Brigham Young University BYU ScholarsArchive All eses and Dissertations 1962-8 A Literature Review Covering the Effect of Residual Stresses on Fatigue Strength of Steel Clarence A. Calder Brigham Young University - Provo Follow this and additional works at: hps://scholarsarchive.byu.edu/etd Part of the Mechanical Engineering Commons is esis is brought to you for free and open access by BYU ScholarsArchive. It has been accepted for inclusion in All eses and Dissertations by an authorized administrator of BYU ScholarsArchive. For more information, please contact [email protected], [email protected]. BYU ScholarsArchive Citation Calder, Clarence A., "A Literature Review Covering the Effect of Residual Stresses on Fatigue Strength of Steel" (1962). All eses and Dissertations. 7080. hps://scholarsarchive.byu.edu/etd/7080
Transcript
Brigham Young UniversityBYU ScholarsArchive
All Theses and Dissertations
1962-8
A Literature Review Covering the Effect of ResidualStresses on Fatigue Strength of SteelClarence A. CalderBrigham Young University - Provo
Follow this and additional works at: https://scholarsarchive.byu.edu/etd
Part of the Mechanical Engineering Commons
This Thesis is brought to you for free and open access by BYU ScholarsArchive. It has been accepted for inclusion in All Theses and Dissertations by anauthorized administrator of BYU ScholarsArchive. For more information, please contact [email protected], [email protected].
BYU ScholarsArchive CitationCalder, Clarence A., "A Literature Review Covering the Effect of Residual Stresses on Fatigue Strength of Steel" (1962). All Theses andDissertations. 7080.https://scholarsarchive.byu.edu/etd/7080
Department of Mechanical Engineering Brigham Young University
In Partial Fulfillment
of the Requirements for the Degree Master of Science
Clarence A. Calder August, 1962
This thesis,, by Clarence A. Calder^ is accepted in its present form by the Department of Mechanical Engineering of Brigham Young University as satisfying the thesis requirement for the degree ofMaster of Science.
ACKNOWLEDGEMENTS
The author wishes to acknowledge the suggestions and the guidance of Dr. Cliff S. Barton during the course of this thesis. The
encouragement and advice of Dr. Richard D. Ulrich is also appreciated.
To my wife, Judy, I express my gratitude for typing this thesisand for her patience and encouragement
5. Finite life Goodman D i a g r a m .......................... 126 . Overstress and final rupture location ................ 13
7 • S-N curve for high temperature ...................... 15
8 . Endurance limit versus ultimate strength for cast andwrought steels ....................................... 16
9. S-N curve-Influence of residual stresses for an aluminumalloy ............................................... 20
10. S-N curve illustrating corrosive effect of air on iron . 2111. Goodman Diagram and residual stresses ................ 2612. Summation of applied and residual stresses ............ 2713* Stress conditions at decreasing depths plotted on a
2 5. Residual stresses induced by tensile,compressive, andconventional shot peening of leaf s p r i n g s .......... . 56
26. Effect of straightening crank shafts on the fatigue life 58
27. S-N diagram for rolled and not rolled railway axles . . 5928. Effect of peening intensity on fatigue l i f e .......... 6029. Increase of fatigue strength by shot blasting on 0.1+5
30. Endurance limit as a function of peak residual stressnear the test s u r f a c e ................................... 62
CHAPTER I
INTRODUCTION
Fatigue fracture usually is defined as the failure of a part at
a stress below its breaking stress due to repetitive loading conditions. It is now a well known fact that a part, designed for a maximum stress well below the yield point of the material, may be very apt to fail
■under cyclic loading conditions over a period of time. The metal appears to "wear out" after a time just like humans do and fatigue failure occurs. Metal fatigue may be contrasted to animal fatigue in that l) its
detection before the latter stages is normally difficult if not impossible, 2 ) the condition is not dissipated by recovery, and 3 ) damage is cumulative.
Men associated with automotive and aircraft industries have stated that from 80 to 95 per cent of all failures brought to their attention were caused by fatigue failure.(l) Thus, it is easy to
understand the vast increase in research in this area the last few years.
I. THE OBJECTIVEThe purpose of this study was to present a literature survey
and research on the problem of fatigue of metals, and in particular, the effect of residual stresses on fatigue properties. It is hoped
that this study, together with the bibliography presented, will be a guide and aid to future experimentation and research in this field.
1. Numbers refer to list of references
II. TERMINOLOGYAs there is often some confusion in the terminology of fatigue
and strength of materials, the following terms applicable to this thesis are defined. Most of the strength of materials definitions have been condensed from and are explained more fully in reference 2 and other
’strength of materials” books. The fatigue nomenclature was standardized by the American Society for Testing Materials in their "Manual on Fatigue
Testing" (3) in 19^9• Since then most fatigue work has utilized these symbols and definitions.A. Elastic Strength- A limiting stress below which the permanent distortion of a material is so small that the structural damage is negligible, and above which it is not negligible.
Some indexes of elastic strength are:1) Elastic Limit- The greatest stress which a material is capable of developing without a permanent set upon complete release of the stress.
2) Yield Point- The stress in a material at which there occurs a marked increase in strain without an increase of applied stress.3) Proportional Limit- The greatest stress a material can withstand and still remain linear with strain. (Hooke's Law)
I
U ) Yield Strength- The stress at which a material exhibits a specified limiting permanent set.
B. Ultimate Strength (Su or UTS) The maximum computed stress which a material is capable of developing under a slowly applied load.
C. Ductility- The capacity of a material for taking plastic deformation in tension without rupture. Usually measured by the 'percentage of elongation", or by the "percentage reduction in area".D. Elasticity- The capacity of a material for taking elastic (recov- erable) deformation.
E. Stiffness- Resistance to deformation caused by stress.The most common indexes of stiffness are:
1) Modulus of Elasticity- Commonly called "Young's modulus", is evaluated as the slope of the stress-strain diagram below the
proportional limit.
♦
3
2) Secant Modulus of Elasticity- This is evaluated as the slope of the stress-strain curve above the proportional limit. It is of use in plastic deformations.
F. Hardness- The capacity of a material to resist penetration, abrasion, etc.
G. Fatigue- A fracturing process which begins and spreads progressively under repeated stressing of much less severity than that required to cause fracture under a single load application.
1) Fatigue Strength- The ability of a structure to withstand repeated loading— usually it signifies the greatest stress which can be sustained for a given number of stress cycleswithout fracture. a.
/ 0% ^ -'
2) Fatigue Endurance Limit (Se ) (Often shortened to fatigue *\s limit or endurance limit) The critical stress below which the specimen can presumably endure an infinite number of stress
Figure 1. Cyclic stress systems end symbols.See Figure 1 for a graphical definition of the following terms.3) Maximum Stress (SMax) The highest algebraic value of the stress in a stress cycle, tensile stress being considered positive and compressive stress negative.
U) Minimum Stress (Sjjin) The lowest algebraic value of the stress in a stress cycle.
5) Range of Stress (s) The algebraic difference between the maximum and minimum stress in one cycle.6 ) Alternating Stress Amplitude (Sa ) One half the range of stress.
7) Mean Stress (Sm) The algebraic mean of the maximum and minimum stress in one cycle.
8 ) Stress Ratio (R) The algebraic ratio of the minimum stress to maximum stress in one cycle.
k
III. HISTORICMan first began to recognize the phenomenon of metal fatigue
about the middle of the 19th Century. This had undoubtedly come
about with the machine age and the corresponding use of metal components under dynamic loading conditions. Prior to this time, few occasions arose with failure due to fatigue.
August Wohler is generally credited as being the "father of fatigue". He invented the first fatigue testing machines which were very much like the ones in use today. Some authorities (4) believe
that, essentially, not much has been accomplished in the area of fatigue in the one hundred years since Wohler*s time. Actually, not much was done in fatigue research until the early 1900's when interest in fatigue
suddenly increased rapidly. Undoubtedly, this was greatly influenced by the advent of the airplane and automobile.
Since the 1900's there has been a voluminous amount of material published on the subject of fatigue failure. Considering the many parameters affecting fatigue life of a machine component, this is certainly understandable. Most fatigue research has been experimental
work in trying to establish definite criteria for the effect of a variable or a combination of variables on the fatigue life of a specimen.
One can easily see the many problems encountered in trying to determine the effect of a single variable on fatigue strength, without other variables entering into the results.
In general, fatigue testing may be divided into two areas: lowcycle, and high cycle fatigue. Work in the former has been confined to the last few years and presently not much is known about it. The low cycle area concerns experimental fatigue testing where failures
5occur in a low number of cycles. The upper limit for low cycle fatigue testing is classified as high cycle fatigue, or in other words, fatigue testing where failures occur after passing 10^ cycles of repeated loading. It is in this area that the great amount of work in fatigue has been done and with which this study is concerned.
About 90 per cent of all fatigue testing to date has been done with rotating beam type of testing machines*, much like those first used
by Wohler.(5 ) The fatigue specimens act as the beams and are rotated mechanically with a load on one end (cantilever type) or loaded at two
points equidistant from the mid-span of the beam (simple supported type). In either case, the outer fibers are the only part of the specimen
reaching a maximum and minimum stress. This is reached in a sinusoidal fashion as the beam rotates. Other testing machines include the social load type and torsion load type. By preloading the specimen any
combination of maximum stress and mean or average stress within the limits of the testing machine may be obtained.
As most industrial fatigue failures occur through stressing in
cycles of alternating tension and compression (6 ), the great majority of testing has been with this type of repeated loading. Also, it has been fairly well established that fatigue failure occurs more rapidly
under this loading than any other.
CHAPTER II
FATIGUE FAILURE THEORY From inspection of fatigue fractures it is generally believed
that failure occurs in three stages: l) the start of a crack, spreading
out from some nucleus; 2 ) propagation of the crack under successive cycles of loading; 3 ) final rupture of the piece when the spreading crack has weakened the section. Most efforts in developing a fatigue
theory have been devoted to the first stage of crack initiation. The major problem is how a crack can start at repeated stress levels lower than the ultimate or rupture strength of the material.
A common belief is the existence of high stress concentrations due to such conditions as surface irregularities, abrupt changes in cross-section, or residual stress which, when added to the applied
stress, exceed the ultimate strength in a localized area and rupture occurs. This belief has led to a large amount of testing being done
with "notched" specimens to create a high stress concentration. Many
authorities believe that research with this method is of little value, mainly because the magnitude of the actual stress is uncertain.
J. 0. Almen (7) states that generally fatigue failures are due to high tensile stress concentrations with the crack propagation initiating at the surface. Most research and experimental data uphold this point very well. There is definitely some evidence of compressive
failures ( 6 , 9 )<> but the experimenters admit the extreme difficultyin attaining it. Almen (7) also points out a case in which fatigue
7cracks formed in a metal that was apparently subjected to compressive stress only, but actually they formed from a residual tensile stress that was produced by yielding in compression.
Many more complicated theories of fatigue failure have been developed the last few years. All of them, in general, require simplifications that often do not hold for a particular case. Machlin (10)
has developed a mathematical theory on fatigue failure that depends on stress, temperature, material parameters, and frequency for annealed solid solutions only. He states the theory agrees with experimental
data but admits much additional data are needed to completely verify the theory.
In his article in '‘Engineering" Kennedy (k) rebukes engineers
for their little knowledge of fatigue as compared to dynamics, electricity, and metallurgy, and for "their contentment to rest on a bed of S-N curves". He believes the fixed pursuance of the S-N test, and the use of the data which it provides has been a sterile strategy in fatigue analysis. Its use in design has value for specific conditions but the philosophy of the system is one of Jtbreak it and see". Using fine
testing machines, stress and temperature conditions of great stability, and specifically prepared test specimens, high reproducibility is
achieved in the laboratory, from which the material behavior is described. Then the data are of such limited direct application that interpolations
and extrapolations abound, and the approximations make nonsense of the test laboratory precision.
Many theories exist, but up to the present there is no wholly satisfactory explanation for the reason why an alternating stress can develop a microcrack in a crystal lattice. Kennedy believes that crystal
defects such as vacancies or dislocations must be involved* and that it should not be assumed that fatigue can be made simple if only once
it could be understood.Despite Kennedy's opposition to relying on S~N curves* they
still remain (together with the Goodman diagram) the best apparent
method of explaining and designing for the fatigue phenomenon. Until someone develops something better for describing fatigue* the future work in this area will still utilize the S-N curves and Goodman diagrams
I. S-N CURVEThe S-N curve* a plot of maximum applied stress versus cycles
to failure* is explained in most mechanical properties books. In
Chalmer's book (11) the S-N curve has been started at zero cycles for the ultimate strength and carried out to where the curve remains
essentially flat as shown in figure 2a.
(b )
Figure 2. Typical ferrous and non-ferrous S-N curves.
The flat part of the curve is termed the endurance limit and below this stress* failure should never occur due to fatigue. This is a general curve for most ferrous metals. A similar curve for some non- ferrous metals as aluminum and magnesium, figure 2b* often does not
show such a distinct endurance limit. At the present* this difference
9in S-N curves for ferrous and non-ferrous metals has not been explained. It is thought that the ferrous curve is normal and the non-ferrous curve
is really due to a combination of fatigue and corrosion effects. For cases where it is not entirely certain that the S-N curve becomes completely flat, it is common practice to define an endurance limit at
some arbitrary, long lifetime.Most S-N curves are not plotted in the 0 to lCp cycles range
because there is a surprising lack of information in this area. As mentioned previously, this is called the low cycle fatigue area requiring applied stresses above the yield point.
The endurance limit is determined from S-N data and is a statis
tical evaluation. Any stress applied to the specimen will either be above or below the endurance limit regardless of how close it may be.
?- W. A. Hijab (12) presents and compares two successful statistical techniques used for endurance limit determination.
Approximations to the number of cycles normally required todetermine the endurance limit are given by Churchill (l) for various
xmetals. Steel requires from about 500,000 for hard, to 5X10° for very
7soft steel, with cast steel or iron requiring at least 101 cycles. Non- ferrous metals may require anywhere from one to several hundred million
cycles to determine their endurance limit. At least twelve dependable tests are required for an S-N plot. Some specimens, depending on speed
of testing, may take up to several days of continuous testing to reach
failure, or assurance that the stress is below the endurance limit.Thus, much time is required to obtain a reasonably reliable
S-N curve and corresponding endurance limit. No short-time test has
been developed yet, but special correlations have been found between
endurance limit and such properties as hardness, proportional limit,
and ultimate strength.
10
II. GOODMAN DIAGRAM
When endurance data of a proposed design are not available, the
permissible cyclic stress and superimposed steady stress may be estimated by a graphical method called Goodman's diagram. The diagram is
an approximation of the effect on fatigue when the mean stress is not zero. Goodman first proposed the straight line relationship shown in figure 3> ^ut since there have been many changes and modifications to
obtain a more optimum fatigue design diagram.
Figure 3* Goodman Diagram.
The straight line Goodman diagram is based on design for infinite life and is generally considered as conservative. The ultimate strength
is based on static tensile tests of the material and the endurance limit determined from an S-N curve of reversed cyclic loading (mean stress equal to zero). If no fatigue data is available, the endurance
11limit is often approximated as one-half of the ultimate tensile strength. However, some authorities use one-third of the UTS.(13, 1^)
Another form of the Goodman diagram is shown in figure 4. It
is actually the same diagram except it represents the upper half of the triangle of the original diagram, the part above the mean stress line.
This gives a direct plot of stress amplitude ( l/2 Sr ) versus mean stress. *
Figure 4. Goodman Diagram (modified).For use in design, the Goodman diagram is usually modified to
suit the designer. Most modifications are aimed at making the diagram
more conservative, such as the use of a factor of safety on the endurance limit and TITS, or replacing the UTS with the yield point. Gina (6 )
found that better correlation with fatigue test results was obtained by using the true fracture stress value in place of the usual UTS (nominal
stress fracture).The Goodman diagram is often used for finite life fatigue design
when experimental fatigue data are available. Grover (13) shows an illustration of both Goodman diagrams with fatigue data of finite life plotted on them. These are shown in figure 5.
12
Figure 5. Finite Life Goodman Diagrams.
III. FRACTURE EXAMINATION
Fractures of metals are usually classified as either ductile or "brittle fractures. A ductile failure is usually obvious with the observance of a necked-down section, or evidence of gross plastic
deformation caused by static overload. Brittle failures are fractures in which necking-down or large plastic deformations are not apparent.A fatigue fracture of this kind is often termed a brittle fracture.
Some brittle fractures are not caused by fatigue; so it is often difficult to distinguish between a brittle fracture and fracture of a
brittle material under a tensile load.
Not only the level of loading, but also the type of loading (tension, bending, or torsion) and environmental conditions (temperature, corrosive surroundings) influence the final appearance of a fatigue fracture. Consequently, it is difficult to determine any
characteristic appearance of a fatigue fracture.In general, a fatigue fracture shows two regions of distinctly
different appearance: l) an area with a ground or rubbed smooth sur-
face, and 2) a region of more jagged surface texture. The first region represents the spreading of the fatigue crank across the section. The
region of more jagged surface texture represents a final tensile fracture after the crack has greatly weakened the section.
Peckner (15) states that by examining the fatigue surfaces—
either macroscopically or microscopically— and by proper interpretation, it is possible to determine the origin of a fracture and the degree of
overstressing that prece des failure. By testing round specimens in fatigue bending, Peckner found that a relation exists between the amount of over-stress and the distance of the final rupture area from the center. This relation is shown in figure 6 . Similar results are given by R. E.
This curve shows how the final rupture area shifts with stress
level. If the final rupture area is close to the bar surface, the amount of overstress is slight. As the overstress increases, the rupture area
moves to the center. Thus, the engineer is able to determine the major design modifications necessary. It was also noted that a centrally located rupture will probably fail in less than 300,000 cycles, whereas,
several million cycles are needed to cause near peripheral rupture
areas in the specimen.
CHAPTER III
CONDITIONS AFFECTING FATIGUE STRENGTH
There are numberous factors which directly affect the endurance
limit or fatigue strength of a metal. The Goodman diagram gives an indication of the effect of the type of stress loading, and it has already been noted that fatigue fracture will probably begin at a local
ized area of high stress concentration. Other factors commonly accepted as influencing fatigue failure, of which some are interrelated, are
residual stresses, corrosion, frequency, size, and load history. Present knowledge on these factors is briefly outlined with some selected references for each section in the bibliography. I.
I. TEMPERATUREMuch research is presently being done in the areas of high and
low temperature fatigue to determine the effect of temperature on the
endurance limit. Other factors, such as structure changes and metal creep, conplicate the problem and make it difficult to separate the effects on fatigue.
Young (17) stated that the data available on steels at low temperatures indicated a higher endurance limit than at room temper
atures. It was noted that the tensile strength increased with a
decrease in temperature also, strengthening the validity of the relation between endurance limit and tensile strength.
15A moderate elevation in temperature has only a minor effect on
the endurance limit, and can actually increase it by allowing plastic deformation when the metal might otherwise crack. Tests on 0 .1*4- per cent carbon steel showed a decrease of 9 per cent in static tensile strength at 750 °F, but had an increase of 16 per cent in the 10 million cycle fatigue strength at the same temperature.
Creep complicates the very high temperature fatigue properties,
but the endurance limit is definitely lower than at room temperature.It is thought that tests, in which the stress is completely reversed
(alternating) during each cycle, give a good indication of fatigue
strength independent of the creep phenomena. Figure 7 was taken from reference 13 and illustrates the decrease in endurance limit at high temperatures of an alloy.
Figure 7. S-N curve for high temperature.
II. MECHANICAL PROPERTIES16
Considerable effort has been expended in attempts to correlate
fatigue strengths of metals with other engineering properties such as tensile strength, yield strength, hardness, and proportional limit. For some materials such as steel, there appears to be a correlation between fatigue strength and tensile strength. For the most part, however,
attempts at finding correlations between fatigue strength and other engineering properties have been unsuccessful.
A plot of endurance limit versus ultimate tensile strength for cast and wrought steels in figure 8 shows why an approximation of the endurance limit equal to one-half the UTS is fairly good for steels.
However, most alloys do not maintain the one-half ratio at the higher tensile strengths.
Figure 8 . Endurance limit versus ultimate strength for cast and wrought steels.(l8 )
Dolan (1 9) states that the fatigue ratio for steels (endurance limit to UTS) is one-half up to a UTS of around 200,000 psi. Above that point the ratio drops below the one half level. In general, it can
17be stated that the fatigue ratio varies from 0.^0 to 0 .6 0 for steels.
There is also some evidence that the endurance limit of a metal
particularly of steels, bears an approximate linear relationship to Brine11 hardness for polished specimens up to a very high hardness, where the correlation ceases to remain linear.
III. C0MP0STX0NIt is now generally accepted that alloy content of steels, other
than carbon, has little if any effect on fatigue life. Some other metallurgical variables, including carbon content, do have a definite effect on fatigue properties. Work by Frankel, Bennett, and Pennington
(20) has confirmed the belief that retained austenite in the micro-
structure has a detrimental effect on fatigue. Their experimental results showed that an increase in retained austenite decreased the fatigue strength up to a carbon content of 0 .6 0 per cent , beyond
which increased austenite seems to have little effect. Removal of retained austenite by refrigeration or fatigue stressing of a certain stress amplitude tends to increase fatigue strength] indicating a
superiority of tempered martensite micro-structure. On the same subject, Unterweiser (21) wrote that some of our strongest steels have
failed in fatigue because they tend to retain some austenite after heat treatment. These steels are leading the lists of popularity for ultra-high-stress service. He pointed out that steels less prone to
austenite retention should now become more popular than in the past.Recently, work has been done to point out the importance of
case depth in carbo-nitrided steels.(22), (2 3) Tests showed fatigue life was increased by a factor of twenty when case depth was increased
from 0 .0 3 0 to 0.01+2 inches.
IV. SURFACE CONDITIONS18
In general, stresses usually reach their maximum value at the surface of the metal due to the existence of some torsion or bending stresses. By recognizing that the surface metal is normally weaker
than the core, it is easy to understand why most fatigue failures start
at the surface. There has probably been more work done on surface effects than all other areas of fatigue study combined.
Surface conditions can affect the fatigue life of a metal in two ways; l) stress raisers exist due to surface roughness caused by the mechanical finishing process; and 2) a strength difference exists
between the outer shell and the core of the material. Moore and Kommers
(24) rotating beam tests on 0.49 per cent carbon steel showed a definite decline of endurance limit with increase of surface roughness, as shown
below in order of increasing surface roughness.SURFACE FINISH ENDURANCE LIMIT,- prariHigh polish 50,500Standard polish 49 ,000Ground 45 ,0 0 0Smooth turned 43 ,000Rough turned 41 ,500
It should also be noted that mechanical finishing processes usually produce detrimental tensile residual stresses. This area is
covered in the following subsection and in the main body of this thesis.It has been pointed out that the fatigue limit of a steel
normally increases with its ultimate strength. Consequently, a material whose shell has an ultimate strength greater than the core should show a longer life than the basic core material, and conversely, for the core having the greater ultimate strength. Investigations have found this to
v /
be true.
19Such surface hardening processes as carburizing, nitriding,
induction hardening, cyaniding, and flame strengthening increase surface hardness, tensile strength, and correspondingly, the fatigue strength.As would be expected, processes weakening the surface decrease fatigue strength of a material. These include decarburizing and various electro
plating processes.
The presence and magnitude of tensile and compressive residual stresses has been found to have a very large effect on fatigue properties
of metals, particularly of steel. Residual stress formation is classified by Horger (2 5) as originating by three general methodst
1) Mechanical- cold working from shot peening, rolling, cold drawing, and various machining processes.
2) Chemical- nitriding and electrodeposition as in chrome plating, anoding, etc.3) Heating or cooling- such as occurs in heat treating, surface hardening, or various welding operations.
Residual stresses of type (l) and (3 ) are produced when a nonuniform plastic deformation occurs in different zones through the
cross-section of the part. Often the higher degree of plastic strain
is produced in the surface layers, leaving high residual stresses localized at or very near the surface. These residual stresses have a profound effect on the fatigue strength of the part. Many authorities (2 6) believe that the discrepancies in a large amount of past fatigue work have been in the failure of the experimenter to accurately determine existing residual stresses during testing and just prior to fail-
Fatigue failures are generally accepted as tensile surface
V. RESIDUAL STRESSES
ure.
20failures.(7) Thus, if the surface contains a compressive residual stress the surface tension stress will not reach as high a value and fatigue strength should increase. Compressive residual stresses have also been shown to prohibit propagation of a fatigue crack when it is initiated. Correspondingly, a surface containing a tensile stress will have a lower fatigue strength, due to the additive value of the residual and applied tensile stresses.
The S-N curve of figure 9 shows the influence of compressive and tensile residual stresses as compared to no residual stress for an aluminum alloy.
Figure 9* S-N curve - Influence of residual stresses for an aluminum alloy.
A much more thorough coverage on type and magnitude of residual stresses induced by various methods, their effect on fatigue properties, and various methods of residual stress measurement, is presented in the
following section.
VI. CORROSION
21
Numerous references oil the effect of corrosion and corrosion
fatigue are available In reviews by Gough (2 9) and more recently by Gilbert (3 0) to prove, conclusively, that corrosion in any form is harmful to the fatigue life of a metal. Wadsworth (3 1) concluded that
simultaneous corrosion and fatigue were much more serious than either separately, or than alternately, probably because stressed metals are known to corrode more readily. He also pointed out that lack of evidence
of corrosion in a certain medium did not mean that it can be ignored as
having no effect on fatigue. Figure 10 illustrates very well the corrosive effect of air on an S-N curve for iron as compared to a
vacuum. Wadsworth stated that this curve showed a greater effect than some work done by other experimenters, and recommends that further work in this area continue.
iron.
22Grover et al. (1 3) came to similar conclusions for corrosion
fatigue, explaining that corrosion not only occurs on the surface hut
also in the crack after its formation, thus hastening failure. Surface corrosion roughens the surface and causes pitting which in turn produces high stress concentrations and higher stress amplitudes due to the
reduced cross-sectional area.VII. FREQUENCY AND REST PERIODS
Compared with other conditions affecting fatigue, frequency and rest periods appear to have a relatively small influence although much
research remains to be done in this area. In comparing some available experimental data on the subject, Walsman (9 ) noted that no effect on endurance limit was apparent up to 5,000 epm. Beyond that point, the endurance limit began to increase with frequency. For tests carried
out at stresses above the endurance limit and high frequency, the metal
was heated due to energy lost in mechanical hysteresis with results of premature fatigue failue.
A task group representing the American Society for Testing
Materials (3 2) similarly concluded that in the range of 200 to 7,000 epm there was no effect caused by varying frequency, if no temperature change or corrosion existed.
In considering the time lapse between cycles and groups of cycles the available evidence indicated that, for some materials, rest periods between groups of cycles had no effect, while in other cases the rest
periods considerably improved the fatigue life. There appears to be some controversy on the rest period effect on steels. Some workers (33) have found no effect while others (3^) have found that resting at
room temperature between groups of cycles definitely improved the
fatigue strength.23
VIII. SIZE
The size of a part has a significant influence on endurance limit values. Young (17) related an example of a 1 inch diameter bar of
mild steel at room temperature having a 20 par cent less endurance limit than the same material in ~L/b inch size. Larger diameters have even less endurance limit, but there was some doubt whether this was due to size
alone or to the greater possibility of defects in material of such size.IX. LOAD HISTORY
Load history is another area that needs extensive research to establisn effects of previous loading on fatigue properties. It is generally believed that stressing the material below the endurance
limit (understressing) increases the fatigue strength, and raises the original endurance limit. Overstressing appears to produce damage, causing early failure, but there appears to be a limit of permissibleoverstressing before the damage occurs.
CHAPTER IVEFFECT OF RESIDUAL STRESSES ON FATIGUE
Residual stresses have been introduced in the last chapter.This chapter is concerned with residual stresses and their resulting effect on fatigue. The first three sections present a basis for the
residual stress phenomenon. The effect of fatigue loading on residual stresses is discussed, and an outline of current residual stress
measurement methods is introduced with some discussion on the relative merits of each. The last section covers residual stress induction methods and the resulting fatigue effects. Of the three methods of
producing residual stresses, mechanical, heating and codling, and chemical, just the first two are presented in detail here.
The heating and cooling section is concentrated mainly on quenching and tempering conditions, and resulting effects with a brief
introduction to various welding influences on fatigue.Mechanical methods are covered in two sections. One deals with
the published literature for various machining and finishing operations.
The second includes work done on the cold working of metals, a major part being shot and strain peening effects.
I. RESIDUAL STRESSES-BENEFICIAL AND DETRIMENTAL
As was previously noted, it has been generally accepted that compressive residual surface stresses are beneficial to fatigue and tensile residual surface stresses are detrimental. Beneficial to fatigue
means an increase of fatigue properties over the normal fatigue properties of the metal. This may include an increase in fatigue strength,
and increase in endurance limit, or both. Thus, the higher and the
25further to the right the curve is located on an S-N plot, the better
the fatigue properties are.In practice most of the fatigue failures have originated at
the surface. Rosenthal (35) noted that by setting up the proper type
of residual stress, it should be possible to improve the fatigue properties of metals. A good majority of the literature available has rein
forced this statement. However, several authorities (36, 375 38, 39) have failed to show any definite influence of residual stress on fatigue properties.
Rosenthal and Sines (ho) noted that some discrepancy was undoubtedly due to the change of residual stress level during cyclic loading. Like the authors cited previously, most experimenters have made
residual stress measurements at the beginning of testing, therefore, they did not know the actual residual stress during most of the testing period. The following section discusses the investigations on relaxation and fading of residual stresses.
In 1955» the ASM Committee on residual stresses (Ul) pointed out that the relationship of residual stress and fatigue was still
controversial. Compressive residual stresses in the surface usually raise the fatigue limit. Many oppose giving residual stresses the
credit, however, because methods of inducing residual stresses often
cause changes which affect fatigue properties. As an example, shot peening also cold works the surface which causes higher tensile strength and thus a greater endurance limit, (see figure 8)
Boegehold (26) concluded that residual stresses were a major cause of the difference between test bar results and tests on components made from heat treated steel. For fatigue tests on axles, fatigue
26
limits had a 40 per cent spread for material that varied only up to 15 per cent in tensile strength and hardness, as determined on test bars.
The vast majority of recent work in this area indicates a strong influence of residual stresses on fatigue. Almen (7, 8 , 42, h-3j,), Grover (44), Rosenthal and Sines (27* 28, 45), and Horger (25, 46, 47,
48), to name a few, have all found increased fatigue strength with beneficial compressive surface stresses.
The detrimental effect of a tensile residual surface stress can
be clearly shown on a Goodman diagram.(49) A metal part that is reverse
Figure 11. Goodman Diagram and residual stresses.
By inducing a residual tensile stress in the surface of thepart, the additive effect of the external and internal stresses produces a mean tensile stress moving line A~B to the right and up. The
resultant line is indicated by C-D. It is now noted that the range ofthe Goodman diagram has been exceeded and theoretically, failure will
27occur. Correspondingly, a compressive residual stress will produce a
mean compressive stress, moving line A-B to the left and down. This condition, E-F, has a range stress much below that allowed by the diagram, and thus a greater fatigue strength.
Grover (MO has shown with a modified Goodman diagram, the value of protecting the surface with a compressive residual stress for greater fatigue strength in bending. A sketch of how this works is shown in figures 12 and 1 3.
The dotted line in figure 12 represents a compressive residual
stress on the top surface induced by peeming. The bending stress and the resultant of the applied and residual stresses are also shown.From this graph and with a few calculations, the stress amplitude and mean stress can be determined at various depths.
Figure 12. Summation of applied and residual stresses.Plotting the calculated stress conditions at various depths on
a finite life modified Goodman diagram indicates there will he a subsur
face failure. The decreased mean stress and stress amplitude due to the compressive residual stress nas strengthened the surface. The plot is shown in figure 1 3.
28
Figure 13. Stress conditions at decreasing depths plotted on a modified Goodman Diagram.
II. RELAXATION OF RESIDUAL STRESSES
Substantial proof exists that residual stresses originally
present before testing will change and generally level off or fade under repeated stressing. This fact alone causes much variation in the conclusions of various experimenters on the effect of residual stresses in fatigue.
One of the earlier tests on relaxation of residual stresses was done by Buhler and Buchholtz.(50) This work is reviewed by Horger.
(2 5 ) Four steels were tested by rotating bending of 1 .0 7 inch specimens. A O .36 per cent carbon steel showed an 87 per cent decrease in axial residual stress slightly below the endurance, limit of 1+9,800 psi. A
0.57 Per cent steel behaved similarly. The surface residual tangential tensile stresses for the 12 per cent nickel steels decreased 1+0 per cent after 1 .35 X 10^ cycles, at a bending stress equal to the endurance
limit. At 2 .3 6 X 10 reversals, the reduction was 55 per cent. A
2916 per cent steel showed a decrease of only 30 per cent.
Results on 0»3h- per cent carbon steel tubular specimens were also reported. The quenched tubular specimens had residual tensile surface stresses initially, but changed to compression after various degrees of bending stress and a number of stress reversals were applied.
Barrett (51) has reviewed a work by Gisen and Glocker (52), in which the fading of residual stresses was established using X-ray
measurements. Studies by Jasper and Stewart (53) established a 90 per cent reduction in residual stresses for quenched steels at two million cycles loaded to 50 per cent of the endurance limit. Greater
relief was disclosed at higher stress levels. Moore (54) found a 76 per cent removal of residual stress in one cycle when a 0 .0 2 per cent plastic action was present. No relaxation was observed in hardened
steel by Morrow, Ross and Sinclair (55)# but soft steel was found to have a high reduction. They concluded that the changes in residual stress were largest in early life. Although later changes were small,
over millions of cycles the cumulative effect was significant. Four factors presented that determine the changes of residual stress during fatigue were:
1. Composition and hardness of the material.2. Magnitude and sense of initial residual stress present.3 . Magnitude and direction of applied fatigue stress.4. Number of cycles of fatigue loading.Stress relief can be accomplished by heating the metal. Stresses
can always be reduced to the yield point at the temperature used.(4l) Higher temperatures promote stress relaxation, but theoretically, residual stresses will relieve or die out at any temperature. Jasper
and Stewart (53) have presented data on stress relief by heat. The
30
remaining stress in a carbon steel boiler plate pre stressed to the yield point (25>000 psi) was determined for various temperatures and heating
times. (See table l) Temperatures varied from 400 to 1400 °F and heating time from l/2 to l6 hours. Data has conclusively shown decreasing residual stresses for increasing temperature and heating times.
Table I. Remaining stress in carbon steel boiler plate prestressed to yield (25>000 psi).
It should also be noted that some research has indicated anincrease in residual stress with fatigue loading.(2 8) Buhler and
Buchholtz (50) found that longitudinal surface compressive residual stresses of 14,000 to 35 ,000 psi were produced in stress-free steel
subjected to rotating bending fatigue tests at stresses near the endurance limit. The compressive residual stresses induced in this manner might explain why understressing and overstressing have been
known to increase the endurance limit of many materials by as much as 25 to 35 per cent. (See Chapter III, part IX)
III. RESIDUAL STRESS MEASUREMENT
Fatigue testing to find the effect of residual stresses is of little value unless the type, direction, and magnitude of residual stresses present during testing are accurately determined. Much of the
31past work in this area has neglected the residual stresses, or not
determined them accurately. Thus, results have sometimes been unusual and not in agreement with more carefully conducted studies.
While a variety of methods have been devised to measure residual
stresses, only two methods have had practical application.(5 6) One is the mechanical or dissection method, in which the specimen or member is cut apart, permitting the residual stresses to be calculated from
the resulting geometric changes in the member. The other is the X-ray diffraction method, in which the residual stresses are computed from measurements of the atomic lattice distances determined by Bragg’s Law.
Mechanical Methods: The dissection method is extremely difficultbecause only average stresses can be computed in the layers which have
been removed from the parent member. This makes it necessary to remove a large number of extremely fine portions from the parent member, which results in an expensive and time consuming analysis. As the layer removal is refined, this method is further complicated by the necessity
of measuring the resulting small geometric changes in the parent member with extreme accuracy. Other disadvantages are the normally involved equations used and the destructive character of all the mechanical
methods. Much care has to be taken to make sure no residual stresses have been introduced by the removal method. Grinding is definitely known to induce residual stresses (57> 58> 5 9)* and etching under certain
conditions has been shown to induce them.(2 5)Recent advances and simplifications of the technique have
improved many disadvantages of the mechanical methods.(6 0, 6l, 6 2, 6 3, 6U) Letner (6 5) developed the use of optical interference for accurately
measuring the small dimensional changes. A device designed to measure
32curvature while the specimen was in the etching solution was utilized by Waisman and Phillips.(60)
No less than sixteen different mechanical techniques have been listed.(6 6) Some of them have been reviewed critically by Parrett (51,67), Sachs and Van Horn (6 8), Sachs and Espey (6 9), and Rosenthal.
(35) An excellent evaluation of the more popular methods of residual stress determination was developed in an SAE technical report by D. E.
Martin.(5 6) Seven specimens of various composition, heat treatment, cold working, and resulting residual stresses were sent to twenty laboratories for a residual stress analysis by their method. Four dif
ferent mechanical methods were used along with the X-ray diffraction method. Results of the cooperative research program showed close agreement of the beam dissection and X-ray methods, the beam dissection
being the most consistant of all methods.
One essentially non-destructive mechanical method of note is presented by Sines and Carlson.(6 2 ) They have found that stress has
an effect on penetration hardness of the surface. Compressive stress was noted to cause a slight increase in hardness over the unstressed state. Increasing tensile stress caused a linear decrease in hardness.
A statistical approach was used with ten readings at a point. Authors admit the method is not developed to useful application yet but believe it has possibilities.
The most common mechanical methods for residual stress determination are presented here with the shapes to which they are applicable and the type of stresses found. The stress equations for most of
these methods are presented by the American Society for Metals Committee on residual stresses.(^l) Also see reference 70.
33Johnsons Method; This is a beam dissection method developed especially for irregular shapes such as an I beam. Longitudinal stresses are determined from rectangular sections dissected from the part.
Cramptons Method; The method is for tubes which have been split- lengthwise and the resulting crack width measured. The method evaluates
tangential (hoop) stresses. See reference 70.
Anderson and Fahiman Method”. This method may be applied to a tube or sheet. For a tube, a tongue is milled from the tube wall and movement of tongue end measured. The same equations apply to sheet spilt on
the midplane. Stresses determined are longitudinal. Baldwin has described modified versions of this method.(7 0)
Kreltz 1 Method: The method of Anderson and Fahiman is applicable to
rods. The rod's center diameter slice is taken and cut in half.Treuting-Read Method t This method can be applied to sheets where surface removal is accomplished by an etching solution and the resulting changes
in curvature measured. This method gives longitudinal and transverse residual stresses. See reference 71*Siebel and Pfender Method: This method has been developed for a sheet.
Rectangular blocks are cut out of the sheet at positions perpendicular to each other. The length is measured before and after cut-out to evaluate stresses.
Mathar*s Method: This method can be used on the surface of any metalpart. A hole is drilled into the surface with strain gages at 120°
intervals around the hole. See reference 72. Kelsey (6l) has extended this method to evaluate stresses to a depth below the surface of approximately one half the hole diameter. This is a relatively fastmethod.
3^Heyn and Bauers Method: This method was developed for rods where thesurface is removed by machining or pickling with length and diameter
measurements taken at each removal- This method could be as much as 30 per cent in error.Mesnager-Sachs Method: Uiis method is applicable to rods and cylinderswhere the center hole is bored out at increasing radii and measurements
of length and diameter (O.D. and I.D.) are taken. An alternate method is also available where the center is bored out and then the outside
surface machined.
Brittle Laquer: This is essentially a qualitative method only. Ibismethod locates residual stress, gives direction of stress, and determines
kind of stress present. Brittle laquer is coated on the surface,
allowed to dry, and then the surface is drilled with 1 /8 inch diameter drill to a depth of about l/l6 to 1 /8 inch and the resulting cracks are
observed. (See reference 73) Figure l4 indicates the stress patterns
that will develop under uniaxial and biaxial stresses.
fUniaxial Biaxial Uniaxial Biaxial
TENSION COMPRESSIONFigure lUo Brittle laquer stress patterns.
X-Ray Method: Other than the fact that X-rays measure only surface
stresses, they have many advantages over the mechanical methods. The X-ray method is the only non-destructive, accepted means of determining
residual stresses. Macrostresses and microstresses are found by the
35X-ray technique whereas mechanical methods only evaluate macrostresses. Through non-destructive X-ray testing the stress state can be evaluated at any time. This is especially useful in work on relaxation and fading of residual stresses.
Rosenthal (6 6 ) has clearly described the basic operation of residual stress measurement by X-rays. A monochromatic beam of X-rays
of wave length /\ impinging on a crystalline solid is diffracted in accordance with Bragg's Law with the direction given by:
For the unstressed state a value d = d0 for a given crystal
lographic direction will be found regardless of the orientation. Figure 15a represents such a stress free specimen with impinging and diffracted X-rays.
Figure 15. Principle of X-ray stress measurement.Figure 15 b, however, is for an axially loaded case and the bar
stretches in the direction of the force and contracts in the transverse direction. It is easily seen that the lattice planes parallel to the axis come closer together and those transverse to the axis are drawn
36further apart. If the incident X-rays are inclined at 90° and k5° they will reveal two different values of d. The difference between these
two values is proportional to the applied stress, and it can be converted to a stress by a suitable calibration factor. It should be noted that knowledge of the unstressed state is not required for stress determin
ation.Much work has been done since 191»-0, in the use of X-rays for
residual stress measurements. Barrett (7^) described in detail the
methods in X-ray use for determining applied and residual stresses.
Precautions to be used in the measurement and interpretation of residual stresses by the X-ray technique have been presented by Hyler and Jackson.
(75) Christenson and Rowland (7 6) have presented an extrapolation method for locating the peak of a diffraction curve and have made several contributions to correct errors in the X-ray measurement method.
Until the last few years X-rays were limited to steels below a hardness level of around Rockwell C 40.(U8) Christenson and Rowland, and more recently, Marburger and Koistinen (77) have developed methods
of accurately measuring residual stresses in hardened steel. The latter work was concerned with an accurate but less time-consuming method. The results have compared well with mechanical methods.
A thorough and extensive treatment of the theory and practice
of measuring residual stresses by X-ray analysis has been done by Barrett (51, 7 8, ), Norton (19), and Isenburger.(80) Residual stress
measurement in welds by X-ray has been summarized by Spraragen and
Claussen (81, 8 2 ), Spraragen and Cordovi (8 3), and Spraragen and Rosenthal. (3 6)
IV. RESIDUAL STRESS AND FATIGUE37
The general conditions for beneficial or detrimental residual stresses have already been presented. Hie methods of producing these residual stresses, the magnitudes of stress produced, and their resulting effect on fatigue as found by many researchers in this field are presented here.
HEATING AND COOLINGResidual stresses induced in metals by the various heating and
cooling methods in use have long been known to exist, but their bene
ficial use in fatigue design has been confined to the last few years.In the past, thermal and transformation residual stresses due to quenching have been relieved by tempering the metal.
Attention is now given to retaining thermal and transformation stresses. It has been shown that the residual stresses are normally
compressive on the surface and tensile in the core, which increases the Atigue properties of the stress free metal. Also, investigations indicate that the metal can be tempered and retain most of the beneficial compressive quenching stresses by not using temperatures above the
lower critical temperature, A]_ of the metal.It is intended to present here only a very brief coverage of
the work done on welding residual stresses, and their resulting effect
on fatigue. Much work has been done in this area to determine the fatigue strength of welded joints both with and without stress-relieving
treatments designed to show the effect of residual stresses. Summary reports outlining conclusions of investigations that have been conducted may be found in the references.(8 1, 8 2, 8 3, 8*0
Residual Stresses Induced: Residual stresses induced by heating and then
38sudden cooling of a metal can be due to thermal stresses or a combination of thermal and transformat ion stresses. If the quenching temperature
is below the lower critical, no transformation stresses will occur.Thus, any residual stresses present will be due to thermal stresses.
Thermal stresses come about due to the faster cooling rate of
the surface material over the core, therefore, its faster contraction.(8 5) This brings about, momentarily, tension in the outer shell and compression in the core. As cooling continues the outer shell nears the quenching medium temperature, but the core still cools over a large range and ends up in tension, putting the outer shell in compression. This is the final result of a purely thermal change; all metals
having no transformation behave similarly. A stress-time plot for rapidly quenched cyclinders as taken from Horger (1*8 , 8 6 ) is shown in figure 16.
Figure l6 . Transient change of stress distribution in rapidly cooled cylinders.
39The magnitude of these thermal stresses is greatly dependent
upon the method of quenching or cooling. This is especially noticeable in steels having carbon contents from 0.25 to 0.50 per cent. Figure 27 shows the effect on residual stresses by cooling in water, oiljand air
from the tempering temperature of 1200 °F for 0 .3 0 per cent carbon steel as found by Horger.(8 6)
Figure 17• Influence of methodQof cooling from tempering temperature. Water quenched from 1560 F.
If there is a transformation from austenite to martensite, a volumetric change occurs due to it alone. This happens when steels
are heated to the austenitic condition (above the upper critical temperature, point) and then suddenly cooled. Under these conditions
three influences act to produce residual stresses:1. First thermal shrinkage occurring before transformation.2. Volume expansion as a result of transformation.3 . Second thermal shrinkage occurring after transformation.Cooling velocity, carbon content, and diameter are important
factors in determining magnitudes of the above stress formations.(8 7)A chart similar to figure 17 is presented in figure 18 for the same
40steel, but for quenching from above the upper critical temperature, A3 . This represents the combination of thermal and transformation stresses
to form high compressive residual stresses for high velocity quenching only. Low velocity quenching produces small stress values for this steel. As mentioned for thermal stresses, this steel has carbon
content in the range of greatest effect on residual stresses due to cooling velocity.
Figure 18. Influence of cooling velocity after heating above A^.
For solid cyclinders condition 2 results in tensile stresses
in the surface and compression in the core. As stated previously,
thermal stresses such as 1 and 3 produce surface compressive and core tensile residual stresses. The order of magnitude of the stresses determines the final residual stress state of the metal.
Investigations by Boegehold (8 5 ) and Horger (8 6, 8 7, 48) have found the conditions for either dominant thermal stresses, (compressive surface) or dominant transition stresses (tensile surface). In his
work with constructional steels, Horger found that combined thermal
hi
and transformation stresses produced a compressive surface and a tensile core. This study included many plain carbon and a few alloy steels.
Further investigations with high carbon steel, and very high alloyed metals resulted in high surface tensile stresses. The low temperature
range of martensite formation caused transformation stresses to overweigh the thermal residual stresses. Depending on conditions, it is evident that the surface of a hardened steel object may contain
residual stresses of any amount between the yield strength in tension and the yield strength in compression.
Most of the past cited studies also note the extreme importance
of tempering temperature. High tempering temperatures cause a decrease in magnitude of beneficial residual stresses, whereas, lower temperatures retain a large portion of the compressive surface stresses. This is
illustrated by figure 19 taken from reference 86 on data for 0 .3 0 per cent carbon steel that was water quenched from 1560 °F.
Figure 39. Influence of tempering temperature on residual surface stresses.
1+2The heat generated during the welding cycle and the subsequent
natural or forced cooling which follows, gives rise to residual stress fields by the simple mechanism of differential expansion and, in the case of alloys, by the expansion due to phase transformations.(8 8)Thus, in essence, the residual stresses due to welding processes are the
same thermal and transformation stresses found in heat treatment of metals.
C. S. Barrett (7*+)# in using X-ray diffraction, found the variation of residual stresses across the thickness of a weld in a one inch
mild-steel plate. The longitudinal stresses were greater than the transverse stresses and reached a maximum tensile stress of over
50.000 psi. Weld residual stresses were tensile with the immediate area surrounding the weld being in compression.
Residual stresses due to intense local heating of a metal were
investigated by Norton and Rosenthal (3 8) in a plate 0 .3 inches thick. Local heating was done over an area 0.5 inches in diameter using a spot welder. Results showed high tensile residual stresses nearing60 .0 0 0 psi in the locally heated area.
Experimentation with actual spot welding and resulting residual stresses was conducted by Hauk (8 9) on 0.1+9 per cent carbon steel
sheets. Around a single spot weld, radial and tangential stresses were found by the X-ray method to be equal and opposite in sign. The radial stresses were tensile and the tangential stresses compressive.
The maximum stress was 1+3,000 psi. It varied inversely with the square of the distance from the center of the spot. The results were noted to be in good agreement with theoretical relationships for
magnitude and distribution.
43Effect: on Fatigue: Much of the work cited in references authored by
Horger in this section has been done by Germans, Buhier and Buehholtz, in the early 1930's. They presented very convincing data that thermal residual surface compressive stresses would increase the bending endur
ance limit, whereas, it would be decreased with initial tensile stresses.
Fatigue tests were made on ten different steels in rotating bending on plain specimens. The endurance limit was increased up to 22 per cent
for specimens with various degrees of residual compressive stresses.Similar tests on nickel alloy steels gave tensile residual
surface stresses on quenching. In one steel with a 52,000 psi tensile
stress the endurance limit was decreased by 12 per cent as compared to a stress free specimen. A 16 per cent reduction in endurance limit
was achieved with another nickel alloy steel having an 18,000 psi tensile
quenching stress.Rotating bending tests on 1050 steel quenched by either air or
water mediums was conducted by Horger.(87) The specimens were quenched
from the tempering temperature and resulting residual stresses were measured mechanically by the bore out method and strain gages. Water
quenched specimens had the higher endurance limit. Residual stress measurements showed water quenched specimens to have surface compressive
stresses of 40,000 psi, whereas, air cooled specimens were essentially
stress free. Horger concluded that thermal stresses were a major contribution to the increased fatigue strength.
Additional fatigue tests by Horger and Neifert (9 0) were made on 9 l/2 inch diameter locomotive crankpins of quenched and tempered SAE 1050 steel. One group was tempered at 1000 °F, leaving small residual surface stresses giving an endurance limit of 12,500 psi . Another group, tempered at 750 °F leaving over 50,000 psi in compression.
had an endurance limit of over 22 ,0 0 0 psi.kk
Dolan (91) has shown an S-N curve of specimens slowly cooled
in quenching and of specimens rapidly cooled in quenching. Data are given for notched and unnotched specimens. The band of data for the raidly cooled specimens was always above the slowly cooled band,
definitely illustrating better fatigue properties.Many attempts have been made to determine the fatigue strength
of welded joints, both with and without stress-relieving treatments designed to show the effect of residual stresses. It has generally
been found, that under the best conditions the fatigue strength of the welded joint is considerably lower than that of a solid specimen of
the same dimensions. Due to the presence of discontinuities in the weld metal, and of the difficulty in measuring residual stresses, the importance of the residual stresses weakening the joint as a whole has not
been clear. Experimental data illustrating the weakness of welds and effects of various conditions and treatments may be found in references 92 and 6 6.
Conclusions': Residual stresses induced into a metal by heat treatmentare usually compressive. An exception is high carbon and high alloyed steel quenched from above the upper critical temperature. If the
compressive residual stresses in a heat treated part are not relieved, the part will exhibit better fatigue properties than a similar stress free part.
Welding produces high residual stresses, in most cases, being tensile in the weld. Although welded parts show a definite decrease in fatigue strength, it is presently not known if this decrease should
be attributed to the residual stresses, or to imperfections and discon-
tinuities in the weld45
SURFACE MACHINING AND FINISHINGUntil recently it was generally thought that residual stresses
induced by machining and finishing processes such as grinding, polishing,
honing, and cutt ing were insignificant and had little affect on the fatigue properties of the metal. Recent studies on the residual stresses induced by these processes and their resultant effect on fatigue of the
past have brought out the importance of their consideration when machining and finishing are required.
In some cases, choosing the right variables for the process can leave beneficial surface compressive residual stresses, or tensile stresses of small enough magnitude to be of no importance. Also, knowledge of the presence of a high tensile surface stress due to the pro
cess is of great value as the detrimental stress may often be alleviated by a subsequent surface treatment.
Residual Stresses Induced: Letner, (5 8) using hardened (Rockwell C 59),ball-bearing type steel similar to AISI 52,000 used by Tarasov and Grover (93)* studied the effect of steel grade, unit downfeed, and grinding fluid, upon the residual stresses generated. By using a deflec
tion method, the residual stresses parallel and perpendicular to the direction of abrasive travel were determined.
The effect of the wheel grade upon residual grinding stresses
was insignificant. Very soft wheels appeared to reduce the magnitude and depth of penetration somewhat.
Tensile stresses as high as 120,000 psi were found less than
0.001 inches below the surface for a downfeed of 0.001 inches. In certain cases, compressive stresses of about the same magnitude, but
k6
on the surface, were found. The finding of the possibility of a compressive surface stress was remarkable and valuable information,
especially because in some cases high tensile stresses were not induced deeper in the metal. This information is contrary to the popular engineering generality that grinding stresses are tensile stresses.
Letner also found that increasing unit downfeed increased
both the magnitude and depth of penetration of the resulting stresses.A. L. Christenson and W. E. Littmann, discussing the work of Letner,
speculated a logical explanation to the origin of grinding stresses. Temperature measurements within ground samples show that grinding can produce sufficient, nonuniform thermal expansion in the work to cause compressive yielding of the materials just below the surface, thus,
generating a residual tensile stress. If heating is insufficient to cause yielding, the cold work of the surface may produce the compressive stresses which were observed. Letner agreed with this speculation also.
In similar work on hardened SAE 43^0 steel, Colwell, Sinnott, and Tobin (9*0 used X-ray diffraction for measurement of residual stresses induced by grinding. Their results compared favorably in most
areas to Letner*s. All grinding stresses were found to be superficial, not exceeding 0 .006 inches in depth on the average, with the critically
high stresses not exceeding 0.002 to 0.003 inches in depth. In general, severe grinding produced dominately tensile surface stresses, while less severe grinding could produce compressive surface stresses. Hie
greater the severity of grinding, the greater was the magnitude of the
residual stress. Glickman and Stepanov (57) ground low-carbon normalized steel bars to a depth of 0 .022 inches and found a maximum tensile surface stress of 25,000 psi. The stressed zone had a depth of
47about O.O36 inches. It was noted that the heavy grinding cuts produced severe heating which would affect the magnitude of the residual stresses.
Experiments at General Motors Research Laboratories by J. 0. Almen (8 ) have shown filing and honing to produce residual compressive stresses under normal operations, and grinding to produce residual
tensile stresses. Residual compressive grinding stresses have been found using a soft, sharp, course grit wheel sued removing shallow cuts of 0.0001 inches or less per pass. Almen adds that practical grinding conditions always produce tensile residual stresses, this is in contrast to the jrerious works cited, wherein, compressive residual stresses with a 0 .001 inch cut were found in some cases.
Dissection stress measurements indicate that the initial residual compressive stress from polishing may exceed 20,000 psi. Even
though a file finish also produces a compressive residual stress,
Almen states it should not be considered as effective as honing. Filing produces surface scratches which, as stress raise:®, reduce the beneficial effect of the compressive surface stress.
In another work, Almen (42) estimated the magnitude of residual grinding stresses in a specimen of annealed spring stock that was ground to a depth of cut of 0.002 inches. A surface layer removal
method was utilized using hand honing to remove very thin layers from the ground side. The results were as follows;
DISTANCE FROM SURFACE TENSION STRESS
0.00005 in. 270 ,000 psi0.00013 110,0000.00025 57,5000.00035 37,5000.00045 27,500
48A stress of 270,000 psi could not be supported by the steel in
the annealed state, from which it follows the stressed layer must have been hardened by the heat of grinding. Hardness measurements did not confirm this, probably due to the inadequacy of present hardness instruments for measuring the extremly thin surface hardened layer.
Some work was done on mild steel by Frisch and Thomsen (59) ifaxng a medium soft grinding wheel. A surface layer removal method for residual stress determination was utilized, the surface removal being done by a 5 to 20 per cent nitric acid solution. This proved to be a satisfactory method of elimating surface layers without inducing new residual stresses, as grinding removal might do.
Results indicated the maximum residual stress was at the surface and in all cases was above the yield strength of the material. See figure 20. The depth of residual stress was found to be 0.012 to 0.018 inches for grinding cuts from 0.0003 to 0.0029 inches. This was considerably greater than the residual stress depth found in previous works cited for hardened steel.
Figure 20. Residual stress distribution below surface of mild- steel bars.
49Frisch and Thomsen noted that the maximum surface stresses were
smaller for heavier cuts, hut the depth of residual stresses were found to increase with depth of cut. They also pointed out that the depth of residual stress was probably somewhat in error, due to the large number of etchings and, correspondingly, roughened surface which make accurate
measurements difficult.A study by Henriksen (95) concluded that extremely high residual
stresses were induced in the surface of metal by the action of a cutting tool even when light cuts were taken. Highly concentrated stresses up to 100,000 psi were found. For ductile materials, such as carbon steel, the residual stresses were generally tensile, while in cast iron they were
found to be compressive.The residual tensile stress was found to increase with depth of
cut as it was varied from 0.002 to 0.014 inches. Increases in carbon content of the steel tested apparently decreased the residual stress induced. It was also noted that the resultant stress was somewhat affected by the shape and angles of the tool.
Henriksen observes that much information is still needed on the effect of high speed cutting, cutting fluids, and on other machining
processes such as milling, broaching, drilling, reaming, and grinding. Effect -on Fatigue: Very little information has been published on theeffect of machining and finishing residual stresses on fatigue and much of that is controversial. Most studies on grinding, polishing, and
cutting have been concerned with the surface roughness effect on fatigue, assuming the induced residual stresses to be zero or insignificant.
Boyer (9 6) made rotating bending fatigue tests of hardenedsteel specimens with various amounts of stock removed by dry grinding
50
of cuts not more than 0.001 inches per pass. His findings indicated the greatest endurance limit without grinding* and a continuous reduction was noted due to grinding with the most rapid decrease of 17 per cent in
the first 0.025 inches. A discussion of this paper questions the validity of the data. The surface roughness effect was not considered.
An investigation by Tarasov and Grover (93) made use of data from reversed bending tests on flat bars and rotating bending tests on round bars of AISI 521000 steel to determine the influence of grinding. Conclusions were that careful longitudinal grinding of both flat and
round specimens would not have any adverse effect on fatigue strength. Severe grinding was found to lower the endurance limit of the flat bars about 20 to 25 per cent.
A more recent work by Tarasov* Byler, and Letner (97) indicated no effect on fatigue strength for careful grinding conditions on hardened (Rockweel C 59) steel. Severe grinding conditions were found to decrease
fatigue strength by as much as 25 per cent, while some grinding with straight grinding oils gave up to 38 per cent over the base line fatigue limit.
The fatigue limit was shown to remain essentially constant up to a peak tensile grinding stress of 50,000 psi. Beyond this value a reduction in fatigue limit occurred.
Concrlusfons'S Normal grinding conditions usually cause a tensile residual stress but under certain conditions the residual stress may be compressive.
Toning and filing induce compressive residual stress. Cutting residual tresses are tensile for ductile steels and compressive for cast iron.
No machining or finishing residual stresses reach more than a few thousandths of an inch in depth, with maximum residual stresses reaching
51values near the ultimate strength in some eases.
Fatigue properties improve with a compressive residual stress
and decrease with a high tensile residual stress. Careful grinding causes little effect whereas severe grinding decreases the fatigue limit.
COLD WORKING “SHOT AND STRAIN PEENINGCold working, including the various shot peening processes, is
generally known to produce residual compression stresses in the surface
of the part. Methods classified as cold working processes include peening, surface rolling, drawing, sinking, local pressing or air hammering, and stretching. In general, cold working is induced by plastic deforma
tion of the surface layers while the core is elastically strained, leaving a compressive stress in the surface layer and a relatively small tensile stress in the core.
The beneficial influence of surface cold working to increase
fetigue resistance was first used in 1928, by Foppe, in Germany. In 1938# the first paper was published by Frye and Kehl (9 8) on shot blasting
and fatigue resistance. The history and development of the phases of cold working has been presented and discussed by 0. J. Horger. (99, iOO)
Results of various investigators have been reviewed and an extensive bibliography compiled.
Probably the most popular method of securing surface compressive stresses is by shot peening. The process consists of impinging the
surface of a part with round metallic shot, usually of chilled or malliable cast iron ranging in diameter from 0 .007 to 0 .175 inches, with a relatively high velocity of the order of 100 to 200 feet per second.
The shot, upon striking the surface, makes a series of small dents, and
radically expands the small areas siruck by each ball. Plastic flow is
52then caused on the surface fibers. The fibers beneath the affected layer are not stretched beyond their yield and* as a result, force the surface
• fibers to return to a shorter length. When equilibrium is obtained,
the surface fibers are in residual compression and the inner fibers are in compression.
Moore (lOl) has noted that this type of treatment can be applied
to parts of irregular shape on which cold rolling and cold drawing cannot be used, or in which heat treatment would cause excessive distortion and undesirable residual stresses. It can also be applied to specific parts of a machine element, such as the fillet at the shoulder of a shaft, to offset the effect of a stress concentration, or to the faces and fillets of gear teeth.
Strain peening is the process of shot peening a stressed surface. Compressive strain peening and tensile strain peening are illustrated in figure 21 and 2 2 , respectively, and covered thoroughly in references 102
53For compressive strain peening the specimen is held under a
condition of longitudinal bending to a fixed curvature with the compressive surface being shot peened. If the compressive stress is high enough the resulting residual stress will be tensile. In tensile strain peening, the shot peened surface is strained in tension by a couple during peening.
This produces higher compressive residual stress than peening in the unrestrained condition.
Harris (8 8) lists six main variables in shot peening whose control is required to achieve refroiucible intensities of stress.
1. M r pressure.2. Shot size, (ball diameter)3. Nozzle bore diameter.4. Nozzle to workpiece, (angle and distance)5. Time of peening.6 . Coverage.These variables have been investigated as to their effect on
residual stress, and the resulting fatigue effect by Richards (lOh-) and Horger and Neifert.(105)
J. 0. Almen (42, 43) has devised a method of measuring shot
peening intensities which has become the standard the last few years.Strips of steel of special composition are subjected to shot peening on one face when attached to the piece being peened. The amount of curva
ture of these gage strips, measured with an Almen gage, is a measure of the peening intensity they have received.
Residual Stress Induced The results of some early work on cold drawing
by foreign investigators are reviewed by Horger.(48, 25) Fahrenhorst and Sachs (106) subjected 40 hot-rolled bars of 0.06 per cent carbon steel to a 10 to 24 per cent reduction by cold drawing. On bars cold
drawn to 7*5 to 9*1 per cent reduction, the residual stresses measured
by the boring out method were about 40,000 psi in tension. A reversal of the tensile surface stress to a compressive stress of 30 ,000 to
5^U0,000 psi was obtained by straightening. Buhler and Buchholtz (5 0) determined cold drawn residual stresses for 0 .1 0, 0 .1 9, and 0 .5 0 per
cent steels up to 9 per cent cross-sectional reduction. The longitudinal residual stresses for the 0.10 and 0.50 per cent steels Eire plotted in figure 2 3 -
Figure 2 3 . Influence of per cent reduction on cold drawing residual stresses.
It was also stated that compressive surface stresses resulted
for reductions less than 0 .6 per cent for the 0 .1 0 per cent carbon steel and 0.8 per cent for the 0.50 per cent carbon steel. Results were com
patible to conclusions established by Nachtman (107)# that cold drawing
produced surface tension and core compression for all three directions: longitudinal, tangential, and radial. An exception was noted for very low reductions of less than two per cent where surface compressive
residual stresses were found.The residual stresses set up by straightening have the same distri
bution as those set ap by overstressing, i.e., compressive residual stress
55for a tension yield, and tensile residual stress for a compression yield.(108) Cold straightening kas been normally found to produce high
tensile stresses. In axle straightening, Horger and Lipson (109) found tensile surface stresses as high as 120,000 psi. X=ray measurements of the tensile residual stress induced by crankshaft straightening was
found to vary between 85,000 to 100,000 psi by Schmidt. (h-T)Surface rolling has been applied to many production parts to
improve fatigue resistance, but usually residual stresses were not
measured. Tests on 9 l/2 inch diameter shafts of SAE 1050 steel that was cold rolled gave resulting compressive stresses of 103,000 psi longitudinally and 1+5,000 psi tangentially. (110) Work done by Buhler
presented in reference 48 indicated surface compressive stresses due to
rolling of over 80,000 psi for a 2 3 A inch diameter, 0.19 per cent carbon steel specimen.
Shot peening two opposite surfaces of an unloaded beam should
give a pattern similar to figure 24. The surface layers are seen to be
COMPRESSION
Figure 24. Residual stress induced by peening.
highly compressive with a steep stress gradient to tension a few thousands
of an inch below the surface. Almen (k2, 8) has reported this compressive stress to be as high as 160 ,000 psi for hardened steel, dropping off to
tension about 0.007 inches below the surface. Normalized bar stock of SAE 10^5 steel cylinders were shot peened and found to have longitudinal and tangential compressive stresses of 37*000 and 50 ,000 psi, respectively, (ill) Richards (10^) found residual stresses by a modified Sachs method for a shot peened aluminum alloy. Compressive residual stresses up to 66,000 psi were induced to a depth of up to 0.029 inches. Shot size
varied residual stress magnitude and depth somewhat but blasting pressure and time effect were found to be small.
Strain peening by Mattson and Roberts (102, 103) produced
residual stresses in either tension or compression. Figure 23 illustrates
the tensile residual stress from compressive strain peening, and the increased compressive residual stress over conventional shot peening
from tensile strain peening.
Figure 25- Residual stresses induced by tensile, compressive, and conventional shot peening in leaf springs.
Tensile strain peening of the leaf springs increased the magnitude of the compressive residual stress from 8C*000 psi to over 160*000
psi and increased the depth of the beneficial compressive stresses.The authors noted that compressive strain peening induced compressive stresses for the lower applied strains and changed to tensile stress
at the larger strains. Similar results are found in reference 112 where the conventional peening stress of 110*000 psi was increased to 140*000 psi by tensile strain peening.
Effect on Fatigue; It is apparent that little fatigue research on cold drawn specimens has been done. Osgood (113) has noted* however* that cold drawing may induce residual surface tensile stresses* and yet the
fatigue strength may be improved. The improvement is presumably due to the fact that the beneficial effect of the surface hardening is greater than the detrimental effect of the residual tensile stresses.
The endurance limit for full-sized automobile axles was 13*000 to 16*000 psi for production straightened shafts. Horger and Lipson (1 09) found that the endurance limit for similar unstraightened axles
was 20*000 psi or about 25 per cent greater fatigue resistance than that of the straightened shafts. Shot peening the axles raised the endurance limit to 43*000 psi. In reversed bending fatigue tests of aircraft engine crankshafts* press straightening gave an endurance limit 20 per
cent lower than unstraightened crankshafts.(47) The loss of fatigue strength was even greater for a finite life* being 35 per cent for
50*000 cycles and 27 per cent for 100*000 cycles. An S-N diagram of the results is plotted in figure £6 .
Figure 26. Effect of straightening crankshafts on the fatiguelife.
Surface rolled components have definitely exhibited better
fatigue properties due to the induced compressive residual stress.
Fatigue tests by Horger (1*8) on press-fitted assemblies gave over 22,000
psi endurance limit for pins rolled at 21,000 pounds roller pressure.
The endurance limit was 11,000 psi for similar pins not rolled. As
tensile strength is also increased, the higher fatigue resistance is
in part due to strain hardening and in part due to residual stresses.
(100) Horger noted that the increased fatigue strength due to the
favorable residual stresses of surface cold rolling, should not be
confused with the fatigue properties and residual stresses of the usual
mill operations in production of cold rolled or cold drawn bar stock.
Starting at less than one per cent reduction of area in mill operations
with some steels, it was found that the surface stresses began changing
from favorable compression to unfavorable tension.
A summary of results of several investigators (25) on fatigue tests of surface rolled fillets, showed improvement by cold working over not rolled specimens of 3° to 69 per cent. The increased fatigue
59strength due to surface rolling is clearly shown by figure 25 > which compares normally finished railway axles with axles that have been sub
jected to a rolling operation.(ilk)
Figure 27- S-N diagram for rolled and not rolled railway axles.It is generally believed that residual stresses due to peening
have a greater effect in bending and torsion cases where there is a
large stress gradient.(5*0 However , Almen (7) has found high increases in fatigue properties for axially loaded specimens properly peened.
Grover (¥»■) has stated three ways shot peening might improve the fatigue strength of a metal component.
1. Surface roughening- This may induce a fatigue notch factor which reduces fatigue strength from k to 35 per cent.2. Surface' work-hardening- The amount of fatigue strength gained by work-hardening is not known, but it should about balance the surface roughening loss.3. Residual stress- Peening leaves a macroscopic residual compressive stress which is probably the most important factor in fatigue strength improvement.
Shot peening intensity is a very important factor in increasing fatigue properties and, according to Almen (7 ), may even be detrimental to fatigue if high enough. The fatigue strength is increased as the
intensity of peening is increased until a maximum improvement is obtained. Increasing peening intensity beyond this level causes the surface effects
6oand very high internal tensile stresses to dominate, and the fatigue strength rapidly decreases. This is clearly illustrated in figure 28
Figure 28* Effect of peening intensity on Fatigue life.
Studies by Horger and Neifert (115) noted greater improvements
of endurance by shot peening for higher levels of hardness. See figure
29 This belief is also discussed by Almen.(8)
Figure 29* Increase of 1 fatigue strength by shot blasting on O.k^ Carbon steel. , ,
6l
Shot peening various machine parts gave increased life which var
ied from 310 per cent increase for welded joints to 1370 per cent increasefor helical springs.(4 3) Smith (ll6) shot peened compressor valves and
6 6increased the life from 10° to over 20 X 10 cycles without failure.These life improvements are relative and depend on the magnitude ofloading. This should be kept in mind when interpreting fatigue data.
A summary of fatigue tests by rotating cantilever bending on shot peened shafts with and without fillets is presented by Horger and Neifert.(105) Endurance limit improvements from 3 to 19 per cent over
the polished condition were found for plain specimens. Filleted specimens had improvements varying from It- to 54 per cent depending on peening condi
tions .Fatigue tests on three different gauge size wires in the as
drawn and peened conditions were conducted by Harris.(8 8 ) The effect of shot peening was to increase the basic fatigue limit of the wire in
all three cases, being an increase of 4l per cent in the larger wire. Harris also has discussed the shot peening of induction hardened zones.In tests on 0.40 per cent carbon steel the endurance limit was increased
from 6 0 ,8 0 0 to 6 6 ,0 0 0 psi by peening.There still remains some confusion as to the relative roles of
the cold work and residual compressive stress of peening in the increased fatigue properties.(115) A recent study by Mattson and Roberts (102,103) has used a strain peening method suggested by J. 0. Almen to get varying magnitudes of residual stresses with essentially the same amount
of work-hardening. This allowed comparisons of fatigue data and residual stress changes without other effects usually involved with peening entering into the results.
62Good correlation was found between residual stresses and fatigue
strength tending to substantiate the concept of superposition of residual
stresses and load stresses. Figure 30 is a plot of the results and clearly indicates the higher endurance limit for high compressive residual stresses.
Figure 30. Endurance limit as a function of peak residual stress near the test surface.Conclusions: Most cold working operations induce favorable residual
stresses in metal parts. Straightening and cold drawing* however* were exceptions with surface tensile residual stresses and decreased fatigue
properties noted. The peening process induces compressive residual stresses and work hardens the surface. Strain peening can be utilized
to obtain compressive or tensile residual stresses with approximately the same amount of work hardening. By carefully controlling the variables* peening can greatly increase the fatigue strength of a metal.
CHAPTER V
SUMMARY
A literature survey, and study on the fatigue of metals has been presented as was the objective of this thesis. The survey was
concentrated on the effect of residual stresses on fatigue of steels, and especially for residual stresses induced by heating and cooling, machining, and cold working methods. A bibliography of over 200 refer
ences was included as a major contribution to this work.I. CONCLUSIONS
Fatigue was found to be a very complex phenomenon of metals
that is not very well understood at the present time. Much work and study is needed in most areas of fatigue so that information may be
correlated to develop basic relationships in fatigue.Many conditions affect the fatigue properties of a metal. Such
conditions as high temperature, surface roughness, tensile residual surface stress, and corrosion, definitely lower the fatigue strength.
Conversely, low temperature, high tensile strength, compressive residual surface stresses, and very high frequency tend to raise the fatigue
strength.
Strong evidence is presented that fatigue failures are tensile surface failures. Fatigue rarely, if ever, occurs in pulsating compression. Processes inducing residual compressive stresses are found to
increase the fatigue strength while processes inducing residual tensile surface stresses decrease the fatigue strength of a part.
The bibliography should be an aid to future research in fatigue and especially in the residual stress effect area. References are selected to give general research information and background.
II. RECOMMENDATIONS FOR FUTURE WORK IN FATIGUE
64
Basic fatigue research is needed in all areas before relations
can be found to minimize the present need of testing for almost any new application. Goodman relationships need to be more accurately
determined to eliminate the many approximations now used in design.A short time method of accurately determining the endurance
limit would be extremely valuable. Better and more accurate methods of residual stress measurement are needed. A non-destructive method
that would measure subsurface stresses, with good accuracy^ would be a tremendous contribution to fatigue studies.
Further research is needed in studying the inducement and relaxation of residual stresses due to cyclic stressing. Knowledge in these areas would then lead to more extensive testing on the residual
stress effect in fatigue. Knowing the stress at all times during the
testing would provide very useful information in compiling the fatigue results.
LIST OF REFERENCES
ANDBIBLIOGRAPHY
LIST OF REFERENCES
1.
2.
3-k.
5-
6.
7-
8 .
9.
1 0.
11.
12.
13.
ll+.
Churchill, H.D. Physical Testing of Metals and Interpretation of , Z 0'Test Results. Cleveland: Am. Soc. Metals, (1938), 7*+-90.
f O O I IGilkey, H.J., Murphy, G ., and Bergmann, E.O. Materials Testing.1st ed. New York: McGraw-Hill Book C o . , Inc . , (19*+1) , 185 PP *
eds. Sines, G., and Waisman, J.L. New York: McGraw-Hill Book p 5Co., Inc., (1959), 7-3*+•
Machlin, E. "Dislocation Theory of the Fatigue of Metals," NACA Report 929, (l9*+9), 10 pp.
_ 0Chalmers, B. The Structure and Mechanical Properties of Metals.New York: John Wiley and Sons, Inc., (l95l), 7^-123.
Hi jab, W.A. "a Statistical Appraisal of the Prot Method for the Determination of Fatigue Endurance Limit," J. of App. Mech.,21+(June, 1957), No. 2, 211+-18.
Grover, H.J., Gordon, S.A., and Jackson, L.R. Fatigue of Metals and Structures. U.S. Government Printing Office, Washington, D.C.,1195*+), 39^ PP-
15. Peckner, D. "Why Metals Break and What to Do About It," Materialsin Design Engrg, 5l(Apr., i960), 127-42.
16 . Peterson, R.E. "Fatigue Cracks and Fracture Surfaces - Mechanics of £Development and Visual Appearance," Metal Fatigue, eds. Sines, G. > and Waisman, J.L. New York: McGraw-Hill Book Co., Inc., (1959),68-88.
17. Young, J.F. Materials and Processes. New York; John Wiley andSons, Inc~ (195I+), 113-24. ’
18. Moore, H.F.. and Jasper, T.M. "An Investigation of the Fatigue ofMetals, Univ. 111. Eng. Exp. Sta. Bull. 136, 1921.
19. Dolan, T.J. "Physical Properties," Metals Engineering - Design,ed. Horger, O.J. New York: McGraw-Hill Book Co., Inc., (1953),93-100.
20. Frankel, H.E., Bennett, J.A., and Pennington, W.A. "Fatigue Properties of High Strength Steels," Metal Prog., 76(Oct., 1959),260 ff.
21. Unterweiser, P.M. "Steel's Fatigue Strength Loss Linked to RetainedAustenite," Iron Age, l83(Mar. 19, 1959), No. 12, 115-18.
22. Powel, G.W., Bever, M.B., and Floe, C.F. "Surface Fatigue of Carbo-Nitrided Steel," Metal Prog., 73(Mar., 1958), 67-6 9.
2 3. Powel, G.W., Bever, M.B., and Floe, C.F. "Surface Fatigue of Carbo-Nitrided Steel," Metal Prog., 75(Apr., 1959), 88-90.
24. Moore, H.F.. and Kommers, J.B. "An Investigation of the Fatigue ofMetals, ' U. 111. Eng. Exp. Sta. Bull. 24, Oct., 1921.
26. Boegehold, A.L. "Test Bar Results Compared with Tests on Components,"Metal Prog., 57(Mar., 1950), 349-57*
27. Rosenthal, D., Sines, G., and Zizisas, G. "Effect of ResidualCompression on Fatigue," Welding J., 28(1950), Pt. 2, 98s.
28. Rosenthal, D., and Sines, G. "Residual Stress and Fatigue Strength,"Metal Prog., 58(July, 1950), 7 6.
2 9. Gough, H.J., and Sopwith, D.G. "Atmospheric Action as a Factor inFatigue of Metals," J. Inst. Metals, 49(1932), 93*
30. Gilbert, P.T. "Recent Review of Corrosion Fatigue," Metal Reviews,1(1956), 379.
6831. Wadsworth, N.J. "The Effect of Environment on Metal Fatigue,"
Internal Stresses and Fatigue in Metals, eds. Rassweiler, G.M., and Grube, W.L. New Tork: Elsevier Pub. Co., (1959), 382-97.
32. Moore, H.F., et al. "Report of the Task Group on the Effect ofSpeed of Testing on Fatigue Test Results, ' ASTM Proc., 50(1950), *421-2*4.
33* Moore, H.F., and Putnam, W.J. "Effect of Cold Working and of Rest on Resistance of Steel to Fatigue Under Reversed Stress," A M E Bull. 1b6, (Feb., 19*49), 391.
3*4. Freudenthal, A.M., Yen, C.S., and Sinclair, G.M. "The Effect of Thermal Activation on the Fatigue Life of Metals," U. of 111. Press, Urbana, 111., 19*48.
6 z35* Rosenthal, D. "Measurement of Residual Stress," Residual Stresses ~ in Metals and Metal Construction, @d. Osgood, W.R. New York: Reinhold Pub. Carp., '(195*4), 271“8 5.
3 6. Spraragen, W., and Rosenthal, D. "Review of the Literature onFatigue Strength of Welded Joints," Welding J. Res. Suppl.21(July, 19*42), 297s -3^8s .
37. Ros, M. "Experiments for the Determination of the Influence ofResidual Stresses on the Fatigue Strength of Structures,"Welding Research, *4(0ct., 1950), No. 5# 83r-93r.
3 8. Norton, J.T., and Rosenthal, D. "An Investigation of the Behaviorof Residual Stresses under Load and Their Effect on Safety," Welding J. Res. Suppl., 2 8(19*49), 98s.
39. Soete, W. "Residual Stresses - How Dangerous Are They?" MetalProg., 67(Jan., 1955), 108-1 3.
*40. Rosenthal, D., and Sines, G. "Effect of Residual Stress on theFatigue Strength of Notched Specimens," A S M Proc., 51(1951),593-608.
bl, "Residual Stresses," Metal Prog., 68(Aug. 15, 1955), 89-9 6.b2, Almen, J.O. "Peened Surfaces Improve Endurance of Machine Parts,"
Metal Prog., *43 (Feb., 19^3), 209-15.*43. Almen, J.O. "Shot Blasting to Increase Fatigue Resistance," SAE
J., 6*1-(Aug., 1956), 28-30.14-5 . Rosenthal, D., and Sines, G. "Effect of Residual Stress on Fatigue
Strength of Notched Specimens," ASTM Proc., 51(1951), 593.
5' V
6946. Horger, O.J., Neifert, H.R., and Regan, R„R. "Residual Stresses
and Fatigue Studies/* SESA Proc., 1(1943), No . 1# 10-l8.47. Horger, O.J., and Neifert, H„R. "Correlation of Residual Stresses
with Fatigue Strength of Machine Elements and Related Phenomena," Residual Stresses in Metals and Metal Construction, ed. Osgood, W.R. New York: Reinhold Pub. Corp., (1954), 219-255.
48. Horger, O.J. "Residual Stresses," Handbook of Experimental StressAnalysis, ed. Hetenyi, M.I. New York: John Wiley and Sons, ft11Inc., (1950), 459-578.
49. Benson, L.E, "Some Considerations Regarding the Generation andImportance of Residual Welding Stresses," Residual Stresses in Metals and Metal Construction, ed. Osgood, W.R. New York:Reinhold Pub. Corp., (1954), 75-84.
50. Buhler, H., and Buchholtz, H. "Uber die Wirkung von Eigenspannun-gen auf die Sehwingungsfestigkeit," (The Effect of Residual Stress on the Dynamic Bending Strength), Mitt. Forsch. Inst., Dortmund, 3(Sept., 1933), Wo. 8, 235-248.
52. Gisen, F., and Glocker, R. "Rontgengeographisehe Bestimmungen derzeitlichen Anderung des Eigenspannungszustandes bei Biegewech- selbeanspruchung," Z. Metal,Ikunde, 30(1938), 297-98.
53* Jasper, T.M., and Stewart, W.C. "Stress Relief," Metal Prog.,58(july, 1950), 79-80.
54. Moore, H.F. "A Study of Residual Stress and Size Effect," SESAProc., 2(1944), No. 1, 171-77.
55. Morrow, J., Ross, A.S., and Sinclair, G.M. "Relaxation of ResidualStresses Due to Fatigue Loading," SAE Trans., 6 8(1960), 40-48.
5 6. Martin, D.E. "Evaluation of Methods for Measurement of ResidualStresses," SAE Tech. Report 147, (Sept., 1957)# 43 pp.
57* Glickman, L.A., and Stepanov, V.A* "Residual Stresses Caused by Grinding," Er.gr. Dig., 4(Aug., 1947)# 378-79.
6 5. Letner, H.R. "An Application of Optical Interference to the Studyof Residual Stress," SESA Proc., 10(1953), No. 2.
6 6. Rosenthal, D. "Influence of Residual Stress an Fatigue," MetalFatigue, eds. Sines, G«, and Waisman, J.L. New York: McGraw-Hill Book Co., inc., (1959), 170-96.
6 7. Barrett, C.S. "A Critical Review of Various Methods of ResidualStress Measurements," SESA Proc., 2(1944), No. 1, 147-55•
6 8. Sachs, G., and Van Horn, K.R. Practical Metallurgy. Cleveland:Am. Soc. Metals, 194-0.
6 9. Sachs, G., and Espey, G. "The Measurement of Residual Stresses inMetal," Iron Age, l48(Sept. l8, 1941), 63-71 and l48(Sept. 25, 19^1), 36-UO.
70. Baldwin, W.M. Jr. "Residual Stresses in Metals," ASTM Proc.,^9(19^9), 539-583.
71. Treuting, R.G., and Read, W.T. Jr. "A Mechanical Determination ofBiaxial Residual Stress in Sheet Metals," J. of Appl. Hays.,22(1951), No. 1, 130-34.
72. Mathar, J. "Determination of Initial Stresses by Measuring theDeformations Around Drilled Holes," ASME Trans., 56(1934), 249-54.
73. DeForest, A.V., and Stem, F.B. Jr. "Stress Coat and Strain forResidual Stress," SESA Proc., 2(1944), No.l, 161-6 9.
74. Barrett, C.S. "X-Ray Analysis," Handbook of Experimental StressAnalysis, ed. Hetenyi, M.I. New York: John Wiley and Sons,Inc., (1950), 977-1012.
75» Hyler, W.S., and Jackson, L.R. "Precautions to be Used in theMeasurement and Interpretation of Residual Stresses by X-Ray Technique," Residual Stresses in Metals and Metal Construction, ed. Osgood, W.R. New York: Reinhold Pub. Corp., (195*0, 297.
71
76. Christenson, A.L.* and Rowland* E.S. i!X-Ray Measurement of Residual Stress in Hardened High Carbon Steel*" Am. Soe. Metals* Trans,*^5(1953).
77* Marburger* R.E., and Koistinen* D.P. "X-Ray Measurement of Residual Stresses in Hardened Steel*" Internal Stresses and Fatigue in Metals* ed. Rassweiler* G.M.* and Grufoe* W.L. New York:Elsevier Pub. Co.* (1959)? 98-109•
Barrett* C.S. Structure of Metals. New York: McGraw-Hill Book Co.Inc.* 19^3•
79. Norton* J.T. "X-Ray Methods in the Field of Residual Stresses,"SESA Proe.* 2(19^)* No. 1* 157-6 0.
8 0. Isenburger* H.R. "Bibliography of Stress Analysis by Means of X-RayBack Reflection Method*" Welding <J. Res. Suppl.* 9(Ncv.* 19VO* 571s-72s.
81. Spraragen* W.* and Claus sen* G.E. "Review of the Literature onFatigue of Welds," Welding J. Res. Suppl., l6 (jan., 1937)* l-tes.
82. Spraragen* W., and Claus sen* G.E. "Shrinkage Stresses in Welding -A Review of the Literature to January, 1937*11 Welding J. Res. Suppl., l6 (Nov.* 1937)? 2s-52s.
8 3. Spraragen, W., and Cordovi* M.A. "Shrinkage Stresses in Welding -A Review of the Literature from January* 1937 to September, 1940," Welding J. Res. Suppl.* 19(May, I9U1 )* 209s-^6s.
8^. Welter, G. "Stresses Around a Spot Weld under Static and Cyclic Loads," Welding J. Res. Suppl.* 2 9(Nov., 1950), 5^5s-76s.
8 5. Boegehold* A.L. "Some Effects of Quenching and Tempering onResidual Stresses," 57(F®b.* 1950), 183-8 8.
8 8* Harris* W.J. Metallic Fatigue. New York: Pergamon Press* (1961),331 PP.
8 9. Hauk* V. "Internal Stresses in Spot Welds," Metal Prog., 56(Oct.,19^9 ), 582.
90. Horger* O.J.* and Neifert* H.R. "Internal Stresses and Fatigue*"MIT Conference cm Fatigue and Fracture of Metals* June, 1950.
91. Dolan* T.J. "Basic Concepts of Fatigue Damage in Metals," MetalFatigue, ed. Sines* GU* and Waisman* J.L. lew York: McGraw-Hill Book Co.* Inc.* (1959)? 39-67.
I n ?'-m v. X
72
92. Wilson, W.M. !,W®lded Structural Joints," Metals Engineering -Design, ed Horger, O.J. New York: McGraw-Hill Book Co., Inc.,T19537, 190-92.
93. Tarasov, L.P., and Grover, H.J. "Effects of Grinding and otherFinishing Processes on the Fatigue Strength of Hardened Steel," ASTM Proc., 50(1950), 668-9 8.
9*1. Colwell, L.V., Sinnott, M.J., and Tobin, J.C. "The Determination, of Residual Stresses in Hardened, Ground Steel," ASME Trans., 77(1955), 1099-1105.
9 6. Boyer, H.E. "Effects of Grinding on Physical Properties of HardenedSteel Parts," Am. Soc. Metals Trans., ^0(19^8), ^91-503.
97. Tarasov, L.P., Hyler, W.S., and Letner, H.R. "Effect of GrindingConditions and Resultant Residual Stresses on the Fatigue Strength of Hardened Steel," ASTM Proc., 57(1957), 601-18.
9 8. Frye, J.H., and Kehl, G.L. "Fatigue Resistance of Steels as Affectedby Some Cleaning Methods," Am. Soc. Metals Trans., 26(1938),192.
99* Horger, O.J. Stressing Axles and other Railroad Equipment by Cold Rolling. Cleveland: Am. Soc. Metals, (Feb., X9I4-6 ).
100. Horger, O.J. "Mechanical and Metallurgical Advantages of ShotPeening," Iron Age, 155(Mar. 29, 1945), and 155(Apr. 5, 19^5).
101. Moore, H.F. "Shot Peening," Metals Engineering - Design, ed.Horger, O.J. New York: McGraw-Hill Book Co., Inc., (1953),121-23.
102. Mattson, R.L., and Roberts, J.6 . "Effect of Residual StressesInduced by Strain Peening Upon Fatigue Strength," Internal Stresses and Fatigue in Metals, eds. Rassweiler, G.M., andGrube, W.L. New York: Elsevier Pub. Co., (1959), 337-62.
103. Mattson, R.L., and Roberts, J.G. "The Effect of Residual StressesInduced by Strain Peening upon Fatigue Strength," SAE Trans.,68(1960), 130-3 6.
IOU. Richards, D.G. "A Study of Certain Mechanical-Induced Residual Stresses," SESA Proc., 3(19^5), No. 1, 0-6,1.
105. Horger, O.J., and Neifert, H.R. "Shot Peening to Improve FatigueResistance," SESA FToe., 2(l9W-), No. 2, 1-10.
106. Fahrenhorst, W., and Sachs, G. "Uber das Aufreiben von KaXtgezo-genem Rundeisen," (The Cracking of Cold Drawn Steel Bars), Metallwirtschaft, 10(1931), No. kl, 783-88, and 880-81.
73107. l&chtman, E.S. "Residual Stresses to Cold Finished Steel Bars and
Their Effect esa Manufactured Parts," Lasaile Steel Bull. 16, (June, 3555), 1-32. ! \
108. Fuchs, E.D. '’Techniques of Surface Stressing to Avoid Fatigue,"Metal Fatigue, eds. Sines, G., and Waisman- J.L. New York: McGraw-Hill Book Co., Inc., (1959), 197-231.
109.no.
111.
longer, O.J., and U p s o n , C.H. "Automotive Rear Axles and Means of Improving Their Fatigue Resistance,” ASTM Tech. Pub. 72, 1946.
Ql°longer, O.J., and Neifert, E. Fatigue and Fracture of Metals. New
York: John Wiley and Sons, Inc., -1953.----- “(l*
Greaves, R., RLrtcwsky, E., and Lipson, C. "Residual Stress Study,” f SESA Proc., 2(19^5), No. 2, 44-58.
113. Osgood, W.R. Residual Stresses to Metals and Metal Construction. New York: Retohold Pub. Corp., T l « p i 7 , ^ 6 3 " p p 7
12.4. Horger, O.J., and Maulbetsch, J.L. "Increasing the Fatigue Strength of Press-Fitted Axle Assemblies,” ASME Trans., 58 (Sept., 1936), A 91-A 98.
115. Horger, O.J., and Neifert, H.R. "Improving Fatigue Resistance by Shot Peentog," SESA Proc., 2(1944), No. 1, 178.
Smith, E.P.W. "Effect of Residual Stresses on the Fatigue of Compressor Valves," Metal Prog., 57(Apr., 1950), No. 4, 48o-8l.
BIBLIOGRAPHY
FATIGUE - GENERAL
1. Grover, H.J., Gordon, S.A., and Jackson, L.R. Fatigue of Metalsand Structures. Bureau of Aeronautics, Dept, of the Navy,X1960), 399 PP.
2. Astles, G.M. "Introduction to Problem of Metal Fatigue," Metropolitan Gaz., 30(0ct., 1959)/ 263-6 9.
3. Pope, J.A. Metal Fatigue. London: Chapman and Hall, Ltd., 1955*4. Moore, H.F. "Fatigue of Metals", Metals and Alloys, 10(May, 1939)t158-62.5. Murray, W.M., and Hunsaker, J.C. Fatigue and Fracture of Metals.
New York: John Wiley and Sons, 1952.
6 . Thompson, N., and Wadsworth, N.J. "Metal Fatigue," Adv. in Phys.,7(Jan., 1958), 72-170.
7. Averbach, B.L. et al. Fracture. New York: John Wiley and Sons,Inc., (1959)> 6^6 PP*
8 . Wood, W.A. "Some Basic Studies of Fatigue," Fracture, ed. Averbach, B.L. et al. New York: John Wiley and Sons, Inc., 1959*
9 . Honeycombe, R.W.R. "Session on Fatigue and Ductile Fracture,"Fracture, ed. Averbach, B.L. et al. New York: John Wiley andSons, Inc., 1959*
10. Thompson, N. "Some Observations on the Early Stages of FatigueFracture," Fracture, ed. Averbach, B.L. et al. New York: John Wiley and Sons, Inc., 1959*
11. Hetenyi, M.I. Handbook of Experimental Stress Analysis. New York:John Wiley and Sons, Inc., (1950), 1077 PP*
12. Teed, P.L. "Fatigue - What It is and Improvement," Aircraft Prod.,1M1952), 362.
13. Head, A.K. "The Mechanism of Fatigue of Metals," J. of Mech. andRiys. of Solids, l(Feb.,1953), 13^*
I1*. Sines, G., and Waisman, J.L. Metal Fatigue. New York: McGraw HillBook Co., (1959)> ^15 PP.
7515. Sines, G., Waisman, J.L. "The Problem of Metal Fatigue," Metal
40. Moore, H.F. "How and When Does A Fatigue Crack Start?" Metals andAlloys, 7(1936), 297-99.
41. Horger, O.J. Metals Engineering - Design. New York: McGraw-HillBook C o., (1953), 405 pp.
42. Strehelle, J. "Presentation of Fatigue Test Results," Brit. Weld.,6 (Feh., 1959), 65-71.
43. Spaulding, E.H. "Design for Fatigue," SAE Trans., 62(1954), 104.44. Stuessi, F. "Theory and Test Results on Fatigue of Metals," ASCE
Proc., 85(1937).45. Karpov, A.V. "Fatigue Problems in Structural Design," Metals and
Alloys, 10(1939), 346,381.46. Templin, R.L., Hartmann, E.C. "How to Design for Repeated Loads,"
Iron Age, 169(1952), 9 8.
47. Hartmann, E.C., and Templin, R.L. "Fatigue Data Used in Design,"Metal Prog., 39(l9**-l), 6o4.
48. Hartmann, E.C. "Fatigue Test Results, Use in Design," Prod. Engr.,12(1941), 74.
4 9. Anon. Prevention of the Failure of Metals under Repeated Stressing.Battelle Memorial Inst. New York: John Wiley and Sons, Inc.,1941.
77
50. Almen, J.0„ "Useful Data From Fatigue Tests/' Metal Prog.,kk(Aug.,19^3 )> 25^-61•
51. Peterson, R.E. "Relation Between Stress Analysis and Fatigue,"SESA Proc., 11(195*0, No. 2, 199-206.
52. Stulen, F.B., and Cummings, H.N. '̂ Failure Criterion for Multi-axial Stresses," ASTMProc., 5*+(l95*0, 822.
53. Yokobori, T. "Stress Criterion For Fatigue Fracture of Steels,"J. Mech. and Pbys. of Solids, 8(May, i960). No. 2, 81-86.
5*+. Valluri, S.R. "A Unified Engineering Theory of High Stress Level Fatigue," Aerospace Engr., 20(0ct., 1961), 18.
55- Peterson, R.E. "interpretation of Service Failures," Handbook of Experimental Stress Analysis, ed. Hetenyi, M.I. New York:John Wiley and Sons, Inc., (1950), 593*
5 6. Richart, F.E. Jr., and Newraark, N.M. "An hypothesis for theDetermination of Cumulative Damage in Fatigue," ASTM Proc.,k8 ( 19*18), 1-3 1.
57* Miner, M.A. "Cumulative Damage in Fatigue," J. Appl. Mech.,12(Sept., 19*̂ 5), No. 3, A159-64.
58. Miner, M.A. "Cumulative Damage Affect on Life," Machine Design,17(19*^5), 1 11.
59* Miner, M.A. "Estimation of Fatigue Life With Particular Emphasison Cumulative Damage," Metal Fatigue, ed. Sines, G., Waisman, J. New York: McGraw-Hill Book Co., (1959), 278-97-
60. Coffin, L. "Cyclic Straining and Fatigue," Internal Stresses andFatigue in Metals, ed. Rassweiler, G.M., and Grube, W.L. New York: Elsevier Pub. Co., (1959)> 363-82.
61. Dolan, T.J. "Stress Range," Metals Engineering - Design, ed.Horger, O.J. New York: McGraw-Hill Book Co., (1953), 82-8 9.
62. Findley, W.N. "Effect of Mean Stress on Fatigue of Metals," ASMEPaper 58-A-6 1, (Nov. 3 - Dec. 5> 1958), 5 PP-
6 3 . Findley, W.N. "Fatigue of Metals Under Combinations of Stresses,"ASME Trans., 79(Aug., 1957)> 1337-*+7-
6k. Findley, W.N., and Mather, P.N. 'Modified Theories of FatigueFailure Under Combined Stress," SESA Proc., 1^(1956), No. 1,35-U6 .
6 5 . Gough, H.J., and Pollard, H.V. "The Strength of Metals Under Combined Alternating Stresses," Inst. Mech. Engr., 131(1935), 37.
786 6. Lea, F.C., and Budgen, H.P. "Combined Torsional and Repeated Bending
Stress," Engineering, 122(Aug., 1920), 21+2-1+5.6 7. Sines, G. Behavior of Metals Under Complex Static and Alternating
Stresses," Metal Fatigue, ed. Sines, G., and Waisman, J.L.New York: McGraw-Hill Book Co., (1959), 11+5-69*
6 8. Moore, H.F. ''Types of Stress," Metals Engineering - Design, ed.Horger, O.J. New York: McGraw-Hill Book Co., (1953)>80-82.
75- Seliger, V. "New Parameter for Fatigue Strength Analysis," ASTM Bull. 132, (191+5), 29.
7 6. ASTM Research Committee. "The Effect of Type of Testing Machine on Fatigue Test Results," ASTMProc., l+l(l9l+l), 133*
77* Moore, H.F. "Effect of Type of Testing Machine on Fatigue," ASTM Proc., 1+1(191+1), 133-
7 8. Peterson, R.E. "Relation Between Life Testing and Conventional Tests of Materials," ASTM Bull. 133, (Mar., I9U5 ) , 9 -1 5•
79• Lazan, B.J. “Fatigue of Structural Materials at High Temperature," AGARD Report 156, (Nov., 1957), 28 pp.
80. Grover, H.J. "Fatigue of Materials at High Temperature," Metal Fatigue, ed. Sines, G., and Waisman, J.L. New York: McGraw-Hill Book Co., (1959), 232-1+6.
"Basic Studies Probe of Metals' Mechanical Properties," Space Aeronautics, 3^(Aug., i960), No. 2, 79=80.
8 1 .
79
82. Jackson, L.R., and Pocharpsky, T.E. "The Effect of Composition on the Fatigue Strength of Decarburized Steel," Am. Soc. Metals Trans., 39(1947), 45-60.
83• McAdam, D.J. "Endurance Properties of Steel: Their Relation toOther Physical Properties and to Chemical Composition," A S M Proc., 23(1923), 56-105.
84. Sinclair, G.M., and Dolan, T.J. "Some Effects of Austenitic GrainSize and Metallurgical Structure on the Mechanical Properties of Steel," ASTMProc., 50(1950), 587*
8 5 . Williams, W.L. "The Effects of Metallizing Procedures on theFatigue Properties of Steel," A S M Proc., 49(194-9)•
91. Almen, J.O. "Fatigue - Loss and Gain By Electroplating," Prod.Engr., 22(June, 1951), Ft. 2.
92. Horger, O.J., and Buckwalter, T.V. "Fatigue Strength Improved ByFlame Treatment," Iron Age, Dec. 18, 1941.
93* Caswell, J.S. "Effect of Surface Finish on Fatigue Limit of Mild Steel," Prod. Engr., 18(Mar., 1947), 152.
94. Wilson, W.K. "Effect of Surface Conditions on Fatigue Strength," Inst. Mech Engrs. Proc., 153(1945), 347-51*
95- Horger, O.J. "Fatigue Strength of Members as Influenced by Surface Conditions," Prod. Engr., ll(Dec., 1940), Pt. 2, 562-6 5 .
9 6. Horger, O.J. "Fatigue Strength of Members as Influenced by Surface Conditions," Prod. Engr., 12(Jan., 194l), 22-24.
97* Hempel, M.P. "Surface Condition and Fatigue Strength," Internal Stresses and Fatigue in Metals, ed. Rassweiler, G.M., and Grube, W.L. "Hew York!” Elsevier Pub. Co., (1959), 311-37*
98. ft
80
99.
100.
101.
102.
103.
104.
105.
106.
107.
108.
109.
no.
1 11.112.
Hanley, B.C., and Dolan, T.J. Design, ed. Horger, 0.J . 100-107.
Surface Finish, New York:
Metals Engineering- McGraw-Hill Book Co., (1953),
Hankins, G.A., Becher, M.L., and Mills, H.R. "Further Experiments on the Effect of Surface Conditions on the Fatigue Resistance of Steels," Iron and Steel Inst., 133(1936), No. 1 , 399-453.
Thomas, W.N. "Effect of Scratches and of Various Workshop Finishes Upon the Fatigue Strength of Steel," Engineering, 116(1923), 449-54.
Mowbray, A.Q.Jr. "The Effect of Superposition of Stress Raisers on Members Subjected to Static or Repeated Loads," SESA Proc., 10(1953), Pt. 2, 153-66.
Fluek, P.G. "The Enfluence of Surface Roughness on the Fatigue Life sind Scatter of Test Results of Two Steels," ASTM Proc., (1957), 584.
Timoshenko, S. "Stress Concentration and Fatigue Failures," Inst. Mech. Engr. Proc., 157(1947), 163.
Peterson, R.E., and Wahl, A.M. "Stress Concentration in Comparison With Fatigue, " SESA Proc., 1(1944), Pt. 2, ll6 .
Cledwyn-Davies, D.N. "Effect of Grinding on Fatigue Strength," Engineer, 198(Aug. 20, 1954), 270-72.
81lll+. Sopwith, D.G., and. Gough, H.J. 'The Effect of Protective Coatings
on Corrosion Fatigue Resistance of Steel," J. Iron and Steel Inst. (London), 135(1937), 315.
115. Wyss, T. "influence of Testing Frequency on Fatigue," ASTM Bull.188, (1953), 31.
116 . Harris, W.J. "Cyclic Stressing Frequency Effect on Fatigue,"Aircraft Engr., 3l(Dee., 1959)# No. 370, 352-57.
117. Hudson, R.A., and Chick, J.E. "Acceleration of Fatigue Tests,"Aeronautical Dig., 3 1(1937), No. 3, 7 8*
118. Markoven, D.. and Moore, H.F. "Effect of Size of Specimen onFatigue, ASTM Proc., U M I 9W+ ), 1^3,4.
119. Moore, H.F., Markovin, D. '̂ The Effect of Size of Specimen on theFatigue Strength of Three Types of Steel, "Ref. 118, Pg. 137.
120. Phillips, C.S., and Heywood, R.B. '̂ The Size Effect of Plain andNotched Steel Specimens Loaded Under Reversed Direct Stress,"Inst. Mech. Engr., 165(1951), 113.
121. Afanasiev, N.N. '̂ The Effect of Shape and Size Factors on the FatigueStrength," Engr. Dig., 5(19^8), No. 3 .
122. Dolan, T.J., McClow, J.H., and Craig, W.J. "The Influence of Shapeof Cross Section on the Flexural Strength of Steel," ASME Trans., 72(1950), No. 5, ^6 9 .
123. Langer, B.F. "Fatigue Failure From Stress Cycles of VaryingAmplitude," J. Appl. Mech., 4 (Dee., 1937)# No. 4, A-l60-2.
12U. Dolan, T.J., Richart, F.E., and Work, C.E. "influence of Fluctuations in Stress Amplitude on the Fatigue in Metals," ASTM Proc., 1*9(19^9).
125* Feltham, P. "Fatigue of Metals Caused By High Load Amplitude,"Met. Rev., 3(1958), No. 11, 203-3I+.
126. Liu, H.W., and Corten, H.D. "Fatigue Damage During Complex Stress Histories," NASA Tech. Note D-256, (Nov., 1959)# 56 pp.
127- Russell, H.W., and Welker, W.A. "Damage and Overstressing in the Fatigue of Ferrous Materials," ASTM Proc., 36(1936), No. 2, 118-38.
128. Kommers, J.B. "The Effect of Understressing on Cast Iron and Open- Hearth Iron," ASTM Proc., 30(1930)# No. 2, 368-8 3*
Kommers, J.B. !,The Effect of Overstressing and Uhderstressing in Fatigue," ASTM Proc., 38(1938), No. 2, 2^9*
129.
82130. Kommers, J.B. ''The Effect of Overstressing and Understressing in
Fatigue/' ASTM Proc., 1+3(191+3), 7^9»131. Kommers, J.B. ""The Effect of Overstress in Fatigue on the Endur
ance Life of Steel," A S M Proc., 1+5(19^5), 532-43*132. Kommers, J.B. "Overstressing and Understressing in Fatigue,"
Metals Engineering - Design, ed. Horger, O.J. New York; McGraw- Hill Book Co., (1953/ 192=98.
133. Sinclair, G.M. "An Investigation of the Coaxing Effect in Fatigueof Metals," ASTM Proc., 52(1952).
13^. Almen, J.O. "Endurance of Machines Under a Few Heavy Loads," Metal Prog., U3(Sept., 191+3 ), 1+35-1+0.
135* France, R.D. "Endurance Testing of Steels Comparison of Results Obtained With Rotating Beam Versus Axially Loaded Specimens," ASTM Proc., 3l(l93l), No. 2, 176.
RELAXATION OF RESIDUAL STRESS
136. Jasper, T.M., and Stewert, W.C. "Stress Relief," Metal Prog.,5 8(July, 1950), 79-80.
137. Richards, D.G. "Relief and Redistribution of Residual Stress inMetals," Am. Soc. Metals, 1+3(1951), 129-91*
138. Findley, W.N., and Worley, W.J. "Stress Relaxation and StaticTensile Tests," SESA Proc., 17(1959), No. 1, 15-22.
139* Wallace, W.P., and Frankel. J.P. "Relief of Residual Stress by a Single Stress Cycle, ' Welding J., 28(Nov., I9I+9 ), 565s.
MEASUREMENT OF RESIDUAL STRESS
ll+O. Heindlhofer, K. Evaluation of Residual Stress. New York: McGraw-Hill Book Co., (19*4-8 ), 195" pp.
ll+2. Soete, W., and Vancrombrugge, R, "Determination of ResidualStresses Below the Surface," Residual Stresses in Metals and Metal Construction, ed. Osgood, W.R. New York; Reinhold Pub.Corp., (195*0, 331-34 *
ll+3. Johnson, L.G. "Derivation of Fundamental Equation of Residual Stress Analysis by Dissection," Ind. Math., 5(1955), 7*
162. Barrett, C.S. "Predicting a Fatigue Failure - Are X-Rays Competent?,"Metal Prog., 32(Nov., 1937)* 677-78.
m
162. Gough, H.J. "incipient Fracture Revealed By X-Rays, " Metal Prog.,32(Sept., 1937), 276.
163. "Fatigue Damage Shown by X-Rays," Machine Design, 48(Nov., 19*+8),100.
164o Norton, J.T. "X-Ray Methods in the Field of Residual Stresses," SESA Proc., 2(19*+*+), No. 1, 157-60.
RESIDUAL STRESS AND FATIGUE165. Mattson, R.L. "Effects of Residual Stress on Fatigue Life," Auto.
Ind., 110(Mar. 15, 195*+), 185 ff.166. Mattson, R.L. "Effects of Residual Stress on Fatigue Life," Steel
Processing, 40(June, 195*0, 365-75, 390.167. Mattson, R.L. "Effects of Residual Stress on Fatigue Life," SAE
Preprint 220, Jan. 11-15, 195**°16 8. Greene, T.W. "Evaluation of Effect of Residual Stresses," Welding
J. Res. Suppl., 28(19^9), 193s-203s.
169. Dugdale, D.S. "Effect of Residual Stress on Fatigue Strength,"Welding J. Res. Suppl., 38(Jan., 1959), *+5s-48s.
170. Campus, F. "Effects of Residual Stresses on the Behavior ofStructures, " Residual Stresses in Metals and Metal Construction, ed. Osgood, W.R. New York: Reinhold Pub. Corp., (195*0, 1-23°
171. Bijlaard, P.P. "Some Remarks on the Influence of Residual Stresseson the Brittle, Plastic, and Fatigue Behavior of Structures," Residual Stresses in Metals and Metal Construction, ed. Osgood, W. New York: Reinhold Pub. Corp., (1954), 127-39*
172. Rassweiler, G.M., and Grube, W.L. (eds.) Internal Stresses andFatigue in Metals. New York: Elsevier Pub. Co., (1959), *+51 PP°
173° Forest, G. "Some Experiments on the Effects of Residual Stresseson the Fatigue of Aluminum Alloys," Inst. Metals J., 72(l9*+6),498-527.
17*+. MacGregor, C.W. ''The Significance of Residual Stresses," Residual Stresses in Metals and Metal Construction, ed. Osgood, W.S.New York: Reinhold Pub. Corp., (1954), 103-127.
175° Iron and Steel Technical Committee. "Bibliography on Residual Stress," SAE Paper SP-I6 7, No. 1, (Feb., 1959), 110.
177» Treuting, R.G. "Nature, Origin, and Effect of Residual Stresses,"Am. Soc. Metals, Sp. Pub., (Oct. 15-19* 1951), l-4l.
178. Dolan, T.J. **Residual Stress, Strain Hardening, and Fatigue,"Internal Stresses and Fatigue in Metals, eds. Rassweiler, G.M., and Grube, W.L. New York; Elsevier Pub. Co., (1959), 284-311.
179* Bruchner, W.H., and Munse, W.H. "toie Effect of Metallurgical Changes Due to Heat Treatment Upon the Fatigue Strength of Carbon Steel Plates," Welding J., (Oct., 1944), 499s-510s.
180. Campbell, J.E., and Mclntire, H.O. "How to Develop Favourable StressPatterns," Iron Age, 172(1953), Pt. 2, 102.
181. Reeve, L. "internal Stresses in Welding and Their Determination,"Welding Ind., 4(1936), 344-55-
182. Spraragen, W. "Residual Stresses in Welding," Residual Stresses inMetals and Metal Construction, ed. Osgood, W.S. New York:Reinhold Pub. Corp., (1954), 85-103.
183» Wishart, H.B. "Residual Stress States Produced by Processes," Am. Soc. Metals Sp. Pub., (Oct. 15-19, 1951), 97-128.
184. Van Horn, K.R. "Residual Stresses Induced During Fabrication," J.Metals Trans., 197(1953)* 405-22.
18 5 . Tarasov, L.P., Hyler, W.S., and Letner, H.R. "Effect of GrindingConditions and Resultant Residual Stresses on the Fatigue Strength of Hardened Steel," ASTM Proc., 57(1957)> 601-18.
186. Letner, H.R. "influence of Grinding Fluids on Residual Stress inSteel," ASME Trans., 79(1957)* Pt. 1, 149-153-
187• Polakowski, N.H., and Palehoudhurri, A. "Fatigue Softening of Cold- Worked Metals , " ASTM Proc., 54(1954), 701-12.
188. Heyn, E. "internal Strains in Cold Wrought Metals," Inst. Metals J., 12(1914), No. 2, 1-37-
189- Williams, C., and Hammand, R.A.F. "Effect of Shot Peening and Grinding on Fatigue," Am. Electroplaters Soc., Tech. Proc., (1959), 195-204.
190. Lessells, J.M., and Murray, W.M. "Effect of Shot Blasting on Fatigue,ASTM Proc., 4l(l94l), 659-8 1 .
191. Felgar, R.P. Effect of Shot Peening of Fatigue Strength," ASME Paper 58-SA-46, (1958).
Coombs, A.G.H. "The Effect of Shot Peening on the Fatigue Life of Steel," Engineering, 174(1952), 545.
Metal Fatigue, eds. Sines, G. and Waisman, J.L. New Yorks McGraw-Hill Book Co., (1959), 112-45.
1 9 5. "Guide for Fatigue Testing and Statistical Analysis," ASTM stp 91“A,(1958).
196. Bore, C.L. "The Presentation of Fatigue Data for Fatigue LifeCalculations," Royal Aero. Soc. J., 6o(May, 1956), 331-46.
197* Tavernelli, J.F., and Coffin, L.F. "Compilation and Interpretation of Cyclic Strain Fatigue Tests on Metals," Am. Soc. Metals Preprint 112, (1958).
198. Tavernelli, J.F., and Coffin, L.F. "A compilation and Interpretation of Cyclic Strain Fatigue Tests on Metals," Am. Soc. Metals, 51(1959), 438-50.
199* Leybold, H.A. "Axial Load Fatigue Tests on 17-7 PH Stainless Steel Under Constant Amplitude," NASA Tech. Note D-439, (Oct., i9 60).
200. Seelig, R.P. "European Research in Fatigue," ASTM Bull. 95,(Dec., 1938), 15-23.
201. Grover, H.J. "Recent Survey of Current Activities on Fatigue,"ASTM Bull. 235, (Jan., 1959), 26-2 9.
202. Dolan, T.J. 'Method of Testing," Metals Engineering - Design,ed. Horger, O.J. New York: McGraw-Hill Book Co., (1953), 89-93.
203. Freudenthal, A.M. "A Random Fatigue Testing Procedure and Machine,"ASTM Proc., 53(1953), 8 9 6.
204. Morrison, J.L.M., Crossland, B., and Parry, J.S.C. "Fatigue UnderTriaxial Stress: Development of a Testing Machine and Preliminary Results," Inst. Mech. Engr. Proc., 170(1956), No. 21.
205. "Symposium on Large Fatigue Testing Machines and Results," ASTMstp 216, (1958), 151 PP.
207. Krouse, G.N. "a High Speed Fatigue Testing Machine and Some Testsof Speed Effect on Endurance," A S M Proc., 34(1934), Pt. 2, 156.
208. Findley, W.N. "New Apparatus for Axial Load Fatigue Testing,"ASTM Bull. 147, (1947), 54.
A LITERATURE REVIEW
COVERING THE EFFECT OF RESIDUAL STRESSES
ONFATIGUE STRENGTH OF STEEL
An Abstract of
A Thesis Presented to the
Department of Mechanical Engineering Brigham Young University
In Partial Fulfillment
of the Requirements for the Degree Master of Science
byClarence A. Calder
August, 1962
ABSTRACT
The purpose of this thesis was to present a literature review and study on the problem of fatigue in metals, and in particular, the effect of residual stresses on fatigue properties. Current knowledge
on other factors affecting fatigue is also briefly outlined.Processes inducing surface residual stresses have a significant
influence on the fatigue strength. Surface compressive residual stresses
were found to be beneficial to fatigue strength, whereas, surface tensile residual stresses were detrimental. The various methods of inducing residual stresses and their resulting effect on fatigue were
discussed.A selected bibliography of over 200 references is included
together with the list of references cited in the thesis.
Recommendations are also made for future research on fatigue of metals.
