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Full text of "Mean strain effects on the strain life fatigue curve"

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MEAN STRAIN EFFECTS 
ON THE 
STRAIN LIFE FATIGUE CURVE 

by 



Byron L. Smith 
Lieutenant, United States Navy 
B.S., Florida Institute of Technology, 1983 



Submitted in partial fulfillment 
of the requirements for the degree of 

MASTER OF SCIENCE IN AERONAUTICAL ENGINEERING 

from the 

NAVAL POSTGRADUATE SCHOOL 
March 1993 



ified 

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REPORT DOCUMENTATION PAGE 



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7a Name of Monitoring Organization 

Naval Postgraduate School 


ess (city, state, aiid ZIP code) 

rev CA 93943-5000 


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Monterey CA 93943-5000 


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(include security classification) MEAN STRAIN EFFECTS ON THE STRAIN IJFE FATIGUE CURVE 

)nal Author(s) Smith. Byron L. 



e of Report 
's Thesis 



13b Time Covered 
From To 



14 Date of Report (year, month, day) 

1993, March, 25 



15 Page Count 51 



lementary Notation The views expressed in this thesis are those of the author and do not reflect the official policy or position 
Department of Defense or the U.S. Government. 



ti Codes 


18 Subject Terms (continue on reverse if necessary and identify by block number) 




Group 


Subgroup 


Fatigue, Strain Life, Aluminum 7075, Mean strain 



















ract (continue on reverse if necessary and identify by block number) 

Aluminum 7075-T6 was tested using a Fafigue Material Test System. After creating the monotonic and cyclic stress-strain 
to verify material properties, strain life test data were replicated twenty times each to obtain the statistical description of 
rd strain life curve for zero mean strain. The mean strain was then varied to create a total of four statistically described 
. Accounting for the statistical distribution, various characteristics were plotted in order to better understand the effects of 
strain. For example, strain range was plotted against the mean strain for given lives and results were compared to equation 
today that account for mean stress. 



•ibution/ Availability of Abstract 

assified/unlimited _x_ same as report DTIC users 


21 Abstract Security Classification 
Unclassified 


ne of Responsible Individual 
H. Lindsey 


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RM 1473,84 MAR 



83 APR edition may be used until exhausted 
All other editions are obsolete 



security classification of this t 

Unclassifi 



ABSTRACT 

Aluminum 7075 -T6 was tested using a Fatigue Material Test 
System. After creating the monotonia and cyclic stress-strain 
curves to verify material properties, strain life test data 
were replicated twenty times each to obtain the statistical 
description of a standard strain life curve for zero mean 
strain. The mean strain was then varied to create a total of 
four statistically described curves. Accounting for the 
statistical distribution, various characteristics were plotted 
in order to better understand the effects of mean strain. For 
example, strain range was plotted against the mean strain for 
given lives and results were compared to equations in use 
today that account for mean stress. 



Ill 






TABLE OF CONTENTS 

I. INTRODUCTION 1 

II. TEST FACILITY 3 

III. EXPERIMENTAL PROCEDURES 10 

A. SPECIMEN DESCRIPTION 10 

B. TENSILE TESTS 11 

C. CYCLIC TESTS 11 

IV. MATERIAL PROPERTIES 13 

V. PROBABILITY DISTRIBUTION 16 

VI. STRAIN- LIFE CURVES 27 

VII. EFFECTS OF MEAN STRAIN 30 

VIII. CONCLUSIONS AND RECOMMENDATIONS 3 5 

APPENDIX A. MATERIAL PROPERTIES 3 7 

APPENDIX B. EXPERIMENTAL DATA 39 

iv 



DUDLEY KNOX LIBRARY 



LIST OF REFERENCES .PA ^.3943-j5l0l 43 



INITIAL DISTRIBUTION LIST 44 



ACKNOWLEDGMENT 

I would like to express my appreciation to the 
professionals affiliated with the Naval Postgraduate School. 
Their assistance given me was vital to the completion of this 
study. I would like to thank Mr. John Moulton for his time 
and effort spent on making over 400 test specimens at the 
school's facility, thereby saving time, and more importantly, 
the Navy's money. Further thanks are due to the Mechanical 
Engineering Department and Mr. Jim Scholfield for the use of 
the department's MTS machine and Mr. Scholfields' knowledge 
and assistance. Without the help of the above mentioned, this 
testing would not have been possible. 



VI 



I . INTRODUCTION 

Cyclic fatigue properties of a material are obtained from 
completely reversed, constant amplitude strain- controlled 
tests. Components seldom experience this type of loading, as 
some mean stress or mean strain is usually present. An 
aircraft load history is a perfect example. The majority of 
time, during a typical mission profile, the aircraft 
experiences 1 g loads with excursions above and below. 

The Strain life approach is the method employed by the 
Navy to predict fatigue life. Current practice is to only 
address the mean stress effects on the strain life cu2rve . 
Considering that some current aircraft, and all newer ones, 
will most likely utilize strain gage data to determine 
aircraft life, it is important to understand the statistics of 
the strain life approach, the effects of mean stress and 
strain and varying load history effects. Recent studies at 
the Naval Postgraduate School have researched aircraft load 
histories and how best to model them. Further strain life 
analysis is necessary to assist in this endeavor. 

Crack growth is not explicitly accounted for in the strain 
life method. Because of this, strain life methods are often 
considered "crack initiation" life estimates. Initiation of a 
crack in an aircraft is considered very critical by the Navy 
and constitutes the end of life for that component. It is 



believed that the results of this thesis provide a better 
understanding of mean strain influences on fatigue life crack 
initiation. 



II. TEST FACILITY 

The Mechanical Engineering Department Solid Mechanics Lab 
(SML) provided all test equipment necessary for this thesis 
study. The primary test equipment utilized was the Material 
Test System 810, which is used to test material specimens and 
components at loads up to 55 kips, tension or compression, 
with a 6 inch actuator stroke, static or dynamic. A pictorial 
drawing of the system is shown in Figure (1) . The MTS system, 
which was acquired in 1985, operates on a closed loop 
principle. A command signal, an analog program voltage 
representing the desired load, stroke or strain to be applied 
to the specimen, is compared to a feedback signal that 
represents the actual load, stroke or strain measured by 
transducers. Any deviation between command and feedback 
causes a corrective control signal to be applied to a 
servovalve. The servovalve, in response to the control 
signal, causes the actuator to stroke in a direction required 
to reduce the deviation to zero. A diagram of this closed 
loop control along with other system components is shown in 
Figure (2) . 

Through manipulation of the system controls, various tests 
can be conducted, such as constant amplitude fatigue tests, 
crack initiation or crack growth tests, stress relaxation, 
creep, constant cycle fatigue and tensile tests. 



AC Controller DC Controller 



Function Generator 





Range 
C»rtridget 



458.20 MicroConsole 
Load Cell 



Gript 



Load Frame 

Lock/Lift 

Control Module 




OtO-l 20M 



Hydraulic Power Supply 
Load Frame 

Figure 1: Material Test System 



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Figure 2: Closed Loop Control 



A hydraulic power supply (model 506. Old) delivers 3.1 
gallons per minute at 3000 psi to the load frame, which 
contains the Load Cell rated at 55 kips. Mechanical grips 
designed for tensile testing require the operator to impart a 
pre-load to initially hold the specimen. As the load 
increases on hard or tough materials this pre-load may be 
insufficient and allow slippage due to a load decline during 
the initial phase of the test or during load reversals, or it 
is possible to exert enough pre-load initially that a stress 
concentration at the end of the grip wedge may cause failure 
at that point, rendering the test invalid. Hydraulic grips on 
the other hand apply a constant force throughout the test 
eliminating load fall off, slippage or excessive gripping 
pressures. The MTS 810 utilizes 647 Hydraulic wedge grips as 
shown in Figure (3) . 



Wedge 
Chamber 



Specimen Guide - Flal 
Specimens Only 



i lydraulic 
Release 

llydradlic 
Pressure 




Preload 
Chamber 



Grip 
Piston 



End Cap 



Figure 3: Hydraulic wedge grips 



The machine 410.8 Function Generator is a versatile 
instrument capable of generating stable electrical functions 
(waveforms) for systems programming. The Function Generator 
can be set up to provide sine, haversine, and haversquare 
waveforms as well as ramp waveforms for test program command. 
Examples of each are shown in Figure (4) . 




fufJcnoM 



n«Mr Tiinu ii«o not Sdictto 



fentAKroiNi NonPMAi tntAKroiNt nivtnst 



KAMT fMRO «B0 (lltCIID 



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NO' 




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M0< 




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Hoirt it dntrrt 




Figure 4 : MTS waveforms 



Most of the programming was done on the 458.20 
Microconsole which is shown in Figure (5), along with the 
interchangeable range cartridges. For this thesis, rai -e 
cartridges were chosen just larger than the maximum expected 
values. These were the 458.13 AC Displacement Controller (+/- 
0.5 in.), the 458.11 DC Load Controller (+/- 5 kips) and the 
458.11 DC Strain Controller. The extensometer used was the 
632.13B20 model, which has a gage length of 0.5 inches and a 
range of +/- 0.075 inches. This corresponds to a +/- 0.150 
in/in strain range. The strain gage extensometer used is 
shown in Figure (6) . 



M ) Pow»r On 
(Switch on 
Rest Pir>«ll 



Specimen 

' InitallRtion 

(Actuator Rod 

Pojitioning) 




(T) Hydrtollc 
Prmturc 
Control 



Figure 5 : MTS Microconsole 



M2.13n 

.28 ■ ot 7,f mm 

632,13c 

.33" or 8,4 mm 




n 



I.3" 
33 mm 



H 



L&-= 



.7- 
17 



MODEL Ci.glhl. 
Metric 


632 130 20" 
632.I3C20 


632 130 21 
632.13C21 


832 130 23 
632.13C23 


Gage Length 
(Dimension A| 


.500" ♦ 002 
lOntm 


.500' ♦ .002 
10mm 


.500" + 002 
10mm 


Max. nat^ge of 
Travel (Strainl" 


♦ 150 strain 


♦ 150 strain 


♦ 150 strain 


Linearity'" 


25% of range 


25% of rar»ge 


0.25% of range 


nangps where extensomclcr 
may be calibrated to ASTM 

Cla«B1 
Clas? C 


to 01 
to.15 


Oto .01 
0to.15 


to .01 
Oto .15 


Max. Ilyilcreili 


1% of range 


0.1% ot range 


0.1% of range 


Temperature Range 


115" to 250"r 


150° to 150^^^ 


ASO^ to 350"F 


Immerjlbillty 


Yes' 


Yes" 


Yes' 


Max. operating frequency 
with negligible distortion 


100 fl? 


100 III 


100 11? 


Weight (less cable and 
connector! 


22 gm 


22 gm 


31 gm 


Operating force English 
full scale Metric 


35 gm 
15 gm 


35 gm 
15 gm 


10 gm 
50 gm 


Hecommended calibrated 
rftnges for lOv full scale 
output from MTS Iranj- 
ducer condltloncf " " 


♦ 20 

♦ 10 strain 

♦ 01 
+ 02 


♦ 20 

♦ 10 strain 

♦ 01 

♦ 02 


♦ 20 

♦ 10 strain 

♦ 01 

♦ 02 



Figure 6 : Extensometer 



III. EXPERIMENTAL PROCEDURES 

A. SPECIMEN DESCRIPTION 

Over 400 test specimens were prepared in accordance with 
the dimensions and specifications indicated in Figure (7) and 
set forth by ASTM Standards. Aluminum 7075-T6 sheets (4'x 8') 
were sheared in the short direction into 0.75 inch by 4 foot 
pieces. These were sheared into 6 inch long bars. They were 
then machined to meet ASTM standards, which call for the test 
section width to be between 2 and 6 times the thickness, the 
test section length to be greater than 3 times the test 
section width, and the radius of curvature to be at least 8 
times the thickness. Furthermore, no milling cuts were 
greater than 0.1 inch, and the last 3 cuts were less than 0.01 
inch in order to eliminate residual stresses caused by 
machining. 



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~5830" 



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Figure 7: Test Specimen 



10 



B. TENSILE TESTS 

Prior to mounting the specimens in the grips, the load was 
zeroed to null out the grip weight. The grips were then 
closed to securely hold the specimen. Load was adjusted to 
zero force, and the displacement and strain cartridge 
transducers were calibrated to their proper zero reading. 
Once this was completed, the machine could be switched to the 
desired controller. 

Initial tensile tests were conducted to create stress- 
strain plots. The machine was driven via displacement, with 
a ramp signal. Load was recorded along the y-axis and later 
converted to stress, and displacement from the extensometer 
output was plotted along the x-axis and converted to strain. 
These tests also served to verify that the machine, 
controller, grips, extensometer, etc. were operating correctly 
and providing accurate data. The plots provided values which 
correlated with the parameters listed in Appendix (A) . A 
summary of the above mentioned properties is shown in Table 1 
of the Material Properties section. 

C. CYCLIC TESTS 

The MTS machine was then used to subject the specimens to 
sinusoidally alternating compressive and tensile loads. An 
attempt was made to create a representative strain life curve 
at zero mean strain. Twenty tests were conducted each for 



11 



lives of approximately 1E3 , 1E4, 1E5 , and 1E6 cycles at their 
respective theoretical values of strain amplitude (0.007, 
0.005, 0.003, and 0.0025 in/in) determined by the strain life 
equation (Ae/2 = ( af ' /E) (2Nf ) ^b + Aef ' (2Nf ) "c) . All tests 
were started at zero load and were run in strain control at 10 
Hz. The set point was adjusted to obtain zero mean strain, 
and the span was utilized to produce the specified amplitude. 
A counter measured the reversals in transducer voltage 
feedback, and both displacement and strain limit detectors 
were adjusted to terminate the test upon specimen failure. 
The limit detectors were set on each range cartridge to 10% 
greater than the expected maximum and minimum values. This 
caused the test to be terminated upon specimen failure or if 
the controller outputs exceeded the desired response. 

Probability plots were constructed for each strain 
amplitude and will be discussed further in the later sections. 
The 50% mean was used to produce a strain life curve 
representative of typical e-N cuirves found in the literature. 
The mean strain was then increased to 0.030 in/in and tests 
were conducted at the same four values of strain amplitude. 
This procedure was repeated again at 0.063 and 0.100 in/in 
mean strain. 



12 



IV. MATERIAL PROPERTIES 

As mentioned earlier, Aluminum 7075 -T6 was chosen for 
testing. This choice was made due to its availability, the 
abundance of corresponding data, and its widespread use in 
Naval aircraft and in the aircraft industry today. Its 
material properties are listed in Appendix (A) . Uniaxial 
stress -strain curves were generated to verify experimental 
procedures and test data. The material was then fatigued 
cyclically to 50% of its life and cyclic stress-strain curves 
were created. The cyclic stress- strain curve is shown, along 
with the monotonic stress -strain curve, in Figure (8). From 
these plots, several material properties were determined and 
compared to published data. Young's modulus was determined by 
the slope of the initial portion of the curve. The ultimate 
stress came from the peak in the curve, while fracture stress 
and strain came from the breaking point. Then the strain 
hardening exponent was determined and the strength coefficient 
was calculated. The properties were determined for five 
different graphs and then averaged. This comparison is shown 
in Table (1) . The stress -strain curves along with the 
experimental material properties are similar to published 
curves and data. This similarity provided confidence in the 
test equipment and procedures. 



13 



x\r\' 



Mdfunonir ant) Csrlic Strp'^ Sirnin 




002 



n.M 0.16 



Sirain (iti'ln) 



n.iR 



Figure 8: Stress-strain curve 

Some consideration was given to dividing the strain data 
into its plastic and elastic portions; however, for the strain 
ranges used in these tests, the plastic portion was negligible 
when compared to its elastic counterpart. This is due to the 
lower level strain amplitudes necessary to obtain 1E3 cycles 
or more before failure. 



14 



TABLE 1 : COMPARISON OF MATERIAL PROPERTIES 



ALUMINUM 7075 -T6 



PARAMETER 


PUBLISHED DATA 


EXPERIMENTAL DATA 


Ultimate stress 
Su 


84 ksi 


84 ksi 


Yield stress 
Sy 


6 8 ksi 


66 ksi 


Cyclic yld. stress 
Sy' 


76 ksi 


70 ksi 


Strenth coeff. 
K 


120 ksi 


116 ksi 


True frac strength 

(7f 


108 ksi 


108 ksi 


Fatigue str. coef . 
of 


191 ksi 


151 ksi 


Youngs modulus 
E 


1.03E7 psi 


1.10E7 psi 


Strain hardening 
exponent n 


0.110 


0.093 


Cyclic strain 
hardening exp. n' 


0. 146 


0.132 


True fracture 
ductility ef 


0.41 


0.46 


Fatigue Ductility 
coefficient ef 


0.19 


0.22 



15 



V. PROBABILITY DISTRIBUTION 

With the continued growth of the stock pile of 
experimental evidence gathered by fatigue investigators, 
it has become increasingly apparent that the basic 
problems of failure by fatigue are inherently statistical 
in nature. Fatigue data appear to exhibit more scatter 
than any other type of mechanical test data currently 
utilized by the design engineer, (Sinclair, 1990, p. 867) 

In order to obtain reliable estimates of means, standard 

deviations and percentiles of the data, 20 measurements were 

taken at each of four strain amplitudes, each of which were 

tested at four mean strain levels making a total of 16 

different tests and 320 samples. Occasionally errors were 

made in using the test equipment, necessitating that the test 

results be thrown out and rerun. Results were only 

invalidated when it could be confirmed that the test was 

conducted improperly. Once all the data were compiled, the 

population mean and standard deviation were computed for 

normal, lognormal and Weibull distributions at each of the 16 

levels of concern using AGSS, which is a comprehensive IBM 

software package resident on the Naval Postgraduate School 

main frame computer. AGSS is an interactive system for 

dimensional graphics, applied statistics and data analysis. 

The acquired data, along with the calculated population means 

and standard deviations, are shown in Appendix (B) . The 

normal population standard deviation was then compared with 

the strain amplitude. According to Sinclair (3) , fatigue data 

16 



standard deviation will decrease at the higher strain ranges 
and shorter lives. Figure (9) plots the standard deviations 
versus strain amplitudes for four mean strain levels. These 
figures substantiate Sinclair's findings. 



o 






f3 

c 

C3 



std. dev. vs amp for means of (0"-".0.03"--".0.06?":".0.1 "-.") 




strain amplitude 



Figure (9): Standard deviation vs. strain amplitude 



17 



By means of probability plotting, a probability 
distribution function was selected to describe the data. 
Probability plotting is the plotting of data in specialized 
coordinates. The data (x) was plotted on the arithmetic or 
logarithmic horizontal axes, and the probability coordinates, 
or z, (where z=sign(F(x) - 0.5)(1.238t(l + .0262t) and 
t={ -ln[4F(x) (1-F (x) ] }^l/2 ) is plotted on the vertical axis. 
Weibull plots were also made of the data with ln(x) on the 
horizontal axis and z on the vertical axis where the value z= 
ln(-ln(l-F(x) ) ) , F(x) is the cumulative distribution function 
of x, calculated by F = (i - .5)/n. After looking at the 
Kolmogorov-Smirnov and the Anderson -Darling statistics of the 
normal, Weibull and lognormal distribution functions, it 
became apparent that the normal distribution fit the data the 
best. A comparison of the normal, lognormal and Weibull fits 
is shown in Figure (10) . Figure (11) through (13) show 
statistical numbers associated with the plots in Figure (10) . 
On normal distribution plots, population means and standard 
deviations were estimated using the maximum likelihood 
estimator (MLE) . Normal distribution plots are shown for the 
four mean strain levels in Figures (14) through (17) . 



18 



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19 



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20 



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24 



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26 



VI. STRAIN-LIFE CURVES 

After the data were compiled, the mean values were plotted 
on a log- log scale to obtain the standard strain- life curve as 
shown in Figure (18) . Curves in the literature typically use 
an average of the data gathered, which would be a crude 
approximation to the 50% mean as a standard. However, due to 
the large spread in the data, curves were also created for 5%, 
25%, 75% and 95% probability values. The curves are not 
affected significantly by using these values and actually show 
the scatter at various lives. Figure (19) demonstrates how 
the lives vary for certain probabilities and presents a 
Strain- life "band" between the 5% and 95% probability curves. 
When utilizing common strain life equations, the expected 
values tend to fall within this band. Material properties 
provided by Aerostructures predicts strain amplitudes of 
0.0071, 0.0048, 0.0033 and 0.0023 for lives of 1E3 , 1E4 , 1E5 
and 1E6 cycles respectively, while the classical strain life 
equation using parameters from the literature predicts 0.010, 
0.0064, 0.0043 and 0.0031 respectively. These predictions 
have been added to Figure (19) and are annotated by the letter 
A for Aerostructures and S for strain life results. 



27 




3o| - 9pnjj|duiB uicjjs 



Figure (18) : Strain life curve 



28 




opnijidiun uicJis 



Figure (19) : Strain life band 



29 



VII EFFECTS OF MEAN STRAIN 

After establishing ■ -ero mean, strain life curve, the 
mean strain was varied j L 030, 0.063, and finally 0.100 
in/in. Tests were run at e. -^vel , and distribution plots 
were created as mentioned before. From these plots, the means 
were determined and plotted to create ^h9 four strain life 
curves shown in Figure (20). 



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Figure (20) : 4 mean strain life curves 



30 



These four curves were then combined to create the plot 
shown in Figure (21) . This figure is quite similar to strain 
life curves in textbooks, which show the effect of mean 
stress. As with mean stress effects, it is evident that mean 
strain has very little effect on shorter lives, while its 
effect becomes more and more pronounced at longer lives. This 
is consistent with the observations that mean stress / mean 
strain effects are significant at low values of plastic 
strain, where the elastic strain dominates, but has little 
effect at shorter lives, where plastic strains are large. 



Strain Life 




3.5 



5.5 



4 4.5 5 

Life - log 
Figure (21) : Strain life curves 



6.5 



31 



Figure (22) shows plots of strain amplitude versus mean 
strain for four given lines of constant life. These four 
plots were then combined to create a graph very similar to 
what is known as a Haigh diagram. This "strain Haigh" diagram 
suggests that for a given life as the mean strain increases, 
the strain amplitude necessary to achieve this life decreases. 
With further testing this diagram could be refined and even 
expanded to create a master diagram which includes the effects 
of amplitude ratio and stress or strain ratio. 

While using the Aluminum 7075 -T6 parameters shown in 
Appendix (A) and the strain life equations provide adequate 
results, the information provided by Aerostructures , (Ref 4) , 
suggests that Al 7075 -T6 is better modeled by the equation 
ea = .02035* (Nf) ^- .1573 + 565860* (Nf) ^ - 3 . 1484 . Where the 
total strain amplitude is divided into its first term (elastic 
part) and its second term (the plastic part) . This same 
information does not however suggest any relationship between 
mean strain and the fatigue life. The strain life curves for 
the four mean strains suggest a relationship that is dependent 
upon both mean strain and the cyclic life. The strain 
amplitude versus mean strain curves shown earlier suggest a 
linear relationship to mean strain. The Aerostructures 
equation would most likely be amended by subtracting a third 
term to account for mean strain in the form of (-em*Nf^x). 
However at this point it would be premature to formulate an 
equation that matches these lines. 

32 



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33 



Further testing would be necessary to more precisely 
determine the strain life curves and add lines at additional 
mean strains. Several equations have been developed to 
account for mean stress effects on the strain life curve. 
Most notable are Morrow, and Manson and Hal ford. Figure (23) 
places Morrow's predictions on the previously mentioned Figure 
(22). It can be seen that Morrow equations consistently 
overpredict the fatigue life. 



00 

a 



a. 

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a 

c 

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I. 



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Strain Life 




Life - log 



Figure (23) : Morrow comparison 



34 



VIII. CONCLUSIONS AND RECOMMENDATIONS 

Fatigue data has such a large amount of scatter associated 
with it, that a statistical treatment is required to express 
its values; however, much of the classical treatment of 
fatigue has not included statistical treatments. Researchers 
have utilized different parametric values to describe fatigue 
life and there are several different equations to account for 
mean stress effects, but most have not accounted for these 
effects statistically. It is because of this need to 
characterize large scatter and distribution of fatigue lives 
that a great deal of testing is required to obtain useful 
data. 

This study has tested 32 samples and has shown the large 
scatter involved in fatigue testing and characterized it. 
Strain life curves for a range of percentiles, were created 
that are consistent with previously recorded results that 
provide some insight into mean strain effects. While this 
thesis has provided useful data on mean strain influences, 
more is required to reach any definitive relationships. 

It is recommended that follow- on testing be conducted at 
intermediate lives, strain amplitudes and mean strains with 
special emphasis on mean strains between and 0.03 in/in. In 
this way definite relationships may possibly be established 
with regards to mean strain effects. Eventually load 

35 



histories from Navy aircraft can be analyzed using the results 
of this thesis and expected service lives predicted with 
specified statistical limits, which correctly incorporate the 
mean strain effect present in every load cycle. 

The Navy is moving away from counting g's to determine 
aircraft life and toward strain monitoring, which requires 
mean strain influences to accurately predict fatigue life. It 
is because of this need that further testing should continue. 



36 



APPENDIX A. MATERIAL PROPERTIES 



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VI 








^ 




r- 


?: 


m 


£7^ 


^ 


O 


fl 


* 




fn 


ro 


r 1 


t 


o 


fjN 


vr> 


8 


O- 




nO 


r^ 


r- 



u*3: 



13 



• ^ • 

a: "*- Qj 

• (/I 

X < I 



a 

H ^y ^ 

rl 



T3 



^ ^ ^ 






■o 
> 



xS 



o 5b 



8 

— ri r« fNi p Q p 

f j 't '^ '* 5 5 5 

w ^ •-" •— ro rn c^ 

^ n -t -t -t -t -t 

DC 



M rl 
ri 



SJ 



p 




a: H 


4 


4 


m!> ^•, 


r-4 
o 


s 


^& 


r 1 


r 1 


u-i r> 



^ 



38 





APPENDIX B. EXPERIMENTAL DATA 






MEAN STRAIN = 


= 0.0 in/in 




XI 


X2 


X3 


X4 


amp=. 007 


amp=.0 05 


amp=.003 


amp-. 0025 


971 


21884 


79316 


897702 


1002 


22046 


84150 


899463 


1261 


24821 


87636 


900983 


2200 


25783 


87768 


911760 


2489 


26662 


88058 


929722 


2500 


27663 


91271 


948989 


2660 


30013 


100540 


956620 


2783 


31468 


108722 


1000654 


3015 


32266 


116234 


1100362 


3426 


38904 


121783 


1140783 


3624 


41768 


125777 


1180456 


3642 


42036 


126239 


1221588 


3681 


42255 


147686 


1259846 


3843 


44016 


176532 


1270138 


4013 


44322 


177003 


1302555 


4100 


45167 


178180 


1359872 


4226 


47562 


204188 


1364563 


4512 


49127 


204984 


1381112 


4672 


58236 


217489 


1390046 


5080 


62000 


224254 


1400012 


[1 = 3185 


37899 


137391 


1141411 


a = 1163 


11378 


48321 


188965 



6.5 



5.8 ^f 









3580.7 



39 







MEAN STRAIN = 


-- 0.03 in/in 






X5 


X6 


X7 


X8 




amp=.0 07 


amp=. 005 


amp=. 003 


amp=.002 5 




1348 


2014 


50265 


70015 




1512 


2235 


50987 


96548 




1597 


2477 


51331 


97036 




1704 


2506 


52242 


101047 




1812 


2896 


53310 


117108 




1987 


3135 


55204 


202111 




2056 


3152 


56897 


266504 




2144 


3290 


56943 


307564 




2247 


3438 


58883 


399176 




2369 


3526 


59468 


445563 




2438 


3603 


60014 


458118 




2527 


' 3668 


61156 


497063 




2604 


3789 


61783 


595181 




2756 


3880 


63464 


686744 




2844 


3997 


64987 


701168 




2997 


4002 


66663 


707984 




3016 


4176 


68007 


862564 




3111 


4651 


70977 


887032 




3244 


5200 


71149 


887564 




3650 


5240 


72465 


1107363 


M = 


2398 


3544 


60309 


474672 


a = 


616 


864 


6883 


310335 




l^ ^;./ 


s-.-i ^-'n/ 


/.Cb l^r/ 


/3.2 ht/ 




foa 7/ ' 


//.^ \n. 


H3-^ *^^ 


n3.7 *^^ 






I' 



nC-x'^O 



40 



MEAN STRAIN = 0.063 in/ in 



X9 


XIO 


Xll 


X12 


amp=.007 


amp-. 005 


amp=.003 


amD=. 02 5 


1030 


1206 


7500 


12940 


1106 


1370 


10003 


32431 


1202 


1846 


13250 


43250 


1252 


2099 


18057 


50893 


1369 


2204 


21989 


57122 


1483 


2256 


27003 


59257 


1546 


2275 


34256 


63587 


1661 


2350 


36651 


70633 


1794 


2403 


40077 


77752 


1817 


2800 


43001 


80008 


1892 


3101 


43987 


86554 


2054 


3267 


45554 


90119 


2176 


3311 


50117 


92655 


2234 


3380 


56462 


99875 


2304 


3580 


60987 


103003 


2457 


3929 


70543 


109968 


2512 


4238 


74054 


118578 


2606 


4900 


74988 


119972 


2690 


5650 


75051 


120875 


2735 


5801 


78239 


146113 


1896 


3098 


44088 


81779 


540 


1263 

r 


22620 


33574 


.(^f? ^-Z 


.o86> ^'/ 


/^^X./ 


^.:i-7 Ay 


^/, d?S' ^r 


PI , 72 A,K 


"^jt.^Uy 





y^r. v^ 



fS. i A. 



41 







"TEAN STRAIN = 


-- 0.100 in/in 






X13 


X14 


X15 


X16 




amp=.007 


■\v- -.005 


amD=. 003 


amD=.002 5 




776 


-.6^.. 


6246 


13017 




812 


n Q : -, 


7732 


13298 




946 


2 


8501 


14983 




1063 


20. 


8545 


15564 




1097 


2197 


8601 


16088 




1288 


2256 


P988 


17599 




1327 


2311 


'234 


18424 




1402 


2434 


-.-6 


19312 




1459 


2486 


^0008 


20987 




1540 


2528 


14062 


21897 




1605 


2605 


14783 


22056 




1643 


2747 


15033 


22987 




1706 


282 8 " 


15507 


24016 




2007 


2897 


16389 


25987 




2046 


2963 


17422 


26013 




2197 _ 


3069 


19564 


27883 




2373 


- r- ■ ■-, 


21018 


28413 




2404 




-^8762 


28997 




2456 




413 


29012 




2554 


3d;Do 


.442 


29135 


M = 


1645 


2692 


15450 


21783 


G = 


552 


630 


8314 


5401 




/ 


.<i>7i'^y 


W^^y 


Jifl 




/P,^ ^r 


. ilS l^r 


/^.(, ^^ 


J2.I '-'■ 



n." ^^ 



42 



LIST OF REFERENCES 



1. Bannantine, Julia A., Ph.D., Cromer, Jesse J., Ph.D., 
Hardroc, James L., Ph.D., "Fundamentals of Metal Fatigue 
Analysis" , Prentice Hall, 1990. 

2. lyyer, N. S., Aerostructures , Inc., "Aerostructures 
Facsimile ", Aerostructures Facsimile sent to Naval 
Postgraduate School, 1990 

3. Sinclair, G. M. , & Dolan, T. J. "Effect of Stress 
Amplitude on Statistical Variability in Fatigue Life of 
75S-T6 Aluminum Alloy" , Transactions of the ASME, July, 
1953. 

4. The American Society for Testing and Materials 
Committee, "Annual Book of ASTM Standards" Vol 03.01 
ASTM, 1991. 



43 



INITIAL DISTRIBUTION LIST 



1. Defense Technical Information Center 
Cameron Station 

Alexandria, Virginia 22304-6145 

2. Library, Code 52 

Naval Postgraduate School 
Monterey, California 93943-5002 

3. CDR Duym, Code 31 

Naval Postgraduate School 
Monterey, California 93943-5000 

4, Professor Lindsey, Code AA/Li 
Naval Postgraduate School 
Monterey, California 93943-5000 

5. Professor Newberry, Code AA/Ne 
Naval Postgraduate School 
Monterey, California 93943-5000 

6. LT Byron L. Smith 

USS EISENHOWER Air Department 
FPO, New York, NY 09501 



44 



DUDLEY KNOX LISrUi v ^ 

NAVAL POSTGRADUATE Si.HOOL 

MONTEREY CA 93943-5101 



r 



GAYLORD S