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"1

-,I,

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The Department of Theoretical and Applied Mechanics at the Universityof Illinois, established in ~890 as a separate unit of the College ofEngineering,has the following threefold purpose: (1) to offer instruction in engineeringmechanics to undergraduate students, (2) to teach and train graduate studentsin the field of mechanics, and (3) to conduct a comprehensive research programresulting in the extension of knowledge in all branches of mechanics andrelated fields. From its inception, the department has offered courses inmechanics in partial fulfillment of the degree requirements of the other depart­ments of the College and, since 1957, the degree of Bachelor of Science inEngineering Mechanics has been administered by the department. The grantingof graduate degrees originated in 1908, both Master of Science and Doctor ofPhilosophy degrees being offered. Research is considered to be a basic partof the educational program; strong emphasis is placed on the fact that thefunctions of teaching and research go hand in hand for the most complete andeffective development of both students and staff.

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

LIST OF REFERENCES

1. A. G. Sisco, Re'aumur's Memoirs on Iron and Steel, (A translationfrom the original printed in 1722), University of ChicagoPress, Chicago, Illinois 1956.

2. G. V. Kurdjumov, "Phenomena Occurring in the Quenching andTempering of Steels, " Journal of the Iron and Steel Institute,Vol. 195, 1960, p. 26 -48.

3. P. G. Winchell and M. Cohen, "The Strength of Martensite, "Transactions, American Society for Metals, Vol. 55,1962, pp. 347 -361.

4. P. M. KellyandJ. Nutting, "Strengthening Mechanisms in Steel,"High Strength Steels, Special Report No. 76, Iron and SteelInstitute, London, 1962, pp. 7 -11.

5. K. J. Irvine, F. B. Pickering and J. Garstone, "The Effect ofComposition on the Structure and Properties of Martensite, "Journal of the Iron and Steel Institute, Vol. 196, 1960,pp. 66 -81.

6. C. H. Shih, B. L. Averbach and M. Cohen, "Some Effects of Siliconon the Mechanical Properties of High Strength Steels, "Transactions, American Society for Metals, Vol. 48, 1956,pp. 86-118.

7. H. B. Nudelman and J. P. Sheehan, "Development of Ultra-HighStrength, Temper -Re ststant Steels Designed for Improvementof Fatigue Properties through Relief of Residual Stress, "Wright Air Development Center Technical Report 59-86,June 1959.

8. R. A. Grange, "Strengthening Steel by Austenite Grain Refinement,"Transactions Quarterly, American Society for Metals, Vol.59, No.1, 1966, pp. 26 -48.

9. R. F. Decker, J. T. Eash and A. J. Goldman, "18% Nickel MaragingSteel, "Transactions, American Society for Metals, Vol. 55,1962, pp. 58 -76.

10.

11.

A. J. Baker and P.. R. Swann, "The Hardening Mechanism in MaragingSteels," Transactions, American Society for Metals, Vol. 57,1964, pp, 1008-1011.

E. B. Kula, "Strengthening of Steel by Thermomechanical Treat­ments," Strengthening Mechanisms, Metals and Ceramics,Syracuse University Press, Syracuse, New York, 1966,pp. 83-122.

30

12. E. M. H. Lips and H. Van Zuilen, "Improved Hardening Technique, "Metal Progress, Vol. 66, 1954, p. 103.

13. J. C. Shyne, V. F. ZackayandD. J. Schmatz, "The Strength ofMartensite Formed from Cold-Worked Austenite, " Transactions,American Society for Metals, Vol. 52, 1960, pp. 346-375.

14. Victor, F. Zackay, Earl R. Parker, Dieter Fahr and Raymond Busch,"The Enhancement of Ductility in High-Strength Steels,"Transactions Quarterly, American Society for Metals, Vol. 60,No.2, June 1967, pp, 252-259.

15. E. T. Stephenson and M. Cohen, "Effect of Prestraining andRetempering of AISI Type 4340, " Transactions Quarterly,American Society for Metals, Vol. 54, No.1, March 1961,pp. 72-83.

16. N. N. Breyer and N. H. Polakowski, "Cold Drawing of MartensiticSteels to 400,000 psi Tensile Strength, " Transactions,American Society for Metals, 1962, 55, pp. 667 -684.

17. V. F. Zackay, W. W. Gerberich, R. Bush and E. R. Parker,"The Strength and Toughness of Dynamically Strain AgedAlloy Steels, " Paper No. BlI-3, International Conference onFracture, Vol. 2, Sendai, Japan, September 1965, pp, 813 -834.

18. L. Bairstow, "The Elastic Limits of Iron and Steel Under CyclicVariations of Stress, " Philosophical Transactions, RoyalSociety of London, Series A, Vol. 210, 1910, pp. 35-55.

19. N. H. Polakowski and A. Palchoudburi, "Softening of Certain Cold-Worked Metals Under the Action of Fatigue Loads, "Proceedings, American Society for Testing Materials, Vol. 54,1954, pp. 701-716.

20. L. F. Coffin, Jr. and J. F. Tavernelli, "The Cyclic Straining andFatigue of Metals, " Transactions, Metallurgical Society,American Institute of.Mining, Metallurgical and Petroleum,Engineers, Vol. 215, October 1959, pp. 794-806.

21. C. T. MacKenzie and P. P. Benham, "Cyclic Strain Softening of aHeat Treated Steel," The Engineer, December 28, 1962,pp. 1104-1105.

22. R. W. Smith, M. H. Hirschberg and S. S. Manson, "Fatigue Behaviorof Materials Under Strain Cycling in Low and Intermediate LifeRange," National Aeronautics and Space AdministrationTechnical Note, D-1574, April 1963.

23. N. H. Polakowski, "Observations on the Mechanical Behavior of HeatTreated Steel at High Hardness Levels, " Journal of the Ironand Steel Institute, Vol. 185, 1957, pp. 67-74.

31

24. JoDean Morrow, G. R. Halfordand J. F. Millan, "Optimum Hardnessfor Maximum Fatigue Strength of Steels, " Paper No. DI-13,International Conference on Fracture, Vol. 3, Sendai , Japan,September 1965, pp. 1611-1636.

25. P. H. Firth, "Fatigue of Wrought High Tensile Alloy Steels, "International Conference on FatigueInstitute of MechanicalEngineers, 1956, p. 462 -500.

26. H. E. Frankel, J. A. Bennett and W. A. Pennington, "FatigueProperties of High Strength Steels, " Transactions, AmericanSociety for Metals, Vol. 52, 1960, pp. 257 -276.

27. R. F. Thomson, "Fatigue Behavior of High-Carbon High-HardnessSteels, " Campbell Memorial Lecture, Transactions, AmericanSociety for Metals, 1963, Vol. 56, pp;803-833.

28. M. F. Garwood, H. H. Zurburg and M. A. Erickson, "Correlationof Laboratory Tests and Service Performance, " Interpretationof Tests and Correlation with Service, American Society forMetals, 1951, pp. 1-77.

29. F. Borik and R. D. Chapman, "The Effect of Microstructure on theFatigue Strength of a High Carbon Steel, " Transactions,American Society for Metals, Vol. 53, 1961, pp. 447 -463.

30. F. Borik, W. M. Justusson and V. F. Zackay, "Fatigue Propertiesof an Ausformed Steel, r r Transactions, American Society forMetals, 1963, Vol. 56, pp. 327-338.

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