H
ILLIN I
UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN
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UNIVERSITY OF ILLINOIS
BULLETIN
VoL XXXIX Pebruary 17, 1942 No. 26
ENGINEERING EXPERIMENT STATION
BULLETIN SERIES No. 334
THE EFFECT OF RANGE OF STRESS
ON THE FATIGUE STRENGTH
OF METALS
BY
JAMES 0. SMITH
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PUBLISHED BY THE tNIVERSITY OF I INOIS
URBANA
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HE Engineering Experiment Station was established by act
of the Board of Trustees of the University of Illinois on De-
cember 8, 1903. It is the purpose of the Station to conduct
investigations and make studies of importance to the engineering,
manufacturing, railway, mining, and other industrial interests of the
State.
The management of the Engineering Experiment Station is vested
in an Executive Staff composed of the Director and his Assistant, the
Heads of the several Departments in the College of Engineering, and
the Professor of Chemical Engineering. This Staff is responsible for
the establishment of general policies governing the work of the Station,
including the approval of material for publication. All members of
'the teaching staff of the College are encouraged to engage in scientific
research, either directly or in cooperation with the Research Corps,
composed of full-time research assistants, research graduate assistants,
and special investigators.
To render the results of its scientific investigations available to
the public, the Engineering Experiment Station publishes and dis-
tributes a series of bulletins. Occasionally it publishes circulars of
timely interest, presenting information of importance, compiled from
various sources which may not readily be accessible to the clientele
of the Station, and reprints of articles appearing in the technical press
written by members of the staff and others.
The volume and number at the top of the front cover page are
merely arbitrary numbers and refer to the general publications of the
University. Above the title on the cover is given the number of the
Engineering Experiment Station bulletin, circular, or reprint which
should be used in referring to these publications.
For copies of publications or for other information address
THE ENQINEE NG- EXPERIMENT STATION,
J UNIVERSTY OF ILLINOI,
UnatRBA, ILLINOIS
UNIVERSITY OF ILLINOIS
ENGINEERING EXPERIMENT STATION
BULLETIN SERIES NO. 334
THE EFFECT OF RANGE OF STRESS
ON THE FATIGUE STRENGTH
OF METALS
BY
JAMES O. SMITH
ASSOCIATE IN THEORETICAL AND APPLIED MECHANICS
PUBLISHED BY THE UNIVERSITY OF ILLINOIS
PRICE: FIFTY-FIVE CENTS
4060-2-42VS-22
4060--2-42--22996 OF ILLINoS
,= PRESS :;
CONTENTS
PAGE
I. INTRODUCTION . . . . . . . . . . . . . 7
1. Preliminary . . . . . . . . . . . . 7
2. Purpose of Investigation . . . . . . . .10
3. Acknowledgments . ... . . . . . . 10
II. METHOD OF INTERPRETING RANGE OF STRESS DATA . 13
4. Description of Range of Stress . . . . . . 13
5. Goodman Diagram . . . . . . . . . . 13
6. Steady Stress-Alternating Stress Diagram . . . 16
7. Maximum Stress-Alternating Stress Diagram . 17
III. INTERPRETATION OF RANGE OF STRESS DATA FOR
DUCTILE METALS .. . . . . . . . . 19
8. Ranges of Torsional Shearing Stress in Unnotched
Cylindrical Specimens of Ductile Metal . .19
9. Ranges of Axial Stress in Unnotched Specimens of
Ductile Metals . . . . . . . . . .21
(a) Ranges of Stress in Which Steady Stress Is
Tension . . . . . . . . . . 21
(b) Ranges of Stress in Which Steady Stress Is
Compression . . . .. . . . . 21
10. Ranges of Torsional Shearing Stress in Notched
Specimens of Ductile Metals. . . . . . 22
11. Ranges of Axial Stress in Notched Specimens of
Ductile Metals . . . . . . . . . . 24
(a) Ranges of Stress in Which Steady Stress Is
Tension . . . . . . . . . . 25
(b) Ranges of Stress in Which Steady Stress Is
Compression . . . . . . . . .27
IV. INTERPRETATION OF RANGE OF STRESS DATA FOR
BRITTLE METALS . . . . . . . . . . . 28
12. Ranges of Torsional Stress in Unnotched and in
Notched Specimens of Brittle Metals . . .28
13. Ranges of Axial Stress in Unnotched and in Notched
Specimens of Brittle Metals . . . . . . 31
(a) Ranges of Stress in Which Steady Stress Is
Tension . . . . . . . . . . 31
(b) Ranges of Stress in which Steady Stress Is
Compression . . . . . . . . 32
CONTENTS (CONCLUDED)
V. RELATION BETWEEN STATE OF STRESS AND EFFECT OF
RANGE OF STRESS UPON ENDURANCE LIMIT IN
METALS . . . . . .
14. Effect of Ratio "max When Steady Stress Is Tension
Tmax
15. Effect of Ratio Omax When Steady Stress Is
Tmax
Compression . . . . . . . . . .
VI. WORKING STRESSES FOR VARYING RANGES OF
REPEATED STRESS
16. Method of Selecting Working Values of Axial (or
Bending) Stress . . . . . . . . . .
VII. CONCLUSIONS
17. Summary
18. Conclusions
. . . 43
. . . 43
. . . 44
APPENDIX
BIBLIOGRAPHY . .
PAGE
32
32
37
. . . 47
LIST OF FIGURES
NO. PAGE
1. Stress Symbols for Varying Range of Stress . . . . . . . . . 13
2. Goodman Diagram Showing Effect of Range of Normal Stress Upon
Endurance Limit ..... . . . . . . . . . . . 14
3. Steady Stress-Alternating Stress Diagram for Ranges of Repeated Tension-
Compression Stress in Which Steady Stress Was Tension . . . . 16
4. Maximum Stress-Alternating Stress Diagram for Fatigue Tests for Notch-
free Cylindrical Torsion Specimens of Twenty-seven Ductile Metals . 18
5. Range of Stress Diagrams for Notch-free Specimens of Thirteen Ductile
Metals Subjected to Ranges of Repeated Axial Stress Superimposed
on a Steady Stress ..... . . . . . . . . . . 20
6. Steady Stress-Alternating Stress Diagram for Torsional Fatigue Tests of
Notched Specimens of Seventeen Ductile Metals . . . . . . . 22
7. Range of Stress Diagrams for Notched Specimens of Ductile Metals Sub-
jected to Ranges of Repeated Axial Stress Superimposed on a Steady
Stress . . . . . . . . . . . . . . . . . .. . 26
8. Steady Stress-Alternating Stress Diagram for Fatigue Tests of Torsion
Specimens of Eight Cast Irons ... . . . . . . . . . 29
9. Range of Stress Diagrams for Cast Irons Subjected to Ranges of Repeated
Axial Stress Superimposed on a Steady Stress . . . . . . . . 30
10. Stresses in Circular Cylinder Subjected to Torsional Load . . . . . 33
11. Torsional Fatigue Specimens of Ductile Metal Showing Effect of Notch on
Mode of Fatigue Fracture ..... . . . . . .... . 34
12. Steady Stress-Alternating Stress Diagram Showing Influence of Ratio ".aX
Tmax
Upon Law Governing Effect of Range of Stress Upon Fatigue Strength
of Ductile and of Brittle Metals . . . . . . . . . ... . 35
13. Working Stresses for Varying Ranges of Normal Stress for Quenched and
Tempered S.A.E. 3140 Steel Having Yield Ratio of 0.94 . . . . . 39
14. Working Stresses for Varying Ranges of Normal Stress for 0.7 Per Cent
Carbon Steel Having Yield Ratio of 0.6 . . . . . . . . . 40
THE EFFECT OF RANGE OF STRESS ON THE
FATIGUE STRENGTH OF METALS
I. INTRODUCTION
1. Preliminary.-Many investigators have shown that the maxi-
mum tensile or compressive stress to which a metal member may
be repeatedly subjected without causing fracture (endurance limit as
usually defined) depends upon the range of stress applied, that is,
upon the values of the maximum and minimum stresses of a repeated
cycle; the maximum tensile stress that can be applied a very large
number of times without causing fracture can be increased if the range
of stress is decreased. Most of the data upon which this conclusion is
based were obtained from tests1, 12* in which the stress varied from
a small tensile stress to a larger tensile stress, or from a small com-
pressive stress to a larger tensile stress. The specimens used in these
tests were usually subjected to axial loads, mainly because varying
ranges of normal stress are easily obtained by this method of loading;
it is assumed, however, that bending tests would reveal substantially
the same results. Furthermore, most of the data were obtained from
tests of polished unnotched specimens of ductile metals; the term
"unnotched (or notch-free) specimen" is used to denote a specimen
free from stress raisers such as abrupt changes in cross-section, sur-
face scratches, defects, etc., and a "notched specimen" is one which
contains a stress raiser of any kind.
If, on the other hand, notch-free polished cylindrical specimens of
a ductile metal are subjected to repeated cycles of torsional shearing
stress, it has been shown7' in a number of investigations that the
maximum range of shearing stress that can be repeated a large num-
ber of times without causing fracture is the same regardless of the
value of the maximum stress in the range; that is, the range of stress
remains constant. This fact may be expressed in a somewhat different
way as follows: The maximum torsional shearing stress that can be
repeatedly applied to a notch-free cylindrical specimen of ductile
metal without causing fracture may be increased'if the minimum
stress of the cycle or range of stress is also increased by the same
amount, thereby keeping the range of stress constant. In this con-
clusion, however, it is assumed that the maximum shearing stress does
not reach a value that causes the material to fail by general yielding,
*Index numbers refer to items in Bibliography.
ILLINOIS ENGINEERING EXPERIMENT STATION
that is by permanent plastic deformation of a relatively large portion
of the specimen on the first application of the load.
The generally accepted laws governing the effect of range of stress
on the resistance to fracture of metals subjected to repeated stress
(fatigue strength), therefore, have been based mostly on fatigue tests
of polished, notch-free specimens of ductile metals. There are, how-
ever, many ductile metal members that contain notches of various
types, such as keyways, fillets, holes, corrosion pits, surface scratches,
etc., that are subjected to various ranges of repeated stress. Likewise
brittle metal members, such as high strength cast iron, special alloys,
etc., both with and without notches, are subjected to various ranges
of repeated stress. Thus, there is need for further study of this prob-
lem. The term ductile is used here to describe metals which are
capable of rather large plastic deformation without fracture when
subjected to the usual tension test, and the term brittle is used to
describe metals which fracture with little or no plastic deformation in
the tension test.
The significance of the results presented in this bulletin will
probably be more evident if attention is here called to the fact that
two modes or types of fatigue fracture are recognized. In one type,
the formation and spread of the fatigue crack is considered to be
related most closely to the maximum normal (tensile) stress, and in
the other type to the maximum shearing stress. Furthermore, the
factors that primarily determine which one of these two types of
fracture will occur are considered to be (1) the relation of the re-
sistance of the material to separation without accompanying plastic
deformation (cohesion strength) to its resistance to plastic deforma-
tion (yield strength) and (2) the relation of the maximum tensile
stress, amax, at a point where fracture occurs to the maximum
shearing stress, rmax. The relative values and qualitative use of
e to r s cohesion strength a max
these two ratios, and , assume considerable
yield strength rmax
importance in the explanation of the fatigue results presented in
this bulletin even though their numerical values are seldom definitely
known.
Attention should also be called to one other idea that is given
prominence in the subsequent discussion. The endurance limit of a
material has usually been considered to be the value of the maximum
stress in any cycle or range of stress that can be repeated an in-
definitely large number of times without causing the material to
EFFECT OF RANGE OF STRESS ON FATIGUE STRENGTH
fracture. This definition has resulted from the desire to follow, in
dealing with repeated loads, the same procedure that is used with
static loads. For example, a ductile metal under static loads usually
serves its purpose satisfactorily in a load-resisting member until the
maximum stress reaches a value at which general yielding occurs;
thus a maximum value of stress serves satisfactorily as a measure of
the limiting (utilizable) strength for resisting static loads. If, how-
ever, the same ductile metal member is subjected to repeated stress,
its usefulness (utilizable strength) is not limited by yielding, but by
the formation and spread of a crack designated as a progressive local-
ized fracture (or fatigue fracture), and this type of fracture is asso-
ciated, not with the maximum stress alone, but also with the minimum
stress in the stress cycle, or, more briefly, with the repeated range of
stress, evidence of which will be presented in this bulletin. If the
stress in the cycle is completely reversed (changing from a value in
one direction from zero to an equal value in the opposite direction
from zero) the maximum value of the stress in the cycle serves also
to measure the range of stress, and hence the foregoing definition of
endurance limit is satisfactory; but for other ranges of stress it is in-
adequate and misleading, and has led to confusion concerning the
effect of range of stress on fatigue strength.
A more satisfactory definition of endurance limit or fatigue
strength has grown out of the relatively recent method of treating a
range of stress as made up of two components, namely, a steady
(mean) stress and an alternating (completely reversed) stress that is
superimposed on the steady stress. The influence of the steady stress
on failure is important when the steady stress plus the alternating
stress (the maximum stress) exceeds the static yield strength, resulting
in a failure of the member by yielding on the first application of the
load before it can fail by progressive fracture; the steady stress alone
would not produce a progressive fracture. The failure by progressive
fracture is controlled mainly by the alternating stress; the value of
the alternating stress required to cause fracture may, however, depend
on the value of the mean or steady stress.
The endurance limit of a material for any range of stress, then,
is defined as the maximum alternating (completely reversed) stress
that can be superimposed on the mean or steady stress of the range
and be repeated an indefinitely large number of times without causing
fracture. The subsequent discussion will show that there are several
advantages to be gained by defining the fatigue strength in this way.
ILLINOIS ENGINEERING EXPERIMENT STATION
2. Purpose of Investigation.-It is the purpose of this bulletin to
make a rather comprehensive study of test data to determine the
manner in which range of stress affects the fatigue strength of metals.
Available test data have been studied, involving ranges of repeated
axial stress from tension to tension, tension to compression, compres-
sion to compression, and of repeated torsional shearing stress, in both
ductile and brittle metals for specimens with and without notches. It
should be stated that the various methods of interpreting the test
data given emphasis in this study have been presented by several
investigators in analyzing the results of fatigue tests as applied to
limited portions of the problem of the effect of range of stress on the
fatigue strength of metals. It has been the main purpose, however, of
the investigation herein reported to extend the interpretations in de-
veloping the general law or laws that control the effect of range of
stress on the fatigue strength of metals for conditions covering a wide
field of applications.
It should also be observed that the test results studied were ob-
tained from relatively small laboratory specimens and hence may not
be directly applicable to much larger members that are likely to be
less homogeneous and less uniform and correspondingly weaker in
fatigue even though they are geometrically similar to the smaller
specimens. Further, the fatigue strength as interpreted in this bulletin
refers to the resistance of the material to an indefinitely large number
of cycles of stress, and no attempt has been made to interpret data for
the fatigue strength for a limited number of cycles of stress above the
endurance limit; and hence it is realized that the results of this in-
vestigation will not apply directly to some types of fatigue problems.
Nevertheless, it is felt that the information concerning the laws
governing the effect of range of stress on the fatigue strength as in-
terpreted here and as indicated by tests of relatively small specimens
is of great importance.
3. Acknowledgments.-This investigation was carried on as a part
of the work of the Engineering Experiment Station of the University
of Illinois, of which DEAN M. L. ENGER is the director, and of the De-
partment of Theoretical and Applied Mechanics, of which PROFESSOR
F. B. SEELY is the head.
The author is indebted to PROFESSOR SEELY for his many helpful
suggestions and for his continued interest during the progress of this
investigation.
EFFECT OF RANGE OF STRESS ON FATIGUE STRENGTH 11
Appreciation is expressed for the generous cooperation of PROFES-
SORS H. F. MOORE and N. J. ALLEMAN in making available the equip-
ment of the Fatigue of Metals Laboratory used in this investigation.
The author also wishes to express his indebtedness to Messrs. E.
W. BURSTADT, C. M. MIDDLESWORTH, R. P. MOLT, and 0. C. WORLEY
who made valuable contributions to this investigation through student
thesis work.
ILLINOIS ENGINEERING EXPERIMENT STATION
SYMBOLS AND DEFINITIONS
(See Fig. 1)
max- (or Tmax) = Maximum (numerical) stress of a range of stress.
Cmin (or rmin) = Minimum (numerical) stress of a range of stress.
umax + fmin
am = Steady stress component of a range of stress. au =
2
max - O'min
an = Alternating stress component of a range of stress. o- = ma2
A- (orAr) = The magnitude of a range of stress; it is the algebraic difference
between amax and amin (or between rmax and -min); or, also, it is
equal to 2ao (or 27T).
Endurance Limit = The maximum value of the alternating stress a, (or r.) which
can be superimposed on a given steady stress am (or r-) and
repeated an indefinitely large number of times without causing a
progressive fracture (fatigue failure). The endurance limit of the
material for a given steady stress is also frequently referred to
as the fatigue strength for the given steady stress.
a, (or Tr) = The endurance limit (as defined above) for a steady stress, a,,
equal to zero, that is, the endurance limit for completely reversed
cycles of stress, as obtained from tests of polished notch-free
specimens.
aor (or Tri) = The endurance limit (as defined above) for a steady stress, am,
equal to zero, that is, the endurance limit for completely re-
versed cycles of stress, as obtained from notched specimens, the
stress being determined by the use of the ordinary formulas of
mechanics.
a, = Static tensile yield strength.
r, = Static. torsional shearing yield strength obtained from tests of
solid cylindrical specimens.
au = Static tensile ultimate strength.
u, = Static torsional modulus of rupture; the torsional modulus of
rupture is the value of r as calculated from the substitution of
Tc
the static ultimate (maximum) torque T in the formula r =-
J'
where c is the radius of the cross-section and J is the polar
moment of inertia of the section.
a,' = Static compressive ultimate strength. For ductile materials the
compressive ultimate strength is considered to be the compres-
sive yield strength.
K = Stress concentration factor.
EFFECT OF RANGE OF STRESS ON FATIGUE STRENGTH
II. METHOD OF INTERPRETING RANGE OF STRESS DATA
4. Description of Range of Stress.-Two methods of specifying a
range of stress have been chosen. These two methods are described
in the following paragraphs. In this description and throughout the
bulletin the Greek symbol a (sigma) will always refer to a normal
(tensile or compressive) stress, and the Greek symbol r (tau) will
always refer to a shearing stress.
First: A range of stress may be partially designated by the mag-
nitude of the change of stress in passing from the minimum stress to
the maximum stress of a cycle, but either the maximum or minimum
stress must be given in addition to the magnitude of the range. Thus
in Fig. 1 a range may be specified by stating the maximum stress Omax
(or Tmax) or the minimum stress cmin (or Tmin) and stating the magni-
tude of the range of stress Aa (or AT). The range could be described
also by simply giving both the maximum and the minimum stresses.
Second: A range of stress may be thought of as being made up of
a steady (mean) stress am (or Ts,) and an alternating (completely re-
versed) stress ao (or Ta) superimposed upon it; the range of stress may
then be expressed as am u± a (or Tm - T,). For example, in Fig. 1, a
range of stress is specified by choosing am, (or T,,) and ao (or Ta).
5. Goodman Diagram.-A diagram such as Fig. 2 for representing
the effect of range of stress on the endurance limit was devised by
Goodman, 2 based chiefly on results of repeated stress tests in bending
FIG. 1. STRESS SYMBOLS FOR VARYING RANGE OF STRESS
ILLINOIS ENGINEERING EXPERIMENT STATION
FIG. 2. GOODMAN DIAGRAM SHOWING EFFECT OF RANGE OF NORMAL
STRESS UPON ENDURANCE LIMIT
and in direct tension of ductile metals by W6hler. In these tests a
value of the minimum stress amin was selected, and then a series of
specimens were tested under repeated stresses which varied from this
value of stress, amin, to a higher stress, max.. For the larger values of
amax the specimens fractured after a number of repetitions of the
stress, but by lowering the value of max. in each successive specimen
tested, a maximum stress was found which could be repeated an in-
definitely large number of times without causing a progressive frac-
ture. In Fig. 2 the minimum stress is plotted as an ordinate to the line
of zero stress with an equal abscissa so that one extremity lies on a
line DB making an angle of 45 deg. with the line of zero stress. Good-
man found that, if omax is plotted as an ordinate at the same abscissa
as the minimum stress, the upper ends of the ordinates (values of .max)
lie approximately on the line AB where FA is 1/3 a. and OC = CE =
% o,, and where ar represents the static ultimate tensile strength of
the material. From similar triangles in Fig. 2 it can be shown that
1
-a = (0ur - 0m).
3
1
EFFECT OF RANGE OF STRESS ON FATIGUE STRENGTH
In Equation (1) a is the maximum value of the alternating stress
which may be superimposed on the given steady stress, am, and re-
peated an indefinitely large number of times without causing ipo-
gressive fracture, that is, aa is the endurance limit of the metal for
the given steady stress a,. This equation has been used extensively
to represent range of stress data. Equation (1) may also be written
in the form
a - f ( - - (2)
However, it has been found by various investigators that a better
agreement with experimental results for repeated bending and of re-
peated direct tension tests of steels may be obtained if Equation (2)
is modified by replacing the factor %1/ a by the endurance limit, a,
for completely reversed cycles of stress, that is, the endurance limit
for the range of stress in which a,, = 0. Equation (2) thus becomes
S= Ur ( - - . (3)
Equation (3) gives the magnitude of the endurance limit, 7a, of the
metal when the steady stress is am. The endurance limit, aa, is sig-
nificant when failure is due to fatigue, but when am is large the value
of a, plus amn, that is, the maximum stress in the range, may be large
enough to exceed the yield point of the material and hence to cause
failure in the specimen by general yielding on the first application of
the stress. It is therefore convenient to have an equation from which
amax may be calculated.
From Fig. 2 it is noted that max, = .m + a, and hence, from
Equation (3)
omax = aSm + ST i - -1 - . (4)
aOu
Equation (4) is represented by a straight line on the Goodman dia-
gram similar to line AB in Fig. 2 in which, however, a, is not neces-
sarily equal to % ao, but is the actual endurance limit for completely
reversed cycles obtained from fatigue tests. A diagram similar to
Fig. 2 in which FA = FD = a, is known as a "modified Goodman
diagram" and the line AB in such a diagram will be referred to as
the "modified Goodman line."
ILLINOIS ENGINEERING EXPERIMENT STATION
Tensile Sfeaody Stress, o,, of Ra7nge
in Termns of l/fimafe Tens/ie Strength1,
FIG. 3. STEADY STRESS-ALTERNATING STRESS DIAGRAM FOR RANGES OF REPEATED
TENSION-COMPRESSION STRESS IN WHICH STEADY STRESS WAS TENSION
6. Steady Stress-Alternating Stress Diagram.-Range of stress
data may be represented in a different way3 by a diagram in which
the steady stress is expressed as a fraction of the tensile or compres-
sive ultimate strength and is plotted as an abscissa, whereas the super-
imposed alternating stress (endurance limit) is expressed as a fraction
of the endurance limit for completely reversed cycles of stress and is
plotted as an ordinate. Such a diagram is called a steady stress-
alternating stress diagram and is illustrated in Fig. 3 for the case in
which the steady stress is tension. The point A whose ordinate is ar,
and whose abscissa is zero represents the range of completely reversed
stress for which the steady stress am is zero and the superimposed
alternating stress aa is equal to r,. The point B whose ordinate is zero
and whose abscissa is the static tensile ultimate strength represents
the range of stress of zero magnitude, that is, there is no superim-
posed alternating stress, since aa is zero. If a straight line is drawn
from A to B, the ordinates of the points of this line represent approxi-
mately the maximum values of the completely reversed stress that can
be superimposed on the steady stress, represented by the correspond-
ing abscissa, and repeated a large number of times without causing
fracture. For example, the ordinate r, of the point D on line AB
represents the endurance limit corresponding to the steady stress a,,
represented by the abscissa of the point D.
EFFECT OF RANGE OF STRESS ON FATIGUE STRENGTH
The equation of the line AB of Fig. 3 may be written in the inter-
cept form as
am Ora
- + - = 1. (5)
* u Tr
If Equation (5) is rewritten in the form
aa = ar (I - ") (6)
an expression for determining the endurance limit, a,, is obtained.
The maximum stress in the range can be obtained if the steady stress,
am, is added to both sides of Equation (6). Thus
max = am + a = am± r 1 ). (7)
It will be noted that Equations (3) and (6) are identical, and that
Equations (4) and (7) are identical, and thus the line AB in the
"modified Goodman diagram" (Fig. 2 with 13 a. replaced by a,) and
the line AB in Fig. 3 are identical in their representation of range
of stress data.
The steady stress-alternating stress diagram as illustrated by
Fig. 3 has an advantage over the "modified Goodman diagram" in
that data may be plotted for varying ranges of stress for different
metals on the same diagram for purposes of comparison. For this
reason the steady stress-alternating stress type of representation for
range of stress data is used frequently in this bulletin.
7. Maximum Stress-Alternating Stress Diagram.-In representing
range of stress data it is sometimes convenient to use a diagram in
which the maximum stress of the range is expressed as a fraction of
either the yield strength or the ultimate strength and is plotted as an
abscissa, and in which the alternating stress is expressed in terms of
the endurance limit or or rr and is plotted as an ordinate. This
diagram is referred to as the maximum stress-alternating stress dia-
gram, and is particularly convenient for representing varying ranges
of torsional shearing stress for polished notch-free cylindrical speci-
mens, as will be seen in the next article.
ILLINOIS ENGINEERING EXPERIMENT STATION
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