to - dtic · antb v. kerlins materials research and production me th ods department ... 20w .t3...
TRANSCRIPT
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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.
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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~)
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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.
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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.
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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.
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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
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Tft t / )
-- 4 /
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itt is tho trac of S
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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
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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
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Ito
0 2 c
coOD
iC:
0L '
1-
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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
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.,,-P- .._. . ., L - ...
" '- . ,.ll " ZU
1-
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C •-
0 01! . - IL t
a.
... a..4d ! -, 2
--... -- "a- .-. 4i-
o)I-
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!.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
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- 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
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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.
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Figur 5. Oen Diple pl Frctrido n dce
Il
Fracture Direction
J 9
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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
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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
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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
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0.125 In. DIA 0.25 In .5In. DIA
V - ~3.125 In. -Figure 7. Configuration of Hydrogen Embrittlement and
Stress Corrosion Specimens
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Figure 8. Specimen Jig Being Loaded~ in a Tensile Machine
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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
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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
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~;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
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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
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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
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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
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*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
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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
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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
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AS
000\
00 0
MachinedStarter Notch
18 in.
Precrackedby Fatigue
0 0 0
8 in. -1Figure 12. Fatigue Crack Propagation Specimen
j2
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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
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MAI.
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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
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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
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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
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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