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Approved for public release; distribution is unlimited,
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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7a Name of Monitoring Organization
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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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408 656 2808
22c Office Symbol
AA/Li
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
intAxroiNT NonMAl tniAKroiNf ntvtntt
N0»
tn»r»»o
loih At im«n
NO'
nilAl iintf
loift «» untrr
M0<
MttuoN "> rf""
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.
l.-»5'
r
A
I*
Ju
1.15'^
•I.IT"-
•.5 wo'
~5830"
FT
1
Hh
rs'
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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Figure (12): Statistics for Fig. (10) lognormal
21
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22
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24
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25
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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
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Figure (18) : Strain life curve
28
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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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