribution parameters and k. In particular,

s is the critical stress of the most severe flaw (lowest critical

o

stress). It follows from equation (3) that the choice, s^ = 0, leads to

the smallest value for PCs^^^), for all other parameters fixed. As

this is the level at which the rejection/acceptance decision Is made,
- 16 -

the choice, = 0, is thus conservative. The value, k = 3.8, has

been used previously to represent some experimental data 7/. Also it

has been shown that the number of bad flaws per lens is not particularly

sensitive to this parameter _7 / . So, from equation (3), using the values

s =0 and k = 3.8, and the stress distribution G(Z) from a representative

o

lens, we obtain:

P(Spg^) = 1%

An analogous procedure can be repeated for edge flaws (Appendix 2.1):

P(s^g^) = 2%

For the safety criteria set in (1), a group of coupon lenses with less

than 1% breakage due to surface flaws and 2% breakage due to edge flaws

is considered to represent an acceptable batch.

In figure 2, an outline of the relationships, which are discussed

in this section, is presented. Equation (3) is thus the relationship

between box A (the safety criteria) and box B (the maximum allowable

percentage of broken lenses)

An essentially unmeasureable parameter, the number of bad flaws per

lens, has now been related to a readily measureable parameter, the percentage of broken coupon lenses. By testing a sample of coupon lenses, it is

desired to infer whether the percentage of broken lenses in a large

population of coupon lenses is less than P(s ). If this inference is

made, it can be stated that the number of bad flaws per lens is less than

N. Then, because the flaw distribution is assumed to be independent of

lens geometry, it can also be inferred that the number of bad flaws per

lens in the general population is also less than N.
- 17 -

For a given confidence limit, the number of coupon lenses required

for testing decreases sharply as P(s ) increases 14/. Without

changing the allowable number of bad flaws per lens, P(s ) can be

DBl

increased by modifying the test method (say, by changing the stress

distribution, G(Z), in equation (3)). Thus, if an alternate test method

is used, in which the tensile stresses are more severe or are applied

over a larger part of the lens, the percentage of broken coupon lenses

will increase, and the number of coupon lenses required for testing will

be reduced.

For this example, we will consider a similar test to that presently

used: a drop ball test with a 7/8-inch (22 ram) diameter steel ball. One

advantage of such a test is that laboratories would not have to purchase

new equipment. The allowable percentage of broken lenses in this new

test, P(s ), can be related to P(s ). This relationship is derived ' new DBT

in Appendix 2.2 and connects boxes B and C in figure 2. Again, if s^

is set equal to zero, this percentage will be a minimum and thus conservative. For our example, the calculated values are:

The number of coupon lenses required to verify these percentages of

broken lenses is correspondingly reduced.

One other relationship may be of interest (see boxes D and B of

figure 2). For a fixed flaw distribution, the percentage of broken

lenses in the drop ball test can be computed for other lens geometries.

Such calculations would follow straightforwardly from the finite element
- 18 -

computer program referred to earlier. An average percentage broken,

P(8j^g^), can then be formed and this average compared to ^^^Qg^)* If

the geometries are selected carefully, the average, P(s ), can be

DBT

considered an estimate for the overall amount of breakage in a laboratory. Of course it may be necessary that the averaging process vary

among laboratories. This relationship also allows for a different, and

possibly more convenient, approach in determining the rejection limits

for the sampling test with coupon lenses. Referring to figure 2, the

path D-^B^C can be used instead of A^B-*C. That is, a limit is first

set on the overall percentage broken that is allowable. As records of

drop ball testing have been mandatory, there should be plenty of data

on which to base this limit. This limit is then a reflection of the

present state-of-the-art and can be modified if new technologies are

developed. The corresponding percentages of broken coupon lenses in the

drop ball test and the new sampling test then follow from the relations

D— B and B-»C (figure 2), respectively. Using the value s^ = 0, the

resulting limits are conservative. This approach is desirable because the

complicated (and somewhat arbitrary) decisions, regarding bad flaw levels

and the tolerable amount of bad flaws, are avoided.

Summary

The results of the research associate program indicate that it is

desirable to replace the drop ball test with a sampling procedure from

which meaningful information on lens quality can be obtained. We have

discussed some aspects of the design of a sampling plan in which the
- 19 -

overall quality of a laboratory's lenses is monitored by regularly

testing a set of coupon lenses. Several methods for determining acceptance/rejection criteria (e.g., based on the number of tolerable bad

flaws or on the present state-of-the-art) have been suggested. Details

for an actual sampling plan (which must also address the questions of

when to produce and test coupon lenses, what steps to take if rejection

is indicated, and how to enforce the plan) are deferred to such time

when a rigorous statistical evaluation can be performed.

The sampling procedure suggested in this report is intended as

a guide. Many modifications to this procedure can be imagined. For

example, it is possible that the manufacturer could verify the surface

quality of lens blanks (by testing coupon blanks, say). Then the

optical laboratory can be assured that the breakage it sustains is not

due to processes beyond its control.

Whatever direction the final sampling plan may take, some testing

may be necessary to verify certain assumptions. For example, in the

suggested approach of this report, a verification is required to confirm

that the flaw distribution is independent of lens geometry (if not,

difficulties can be circumvented by testing a worst case geometry).

The proof test methods discussed in this report (concentric ring

static load and thermal shock) are not suitable for verifying the impact

resistance of individual ophthalmic lenses. However, they may be of

use to the optical industry as a research tool; i.e. these tests would

allow for a more efficient determination of the effectiveness of new

materials or strengthening methods, if they are introduced.
- 20 -

It should be reemphasized , before closing, that the focus of this

report, and the entire program, has been on glass ophthalmic lenses.

Modifications would be required before the proposed sampling test could

be adopted for plastic lenses.

At this point, the NBS/OMA Research Associate Program terminates.

Until now, we have been concerned with the mechanical dynamics of

impact resistance and the drop ball test in order to understand the

limitations of the present test and to make recommendations for improving

it. The refinement of a new testing procedure, such as one suggested

in this report, lies in area of applied statistics.
References

1. OMA/NBS Contract CN-156

2. U.S. Food and Drug Administration, Use of Impact-Resistant Lenses

in Eyeglasses and Sunglasses, Federal Register, Feb. 2, 1972

(37 F.R. 2503)

3. Brandt, N.M. , The Anatomy and Autopsy of an Impact Resistant Lens,

Am. J. of Optom. and Physiol. Optics 51 (12): 982-986, 197A

4. Berger, R.E., Dynamic Strain Gage Measurements on Ophthalmic Lenses

Impacted by Low Energy Missiles, accepted for publication, Am. J.

of Optom. and Physiol. Optics.

5. Berger, R.E., Impact Testing of Ophthalmic Lenses: Stress Distribution

and the Search Theory, Journal of the Am. Optom. Assoc., ^7(1):

86-92, 1976

6. Berger, R.E., The Role of Edge Failures in Impact Testing of Ophthalmic

Lenses, accepted for publication, Journal of the Am. Optom. Assoc.

7. Berger, R.E., Interpretation of the Drop Ball Test in Terms of a Statistical Model for Fracture, accepted for publication. Am. J. of

Optom. and Physiol. Optics

8. Kors, K. and St. Helen, R. , The Use of Guide Tubes and Plastic Covers

in Testing Ophthalmic Lenses for Impact Resistance, Am. J, of Optom.

and Physiol. Optics. 51(12): 969-977, 1974

9. Kao, R., Capps, W. and Perrone, N., A General Numerical Large

Deflection Solution of the Coaxial Ring Circular Glass Plate Flexure

Problem, Catholic University of America, Washington, D.C., October

1970

10. Badaliance, R. , Krohn, D.A. , and Hasselman, D.P.H., Effect of Slow

Crack Growth on the Thermal-Stress Resistance of an Na„0-Ca-SiO_

Glass, J. Am. Cer. Soc. 59(10): 432-436, Oct. 1974

11. Wiederhorn, S.M., Environmental Stress Corrosion Cracking of Glass,

Corrosion Fatigue, Nace-2, pp. 731-742, NACE, Houston, Texas 1972

12. Muehlhause, CO., et . al. Consideration in the Use of Sampling Plans

for Effecting Compliance with Mandatory Safety Standards, National

Bureau of Standards Report NBSIR 75-697, June 1975
13. Duncan, A, J., Quality Control and Industrial Statistics, Richard D.

Irwin, Inc., Homewood, Illinois, 1965

1^. Mainland, D. , Herrera, L. and Sutcliffe, M. I . , Tables for Use with

Binomial Samples, Department of Medical Statistics Report, New York

University College of Medicine, 1956

15. Evans, A.G. and Wiederhorn, S.M., Proof Testing of Ceramic Materials - An Analytical Basis for Failure Prediction, U.S. National Bureau of

Standards Report, NBSIR 73-173, March 1973

16. Verbal communication relating to the Optical Wholesalers Association's,

study of failure modes in ophthalmic lenses.

USCOMM-NBS-DC
Appendix 1

The stress intensity factor, K, is often regarded as the best

measure of crack severity.

K » YqS Ja (1.1)

where s is the applied tensile stress normal to the plane of the crack,

a is the depth of the crack, and Yq is a geometrical parameter 15/ . An

experiment was performed to determine the relationship between the stress

intensity factor and the crack velocity, V, for optical glass. The

results are shown in figure 3.'"' According to Evans and Wiederhorn 1 5/

,

crack growth is mostly controlled by the low velocity region of the curve

where the relationship between V and K can be described by

V = AK". (1.2)

The exponent, n, was determined by least squares fit to be 20.4.

Cracks grow catastrophi cal ly when the stress intensity factor reaches a

critical value, K^, often estimated by extrapolating the high velocity

portion of the V-K curve to 10 ' m/sec. For optical glass then

= 0.84 MN/m^^^ . (1.3)

If a loading stress s is applied for a time At, a typical crack

will grow from an initial depth a. to a new depth a^. From 1.1 the

corresponding stress intensity factors K. and , can be calculated.

The relationship between K. and is found jS./ by integrating equation

K2:

K

2-n . , 2-n ^ At

(^.2)^ 32 2

^^ ^^^

I t z o

These measurements were performed by Dr. Sheldon Wiederhorn, Physical

Properties Section, NBS.
Then from 1.4, using 1.1 and 1.2;

K.

k7

1 n - 2

n - 2

0.5 )

If s. and are the stresses required for failure (i.e. for K

from 1.3), before and after crack growth, then

s. K.

f _ _j_

s. (1.6)

The percentage decrease in the stress required for fracture is an

appropriate measure of strength degradation:

D = ^

" "f = 1 -

n - 2

1 - ^

At

2 a.

I (1-7)

Order of magnitude estimates for the applied stresses on the surface

8 2

and edge of the lens during the drop ball test are 3.5 X 10 N/m and

8 2

0.7 X 10 N/m , respectively 4./. The depths of cracks causing failure are

then obtained from equation 1.1" with K = K^:

surface, a^ = 1.44 micron; edge, a^ = 36 microns

For the purpose of illustration we calculate the strength degradation

for cracks which are initially half as large as those causing failure:

a . = 0.72 micron; a,.. = 18 microns

SI El

From 1.1, the stress intensity factor for both these cracks is about 0.6

MN/m^'^^ for which the velocity (from figure 3) is about 10 ^ m/sec. The

duration of contact is about 0.2 msec V. Then from 1.7

= 10"^, = 5 X 10"^

"Using Yq = 2 for a crack which can idealized as a segment of an

ellipse 7/.
If the duration were increased by two orders of magnitude, to 20 msec,

the same edge flaw would grow to 36 microns and failure would be imminent-.

The corresponding degradation would be nearly 100%.

Append i x 2.1

For a round lens, a reasonable first approximation is to assume

that the applied stress ^^qj 'S uniform at the edge. Let f^^(^Qgj) denote

the fraction of edge flaws with critical stresses less than or equal to

s^g^. If the edge flaws can be represented by a Weibull type distribution 7/, then

^e(=e) =^ (=e - ^0 )

Therefore

^DBT

s* - st

. E 0

+ 1

(2.1.1)

(2.1.2)

The percent of lenses expected to break due to edge failures in the

drop bal 1 test is J/:

It remains to determine the parameter, k^ , for edge flaws. Consider

an experiment in which groups of lenses are subjected to thermal shock-all

lenses which break have failures originating at the edge. The percentage

of broken lenses is recorded as a function of the temperature difference,

AT. As AT increases the number of broken lenses increases. The applied

stress at the edge is proportional to the temperature difference

s £ =«<AT, Sq =<<ATq

is determined from the percent broken data by equation 2.1.2. Then

from 2.1.1 and 2.1.^:
In = b + (kg + )) In (AT - AT^)

(k + 1) C2. 1 .5 ) C

Where b = In

In figure ^4, is plotted as a function of AT - ATq on log-log paper-.

The slope is then + 1. From the figure k^ = 2.2. P( s^^^) then follows

from 2.1.1 and 2.1.2.

Append i x 2.2

For the drop ball test, the following relationship between the stress on

the lens and the input kinetic energy, K, was experimentally verified k/:

'NEW

'DBT

NEW

K

DBT

\_ 2

Now K is proportional to the mass of the impacting steel ball, the mass is

proportional to the volume and the volume is proportional to the cube of

the diameter. Therefore,

1

2

'NEW

'dbt

D

NEW

DBT

7/8 in.

5/8 in.

1

2

= 1.65

From equat ion (3)

' NEW

L" DBT J

k+ 1

= (1.65)^-^ = 10

P is ) For edge flaws ^ NEW^

P( E ) DBT

= (1.65)^'^ =5

"From OWA study 16/.
Table 1 . Parameters that Affect Impact Resistance

Parameters that Affect the Flaw Distribution

1. Quality of grinding and polishing (surface flaws)

2. Quality of edging (edge flaws)

3. Quality of strengthening (surface and edge flaws)

Also changes In the specific piece of equipment

and/or the operator are also likely to affect the

flaw distribution

Parameters that Affect the Stress Distribution

1. Thickness

2. Power

3. Base curvature

4. Shape

These parameters determine the stress distribution

for a given impact or static loading condition.

The presence of cylindrical power and/or multifocal

segments would also affect the stress distribution.
STAINLESS STEEL

F i gure 1Schematic Drawing

Insulate the Lens

Tests

of Apparatus Used To

Edge in Thermal Shock
<11

o

cn

t—\

/n T3 >

II

II 'U O) 4-> G) C

f—\

t > I/)

er

I/)

Li (/) ft)

V-/ >-

c

u 1 o —3 O o 1 

4-1 1 <D <4- 0 i- o E 0 • fO 4-< c

(/)

o a)

0) (U 4-1 O) 4-) 4-) «D

ro CO

o

E

o <u

(/) I.

w > o 03 < 14- |C1- o

N

1-

(U J'

4-> (/) o

ro Li_ i_ro j= o oc (/) o 3

4-1 ro J3 >

1-

E

4-1

(/)

E

-o

ro 5 2: UJ

ro >-

Ll. <

4-) (A

C 0)

c 0 4-* 0

a. Q. 5 3 3 (U 0 0 c 0 ro x> <u

14- V4- .c

a. 0 4-) 0

Q) t_ Q)

c

-0

ro LU ca ro UJ UJ

(U 0 T>

c z

ro in ro (U 0

0) 4-) 0) 4-) L. a. i_ (/) 4-1 Q- XI c J3 0) ro

4-» i_

4-1 4-1 3 c (/) c 1/1 D)

<u (U ca (U (U UJ 0 (/) 0 0 «4- z 1- c 1_ c C I/) 0) (U (U (U Q- Q- Q. 0

01D1

ro

ro

<uu

XIc

c

(U 0

4-1

c 3

0) XI

(U \.

4-1 4-1 0) in XI

</1 CL

S

ro x:

14-

c0 0) X 4-1 ro T3C

ro

1-3

D1
10-2

I I I I I I L_

.50 .55 .60 .65 .70 .75 .80

STRESS INTENSITY FACTOR, K (MN/m3/2)

Figure 3- Crack Propagation in Optical Glass
2.0

1.0-

0.5

UJ

Ll.

CO

z

UJ

LJ 0.2

Q-

<

Q 0.1

<

CD

0.05 -

O UNTREATED

# HEAT TREATED

I I I \ I 5 10 20 50 100

TEMPERATURE DIFFERENCE (AT -ATo)

Figure Results of Thermal Shock Tests 16/. Inferred

From Breakage Data (Equation 2.1.3).
lbS-1l4A (REV. 7-73)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO.

NBSIR76-996

2. Gov't Accession

No.

3. Recipient's Accession No.

I. TITLE AND SUBTITLli

TESTING FOR THE IMPACT RESISTANCE OF

OPHTHALMIC LENSES

5. Publication Date

January 1976

6. Performing Organization Code

213. O^f

'. AUTHOR(S)

Robert E. Berger

8» Performing Organ. Report No.

K PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No.

2130570

11. Contract /Grant No.

2. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

Optical Manufacturers Association

1730 N. Lynn Street

Arlington, VA 22209

13. Type of Report &. Period

Covered

Fi nal

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most sigpificant information,

bibliography or literature survey, mention it here.)

If document includes a significant

The principal findings of the Optical Manufacturers Association's Research

Associate Program are summarized. The limitations of the present drop ball

test for impact resistance are discussed. Essentially, only a small part

of the lens surface and a small part of the edge are subjected to sufficiently

high stresses. It is therefore desirable to replace the drop ball test with

a sampling procedure from which meaningful information on lens quality can

be obtained. Some aspects of the design of a sampling plan, in which the

overall quality of a laboratory's lenses is monitored by periodically testing

a set of coupon lenses, are discussed.

I

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

)

Drop ball test; impact resistance; ophthalmic lens; proof testing; research

associate program; sampling test.

18. AVAILABILITY ;[X] Unlimited

1

' For Official Distribution. Do Not Release to NTIS

1

' Order From Sup. of Doc, U.S. Government Printing Office

Washington, D.C. 20402. SD Cat. No. C13

Order From National Technical Information Service (NTIS)

Springfield, Virginia 22151

19. SECURITY CLASS

(THIS REPORT)

UNCL ASSIFIED

21. NO. OF PAGES

33

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

22. Price

$4.00

USCOMM.DC 29042-P74