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EFFECT OF TWO STRESS RAISERS

ACTING TOGETHER AT A POINT

;. GUHSE

DUDLEY KNOX LIBRARYNAVAL POSTGRADUATE SCHOOLMONTEREY, CA 9*943*101

EFFECT OF TWO STRESS RAISERS ACTING

TOGETHER AT A POINT

*****

Donald E. Guhse


TOGETHER AT A POINT

by

Donald E. Guhse

If

CommandersUnited States Navy

Submitted in partial fulfillment ofthe requirements for the degree of

MASTER OF SCIENCEIN

MECHANICAL ENGINEERING

United States Naval Postgraduate SchoolMonterey

sCalifornia

1960

NOC

\<S<

r. enLEY KNOX LIBRARY

NAVAL POSTGRADUATESCHOOL

MONTEREY, CA 93943-5101


TOGETHER AT A POINT

by

Donald E. Guhse

This work is accepted as fulfilling

the thesis requirements for the degree of

MASTER OF SCIENCE

IN

MECHANICAL ENGINEERING

from the

United States Naval Postgraduate School

ABSTRACT

Stress concentration factors are valuable tools for the machine

designer when they can be accepted as reliable. When one stress con-

centration configuration, such as a hole, fillet, notch, machine fin-

ish, etc, exists there are numerous curves and equations available

that give the theoretical extent of concentration to be expected,, With

two or more of these configurations present at the same point, the de-

signer must decide whether or not to combine factors, and if so, in

what manner, to obtain a good prediction.

Fatigue tests in torsion were conducted in order to search for an

answer to the question of a reasonable design basis for repeatedly

stressed points with two stress raisers.

The author wishes to acknowledge the valuable assistance and en-

couragement given him by Professor Virgil M. Faires, of the U. S.

Naval Postgraduate School, during this project.

ii

TABLE OF CONTENTS

Section Title Page

1. Introduction 1

2. Equipment

Specimens 4

Testing Machine 9

3. Procedure 18

Results and Discussion 21

5o Conclusions 33

6„ Bibliography 36

APPENDICES

A. Tabular Data 37

T '. Machine Difficulties 48

C. Sample Calculations I 1

iii

LIST OF ILLUSTRATIONS

Figure Page

1. Properties Chart for AISI 4140 Steel 5

2. Type M Torsion Specimen 7

3. Basic Specimen Configurations 8

4. Configuration with 1/4-inch Hole 10

5. Dimensional Sketch of Cut-down Specimen 11

6. Photo of Cut-down Specimen 12

7. Baldwin Fatigue Testing Machine 13

8. Torsion Fixture (Long Arm) 14

9. Torsion Fixture (Short Arm) 17

10. Shear Stress Concentration Factor for

Specimen with Transverse Hole 24

11. Stress Concentration Factor due toSurface Finish 25

12. S-N Curves for 50% Survival 26

13. Probability-Stress-Cycle Curves 27

14. Tvnical Fracture Patterns for Specimenswith a 1/16- inch Hole 29

15. Other Typical Fracture Patterns 30

16. Frequencies of Hardnesses, Total Population 32

17. Pattern of Amplitude Change Prior to

Failure 50

iv

lo Introduction

The problem of improved design of machine parts continually confronts

the engineering profession. Untimely failure of parts is costly from the

standpoint of cost of replacement, loss of production time, and, more

seriously, injury or loss of life. On the other hand, use of excessive

safety (or ignorance) factors is becoming less desirable due to weight

limitations, limited availability of some materials, and the necessity of

limiting material and production costs to meet competition.

Improper design is involved in the majority of premature failures.

The situation is well stated as follows in a publication of the U. S. Navy

Bureau of Aeronautics :

While minor improvements in fatigue life may be accomplishedmerely by changing material, few serious fatigue difficultieshave been completely corrected in this way.

The publication also states:

By studying stress concentration factors much can be learnedabout how to produce designs that are superior from the stand-

point of resistance to repeated loads and how to evaluate ap-

proximately the influence of various geometric figures.

The general analytical solution of fatigue failures has yet to be

developed, but much empirical and experimental data have been compiled

over a period of years. The design engineer's basic tool, the "stress

concentration factor", is available in the form of charts, curves, tables,,

and equations. A comprehensive and valuable collection of charts and re-

lations useful in making strength calculations has been compiled by Mr.

°k

R. E. Peterson £ 1 J . This book, as well as other literature on the

* Numbers enclosed in brackets [J refer to bibliography on page 36.

R. L. Templin and E. C. Hartmann, Designing for Repeated Loads,NavAer SM-32, Jan. 30, 1952.

subject, deals only with stress-concentration configurations appearing

singly, and does not treat situations where two stress concentrations

appear together at a point.

The problem of combined stress raisers has generally been solved

by: tests of actual or minaturized parts under maximum anticipated loads,

combination of known stress concentration factors based on experience of

individual designers or manufacturers, application of large safety factors,

and other methods of questionable reliability. A view of the current

situation is expressed by Dr. Horace J. Grover of Battelle Memorial

2Institute in the following quotation :

Composite structures usually involve uncertainties in detailedstress analysis plus inadequate information concerning effectsof stress concentrations such as those around discrete fasteners

in joints. For present design, a useful empirical procedureinvolves experimental stress analysis under static loading plusfatigue tests of specimens carefully designed to include local

stress-concentration effects. Future analysis can be aided by

investigations providing more understanding of effects on fatigue

behavior of some of the types of stress concentrations that exist

in composite structures. Items for which information seems parti-cularly inadequate include: joints with rivets (and bolts or otherdiscrete fasteners) under complex loading, fretting, etc. For com-

posite structures, use of the concept of an effective stress-con-centration factor requires extreme care.

In regard to the object of this project, a statement by Mr. E. C.

Hartman, reporting on the effect of unintentional stress raisers on the

3fatigue strength of structural components, seems appropriate:

2H. J. Grover, Allowance for Stress Concentration in Design to Pre-

vent Fatigue, Proceedings of the International Conference on Fatigueof Metals, Institute of Mechanical Engineers, London, 1956, p 88.

3E. C. Hartman, Effect of Unintentional r ' -ess Raisers on the FatigueStrength of Structural Components, Proceedings of the InternationalConference on Fatigue of Metals, Institute of Mechanical Engineers,London, 1956, p 199.

If a discontinuity happens to be located and oriented exactlyso as to intensify a high stress concentration caused by somedesign feature, then its effect is likely to be a real factorin determining the fatigue strength of the part.

(He defines a discontinuity as a scratch, gouge, cut, nick, undercutting,

or an unwanted hole, in addition to one of a metallurgical nature.)

This investigation deals with a condition where two discontinuities,

a hole and a rough machined surface, appear together. Fatigue tests in

torsion were conducted to obtain an indication of the relationship be-

tween the stress concentration factor for a hole versus the stress con-

centration factor for a hole and a rough machined surface combined. The

effect of the combined stress raisers was also compared with the stress

concentration factor for a rough machined surface.

The tests were conducted by the author in the Mechanical Engineering

Laboratory of the U. S. Naval Postgraduate School, Monterey, California,

under the supervision of Professor Virgil M. Faires during the period from

December 1959 to May 1960.

2. Equipment

Specimens .

Selection of the type of material to be used in the tests was based on

the decision to use a deep hardening steel that is heat treatable to

face hardness of about 350 Brinell. All specimens were fabricated from

four 15- foot bars of 1-1/2 inch round stock, AIS1 4140 steel produced in

an electric furnace, hot rolled, and normalized. The four bars were certifi-

ed to be from the same heat and to contain the following percentages of al-

loying elements by weight: 0.39% carbon, 0.90% manganese, 0.009% phosphorus.

0.019; sulfur, 0.27% silicon, 0.90% chromium, and 0.20% molybdenum. In the

normalized condition, the steel was certified to have the following physical

properties: yield point, 102,500 psi; tensile strength, 125,000 psi;

Brinell hardness, 269; ASTM grain size, 7-6; and Jominy, 5-56 10-48.

As each specimen length was cut from the bar stock, it was identi-

fied by letter (A,B,C, or D) to indicate which bar it came from and by

number (1,2,3, - -, 21) to indicate its original location in the bar. These

pieces were rough machined to within about 1/16- inch of the final dimen-

sions and were then heat treated. The heat treatment was accomplished

by the author, utilizing the facilities of the Metallurgical Laboratory

of the U. S. Naval Postgraduate School. The desired heat treatment was

ascertained from the characteristic curves for AISI 4140 steel shown in

4figure 1 . Four or five specimens were placed in an electric furnace

set at 1550°F (+ 5°) for 2-1/4 hours, quenched in agitated oil, tempered

in an electric furnace at 1000°F (+ 5°) for 1-1/4 hours, and finally air

quenched. The specimens were then finish machined to the desired con-

figuration. It was expected that this procedure would remove surfaces

4Bethlehem Steel Company, Modern Steels and their Properties, Hand-book #268, 1949, p 114.

BETHLEHEM STEEL COMPANY

AISI-4140(Oil Quenched')

PROPERTIES CHART(Single Heat Results)

.530 Rd. SIZE TREATED

.505"Rd. SIZE TESTED

Ac, 1395°F. Ar 8 I330°F.

Ac, 1450°F.| Ari I280°F.

C. Mo. P. S. SL Nl. Cr. Mo..36/ .75/ Mai. Mai. .20/ .'0/ .15//43 /1.00 .04 .04 /35 Ml /1. 10 /.I*

Ortlo

Siu

HEAT TESTED .41 .85 .024 .031 .20 .12 1.01 .24 6-8

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31144

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23534

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MB89 C 339

ROCK,IZOD.

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—1 260000As Quench id Brir iell Ha rdness 601

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NOUM'LZI

1600'* C . NORMALIZED AT 1600°F., REHEATED TO 1550°F., QUENCHED IN AGITATED OIL

Fig. 1

decarburized during heat treatment. A 0. 040- inch mill cut was made

the full length of one shank on each specimen to provide a flat for

hardness readings.

Six specimens were initially fabricated in an effort to determine the

optimum set of configurations for prosecution of this project. They were

all patterned after the standard "M" type specimen, figure 2, recommended

5for torsion testing on the Baldwin Universal Fatigue Testing Machine .

These specimens had rough and smooth finished surfaces in the following

shapes: a) standard solid, b) standard with 1/16-inch transverse hole,

and c) standard specimen modified to incorporate a 1/8- inch radius fillet*

The types of specimens tested in this project were chosen after pre-

liminary tests indicated sufficient variation in fatigue life to give S-N

curves significantly different for each configuration. These configurations

were also chosen because they could be readily repro uced in the U. S„ Naval

Postgraduate School Machine Shop. The four basic configurations,, shown in

figure 3, were: (1) standard specimen with a smooth (4 to 8 microinch)

finish, (2) standard specimen with a rough machined (250 microinch) finish^

(3) standard smooth finish with a 1/16- inch transverse hole through the

narrow section, and (4) standard rough machined finish with a 1/16- inch

transverse hole through the narrow section.

5Baldwin Locomotive Works, Instructions for Operation of UniversalFatigue Testing Machine Model SF-l-U, Sept. 26, 1946.

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The finishes indicated above were determined by visual and finger-

nail comparison with standard finishes.

In addition to these basic configurations, a group of four standard

rough machined specimens, figure 4, with a 1/4- inch transverse hole in

the narrow section were made, and a group of seven smooth finish specimens

of smaller dimensions, figures 5 and 6, were made from specimens that had

been tested for 5 million cycles without failure.

Testing Machine .

The Baldwin Universal Fatigue Testing Machine (Sonntag), model SF-1-U9

figure 7, installed in the Mechanical Engineering Laboratory of the U. S.

Naval Postgraduate School, was used for all fatigue tests. The machine is

designed to apply a vertical vibratory force to any specimen or structure

attached between the heavy stationary frame (E) and the reciprocating

platen (F). The alternating force is produced by an unbalanced rotating

mass, which is supported between two bearings in a cage- like vertical

frame, the top of which forms the reciprocating platen. The rotating mass

is driven by a synchronous motor so that its speed is maintained constant

at 1800 revolutions per minute. The load may be adjusted by moving the

eccentric weight along its displacement scale, which, according to the

manufacturer, is accurate within 2% throughout the range of the scale.

The fixture shown in figure 8 is the standard fixture provided by

the manufacturer for torsional fatigue testing of cylindrical specimens.

The alternating force produced by the reciprocating platen (F) is converted

into an alternating torque in the specimen by means of a crank (R), which

is pivoted at one end and oscillated on the other. The test specimen is

gripped between the oscillating chuck (A) and the stationary chuck (B).

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The oscillating chuck is supported and guided between two bearings in the

pillow block (C) and oscillated by the crank. The stationary chuck is

clamped rigidly on split pillow block (D). Both pillow blocks are rigidly

bolted to the large stationary platen (E).

The standard torsion fixture is supplied with two crank arms. The

longer, 15-1/4-inch, arm was used for all type "M" specimens and is the

one shown in figure 8. It was necessary to shift to the shorter, 6-1/4-in-

ch, arm shown in figure 9 for tests of the cut-down specimens.

The force P (lbs) required to subject a specimen of diameter D (inches)

to a torsional stress X (psi) is calculated from the equation

P = W~ ">* (I)4

where J is the polar moment of inertia of specimen area in inches

and R is the crank arm length in inches.

With any specimen of a given diameter, subjected to a certain repeat-

ed stress, the amplitude of vibration of the reciprocating platen depends

on the specimen length. The maximum recommended amplitude of vibration Y

is 0.37 inches for the type of tests conducted for this project. This

amplitude can be predicted from the following equation:

Y = 2§s

T'* (H)

where L is the specimen free length in inches, D is the specimen dia-

meter in inches, G is the modulus of rigidity (shear modulus) in psi, and

R and 7" are as in equation (I).

The machine is equipped with micro- switches which were adjusted to

cut off the motor when the maximum recommended amplitude of vibration was

exceeded. A counter on the machine records the number of cycles to the

nearest kilocycle and automatically cuts out when the micrc-switches are

tripped.

15

Minor difficulties encountered in the use of this machine are

discussed in Appendix B.

16

3. Procedure

The test procedure was chosen with a view toward obtaining the neces-

sary data within the time and funds alloted to the project. The ASTM "Stan-

dard" Test, Method A-2, contained in STP 91-A Q2] was adopted. In method

A-2, each group at a particular stress level should consist of at least

four specimens in order to estimate the variability of the data. Three

or more different stress levels must be investigated for the determina-

tion of the curves for any particular percentage survival. Such curves

(figure 13) are sometimes referred to as probability-stress-cycle (P-S-N)

curves. Generally, at least four or five stress levels are used in a

test of this nature. The minimum number of specimens to obtain an S-N

curve was determined to be four per group at four stress levels for a

total of 16 specimens. Since an S-N curve was desired for each of four

configurations the total minimum requirement became 64 specimens.

Of the total of 84 specimens obtained from the total stock of four

bars, two were discarded due to errors in machining, five were used in

the preliminary tests, and five were discarded because fretting in the

collets caused heating and/or other conditions of variability not consider-

ed satisfactory for purposes of comparison. Seven of the specimens that

did not fail on original tests were cut down to smaller dimensions and

tested again.

The statistical data from tests conducted on 79 specimens are

contained in Appendix A.

Hardness readings were taken on the milled flats at least one dia-

meter length from the end for uniformity. The hardness of the narrow

portion of the test section was obtained on a few standard specimens and

on all of the cut down specimens after failure. A standard Rockwell

18

hardness testing machine was used. The hardness recorded represents the

average of five readings to the nearest tenth of a point.

The nominal shear stress ( T ) varied between 30,000 and 65,000

psi. It was calculated from the conventional equation

TT = -^ = PR = /6P/? Psl f77T)Z' 72^£3 rr D 3 ( '

for the solid specimen, where P and R are as defined in equation I, D is

the minimum diameter in the test section in inches, T is the torque in

inch-pounds, and Z 1 is the section modulus based on the polar moment of

inertia in inches cubed. In order to conform to Peterson's stress con-

centration factors, figure 10, the stress in the specimens with the trans-

verse hole was computed from

**=-£= *£*& *>*> fr),/6 6

where d is the diameter of the transverse hole. Equation (IV) is approxi-

mate, but it is considered sufficiently accurate for these tests.

In view of the excessive scatter that results from too many variables

involved in the tests [_3j , care was taken to maintain uniformity. As

indicated previously, all specimens were taken from four bars that were

certified to be from the same heat. Precautions were f'-»<en in maintaining

uniform times, temperatures, and techniques in heat treatment. The machin-

ing,, polishing, and drilling were carried out in such a manner that the

specimens of each particular type were as nearly identical as the skill of

the machinist would permit. Precautions were taken in testing the speci-

mens to insure that there were no undesired stresses applied, such as pre-

load, tension, or bending, which would create non-uniform testing conditions,

In spite of precautions, certain irregularities were evident such as

19

the variation in hardness of the heat treated specimens, slight varia-

tions in surface finish, and differences in minimum diameter between

specimens. One of the causes of these variations is the improvement in

technique by the machinist and the heat-treater between the first and

the last specimens. This source of variation could be minimized if a

machinist were fabricating these types of specimens in sufficient quant-

ity to acquire a stable level of skill. The same holds true of the man

doing the heat treating, or better still an automatic heat treating de-

vice would give readily reproducible strength and hardness.

20

4. Results and Discussion

In the presentation of experimental data, it is considered desir-

able to include where possible theoretical values or empirical data for

the purpose of comparison. Figure 10 £lj shows the theoretical stress

concentration factor for various values of d/D for a shaft with a trans-

verse holeo This gives a theoretical stress concentration factor of

approximately 1.73 for the specimens with 1/16- inch holes. The notch

sensitivity factor of the specimen with a 1/16- inch hole is about 0.97

for quenched and tempered steel as based on Peterson's curves |lj Be-

cause the factor is nearly one, a factor of unity is used. Experimental

curves giving stress concentration factors due to the rough surface fin-

ish are. shown in figure 11 [_4J , With the specimens indicating a Brinell

hardness of about 350, a machined finish has a stress concentration factor

of about 1.33. Although the smooth specimens are not mirror polished,

they are so nearly so that no stress concentration factor is considered

necessary.

The above predicted values of stress concentration factor compare

favorably with those obtained from the 50% survival S-N curves of figure

12 „ The comparison is made at 10 cycles which is approximately the endur-

ance limit of this material. The comparison between smooth and rough speci-

mens gives a stress concentration factor for the machined finish of l»31s

compared with the predicted value of 1.33. The stress concentration fac-

tor for the smooth specimen with a transverse hole appears to be about

1.83 from a comparison of S-N curves at 10 cycles. This is reasonably

close to the 1.73 value predicted. Table A presents the comparison be-

tween predicted and actual stress concentration factors for the various

configurations in tabular form.

21

TABLE A

Specimen

Type (a)

Stress Concentration Factor

Predicted (b) Actual|

Rough finish (2) 1.33 1.31

1/16-inch hole, smooth (3) 1.73 1.83

1/16- inch hole, rough (4) 1.33 x 1.73 » 2.30 1.83

1/4- inch hole, rough—

1.33 x 1.44 = 1.92 1.74 (c)

(a) Numbers refer to the basic configurations described in section2, and illustrated in figure 3.

(b) For the combinations of stress raisers the factors were multi-plied together to obtain a conservative and recommended [_4]]

stress concentration factor.

(c) This figure was calculated from the S-N curve of the smooth speci-

men and the one 507o survival point plotted for the rough speci-mens with a 1/4- inch transverse hole. The 50% survival datawere compared at the 3 x 10 cycle life rather than at 10 cycles,

As may be observed in figure 12 and other typical log log presen-tations of S-N curves £4 J , where stress rai' <rs are present theslope of the S-N curve is generally steeper than that of a stan-

dard smooth specimen. Therefore, the actual stress concentra-tion factor at 10 cycles may be expected to be somewhat greaterthan the 1.74 recorded; perhaps it may compare closely with 1.92.

The curves plotted in figure 12 represent the number of stress cycles

that 50% of the population would survive at a particular stress level.

They are fitted to the medians of the groups at the several applied stress

levels. The median, an "order statistic", is the middlemost value when the

observed values are arranged in order of magnitude, or the average of the

two middlemost values if the group size is even.

This procedure for analysis of data was adopted from ASTM STP 91-A

[2 ^ • The following statement is quoted in reference to the above proced-

ure :

22

These techniques should be used when the actual shape of thedistribution of fatigue life values for a material is unknotor sketchy, and the number of specimens tested at each appl;

stress level is too small, say less than 50, to estimate theshape of the distribut ion„ In such cases these techniques giveconservative results.

Figure 13 shows the probability-stress-cycle curves for one con-

figuration. These percentages represent median percentages of survivors

for the population and are based on the number of specimens tested at

h stress level. They are called "median percentages" because 50%

of the time the true percentage will be larger and 5078 of the time it

will be smaller; i.e., the confidence level is 50%. Considering the

limited number of specimens tested at each stress level and considering

the objectives of this project, we conclude that the information to be

obtained from this graphical presentation is limited. Therefore^, no

attempt has been made to compare the fatigue life of the various con-

figurations by use of other than the 50% survival curves.

23

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One of the notable variables of the specimens is the hardness . To

further examine this arc a bar chart showing hs

of hardness within ge of 0.5 points on the Rockwell "C" scale, fig-

ure 16= The bar < urally lite follow the normal bell

oed distribut . clor.e as could be expected

with the I 1 number of specimens (a total of 72), There is only one

group for which ir. is obvious that hardness may have had an effect on the

507c survi >int, namely the standard smooth specimens tested at 55,000

psi sAppendix A, Table I. Specimens A- 12 and A-13 were three and four

Rockwell "C" points softer tl.an the other two and they failed significant-

ly earlier than the harder two„ This in itself would not be significant

considering the wide scatter that can be expected when testing in the

vicinity of the endurance limit of a material; but the 50% survival point

obtained from the group tested at 55,000 psi falls significantly below the

507o survival curve for the stsi imooth configuration.,

There are two points along the S-N curve for the standard smooth

oimens, figure 12, that were obtained from the seven cut-down speci-

mens mentioned on page 9„ Some factors that may have effected the strength

of these smaller specimei e: the Kockwell "C" hardness is about, two

points lower than the larger ^r.s; the size effect gives a slight

stren to th acimens [_4j ; understressing for 5

Hon cycles may have ha<i ^thening effect. These effects ap-

parently cancelled each oth e the points mentioned above agree

closely with the curv; om standard size specimens.

5. Conclusions

In evaluating results obtained from fatigue testSj, one recognizes

that the analysis is of a statistical nature. Furthermore, the applica-

tion of statistical methods to the analysis of the test results of certain

configurations offers a means only for estimating the characteristics of

the aggregate of these configurations jjT] .

In light of the above statements, the following conclusions are drawn

from the results obtained in this project (see Table A8page 22):

a. The stress concentration factor for a round specimen with

a rough surface finish, type 2, subjected to reversed stresses in torsion^

is verified to be approximately as predicted from figure 11,

b c The stress concentration factor for a round specimen with a

1/16-inch hole, type 3 S subjected to reversed stresses in torsion9

is

verified to be approximately as predicted from figure 10.

c. The actual stress concentration factor , for a 1/16- inch

hole and a rough surface finish combined, is not as great as would be pre-

dicted by multiplying the two individual stress concentration factors to-

gether., In the case in which the stress concentration factor for the hole

was considerably greater than that for the rough finish9 it is possible

that the larger stress raiser predominates* The major effect of the

rough surface finish in this combination appears to be to hasten the

failure once a crack has started. This effect may be observed in figure

17 by comparing curve 2, which was taken from a smooth specimen,, with

either of the other three8which were obtained from rough specimens.

do The actual stress concentration factor for a 1/4- inch

hole and a rough surface finish (as indicated from a very small number

of tests) is somewhat less than the value predicted by multiplying the

two individual stress concentration factors together^ but it appears

that the total effect is more nearly equal to the product of the fac-

tors than is true for the smaller hole and rough surface,

e. If the indications in paragraph c above are correct 8 it

seems that where two stress raisers appear at a point and one stress con-

centration factor is considerably larger, the larger one tends to domin-

ates, am* tne effect of the smaller stress raiser will be less than its

stress concentration factor would indicate. Perhaps applying a stress

concentration factor obtained from that of the larger stress raiser in-

creased by 107o would give a good prediction for this combination. Also 8

if the indications in paragraph d are correct, it seems appropriate for

conservative design to multiply the stress concentration factors together

to obtain a prediction of the effect of two stress raisers of similar

value acting together at a point.

The tool marks or scratches which constituted the rough machine fin-

ish on specimens used in this project were all circular,, No attempt was

made to determine the effect of a similar finish consisting of longi-

tudinal scratches. Howevers there is information in the literature [5j 9

[6} comparing the effects of circular versus longitudinal scratches under

various conditions of stress,,

It is recommended that further studies be conducted on chis problem

using a wide variety of stress raiser combinations in bending and push-

pull loads as well as torsion, to ascertain whether the indications of

these tests are valid 9 whether they are applicable to stress raiser

34

combinations in general, and whether the proposed methods of predicting

stress concentration factors are applicable to bending and push-pull

loads as well as torsion,,

It is further recommended that if future tests are to be made on

the Baldwin Universal Fatigue Testing Machine,, the problem of failure

criterion discussed in Appendix B be considered. Proper consideration

in specimen design can provide sufficient allowance for amplitude change

before cut-off to prevent the artificial failure conditions experienced

in this project

o

35

6, Bibliography

lc R. E. Peterson, Stress Concentration Design Factors, John Wiley &Sons, Inc., New York, 1953.

2„ ASTM STP 91-A, A Tentative Guide for Fatigue Testing and the Statis-

tical Analysis of Fatigue Data, American Society for Testing Materials,

1958.

3. F„ A. McClintock, A Criterion for Minimum Scatter in Fatigue Testing,Journal of Applied Mechanics, Transactions ASME, Vol, 22, pp 427 - 432^

September, 1955.

4o V M. Faires, Design of Machine Elements, 3rd Edition, MacmillanCompany, New York, 1955.

5. W„ N. Thomas, Effects of Scratches and of Various Workshop FinishesUpon the Fatigue Strength of Steel, Engineering, Vol. 116,, 1923,

pp 449-454, 483 - 485.

6. L. P. Tarsov, W. S. Hyler, and H. R. Letner, Effects of GrindingDirection and of Abrasive Tumbling on the Fatigue Limit of HardenedSteel, Proceedings ASTM, 1958, pp 528 - 539.

7. W. Weibull and F. K. Odqvist, Colloquium on Fatigue, InternationalUnion of Theoretical and Applied Mechanics, Stockholm, May 25-27,

1955.

8. The Institution of Mechanical Engineers, International Conferenceon Fatigue of Metals, London, 1956.

9. No Thompson and N, J. Wadsworth, Metal Fatigue, Advances in PhysicSj,

Vol. 7, January 1958, pp 72 - 170.

10. H. J. Grover, S„ A. Gordon, and L. R. Jackson, Fatigue of Metalsand Structures, NAVAER 00-25-534, 1954.

11. J. M. Lessells, Strength and Resistance of Metals, John Wiley &Sons, Inc., New York, 1954, pp 161-280.

12 o E. Siebel and M. Gaier, The Influence of Surface Roughness on theFatigue Strength of Steels and Non-ferrous Alloys, The Engineer'sDigest, Vol. 18, March 1957, pp 109 - 112.

36

APPENDIX A

GOSB

HOWPMCO

PCHOoS

g<hw

011-1

a 3QJ i—l

a. ••-(

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to 4-1

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Table 1

37

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PQ •<-< a, i-i

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Table 1

38

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Table 1

40

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41

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42

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44

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Table 5

47

APFEMDIX 3

Machine Difficulties

A few minor difficulties were experienced in testing the large tor-

sion specimens. The high torque required to cause the solid specimens

to fail taxed the ability of the collets to grip the specimens without

allowing slippage. Difficulty was experienced early in the tests with

specimens fretting in the collets. This fretting resulted in fusion of

metal from the specimen onto the collets causing their inner surfaces to

become rough. The rough surfaces in turn permitted only small areas of

contact with the specimen, thereby increasing the fretting and fusion and

eventually rendering the collets useless. They were repaired by a honing

operation, rotating the collects on a 1-1/2- inch brass rod to which grind-

ing compound had been applied. Once the collets were restored, further

fretting was kept to a minimum by applying greater torque during tighten-

ing.

During the latter portion of the testing period, the machine was at

times considerably noisier than normal. Although the increased noise

pointed to the possibility of a faulty bearing in the torsion fixture,

since it was intermittent and no variation in vibration amplitude was

lent, <-ests were completed without dismantling the fixture. There are

no indications that the noisy operation affected the fatigue life of the

specimens tested under those conditions.

The failure criterion used with this machine created a discrepancy

in the number of cycles to failure between the tests at maximum and min-

In the race of maximum load tests, the limit switches cut

off the motor and the specimen was considered to have failed after an

48

increase in amplitude of vibration of perhaps 0.02 inches. However^ with

the minimum load tests, the initial amplitude of vibrations was much lower

and allowed an increase in amplitude of perhaps 0.22 inches before the

machine was stopped by the limit switches. In an attempt to analyze this

problem, several specimens were observed and data recorded during the fin-

al stage before failure. The curves of amplitude versus increase in

number of cycles (figure 17) are of an exponential nature, thus minimiz-

ing the adverse effect of this artificial criterion of failure. From ob-

servation of many specimens, it was noted that there is no appreciable am-

plitude change until the final stages of fatigue failure.

No correction has been applied to the test data of this project,

since any factor applied would be of questionable reliability. The number

of cycles from a change of amplitude of 0.02 inches, which was the minimum

increase in amplitude for failure at high loads, to failure of lightly

loaded specimens varied from 41,000 cycles for curve 2 of figure 17 to

10., 500 cycles for curve 1.

49

APPENDIX C

Sample Calculat ions

Equations III and IV, page 19, permit calculation of the nominal

shear stress ( f ) when other factors are known. Calculations were

made to determine the force (P) to be applied to obtain a desired

nominal shear stress. For these calculations equations III and IV were

rearranged as follows:

Specimen A-4 (Equation III)

r _. /S/°/?

rr O 3

_ //

D

3

- (3Jf)C?3?mf(S2i.bOO £p)

f/6J ( /S<2S/o)'

= S60 /6s

Specimen A- 17 (Equation IV)

PPT =

r> _ XfrrO3__ o/0_

2

)r - /p (~76~ 6 /

_ 3X000 T7T* f (3J4)C?3&"?f _ CO&SiXtet*?'

/5,25<n \_ /6 &

= 3*9 /6s

Determination of the 50% survival value from each group of speci-

mens tested at the same stress level is done by taking the middle most

value of fatgue life when the group contains an odd number of specimens

M

or, as was the case for most of the groups tested in this project,

taking the average of the two middlemost values if the group size is

even

.

EXAMPLE: Group of standard smooth specimens tested at 57,500 psi.

Specimen No . Cycles to failure

C-15 146,000

C-13 358,000

B-18 790,000

B-21 5,000,000 (no failure)

358,000 + 790,000 = 574,000 cycles2

52

thesG863

Effect of two stress raisers acting toge

3 2768 002 13578 2DUDLEY KNOX LIBRARY

of two raisers - internet archive

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