Astm stp 338 1963

i, Number of applications of tensile load m, Empirical parameter obtained from slope of log Ae t versus log N diagram «, Number of applications of tensile load prior to fracture N,

SYMPOSIUM ON FATIGUE TESTS

OF AIRCRAFT STRUCTURES: LOW-CYCLE, FULL-SCALE,

AND HELICOPTERS

Presented at the FOURTH PACIFIC AREA NATIONAL MEETING AMERICAN SOCIETY FOR TESTING AND MATERIALS

Los Angeles, Calif., Oct 1-3, 1962

Reg U S Pat Off

ASTM Special Technical Publication No jj8

Price $10.50; to Member.s $7,35

Published by the AMERICAN SOCIETY FOR TESTING AND MATERIALS

1916 Race St., Philadelphia 3, Pa

BY AMERICAN SOCIETY FOR TESTING AND MATERIALS 1963 Library of Congress Catalog Card Number: 63-15793

Printed in Baltimore, Md

September, 1963

F O R E W O R D The papers in this Symposium on Fatigue of Aircraft Structures were presented during four sessions held on October 1-3, 1962, at the Fourth Pacific Area National Meeting of the Society, Los Angeles, Calif The symposium, sponsored by Committee E-9 on Fatigue, was organized into three broad categories

The first section on Low-Cycle Fatigue was organized by Ivan Rattinger

of Aerospace Corp The second group of papers dealing with Helicopter Fatigue Problems was organized by M J McGuigan, Jr., of Bell Helicopter Corp The final section of this symposium, on Problems in Design and Evaluations of Full-Scale Structures, was presented under the leadership

of M S Rosenfeld of the Navy Air Material Center The over-all chairman

of the symposium program was H F Hardrath, National Aeronautics and Space Administration

A transcript of the panel discussion on low-cycle fatigue held during this symposium was supplied by Ivan Rattinger

Presiding oflScers of the sessions were R E Peterson, Westinghouse Electric Corp.; F B Stulen, Curtiss-Wright Corp.; H J (rover, Battelle Memorial Inst.; and T J Dolan, L^niversity of Illinois Acting as session chairmen were Messrs McGuigan, Hardrath, Rattinger, and Rosenfeld

NOTE.—The Society is not responsible, as a body, for the statements

and opinions advanced in this publication

C O N T E N T S

Introduction—H F Hardrath 1

Low-Cycle Fatigue

Low-Cycle Axial Fatigue Behavior of Mild Steel—J T P Yao and W H Munse 5

The Effect of Mean Stress on Fatigue Strength of Plain and Notched Stainless Steel

Sheet in the Range from 10 to 10' Cjxles—W J Bell and P P Benham 25

Low-Cycle Fatigue of Characteristics of Ultrahigh-Strength Steels—C, M Carman,

D F Armiento, and H Markus 47

Low-Cycle Fatigue of Ti-6A1-4V at - 4 2 3 F—R R Hilsen, C S Yen, and B V

Whiteson 62 Low-Cycle Fatigue Properties of Complex V\'elded Joints of High Strength 301,

304L, 310, and AM-355 Stainless Steel Sheet Materials at Cyrogenic

Tem-peratures—J L Christian, A Hurlich, and J F Watson 76

Effect of Stress State on High-Temperature Low-Cycle Fatigue—C R Kennedy 92

Panel Discussion of Low-Cycle Fatigue 107

Helicopter Fatigue

Empirical x^nalysis of Fatigue Strength of Pin-Loaded Lug Joints—A A

Mitten-bergs 131 Statistical Evaluation of a Limited Number of Fatigue Test Specimens Including a

Factor of Safety Approach—Carl Albrecht 150

Helicopter Fatigue Substantiation Procedures for Civil Aircraft—J E Dougherty

and H C Spicer, Jr 167

Design and Evaluations of Full-Scale Structures

An Aluminum Sandwich Panel Test Under Mach-2.4 Cruise Conditions—W D

Buntin and T S Love 179

Estimation of the Fatigue Performance of -Aircraft Structures—J Schijve 192

Discussion 214 Aircraft Structural Fatigue Research in the Navy—M S Rosenfeld 216

Discussion 238 Small Specimen Data for Predicting Life of Full-Scale Structures—C R Smith 241

Programmed Maneuver-Spectrum Fatigue Tests of Aircraft Beams Specimens—

Leonard Mordfin and Nixon Halsey 251

Discussion 274

STP338-EB/Sep 1963

SYMPOSIUM ON FATIGUE TESTS OF AIRCRAFT STRUCTURES:

LOW-CYCLE, FULL-SCALE, AND HELICOPTERS

INTRODUCTION

BY H F HARDRATH 1 Following a precedent set at previous

West Coast National Meetings of the

Society, ASTM Committee E-9 on

Fatigue again sponsored a Symposium

on Fatigue of Aircraft Structures at the

West Coast Meeting held in Los Angeles,

Calif., Oct 1-5, 1962

As indicated by the presiding officer of

one of the sessions, fatigue research may

concern itself with any of several levels

of complication: (1) the basic mechanism

may be studied from the physical and

metallurgical points of view; (2) simple

specimens may be tested to study the

mechanical behavior of the material

under carefully controlled loading

con-ditions; (3) notches or other

disconti-nuities may be used to introduce

partially the effect of shape of practical

parts; (4) subassemblies may be studied

to introduce the effects of somewhat

more complicated joints; (5) complete

structures may be subjected to

neces-sarily simplified representations of

ex-pected loading conditions; and (6) service

failures may be analyzed The

sym-posium includes papers treating each of

these phases of fatigue study and

1 Fatigue Branch, NASA-Langley Research

Center, Hampton, Va

introduces effects of high and low temperature

As with other symposia on fatigue, this one does not conclude that the problem

is now solved It does, on the other hand, attempt to assemble representative current thinking on the problem with particular emphasis on aeronautical and missile applications Several papers present procedures for correlating obser-vations that should be particularly helpful to designers One paper in-corporating studies of the combined influence of loads and temperatures is almost certain to be the forerunner of a variety of such studies that will be carried out in connection with future vehicles

The papers are organized into three broad categories: (1) low-cycle fatigue problems; (2) helicopter fatigue prob-lems; and (3) problems encountered in design and evaluation of full-scale structures

Grateful acknowledgment is made of the contributions of the authors, the session chairmen, presiding officers, those who reviewed papers prior to the meeting, the West Coast Coordinator, and the participants in the discussions

Low-Cycle Fatigue

STP338-EB/Sep 1963

LOW-CYCLE AXIAL F A T I G U E BEHAVIOR OF M I L D S T E E L

B Y J T P Y A O 1 AND W H M U N S E 2

SYNOPSIS

A general hypothesis that describes the cumulative effect of plastic

defor-mations on the low-cycle fatigue behavior of metals is presented and verified with results of a variety of tests on steel specimens Limited correlations with existing test data from other low-cycle fatigue tests on aluminum-alloy speci-

mens indicate that it may be possible also to extend this hypothesis to metals other than steel

NOTATIONS

A c, Cross-sectional area at the test section

of the specimen after precompression,

sq in

A f , Cross-sectional area at the test section

of the specimen at fracture, sq in

A 0, Original cross-sectional area at the

test section of the specimen, sq in

A r, Cross-sectional area at the test section

of the specimen, re-machined after

precompression, sq in

C, A constant

D c, Diameter at the test section of the

specimen after precompression, in

df , Diameter at the test section of the

specimen at fracture, in

d 0 , Original diameter at the test section of

the specimen, in

d r , Diameter at the test section of the

specimen, re-machined after

precom-pression, in

i, Number of applications of tensile load

m, Empirical parameter obtained from

slope of log Ae t versus log N diagram

«, Number of applications of tensile load

prior to fracture

N, Number of cycles to failure

q, Plastic true strain, per cent

q m , Plastic true mean strain, per cent

qa , Plastic tensile true strain at fracture,

per cent

R, Absolute-strain ratio, cyclic minimum

plastic true strain to cyclic maximum

plastic true strain, q m -,n/qm&x

r, Relative-strain ratio; cyclic

com-pressive change in plastic true strain

to cyclic tensile change in plastic true

strain, Aq c /Aq t

S, Engineering stress, psi

Aq e, Cyclic compressive change in plastic true strain, per cent

Aq t , Cyclic tensile change in plastic true strain, per cent

Aqa , Cyclic tensile change in plastic true

strain at w = 1, per cent

Ae c , Cyclic compressive change in plastic

engineering strain, per cent Aej, Cyclic tensile change in plastic engi- neering strain, per cent

At a , Cyclic tensile change in plastic neering strain at n = 1, per cent

engi-During the past two decades, an

in-creasing amount of information on the

low-cycle fatigue behavior of metals has

been published (1,2).^ Nevertheless, these

studies have provided data of only

lim-ited scope

Since in low-cycle fatigue tests the

applied loads are generally high enough

to cause plastic deformation and a

cor-responding hysteresis in the stress-strain

relationship, limits of either load or

de-formation are usually maintained

con-stant in any particular test Low-cycle

fatigue tests are therefore further

iden-tified as either constant-load or

con-stant-deformation tests

In general the results of constant-load

low-cycle fatigue tests are presented in

the form of conventional S-N curves,

where S and N are respectively the

nom-inal stress or stress range and the

cor-responding life of the specimens

Al-though the shape of a typical S-N curve

can be qualitatively described, it is

diffi-cult to make a precise analysis for this

type of test On the other hand, results

of constant-deformation low-cycle

fa-tigue tests have consistently shown a

linear relationship between the tensile

change in plastic deformation and the

number of cycles to failure on a log-log

basis

Empirical relationships have been

de-veloped to describe the effect of fully

reversed cychc strain on the low-cycle

fatigue life of metals However, these

hypotheses do not portray adequately

the data from all types of low-cycle

fa-tigue tests

The objectives of this investigation

were to study in a general manner the

cumulative effect of the changes in

plas-tic deformation on the low-cycle fatigue

behavior of axially loaded steel

speci-mens and to develop a more general

low-cycle fatigue hypothesis

On the basis of a literature review, a general hypothesis was developed to de- scribe the cumulative effect of various types of plastic strain cycles on the low- cycle fatigue behavior of metals Special tests on three mild steels, ABS-C* as- rolled, ABS-C normahzed, and a rimmed steel, were then carried out to verify the hypothesis In addition, hmited correla- tions were made with published test data from other types of low-cycle fatigue tests on 2024 aluminum alloy to indicate the possibilities of extending the applica- tion of this hypothesis to metals other than mild steel

L O W - C Y C L E FATIGUE H Y P O T H E S I S

In 1912, Kommers (3) concluded from

a series of cyclic bending tests that the magnitude of the cyclic deflection was

an important factor in low-cycle fatigue studies Orowan (4) suggested t h a t the following expression be used for cyclic strain tests:

iV(Ae,) = C (1)

This relationship has served as a basis for most of the hypotheses that have since been developed

On the basis of the results from versed-strain tests, Manson (5), as well

re-as Gross and Stout (6), empirically ified Eq 1 to the following form:

mod-iV"(A€,) = C .(2)

Then Coffin and his associates (7-Q) found that straight lines with a slope of approximately —0.50 (t» = ^) best fit their extensive data Moreover, to cor- relate the results of cyclic strain tests and those of simple tension tests Coffin presented the following equation:

YAO AND MUNSE ON LOW-CYCLE AXIAL FATIGUE OF MILD STEEL

straight-line relationships between the

cydic change in tensile plastic strain and

the specimen life on a log-log scale (5-20),

but the slopes of the hnes have been

found to vary somewhat with the mean

strain

Let us now examine more closely the

empirical relationship shown in Eq 2

If we raise both sides of the equation to

the (l/w)th power, we obtain

If we let n be the number of applications

of tensile load prior to fracture, it is

ap-parent that the lowest possible value for

« is 1 while the counterpart for V

gen-erally has been taken as i or | in the

literature The difference between n and

A^ is small at larger values of N Since

at « = 1

Aci = Aen

Equation 4 then becomes

nl ) = 1.0 .(5)

Drucker et al (21) reported that the

values of Aca vary with the amount of

precompressive strain Moreover, it is

found that the values of m generally

differ between the test results of Evans

(22) (w ^ 1) and those of Cof&n (7,9)

(w = ^) Since Evans conducted his tests

with repeated tensile loadings and Cof&n

conducted most of his tests with fully

reversed strain conditions, it is

reason-able to assume that the quantity w is a

variable dependent upon the change in

plastic compressive strain, Acc •

The assumption, therefore, that

low-cycle fatigue fractures occur only in

ten-sion is generally valid for steels and is

one of the conclusions reached in an

ex-tensive recent low-cycle fatigue

investi-gation by Dubuc (13) It is assumed also

that fracture of a material is produced

by an accumulation of the plastic formations experienced by the material

de-On the basis of the experimental dence and the assumptions discussed above, it is postulated that plastic de-formations accumulate according to an exponential function and more specifi-cally that the hypothesis may be pre-sented in generalized form as follows:

evi-i - l |_V^e,evi-i/ Jevi-i 1.0 -(6)

Since it has been shown (11) that for low-cycle conditions true strain values are approximately proportional to the corresponding engineering strains, a sim-ilar expression may be written as follows

in terms of true strains

E Y A 9 ^ Y ' ' » 1 \^qj J 1.0 (6(a))

If we now introduce the relative-strain

ratio, r, the ratio of the cyclic

compres-sive change in plastic strain, Ae^ or A^^,

to the subsequent tensile change in

plas-tic strain, A«, or Aqi, then

available information regarding the

var-iation of both Aqa and l/m with respect

to r A number of specimens were tested ber of specimens were tested in cyclic

in one-cycle tests with various relative- strain tests with constant r ratios of

strain ratios to find the relationships —0.25, —0.50, —0.75, and —1 to find

between A^d and r In addition, a num- the relationship between \/m and r

TABLE I.—CHEMICAL COMPOSITION OF MATERIALS

Mang-0 6 9

0 3 4

Ch

phorus

Alu-0 Alu-0 3 4

0 0 0 3

" CN, ABS-C normalized steel; CA, ABS-C as-rolled steel; and E, rimmed steel

TABLE II.—AVERAGE RESULTS OF TENSION TESTS (TYPE C-1 SPECIMENS)

137 000

143 000

120 000

True Strain, per cent

Materials and Specimens:

ABS-C as-rolled, ABS-C normalized, and a rimmed steel (respectively desig-nated as CA, CN, and E Steels) were used in this test program The chemical compositions of these materials are listed

in Table I All specimens were fabricated from f-in, thick plates with the specimen axis parallel to the rolling direction of the plates

Standard tension coupon specimens, designated as type C-l specimens, were tested to obtain the mechanical proper-ties shown in Table II Specimens with

a minimum diameter of J in and radii

of curvature of 1 in at the test section were used and designated as the C-2 type specimens The reduced test section of these specimens was designed to confine the critical section within a small region

at mid-length of the specimen to make

it possible to locate and measure the

YAO AND MUNSE ON LOW-CYCLE AXIAL FATIGUE or MILD STEEL

instantaneous diameter at the critical

section (Fig 1)

Description of Tests:

In Fig 1 two types of C-2 specimens

are shown The conventional threaded

specimens were used first, but when

specimens with large precompressive

true strain of zero After the compression loading, the test section in the precom-pressed state was enlarged and had a

new diameter, dc, and a corresponding plastic true strain of qd At this stage,

some of the specimens were re-machined

to approximately the original size and shape These specimens with a new

FIG 2.—Strain-Calculation Procedure for One-Cycle Test

strains failed in the threaded section, the

specimen with flat ends was adopted to

provide more bearing areas at the ends

In testing these latter specimens, the

tensile forces were transmitted through

pin connections and compressive forces

were applied on the flat ends

The strain calculation procedure for

"one-cycle" tests is illustrated in Fig 2

In the virgin state, the test section had

an original diameter of da and a plastic

diameter, dr, are assumed to possess a

plastic prestrain of ^^i • The specimens, either in as-compressed or in re-machined condition, were then loaded in tension to fracture The specimen diameter at the

fractured section, d/, was used for the

computation of the plastic true strain at

fracture, ga , and the tensile change in

plastic true strain, Agn , with the lationships shown in Fig 2

re-All one-cycle tests were conducted on

C-2 type specimens To prevent buckling

of the test section at extremely high

compressive loads, a special guide

assembly was used (Fig 3) The whole

assembly was placed in the testing

machine, and then a dial-type diameter

gage was manipulated through the

key-hole of the "sleeve" to measure the

minimum diameter of the specimen

The subsequent tension tests were conducted in the same testing machine and using the same fixtures After the specimen failed, the diameter at the fractured section was again measured with the optical diameter-measuring device

Cyclic strain tests were conducted at constant relative-strain ratios of —J,

FIG 3.—Compression Fixture

When the specimen was removed from

the fixture, the diameter of the specimen

was again measured in two perpendicular

directions with an optical

diameter-measuring device and the average value

used as the basis for strain computations

In general, the specimens remained

relatively straight after precompression

A typical precompressed specimen (q^ =

— 51 per cent) is shown with a virgin

specimen in Fig 4

FIG 4.—Typical Precompressed Specimen

{left) and Virgin Specimen

1

2> I, and -1 Schematic g-w (strain versus cycles) diagrams illustrating the

cyclic strain for each of these r ratios

are shown in Fig 5

A 50,000-lb lever-type fatigue testing machine, geared down to a speed of about 0.4 rpm, was used for the cyclic strain tests of specimens with lives greater than 30 cycles A set of special reversed-load pull-heads was used to transmit the loads to the test specimens

YAO AND MUNSE ON LOW-CYCLE AXIAL FATIGUE OF MILD STEEL 11

by transmitting the tensile forces through DESCRIPTION AND ANALYSIS OF TEST

forces to the end of the specimen through ^^ ^

special wedging compression blocks A "One-Cycle" Tests:

special gage with SR-4 strain gages was The data for one-cycle tests with mounted at the minimum section of the various degrees of precompression are

n = 3 ( Three-cycle Test)

n = I (One-cyde Test)

n = I (One-cycli Test)

specimen to measure the change in its

diameter The electrical output of the

gage and that of the load dynamometer

of the fatigue machine were recorded on

an X-Y recorder This record was used

for control purposes in the conduct of

the tests Typical stress-diameter

dia-grams selected from the record of test

C-2-CN522 are shown in Fig 6

plotted in Fig 7 for each of the steels tested From these figures, the tensile change in plastic true strain at w = 1 may be obtained for any relative-strain ratio For example, in Fig 7(c) the values of A^^ are 66 per cent and 75 per cent for relative-strain ratios of — 1 and

_ i , respectively

(a) ABS-C as-roIIed (CA) steel

FIG 7.—Tensile Change in Plastic True Strain and Plastic True Strain at Fracture versus Plastic

YAO AND MUNSE ON LOW-CYCLE AXIAL FATIGUE OF MILD STEEL 13

(c) Rimmed (E) steel

FIG 7.—Continued

Cyclic Strain Test: Aqt versus log n plots but with various

The hypothesis presented here for slopes To verify this observation 35

constant relative-strain ratios suggests specimens were tested in cyclic strain

that linear relationships exist for log tests at constant values of r The results

•| ip "iOC T w o Number of Applications of Tensile Load Prior to Fracture, n

(a) ABS-C as-rolled (CA) steel

(b) ABS-C normalized (CN) steel

FIG 8.—Cyclic Strain Test Results

1000

Y A O AND M U N S E ON L O W - C Y C L E AXIAL FATIGUE OF M I L D S T E E L 15

(c) Rimmed (E) steeL

I 15 Number of Applications of Tensile Load

FIG 10.—Various Fractures Resulting from Cyclic Strain Tests

YAO AND MUNSE ON LOW-CYCLE AXIAL FATIGUE OF MILD STEEL 17

of these tests are plotted in Fig 8 for

the three steels tested These data may

be further combined by dividing all

Aqi values by the corresponding values

of Aqa Figure 9 is a diagram of this

normalized cyclic tensile change in

plastic true strain plotted against « on a

log-log scale for all three steels tested

All of these figures indicate that straight

lines with slopes varying with r ratios

row, three CA-steel specimens are shown after being tested at relative-strain ratios of -0.25, -0.50, and - 0 7 5 These gave lives of 10, 14, and 17 cycles respectively All six of these specimens exhibited cup-and-cone type of fractures

In the bottom row of Fig 10 are shown specimens of the three steels tested with

r = — 1 These specimens gave lives of more than 260 cycles and failed with

T L = l 0 8 6 r

-/ /

^'

/ /

x ' 7^

T

-0.2 - a 4 -0.6 ^ Relative-Strain Ratio, r

FIG 11.—Variations of l/m with Respect to the Relative-Strain Ratio, r

fit the test points quite well and that

there does not seem to be any effect of

material on the slopes of these

relation-ships

A group of the fractured specimens

is shown in Fig 10 In the top row,

three one-cycle test specimens are

pre-sented, one for each material Vertical

cracks often appeared on the surfaces of

the E-steel specimens when large

com-pression loads were employed, but only

on the E-steel specimens In the second

propagating fatigue type cracks There was evidence of numerous surface cracks

on the specimens, thereby demonstrating that these specimens were close to failure

at a number of locations

Analysis of Test Results:

Evans (22) obtained a constant true strain at fracture in his repeated tension tests, regardless of the number of cycles applied prior to fracture In the program reported here, it was observed that for a

group of C-2 type CN-steel specimens

subjected to various amounts of repeated

tension, regardless of the number of

cycles of tensile load before fracture, the

final value of plastic true strain at

frac-ture was more or less a constant for

low-cycle tests Therefore, it would seem

reasonable to assume that for tests with

repeated tension only (r = 0), the cyclic

C-2 type CN-steel specimens were tested

in reversed-load low-cycle fatigue tests The plastic true strain history for each

of the specimens is shown in Fig, 12 By evaluating each strain-cycle of the tests and summing, the quantity

Note- Solid Points Show Tests With Initial Load Applied in Tension

11 i I i j ' 11 ' I J - ' ' ' ' ' J - ' ' ' ' ' L ' ' * - ' ' ^

Number of Applications of Tensile Load, i ^ 46 FIG 12.—Strain History for Reversed-Load Low-Cycle Fatigue Tests

tensile change in plastic true strain is

linearly cumulative, that is i/m = 1

The slopes of the four lines in Fig 9

may be described in the form of Eq 6

and give values of l / w equal to 1.22,

1.43, 1.65, and 1,86, respectively, for

r values of —J, — j , —f, and —1 When

these corresponding values of 1/m and r

are plotted (Fig 11), the following

rela-tionship is obtained;

With the empirical relationships for

both l/m and Aga with respect to r, the

hypothesis is now complete

To verify the general hypothesis six

for these tests was found to vary from 0,94 to 1.08, which was close to the value 1.0 presented in the hypothesis

CORRELATIONS WITH OTHER DATA

Data in the literature are generally reported for low-cycle strain tests con-ducted by cycling the specimen between

a constant maximum plastic strain (jmax or €max) and a constant minimum

plastic strain {qmm or tmin)- In most

cases, the tests were started with a tensile load to produce the upper or maximum strain limit which was fol-lowed by fully reversed strains Some tests were carried out with constant

absolute-strain ratios (R = constant)

YAO AND MUNSE ON LOW-CYCLE AXIAL FATIGUE OF MILD STEEL 19

while others were carried out with

constant mean strains (qm or fm = 0)

Since the quantity Aqi is not necessarily

a constant in these tests, these test results

are presented in terms of ^max versus n

(for positive ^^ax) or ^min versus n (for

negative ^^ax)

Based on the general hypothesis

presented here, equations have been

derived for each of the various test

conditions For constant R ratios the

13.—Correlation of Hypothesis with Various Constant-J?-Ratio Tests on 2024 Aluminum

relationship between ^max and n may be

derived as follows: (a) The first cycle

(see insert of Fig 13) is assumed to

consist of a single tensile change in

plastic true strain (r = 0); and (i) the

subsequent cycles of strain are then full

at constant R ratios of +0.75, +0.50, 0,

and —1.0 The plastic true strain at

simple tensile fracture, q^, for this

particular type of specimen was found

to be approximately 34 per cent Since no one-cycle test information is available for this specimen, it is assumed that

Aqa is a constant and equal to q^ for all

r ratios (Aqa = 9/ = 34 per cent) Then

from Eq 9, the following relationships may be obtained:

For R = -1-0.75,

9m a

These equations are plotted in Fig 13

along with the corresponding test data

from reference (19) Despite the

assump-tion made regarding Aqa , the curves

plotted on the basis of this hypothesis

fit the test points reasonably well for

lives up to approximately 200 cycles

Similarly, expressions may be obtained

for tests conducted with constant mean

strains For the first cycle {i = 1), the

relationships are the same as shown

above for the previous examples For

the subsequent cycles (t > 1),

D'Amato (11) reported test results on a

2024 aluminum alloy with constant mean strains of +27.5, +13.5, +7.5, 0, and —7.5 per cent The plastic true strain at simple tension fracture, 5/ , was found to be about 38 per cent

Assuming again that A^a = 5/ = 38

per cent for all r values, the following

equations may be obtained from Eq 10:

14.—Correlation of Hypothesis with Various Constant-Mean-Strain Tests on 2024 Aluminum

YAO AND M U N S E ON L O W - C Y C L E AXIAL FATIGUE OF M I L D STEEL 21

i by Dubi nts ore p plastic er

30 Steel

ic(l3g lotted ginee

on ring tti(

St basis ain mea

-Correlation of Hypothesis with Tests Conducted on the Basis of Engineering Strains

Equations 10(a) through 10((f) are

plotted in Fig 14 in terms of gmax and n,

along with the corresponding test data

from reference (11)

For tests with a negative mean strain

and a negative maximum strain, the

first load will be in compression (see

insert of Fig 15 Assuming that A^c =

qt in the first cycle, the following

equa-tion may be obtained from E q 6(a):

n\

Then, for q,,

2{q„ — qn-.in) Aqn

Equation 11(a) is plotted in Fig 15 in

terms of ^min and n, along with the

cor-responding test data from the same

reference Excellent correlations are

again obtained

Dubuc (13) tested SAE 1030 steel

specimens with a gage length of 1 in

These tests, with «„ = 0, were

con-ducted by controlling the total

engineer-ing strain range T o apply the present

hypothesis, Atn was assumed to be

constant and equal to the elongation a t

static tensile fracture, 44 per cent in this

case From E q 10, assuming Smax and

y max to be approximately equal, we then obtain

engineer-The excellent correlations of the hypothesis presented here with the test results of Plan and D'Amato (19) and D'Amato (ii) indicate that it may be possible to use this hypothesis to describe the low-cycle fatigue behavior of 2024 aluminum alloy specimens I n addition, the correlation made with Dubuc's (13) test data indicates that the hypothesis may be equally applicable to tests of steel specimens conducted on the basis

of engineering strains

SUMMARY AND CONCLUSIONS

1 A general hypothesis describing the cumulative effect of plastic deforma- tions on the low-cycle fatigue behavior

of mild steel for lives up to mately 1000 cycles has been established and may be expressed as follows:

2 For constant relative-strain ratios,

r, a linear relationship exists between

log Aqt and log n

3 There does not seem to be any effect of material on the slope of the

relationship between log Aqt and log n

4 A linear relationship was found also to exist between the quantities 1/w and r, which for mild steel may be expressed as 1/w = 1 — 0.86r

5 Plastic strain-histories obtained from nine reversed-load cyclic tests were analyzed in terms of the general

YAO AND MUNSE ON LOW-CYCLE AXIAL FATIGUE OF MILD STEEL 23

hypothesis It was found that the

condi-tions specified by the hypothesis were

satisfied

6 Correlations of the general

hypothe-sis with various published test data

indi-cate that the hypothesis may be

appli-cable to cyclic strain tests on metals

other than mild steel However,

addi-tional confirmations of this correlation

would be desirable

7 Under low-cycle fatigue conditions,

any tensile change in plastic strain is

cumulative, and the manner in which

this accumulation takes place is

de-pendent upon the amount of compressive

plastic strain in each cycle

A cknowledgment:

The work described in this paper was

conducted in the Structural Research

Laboratory of the Department of Civil

Engineering at the University of Illinois,

under sponsorship of the Ship Structure Committee, National Academy of Sci-ences, through the Bureau of Ships,

U S Navy However, the opinions expressed in this paper are those of the authors and do not necessarily represent those of the Ship Structure Committee

or its member agencies The tion is a part of the structural research program of the Department of Civil Engineering, of which N M Newmark

of this research Special acknowledgment

is due D F Lange, W F Wilsky, and others in the laboratory shop for their excellent workmanship in making speci-mens and maintaining the test equipment

in this program

REFERENCES (1) P P Benham, "Fatigue of Metals Caused

by a Relatively Few Cycles of High Load

or Strain Amplitude," Metallurgical

Re-views, Vol 3, No 11 (1958)

(2) J T P Yao and W H Munse,

"Low-Cycle Fatigue of Metals—Literature

Review," Welding Journal, Research

Sup-plement, Vol 41, p 182s, April, 1962

(3) T B Kommers, "Repeated Stress

Test-ing," Vlth Congress, International Assn

for Testing Mats., New York, N Y

(1912)

(4) E Orowan, "Stress Concentrations in

Steel Under Cyclic Loading," Welding

Journal, Research Supplement, Vol 31,

p 273 (1952)

(5) S S Manson, "Behavior of Materials

Under Conditions of Thermal Stress,"

A'^C.4 TN 2933 (1953)

(6) J H Gross and R D Stout, "Plastic

Fatigue Properties of High-Strength

Pressure-Vessel Steels," Welding Journal,

Vol 34, p 161s (1955)

(7) L F Coffin, Jr and J F Tavernelh, "The

Cyclic Straining and Fatigue of Metals,"

Transactions, Metallurgical Soc, Am Inst

Mining, Metallurgical, and Petroleum

Engrs., Vol 215, p 794, Oct., 1959

(8) L F Coffin, Jr., "The StabiUty of Metals

Under Cyclic Plastic Strain," Journal of Basic Engineering, Series D, Vol 82, No

the Low-Cycle Fatigue Range," WADD

TR 60-175, April, 1960

(12) D A Douglas and R W Swindeman, "The Failure of Structure Metals Subjected to Strain CycHng Conditions," Am Soc

Mechanical Engrs., Paper 58-A-198 (1958)

(13) J Dubuc, "Plastic Fatigue Under Cyclic Stress and Cyclic Strain with a Study of the Bauschinger Effect," Ph.D Thesis, Ecole Polytechnique, Universite de Mon- treal, Montreal, Canada, Jan., 1961 (14) A Johansson, "Fatigue of Steels at Constant Strain Amphtude and Elevated

Temperatures," Colloquium on Fatigue,

lUTAM, Stockholm, Sweden (1956)

(15) S I Liu, J J Lynch, E J Ripling, and

G Sachs, "Low-Cycle Fatigue of the

Aluminum Alloy 24S-T in Direct Stress,"

Melals Technology, Feb., 1948

(16) A C Low, "Short Endurance Fatigue,"

International Conference on Fatigue of

Metals, Inst Mechanical Engrs (London),

p 206 (1956)

(17) H Majors, Jr., "Thermal and Mechanical

Fatigue of Nickel and Titanium,"

Transac-tions, Am Soc Metals, Vol 51, p 421

(1959)

(18) F J Mehringer and R P Felgar,

"Low-Cycle Fatigue of Two Nickel-Base Alloys

by Thermal-Stress Cycling," Journal of

Basic Engineering, Series D, Vol, 82, No 3,

p 661, Sept., 1960

(19) T H H Plan and R D'Amato, Cycle Fatigue of Notched and Unnotched Specimens of 2024 Aluminum Alloy Under

"Low-Axial Loading," WADC TN 5S-27 (1958)

(20) G Sachs, W W Gerberich, V Weiss, and

J V Latorre, "Low-Cycle Fatigue of

Pressure-Vessel Materials," Proceedings,

Am Soc Testing Mats., Vol 60, p 512

(1960)

(21) D C Drucker, C Mylonas, and G Lianis,

"On the Exhaustion of DuctiUty of Steel in Tension Following Compressive

E-Pre-strain," Welding Journal, Research Supplement, p 117s, March, 1960

(22) E W Evans, "Effect of Interrupted Loading on Mechanical Properties of

Metals," The Engineer London, Vol 203:

Part I, No 5274, p 293; Part 11, No

5275, p 325 (1957)

Stainless steel sheet (18Cr-9Ni) was tested in fatigue under axial-load

cycling in plain and notched conditions Various stress ratios were used ranging

from R = —1.0 to +0.91, and endurances (see Definitions) from 10 to 107

cycles were covered using testing frequencies of 5 to 15 cpm and 3000 cpm

The effect of mean stress on notch fatigue strength could not be predicted

empirically solely from unnotched material data; at least one notched fatigue

curve would be required

A fatigue strength reduction factor based on maximum stress for a particular

mean stress and endurance provided the most reliable correlation between

unnotched and notched data

Low-cycle and high-cycle fatigue curves matched up only to a limited extent

at the overlap, but there was generally strength reduction at low frequency

Under certain conditions of mean stress and stress ratio a cyclic creep or

ratchetting mechanism leading to ductile rupture was obtained at low

en-durances

Simple functions existed in the low-cycle region between stress range and

plastic strain range and total energy and cycles to fracture, both of which

were largely independent of stress ratio

SYMBOLS AND D E F I N I T I O N N, cycles to failure

K t, theoretical elastic stress

S a , cyclic stress amplitude K p, theoretical plastic stress

Smax , maximum cyclic stress k f , fatigue strength reduction factor for

S m in , minimum cyclic stress z e r o mean stress

R, stress ratio, S min /S m&x k/ m, fatigue strength reduction factor at

S u , tensile strength constant nonzero mean stress

Sup , tensile strength, plain material Definition:

Sun , tensile strength, notched material J

S v , yield or proof stress Endurance, the term endurance has been

So, fatigue strength for zero mean stress used to express the cyclic lifetime of a

e pr , repeated plastic strain range specimen This has been chosen in

prefer-e pt , total plastic strain range ence to the more generally accepted

"fatigue life" on account of the proposed

i Development Engineer, Rexall Chemical subdivision of the type of fracture being

'Lecturer in Applied Mechanics, Imperial produced into a fatigue fracture and a College, London, England ductile rupture or creep failure The term

25

endurance is used to express cyclic

life-times leading to both types of failure

Stress concentration and mean cyclic

stress are two important aspects of

metal fatigue that have been studied

extensively in the past, both separately

and in relation to each other This paper

is concerned with the eSects of local

and general plastic deformation at a

stress concentration in relation to the

mean stress imposed under axial-load

cycling conditions over a wide range of

endurance Yielding can be caused by

various combinations of mean and

alternating stress, the extreme cases

being a large alternating range of stress

superimposed on a zero or low value of

mean stress, or a high mean stress, which

in itself causes yielding, plus some

alter-nating component Both generally may

result in failure in a relatively few

cycles, but so far more attention has

been paid to the fatigue-limit region

Several investigators (1-3)' have studied

high mean stresses with stress

concen-tration for long endurances, and a

theoretical method of predicting a

notched 5a-S„ diagram to allow for

yielding under high mean stress has

been proposed (4)

The information so far available at low

endurances which deals with notched

material is generally only related to

one or two mean stresses {R = — 1 or 0)

(S-7)

lUg (8) has studied the effect of three

mean stresses on notched aluminum and

steel alloys over a range of endurance

from 2 to 10' cycles The present program

has studied stress ratios from R =

— 1.0 to +0.91 for endurances from 10

to 10' cycles for stainless steel sheet,

plain and notched with several circular

holes Although these are insufficient

data to propound a general law for

' The boldface numbers in parentheses refer

to the hst of references appended to this paper

predicting notched behavior under mean stress, it was hoped that the results would indicate various trends of be-havior at low and high endurances

TEST EQUIPMENT Tests in the range from 5 X 10' to 10' cycles were conducted on a 6-ton Haigh axial-load fatigue machine This operates on the principle of electro-magnetic excitation of a resonant spring and mass system at a frequency of

3000 cpm The required full load can be set up on the test specimen in about 15 sec

Tests in the range from 10 to 10' cycles were carried out on a 6-ton Schenck TABLE I.—CHEMICAL COMPOSITION

Element Per Cent Carbon 0.10 Silicon 0.68 Manganese 0.75 Sulfur 0.019 Phosphorus 0.018 Chromium 18.25 Nickel 9.76 Titanium 0.70 axial-load fatigue machine incorporating

a low-frequency mechanical drive of approximately 10 cpm This machine is described in more detail elsewhere (6)

Some of the tests on the Schenck machine were instrumented to obtain stress-strain records (hysteresis loops) automatically during the life to fracture

The machine is fitted with a ter loop, the deformation of which is proportional to load One variable-inductance probe was mounted across the dynamometer to record the load, while a second was attached by exten-someter clamps to a gage length on the specimen The signals from the probes were fed into amplifiers which gave a visual reading of displacement, and then

dynamome-to the X and Y plates of an oscilloscope

Permanent records were obtained by photography from the latter

BELL AND BENHAM ON ErPECT OF MEAN STRESS ON FATIGUE STRENGTH 27 Two stages of signal amplification

were available to cover strain ranges of

up to 2 and 20 per cent respectively

A simple relay and timer circuit was

arranged to obtain automatically a

suitable number of records during a

test

MATERIAL AND SPECIMENS

Thin sheet material was chosen to give

approximate plane stress conditions,

tained and the number of holes reduced

to two (Fig i{d)) A photoelastic stress

analysis was conducted for both types

of notched specimen The stress tration was the same at each of the holes in both the triple and double

concen-group, giving Kt = 2.44 Fatigue tests

conducted under the same stress tions for each type of notched specimen gave the same average endurance

condi-For the fatigue tests in which the

57

Nominal Tensile Strength, tons per sq in

Rolling tion

Direc-68.5

Transverse Direction

70.1

Young's Modulus, tons per sq in

12 X 10^

Elongation in 2 in., per cent

4.2

Vickers mond Pyramid Hardness

Dia-370

and the width of the test specimen was

sufficient for multiple notches All the

test pieces were taken from one batch

of as-rolled 18Cr-9Ni stainless steel

sheet, 0.039 in thick, to specification

DTD166B (now obsolete) The chemical

composition and principal mechanical

properties are given in Tables I and II

The form and dimensions of the

unnotched specimens used on both

machines are shown in Figs \{b) and

(c) A radiused gage length was adopted

to avoid persistent failure at the fillet

radius of a parallel length specimen A

photoelastic analysis showed a negligible

nonuniformity of stress in the unnotched

specimens

The program was initially planned to

run only on the Haigh machine, and a

notched specimen, Fig 1(a), was

de-signed for this purpose When the work

was extended to include low endurances

on the Schenck machine, the existing

notched specimen was too large to

ob-tain all the stress ratios required Rather

than scaling down geometrically and

possibly introducing a size effect at the

notches, similar proportions were

re-l i

- 2 / 3 1/3'^

X

H K (a) Haigh Machine- Notched Specimen Used With Schenck Jaws

-8 Radius (b) Haigh Machine-Plain Specimen

6

-*i T*;l/8"diam il/V'

I

(d) Schenck Machine-Notched Specimen

NOTE,—All dimensions are in inches ness 0.039 in

Thick-specimen was subjected to some com- (9) Oil-impregnated filter paper at low pressive loading during the cycle, guide loads, and graphite grease at high loads plates were used to prevent the test between the specimen and plates kept

FIG 3.—S-N Curves for Various Stress Ratios, Unnotched Specimens

specimen from buckling The design of frictional effects to a minimum The the guide plates was based on the com- degree of restraint of the plates was ments of Brueggeman and Mayer never such as to prevent them being

BELL AND BENHAM ON EFFECT OF MEAN STRESS ON FATIGUE STRENGTH 29

moved quite easily along the specimen and short-term (up to 30 min) when under load temperature creep tests were conducted

TENSION TESTS to establish the stress-strain curve

It was soon discovered that the ma- accurately The test for static nominal terial had virtually no elastic range, and stress-strain curve in tension (Fig 2) consequently a number of static-tension occupied about 30 min

Unnotched and notched specimens

were also pulled to fracture on the

Schenck machine at the same strain rate

as was used for the low-cycle fatigue

tests, and the load-extension record

obtained from the instrumentation

The "dynamic" stress-strain curve

(strain rate about 5 in per in per min)

for an unnotched specimen is also shown

in Fig 2 up to 2 per cent strain The

tensile strength was raised from 68.5 to

70 tons per sq in at the higher strain

tests On the Schenck machine the upper limit of endurance, 10^ cycles, was selected because of the length of time required for a test at 10 cpm The above limits provided a sufiBxient overlap of endurance to compare the effect of the two frequencies and machines The results of the tests on unnotched speci- mens on both machines are plotted as curves of maximum stress against cycles

to failure in Fig 3

In some of the tests at high loads and

10^ 10*

Cycles, N

FIG 5.—S-N Curves for Various Stress Ratios, Notched Specimens

rate Notched specimens gave an even

higher nominal tensile strength, 74 tons

per sq in

FATIGUE T E S T S

The fatigue program was designed to

cover a wide range of mean and cyclic

stress combinations The tests were

con-ducted at constant values of stress ratio

of: R = - 1 0 , - 0 4 6 , + 0 0 7 5 , + 0 3 3 ,

+ 0 5 , + 0 7 2 5 , and + 0 9 1

The lower limit of endurance, 5 X 10^

cycles, on the Haigh machine was defined

by the time required to set up a test, or

excessive creep in the high-mean stress

short endurance, both at high and low frequency, the specimens exhibited a continuous cyclical extension (ratchet- ting) until failure finally occurred by tensile rupture rather than fatigue cracking I n other cases, a small fatigue crack occurred at one edge or internally

in the specimen, and a small visible zone

of plastic deformation at the tip of the crack soon spread into one or more yield bands at 45 deg to the axis of the speci- men Some of these fractures are illus- trated in Fig 4

The results of the notched fatigue

tests are plotted as Snax against N'

BELL AND BENHAM ON EFFECT OF MEAN STRESS ON FATIGUE STRENGTH 31

curves for the various stress ratios and

both frequencies in Fig 5 In general

the same hmitations on endurance

existed as above for the unnotched

speci-mens

could occur on initial setting-up of a high mean stress, or on introduction of the alternating component, took the form of small dimples on either side of each hole At higher stresses the dimples Fatigue cracks developed on both developed into yield bands looped be-

.S,„ax = 72, fl = 0.91, A' = 7400 X 1 0 '

( u n b r o k e n ) Clearly observable plastic dimples

a t edges of all holes a t a stress below t h e fatigue

limit

Smsix = 71.5, R = 0.725, V = 3 3 F a t i g u e

cracks a t b o t h sides of outside holes N o t e

dimpling effect at holes a n d also 45-deg j i e l d

b a n d a t edges a n d looping between holes

S,„ax = 55.7, R = 0.725, A' = 248 X 10^

F a t i g u e crack a b o u t b o t h sides of central hole

a n d also v e r y small cracks a t outside holes

N O T E — S p e c i m e n s a r e all of t h e s a m e

dimensions

F I G 6 — T y p i c a l Plastic D e f o r m a t i o n P a t t e r n s a n d F r a c t u r e of N o t c h e d Specimens

sides of two or all of the holes, with

little preference being shown between

the outside or the central holes In all

but the very low stress conditions,

intense localized plastic deformation

preceded the crack tip; however, for

very low stresses no permanent

deforma-tion could be observed, and the posideforma-tion

of the crack was difficult to locate The

localized plastic deformation, which

tween the holes and from outer holes to the edges of the specimen at 45 deg In certain circumstances plastic dimpling could be obtained at the notches without any subsequent fatigue failure, while under other conditions cracks would develop and propagate without any prior macroscopic plastic deformation Some examples of yield band and crack formation are shown in Fig 6

ANALYSIS OF FATIGUE DATA

Owing to the infinity of combinations

of mean and alternating stress and the

havior The well-known expressions devised by Goodman, Gerber, and Soderberg were intended to relate to

20 30 40 50 60 70 Mean Stress {Sm),tons per sq in

(a) Unnotched specimens

FIG 7—Sa-Sm Curves for Fatigue Specimens

enormous amount of experimental work fatigue limit values

required to obtain fatigue behavior over

a comprehensive range of S^ and Sm

values, there have been many attempts

to propound laws, based on simple

experimental constants from a few

tests, to predict generalized Sa-Sm

be-However, the current need in some fields to design for finite fatigue life requires a wider appli-

cation of Sa-Sm relationships

The above remarks about mean stress apply equally well for both un-notched and notched specimens How-

BELL AND BENHAM ON EFFECT OF MEAN STRESS ON FATIGUE STRENGTH 33

ever, fatigue initiated by stress

concen-tration is a complex problem in itself

for the case of zero mean stress If the

it becomes extremely difficult to obtain a reliable generalized relationship for

Sa-Sm values in notched material and to

UTS

E

<

10 20 3 0 4 0 5 0 6 0 70 8 0 Mean Stress (Sm), tons per sq in

(b) Notched specimens

FIG 7.—Continued

latter is not zero, there is much

specula-tion and still no certain answer as to the

effect of stress concentration on the

actual local values of mean and

alternat-ing stress Without this latter knowledge

predict notched values on the basis of unnotched data

The results shown in Figs 3 and 5 are reasonably comprehensive and pro-vide a basis for detailed graphical

analysis of the various quantities This

has been done elsewhere (10), but due to

space limitations only some of the

interesting features can be discussed

here

From the S-N curves (Figs 3 and 5)

for unnotched and notched specimens,

the Sa-Sm diagrams in Figs 7(a) and (J)

have been derived for various values of

endurance Considering first the diagram

for unnotched specimens, the curves

are bounded by the lines Sa/2 = 0,

5™ = 0, and 5„/2 + 5™ = 5„ = 70, and

their shape is very much dependent on

the relative positions of the 5-A' curves

For this reason, the rather sharp kink

in the Sa-S^ curves for long endurances

at approximately R = 0 might have

been attributed to a misplaced S-N

curve; however, a study of Fig 3 indicates

that a fairly unreasonable shift of the

curves would be required to smooth out

the Sa-Sn curves This has been noticed

on unnotched specimens by other

in-vestigators (3), but it is certainly not the

general rule A further point of note is

that because the S-N curves intersect

with horizontal line S'max = 70 at various

R values and endurances, the 5o-5„

curves are either asymptotic at low R, or

intersect at high R with the line Sa/2 +

5„ = 70

Empirical expressions devised by

Peterson (11), Stuessi (12), and Burdon

(13) have each been compared with the

experimental results, the last of those

giving the best correlation For this

particular material, difficulties arise

because of the sharp inversion of Sa

versus S^ nt R = 0 A relationship of

the form

(1 - R) -[t]"

where C and n are constants dependent

on N, gives a better fit to the results, but

has the disadvantage of requiring more

initial experimental data for evaluation

Since there are generally more data on fatigue at various mean stresses for unnotched than notched specimens, it is very useful to have a method for pre-dicting the effect of mean stress for notched specimens from unnotched data The simplest approach, when consider-ing, say, a modified Goodman diagram,

is to divide the ordinate and abscissa by the theoretical stress concentration

fatigue seldom achieves the value of Kt

and is, therefore, given a separate symbol

Kf (to be defined later); and (2) the

effect of local and then general yielding around the notch influences the effective

values of Sa and 5„ and hence the

alternating-mean stress diagram The general assumption that when local yielding occurs at the stress raiser the maximum stress is relieved to some extent, but that the range of stress is un-affected implies that the local mean stress will be reduced and a greater range of stress can be maintained for a particular nominal mean stress

Since the nominal static, tensile strength of a notched specimen is gen-erally equal to or slightly higher than for an unnotched specimen, a better approach to obtaining the notched

Sa-Sm diagram would be to join the

points Sa = So/Kt or So/kf to Sm =

Su notched by a straight line

Reference to Fig 1(b) for the present

tests shows that the above method of predicting the notched relationship would be in considerable error Gunn

BELL AND BKNHAM ON EFFECT OF MEAN STRESS ON FATIGUE STRENGTH 35

(4), who has studied this problem,

sug-gests that three distinct stages in a

notched Sa-S^ diagram are: (1) the

condition that the local maximum stress

is still elastic, for which the first part of

These latter parts of the diagram, described in detail elsewhere (4,14), can

be constructed either by using a

plastic-stress concentration factor, Kp , or the

stress-strain curve for the material and a

E

<

20 30 4 0 50 6 0 Mean Stress ( S ^ ) , tons per sq in

Su Plain^

Su (a) iV > 10° (Fatigue endurance limit)

Notched-FIG 8.—Comparison of Experimental and Empirical S„-Sm Curves

the notched Sa-S^ diagram can be

drawn up to the point of intersection

with the line joining Sa = Sy/Kt to Sm =

Sy/Kt or when local yielding

com-mences; (2) occurrence of local yielding,

with the body of the material remaining

elastic, and (3) general yielding in the

material

strain concentration factor equal to the elastic stress concentration factor The three stages mentioned above are self evident in Fig 7(6) at endurances down

to 10* cycles; while for unnotched mens the inversion occurs at constant

speci-stress ratio {R = 0), for the notched

curves the change in curvature occurs

at almost a constant mean stress of

approximately 25 tons per sq in At

endurances below W cycles, where

maximum stresses are high and more

general yielding is taking place, the

dieted curve and the notched Sa-Sm

curve for high, medium, and low

en-durances is shown in Fig 8(a), (b), and

(c), respectively In each case the retical curve is overly conservative

theo-10 20 30 4 0 50 60 Nominal Mean Stress ( S ^ ) , tons per sq in

(b) V = 5 X 10* cycles

FIG 8—Continued

Sa-Sm curves are fairly smooth and

parabolic in form

Gunn's method of analysis avoids the

need of any initial notched fatigue data,

because predictions are made directly

from unnotched results That approach

was applied to the present results, and

the comparison between Gunn's

pre-principally owing to the use of theoretical elastic and plastic stress concentration factors rather than a fatigue strength reduction factor The definition of the latter term is well established in the case of fully reversed stress cycling, that is, constant zero mean stress; however, if various mean stresses also