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FROMDistribution authorized to U.S. Gov't.agencies and their contractors; CriticalTechnology; JUN 1967. Other requests shallbe referred to Air Force Materials Lab.,Wright-Patterson AFB, OH 45433.

AUTHORITY

AFSC ltr, 2 Mar 1972

THIS PAGE IS UNCLASSIFIED

1126-1 .OP146

/ IOUGLAS PAPER NO. 4353

00

,€ .,I

STAT0r #2 UxCL4SSInn

hIs dooment is subject to Speoial ezport controls = owkt ia ttal to foreign governments . tor gan nati ls

gMade only with prior approv of

SPECIAL FRACTOGRAPHIC TECHNIQUESFOR FAILURE ANALYSIS

JUN I007

PREPARED BY

B.V. WHITESONA. PHILLIPS

R.A. RAWEANtb

V. KERLINSMATERIALS RESEARCH AND PRODUCTION

ME TH ODS DEPARTMENTMISSILE AND SPACE SYSTEMS DIVISION

DOUGLAS AIRCRAFT COMPANY

PRESENTED TO70TH ANNUAL MEETING OF AMERICAN SOCIETY

FOR TESTING MATERIALSBOSTON. MASSACHUSETTS

29 JUNE 1967

FEB5 198I I0J ~ /c~)

SPECIAL RACTOGRkPHIC TECHNIQUES FOR FAILRE ANALYSIS

B. V. Wh!'eson, A. Phillips, V. Kerlins and R. A. Rawe

Mosile and Space Systems Division

ABSTRADT vIn order tQo-esist the investigator of srvice failures, york was

performed using electron fractographic methods to resolve problems thathave not been solvable using the more conventional micro- or lightticroacope techniques. Three independant problems were examined, andsolutions were achieved. These were,

11 Determination of fracture direction in thin sheet metalcomponents.

21 Differentiating between hydrogen embrittlement and stresscorrosion in high strength steels.

3.) Determination of applied cyclic stress as a function o.fatigue striation spacing.

The results of the investigation Inlcated that:

1. Fracture direction in thin sheet metal components can beresolved by the combined technique of replicating aroundthe acute angle shear lip of the fracture face and thesheet metal face, and the use of low magnifications on theelectron microscope. The direction of t-r dimplec withrespect to the fracture edge consistently indicated thefracture direction in the plane of fracture propagation.

2. There is reasonable evidence that stress corrosion andhydrogen embrittlement in high strength steel can beseparated by the following:

a. Hydrogen embrittlement fractures initiated subsurface,while stress corrosion fractures initiated on thefree surface.

b. Sti-as corrosion fractures had indications ofsecondary cracking while hydrogen embrittlementfailures did not.

c. The fracture features on the hydrogen embrittlementspecimens were clearer than those on the stresscorrosion fractures.

3. A correlation vas established between cyclic strss andfatigue striation spacing for several aluminum alloysover a wide range of alternating and mean itresses ;nthicknesses of 0.050 and 0.500-inches. The correlationwas empirically derIved and is of the form:

A relationship of the form

did not prove adequate to describe the data in this investigation due tothe fact that M appeared to be stress depandant.

CREDIT

The vor1k presevited herein was accoinpliohed by the Missile and SpaceEystems Div~.sion under a program sponsored by the Air Force J4~terialsfLaboratory (Contract AP33(615)-3014) of the United St&ae Air Force.

Electron Kicroeope

Electron Fractograpby

Ftilure Analysis

Fracture

Fracture Direction

Replication Methods

Hydrogen Embrittlement

Stress Corrosion

Fatigue

Striation Spacing

Crack Propagation Rates

Fmacture Tobuh?ess

Fatigue Testing

Aluminum

Steel

wafsplloy

Sustained Load Testing

Dimpled Fractures

Intergranular Fracture

Cadmium Plating

High Strength Mterials

TA~~~~~--- firu olmalsv,#

Tft t / )

-- 4 /

-- 4--'2 pa

itt is tho trac of S

£ CO~ - - -'h-

MUMCiLe f~tue tba af --erI -fngfjb -if gr-,

-i~t;~, nw- tote-4--to o h msitr

The~~~~ ~ ~ -4- PuI- fti vr a of,4,u ftp,*

4utrial andra thntse ere itsp ii hcf toepel1 cair~raft andssiles (Tabl 1,ehi es. Xs ofi *cs* a

1z oireto mutah ta tene statvo aEW t& cf.*gsti0A trw

Stength 6

-, j 0o stjel 0 20 60.050 .7 T.7

20W .T3 0.050 170.3 184.8

II43WO stee 0.125 215.5 270.3

2-43 AlIi O. 125 174.7 187AIDw stool 0.050 247.4 288.3ID(AO Bteel 0.125 252.1 293.6

AX35O~tee10.050 174.7 2~

AN350 Stoel 0.125 171.9 204.5

7075476 Alum-ID 0,050 75.9 83.9

7075-46 Aluminum 0.125 78.5 84..5

2004T3 Aluinum 0.050 51.5 69.5

2CI4-?3 Aluminu 0.125 56.6 71.8

7079-T6 Aiuminum 0.050 64.9 72.0

7079-T6 Alui-ar 0.125 64.9 72.0

oo050 125.3 It.8

•p ley o 0. 125 130.7T18

Ito

0 2 c

coOD

iC:

0L '

1-

tear fracture (Figure ib). All m=terials failed with fractures tat

Ud 100 percent oblique shear, Figure 2, with no areas of plane strain

tbat Vrovided wq mcroscople Indication of fractue direction.

In all specimens fracture direction was discerIble using the electron

aicroscpe, aM it is belileed that the tecbnique for determining

fracture direction is ofplicatle to all materials that fail by dimple

pure(2) . For sqllcity, none of the individual materials tested

are delineated in the illustr 'ions, since the fractographic features

anlyzed are identioal, except for the relatie size and abundance of

the observed dia"les.

Mwe basic concept of determining fracture direction that applies

to all naterials vhich fail by iple rupture is illustrated in Figure 3.

For all specimens tested, the open elongated dimples (dimples with the

open end of their parabolas toward the fracture edge) along the edge of

the rupture point back to the fracture origin (Figure 3a). The open

dimples occur predominantly oan the acute angle shear lip. The closed

elongated dimples (dimples with the closed ends of their parabolas

toward the fracture edge) along the obtuse angle shear lip and those

found in the center of the fracture were usually randomly oriented and

could not be used for fracture direction determination (Figure 3b and 3c).

The acute angle shear lip was replicated by the plastic-carbon

technique (2) in such a way as to overlap the edge of the fracture. In

order to orient the replica with respect to the fractured specimen, one

or both corners of a rectangular replica were cut so as to indicate the

.,,-P- .._. . ., L - ...

" '- . ,.ll " ZU

1-

I-.-

C •-

0 01! . - IL t

a.

... a..4d ! -, 2

--... -- "a- .-. 4i-

o)I-

!.F.

(a) agn.20I (b) Mg.2OOpen Dimples Closed Dimples

F.D. Fracture Direction

ObatueAnl

Shear Lip

(c) Magn 3500X

Acute Angle Ejuiaxel DimplesShear Lip

Figure 3. Relationship Between Ori nlation of Open DimplesAlong Fracture Edge and Fracture Direction

6

- imi

desired orientation. The replica was then placed in the electron

microscope so that the replica orientation with respect to the fracture

could be maintained in the electron fractograph. The fracture direction4i

was then related back to the actual specimen. The complete t %nique is

illustrated in Figure 4.

It was very important to obtain a good replica of the fracture

edge and the open dimples immediately adjacent to it. This was essential

because the orientation of the open dimples had to be determined locally

with respect to the edge. In order to obtain an accurate indication of

the edge line, low magnification (approximately 50OX) electron micro-

scopy techniques were used. A series of overlapping electron fracto-

graphs were taken along the edge region in order to obtain an accurate

sense of the dimple direction. A typical low magnification electron

fractograph showing open dimples along a fractured edge is shown in

Figure 5.

Discussion

The sensitivity of dimples to fractur) direction can be explained by

considering the basic difference between shear and tear dimples. In

case of a "pure" shear fracture, the dimples point in opposite directions

on mating fracture surfaces (2). In case of a "pure" tear, the dimples

point in the same direction (back to the fracture origin) on both mating

fracture surfaces. Since from a practical standpoint no fracture occurs

by "pure" shear alone, i.e., some tearing alvays accompanies a rnning

fracture in thin sheet material, the resulting elongated dimples observed

on a fracture surface are the end product of a combined shear and tear

7

Fracture Surface Arbitrary Surface

AleReplica Referenceoe~ Direction

Plastic Replica

Fracture -Fracture Edge

STEPEP 2:1Cut to Identify Replica

STEP 3 Reference Directiont Shado w and Deposit Carbon by Normal

Two Stage Plastic-Carbon Techniqoe.

Figure 4. Fracture Direction Replication Technique.

I.

Figur 5. Oen Diple pl Frctrido n dce

Il

Fracture Direction

J 9

type of fracture. If a fr.cture propates prediminantly by a tear

meehanim, the elonoted dimples would point more strongly in the

direction of fracture origin than if it propagated primarily by a shear

mechanim. This concept of resultant combined dimples is illustrated

in Figure 6.

It is not clear, however, why open dimples are consistent in their

orientation with respect to fracture direction while closed dimples have

shown inconsistency. Assuming that a fracture separation can be non-

symmetrical, it is difficult to explain vhy this non-symmetry should only

affect closed dimples since their apparent "twin" is an open dimple which

is oriented in a systematic and orderly fashion. Perhaps discontinuous

propagation at the center of the fracture (voids occurring ahead of the

crack front) could account for the lack of orderly d1imple orientation

in this region.

Conclusions

1. It is possible to determine fracture direction in thin sheet-metal

that fails in an oblique shear mode, and by dimpled rupture, by observing

the orientation of open dimples along the fracture edge at the acute

angle shear lip.

9. Replicas must be taken that overlap the fracture surface and the

sheet metal face, coupled with low magnification microscopy, in order

to obtain an accurate assessment of the open dimple orientation with

respect to the fracture edge.

3. The type of material examined is not important, as long ae dimples

are visible on the fracture surface.

10

CLC

E'

o .rc

*00

IV -UU UU 0 - wE*

CC

o 0 4

E0 6

4' 4

IN I

~00

IL

PION= 2--1lectron Fractographic Technique for Distinguishing Stress

Corrosion From Rydrogen Embrittlement in High Strength Steels

Introduction

Stress corrosion and hydrogen embrittlement have been a comon and

exceptionally perplexing source of service failures in the high strength,

medium-carbon, low-alloy steels. These fractures most commonly occur on

components that have long life spans and exist under some level of sus-

tained stress even when the component is not in use. There have been

attempts to distinguish between the appearances of the fractures caused

by stress corrosion and hydrogen embrittlement without substantial

success because the two failure types exhibit a remarkably similar

fracture appearance(2). It would be of great importance in failure

analysis to have the ability to recognize differences in the fracture

appearances of the two failure mecbanisms so that appropriate corrective

ac ion can be taken.

Experimental Procedure

Sustained lead tosts were conducted to produce failures due to stress

corrosion or hydrogen embrittlement. The alloys selected were forged

434o0, 4330H and D6AC. The mechanical properties are shown in Table 2.

The sustained load specimen configuration is shown in Figure 7.

12

TAML 2.-HEYXANIAL PJOZ WI$0 BMW~ UM M

Strength

Material Thickness, in.* Ftu F y

4340 0.050 277.2 240.9

4330K 0.050 224.4 193.8

D6AC 0.050 289.6 243.2

*Cut from 4-iAa" square billet in the transverse grain direction

1 evaluate hydrogen ebrittlement, three distinct cadmium plating

processes vere used to provide qualitative differences in the hydrogen

levels in the test specimens:

1. Acid pickle plus cadmium fluoborate plating

2. Bright cadmium cyanide plating

3. Cadmium fluoboratr plating,

All plating conforned to the requirements of QQ-P-416, except that

specimens were not embrittlement relief baked after plating. This was

done to insure se~tmen failure. The stress corrosion specimens were

tested in the bare and vacuum cadmium plated condition (MIL-C-8837).

Both nydrogen embrittlement and stress corroion tests were conducted

at 50,- 75 and 90 percent of yield strength. Speciwns were axially

loaded in the spring jigs shown in Figure 8. The hydrogen embrittle-

mwnt tests were conducted in plastic begs containing silica gel

K 13

0.125 In. DIA 0.25 In .5In. DIA

V - ~3.125 In. -Figure 7. Configuration of Hydrogen Embrittlement and

Stress Corrosion Specimens

Figure 8. Specimen Jig Being Loaded~ in a Tensile Machine

desiecent. Th stress corosion tests ,..re eonducted by alternate

iinersion in 6eloniLed ater (10 minutes in vater, 50 Inutes in air).

Results

The electron fractographic exaudntion of known stress corrosion and

hydrogen embrittlement fractures revealed similar characteristics for

the steels examned, and it appeared that no exclusive single feature

precisely identifies either fracture mecbnism. Eovever, a combination

of features could be used to distingaish between the two types of failure.

The features associated with stress corrosion fracture were:

1. Predominantly surface nucleation of intergranular fracture.

2. Intergranular regions show pronounced secondary cracking

or deep crevices.

3. A relatively greater amount of oxidation or corrosion attack

at the nucleus and slow growth region than in the rapid

fracture area.

4. Less pronounced hairline indications on the intergranular

surfaces of stress corrosion fractures in comparison to

intergranular surfaces of hydrogen embrittlement fractures.

The features associated with hydrogen embrittlement were:

1. Predominantly sub-surface nucleation of intergranular fracture.

2. Evidence of partial dimples and distinct hairline indications

in the intergranular regions.

3. Both the nucleus and the rapid fracture areas exhibit rela-

tively equal degrees of oxidation or corrosion products.

1

In order to determine whether a fracture nucleus was surface or sub-

surface, a two stage plastic-carbon replication technique was used. The

suspected nucleus region was marked by placing a fine scribe line on

the free surface next to the nucleus area. The plastic replica was

allowed to overlap the edge so as to include the scribe line on the

free surface. This line as then used aiv a guide to locate the nucleus

area. The differences between the nucleus regions of stress corrosion

and hydrogen embrittlement fractures are shown in Figure 9. In the case

of stress corrosion, the intergranular nucleus area followed the surface

and extended straight back from the surface. In the case of hydrogen

embrittlement, the intergranular nucleus regior formed predominantly

sub-surface.

j-: Other features associated with each type of fracture are shown inFigure 10. Stress corrosion usually showed evidence of secondary cracking

and corrosion products in the nucleus region. The Isirline indications

in the intergranular regions and partial dimples which are thought to be

associated with the fracturing process are somewhat more distinct in

hydrogen embrittlement than in stress corrosion fractures. These subtle

differences are illustrated in Figure 11.

By using a microautoradiographic technique(3), it was sLown that

hydrogen was associated only with the intergranular portion of the frac-

ture. Due to the relatively low resolution of the technique, it was rt.t

possible to relste hydrogen accumulation at specific structural details

such as partial dimples or hairline indications.

17

~;Ae

:~Magn.0X

e Stress Corrosion

Edge, Ma 16X

Hydrogen EmbrittlementMagn. 16X

Magn. 35OOXFigure 9. The Nature of Nucleus Region For Stress

Corrosion and Hydrogen Embrittlement Fractures f

Stress Corrosion -Corrosion Hydrogen Embrittlement -Products (Arrows) Partial Dimples (Arrows)U-

- Stress Corrosion -Secondary Hydrogen Embrittiement -Cracks and Crevises (Arrows) Hairline Indications (Arrows)

Figure 10. Typical Electron Fractographs Showing The Distinguishing

Features of Stress Corrosion and Hydrogen EmnbrittiementMagnified 6,500X

1~9

4V

Hydrog en Embrittlement Stress Co rrosion

Figure 11. Illustration of Subtle Differences Botween Hairlineindications (Arrows) of Stress Corrosion and Hydrogen

Embrittlemdnt Fractures in 4340, 260/280 Steel,Magn. 6500X

20

Discussion

It has been shown that the accumulation of hydrogen with accompanying

crack nucleation occurs at a region of high triaxial state of stress ( 3

and 4). This triaxial state of stress exists sub-surface at the root of

a notch; therefore, it is not unexpected to find evidence of sub-surface

nucleation in hydrogen embrittlement frnctures. In stress corrosion

fractures, however, surface nucleation occurs because corrosion initiates

from the surface and progresses into the material.

Intergranular fracture is associated with both stress corrosion

and hydrogen embrittlement failures, and is generally confined to the

nucleus region. Hydrogen embrittlement intergranular fracture showed

a preponderance of partial dimples and hairline indications on the

grain boundary surfaces. This suggests that a large degree of mechanical

separation has been involved, whereas stress corrosion fractures, dis-

regarding corrosion products with their accompanying surface attack, show

smoother intergranular surfaces, thereby suggesting a high degree of

non-mechanical separation (Dissolution).

When attempting to distinguish stress corrosion from hydrogen

embrittlement fractures it was important to obtain a good overall

impression of the nucleus area. Often, the differences between these

two failure types were subtle and examining only a few isolated areas

might have lead to incorrect analysis.

In addition, because of the subtlety between these two sustained

load failure appearances, we must make use of all the far j available.

This includes knowledge of the part processing practices, service history.,

21

*nd prior service failures of the same type. The electron microscope

should be used primarily to supplement knowledge rather than be the

only source of information vhen analyzing this type of failure.

Conclusions

The features associated with stresE corrosion fracture are:

1. Predominantly surface nucleation of intergranular fracture.

2. Intergranular regions show pronounced secondary cracking or

deep crevices.

3. A relatively greater amount of oxidation or corrosion attack

at the nucleus and slow growth region than in the rapid

fracture area.

4. Less pronounced hairline indications on the intergranular

surfaces than observed on hydrogen embrittlement fractures.

The features associated with hydrogen embrittlement are:

1. Predominantly sub-surface nucleation of intergranular fracture.

2. Evidence of partial dimples and pronounced hairline indications

in the intergranular regions.

3. Both the nucleus and the rapid fracture areas exhibit rela-

tively equal degrees of oxidation or corrosion products.

22

PROBLEM 3--Relationship Between Cyclic Stress and

Fatigue Striation Spacing

Introduction

Fatigue cracking in metal alloys is one of the most cmonly observed

modes of structural failure in the aerospace industry. It occurs as a

result of the repeated application of loads well below the ultimate

strength of the material. When the fracture surface of a fatigue crack

is examined at high magnification by means of electron microscopy,

periodic markings, known as striations, are observed. The spacing

between striations is characteristic of the microscopic progression of

the crack front during one loading cycle.

The major objective of this program vas to develop a correlation

I between the striation spacings and the cyclic load history of through-the-thickness fatigue cracks in various sheet and plate aluminum alloys.

Such a correlation would then be useful in the analysis of fatigue

failures of structures fabricated from these alloys.

Experimental ProcedureThe aluminum alloys studied included 2024-T3, 7075-T6, 7075-T73, 7079-TE

and 6061-T6, Table 3. For the purpose of detecting an effect of material

thickness on the properties to be studied, both 0.050-in. sheet and

0.500 in. plate of 2C4-T3, 7075-T6, and 7075-T73 were used. The

remaining alloys were tested in the 0.050-in. thickness only.

Fatigue cracks were developed in 8-in. wide by 18-in. long Wecimens,

centrally slotted and fatigue-precracked, Figure 12. Growth of the fatigue

4i

TA=I 3--I4ATr.CA PRPZTIEB 0? LON" ALOYS

USMD FOR CRACK PftPALTION TO&M

Str'ength

Material Thickness, in. Fty ksi Ftu, ksi

2024-T3 0.050 51.2 69.551.0 69.452.4 69.6

2024-T3 0.500 56.0 66.056.6 66.656.4 66.6

7075-T'6 0.050 75.6 83.576.1 84.376.1 84.1

7075-T6 0.500 75.6 82.474.7 82.o78.2 84.3

7075-T73 0.050 66.9 77.7

67.8 78.565.8 76.6

7075-T73 0.500 63.8 73.764.1 74.262.o 73.0

7079-T6 0.050 65.7 7.064.6 72.064.4 72.0

6o61-T6 0.050 42.1 47.44.0 47.242.3 47.6

24

AS

000\

00 0

MachinedStarter Notch

18 in.

Precrackedby Fatigue

0 0 0

8 in. -1Figure 12. Fatigue Crack Propagation Specimen

j2

crack was monitored visually &nd by means of 2-in. long crack propagation

gages bonded on one specimen surface in the path of the growing crack,

Figure 13. hach gag consisted of twenty elements, equally spaced at

0.10-in. intervals. Sequential rupture of Sage elements by the propa-

ipting crack was recorded by an oswillograph simultaneously with the

output from the load cell. The oscillogaphic trace provided a detailed

loading and cracking history of each specimen.

The cyclic stresses which were employed were selected to represent

loading environments encountered in military aircraft and to provide

evidence of the effect on striation spacing of mean stress, alternating

stressj, frequency of loading and material thickness.

The cyclic stresses for fatigue crack propagation tests are presented

in Table 4. Standard fatigue crack propagation (Table lea) vas established

in tests with constAnt mean and alternating stresses. In each of these

tests one of the four soheftled man stresses and one of the five sched-

uled alternating stresses characterized the cyclic stress for that test.

The loading frequency for these tests was 1000 cycles per minute. In

several tests, a frequency of 10 cycles per minute was employed.

8pectrum-load fatigue crack propagation tests (Table hb) were also

performed in order to simulate service conditions and duplicate single

mean or alternating cyclic loads. In one series of these tests the mean

stress was held constant while the alternating stress varied every ten

cycles. In the second series, the alternating stress was held constant

fand the mean stress was varied every ten cycles. These tests wereperformed at a frequency of 600 cycles per minute.

26

MAI.

TAM 4--FATIOR C MCKl IG TM CONDITIONS

Table 4&--Standard Fatigue Crack Propaption

(, k2d 8.2 - 13. 5 16.5 22.5

Thick. Freq. (3)Alloy in. qu 'w, ki 6.75 2.5 7.5 11.25 13.5 6.75

2(o4-T3 o.o50 10 x x x x x x10 X X

0.500 1000 x x x

7075-T6 0.050 1000 X X X x X X10 X X

0.500 1000 X X X

7075-T73 0.050 1000 X X X X X X10 X X

0.500 1000 X X X

7079-T6 0.050 1000 X X X X x X

6061-T6 0.050 1000 x X X x X X

Table 4b--Spectrum-Load Fatigue Crack Prapaation

[, ksi 13.75 8.25 13-75 22.5Thick. Freq. a, +k id 2.5 1 7.51 1.25 6.75

Alloy In. CIM , , 6

2o02-T3 o.o5o 600 x x

7075-T6 0.050 600 x x

7075-T73 0.050 600 X X

7079-T6 0.050 600 X X

6061-T6 0.050 60 x x

(i) All Stresses %-sed on Gross Area

(2) n mean stress

(3) "a alternating stress2

(4) Frequency in cycles per minute

28

e standard t-o-stage plastic-carbon technique vas used in pre-

paring replicas of the fatigue crack surfaces for exmination in the

electron microscope. A corner was cut off on aach replica in order to

orient it with respect to the vacroscopic crack propagation direction.

Striation spacings were measured from electron fractograph negatives

taken at a standard magnification of 5300X. Calibration of this magi-

fication vs ccomplished using a replica of a diffraction grating

containing 28,600 lines per inch.

The fatigue cracks exmined ranged from approximately a total length

of 0.7 to 4.3 inches. The selection of areas to be replicated on indi-

vidual specimens vas based on the number of cycles used to propagate the

left or right crack front 0.10 inches. Since it as difficult to observe

distinct fatigue striations in areas where less than about 200 cycles [were used to grow the fatigue crack G.10-ih., these areas vere not rep-

licated. 'For 0.10-in. increments containing more than 200 cycles of

stress, replicas were taken at significant intervals (usually 3 to 4)

along the fracture path.

The fatigue striation qpacing data was obtained by examining a

specific 0.10-in. area to gain an impression of represent-tive striation

spacings in this area. Generally, a fatigue striation spacing for a

specific area represents an average of four readings, depending on the

definition and number of striations present. Where possible, measure-

ments were taken from relatively flat regions that exhibited thb largest

uniform striation spacings over an appreciable distance. Striations

that were influenced by second phase particles, or occurred on steep

slopes were not considered. It was found that distinct fatigue striations

could be observed on both the normal and oblique mode of the macroscopic

fracture profile in the fatigue region.

Results

Completely detailed data from all the tests may be found in Appendix I.

When comparing the macroscopic fatigue crack growth rate (obtained

by dividing the observed 0.10-in. increment crack growth by the number

of cycles used to propagate the crack through that increment) to the

microscopic growth rate (striation spacing), the following behavior as

observed:

1. Macroscopic rate was less than the microscopic rate

2. Macroscopic rate was equal to the microscopic rate

3. Macroscopic rate was greater than the microscopic rate.

Thi is illustrated in Figure 14. The first type of behavior is usually

observed at relatively low crack growth rates. At higher crack growth

rates conditions 1 and 2 are not observed. The large deviation of crack

growth rates between the macro and micro rates in condition 3 can be

explained by the presence of appreciable dimple rupture along with

striation-producing fatigue propagation.

Electron fractograph analysis of spectrum loaded specimens indicates

that when a fatigue striation is produced, it is the result of one cycle

of stress. However, it has been observed that for both varying alter-

nating and varying mean stresses, when the applied mean or alternating

stress range changes abruptly from a high to a lou level, there is a

period (at least 10 cycles) during which the fatigue crack apparently

30

LEGEND-

0 Micro Rate 0 a=-2.50 ksi,

Macro Rate Ilr=13.75 ksiMaterial: 2024-T3Thickness: 0.050 in.Frequency: 1000 cpm

@ 314 micro-inches/cycle

200

180

160

" 140

o 120

" 100 Macroscopic Crack -.....c Growth Rate

0 80... . ..

E 60 .....

Z40 -MicroscopicCrack

20 - Growth Rate

0 10 2 4

Total Crack Length, inches

Figure 14. Relationship Between Fatigue Microscopic andMacroscopic Crack Growth Rate

3J

does not propagate, Figure 15. On the other band, when the low level is

not Imediately preceded by high levels of stress, fatigue crack propa-

gtion is observed.

The striation spacings were examined in terms of a parameter K(5 )

which describes the local intensity of stress in the vicinity of the

crack tip, as:

1/2

where a - gross section stress

w - panel width

f - total crack length

ay - tensile yield strength

A representative plot of fatigue striation spacing, d2/dM, as a function

of K, (max - Kmn), is shown in Figure 16. The dashed lines in the

figure encompass the range of data points and suggest a relationship of

the type:

d 4 (2)

This relationship is somewhat iu agreement with previously published(6, 7, 8)

analyses . However, examination of the figure reveals that

the proportionality constant, M, is some complex function of the stress

environment. For example, knowledge of d.,/dN alone from fractographic

analysis will not define 4K with satisfactory precision. A further

Magn. 13,800X

Figure 15. Characteristics of Spectrum Loading. Mean Stress=13.75 ksl, Three Alternating Stresses (2.5, 7,5 and11.25 kai) Applied In 10 Cycle Intervals. NoteLack of Striations for Lowest Alternating Stress(2.5 k81). Arrow Indicates Fracture Direction.

Legend:

0a on+ ksl ksi

0 2.50 13.757.50 13.75

o 11.25 13.7513.50 16.506.75 8.25

* 6.75 22.50

100 Material: 7075-T73

I_ _ - Thickness: 0.050 in.I__Frequency: 1000 cpm50A

16 0"-A I

A

.4. 0 =

C I- 0 - .... . -

10

tt

10 50 100 500

Microscopic Crack Growth Rate, d), micro-inches/cycledN

Figure 16. Relationship Between Striation Spacing and StressIntensity Range Para.",meter AK

relationship between M and the stress environment =ust be knYM to

make Eq. 2 useful as a correlation between striation spacing and stress

environment.

When the range of the cyclic stresses under investigtion is sall.,

Eq. 2 will appear to define a correlation between AX and striation

spacing (and between &K and iucroscopic growth rate) and tne propor-

tionality constant, M, will have a discrete value.

When the range of cyclic stresses is expanded, however, as was

true in this program as well as in Ref. 9, based on macro-rate, M Is

revesled as a multi-valued function of the stress.

For most aircraft structures the average mean stress is knovn (1-g

load) and is generally constant for a given aircraft gross weight.

Alternating stress. on the other bond, will vary and for many extreme

operating conditions the magnitude of the alternating stress is not

known. For this reason, striation spacings were examined with the

objective of developing a correlation between alternating stress and

the distance between fatigue striations.

Logaritmic plots of striation spacing, s, versus total crack

length, , revealed that striation spacings increase with distance from

the origin (4/2) as:

where 8 V a constant dopending on material,frequency aud thickness

m u a constant depending on the stressenvironment

W - panel width

....5-------------------------.-...........

As shown in Figure 17 the slope, m, of the curves varies with the

cyclic stress in such a manner that all curves intersect at a common

point, (S, W). From this plot, however, the exact manner in which

the cyclic stress influences the slope is not immediately obvious.

Further plots of the slope as a function of alternating stress at

equal mean stresses, Figure 18, and as a function of mean stress at

equal alternating stresses, Figure 19, indicated that the slope, m,

can be described as:

.p ,[ I'1m (4)

where p is a constant nearly equal to 10, as shown in Figure 20. Solving

for alternating stress, 2/ p 2

a =mo (5)

From Eq. 3,

log (a!S,)M, ( 6)log (.'/w)

Substituting in Eq. 5,2

pr '"7 log umS,,, (7)aa 1/3 log (s/S)w

-' m

Equation 7 relates alternating stress to striation spacing by

means of two constants, p and 8, which can be determined by test.

Values for the aluminum alloys tested in this program are given in

Table 5. The value of the constant, p, varies only slightly from alloy

to alloy and does not appear to be affected by cyclic frequency. The

36

1000..Sw=o80oX 10 6 ...... ...

oT. Orm m, _l

jksi ksl for p = 9.73

013.50 16.50 1.040 jIo011.25 13.75 1.210 - -

S6.75 22.50 1.326 1_ 7.50 13.75 1,483b 6.75 13.75 1.563 1( 6.75 8.25 1.853

0 2.5 13.75 2.568

S100C

0 L

UIU

E OF

W = 8.0 In.

0; 10 _f

____ - _h. _ Material: 7075-T73I Thickness: 0.050 in. I

Froquency: 1000 cpm

S = Sw(w)m Solid Symbols are-- Spectrum Load Tests -

lI/2 cm/

L__ - - -- - - -.. - . ....

0.1 1 10

Total Crack Length,, inches

Figure 17. Striation Spacings Versus Crack Length

For 7075-T73, 0.050-in. Thick Panels

10- - -Material: 2024-T3 ___

Thickness: 0.050 i n.Frequency: 1000 cpm--- ___

8.25

(I) _ I~22-50

2 5 1

Alternating Stress, Ora, + ks i

Figure 18. Effect of Alternating Stress on Slope, m

38t

10- - - -10 Materal: 2024-T3

Thickness: 0.050 in.

Frequency: 1000 cpm

I E _ _ _ _±ksi

0 6.75

10 50

Mean Stress, am, ksi

Figure 19. Effect of Mean Stress on Slope, m

/39

Material: All Alloys TestedThickness: 0.050 in.Frequency: 1000 cpm

3

Oa/2 am3

0

E

_.

II

I= Range for alltests exceptfour pointsshown.

0 0.1 0.2 0.3

1

(0a)Y (Gm) 1/3

Figure 20. Determination of the Value of the Constant, p, in Eq. 3

0I

MALE 5--CONSW T FOR USE I CORREIATIG STRMTI0N

SPACINGS Wl C!CLD STEMS (EQ.7)

Material Thick. Frequency p (1) 8 (2)2 -in. - _ _

2024-T3 .050 1000 10.35 550 x 102o 10.35 8oo xo.

.500 1000 10.35 1500 x 10"6

7075-T6 .050 1000 9.90 800 x 10610 9.9o 1oo0 x 10"

.500 1000 ..

7075-T73 .050 1000 9.73 800 x 010 9.73 100 x 10-6

.500 1000 9.73 2000 x o0

7079-T6 .050 1000 10.05 1000 x 10-

6061-T6 .050 1000 10.20 800 x O6 j(1) Constant for Eq. 7 vhen ca and y are in units of kei

(2) Constant for Eq. 7 vhen.-,j W, and a are in units of inches

constant, 8w, varies more from alloy to alloy and shows a definite

trend to increasj with decreasing frequency and increasing thicknese,

An increase in Sw reflects larger striation spacing (higher crack

growth rate).

All elemnta necessary to express the striation spacing, or crack

growth rate, in terms of LKI are present in Eq. 7. After the required

substitutions and rearrangements, the resulting equation is somewhat

cumbersome: 2

s.,s -Sarta2 (8)

ii pwhere m= 1 /2 1/3

Solution of this equation for alternating :!tress (upon which a( itself

is dependant) i3 not convenient. However, it is interesting to note

that the values of the expone.t, m, experienced in this work varied

from about 1.04 to 2.57. One indicated operation in Eq. 8 is the

raising of a? to the power of m, or the raising of K to the power

of 2m. For the values of m indicated above, the range of values for

the exponent of K is from 2.08 to 5 14. Reference 6 sumarizes the

work of various investigators who have fo,imd relationships of crack

growth rate to tK raised to powers from 2 to 5.

The ability of Eq. 7 to descrite the standard fatigue test data iri

demonstrated in Figure 21. In this figure, the alternating stress pre-

di ted by Eq. 7 is plotted versus the actual alternating stress. Each

datA poInt in the figure represents the average pred.cted alternating

20

Legend:

0 2024-.T33 7075-T6SA 7075--T73

15 * 7079-T6A 6061-T6

+1

o AO

0 5 10 15 20

Actual Ga, _ ksi

gigure 21. Comparison of Actual and Predicted Alternating Stress for0.050-in, Thick Panels Fatigue Cracked a, IOC cpm

4,

stress computed for each striation spacing measurement made in a given

test. For most tests, the predicted value of alternating stress is

within 1 or 2 ksi of the actual stress.

Predicted and actual alternating stresses for spectrum load tests

are compared in Table 6 using the onstants developed for a frequency

of 1000 epa.

Equation 7 can be employed in estimating the alternating stress

for a given fatigue crack when the me&n stress is known. To use the

equation it is necessary to measure striation spacing, s, at a partic-

ular distance, ;/2, from the fatigue crack origin. A number of measure-

ments at various distances will improve confidence in the results.

As an example, ass=e that a fatigue fracture from a 10 inch wide

7075-T73 structure operating at a mean stress of 18 ksi is to be

analyzed to determine the maximum cyclic stress experienced during

operation. Five striation spacing measurements are made at/:/2 dis-

tances from the origin. These /2 distances are 0.5, 0.75, 1.0, 1.25,

and 1.5 inches. Assume that the resulting striation spacings are 30,

56, 85, 115 and 150 micro-inches, respectively.

For the total crack length of 1.5 inches (4/2 = 0.75) and the

striation spacing of 56 micro-inches, the alternating stress is

calculated as follows:2

"a 7V3 log W1 I'm

Ta 6--commISom or AcmL AnP IC D ., AL

STRESS FROM SPECTM LOAD WM

Actual Average PredlctedAlternating Alternating

Mean Stress Stress Stress

a a aMterial ksi + ksi + ksi

2o24-T3 (2.5 --13.75 j7.5 7.86

(11.25 16.30

8.25) --13.75 6.75 --22.5 6.46

7075-T6 (2.5 --13.75 7.5 6.42

111.25 12.33

8.25113.75 6.75 6.3622.5) 6.88

705T32.5 --

7075-T73 13.75 7.5 7.52

11.25 10.18

8.25 } --13 75 6.75 5.3122.5) 8.24

7079-T6 2.5 --13.75 7.5 7.60

.11-25 11-78

13:75 6.75 5.4922.5 6.78

6061-T6 2.5 --

13.75 7.5 6.24(11.25 11.82

8.25} --

13:75 6.75 8.2422.5 7.72

Calculated using Eq. 7 and constants from Table 5.

tzl ,

log WL)

800 x o 6

" 7.01 ksi

The results of ealculations for the other crack lengths and striation

spacings are shown in Table 7. The average calculated alternating

stress Is 7 ksi. Therefore, the mauimm stress is

OAX VA + Iff

= 8kei + 7ksi

- 25 ksi

TAML 7--CALCATED ALUETING STRISS FOR

IMLID EXAMPLE GIVEN IN TEXT

Distance Total Striation AlternatingFrom Origin Crack Length, Spacing Stress, 6a

n. in. micro-inches + ksi

0.50 1.00 30 6.78

0.75 1.50 56 7.01

1.00 2.00 85 7.10

1.25 2.50 115 7.04

1.50 3.00 150 7.13

Average 7.01

46

Conclusions

1. The stress intensity range paruaeter A does not satisfactorily

describe the relationship between fatigue striation spacing and

cyclic stress.

2. If one stress condition Is known, such as hean stress,

the empirical relationship

log

Lpermits a reasonably accurate calculation of the manltude of the

other stress, i.e., alternating stress, in through-crack, thin

sheet.

3. The reduction of fatigue frequency from 1000 em to 10 cpm results

in an increase In the striation spacing at equivalent stress

conditions.

4. An increase in thickness from 0.050 in. to 0.500 in., results in

an increase in the striation spacing at equivalent cyclic stress

and test frequency.

5. An abrupt decrease of applied fatigue stress can result in a

period of arrested crack growth.

6. A fatigue striation Is the result of one cycle of stress.

7. The appreciable difference between microscopic and macroscopic

growth rates can be explained by the presence of dimple rupture

areas on a fatigue surface.

8. Fatigue striations can be observed on both the norm.l and the

oblique mode of fracture,

Ackn !ldgwnt

The Authors wish to express their appreciation to the Air Force

Materials laboratory (kAAS), Research and Tecbnolog Division, Air

Force Systems Co~mnd, Wright Patterson Air Force Base. Ohio, for

percnsion to publish this work. The effort was funded under Contract

AF33(615)-3014, vith !r. Russell L. Henderson as the Air Force

Project Engineer.

!IiI

References

(1) "Handbook for Aircraft Accident Investigators", KAVAER 0O-80T-67

U. S. Naval Aviation Safety Center, Office of the Chief of Naval

operations, 195T.

(2) A. Phillips, V. Kerline and B. V. Whiteson, "Electron Fractography

Handbook", AFMp-TR-64-416, Air Force Materials Laboratory, Wright-

Patterson AMh, Ohio, January, 1965.

(3) C. B. Gilpin, D. H. paul, S. K. Asunmaa and N. A. Tiner, "Electron

Distribution in Steel", Symposium on Advances in Electron etallo-

graphy, Am. Soc. Testing and Mater. Spec. Tech. Publ. to be

published. Presented at Lafayett, Ind., June, 1965.

(4) A. H. Troiano, "The Role of Hydrogen and Other intersttials on

the Mechanical Behavior of Metals", Trans., A.S.M. 52 (1960), p. 54.

(5) "Fracture Testing of High Strength Sheet Mlaterials", ASTM Bulletin,

January and February, 1960.

(6) P. Paris and F. Erdogan, "A Critical Analysis of Crack Propagation

Laws", Journal of Basic Engineering, ASME, Decemberp 3.963., .

(T) R. W. ertzberg, "Application of Electron Fractography and Fracture

Mechanics to Fatigue Crack Propagation in High Streng Aluminum

Alloys", Lehigh tniversity, 1965.

(8) J. M. Krafft, I a Prediction of Fatigue Crack Propagation M~te from

Fracture Toughness and Pleetic Flow Properties", Trano. ASM;

* Vol. 58, 1965.

(9) D. A. Eitman and R. A. Rave, "Plane Stress Cyclic ?law Growth of

2219-T8T Aluminum and 5A-2. -5Sn Titanium Alloys", NAUA CR-51956,

June, 1966.

49

APPENDIX IMEASURED AND CALCULATED DlATA FOR TASK C

- -tWl" t f"silul~a - - "4 -. I ...... 0i3, LO-e In Rut (zesV

* *1 .1? 362 150 22.2 3V.1 22.-

8.7 366 ,.80.6 38.8 12.5

ka.? .. 9 11" 339. 0 1.0.6 13.1

3-5.2 70.1. 31A 318.0 W..3 15.1

to" 314 4) 9.030 131T3 7.4 r0 1.00 13.5 5,333 89.9 26.1 t0.4 c o-

I .00 "A.1 3.m3 AA. 31.2 22.1.

IM $.9 93 10.0 3-9 2.3

8A-1.43 vU8) 0.050 13.15 11.2s wm2 0.1.5 1.tl 4.5. 82.0 22.M. 20.319 .e) 31.1. 1,281 0.3 30.9? 98.06

*1.23 31.9 8"? 318.7.87 3h.32

80012(3.10) 2.0.10 165 3. 03 0.36 31.3 1.00 100.0 2h.k 22.1

*0.56 5.5 565 111. 30.5 8M.

*0.% 71.k. lot W900 182 36.5

M" .4(3-1A) 0.030 8.85 6.7$ 1030 IIT? 16.5 8.66 11.6 R1.9 19.5

I'd? 21.6 3,031 IT.%. 23.1. 22.9

2.07 As. 1IA$. 51.2 28.6 23.8

8.6? 689 75813.0 3.3 50.0

2031.4 (3-114 0.03 .5 =0 s 0.31 986 10^01 10.0 28.7 it.* IO.07) 185 S.328 19.3 33.9 16.9

*0.91 87 3,572 89.7 38.5 19.1

*1.11 4.9 L&O 5$.0 1.5 81.3

*S1531 .9 817 U4..0 16823.5

to".-2 (3-:61 01050 13.13 7.5 t0 0. 95 .4 8,536 39.p 87.3 19.6

U.55 69 1.0"8 93.0 32.9 23.6

* 113 15.5 40 23.1 37.8 27.2

2.15 1M.1 1.3215.8 L2.6 50.7

8-1. (3-3) C.03 U-T to3*5 1 0.3M 33 8 ,032.9 24.1 8.kq.1 . 1. rA 57.0 MA.1 25.8

* .8 j7 1.115 119.6 32.5 29.2* .8 6 472 141.. 37.1. 33.9

%A 2.1. 123 "57 !89.0 k1.. 36.8

1.62 1a.8 190 526.0 1.3.6 39.5

M41..3 (5-si) 0."0 UM.7 &S 1= 8.2 53.8 s2o 11.0 31.2 9.98W00083538) 0."0 3.15 7.5 1 ~ 0.89 0.2 M1 W09. 26.3 18.8

*1.09 lua. 368 M-90 "a. 80.9

00345C51. 005 13.7 s .5 60 0.0 . o 3ro4 - ---

13M7 18 0.34 Is5 -

(89.0m Z^42 13.13 T., * 6M PArs "T --"2.5 S," OM01. 9.0 --

(8M sn8 A.0m ot .w v wes 1.41%po 0, 0.12 tool t8lma.

(3) Oalov %V) 1541.41tb 02010 1mb lon-avul crako tv O *actor It "s, vmo t W1.. thep 6-bs fbrwo U2st 1.' Imffo'.

50

APPENDIX I (Cont'd)

Sp. at, M91. u 2,146. %MU ',. lot 025 t *0 Ip. tw p-Is 0.1 ts. (( ~Zk16)~ at w j~

101516 (3,A) 0.00 13.15 1.5 1= 1."5 7. 8.922 111 94

IM U.5 1.8 4.339 1.) 31.) 9.0

S-235 17.7 SIM5 16.8 32.9 103

t .55 Ma. SIM5 fS.8 34.s 10.8

*t1 21.8 3.316 V3.6 36.2 11.3

*2.95 21.6 MIT1 59.8 37.8 11.9

*-3.15 "A. 6vT 15.0 39.5 32.4

T075-16C3.S 00 U."1 750 I=5 1.0% 39.3 3.363 15- 27.9 19.9

5.% " S m. 0.6 21.8

IA II 3.2 421 "37.0 53.1 25.6

115.16 (3.6) 0.05 -. -. -= -.5 -1. 343- -*61.

*0.1% 49.6 1.807 9.6 I7.: 25.1,*..0.0 1S.9 291 Sa.0 31.5 28.A

u lk 82.2 ss8 341.0 34.8 31.4

7013.16 (3.01) 0.050 16.50 13-90 i0 50 30-3 1. YA 13.2 27.7 "A.

I 070 Q2.9 168 21.0 32.9 59.7

7115.16 (3.19) 0.M5 8.23 6.13 ww 1.24 23.2 %c009 32.k 21.4 19.3.06Q 33.9 uso5 62.? 14.8 U2.5

1015.6 (5.59) 0.050 27.5 6.75 um~ 0. 12.6 1041 81. 98.8 13.7

*0.9? 13.3 8U 12 37.8a1.01f

M01-16 (3-33) 0.030 13.15 7.50 to 0.98 4A 133" 0.4 29.8 21.8

*1.12 66.9 23 112.0 32.4 03.0

* .* 1.31 16.3 50 1.0 318 4.8

1 .68 100.3 to0 h16.0 38.3 57.3

7315.6 (33) 4.050 1345s 1.2 to 0AS 1.8 0.6m0 30.* VA 8.4

OA 4 6 0.9 1381 1.4 86. 21.

a 0.8 k9.2 Ohl 111.0 30.1 0A.

1075.16 (3.41) 0.30 13.15 7.S0 4501.19 18n 31.0 03.1 16.5

107516 (3.42) 0.50 13.15 11.25 0A3 2653 1897 58. 21.8 9.

- 0.6) 559 ts 1608.6 2.

101.6(3OAT) 0.00 13.75 8.5 659 0.35 .1t~4 -.

*BHr o 13M1 T.5 *0.5 5.1----

13.15 11.25 Ma5 18 --

W- 131 .3 * 0.00 18.5 ---

10104(3.52) 0.05 8.1 . 6w0 3

APPENDIX I (Cont'd)

1911-95 WA.1 0.05 1..14.3 0% 1.58q "a.1 3(1522 2 .

v.3s k%2 t04 51.4 3M.3 .585 0.3 1."2 73.4 M5. 1.-0

8.70 TO. 4 15 26.0 36.6 11.6

Tal1)-yrs (348) 0.60 13.75 M.O 1tw0 0.54 37.% 1.823 5%.5 26.T 19.0*-1.14 ks.2 1.277 18.5 29.5 21.0*1.34 36.6 81n 114.0 32.1 mg.

Si* 1.34 71.1 609 157.0 3%.6 2.W%14 8T.1 212 36&.0 31.0 26.4

107.00 (3.8 0.30 1." U1." loco 0.11 rt-J 2.419 41.3 23.3 a1 0*0.11 U6.0 1,316 76.0 21-s5 249*0.90 59.0 all 123.0 o 1.0 28 e*1.01 16. 50 193.0 33.0 29.6

1015-8n05 (%2) 0.05 16i.0 13110 10 045 36.0 1."?1 $3.0 X6.7 24.20.@65 66. W 121.0 32.1 29.1

1011-fl) (3.0") t 0M 6.05 1.5 102.27 lilt 5.063 19.9 21 19.6*1.61 "5 2.004. 25.1 ZZ.6S1.91 35 1.8 OA1 1. 24.8

fAT4 53.5 635 1.20.0 S1.3 283

?M1-ffs ()-a) 0 a"0 2.13 C.is "m% 0. n2.6 4,009 %.8 01.9 13.4

:T0 2 36.6 1,1%4 W6 32.9 15.9.-92 16.0 912 110.0 313 180S

1.3-233.t u6.6 h83 W%.0 15.1 21.0O142 133.8 858 39k.0 52.0 25.2 1

Tosvs(-) 0.0"2 %3-7%1 1.0 1o 0.3 31.1 2.066 48.4 .6.8 19.11. Ls S1.9 1.019 63.3 29.6 21.1

1025 15.5 006 121.0 31.0 22.1

1015.913(0.361 0.050 13M1 11.21 10 0.43 22.0 2.1 36.A 21.A 19.3

0652.3 1.700 58.7 25.9 23.40.15 57.8 94T 105.3 21.9 25.21113 I14. 1 30303.0 34.9 31.6

msml1-13.45 0.50 1315 830 10% 2.10 2811,0 0.2 1.0 9.8

1P. 30 43.3 1, )3 7%.4 32.? 10.3

1211-02(3.44) 0.30 0410 130 10% 09s 754 s0o 111.0 26.5 15.9

I.U1 96.0 326 190.909. 20.8

*1.32 its,4 254 540.0 31.9 22.8*12 1.48.8 Ill T4.o 36.8 26.3

2015403(t-kl) 0.30 137 1121 100 043 35.0 8.015 36.4, 21.4 %9.40.963 570 990 101.0 26.0 R3.05N

9803 "a1 333 05.0 89.9 21.0 r703M00 1w1-S 250 60 0551 M 78 - -.- -

1015.?? (3.12) 0.30"8 6. 05 600 Ch4nQ --

Ws 11 1 1 43.)-* * 00 * 04 22 - -

* ~2 090i -[

APPE&DIX I (Cont'd)

'Alt.,.o :.s MI ON 431 (15 2 -. A

194(33) 0.030 f."1 IM I 39 10.2 ,359 13.2 30.7 9-1

2.39 36.%n41 18.3 33.16 Ms.

* 2508. ~ ,3. 26.0 5&4 U2.2

% .f9 68.3 Sh7 120.3 A0T 6

10124-6 (3.1U) 0.0"~ U-7 7.50 loc I' 2..219 19.91A*i.2 M.8. 121 33.% 23.7

I-. 42 63v W3.0 3V.1 81.9

1017.4 (3.10) 0.M3 l3.79 U.21 02 08 07 2434. 812.0.6 5. .14 4. 6.5 24.0 1 1

CA 4. 3.3 660 1%6.* .0.16 IT.3(A6 1096 184 693.0 k2.9 38.8

1946 0271) 0.9 6.30 13.30 10 O.J? 1. 3Y9 39.0o 30.32 MI.T

0.1? l"3.6 VA6 602.0 33.09 31.18 t

10796 (3M) 0.030 a."3 6.7 1000 1.23 30.3 36054 32.8 .. 13

1.63 to.35 8.Te %.I.

*2.33 39.9 -'A 103.0 30.3 17.3

*3.03 195 )21 302.0 37.8 33.611111:33 03.117312.39.7j3.A030 (3.26) 0.0M =4.0 4.n3 10 018 1. 4,M8 20.8 86.8 33.-9

O' 29 2.2"8 W9. 36-s 18.9

1.05 68.1 Um9 7.,4 k0.6 21.0

*1.28 "3.a 619 A47.0 444 2.

10- 9.56T (34q) 0.030 131 .50 6002 O 0.4 3a.. 0w ----

m2 35) 0.050 8. 6.45 602 1.36 Nk' o.fw6 --

6116(3413) 0.0"1 131 .30 30m 1.9 9.0 TIM1 U2.5 50.6 9.9

TS.3 23.1 4.1? 2A. 34.1 3 I

*313 36.1 to02 47.3 41. 13.7

3.3" We. 916 109.0 %3.3 04.41N

3.3 69.4 316 172.6 4P.? 36.6

"J8.16 (3.13) 0.0M U373 12.85 wm 0.31 11.8 3.031 16.1 "..512

OM.7 33.0 UT02 47. ".3 6

6"1456 (3-50) o 030 16.30 13.40 m03 OAS 31.% 1.9m3 32.3 30.3 M77

**0.68 31.1 83998.0 36.t 331l

C06116 (3.18) 0.030 OS 6." *00 lO 1.6 $IRS 3. 21.812

*. 1.63 36.2 2.513 19.8 25A 2.9

8 13 66 9 1.102 90.0 294 26.6f83 OT 402 8u16 31 230

6061.10(3.29) 0.050 22.0 613 1m2 082 *3.1 6,69 13.0 87-3 14.1

028 33 4,031 2%.5 409 .

* 1~~38 89.3 1.18 90472.

W60-66350) 0030 101 t-50 60 0.3 0.'C.4 - - -

(sp~~a2.) * 50 * 033.3 "

6115(3-") 003 ,95 6.75 (600 0." 26C.nb

-su ;404

re 53