.. . \ PB 181505 “ Price $2.25 -( ,<,”} 1,. ,; ,.-+, ~ -. ,. .: ,/’ I LOW-CYCLE FATIGUE BEHAVIOR OF AXIALLY LOADED ,— -.. . ,— . J. SPECIMENS OF MILD STEEL “P. I SSC-151 BY YAO AND W. -H. MUNSE SHIP STRUCTURE COMMITTEE Distributed by U.S. DEPARTMENT OF COMMERCE OFFICE -OF “TECHNICAL SERVIC”ES WASHINGTON 25,D.C. I ., .1 ... .... . ...- . . ....-—. . . ...
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Low-cycle Fatigue Behavior of Axially Loaded Spesimen of Mild Steel
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. . . \
PB 181505 “
Price $2.25
-(
,<,”}1,,.,;
,.-+, ~-. ,. .:,/’
I
LOW-CYCLE FATIGUE BEHAVIOR OF AXIALLY
LOADED
,—-.. .
,— .
J.
SPECIMENS OF MILD STEEL
“P.
I
SSC-151
BY
YAO AND W. -H. MUNSE
SHIP STRUCTURE COMMITTEE
Distributed by
U.S. DEPARTMENT OF COMMERCE
OFFICE -OF “TECHNICAL SERVIC”ES
WASHINGTON 25, D. C. I
.,
.1
........ ...- . . ....-—. . . ...
,_..
SHIP STRUCTURE COMMITTEE
MEMBER AGENCIES:
BUREAU OF SHIPS, DEPT. OF NAVY
MILITARY SEA TRANSPORTATION SERVICE, DEPT. OF NAVY
UNITED STATES COAST GUARD, TREASURY DEPT.
MARITIME ADMINISTRATION, DEPT, OF COMMERCE
AMERICAN BUREAU OF SHIPPING
ADDREsS CORRESPONDENCE
SECRETARY
I SHIP STRUCTURE cou MrfrEg
I U. S. COAST GUARD HEADQUARTERS
WASHINGTON 25, D. c.
24 June 1963 I
I
Dear Sir:I
I
The Ship Structure Committee is sponsorin a project at the
rUniversity of Illinois to evaluate the influence of few load cyclesat high-stress levels upon the mechanical properti~s of ship steels.Herewith is a COPY of the Third Progress Report, SSC -151, Low-CycleFatigue Behavior of Axially Loaded Specimens of Mild Steel by J. T,P.
ofof
Yao and W. H. Munse.
~.
This project is being conducted under the dvisory guidancethe Committee on Ship Structural Design of the ational AcademySciences-National Research Council.
i“This report is being distributed to the indi iduals and agen-cies associated with the project, and to those inte ested in the ShipStructure Committee program.
f
Questions or cornme ts regarding thisreport would be appreciated and should be sent to t e Secretary, ShipStructure Committee.
To:
—
Sincerely yours,
e “Rear Admiral, U4 S. Coast GuardChairman, Ship ~tructure Committ&e
,. —-. . -...—-—-—— . ..—. —
Serial No. SSC-151
Third Progress Reporton
Project SR- 149
to the
SHIP STRUCTURE COMMITTEE
on
LOW-CYC LX FATIGUE BEHAVIOR OF AXIALLYLOADED SPECIMENS OF MILD STEEL
by
J. T. P. Yao and W. H. MunseUniversity of Illinois
under
Bureau of ShipsDepartment of the Navy
Contract NObs-77139
transmitted through
Committee on Ship Structural DesignDivision of Engineering and Industrial Research
National Academy of Sciences-National Research council
Department of the NavyBureau of Ships Contract NObs-84321
Washington, D. C.U. S. Department of Commerce, Office of Technical Services
--.—
24 June 1963
ABSTRACT
Studies have been conducted to evaluate the
low-cycle high-stress fatigue behavior of several
ship steels under a variety of loading conditions. On
the basis of these tests and related studies reported
in the literature a general hypothesis describing the
cumulative effect of plastic deformations has been
developed. With this hypothesis the deformation ob-
tained in a single loading may be used to describe or
predict the basic low-cycle fatigue behavior of mild
steels for lives up to approximately 1, 000 cycles.
Furthermore, limited correlations with existing data
from other investigations suggest that it may also be
possible to extend the hypothesis to metals other than
steel.
.-
CONTENTS
-EKESYNOPSIS
I. INTRODUCTION .....-oooooo”o=”Dw..=” ...”””””” 1
1. General Problem .s . . . . . . . . . . ...9.... t.””.””” 1
Apparently under a complete reversal of =-brain,such as that shown in Fig. 46,
the compressive straining tends to “strain soften” or reduce the “strain
hardening” of the material.
Some of the fractured specfiens are shown in I?iE.47. In the top row,
three “one-cycle’!test specimens are presented, one for each matexi~. It may
be noted that vertical cracks are present on the surface of the E-steel specimen
shown on the right side of the page. These vertical
when large compression loads were employed, but only
b the second row three CA-steel specimens are shown
cracks. oTten resulted
for E-steel specimens.
after being tes’cedat
-45-
FIG. 47. VARIOUS FRACTURES RESULTED FROM CYCLIC DEFORMATION TESTS.
relative-strain ratios of .0.25, -0.50, and .0.750
,lh, and 17 cycles respectively. All six spactmens
These gave lives of 10,
exhi’oitedcup-and-cone type
-46-
In the bottom row of Fig. 47 are shown specimms or the three
with r = -1. There was evidence of numerous surface cracks on
-therebydemonstrathg that these specimens were close to failure
at a number of ,locations.
-N. A LOW-CYCLE FATTGIJEIWPO’TIDHIS
100 Other Investigations of Cyclic Deformation Low-Cycle Fatigue Tests
A. lkcperimentalResults
In 1912, Kommers(6) concluded from a series of cycltc bending tests
that the magnitude of the cyclic deflection was an important factor in low-cycle
fati-o-estudiez. Later, “unit-deformations’tor “engineering strains” were used
as test parameters by various investigators to includ~ the effect of possible
variations in the initial gage length of the specimens. In recent low-cycle
Tattgue investigations there has been an increase in the use of “true strains.”
Nevel+thzlessJ the computations of “unit deformations” “engineering strains,”
and “true strains’iare st~ll based on the measurement or gross deformations or
deflections of the specimens. It is to be noted that the distribution of
‘~engineerings%rains$’within a certain volume, or the distribution of “true
strains” over a certain cross section is not always uniform, especially when
appreciable
in the test
refers to a
changes in geometry, such as the occurrenceof cracks, take place
section<,Therefore,in the followingdiscussionsthe word “strain”
representationof some gross deformationor deflectionexperienced
by a portion of tilespecimen rather than a very localized phenomenon as the
word “strain” sometimesimplies.
Evans~5~ repeatedlyapplied tensile forces to produce constant
incrementsof lon@tudi,nalplastic strain to axially-loadedspecimensmade of
various metals. He observed that while the total engineeringstrain at fracture
Zncreased as a result of repeated lo’adings,the true strain at Tractureremained
constant in most cases. ln Fig. 48, cyclic tensile changes in plastic engi-
neerin~ strainy Act, in percent vs.
on a log-log basis for a mild steel
100
50
10
5
1.0
.5
.1
’47-
nu.der of cycles to fracture N, are plotted
and a copper wire. H may be seen that,
.—
. copper Wire
o Mud steel
\
—
—
—
)00
Nunib@rof Cycles b Failure, Ii
FIG. 48. TYPICAL LOG ~c+VS. LOG NDIAGRAMS OBTAINED FROM
REPEATEDTENSI;N TESTS.
for specimen lives less than about 100 cycles, straight lines with a slope 01
.1 fit the test potnts quite well.
~ow(7,8)car~ied out bending fati~e tests on two aluminm alloys and
three steels at room temperature, and Johansson(9) conducted cycl?c bending
tests on three steels at various temperatures ranging
Again$ both inveskiga~ors found a lineal-‘elationshiP
and corresponding specimen lives on 10g-10E Plois.
(10,11>W}13) haveCoffin and his associates
from +20° to +500°C.
between cyclic sirains
conducted extens?ve low-
cycle fa~ijgue tes%s on 347 stainless steel specimens with thermal and mechanical
strain-cycling. In their earlier works, engineering strains were used as a
bas~s for their tests. Recently, they have placed emphasis on the usage of
true strains
In analyzing
it was found
-48-
both in the testing and in the analysis of their test results.
their own data as well as reversed strain tesi data of others7
the test points on log%
log 11 (number of cycles to
lines with a slope of approximately -0.50 best fit
(cyclic tensile change in plastic true strain) vs.
failure) diagrams as shown in Fig. 49. Iiowever,
Douglas and Swindeman(14)
tested IIaskelloyB, beryllium, and lnconel at
temPeratul~esabove +1300UF and obtained for these materials straight llnes
with slopes ranging from -0.58 to -0.81-on a log As% VS. log IIdiagram. In
1~~~, 14ajors}~5) ‘m reversed-stratn tests on axially-loaded specimens of
titani,umand nickel at high temperatures, Tound the slope to vary Trom -0.48
to -0.51. More recently,Dubuc(16) found a slope of -0.53 for a low carbon
steel and a brass in cyclic axial stratn tests. These
that the slope of’log O.Et (or log Aqt) vs. log N lines
depend upon the test conditions.
differences ind~cate
may be a variable and
Many constant-deformation tests have been conducted on 2024 ST
aluminum alloy. In 1949, Liu et al(19)
carried out under axial-loading,
1()00
100
10
1
.1 1 10 100 Moo
Muuiber of Cycles to F~lure, N
TYPICAL LOG A VS. LOGN DIAGRAMS OBTAINED FROM%
STRAIN LOTWCYCLE FATIGUE TESTS.
1000C
REVERSED-
-49-
reversed “true-strain” tests on this same alloy and to a maximum life of seven
cycles. Following the exploratory experimental study made by kin and Kirsch,(2)
Pian and D%ato(’8) performed low-cycle Tatibme tests on the same material but
with variations in ‘theabsglute-slxaia ratio, R (i.e., ratio of cyclic minimum
strain to cyclic maximum strain), and obtained data for lives up to 200 cycles.
Later, 13’Amato(4)
carried the same type OT tesz up to 10,000 cycles. These
results also show that straight line relationships exist between the cyclic
tensile chan~e in plastic strain and tinespecimen life on a log-log scab.
However, the slope of’the lines was aependen% upon the value of mea strains used.
Sachs et al(19’20) conducted both axial and bending low-cycle fati6me
tests on specimens of A302 steel, 5454-0 aluminum, and 2024-T4 aluminum alloy.
They report that the ef~ect of mean strain becomes insignii’icantwhen the
specimen lives are greater than 10,000 cycles.
In 1960, Mehringer and Felgar(21)
reported a series or thermal strain-
cycling tests on two high temperature alloys, Because of the low ductility
possessed by both metals, the plastic strain values were too small to be
measured with the desired accuracy and the test data had to be pi’esented in
terms of stress vs. life. This experience indicates one of the limitations
on the use of cyclic plastic strain as a parameter in the case of low-
ductility materials.
B. Analysis
‘22’23] -publishedhis theory on the fatigue o~metakSince Orowan
in Igjg, ‘dieresults of many experimental studies have confirmed his pre-
diction that a linear relationship exis%s between log DE% and log N. h his
original theory(22)
emphasis was placed on the assumption that the distributioil
OT stress in the material is not homo~eneouso With an additional assumption
that reversed local plastic deformationscould cause a.progressive work-
hardening in the material, i.twas postulated that failure would occur at
—.
points where either the stress or
critical stress or strain value.
-50-
t,he total absolute plastic strain reached a
Later, Orowan(2jj’
suggested the following
express~on Tor cyclic strain tests,
N .&t=c (lo)
‘here ‘t~S ~~~eCyC~~C t~n~ile chmge in plastic engineeringstrain and C is
a constant.
It is noted that Orowan’s theory was originally intended to explain
the fatibme behavior of an idealized material at pohts where stress-
concentrations exist. Thereforej Eq. (10) must be modified for cases where
strains representin~ the gross de~ormation of a specimen are used Lnstead 01
the localized strain values. Nevertheless, thts relationship has served as a
basis for most of the hypotheses that have since been developed. Gross and
stout}’k~ as well as I@nson,(25)
on the basis of reversed-strain tests,
introduced a new variable, m, into Eq. (10)
Nm .&t=c [11)
where m is an empirical constant obtained from the slope of the 10g Ast VS.
(1~,1~) fo~d +;ha~a corlstan~log N dia~rsm. Later, Coffin and his associates
slope of -1/2$ (i.e., m = 1/2) best fit their test data, as well as tha+ of
many others, and suggestedthe following expression:
where ~ is the plastic true strain at
Recently Martin(26)
obtained
oT an energy criterion.
fracture in tension.
the following expression on the basis
-51-
Extensive comparisons made by Martin show that, for axial strain tests, the
right hand term in Eq. (1~) gives a better prediction of the constant C than
that uaed inEq. (X2). However, the right hsmd term in Eq. (.12)seems io give
a better prediction of the constant C in the case OT Tlexdral strain tests
conducted at high temperatures.
~elberich(27’28) obtained Eq. (14) byiakinE into consideration the
(14)
(15)
the meafistrain. In
subsitw.tedelIR’
the
Test resii’cson
(14) describes very
ve~.1the low-cyc,ie ~ati,gdebehavior for various mean strains. However, it
maY be noted that (a) Vne apparent fracture ductility) E$ iS a nominal value
which is di~flcuit to obtain; and (b) this relaiionshlp applies only to
tests with posit.lvemean strainfi,modifications must be made for other
values of mean strain.
c. ~’one.cycle”Tests
In the above-mentioned reTermcesj it is noted
strain tests had been conducted under reversed-lodin~s.
Jc,hat most cyclic
At the lowest
-52-
possible number @ cycles in a reversed-strain test,
simp,lybecomes a tension test of specimens that have
compressed? or briefly a “one-cycle~ftest3
the cyclic strain test
been plasticallypre-
Md~nan(29) reported a series of ‘~one-cycle”tests in which a low
carbon.steel was austempered-~or tempered* to nine dirferent conditions.
Cylinderswith an initial dimension of 1,5 in. both in diameter and in length
were p-e-compressedh three stages to a single value of true straim or
-125 percent, At each stage, the compressiveload was applied until the
cylinder,leng+~hwas reduced to 2/”3of the original length, and then the
cylinderwas re-machinedto its original 1 to
This process was repeated until the len@h of
O,,K?~no (equivalentto a true strain oT -125
1 ratio of length ‘todiameter.
the cylinder was reduced to
percent). The cylinder was
then.cut to make Ynree small tensile
a’longand one specimen transverseto
Then, tension tests were carried out
specimens (with the axes of two specimens
the longitudinalaxis of the cylinder).
in a speciallydesigned test apparatus.
The instantwieousdiameter or the specimenwa~ opticallymeasured with a
microscope attached to the apparatus. Test results are shown in Fig. 5oy
where the tensile ehauge in plastic true strain at fracture,Aqtl) is plotted
against the amoLmt of @aS~jC true p~ecompressivestrain> ~c~> to Which the
members had been subject,~d(a single vaiue of -125 percent in this case).
Although only two points are shown Tor each of the nine heat treated
COnditions it may be oIJst?rv~~ fl-om Ijheze results tha,t(a) the tensile strain
at Tracture iS ap~ectedby the plastic tx7_wpre-compressivestrain in the
material and [b) the effect of pre.strain appears to vary with the heat
treatment to which the material was su-ojecieilo
—
* Austemperin~ involves the formation of bainite~ the pi-escnceof which enablesthe material to possess relativelyhigh impact resistance. Ternperi,ngproduces temperedmurterwite in the material structure,and thus increasesthe ductility of the steel,,
-53-
100
m
‘-.
--*50650°C
00 -50 -1OJ-150-2&
EE9—-_-.●
50
&OOc
o0 -50 -100 -150 .’200
100
FEEl\\50
L \ 5500Co0 -50 -100-150-Pm
100
EE1950 —- -—
500%
00 -50 -100 -150 -200
XIIIldJw2-J
o -50 .100 -150 -m 0 -50 -100-150-2KPkB~IChe Pre-compremalveStrain,L+l,wrce=t
a) Au ~ed Sp Cimms (b) Tempred Spcimm
Not-e:NumbersIn Figuredenote * t.wpratum mt which Me$pimn m beat-ttenti.
FIG. 50. 13RIDGMAN’ S “O.NE-CYCLE” TEST DATA
Later in a study associatedwith an investigationof the initiation
of ~r~ttle fl-ac_bUre,Drucker, Mylonas, and Lianis(30) conducted “one-cycle”
tests on a rinmledship steel often referred ‘coas “E-steel”in a manner similar
to that used by Bridgman except that more steps were taken in apply~ng the
compressivede~ormationand that standard tensile specimenswere used. ln
addition, some specimenswere arti~iciallyaEed before the tension tests. The
original in~ormationon the amount of pre-compressivestraLn was presented in
terms of’longitudin~ strain (~ _ ~, where ~ ad lo are respectively the finalo
and initial lengths of the cylinderused in pre-compression). By assuming
that there is no volume change in Vne pre-compressionoperation,these longi-
tudinal strains may be converted into equivalenttrue strains (b ~). Theo
-54-
test results so converted are $lott&d in Fig. 51 where ~1 is the true strai]l
at fracture and is equal ‘co
Qtl? the tensile change in
pre-corqycesslon strain. It
the algebraic sum of ccmrespondi~~gvalues
plastic true strain, and qcl, ~ileplastic
may be seen in Fi~. 51 that, (a) the true
a% ihacimre decreases as the amount of pre-compressive strain incl”~ases~
(b) there is no significant difference
wrtifi.ca.llyaged and unaged specimens.
in the strain at Trac%ure betwee~l
l?urthermore~ e~ceP~ fo~”the data
and
the
at
qc17 approximately -G~ percent, thethe highest valuzs of pre-Compression,
data are in good agreement with that presented in Fig. 21 for the study
reported herein and in spite of the differences in k~]es of specimens and in
the test procedures.
100mu
o
-40-40
●
-50- .400 -20 -40 -6o -60 -1oo
plagticTruo Fre-compreesLveStrati,qcl, percent
FIG. 51. !3ROWNUNIVERSITY ’’ONE-CYC~” TEST DATA(30)
-55-
.11. General Low Cycle Fatigue Hypothesis
A+ Assumptions
~e,,er(31)has stated that “Fracture cannot occur i,ndepenfien%lyof
deformation.” Although dei?omat~ons can occur without necessarily causing
fracture in the material, it is reasonable to assume that plastic deformation
is cumulative in some manner toward the total fracture of the material.
Let us now examine more closely the empirical relationshipshown in
Eq. (11),
J! Y.&t=c
H we raise both sides of the equation to (1/m)th
(11)
power, we obtain
(16)
or
If we let n be the number of applications of tensile load prior to fracture, it
is apparent that the lowest possible number of n is 1 while the counterpart for
ITgenerally has been taken as 1/4 or 1/2 in the literature. The difference
between n and IIis small at large values of 1?so for all practical purposes,
Eq. (17) may be rewritten as follows:
Furthermore, since at n = 1
*% = %
—
~q. (.17)becomes
-56-
&t l/ra~ (~) = 1.0 (19)
-M
The slopes of the curves in Figs. 48 and @ are approximately -1
and -1/2 respectively for test results of Evans (5) and those of CofTin(~1>13).
Sfnce Evans conducted hts tests with tensile Loadings only and Coffin conduc%ea
most of his tests under fully reversed-strain conditions,Tt seems reasonable
to assume that this slope, -m, Is a variable that is dependent upon the relative.
strain Tatio,
to the cyclic
of the slopes
1.2’2,1.43,1.65,and 1.86 respectivelyfor r-values or -1/4, -1/2, -3/4, and -1.
When these corresponding values of l/m and x are plotted, as shown in Fig. 52,
the following relationship is obtained.
the ratio of the cyclic compressivechange in plastic “truestrain
tensile change in plastic true strain. On this basis, the inverse
of the curves in Fig. 43 have been determined and found to be
FIG.52.
I
~ ~-------- -j,,
/
]1
b
/,= ‘=1-O. r /
:1 ‘
/
t
●
1.6 ——/
1.4 –++?.<.. :.-–..-----
f] ./’i/
1.2
I
—...
T—-~
./ ,/
/1.0/
o .0.2 -0.4 .0.6 -0.8 -1.0Ralatim.s*ainRa~r
VARIATIONSOF~WITH RESPECT TO THE RELATIVE-STRAINRATIO, r
-57-
l/m= ~ - o.86r (20)
‘I’hisrelationship has been assumed to relate the slope of the fatib~e curves
to the relative-strain ratio for which they were obtained.
Several further assumptions have been made in developing a low-cycle
fatigue hypothesis. Firstly, it is assumed that low-cycle fatigue ?ractures
occur in tension only. This assumption is generally true for steels. Secondly,
it is realized that the specimen geometry would change somewhat at the large
plastic strains in low-cycle constant-deformation tests. However, the effect
of geometrical variations in the specimen profile is assumed to be compensated
when such constants a~ @Etl or ~1, as obtained fi”om“one-cycle”test results,
are used. And, finally, it is assumed that fracture or a material is produced
by an accumulationof the plastic deformationexperiencedby the material.
This assumption is made on the basis Of the observationsof low-cycle fati~e
test data discussed earl~er.
B. Hypothesis
On the basis of the experimentalevidence and assumptionsdiscussed in
the previous section, it is postulated that plastic deformations cumulate
according to an exponential function and more specifically, that the hypothesis
may be presented in generalized form as ~ollows:
(21)
Since it has been shown(4)
that for low-cycle fatigue conditions true strain
values are approximately proportional to the corresponding engineering strains,
a similar e“kpressionmay be written as follows in terms of true strains.
(22)
‘t‘tl
i
n
m
%
~.~~
As noted previously,
is the cyclic
is the cyclicat n = 1,
is the number
is the numberf~acture
is a variable
-58-
tensile change
tensile change
of
of
applications
applica’cions
in “plastic
in plastlc
engineering strain,
engineering strain
or tensile load,
of tensile load prior to
depending upon the wountpressive s’train,-orth; relative-strain
is the cyclic tensile change in plas-~ic
is the cyclic tensile change in plaeticn=lo
of cyclic com-ratio,
true strain>
true strain at
both l/m and As+l (or Q%,,) are functions of r, the relative.4A .—
strain ratio. Therefore, for constant values of the relative-stl”ain ratio, 1“,
Eqs. (21) ‘cakethe form ofEq. (19).
X2. Corxela%ions wLth Test I)aka
Six type C-2 and three type C-2A specimens of CN-steel were previously
tested in reversed-load low-cycle Tatitimetests. The plastic true skrain history
for each of the~e six specimens is listed in Table 8 (also see Figs. 35 and 36).
I?Jyanalyzlng each strain-cycle with the hypothesis, the quantity
was eva~uated for these tests and found to vary from 0.94 to ~.08 as shown in
Table 8. These values.are close to the value of 1.0 required bY the h~othesis.
Data in the literature are generally reported for cyclic strain tests
conducted by cycling a specimen between a constant cyclic maximum plastic strain
(q= or emu) and a constant cyclic minimum plastic strain (~n or Emin).
In most cases, the tests were started with a tensile load t.oproduce the upper
m? maximum strain limit which was followed by fully reversed strains. Some
-59-
TA13LE 8. ANALYSIS Ol? PLASTIC STRAINS FROM REVERSED-LOAD TESTS.
is cumulativeand the manner In which this accumulationtakes place is
dependentupon the amcm.ntof compress~veplastic strain in each cycle.
With this hypothesisa “one-cycle”test may be used to describe,. —
-71-
on the basis of the relative-strain ratio, the basfc 10W-cyCle Ta’Ki=@ebehavior
of mild steel for lives up to approximately ,IJOOOcycles. A limited number
of correlations were obta~ned for otitier materials and indicate that the
hypotlms~s may express also the low-cycIE fatigue behavior of other metallic
alloys. However, additional confimnations or this correlation would be
desirable.
RFIFERmcEs
1. Yao, J. ‘T.P., and Munse, W. H., “Low-Cycle Fati&ue of lletals--Li’~eratureReview,” The Welding Journal, 41:4, Research Supplement, P. 182s (1962).—— —
2. Lin, H., and Kirsch, A. A., “An Exploratory Study on lligh-StressLov-CycleFatigue of 2024 Aluminum Alloy in Axial Loading,” (WADC TN 56-317),August 1956.
3. MacGregor, C. W., “Relations Between Stress and Reduction in Area forTensile Tests of I@ta&,” Trans. ADIE, vol. 124, p. 208, (1937).—.
4. D’Amato, R., “A Study of the Strain-IIardening anil Cumulative DamageBehavior of 202-T4 Aluminum Alloy in the Low-Cycle Fati.&ue Range,”(WADDTR 60-175), April 1960.
5* Evans, E. W.j “Effect of Interrupted Loading on Mechanical Propertiesof Mescals,” The Engineer (London), 205:5274, Part I, p. 293; 203:5275,Part 11, p. 325 (1957).
6. Kommers, T. B., “.RepeatedStress Testing,!’New York: Internation~flAssociation for Testing Materials (V1th Congress), 1912.
7. Low, A. C., “The Bending Fatigue Strength of Aluminum Alloy MG5 Between10 and 10 Million Cycles,” JouT. Roy. Aeronautic SoC., vol. 59,—.p. 502 (19,55).
8. LOW, A. C., “Short Endurance Fatigue,” International Conference on FatiQ~eof~et~s, p. 206, 1956.
9, Johansson, A., “Fatigue of Steels at Constant Strai~ Amplitude andElevated Temperatures,” Stockholm: colloquium on Fati~e (ILPYAM),~9%.
100 Coffin, L. F,, Jr., and Read, J. Il.,“A Study of the Strain Cycling andl?atihweBehavior of a Cold-WorkedMetal,” InternationalConference onFatigue, p. 415, 1957.
11 b Coffin, L. F., Jr., and T’avernelU, J. F-j “me CYc~ic Straining ‘dFatigue of Metals,” Trans. M?tdlurgical Society of AlME, vol. 215,
p. 794 (October 1959~
.,
-72-
12. Coftin, L. l?.,Jr., “The Stability of lle’calsunder Cyclic Plastic Strain,”Journal of Basic Engineering,&?:3, ser. D, p. 671 (September1960)..—
13, ~a~er~e~~i, J. F., and Coffin, L. F., Jr., “A Compilation and I~~~~p~-e-talxionor Cyclic Strain Fatigue Tests on Metals,” Trans. ASM, vol. 51,——p, 438 (1959).
14.
15.
16“
17.
20.
21.
22.
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Notations
Ac
Af
A.
Ar
c
dc
‘f
do
dr
i
Cross-sectional area at -thetest section of the specimen afterpre-cornpression, sq. in.
Cross-sectionalarea at the test section of the specimen at fracture,sq. in.
Original cross-sectionalarea at the test section of the specimen,sq. in.
Cross-sectional area at the test section of the specimen,re-machined after pre-compression, sq. in.
A constant
Diameter at the test section of the specimen after pre-cornpression,in.
Diameter at the test section of the specimen at fracture, in.
original diameter at the test section of the specimen, in.
Dismeter at the test section OT the specimen, in., re-machinedafter pre-compression
Number or applicationsof tensile load
Number of applicationsor tensile load prior to fracture
Immbel” of cycles
Number of cycles to crack initiat~on
Number of cycles to fracture
Plastic true strain, percent
%
qf
%
!m.aX
qmin
%
RS
s
sc
smax
smin
sn
4C
4t
%&c
L&t
‘tl
‘f
cm
o
_74-
Plastlc true p-e-compressive strain, percent
Flastic true strain at fracture in simple tension, percent
Mean cyclic plastic true strain, pe~cent
Cyclic maximum plastic true strain, percent
Cyclic minimum plastic true strain} percent
Plastic tensile true strain at fracture, percent
Relative-strainratio; cyclic compressivechange in plastic tmestrain to cyclic tensile change in plastic true strain,4C/~