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"1
-,I,
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T. & A. M. Report No. 320
CYCLIC DEFORMATION AND FATIGUE BEHAVIOR
OF HARDENED STEELS
by
R. W. Landgraf
Sponsored by
Caterpillar Tractor CompanyLa Salle Steel Company
United States Steel Corporation
Department of Theoretical and Applied MechanicsUni versity of Illinois
November 1968
ABSTRACT
Changes in deformation resistance are studied during completely
reversed strain cycling of steels hardened to yield strengths in excess of
200 ksi by quenching and tempering, quenching and deforming at elevated
temperature, ausforming and maraging.
Untempered steel and ausformed steel exhibit cyclic hardening;
slightly tempered steel is cyclically stable. Varying amounts of cyclic
softening occur in intermediate hardness quenched and tempered steel,
quenched and deformed steel and maraging steel. Such cyclically induced
changes can be predicted from a steel's monotonic strain hardening exponent
and are characterized in terms of a cyclic stress -strain curve.
Log-log linear relations between elastic strain and fatigue life and
plastic strain and fatigue life adequately describe the fatigue behavior of
hardened steels. Monotonic true fracture strength and ductility approximate
intercept values in the relations thus providing reliable indications of a steel's
fatigue resistance. The optimum condition for maximum fatigue resistance
shifts from high hardnesses at long lives, where strength is the determining
factor, to lower hardnesses at shorter lives, where ductility becomes more
important.
Trends between structure and cyclic behavior are discussed along
with approaches for attaining improved fatigue resistance in steel.
1,J
iii
ACKNOWLEDGMENT
This investigation was conducted, in cooperation with Caterpillar
Tractor Company, LaSalle Steel Company and United States Steel Corporation,
in the H. F. Moore Fracture Research Laboratory, Department of Theoretr
cal and Applied Mechanics, University of Illinois, Urbana.
Appreciation is due Professor JoDean Morrow for his suggestions,
criticism and support, as well as J. F. Millan, Caterpillar Tractor Company,
E. S. Nachtman, Dr. J. L. Peterson and M. J. Rowney, LaSalle Steel
Company, and ], M. Holt and ], M. Hodge, United States Steel Corporation
for their interest in, and support of, the program, for their helpful dis
cussions' and for making available material and specimens. Ausformed
steel was provided by W. M. justusson, Ford Scientific Laboratory; mar-aging
steel by T. W. Landig, International Nickel Company.
The author is indebted to J. E. Matheny for supplying ausformed
steel data from his master's thesis which was completed as part of the
present program. The assistance of J. F. Martin and D. T. Raske in the
testing program, and Miss Kristina Lauraitis, P. Bradbury and Mrs. H.
Corray in preparation of the manuscript, is gratefully acknowledged.
iv
I.
II.
III.
IV.
V.
TABLE OF CONTENTS
INTR ODUCTION ........•..•.•.....•..•.....••••.••
A. General ...••.......••••.•..•••.••........•...
B. Strengthening of Steel ..........•..•..••.......
C. Cycle -Dependent Deformation ..••.•.•.••...••...
D. Fatigue Resistance .••......•.••.•.••...•.•.....
E. Object and Scope ..••.••.....•....••••...••....
CYCLIC DEFORMATION BEHAVIOR .••.•............
A. Experimental Program .•••...........•.•.•••...•
B. Results .•....•.•••..•••••......•...•......•.
C. Conclusions ......•..........•..••..•..•...•..
FATIGUE BEHAVIOR ..•.•.....••.•••.....••.....•.
A. Experimental Program ...••••.....••••.•.....••
B. Results .•...........••.•....•••..•••.....•.•.
C. Conclusions ...•.......•.•.....•••.....•.••..•
DISCUSSION AND INTERPRETATION ••••....•.••...
A. Characterization of Cyclic Behavior .••••••......
B. Structure and Cyclic Behavior .......•.••.•...••..
C. Achieving High Fatigue Resistance ...•.•.•.•.•.•.
SUMMARY, CONCLUSIONS AND RECOMMENDATIONS •.
A. Summary and Conclusions ..••...•.•••.•••....
B. Recommendations ....•...........•..•••..•....
Page
1
1
2
3
4
5
6
6
7
12
13
13
13
18
20
20
23
25
27
27
27
LIST OF REFERENCES
TABLES
FIGURES
• 0 •. ~ ••••••••••••••••••••••••••••
................................................
...............................................
29
34
46
APPENDIX
A. STRESS-STRAIN HYSTERESIS LOOPS FORHARDENED STEELS . • • . . . . • . • . • . • • • • • • . . . • . • . • . • . 83
B.
VITA
FRACTURE SURFACE APPEARANCE OFHARDENED STEELS ..•.•.••..•..••••••..••••••••.
............... " ~ .. " ..91
98
v
NOMENCLATURE
6€ Total strain range
6€ e Elastic strain range
6€ p Plastic strain range
€f True fracture ductility; true strain at fracture in monotonic tension
Fatigue ductility coefficient; intercept of log 6€p12 - log 2Nfplot at 2Nf = 1
aa Stress amplitude
af
True fracture strength; true stress at fracture in monotonic tension
a'f
ao
BHN
b
c
E
n
n'
6W
Fatigue strength coefficient; intercept of log aa - log 2Nf plotat 2N
f= 1
Mean stress
Brinell hardness number
Fatigue strength exponent; slope of log aa - log 2Nf plot
Fatigue ductility exponent; slope of log 6€/2 - log 2Nf plot
Modulus of elasticity
Monotonic strain hardening exponent
Cyclic strain hardening exponent
Fatigue life; number of cycles to failure
Number of reversals to failure
Transition fatigue life; Nf when 6€e = 6€p
True monotonic toughness; area under monotonic true stress -truestrain curve
Plastic strain energy per cycle
Total plastic strain energy to failure
1
r, INTR ODUCTION
A. General
Significant advances in the strengthening of metals have, not sur
prisingly, been devoted largely to steel. Considerable effort is presently
being expended in the achievement of yield strengths in steel well in excess
of 200 ksi without an attendant decrease in ductility. Such a combination of
high strength and ductility, appropriately termed toughness, is considered
essential in allowing structural metals to accommodate the stress concen
trations due to notches, flaws and defects which lead to catastrophic service
failures in low ductility materials.
A number of strengthening" processes are now available for attaining
yield strengths above 200 ksi. A corresponding increase in fatigue strength
is not observed however, and some processes may, in fact, decrease re
sistance to cyclic loading. This breakdown in correlation between traditional
engineering properties and fatigue resistance is a source of concern to the
designer, who does not receive the added reliability needed to justify using
these steels, and to the material processor, who must consider this a
significant obstacle to the widespread utilization of high strength steels.
Much of this dilemma can be resolved by recognizing the role of
plastic strain in the fatigue process. Specifically, cyclic plastic strain is
essential if fatigue fracture is to occur. This being true, it is necessary
to determine the mechanical response of a material to these cyclic plastic
strains, that is, its cycle-dependent deformation behavior.
Such a phenomenological approach highlights the events leading to
fatigue fracture and results in a mechanics description of the fatigue process.
From this the designer gains insight into the stress -strain response at
critical locations in his machine, and the mechanist confronts a pattern of
matcrtal behavior which must be explained from his knowledge of metallic
structure, hopefully leading to increased understanding of the strengthening
mechanisms involved.
* Unless otherwise indicated, the terms" strengthening" and "hardening"will be used interchangeably.
2
B. Strengthening of Steel
"If we consider the simplicity of the operation which givessteel so much hardness, and after having recognized the greatusefulness of this effect, we will not hesitate to include quenchhardening among the most wonderful phenomena in nature. "
- Rene Reaumur, 1722 (1)*
The intervening 246 years have served to alter little this remarkable
observation by the renownedErench scientist. The martensitic transfor
mation (quench-hardening) still serves as the basis for virtually all of the
major strengthening processes for steel. Researchers remain perplexed
however, by the complexities concerning the nature of martensite. Excellent
articles by Kurdjumov (2), Winchell and Cohen (3), and Kelly and Nutting (4)
provide detailed accounts of hardening by martensitic transformation.
Two major approaches have been employed in attempts to improve
the strength and ductility of steel. The first, and oldest, involves alterations
in composition (5,6,7) and heat treatment (8) with the intent of affecting the
hardening behavior and tempering response. The most recent example is
the development of nickel maraging steels (9,10).
The second is based on thermomechanical techniques in which plastic
deformation is introduced into the normal heat treat process thus adding an
increment of hardening to that obtained by martensitic transformation.
Thermomechanical treatments can be further characterized by the stage in
the heat treat cycle in which the deformation is carried out (11): i) before
austenite transformation, ausforming (12, 13); ii) during austenite transfor
mation, strain-induced transformation hardening (14); iii) after austenite
transformation, straining and aging (15, 16) and dynamic strain aging (17).
Since the extensive literature in all of the above mentioned areas
provide ample background for the interested reader, only a brief review of
the effect of hardening method on mechanical properties will be given here.
Conventionally quenched ferrous martensite is extremely hard and
brittle and is nearly always subjected to a tempering treatment resulting in
decreased strength with significant increases in ductility. Composition
* Numbers in parentheses refer to list of references.
)~J
I. J
3
modifications can retard the tempering process allowing higher strengths at
comparable ductilities. In maraging steels the composition has been altered
to the extent that low strength martensite is formed upon air cooling and
further strengthening is obtained by a precipitation hardening process upon
subsequent aging. The result is a relatively strong material with good
ductility but with low uniform elongation.
Ausforming appears to offer the most attractive strength levels to
date, approaching 500 psi, coupled with adequate ductility. Straining and
aging treatments result in significant increases in strength but are often
accompanied by decreases in ductility. It should be noted that these latter
two therrnomechanical techniques can result in strongly anisotropic properties.
Finally, it is worth commenting here that while all of these strength
ening processes are rated on the basis of their effect on tensile yield and
ultimate strengths, such an approach can be most deceiving when assessing
the cyclic deformation resistance of a metal.
C. Cycle -Dependent Deformation
Since Bairstow's experimental verification in 1910 (18) of Bauschinger's
theory that "the limits of elasticity of iron and steel are not fixed, but can•
be raised or lowered by repetitions of stress, " it has become well established
that cycliC deformation can greatly alter the flow properties of metals.
Generally, annealed metals exhibit cyclic hardening, as evidenced by an
increase in deformation resistance, and cold worked metals exhibit cyclic
softening or a decrease in deformation resistance (19,20).
The situation is not so clear cut for hardened steel. MacKenzie and
Benham (21) and Smith et al (22) have found that quenched and tempered steel
at intermediate hardnesses undergoe s cyclic softening not unlike a cold
worked material. As quenched steel, however, shows a cycle -dependent
hardening similar to an annealed metal, a phenomenon discussed in some
detail by Polakowski (23) and experimentally verified by Morrow et al (24).
In spite of this anomalous behavior there has been no systematic
investigation of the cycle -dependent deformation behavior of hardened steels
as influenced by hardening process. Considering the intimate relationship
between cyclic deformation and fatigue behavior, such research should prove
fruitful in establishing criteria for designing alloys to resist fatigue.
4
D. Fatigue Resistance
Fatigue resistance of steel has traditionally been evaluated on the basis
of rotating bending tests from which an endurance limit or some limiting
alternating stress resulting in a long fatigue life is determined. Estimating
this endurance limit by taking one half of the tensile ultimate strength is not
valid at yield strengths in excess of 200 ksi (25) and, in fact, it is doubtful
that an endurance limit even exists at high hardnesses (26,27).
From the large amount of long life rotating bending data in the litera
ture, the following trends are noted. Quenched and tempered steel exhibits
an increase in fatigue strength with increasing hardness up to some optimum
hardness above which fatigue strength decreases (28). This effect is treated
in detail by Morrow et al (24) and is extended into the low cycle fatigue region.
Altering the structure by austempering results in improved fatigue resistance
at high hardnesses (29). Ausforming affords the highest fatigue strengths
presently attainable and appears to maintain reasonably high notch strength
(30). Fatigue strengths of 18% nickel maraging steels are comparable to
those of quenched and tempered steels of equal ultimate strength (31).
At long lives the fatigue behavior of hard steels is subject to a high
degree of scatter due to a sensitive dependence on stress concentrations and
residual stresses. Such effects tend to mask the actual materials response
to cyclic loading and lead to conflicting conclusions in evaluating material
behavior (32).
More fundamental materials information can be obtained by cyclic
tests in the low and intermediate life range where plastic strains are measur
able and the var-ious geometric and environmental effects are minimized.
Along with supplying useful finite life fatigue data, a deeper insight into the
processes controlling fatigue failure at all lives is gained. The rotating
bending test is obviously unsuited for this endeavor because of its elastic
assumptions and the difficulty involved in measuring plastic strains.
Hardened steel low cycle fatigue data are available for quenched and tempered
4130 (33) and 1045 (34) and ausformed H-ll (35).
5
E. Object and Scope
The objective of this investigation is to study the effect of hardening
process on the cycle -dependent deformation and fatigue behavior of steels
with yield strengths greater than 200 ksi. Completely reversed strain
control tests of axial specimens are employed to characterize the cyclically
induced changes in deformation resistance accompanying the fatigue process.
These changes are correlated with initial monotonic properties and resulting
fatigue behavior to provide a basis for assessing the effectiveness of various
hardening procedures in improving fatigue resistance. Behaviors are
interpreted in light of existing knowledge of strengthening mechanisms with
the ultimate goal of achieving increased fatigue resistance in hardened steel.
6
II. CYCLIC DEFORMATION BEHAVIOR
A. Experimental Program
Materials and Specimens - Steels strengthened by four different
processes were chosen for the investigation. These processes are shown
schematically in Fig. 1 and include conventional quenching and tempering,
quenching and deforming at temperature, ausforming and maraging. Specifi
cally, plain carbon SAE 1045 and low alloy SAE 4142 steels were each
quenched and tempered to five high hardness levels. The same SAE 4142
steel was also quenched and deformed at temperature to three strength
levels. In addition, ausformed H -11 tool steel and three strengths of 18%
nickel maraging steel were tested. The chemistry and details of processing
of the steels can be found in Table 1.
Test specimens with the dimensions shown in Fig. 2a were machined
from the 1045 and 4142 bar stock. When buckling problems were encountered
with this configuration, the redesign shown in Fig. 2b was instituted for the
ausforrned and maraging steel specimens.
Specimen preparation for the quenched and tempered steels involved
rough machining, heat treating and final machining by a plunge grinding.technique utilizing a contoured wheel. The maraging steels were heat treated
in the form of rods and then final machined by plunge grinding. The quenched
and deformed and the ausformed steels, requiring no additional heat treat
ment, were simply final machined by plunge grinding.
Apparatus - All testing was carried out on a 20 kip MTS closed-loop
servo controlled hydraulic test system. Programming was accomplished by
means of a sine wave function generator and an electrostatic curve follower.
A strain gage based load cell and clip on extensometer measured load and
strain and provided the necessary feedback for the control circuit. The
transducer signals were monitored on a two pen high response strip chart
recorder and an X-Y recorder.
Specimen alignment, which is particularly critical for low ductility
materials, was accomplished with a liquid-solid grip in which a button head
attached to the end of the specimen is frozen in a pot of Wood's metal, thereby
eliminating all clamping distortions.
IJ
7
Test Procedure - Monotonic tension tests were first performed for all
conditions of the steels. Constant amplitude, completely reversed, uniaxial
strain controlled tests resulting in lives from approximately 10 to 106 cycles
were then carried out. Stress -srrain hysteresis loops were recorded at
logarithmic intervals during each test to determine cycle -dependent changes
in stress amplitude, plastic strain and plastic strain energy.
In addition, incremental step strain tests (36,37), in which a specimen
is subjected to blocks of gradually increasing and then decreasing strain
amplitudes, were conducted to compare cyclic data thus obtained with constant
amplitude data.
B. Results
Monotonic Properties - Complete monotonic tension properties,
augmented by some monotonic compression flow properties to illustrate
anisotropy, are shown for 17 conditions of steel in Table 2. Strength,
ductility and strain hardening behavior, and toughness as a function of hard
ness are shown in Figs. 3, 4 and 5 respectively. True fracture strength is
seen to increase linearly with hardness, in Fig. 3, up to 600 BHN where the
quenched and tempered strengths, although not the ausformed strength, fall
off. The compression strength of untempered martensite is also found to
remain high.
In Fig. 4, the true fracture ductility falls off rapidly for the quenched
and tempered steels but not for ausformed steel. Both the tempered and
deformed conditions of 4142 steel exhibit lower ductility than the other steels
at the same hardness. Maraging steel has the highest ductility at a given
hardness.
In determining strain hardening exponents it was observed that some
of the steels, notably the ausformed condition, did not obey a linear log true
stress -log true plastic strain relation. In this case the exponent was deter
mined for the Initialportton of the flow curve, up to about 3% plastic strain,
since this is the range in which subsequent cycling was carried out. Because
of the anisotropy of the deformed and rna raged conditions, strain hardening
exponents were determined for both the tension and compression flow curves.
Tension values are plotted in Fig. 4.
8
The strain hardening exponent for quenched and tempered steel
exhibits a minimum at intermediate hardnesses and then increases rapidly
with hardness to a high value for the untempered condition. Ausformed
steel also falls on this curve. The quenched and deformed and the maraging
steels posses extremely low exponents.
Reflecting its lower ductility, the 4142 steel is seen to have corre
spondingly lower true toughness values in Fig. 5. Ausforming maintains
good toughness at a high hardness while maraging results in maximum tough-
ness.
Strongly anisotropic flow properties as indicated by differences in
tension and compression yield strengths, are noted for untempered steel and
both deformed conditions with a smaller effect in the maraging conditions
(see Table 2).
Cyclic Stress -Strain Behavior - Appendix A contains reproductions of
several sets of hysteresis loops for representative steels and tests. From
these it can be seen that under total strain cycling, the resulting hardening
or softening behavior can be characterized in terms of changes in stress
amplitude, plastic strain amplitude and plastic strain energy (area of
hysteresis loop).
Figures 6 through 10 indicate the plastic strain response of the various
steels to different amplitudes of imposed total strain. Cyclic hardening is
reflected as a decrease in plastic strain with cycles, cyclic softening as an
increase in plastic strain with cycles.
The amount and, in some instances, the direction of the changes are
seen to depend upon the imposed strain level. Also note that for lives in
excess of about 2000 cycles the plastic strain becomes vanishly small and
difficult to measure conveniently. This creates problems in characterizing
cyclic behavior at high hardnesses.
Generally it can be seen that cyclically induced changes in stress
strain response occur early in the life such that the majority of the life is
spent under reasonably stable conditions. Thus the dimensions of the half
life hysteresis loop serve as a measure of the cyclic steady state behavior
of the material. Half life values of stress amplitude, mean stress, plastic
strain amplitude and plastic strain energy per cycle are given in Table 3 for
all steels and test conditions.
9
The locus of tips of stable hysteresis loops from companion tests
pr-ovides an indication of a metal's steady state deformation resistance
commonly called the cyclic stress -strain curve (37). Such a stress amplitude
strain amplitude curve can be compared directly with a monotonic stress
strain curve so that the magnitude of cyclically induced changes becomes
immediately apparent. The incremental step test discussed previously is
an attempt to obtain this curve from a single specimen. A sample stress
strain record from such a test is displayed in Appendix A.
Figures 11 through 15 show the monotonic and cyclic stress -stram
curves, obtained by both companion specimen tests and incremental step tests,
for the various steels. Quenched and slightly tempered steel and ausformed
steel exhibit some cyclic hardening, i. e. the cyclic curve falls above the
monotonic. All other conditions show varying amounts of cyclic softening.
In certain cases cyclic yielding is observed at a stress less than half of the
original monotonic yield strength (Fig. 13). This emphasizes the folly of
evaluating a metal's cyclic behavior on the basis of monotonic yield or
ultimate strengths. The two methods for obtaining the cyclic curve are in
good agreement except occasionally at small plastic strains where the
companion specimen points tend to fall above the incremental curve.
The relation between stress amplitude, (J , and plastic strainaamplitude, ,6E /2, can be expressed by a power function of the form used
pfor the monotonic curve (38):
(J =K'(,6E /2)n'a p
(1)
1U
where K' and n' are the cyclic strength coefficient and cyclic strain
hardening exponent, respectively.
Log-log plots of stress amplitude -plastic strain amplitude from
companion specimens are shown in Figs. 16 and 17. Cyclic strain hard
ening exponents (slopes of the lines) are found to fall in a range of O. 11 to
0.14 for the 1045 and 4142 steels fitting the pattern that most metals exhibit
values of n' between O. 1 and 0.2. Somewhat smaller values, 0.06 to 0.09,
are found for the ausformed and maraged conditions however. In Fig. 18,
n' is seen to decrease with increasing hardness.
10
The general rule that metals with high monotonic strain hardening
exponents can be expected to cyclically harden while those with low monotonic
exponents can be expected to soften (38) is found to fit the observed trends.
Untempered and ausformed conditions have high monotonic exponents and
exhibit cyclic hardening. Slightly tempered steel shows little change while all
other conditions, having low monotonic exponents, are found to soften.
Generalizing for hard steels, cyclic hardening should occur for n> 0.1,
cyclic softening for n < 0.06, with essentially stable behavior in between.
Monotonic and cyclic values of yield strength and strain hardening
exponent are given for the various conditions in Table 4. Note that n'
determined from incremental tests is generally higher than that determined
from companion specimens. This reflects the influence of the higher strains
in promoting greater softening at lower strains in the incremental test. The
agreement is such that reliable approximations of cyclic behavior can be
obtained quickly from one specimen with the incremental test.
Interesting cyclic effects due to material anisotropy, as evidenced by
differences in monotonic tensile and compressive yield strengths and strain
hardening exponents, were observed in several of the tests. For example,
deformed 4142 steel, when subjected to completely reversed strain cycling,
Initially exhibits a preferential softening in compression due to its lower
compressive yield strength. Tensile mean stresses are thus developed, as
indicated in Table 3, which, depending on the amplitude of the strain, may
or may not relax to zero. Under load cycling conditions cycle-dependent
buckling may occur as is demonstrated in Appendix A.
Maraging steels, having a lower tensile yield strength, tend to develop
compressive mean stresses under strain cycling conditions. Similar effects
are observed for untempered and ausformed conditions. Load cycling condi
tions can cause a cycle-dependent elongation resulting in eventual necking and
tensile failure (see Appendix A).
Directional strain hardening effects can also affect cyclic behavior.
Ausformed steel has a lower monotonic strain hardening exponent in com
"pression than in tension. Upon strain cycling, the stress limit in compression
is found to change little while the tensile stress limit increases resulting in a
net hardening. A similar effect is noted in untempered steel. Such behavior
11
emphasizes the importance of determining both monotonic tension and
compression properties of materials before predicting deformation changes
due to axial cycling.
In addition to characterizing steady state cyclic deformation, a
complete mechanics description requires consideration of transient behavior
as well. In particular, knowledge of changes in stress amplitude with cycles
as influenced by strain amplitude is helpful in analyzing members subjected
to complex loading sequences.
In Fig. 19 changes in stress amplitude accompanying various imposed
strain amplitudes are shown for an intermediate hardness 1045 steel. These
same data are replotted in dimensionless form in Fig. 20a. Namely,
(J ./(J I.' where (J • is the stress amplitude on the ith cycle and (J 1 theai a ai astress amplitude on the first cycle, is plotted versus N/Nf" All data can
now be reasonably described by one curve.
This curve, along with analogous curves for other hardnesses, is
found to be linear on the logarithmic coordinates in Fig. 20b, thus giving the
relation:
(J ./(J 1 = C(N./Nf)gai a 1(2)
]
. J
where C is the intercept at N./Nf
= 1 and g is the slope of the line.1 .
Experimental values of C and g are given in Table 4. The stress ratio
at failure, C, can be approximated from the monotonic and cyclic stress
strain curves by taking the ratio of cyclic stress to monotonic stress at a
total strain having equal elastic and plastic components on the cyclic curve. *The slope, g, which must be related to the strain hardening behavior of the
material, was found to be approximately equal to --} (n-n').
In the low to intermediate life range, where such cyclic changes are
important, Eq. (2) successfully predicts stress amplitudes for all steels
within five percent. Maximum errors occur at short lives where cyclic
stabilization is interrupted by fracture.
* This will be introduced later as the transition life strain amplitude.
12
C. Conclusions
Mechanical cycling can greatly alter the deformation resistance of
hardened steels. The cyclic stress -stram curve describes steady state
cyclic deformation behavior and, when compared with the monotonic curve,
indicates the magnitude of cyclically induced changes.
Prediction of a particular steel's response to cyclic straining can be
made from knowledge of the monotonic strain hardening exponent. Cyclic
hardening can be expected when n > O. 1, cyclic softening when n < O. 06.
Stable behavior occurs at intermediate values. For anisotropic steels,
properties in tension and compression must be considered.
Untempered and ausformed steel hardens cyclically. Slightly tempered
steel is cyclically stable. The remaining quenched and tempered conditions,
as well as the quenched and deformed and the maraging steel, cyclically soften.
Changes in stress amplitude accompanying strain cycling of steels in
the low and intermediate life range can be described by a simple nondr
mensional relation (Eq. 2).
13
III. FATIGUE BEHAVIOR
A. Experimental Program
From the completely reversed strain controlled tests described in the
previous section, half life values of stress amplitude and plastic strain ampli
tude were used to determine appropriate fatigue life relations. In addition,
a number of completely reversed load controlled tests were performed to
check the vali.dity of using strain controlled tests to predict load cycling
behavior. Fatigue failure is defined as complete separation of the specimen
into two pieces.
B. Results
Table 3 summarizes the fatigue results for the 17 conditions of steel
tested. Logarithmic plots of elastic, plastic and total strain versus fatigue
life, after Manson (33), are shown for each condition in Figs. 21 through 25.
Assuming log-log linear relationships between elastic strain and life and
plastic strain and life, the total strain-fatigue life relation can be expressed
by
t:£2
(3)
The fatigue strength coefficient, at' divided by the elastic modulus is the
intercept of the elastic line at one reversal (2Nf
= 1) while b, the fatigue
strength exponent, is the slope of the elastic line. Similarly Et, the fatigue
ductility coefficient, and c , the fatigue ductility exponent, are the corresponding
intercept and slope of the plastic strain-life line in the figures.
A survey of the plots reveals that such linear relations give good
agreement in most cases but do not strictly apply for all steels. In particular,
the elastic lines for the ausformed and maraged conditions, Figs. 24 and 25,
show a shallower slope at short lives than at long lives. A similar trend is
noted for two of the tempered conditions in Figs. 21b and 22b. Two values
of the exponent b can be used to characterize behavior in such instances.
Load controlled life data agree well with strain controlled data in determining
the elastic line.
14
The fatigue strength coefficient and fatigue ductility coefficient are
related to the true fracture strength and true fracture ductility, respectively,
and are often approximated by setting <Jf= <Jf
and Ef=Ef
(35). Intercepts
arrived at in this way are plotted in Figs. 21 through 25. Agreement is
excellent for the elastic intercept, <J/E, however the plastic intercept falls
too high in several cases. Comparative values of the intercepts are given
in Table 4.
Stress Resistance - By rearranging the elastic strain-life relation into
the dimensionless form
(4)
stress amplitude -Iife data for all the steels can be plotted on one master
curve as shown in Fig. 26. Convergence toward a stress ratio of unity at
one reversal is noted as expected. In addition, with the exception of the low
life points for ausforrncd and maraged steel noted earlier, little variance is
observed in the slopes of the various data sets. As seen in Fig. 28a, values
of b range from -0. 065 to -0. 09 with an average of -0. 08. No particular
trend with hardness is found. This means that the stress cycling resistance
of hard steels is largely dependent on the true fracture strength.
Plastic Strain Resistance - Similar rearrangement of the plastic strain
life relation yields:
(5)
Figure 27a is a plot of high strain data for all steels on this basis. The
higher hardness data do not converge toward an intercept of unity due to
inaccuracies in approximating Ef by Ef"
Approximation of the cyclic intercepts by monotonic fracture properties
assumes cyclic deformation does not alter fracture behavior. While this
seems to be true for fracture strength, it is not necessarily true for fracture
ductility. A better estimate of Ef can be made from knowledge of the cyclic
stress -strain curve. Equation (1) can be rewritten in the form:
.6EP
2E'f
15
(la)
Setting crt = crf' introducing the cyclic 0.2% offset yield stress and rearranging
terms, produces:
Ef = O. 002 (;'f )1/n' (lb)
y
Good correlation between calculated and experimental values of Ef is found
particularly at high hardnesses where fracture ductility approximations are
badly in error (see Table 4). Further, the necessary quantities can be deter
mined from one monotonic tension test and one incremental step strain test.
A replot of plastic strain data using calculated values of Etin Eq, (5), is
shown in Fig. 27b. The improved intercept correlation can be seen by
comparison with Fig. 27a.
Values of c as a function of hardness are shown in Fig. 28b. As with
b, the variation is small with extremes of -0.60 and -0.79 and an average
of -0.72. Again no trend with hardness is observed. These slopes tend to
be appreciably steeper than the -0.6 average found for a large number of
metals. This might be explained by the rather limited life range over which
plastic strains can be measured for such hard metals. The plastic line for
softer metals is found to take on a steeper slope at small plastic strains which
is the area where most of the present data was obtained.
Transition Fatigue Life - Insight into the relative roles of strength
and ductility in resisting fatigue failure at various lives can be gained from
knowledge of the transition fatigue life, that is, the life where the total strain
amplitude consists of equal elastic and plastic components. For lives greater
than the transition life, elastic strain predominates emphasizing the importance
of strength. Lives less then the transition life are governed largely by plastic
strain resistance emphasrzing the importance of ductility.
In Fig. 29 transition fatigue life is seen to decrease rapidly with in
creasing hardness falling from 100 reversals at 500 BHN to 10 reversals at
620 BHN. Thus for unnotched members in the useful life range, hardened
steel resists fatigue largely on the basis of strength with ductility playing a
secondary role. This also tends to minimize the effect of errors in locating
the Plastic line in estimating total strain-life behavior.
16
Also of interest is the total strain amplitude at the transition life as
a function of hardness (Fig. 30) which tends to reflect the toughness of a
metal. Noteworthy here is the fact that ausformed steel continues the
upward trend in strain amplitude with increasing hardness even though the
untempered steels fall off.
Total Strain Resistance - Summary plots of total strain amplitude
fatigue life in Fig. 31 further emphasize the relative effects of strength and
ductility on fatigue resistance. Material rankings generally reverse them-
selves when proceeding from long life to short life regions because of the
reciprocal strength -ductil.ity relationship. It will be observed that the
hardest conditions of steel are superior at long lives, the softest conditions
superior at short lives, while at roughly 1000 reversals little difference is
noted. Although the total strain resistance is nominally the same for all
steels at some intermediate life, it should be noted that this is accomplished
primarily by elastic strain resistance (strength) at high hardnesses and
plastic strain resistance (ductility) at low hardnesses.
Figure 32 illustrates the shift in optimum hardness for quenched and
tempered 1045 steel subjected to strain cycling. At long lives where
behavior is nominally elastic, the untempered condition is found to resist the
highest strain amplitude. This is a result of the shallower slope of the
elastic strain life plot (smaller absolute value of b) since the elastic intercept
is lower for the untempered condition than for the next softer condition. At
shorter lives where plastic strain becomes a factor, the softer more ductile
conditions offer the highest strain cycling resistance. Thus optimum hard
ness for maximum fatigue resistance decreases with decreasing life or
increasing strain amplitude.
Such long life behavior conflicts somewhat with the observations of
Garwood et al (28) who found that highest endurance limits occurred in
tempered conditions. Because of the sussceptibility of untempered martensite
to inclusions, the cleanliness of the steel is undoubtedly a factor in such
evaluations. Further, recent evidence (27) throws doubt on the existence
of an endurance limit in highly hardened steels thus such comparisons should
be made on the basis of the fatigue strength at a specified life.
I !
17
Quenched and tempered 4142 data, shown in Fig. 33, shows long life
behavior similar to 1045. At intermediate lives a minimum in fatigue
resistance is observed at 475 BHN while at short lives a sharp decrease in
resistance occurs at about this hardness. This unexpected trend may be a
result of "500o
F embrittlement" to which such steels are vulnerable. Temper
brittleness has been found to reduce finite life fatigue strength while not
affecting the endurance limit of steel (39).
To complete the comparison, strain-life plots for four representative
condttionsappear in Fig. 34. The maraging and 1045 steels would be
classed as strong, high ductility steels offering good.low cycle fatigue re
sistance with fair long life fatigue strength. Unternpered 4142 is a high
strength, low ductility steel with good long life properties. High strength,
moderately ductile ausformed steel shows superior fatigue resistance at
intermediate and long lives. The "theoretical steel" will be discussed in
the next section.
Notch Resistance - Indications of notched fatigue resistance can be
obtained from smooth specimen data using relations ,derived by Topper
et al (40) from a rule proposed by Neuber. In short, the parameter
(6cr .6£ E)1/2, where 6cr is the stress range, .6£ the strain range, from
smooth specimen data and E the elastic modulus, successfully predicts the
life of completely reversed notched members when the nominal loading and
stress concentration factor is known. This parameter as a function of life
is shown for several steels in Fig. 35. The ausformed condition exhibits
the highest notch strength at intermediate and long lives consistent with
previous observations (30). Maraged and deformed 4142 tend to be superior
at lives less than 100 reversals while the two quenched and tempered conditions
fall below and roughly parallel the ausformed curve.
Noting the form of the parameter, it can be seen that notch resistance
is dependent upon the product of stress and strain resistance. True
monotonic toughness shows a similar dependence and provides an indication
of a steel's notched fatigue resistance.
18
Additional Observations - A number of fatigue failure criterion have
been proposed based on accumulated plastic strain energy or work to fracture
(38,40). Values of this quantity, which are simply the summation of
hysteresis energies throughout a test, are given in Table 3. A general trend
of increasing work to fracture with increasing life is noted but the large
scatter and numerous exceptions to the trend would seem to discount the
reliability of such an approach for hardened steel.
Finally, a study of the macroscopic fracture surface features of
fatigued specimens was made. Representative fratographs are included as
Appendix B.
C. Conclusions
Log-log linear relations between elastic strain and fatigue life
and plastic strain and fatigue life adequately describe the fatigue behavior
of hardened steels. Ausformed, maraged and two high hardness tempered
conditions require two values of the fatigue strength exponent to account for
different slopes of the elastic line at long and short lives.
The fatigue strength coefficient can be approximated by the true
fracture strength for all steels thus making .cycltc stress resistance essentially
a function of fracture strength.
True fracture ductility does not quantitatively predict the fatigue
ductility coefficient at the highest hardnesses, however it does supply relative
information regarding a steel's plastic strain resistance. Reliable approxi
mations of the ductility coefficient can be made from knowledge of the cyclic
stress-strain curve.
Transition fatigue life varies inversely with hardness ranging from
approximately 1000 reversals at 380 BHN to 10 reversals at 620 BHN.
The optimum condition for maximum fatigue resistance shifts to lower
hardnesses as the strain amplitude increases and ductility becomes important.
The ausformed condition affords the highest resistance to stress cycling or
to strain cycling at long lives. The maraged and softest tempered conditions
display the highest resistance to plastic strains.
1,J
19
Estimates of notched fatigue strength, based on a parameter utilizing
smooth specimen cyclic data, indicate the ausformed steel to be superior at
intermediate and long lives with the maraged and the quenched and deformed
steels exhibiting superior low cycle resistance.
20
IV. DISCUSSION AND INTERPRETATION
A. Characterization of Cyclic Behavior
The results of Sections II and III indicate that cyclic deformation and
fatigue behavior of hardened steels can be adequately described in terms of
the quantities crt' Et' b, c and n'. These along with the fatigue strength
limit, S/, can be considered as cyclic properties of steel (38). Correlating
such properties with their monotonic counterparts, crf,
Ef
and n, greatly
extend the usefulness of monotonic tension data in quantitatively predicting
cyclic behavior in terms of the strength, ductility and strain hardening
properties of a particular steel. Further, the ease of obtaining cyclic
stress -strain data by means of the incremental step test recommends it as
a promising standard materials test..
By correlating the monotonic strain hardening exponent with cyclic
deformation behavior an indication is obtained of the cyclic stability of a
particular strengthening procedure. Those processes, such as maraging
and deformation after quenching, which significantly increase the flow stress
while having little effect on fracture stress, substantially reduce the strain
hardening exponent. Hence large amounts of cyclic softening are observed.
The degree of cyclic changes can be controlled by altering a steel's strain
hardening behavior. A strain hardening exponent of about O. 1 appears to
result in stable cycle deformation resistance.
True fracture strength accurately determines the fatigue strength
coefficient thus providing a more reliable indication of a steel's fatigue
resistance than either the yield or ultimate strengths, which are subject to
cyclically induced instabilities. Since fracture strength varies nearly
linearly with hardness (Fig. 3), improvements in fatigue strength must be
associated with increased hardness. Also, on this basis, steels processed
by different methods to the same hardness will show similar fatigue strengths,
as is observed.
* This "endurance limit, " characteristic of steels showing a yield point, canbe approximated by the stress at the point of departure of the cyclic stressstrain curve from the elastic line.
t ..•
,I,
,)
I~....J
21
True fracture ductility provides useful relative information as to a
steel's cyclic plastic strain resistance and successfully predicts the fatigue
ductility coeffi.cient at lower hardnesses. Values of Ef at high hardnesses
can be accurately calculated using the cyclic stress -strain curve as demon
strated in Section III.
A distinct advantage to using monotonic fracture properties is that
they are sensitive to many of the internal defects which are known to affect
fatigue behavior. Thus anisotropic effects, such as inferior transverse
fatigue properties in directionally worked rods, would be predicted by (Jf
and Ef
values measured from tranverse tensile specimens.
Such an effect in ausformed steel has been dramatically demonstrated
by Toth and Polakowski (42). Steel bars ausformed in torsion to develop a
helically fibered structure were subsequently torsion tested to failure. A
bar twisted in the same sense as the prestrain showed high strength and
ductility and a shear type fracture. Twisting in the opposite sense resulted
in low stre ngth and ductility with a helical tensile type fracture.
Bush et al (43) measured longitudinal and transverse mechanical
properties of several ausformed steels finding impaired transverse ductility
but no difference in yield and ultimate strengths. The transverse fracture
strength would most certainly be lower however, as would be reflected in
inferior transverse fatigue strengths.
In this respect, it should be emphasized that all of the present results
were obtained under axial loading conditions corresponding to the sense of
the deformation during material processing. Prediction of cyclic behavior
in other orientations or states of stress, such as torsion, would require the
appropriate monotonic data.
Such characterization techniques provide the materials engineer with
a basis for materials evaluation and for determining the effect of variables
on fatigue performance. For the metallurgist, a criterion for designing
and processing alloys to resist fatigue is established. In either case,
information is available to guide selection of the proper combination of
properties to optimize fatigue performance for a given set of conditions.
22
The obvious conditions of unnotched members subjected to reversed
stresses or strains can be assessed directly from the presented data. More
practical engineering problems, typically involving notched members sub
jected to cyclic loading in the intermediate to long life range, require additional
insight.
In such instances consideration must be given to the material at the
root of the notch whichvdue to constraint, is subjected to nominally reversed
strain conditions. Thus the problem can be considered one of localized
low cycle fatigue with "failure" resulting in the formation of a fatigue crack.
Parameter techniques utilizing smooth specimen data (Fig. 35), as employed
by Topper et al (40) and Wetzel (44), deal quantitatively with such problems.
Generally, it can be argued that a cyclically softening metal is
desirable in such applications since plastic flow at the notch root decreases
the effectiveness of the notch by decreasing the stress concentration factor.
Analogously, cyclic softening at the tip of a fatigue crack would cause a
blunting effect making propagation more difficult.
Indications of such behavior can be seen in the fractographs in
Appendix B. Higher ductility softening conditions show consistently larger
critical fatigue crack lengths than the high hardness low ductility conditions.
The maraged condition so effectively resists crack propagation that the
fatigue cracks are found to grow macroscopically on planes approximately
45 degrees to the specimen axis.
The relatively high notch resistance of ausformed steel, which
exhibits cyclic hardening, Is explained by its extremely high strength coupled
with moderate ductility. The influence of mechanical fibering on crack
propagation may also contribute to the improved notch toughness. English. (45)
has shown that cracks can be diverted perpendicular to their original path by
the weak interfaces in such structures.
!
23
B> Structure and Cyclic Behavior
In order to more intelligently approach the problem of improving
steel's fatigue resistance it is of use to consider the relations between
structural strengthening and observed cyclic behavior. While the literature
on strengthening mechanisms in steel is extensive, many areas remain open
to speculation,
Quenching and tempering provides a good base for such comparisons
since it is common to all techniques and virtually all cyclic behavioral
patterns are represented. The nature of the strength of untempered
martensite remains a subject of much debate. Whether martensite is initially
"hard, " with a high density of pinned dislocations and high internal stresses,
or "soft, " with large numbers of unpinned dislocations, is not completely
clear (19).
A high dislocation density in a supersaturated solid solution would
account for the high work hardening rate and hence the cycle -dependent
hardening of martensite on the basis of dislocation - solute atom or dis
location-dislocation interactions. Likewise deformation twinning, observed
in medium and high carbon alloys (46), would contribute to a high work
hardening rate and low ductility. The presence of internal stresses is
indicated by the directional nature of the cyclic changes. Greater hardening
is noted in tension then in compression.
Low temperature tempering (300-4000F) causes precipitation of
E -carbidc resulting in a dispersion hardened lower carbon martensite (47).
Wilson (48) has shown that plastic deformation can cause partial re-solution
of E -carbide in such steels. Dislocation pinning is not yet well established
since no yield point is observed. Hence, the cyclically stable behavior of
such conditions may still be due to preferential dislocation-solute atom
interactions on active slip planes. Increased ductility results from the
lower carbon martensite and partial stress relief.
At high tempering temperatures, E -carbide redissolves and is re
placed by cementite precipitates which coarsen with increasing temperature
(47). A well-defined yield point and low work hardening rate are noted.
The large cyclic softening effects observed at these intermediate hardnesses
24
are partially due to mechanical removal of the yield point. In addition,
cyclic deformation, instead of causing re -solution of the coarser more stable
cementite, may actually induce further precipitation thus hastening the
tempering reaction.
Quenching and deforming at temperature is similar to strain aging
treatments and results in directional strengthening due to a combination of
strain hardening and dispersion hardening. The resulting precipitate is
found to be finer and more uniform than that obtained conventionally (49).
As noted previously such techniques greatly alter the tensile flow properties
but result in low uniform elongation and decreased ductility. Cycle -dependent
softening of such structures under completely reversed straining is largely
due to inferior compressive deformation resistance. The stability of the
precipitate to deformation is not presently known, however the cyclic defor
mation resistance is nearly identical to a quenched and tempered structure
at the same hardness.
Ausforming affords appreciable strength improvement through a
combination of increased dislocation density and dispersion strengthening
(50,51). Reorientation of internal defects during deformation ~lso contributes
to improved axial properties. Increased ductility may be due to the high
dislocation density and an absence of twinning (52). In addition, ausforming
is found to effectively retard the tempering process (51) thus allowing
retention of strength after high temperature tempering. Cyclic hardening is
presumably a result of a high work hardening rate due to dislocation - pre
cipitate interactions.
The different slopes of the elastic strain-life line at short and long
lives for the ausformed steel suggest that different fatigue mechanisms may
be predominating in the two regions.
Maraging produces strengthening through precipitation of interrnetallic
phases in low carbon martensite (53,54). The reason for the cyclic in-
stability of this structure is not clear. Hinton (55) found no indication of
precipitation during low cycle fatigue of a 12% nickel maraging steeL
Possibly reversion of precipitates, similar to that observed in age hardened
aluminum alloys (56), may account for the cyclic softening.
I~ J
25
Maraging steels also show a shallower slope for the elastic strain
life line at short lives than at long, indicating a shift in structural response
to cycling dependent upon strain range.
C. Achieving High Fatigue Resistance
From the foregoing discussion it is concluded that fatigue resistance
can be assessed on the basis of true fracture strength and true fracture
ductility and cycle -dependent changes predicted on the basis of the strain
hardening exponent. Since, of the processes investigated, ausforming
offers the most attractive combination of these properties, it appears that
a structure conststing of a high dislocation density and finely dispersed
precipitate in a refined martensitic matrix would result in high fatigue
resistance. Deformation introduced before martensttic transformation
most effectively accomplishes this goal.
Ausforming of maragtng steel results in modest increases in flow
stress while maintaining goad ductility (57). Yield and ultimate strengths
are nearly idential however, indicating a low strain hardening exponent
and expected cyclic softening. This also suggests that the fracture
properties are altered little. Such an approach would seem promising,
none -the -Iess , from the standpoint of combining the high dislocation density
of the ausforming process with the fine dispersion associated with maraging,
Mihalisin and Bieber (58) have obtained a fracture stress of 666 ksi
in an experimental 8% nickel maraging steel, This strength value was
~measuredwith the specimen under hydrostatic pressure to prevent brittle
fracture, the conventional reduction in area being only 0.5%. Strengths
of the order of 800 ksi are predicted, however the problem of maintaining
adequate ductility remains unsolved.
Dynamic strain aging combined with ausforming (49) results in
appreciable increases in yield and ultimate strength. Such strengthening
is highly directional and while Offering little improvement in completely
reversed fatigue strength would be resistant to tension cycling. The
possibility of employing cyclic deformation in a strain aging procedure also
offers promise in obtaining improved completely reversed fatigue resistance.
26
Kelly and Nutting (4), observing that the theoretical shear strength
of steel is approximately 1. 2 x 106
psi, state: "The practical ideal would
be to produce a steel which yielded at about 0.8 x 106 psi and then work
hardened up to a stress of 1. 2 x 106
psi after plastic strain of rv 0.1. "
It is interesting to speculate as to the fatigue performance of this
"ideal" steel. Such a steel would have a strain hardening exponent of
about O. 1 and thus would be expected to exhibit cyclically stable behavior.
A total strain-life curve predicted from the fracture properties is shown
in Fig. 32. The fatigue strength of 106
cycles would be 750,000 psi.
J
i~"..J
27
V. SUMMARY, CONCLUSIONS AND RECOMMENDATIONS
A. Summary and Conclusions
Completely reversed strain cycling tests have been employed to
investigate the cyclic stress -strain behavior of steels hardened by different
methods to yield strengths in excess of 200 ksi. These results, together
with monotonic and fatigue data and structural considerations, suggest the
following generalizations.
Cyclic straining can cause large softening effects in hardened steel
resulting in greatly reduced flow properties. In particular, dispersion
strengthened structures, as found in intermediate hardness quenched and
tempered steel, quenched and deformed steel and maraging steel, are in
effective in resisting cyclic plastic deformation.
Slightly tempered steel and ausforrned steel, both known to have
extremely high dislocation densities, exhibit either increased or stable
deformation behavior when subjected to mechanical cycling.
An indication of the cyclic stability of various strengthening processes
is furnished by the monotonic strain hardening exponent. For the steels
investigated, an increasing exponent can be associated with increases cyclic
stability.
In light of these cycle-dependent changes in flow properties, monotonic
true fracture properties are found to provide a more realistic indication of
a steel's fatigue resistance. Because of the varying influence of strength
and ductility in determining fatigue resistance at different lives, the optimum
condition of steel for maximum fatigue performance will be dictated by the
specific loading environment.
B. Recommendations
Investigations into the effect of mechanical cycling on carbide and
intermetallic precipitates in hardened steels is essential to the development
of higher strength steels. Correlation of cyclic changes with re -solution
or enhanced precipitation of dispersed particles would provide insight into
possible fatigue mechanisms.
28
Various combinations of thermomechanical processes appear
promising in attaining further strengthening increments in steel. It is
important that consideration be given to the true fracture properties and
strain hardening behavior in such investigations if high fatigue resistance
is also to result.
Further development of methods to predict notched fatigue behavior
using smooth specimen data would greatly extend the usefulness of
characterization techniques. Incorporating cyclic deformation concepts
in fatigue crack growth studies may also prove beneficial.
Stored energy of cold work changes accompanying cyclic deformation
have been measured in annealed and cold worked copper by Halford (59)
using a rise in temperature technique. Similar measurements on hardened
steel would be useful in determining the effect of strengthening mechanism
on such energy changes. Additional information relating to the deformation
behavior of untempered martensite would also be gained.
29
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31
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31. G. W. Tuffnell, D. 1.. Pasqui.ne and J. H. Olson, "An Investigationof the Fatigue Behavior of 18% Nickel Maraging Steel, " Transactions Quarterly, American Society for Metals, Vol. 59,1966, pp. 769-783.
32. G. Sachs, "Survey of Low Alloy High Strength Steels Heat Treatedto High Strength Levels, " Part 2: Fatigue, Technical Report53-254, Wright Air Development Center, 1954.
33. S. S. Manson and M. H. Hirschberg, "Fatigue Behavior in StrainCycling in the Low-and Intermediate-Cycle Range, " FatigueAn Interdisciplinary Approach, Syracuse University Press,Syracuse, New York, 1964, pp. 133 -178.
34. JoDean Morrow, "Low Cycle Fatigue Behavior of Quenched andTempered SAE 1045 Steel, " T. A. M. Report No. 277,Department of Theoretical and Applied Mechanics,University of Illinois, Urbana, April 1965.
1._•.J
i. J
35. J. E. Matheny, Jr., "Low Cycle Fatigue Properties of an AusformedSteel, " T. A. M. Report No. 308, Department of Theoreticaland Applied Mechanics, University of Illinois, Urbana,February 1968.
32
36. Floyd R. Tuler and JoDean Morrow, "Cycle-Dependent Stress-StrainBehavior of Metals, " T. A. M. Report No. 239, Department ofTheoretical and Applied Mechanics, University of Illinois,Urbana, March 1963.
37. R. W. Landgraf, JoDean Morrow,and T ..Endo, ,"Determination of theCyclic Stress-Strain Curve," Paper presented at the 70thAnnual Meeting, American Society for Testing and Materials,Boston, Massachusetts, June 1967.
38. JoDean Morrow, "Cyclic Plastic Strain Energy and Fatigue of Metals, "Internal Friction, Damping and Cyclic Plasticity, SpecialTechnical Publication No. 378, American Society of TestingMaterials, 1~65, pp, 45 -87.
39. B. Z. Weiss, S. Niedzwiedz and M. Brener, "Influence of TemperBrittleness on Fatigue Properties and the Iniation and Propagationof Fatigue Cracks in Silicon Steels, " Journal of the Iron andSteel Institute, Vol. 204, No.2, 1966, pp. 152-156.
40. T. H. Topper, R. M. Wetzel and JoDean Morrow, "Neuber's RuleApplied to Fatigue of Notched Specimens, " Paper presentedat the 70th Annual Meeting, American Society for Testingand Materials, Boston, June 1967.
41. G. R. Halford, "The Energy Required for Fatigue, " Journal ofMaterials, American Society for Testing and Materials,Vol. 1, No.1, March 1966, pp. 3-18.
42. R. G. Toth and N. H. Polakowski, "Directional Properties of aModified 5% Cr Tool Steel Ausformed by Torsion," Transactions Quarterly, American Society for Metals, Vol. 55,1962, pp. 420-428.
43. R. H. Bush, A. J. McEvily, Jr. and W. M. justusson, "An Investi-gation of the Mechanical Anisotropy of Ausformed Steel, "Transactions, American Society for Metals, Vol. 57, 1964,pp. 991-999.
44. R. M. Wetzel, "Smooth Specimen Simulation of Fatigue Behaviorof Notches, " Journal of Materials, American Society forTesting and Materials, Vol. 3, No 3, September 1968,pp. 646 -657. .
45. A. T. English, "Influence of Mechanical Fibering on Anisotropy ofStrength and Ductility, "Journal of Metals, April 1965,pp. 395 -401.
46. R. H. Richman, "Plastic Deformation Modes in Fe-Ni-C Martensites,"Transactions, Metallurgical Society, American Institute ofMining, Metallurgical and Petroleum Engineers, Vol. 227,1963, pp. 159-166.
33
47. B. S. Lement, B. L. Averbach and M. Cohen, "MicrostructuralChanges on Tempering Iron-Carbon Alloys," Transactions,American Society for Metals, Vol. 46, 1954, pp. 851-881.
48. D. V. Wilson, "Effects of Plastic Deformation on Carbide Pre-cipitation in Steel, " Acta Metallurgica, Vol. 5, June 1957,pp. 293 -302.
49. V. Goe], R. Busch and V. F. Zackay, "Dynamic Strain Aging of aHigh Strength Steel, " Transactions, American Society ofMechanical Engineers, Journal of Basic Engineering, December1967, pp. 871-876.
50. G. Thomas, D. Schmatz and W. Gerberich, "Structure and Strengthof Some Auforrned Steels, " High Strength Steels, John Wiley,New York, 1965, pp. 251-306.
51. R. Phillips and W. E. Duckworth, "The Effect of Alloying Additionson the Ausformlng Response of Steels, " Applied MaterialsResearch, Vol. 5, No.1, January 1966, pp. 13-20.
52. O. johari and G. Thomas, "Structures and Strength of AusformedSteels, "Transactions, American Society for Metals, Vol. 58,1965, pp. 563 -579.
53. A. J. Baker and P. R. Swann, "The Hardening Mechanism in MaragingSteels, "Transaction, American Society for Metals, Vol. 57,1964, pp. 1008 -1011.
54. W. A. Spitzig, J. M. Chilton and C. J. Barton, "Structure andStrengthening Mechanisms in 300-Grade 18Ni-Co-Mo-TiMaraging Steel," Transactions, American Society for Metals,Vol. 61, 1968, pp. 635-639.
55. R. W. Hinton, "Stress Relaxation and Cyclic Hardening of 12Ni-5Cr-3Mo Maraging Steel During Low Cycle Fatigue, " Transactions,American Society for Metals, Vol. 61, 1968, pp. 176-183.
56. J. B. Clark and A. J. McEvily, "Interaction of Dislocations andStructures.m Cyclically Strained Aluminum Alloys, " ActaMetallurgica, Vol. 12, 1964, pp. 1359-1372.
57. R. H. Bush, "Mechanical Properties of an Ausformed Maraging Steel, "Transactions, American Society for Metals, Vol. 56, 1963,pp. 885 -887.
58. J. R. Mihalisin and C. G. Bieber, "Theoretical Strength with Iron-Nickel Maraging Steels, " Journal of Metals, September 1966,pp. 1033 -1036.
59. G. R. Halford, "Stored Energy of Cold Work Changes Induces byCyclic Deformation, "PhD Thesis, Department of Theoreticaland Applied Mechanics, University of Illinois, 1966.
TABLE 1 DESCRIPTION OF STEELS
a, ) Chemistry
Material C Si Mn S P Cr
SAE 1045 0.48 0.20 0.71 0.025 0.014 <0.05
SAE 4142 0.45 0.30 0.95 0.028 0.017 1. 09
Ausformed H -11 0.41 0.80 0.27 0.006 0.010 4.96
18% Ni Maraging (300) 0.007 0.01 0.03 0.006 0.003
(250) 0.02 0.05 0.08 0.009 0.005
(200) 0.02 0.03 0.05 0.009 0.005
b) Processing
v
0.52
Mo Co Ni Cu Al Ti B Zr Ce Fe
<0.03 -- <0.05 0.05 -- -- -- -- -- Bel
0.16 -- 0.14 0.12 -- -- -- -- -- Bal
1. 31 -- -- -- -- -- -- -- -- Bel
4.83 9.00 18.59 -- 0.10 0.67 0.001 0.004 0.05 Bel
4.84 7.68 18.09 -- 0.05 0.42 0.004 0.011 0.05 Bel
3.25 8.48 18.36 -- O. IS 0.14 0.003 0.009 0.05 Bel
W>I>-
........_-"-,,~
SAE 1045:
SAE 4142:
SAB 4142 Def:
Aus H-11:
18% Ni Maraging:
Cold drawn to 9/16" rounds from hot rolled rod.Austenitized 15000p {oxidizfng atmosphere) /20 minutes, water quenched at 70 oP.
Cold drawn to 9/16" rounds from annealed rod.Austenitized at 15000 p (neutral atmosphere), quenched in-agitated oil at 180 oP.
Austenitized at 1500oP , oil quenched. Reheated in molten lead, drawn
14% through die at reheating temperature to 5/8" rods.
Consumable electrode, vacuum melted. Annealed 2. 5" diam bars forged to1. 5" dlarn bars at 2000op, air cooled, annealed twice 13000p/three hours.Preheated 12000p/two hours, austenftzed 1900oP/one hour, air cooled 1050
oP,
83% deformation by rolling to 0.62" diam bars, oil quenched, double temperedat 10000FItwo hours.
Consumable electrodeb
vacuum melted. Hot rolled to 5/8" rounds.Solution annealed 1450 Plane hour, air cool, aged 900
op/fourhours, air cool•
l__
TABLE 2 MECHANICAL PROPERTIES OF STEELS
Material: SAR 1045, Q&T BAE 4142, Q & T SAB 4142, Q & Ausformed 18% Ni MaragingDeformed 14% at u-u
Property T(80oP) T(360) T(500) T(600) T(720) T(80oP) T(400) T(600) T(700) T(840) 5500P 650 800 83% Def. 300 250 200
Hardness, BHN 705 595 500 450 390 670 560 475 450 380 475 450 400 660 480 460 405
Mod. of Elasticity 29 30 30 30 30 29 30 30 30 30 29 29 29 30 26 27 27x 106 psi, E
Yield Strength (0. 2%), 265T* 270 245 220 185 23ST 245 250 230 200 27ST 270T 210T** 295T 280T 260T 21STksi, Sy sooc 275C 225C 20Se 175C 265C 290C 28Se Z3De
Ultimate Strength, 300 325 265 230 195 355 325 280 255 205 295 280 225 375 290 270 220ksi, Su
Reduction in Area, 2 41 51 55 59 6 27 35 42 48 20 37 47 33 55 56 67%RA W
01
True Fracture 3 lOT 430/ 370/ 345/ 315/ 375 405/ 340/ 320/ 295/ 310/ 330/ 305/ 495/ 375/ 355/ 325/Strength,ksi, -r: (420C) 395 330 305 270 385 315 290 265 300 305 275 460 325 310 275
True Fracture 0.02 0.52 0.71 0.81 0.89 0.06 0.31 0.43 0.54 0.66 0.22 0.46 0.63 0.40 0.81 0.82 1.10Ductility, E
f
Strain Hardening 0.186 0.071 0.047 0.041 0.044 0.136 0.091 0.048 0.043 0.051 O.OIOT O.016T O.G32T O.120T O.OlST O.020T O.030TExponent, n O.060C O. 070C O.085C O.065C O.030e O.030e O.040C
True Toughness, 6 200 225 240 230 21 105 130 150 165 65 140 170 170 260 250 290in lb/in3 x 103, Up
* T == tension, C = compression
** Proportional limit in tension
*** PlAf I Pi~ (Bridgman's correction for necking)
TABLE 3 SUMMARY OF CYCLIC DATA
Strain Reversals Half Life Values Work toAmplitude, to Failure,
D.W, in lb/in3Fracture,
Material D.E/2 2Nfa /a , ksi D.Ep/2 Wf x 103
a 0
SAE 1045 0.0104 5 292/ - 7 0.0007Q & T (R. T.) 0.0100 28 286/ - 4 0.0005
0.0088 94 258/+ 5 0.0002
0.0082 204 245
0.0075 614 220
0.0072 516 200
0.0060 5,470 180w
D.0050* 152,000 150 0-
SAE 1045, 0.0220 12 325/-20 0.0102Q & T (360
oF)0.0177 40 303/ - 8 0.0072 7,025 140
0.0150 80 286/ 0 0.0049 4,300 170
0.0125 182 280/ - 5 0.0030 2,500 230
0.0095 490 254/+ 4 0.0011 n2 175
0.0090 952 230/+11 0.0007 425 200
0.0075 2,260 221/ 0 0.0002 125 140
0.0072 1,600 200/+20
0.0050* 37,900 150
0.0040* 773,000 120
* Load Control
L...... '-- -''---..--..' ' .. --
Table 3 continued
Strain Reversals Half Life Values Work toAmplitude, to Failure, Fracture,
Material 6E/2 2Nf rJa/rJo' ksi 6E /2 6W, in lb/in3
Wf
x 103P
SAE 1045, 0.0130 276 205/ - 3 0.0055 3,600 495Q & T (500°F) 0.0115 410 196/ - 2 0.0040 2,070 430
0.0095 978 190/+ 2 0.0026 1,380 675
0.0090 1,130 182/+ 5 0.0020 960 565
0.0080 1,580 180 0.0017 950 710
0.0073 2,100 177 0.0012 575 630
0.0067 4,420 165 0.0010 418 924'"0.0052 21,000 152 "
0.0040' 284,000 120
SAE 1045, 0.0168 140 185 0.0110 5,650 405Q & T (600°F) 0.0105 828 165 0.0046 2,260 930
0.0084 980 161 0.0035 1,580 785
0.0078 1,630 156 0.0024 970 795
0.0075 1,310 155 0.0019
0.0068 1,960 145 0.0013 570 1,100
0.0063 4,770 145 0.0012 530 1,120
0.0060 6,200 145 0.0012 475
0.0052 11,000 143 0.0003 120 690
0.0040' 190,000 120
• Load Control
Table 3 continued Work toStrain Reversals Half Life ValuesAmplitude, to Failure,
Fracture,Material /:;E/2 2Nf
o /er , ksi /:;E /2 /:;W, in lb/in3 Wf x 103a 0 p
SAE 1045, 0.0160 240 148 0.0105 4,640 670Q & T (720 op)
0.0100 722 135 0.0051 2,000 720
0.0090 1,020 128 0.0043 1,600 815
0.0084 1,250 125 0.0034 1,230 770
0.0080 1,350 125 0.0034 1,250 840
0.0072 1,760 122 0.0028 930 820
0.0060 3,000 120 0.0018
0.0052 6,000 115 0.0012 370 1,140
0.0042 15,000 112 0.0003 100 940 '"00
0.0033* 82,000 100
SAE 4142, 0.0130(T)** 3 330/ -54 0.0026 2,970 3Q & T (R.T.) 0.0130(C) 26 310/-15 0.0022 2,100 25
0.0100(T) 14 305/ -25 0.0003 300 2
0.0100(C) 88 285/ -10 0.0004 500 20
0.0090 164 271/ -15
0.0088 252 263/ -12
0.0075 1,560 225/ 5
0.0065 3,350 192/ 10
0.0055" 30,400 165
0.0045* 450,000 135
* Load Control** Indicates sense of first loading. T = tension, C = compression
l.______ .....__~ i"---__~
Table 3 continued
Strain Reversals Half Life Values Work toAmplitude, to Failure,
D.W, in lb/in3 Fracturr,Material D.E/2 2N
f0" /0" , ksi D.E /2 W
fx 10
a ° p
SAE 4142 0.0140 38 294/ -15 0.0039 2,650 50Q & T (400°F) 0.0115 108 275/ -10 0.0017 1,200 65
0.0083 488 228/+10 0.0005 300 75
0.0062 4,310 175
0.0050' 38,300 150
0.0040' 552,000 120
SAE 4142 0.0130 92 218/ - 3 0.0060 3,250 150 ccQ & T (600°F) 0.0110 198 213/ - 2 0.0040 2,000 200
'0
0.0085 572 190/+ 2 0.0022 900 255
0.0068 876 174 0.0007 365 160
0.0052 7,160 158
0.0043' 46,800 129
0.0034' 1,120,000 102
• Load Control
Table 3 continued
Strain Reversals Half Life Values Work toAmplitude, to Failure, Fracture,
Material &/2 2Nf 0" /0" , ksi & /2 ,e"W, in lb/in3 Wf x 103a ° p
SAE 4142 0.0135 .178 190 0.0072 3,250 265Q & T (700°F) 0.0125 258 184 0.0062 3,000 420
0.0110 266 185 0.0054
0.0100 488 185 0.0040 2,400 585
0.0083 584 184 0.0022 825 240
0.0075 956 166 0.0020 700 335
0.0058 2,350 152 0.0008""0.0050 6,880 1460
0.0040· 63,400 120
0.0033* 785,000 100
SAE 4142 0.0130 382 162 0.0068 3; 250 620Q & T (840°F) 0.0110 582 160 0.0049 2,200 640
0.0082 1,380 150 0.0028 1,150 790
0.0052 5,350 125 0.0009 315 840
0.0042· 12,300 126
O. 0040~ 15,700 120
0.0033· 42,700 100
0.0030· 1,720,000 90
• Load Control
L.__..__ L__._~
Table 3 Continued
Strain Reversals Work toAmplitude, to Failure, Half Life Values Fracture,
Material .6.E/2 2Nf 0- /0- , ksi .6.E /2 .6.W, in lb/in3Wf x 103
a ° p
SAE 4142 0.0125 284 206/+11 0.0056 3,300 470Q & Def. (550°F) 0.0116 106 200/+10 0.0055
0.0100 238 190/+15 0.0036 1,900 225
0.0075 410 184/+45 0.0015 600 125
0.0060 2,110 164/+30 0.0005 200 210
0.0050 3,950 150/+90 0.0001
0.0050* 8,580 150
0.0042* 35,400 126 >l>-f-'
0.0040 49,600 120
0.0035' 2,000,000** 105
SAE 4142 0.0150 324 180/+ 2 0.0078Q & Def. (650°F) 0.0100 992 159/+ 4 0.0043 1,800 895
0.0075 1,620 158/+18 0.0020 900 730
0.0063 2,760 142/+15 0.0013 500 690I
0.0055 5,570 143/+50 0.0005 200 560
0.0043 11,300 126/+65
0.0042* 25,300 126
0.0040 49,000 120
0.0035' 1,000,000** 105
* Load Control** Unbroken
.'L..-...._ L.-.~
Table 3 continued
Strain Reversals Half Life Values Work toAmplitude, to Failure,
6W, in lb/in3Fracture,
Material &/2 2Nfcr Icr , ksi 6E 12 Wf x 103
a 0 p
18% Ni Maraging 0.0300 94 234/-14 0.0201 16,500 765(250) 0.0198 276 222/- 8 0.0107 8,000 2,500
0.0142 630 218/- 4 0.0060 4,200 1,360
0.0100 2,100 209/+ 8 0.0020
0.0067 9,320 183/+24 0.0002 100 500
0.0054' 35,200 140
0.0040' 2,000,000*' 104
"'"co18% Ni Maraging 0.0305 60 194/-16 0.0228 16,000 340
(200) 0.0200 156 1901-10 0.0122 8,270 655
0.0140 536 178/- 6 0.0075 4,470 1,200
0.0100 1,310 178/- 5 0.0034 1,940 1,260
0.0068 7,550 164/- 5 0.0008 410 1,470
0.0060' 9,430 160
0.0038* 169,000 100
* Load Control
** Unbroken
Table 3 continued
Strain Reversals Half Life Values Work toAmplitude, to Failure,
DW, in lb/in3 Fracture,
Material DE/2 2Nfa /a , kst DE /2 W
fx HJ3a 0 p
Ausformed H-ll 0.0310 8 395/ -23 0.0168 24,100 190
0.0200 28 375/- 9 0.0070 8,600 120
0.0156 86 366/ -12 0.0031 3,500 155
0.0122 418 343/ - 6 0.0009 890 180
0.0115 768 320/+ 7 0.0007 660 265
0.0102 1,040 306/+ 2 0.0001
0.0084 3,740 250/+13
0.0083' 5,700 250 ol'>ool'>o
0.0075- 11,500 225
0.0069' 31,900 208
0.0066' 49,700 199
0.0060' 155,000 180
, Load Control
~~- ,--~
TABLE 4 SELECTED MONOTONIC AND CYCLIC PROPERTIES OF STEELS
Material: SAR 1045, Q&T SAR 4142, Q & T SAE 4142, Q & Ausformed 18% Ni MaragingDeformed 14% at H-ll
Property T(SOo) T(360) T(500) T(600) T(720) T(80op) T(400) T(600) T(700) T(840) 5500P 650 800 83% Red. 300 250 ZOO
Yield Strength (0.2%), 265T 270 245 220 185 23ST 245 250 230 200 27ST 270T 2IOT 295T 280T 260T 21STksi: Mono, By 300e 275C 225C 20Se 175C 365C 290C 28Se Z3De
Cyclic, s; 250 185 140 110 300 250 195 155 120 160 155 130 340 215 195 150
Strain Hardening 0.186 0.071 0.047 0.041 0.044 0.136 0.091 0.048 0.043 0.051 O.QlOT O.016T O.032T O.120T O. GIST a.02OT O.03OTExponent: Mono•• n O.060C O.070e O.Q8Se O.Q65C O.030e a.D30e O.040e
Cyclic, n'" 0.10 0.13 0.12 0.12 0.14 0.05 0.11 0.14 0.12 0.14 0.12 0.13 0.14 0.06 0.08 0.075 0.090.14 0.13 0.15 0.17 0.12 0.13 0.15 0.17 0.15 0.16 0.16 0.07 0.08 0.075 0.08
Constants in Eq, 2:Coefficient, C 0.95 0.79 0.73 0.63 0.96 0.81 0.73 0.70 0.76 0.69 0.67 1. 15 0.78 0.83 0.82Exponent, g -0.01 -0.04 -0.05 -0.07 -0.01 -0.05 -0.06 -0.07 -0.06 -0.06 -0.07 +0.01 -0.05 -0.04 -0.04 >l>-
(JITrue Fracture 310 395 330 305 270 375 385 315 290 265 300 305 275 460 325 310 275Strength, ksi, O"f
Fatigue Strength 310 395 330 260 230 375 385 315 290 265 300 305 275 460 325 310 240Coefficient, ksi, O"f
True Fracture 0.02 0.52 0.71 0.81 0.89 0.06 0.30 0.43 0.54 0.66 0.22 0.46 0.63 0.40 0.81 0.82 1. 10Ductility, €f
Fatigue Ductility 0.07 0.25 0.35 0.45 0.07 0.09 0.40 0.45 0.20 0.60 0.50 0.08 0.60 0.80 0.30Coefficient, €f ** 0.06 0.18 0.36 0.40 0.07 0.09 0.20 0.25 0.14 0.14 0.22 0.14 0.40 0.90 1.2
Fatigue Strength -0.065 -0.055 -0.080 -0.070 -0.074 -0.075 -0.076 -0.081 -0.080 -0.080 -0.082 -0.090 -0.090 -0.061 -0.060 -0.055 RO.030Exponent, b *** -0.080 -0'.089 -0. err -0.070 -0.071 -0.065
Fatigue Ductility ........ -1.0 -0.60 -0.68 -0.69 -0.68 .......-1.0 -0.76 -0.66 -0.73 -0.75 -0.77 -0.76 RO.75 -0.74 RO.75 -0.79 -0.62Exponent, c
'" Top value determined from companion specimen tests; bottom value from incremental step tests*,~ Top value -experrmental: bottom value - calculated from Eq, 1b
*~,* Two values indicate different slopes at short lives (top value) and long lives (bottom value).
a) Quenching 8r-.----'--.. Tempering
b) Quenching 8 DeformingI, i at Temperature
-vy ...v
~~-ecuQ.
E~
Tempered Martensite
'/.......... L.J
Deformed TemperedMartensite
I
cu...~-e~~
c) IAusforming....---.
Tempered Martensite from~ Deformed Austenite
, 'I..........
d) Maragingi ,
Age Hardened,....----" Martensite
I
~
Time
Fig. I
Time
Strengthening Processes for Steel
47
a)
O.SOia.
1- x 20 NF (both ends)
0.190 D'0.185 io.
). .1
I.. .1
),..J
b)
11111111 ~ III1IIIIIIII
1 3 L I 0.755 J.!L 1-'I--Is -l 0.745 8 2-+1
k-------S Ref -----+1
t x 20 NF (both ends)
0.205 D'0.'95 rc,
11111111 ~ ~ IIIIII11
I --1.L~ 0.505 J.LI--114 OA95 4
14---- 4 Ref -----
Notes:
I. All dimensions in inches.
2. Fractional dimensions within ± 3'21/
3. Test section diameter uniform towithin ± O.OOOS" along gage length.
Fig.2 Test Specimens
500
til..x:
~ 400..c-OlCCD...-Cf) 300~::J-Uo...u, 200CD::J
~
100
flOA~
df:5
/''Y • _ Compressive
,/ StrengthL
01045, Q 8T04142, Q8 Tf::" 4142, Def\lAusH-11OMar
>l>00
0 10 0 200 300 400 500
Hardness, BHN
Fig. 3 True Fracture Strength as a
,,-
600 700
Function of Hardness
49
010.45, QaTo 4142, Q aTt::. 4142, oet
1.0 v Aus H-II 0.20<> Mar
\ C0.8 \ 0.16 '"c,.,
0- \ a.:;:: xo \ w"Cl 0.6 \ 0.12
0>c:
'" \ ·c~
'"" -eU \ ~
Ie 0
\ Iu, 0.4 , 0.08 .s'"" 0
F <, ~
<IiwO.2 0.04
C
••......0100 200 300 400 500 600 700 80eP
Hardness, BHN
Fig.4 True Fracture Ductility and Strain Hardening Exponentas a Function af Hardness
J200
o
700 800
Fig.5 of Hardness
1
j
50I.
o c
a
o
0- 0-_<>----<>--"'"0-<>-.< 0.0095__0-"" 0.0090
SAE 1045, 595 BHN
:::::;:;:::::::~t.€ /2 ~ 0.022-0-__• 0.0177
_--~-<>--oD---X 0.0150o---"- -<>-_o-_."...v_.. 0.0125
0 0 a 0 "" 0.0075
10"I 10 10' 10' 10' 10'
2N, Reversals
Fig. 60 Plastic Strain Amplitude During Reversed Total Strain Cycling
a_-0_-:=::=::=:::::::>-0<:'-<> t.€/2~ 0.0130- ~.... J' , 0.01150-0-0--<> ~ __~ 0.0095
~~Q":go,,,~~ . 0.0073
/I
II
I
SAE 1045. 500 BHN
iO··iO' iO' 10'I 10 10'
2N, Reversals
Fig. 6b Plastic Strain Amplitude During Reversed Total Strain Cycling
51
SAE 1045, 450 BHN
0---< -0-:--0---0:>->< t:.e / 2 =0.0168
a
0.0063
Fig.6c
10 10'2 N, Reversals
Plastic Strain Amplitude During
0.0052
10'
Reversed Total Strain Cycling
SAE1045, 390 BHN
,,10-'
10' 10' 10' 10'I 10
2N, Reversals
Fig.6d Plastic Strain Amplitude During Reversed Total Strain Cycling
52
SAE 4142, 670 BHN
o --e...< ~€ /2 • 0.0130 C0..
o
~~..'. 0.0010 T
0.0010 C
T = Tension startC= Compression slort
la' 10'2 N, Reversals
Fig. 70 Plastic Strain Amplitude During Reversed Total Strain Cycling
SAE 4142, 560 BHN
().0 0-·- oj( ~€12 • 0.0140
0 9 0 " 0.0115Xl
c 0 > 0 ~.. 0.0083c
10410 la' 10'2 N, Reversals
Fig. 7b Plastic Strain Amplitude During Reversed Total Strain Cycling
10-4 L---L....LJ....LlllJLL.-I.-'-..J..l.lllJ.L~-I....LJULuL-:-L..J--Ll..Li.llL--:-..L-.L.J...L.LWJ
I 10'
53
10'
0.0068
oo
oc
o
o
10
SAE 4142, 475 BHN
o~_--.,----o,---« L>€/2=0.0130__,.--,,"-",,'---<>:- --. 0.0110
o-e~_. 0.0085
0_--0-....0---<'---
10' 10'2N, Reversals
Fig.7c Plastic Strain Amplitude During Reversed Total Strain Cycling
SAE 4142, 450 BHN
c
oJ'o
A
o
>--__..o---o-<>--~-"K L>€/2 =0.0125o ~x 0.0100
..x 0.0083
o-__-o-.o----::::::?::::::;::::::c>-~0.0075
~~
oa:NIO-'....~
~
10'10 10' 10'
2 N, Reversals
Fig. 7d Plastic Strain Amplitude During Reversed Total Strain Cycling
54
SAE 4142, 380 8HN
o
o
o
o
o o
-: A'
.< 0.0052
.-/
la' 10'2N, Reversals
Fig. 7e Plastic Strain Amplitude During Reversed Total Strain Cycling
0.0060
0.0075
SAE 4142 Def. 475 BHN
o,
10' 10'
2N, Reversals
Fig. 80 Plastic Strain Amplitude During Reversed Total Strain Cycling
55
SAE 4142 Def, 450 BHN
o
o
o
o
c
10'
2N, Reversals
0.0055
Fig. 8b Plastic Strain Amplitude During Reversed Total Strain Cycling
SAE 4142 Def, 400BHN
o
o
o
D;c
c
10'10 10' 10'
2N, Reversals
Fig. 8c Plastic Strain Amplitude During Reversed Total Strain Cycling
i0 0
' 1..--'----'---'--'-.1..lJ.l.L_.l-L.1.-U..l.l.l:"-=----'-----'--..L.l..1..lJ.l..l..-:-I..-LLJ..l..u.J.J--c--'--'-J.cL.LLUJ
I 10'
56
Ausformed H-II
g~~ 0.0122
---'x 0.0115
Q
0--0_--<:0_-<:>-" 0.0200
<>---<>---x l>E/2' 0.0310
"--o-~_""--o-_0-_ -x 0.0156
10'10 10' 10'
2N, Reversols
Fig. 9 Plastic Strain Amplitude During Reversed Total Strain Cycling
18% Ni Maraging (300)
0---0__>--0--0--00-.. l>E/2' 0.0300
v
• __x 0.0100
10°'1 10 10' 10' 10' 10'
2N, Reversols
Fig. IDa Plostic Strain Amplitude During Reversed Total Strain Cycling
57
18% Ni Maraging (250)
:r.c <;0-__":>--..-,..----<>0- - x 0.0100
o
/' 0
--
o
0>-__-<>--0--"0>---0----0... 0.0200
0-......0_.--<>---,,>--0--",,0--0---00 .... 0.0140
~-",_-"_-O---<O.---X L':.€/2 =0.0300
----x 0.00670 0
10·'I 10 10' 10' 10' 10'
2N. Reversals
Fig. lOb Plastic Strain Amplitude During Reversed Tatal Strain Cycling
10'10'
o 0
_-",_-rr--"-_O•." 0.0068
o
18% Ni Maraging (200)
0--0_<>---0--0--0---<0-.. 0.0100
__J>--o---<>O.X L':.€ 12 =0.0305
>---">-_-0-""---<>----00..•~ 0.0200
o 0 o__x 0.0140
10' 10'
2N. Reversals
Fig.IOc Plastic Strain Amplitude During Reversed Total Strain Cycling
10"
Q)"0
£0a.
E a---"<l
0 c 0 0<: 10·'"e 0 0 0 0
en.'d cu; 0-
0a::NIO"-,
Ia
'".J<J
~
10"I 10
_ J
f100ksi
!
Monotonic
595 BHN
-0.01-
Monotonic
aCyclic
450 BHN
58
a Companion Specimens- Incremental Step
Monotonic
Cyclic
500 BHN
Monotonic
Cyclic
390 BHN
< 1,
Fig. II Monotonic and Cyclic Stress - Strain Curves forFour Hardnesses of Quenched and TemperedSAE 1045 Steel
-.L __.__ L.-~ J
~0.01-
670 BHN
Monotonic
Cyclic
450 BHN
560BHN
Monotonic
Cyclic
380 BHN
Monotonic
475 BHN
o CompanionSpecimens
- Incremental Step
C/l'0
Fig.12 Monotonic and Cyclic Stress - Strain Curves for Five Hardnesses ofQuenched and Tempered SAE 4142 Steel
t100ksi
~-0.01-
Ten.-Monotonic- -
- Comp-Cyclic
475 BHN
Ten
Monotonic_ - - -Comp.--
Cyclic
450 BHN
o Companion Specimens- Incremental Step
MonotonicTen
- - Comp
- Cyclic
400 BHN
C1'o
Fig. 13 Monotonic and Cyclic Stress -Strain Curves for ThreeHardnesses of SAE 4142 t Quenched and Deformed atElevated Temperature
61
MonotonicTen
Cyclic
o Companion Specimens- Incremental Step
MonotonicComp ,/ .... --0
'"
t100ksi~~0.01-
Fig.14 Monotonic and Cyclic Stress - StrainCurves for Ausformed H - II Steel-660 BHN
IL1
1_.J
Monotonic
300ksi
Monotonic
250 ksi
o Companion Specimens- Incremental Step
Monotonic
200 ksi
Cl'
'"
~0.01-
Fig. 15 Monotonic and Cyclic Stress - Strain Curves forThree Strengths of 18 % Nickel Maraging Steel
,
o
Q
63 j
j
j
j
j
j
j
j
j
j
j
j
j
j
j
j
j
j
j
j
j
j
j
j
j
j
J
0':::0./3
5958HN.J'l
-
0':::0./2- 500
0<').- 4500::0./2.n- 390rt,
0'::: 0./4..... ..L ...... ..1. J-IJ
J
SAE 4/42
0':: 0./1
400 t"-SAE/045
300 t"-
o
200 ,..-"_D
r'0I'en
oX
,_0-~
QQ)100
..L"0
10-a:3-a.E
<:(
100 , ,10- 10-
~€p/2, Plastic Strain Amplitude
Fig. 16 CYClic Stress - Plastic Strain
• j
i.J
IL.J
64
300 SAE 4142, Def.
200
-:r 9
g
n':0.12
-::r= n': 0.14
475 BHN450400
~
~ 100l-__---I._----JL--L..---I.---I.---L....L..JL...L. ...L...._...J::::l....a.E«en 500enQ)
~ 400(J)
bC, 300
200
Aus H-II
n':0.06o
18 % Ni Maraging
o
a
o
10-2
~€p/2, Plastic Strain Amplitude
Fig. 17 Cycl ic Stress - Plastic Strain
I00L.-_3----I.--L...--..L--I.--I.~....L...;L.....L-::---...L....-...J10
65
C 0.20~o0-
"W'" 0.16c:.~
10~ 0.12c:.~
iiio O.oS
~o
-,; 0.04
01045, QaTo 4142, QaT" 4142, Defv Aus H-IIo Mar
= 0
" 0[J) " 0
00
<)
<><>v
0
300200
Fig. 18 Cyclic Strain
400 500 600Hardness, SHN
Hardening Exponent as 0
700 SOO
Function of Hardness
300
0.0067o
~~~.~.--x t,€/2=0.0130~~0.0115_ --_-.:;~::::-<J~x 0.0090
o ~--<l'----<>--__-ex~ ex 0.0052
250
.,- 200-e.2c.E<t 150
50
2N, Reversals
Fig. 19 Stress Amplitude Chonges During Reversed Strain Cycling of SAE 1045Steel, 475 BHN
1.0
o.o./€f
/<v: . '. /otal
-'T-~ _ __Elastic
SAE 1045, 705 BHN
10-1
10-
a.E«s:'0~-(f)
Q)
'0::>-
- - BHN
0.8 1.00.4 0.6
N;fNf
0.20.4
0
I.O~. :>90
0.9 -0.01-0040.8~5 500
"_OS[ ~, 2 g 0 _0'"b" '"
<, tJ.e/2bC
o 0.01300.6 lJ 0.0115
a) SAE 1045. 500 BHN '" 0.009000.0067
bC
'- 0.7be
Life
- 10~ 10'
2 Nt, Reversals to Failure
Elastic, Plastic and Total Strain - Fatigue
10
Pig. 210
10-31 _-,-I -'-,..JJIIWit","II~I;-...L.I ..J....u.J..U~"1-'--'-U1.U.~r'-J.....l..L~~,-J-'-L.wJl;;-'--'...L.l.JCL.liI " lIu
l ~' "I! '!I! I 111",,1 I ,. ' I ""I , t I II !IIV.IV 1.0
N;fNf
Dimensionless Representation of StressAmplitude Changes with Cycling
b) SAE 1045
Fig.20
0.5' ", I!" ,I '" I'" ,I
0.01 r"\1r"\
0.6
'~---.'
'----..~ ~"---''"''.-pi" 7.:*i"*'»":~;;;;:"~~:""-#wr:" -',", 1;{:l~ -'\~1J!;*~4~;;- :",,;~%¥%i~~JlrJrntt'~:~; n7?'rr'(;~'>: ';'l'fK~' rr\
Ef
Ef
0'<'-1
SAE 1045, 500 BHN10.'
10·'
I 10 10' 10' 10' 10' 10'
2 Nf• Reversals to Failure
Fig. 21c Elastic, Plastic and Total Strain - Fatigue Life
''''Plastic/~
'\
o;f/E \ -c~ ~-a:r-~_ .x (0;
10 -~-~~~-e-.-=___.Elastic \ ~
\
~
-0~
Q.E«c.~
iii
10'10'10'
SAE 1045, 595 BHN
) 10'
e/ Buckled
/Of/E
"7 ""'-ce, "",-cElastic "\
\Plastic/"\
\\
2 Nf, Reversals to Failure
Fig. 21b Elastic I Plastic and Total Strain - Fatigue Life
10-31 1 '1",,1 ,I ",,! .,I Ie ! ,,,,,I I """I ! rI",,1 "I"!!I
~
10.'-0
.20.E«c·0..:=(f)
10-21
EfEf
'"00
SAE 1045 , 390 BHN
\~....- Buckled
Oj/E \- \._ ~T___ otal
Elastic/ c-c-,) . /'tbB-,...~ <>--a::
Plastic/\ ---
\10"
I 10 10' 10' 10' 10' la'
2 Nf 1 Reversals to Failure
Fig,2le Elastic 1 Plastic and Total Strain - Fatigue Life
10"~
"0
~c.E<Ic·eiii
10"
SAE 1045, 450 BHN
~..\-Ela~-""';' \ xTatal
~,,-'
\~Plastlc .............\
\IQ.
10'10- 4" ",,110 !5' "I .. ,,'
10 la'
2 Nf 1 Reversals to Failure
Fig. 21d Elastic. Plastic and Total Strain - Fatigue Life
10"
10~3! , "",,! "",,' ""!,,, . '\",,! I .,. ,I 10
10-',J,,,.Alf/E
~
"0~
a.E<Ic.~
iii
c __ !'---.- '---
€f
10"
~ V€t SAE 4142, 670BHN '""0~
10.1
SAE 4142. 560 BHN
0.E
'"0.E
'"e.~
if,
/Oi/E
C- - ~:... -10" / --a-"l
Elastic
A
. /TotOI~
c·2if,
/Of/E\
10'{-- '\ . /'
Elastic
\A
. /' \Plcsfic
'"'>0
10'10'10'10'
\\
10
2 Nf , Reversals to Failure
Fig.22b Elastic, Plaslic and Talal SIrain - Faligue Life
IO~31~_~c, .,1'.,",,,~~I;-L'~"'JI"'.'""~ll:"'~LL'"'~r'--'~1.u~:;<~~L1LU..L.~~J..wI ! 1.. ,,1 1 01''1'1 . 01",,1 "',,1.110'10'10'10'10
10-3,I ·,lll"! .!",,' , ,1",,1 .,,j,",l ,,f, ..,!, "'11.1
F,g. 220 Elaslic and Total SIrain - Faligue Life
A
2 Nf , Reversals to Failure
Ef
Ef
ID'0
.2c.E<
10·'SAE 4142, 475 BHN ..
'0~
C.E<r
10"SAE 4142, 450 BHN
...,o
10', , 4
1010
10.3 , , "'".1 J ,1,,,,1I ' ! l! ,,',I",.. ,1",,' ,l,.,r!
c.~
if>
10·10'
ChflE Tolol. / . ------10 "ib- - - -\.a -Ji!.... -....g .
Elasfle \ '- ----.-~-<>-----_o\
.>,Plastic \
1",,1\ <I1 ,,01 ""I '" 0' 1010·'1 ,,01 ''';0 10' II
c.~
if>
2 N, I Reversals to Failure 2 Nf 1 Reversals to Failure
Fig. 22e Elaslie, Ploslie and Tolal SIrain - Faligue Life Rg. 22d Elaslie, Plaslie and Tolal SIrain - Faligue Life
'~'--" ~
Ef
Ef
~
'C;:'
10·'SAE 4142, 3808HN
~
'C~
iO·' SAE 4142 Del, 475 BHN
C.E<
C.E<{
v Load Control
.s~
<J)
~
.~
u;;::!
Plastic .......... \ ..10·'1 , ! ,I",,! \ \ I II "I ,J
I 10 10' 10' 10' 10' 10·
10·'J.-...::::.Of/E \ ~0 ~1_ _ \......-.,,"<.Tatal
Elostie'---~~\ --...-..,\ '" ,...
10'10'10'10'10
10-3 , !I .Ill..! ' .1'",1 .I",,'! ! Mil,,! ,! ",,"! ! .!"!I'
10·2~ \:---Of/E---- \ ~__ \ " /Totol
Elostie-----~"'-"<\ --",...
Plost'/"\ ~rc \ - ~
2 Nf
, Reversals to Failure 2 Nf 1 Reversals to Failure
Fig. 22e Elastic, Plastic and Total Strain - Fatigue Life Rg.230 Elosfic, Plastic and Total Strain - Fatigue Life
EfEf
...,N
10'10'10'10'10
v Load Control
SAE 4142 oer, 400 BHN
,vOf/E \
- -""'- ~ ""~ ..............Total
Elastic'>- - ~~~
Plastic ..-/'\
~10. 3 1 ,I """I "11,,1. '!",,' "'",,1 .Ill,," "",,!
"10·'
"0
~c,E«c.~
Vi
10·'
10'
"Load Control
10'
SAE 4142 Def, 450 BHN
Plastic..-/' \
"\10' 10'10
10·'
10.31I .!""I "",,!' ,I",,! " ""I . " .."f. "I",,'
\10"'\h<()c:. _ \ ~ ..........---Totol
-~ ~Elastic ---''"'\:B-a.",_1
'\
""0~
a.E«c.~
Vi
2 Nf 1 Reversals to Failure 2 Nf 1 Reversals to Failure
Fig.23b Elastic, Plastic and Total Strain - Fatigue Life Fig.23c Elastic. Plastic and Total Strain - Fatigue Li te
'~_.~"-
~" L._~
Ef
€f
18 % Ni Maroging (300)
ID"0
.2
10.' Ausformed H-II, 660 BHNID
"0~
10-'VI Load Control
....,W
10'10'la'la'10
2 Nt 1 Reversals to Failure
Fig, 25a Elastic, Plastic and Tatal Strain .. Fatigue Life
10'" _~-"..w, lu'L,~"~I;-L'~L'LIU!1~"~ll~LL.L.~rf~~~~-;:.~~LL~L,c"-~.L1.LWI ' ! ""I t )I ' ""I , I ",,' , " ""I
<i
E .
'" \~ t \", "if) ~/E \
/f h -cL- - - t:l>\ .N:o. _ ....
10·' . / ~ "'\_ -a... _-...,,>-Elastic \
\Plastic.-----\\
\
iO'
v Load Control
10'
'~
10''"10'10
2 Nt 1 Reversals to Failure
\..--Of/~ yTotal
-a\."\
v--oJ.-\ Elastic7
Plastic .............\
\\
Fig.24 Elastic, Plastic and Tatal Strain .. Fatigue Life
10'" I rI",,!! " '!!,,! ''\'''",,1 ! ,1",,1 .1",,1, tI. Il.,
10·'
<iEerc.~
if)
EfEf
~ t, v Load Control<[
~ lol-18% Ni Moraging (200)
v Load Control;:a.E
t'\<[
c \>.~
en \
10_~Of/E \\~Total ~
-- \ ..7--....c;] ---e....J;f}-. B--V
Elastic \
/'\Plastic \
\10"
I 10 la' la' 10' 10' 10·
2 Nf , Reversals to Failure
Fig. 25c Elastic, Plastic and Total Strain .. Fatigue Life
10'10'la'
18% Ni Moroging (250)
la'10
2 Nf , Reversals to Failure
Fig.25b Elastic, Plastic and Total Strain- Fatigue Life
10-'
10-3 ,~_~c, .,jl.,",~,,~I;-"'~-'.Jw~)'~~u-u.c~r'~~.w.~;:;;;~~.J.coL.~"".L"""I ,1'11.1 I 1.",1 ,\1 ""I , ,I 'II'! t!, 1. 11,1
""0~
\'t6 t ~~ \
Of/E Y.10-f'~':::"" - ~:::--""'" ~~ .......
Elastic \
.>,Plastic \
\
L~. ~
L~ L_~
104 10' 10·to Failure
Amplitude - Fatigue Life
Jr It x
10' 102 10'2 Nt, Reversals
Dimensionless Stressfor Hardened Steels
'-J
""
Plot
Materials:SAE 1045, Q 8T
0705 BHN0595Ii. 505V45003BO
SAE 4142, QaT.670 BHN·560"'475T450·380
SAE 4142, Def.~ 475 BHNIi 4504405
Ausfarmed H-IIx 655 BHN
18% Ni MaraQinQ+ 300ksi., 250~ 200
tn~
if °
+~
x +• "" x
• T + do~ • TXTI.fI J"'~ TXt
°"'~ "a tli.v 4lt •
~;r Ii. t4 4. x ,.
(TOQ011"',. tx
...V vox
o
x
t. ·x•
Fig. 26
1.0
:z 0.9Q)....+-
U> 0.8
«iO.3'" IbO
Q)....::J'0 0.7oItQ) 0.6::J
F<,
:z 0.5Q)....+-U>
01.s 0.4+-oc....Q)+-
()(
aV<l>v
Materials:SAE 1045, OST
0705 BHN0595r>505V4500380
SAE 4142, 0 ar.670 BHN·560&475.450·380
SAE 4142, Dof.~ 475 8HN,.. 4504405
AUlformod H-II,,655 BHN
18% Hi Maroging+ 300ksi't 250~ 200
vi
103
vi
o
""+
•
Ii
• vr'l t+o ~....L.o.x • 'lfF"OV
• 0 ~. ~o.,.,
• •a' r"lLl. ,.'"V ''11"" oX
o <I'. ~.
o
4
102
Reversals to Failure
Plastic Strain Amplitude - FatigueHardened Steels
o
•
o
x
•
•
c
10
x
o
2Nf ,
DimensionlessLife Plot for
•
Fig.27a
.....o='o
>-.....
Q)~
='.....ooIt 10-1
<,Q)"0='
:!::a.~c·0~ 10-2
.!:!.....13a..
-s:C\J<,
..?"10-3 , 1
<]..... , __..1__...1.1-1.1...1.1.11.J1.J1~"[)_~_..l-...1..LJ..J...u.~~--JL--1....J.~...L.:~:i"~~~~~~:""..uI 1 1 1 1 ""I I , ! , , "II•• ! I• ' I~I" I ,
....,....,
+\7%,
Material. :
SAE 1045, Q 8 To 705 BHN0595A505V450<> 3BO
sAE 4142. QaT.670 BHN- 560"'475"450+ 380
SAE 4142. Oaf.~ 475 BHNIi 450... 405
AUlformad H-IIx 655 BHN
18% Ni Moroging+ 300klil' 250~ 200
t•
Ii~+ A.I>~
0+
+w~.I> ;.iIrI" a ...
00.1> jt_ A A
X t t 'PIS ,j..,j..x \7+ .I>
o~
0
a
- Ax + a "" ". ~
'V ""
• 4'- +~
4...
o
x
10 10" 103
104
2Nf• Reversals to Failure
Dimensionless Plastic Strain Amplitude - FatigueLife Plot for Hardened Steels
Fig. 27b
-cQ)
o..........Q)0u>--+=o::;)
Cl
Q)
10-1::;)Cl-~
.......Q)"0::;)-0-E
-2<l: 10c0...-(f)
UJN<,
CoUJ<l
, I II .1I , ,." , , "",- I IVI 1111
11o I I ...- I ,a... -3 '" , "!• 10 I
~ - I
78
+-a)c:::
Q) -0.10c:::0 f:. f:.0- 0
~ -0.08 0 o e 0 0V'o0 00<>s: o 0
0. -0.06c:::Q)'"- 01045, QaT(j) -0.04
o 4142,QaTQ) f:. 4142, Def5, -0.02 V' Aus H-II+- <>Mor(r 0
200~ 300 400 500 600 700.0
Hardness, BHN
-c:::Q) -\.O b)c:::00-x -:0.8 ~<>~W Of:. 0
>- 0 o 0+- -0.6 o 0
+-U:J -0.40Q):J -0.20>+-
~ 0200~ 300 400 500 600 700o
Hardness, BHN
Fig. 28 Fatigue Life Exponents as Functions of Hardness
79
10'
.ZN
o 1045,OaT[J 4142,OaT'" 4142, DelIT Aus H-IIo Mor
[Jo
[J
Function of Hordness
1100 200 300 400 500Hardness, BHN
Fig. 29 Transitian Fatigue Life as a
600 800
.,.....::Jc:0
:;:";;;c:0~-0.,..,".'!=C.E
I<l:c:I '0.. J ~-CIl
0.025
0.020
0.015
0.010
01045 OaT04142 csr'" 4142 Del\7 Aus H-IIOMar
00
DO0
'b'"0 0c:
0
oo
oo
11F!• 0.005
N<,w<l o 100 200 300 400 500 600 700
Hardness, BHN
Fig. 30 Transition Fatigue Life Strain Amplitude as aFunction of Hardness
800
18 % Ni Maraging 00o
SAE 4142, Oef.
400 BHN~5
Ausformed H-II
SAE 4142, QaT
450 BHN560-,670
SAE 1045, QaT
450 BHN
o;;0. _.1 \300 ksiN"IO r250<,11/
<J162
roraE<{ -"
10~' Ic: I I- I Ie I
-Cf)
-5
10 , ,~. ,~.. '0. I 102 104 10.
2Nf , Reversals to Failure
Fig. 31 Total Strain Amplitude - Life Plots for Hardened Steels
L._•••_~
,~---~
0.030SAE 1045
0.030
00.....
SAE 4142
3~10 '. :4104~:g: :::2Id . .
22 x 10
01 I I I I I I I I I I200 300 400 500 600 700
Hardness, BHN
Fig.33 Total Strain Amplitude - Hardness Relationsat Various Lives
oj§NO.OIO<,
~
0,005
a.E
<J: 0.020c:o~
en 0.015
Q)
"0 0.025::J-
Id
2 x ,d
0 1 I I I I I I I I I I200 300 400 r~~ r~~ ~~~
Hardness,
Fig. 32 Total Strain Amplitude - HardnessRelations at Various Lives
E"0.020<J:
~0.005(j)
<J
.:= 0.010~
Q) 0.025"0::J-
c:.~ 0.015-en
82
Q)
"0::J-
Aus H-II
Theoretical Steel',~ar 300
, ,~
--- '~4142 (670 BHNJ-- - _____
0-E<!c'0~-If)
-- - ----1045 (390 BHN)
105
2 Nf , Reversals to Failure
Fig,34 Strain Amplitude - Life Curves for Representative Hardened Steels
Materials:a 1045 QaT (595 BHNl04142 QaT (56aBHNl~4142 Det (45aBHNlvAus H-llOMor 300
2000
'.. 1000~
w 500
~b<]
200
-~--_!:J._ -- --"-
Fig, 35
10 10' 10'2N t , Reversals to
Fatigue Notch Parameter as aRepresentative Steels
10' 10'Failure
Function of Life for
83
APPENDIX A - STRESS-STRAIN HYSTERESIS LOOPS FOR HARDENED STEELS
Reproductions of representative hysteresis loops for the various
conditions of steel are shown in the accompanying figures.
Determination of the cyclic stress-strain curve from one specimen
using the incremental step strain test is illustrated in Fig. A-I for a maraging
steel. The locus of loop tips is seen to define the cyclic curve which falls
considerahly below the initial monotonic curve indicating cycle -dependent
softening.
In Figs. A-2 through A-4 is shown the stress-strain response of five
hardnesses of quenched and tempered 4142 steel each subjected to a strain
amplitude of approximately 0.01. The untempered condition is seen to under
go cyclic hardening in Fig. A-2. Note the difference in response and life
between tests started in tension and in compression. Apparently the life is
extended if the initial plastic readjustments take place in compression. This
suggests relief of residual stresses through plastic deformation as an important
factor in such structures. The 560 BHN condition exhibits cyclically stahle
behavior while cyclic softening becomes predominate with further decreases
in hardness (Figs. A-3 and A-4).
Cyclic-dependent hardening of ausformed steel is shown in Fig. A-5.
Note that all hardening takes place in tension with the compressive stress
limit remaining constant.
Pronounced cyclic softening of quenched and deformed 4142 steel is
shown in Fig. A-6 under both controlled strain and controlled load conditions.
In the latter case, preferential compressive softening leads to a buckling
failure.
Maraging steel likewise exhibits softening under strain and load cycling
as shown in Fig. A-7. In this instance preferential tensile softening under load
control leads to necking and eventual tensile failure.
TIOOksi
1o.oo5-1
Increasing Strain
Monotonic Curve
\ ~-----/
/
Decreasing Strain
Cyclic Curve
~
Fig. A-I Stress -Strain Record of Incremental Step Test on 18% Ni Maraging Steel
Cycle 1,2
TensionStart:
5
85
TIOOksi
Lo.oos...
Cycle 1,2
CompressionStart:
5 10 20 30
:JFig. A - 2 Stress- Strain Hysteresis Loops During Strain c:}\:ling of SAE 4142 Steel t
670 BHN - !>€/2 =0.010
86
TIOOksi
LO.oo5-
Cycle 1,2
Cycle 1,2
5
5
10 20 50
0) 560 BHN, L;€I2=0.0115
10 20 50
b) 475 BHN, L;E/2 = 0.0110
Fig. A- 3 Stress - Strain Hysteresis Loops During Strain Cycling of SAE 4142 Steel
87
IIOOksi
LO.o05~
Cycle 1,2 5 10 20 50 100
c l 450 BHN, l>E/2' 0.010
2005 10 50 100
b) 380 BHN, l>E/2 • 0.0110
Fig. A- 4 Stress - Strain Hysteresis Loops During Strain Cycling of SAE 4142 Steel
Cycle 1,2
88
fIOOksi
lo.oos-
Cycle 1,2 s 10 20
Fig. A- 5 Stress -Strain Hysteresis Loops During Strain Cycling of Ausformed H-II Steel - t.€/2 =0.015
89
fIOOksi
lO.005_
Cycle 1,2 5 10 20 50
a) 475 BHN, ll.€/ 2' 0.01
100
Buckled an 44'h Cycle
Cycle 42 20 10 21
b) 400 BHN, 0;;' 175 ksi
Fig. A~6 Siress - Strain Hysleresis Loops lor SAE 4142 Del Steel During a) Strain and b) Stress Cycling
90
fIOOksi
LO.005~
Cycle 1,2 5 10 50
0) 6€/2' 0.015
200
Cycle 1,2 5 10 20 50 70 100 120 126
Tensile failureon 134th cycle
b) (1" 250 ksi
Fig. A-7 Stress- Strain Hysteresis Loops for 18% Ni Maroging Steel During a) Strain and b) Stress Cycling
Jj
1,...1
I~~.J
91
APPENDIX B - FRACTURE SURFACE APPEARANCE OF HARDENED STEELS
Fractographs illustrating general macroscopic surface features are
presented for representative conditions of steel in the accompanying figures.
The effect of hardness on fracture appearance can be seen by com
paring the fractographs for five conditions of quenched and tempered 4142
steel, all cycled at a strain amplitude of approximately 0.013, in Fig. B-l.
Critical crack size decreases with increasing hardness as would be expected
on the basis of decreasing ductility. The extent of the shear lip also de
creases with increasing hardness. Absence of a shear lip in the softest
condition is due to the circumferential growth pattern of the fatigue crack.
Strain amplitude effects are illustrated in Fig. B-2 for quenched and
tempered 4142 steel at 450 BHN. Crack size decreases with increasing
strain amplitude. Shear lips are observed for all but the 0.0075 strain
amplitude test in which several separate fatigue cracks formed at various
points around the circumference. Such behavior favorably reflects on the
alignment and rigidity of the load frame used in the investigation.
Fractographs representative or short life and intermediate life be
havior are shown for three conditions of quenched and deformed 4142 steel in
Fig. B-3. Again the softer conditions can accommodate larger fatigue cracks
than the harder condition. At least two large increments of crack growth
are noted in the 450 BHN short life specimen. Irregular surface features
are found in the 475 BHN intermediate life specimen While the 400 BHN inter
mediate life specimen exhibits a fatigue crack completely circumventing the
fracture surface.
Rather unusual fracture features are shown by maraging steel in Fig.
B-4. With the exception of the short life 300 ksi condition, fatigue cracks are
observed to grow macroscopically on approximately 45 degree planes. A
nearly perfect helix is described by the 200 ksi short life specimen. This is
an indication of the relatively high crack toughness of these materials. Cyclic
softening may so effectively blunt the crack tip that growth occurs in a step
wise fashion on inclined planes.
92
Weak longitudinal planes in ausformed steel are seen to result in
cracking in monotonic tension in Fig. B-5. Both short and intermediate
life fatigue surfaces exhibit small crack lengths and slight shear lips.
Shot peening* effectively offsets surface weaknesses so that the
fatigue crack is seen to propagate internally. The internal defect
responsible for failure appears to be either an inclusion or a void.
"' Shot peened specimens were. tested by N-. E .. Dowling as partofagraduate term paper, .
rc"_~ ," _
103
102
.,~
:::>-0
LL
0-Ul-0Ul~.,>.,
10a::--Z
N
Fraclograph Scale:
I "I o. 1
'"cc
700600500400I I r 1 ! I
300
Hardness, BHN
Fig. B-1 Fractographs of Five Hardnesses of SAE 4142 Steel Cycled at a Strain Amplitude of 0.013
0.020
.(\J......<J) 0.005<l I Fractograph Scale:
Gl"Q~-Q.
E<:(
<:
o~-Cf)
o-ot-
0.010
10
I 0,1"I
102
2Nf , Reversals to Failure
103 104
~
Fig. B- 2 Fractographs of SAE 4142 Steel (450 BHN) Cycled at Various Strain Amplitudes
l._"
Short
Life
IntermediateLife
Fractograph Scale:
I 0.111
I
475 BHN
l!.€/2 =0.0£25, Nf= 142
lIE/2=0.0042, Nf =17.700
450 BHN
IIE/2= 0.0150. Nf = 162
lIE/2 =0.0050. Nf=4.540
400 BHN
lIE/2=0.0125, Nf=195
IIE/2 =0.0065, Nf = 1,060
\0CJI
Fig. B- 3 Fractographs of Three Hardnesses of Deformed SAE 4142 Steel
L~ L-..
ShortLife
IntermediateLife
Fraclograph Scale:
I 0.211
I
300 ksi
6e12 =0.05, Nf=59
(jo=20q ksi, Nf=2,570
'''-'_'_:n,,__
250 ksi
6€/2=0.05, Nf= 47
0;,=200 ksi, Nf= 2,430
200 ksi
6€/2 =0.05, Nf= 50
O"a= 175 ksi, Nf =1,660
~
Fig.8-4 Fractographs of Three Strengths of 18% Ni Maraging Steel
. )
MonotonicTension
Fatigue
Fatigue(Shot peened)
97
LI€l2=0.03I, Nf =4
oa =176 ksi, N =204,000
Fractograph Scale:
0.1"
0;, =225 ksi, Nf =5,770
Defect MagnifiedO "Scale: I .02 I
. j
]
iJ
Fig.8-5 Fractographs of Ausformed H-II Steel
II.··II
D
No.
301
302
303
304
305
306
307
308
I309
310
311
312
Recent T. &A. M. Reports
Title Date
"Piecewise Polynomials and the Partition Method for Ordinary September 1967Differential Equations, " by H. L. Langhaar and S. C. Chu.
"A Comparison Plain Strain Fracture Toughness in the IsothermalFlow Properties of a Structural Steel, " by W. Kove s , August 1967
"Preliminary Investigation of Measurement of Elastic Moduli of September 1967Composites Using Strain Gages, " by G. Trantina.
"A Sequentially Modulated Ruby Laser System for T'ransmttted September 1967and Scattered Light Dynamic Photoelasticity~"by R. Rowlands.
"Crack Control in One Way Slabs Reinforced with Deformed October 1967Welded Wire Fabric," by J. Lloyd, H. Rejali, and C. E. Kesler.
"Splice Requirement for Deformed Wire Fabric in One Way December 1967Slabs," by J. Lloyd and C. E. Kesler.
"Modes of Failure of Glass Fiber Reinforced Plastics Under September 1967Compressive Loads," by J. W. Gillman and H. T. Corten.
"Low Cycle Fattgue Properties of an Ausformed Steel, " by February 1968J. E. Matheny.
"Discontinuous Mode of Crack Extension in UnidirectionalComposite," by E. M. Wu and H. T. Corten. March 1968
"Turbulent Friction in EccentrtcAnnular Conduits," byJ. M. Robertson. March 1968
"Alleviation of Fatigue Damage," by B. 1. Sandor. March 1968
"Environmental Cracking in AISI 4340 Steel," by W. A.Van Der Sluys , April 1968
o
313
314
315
316
317
318
319
"The Conference on the Matrix of Concrete, IT by J. L. Lott,
"Fracture Toughness of Portland Cement Concretes, " byD. Naus and J. L. Lott,
"Conformal Mapping of the Interior of a Unit Circle on tothe Interior of a Class of Smooth Curves, " by Thomas F.Moriarty and Wlll J. Worley.
"Effect of Temperature on the Drying of Concrete, " byRobert Yuan, Hubert Hil sdorf, and Clyde Kesler.
"On the Treatment of Partial Differential Equations by thePartition Method, " by H. L. Langhaar and S. C. Chu,
"Effects of Mean Stress and Pre-Strain on Fatigue DamageSummation, " by T 9 Topper and B. Sandor.
"Enhanced Drain Boundary Sliding During Reversed Creep ofLead, " by Masaki Kitagawa.
April 1968
May 1968
August 1968
August 1968
August 1968
August 1968
September 1968
II\111111~m~I\~\I~\I\~lli~\ii\~i~ili \III1\113 0112 046058506
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