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Dr. A. Aziz Bazoune Chapter 7: Fatigue Failure Resulting from Variable Loading
ME 307 Machine Design IME 307 Machine Design I
Dr. A. Aziz Bazoune
King Fahd University of PetroleumKing Fahd University of Petroleum& Minerals& Minerals
Mechanical EngineeringMechanical EngineeringDepartmentDepartment
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ME 307 Machine Design IME 307 Machine Design I
CH-07 LEC 25 Slide 2
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ME 307 Machine Design IME 307 Machine Design I
CH-07 LEC 25 Slide 3
7-11 Characterizing Fluctuating Stresses7-11 Characterizing Fluctuating Stresses
Fluctuating stresses in machinery often take the form ofsinusoidal
pattern because of the nature of the nature of some rotating machinery.
Other patterns some quite irregular do occur.
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ME 307 Machine Design IME 307 Machine Design I
CH-07 LEC 25 Slide 4
7-11 Characterizing Fluctuating Stresses7-11 Characterizing Fluctuating Stresses
In periodic patterns exhibiting a single maximum and single minimum offorce, the shape of the wave is not important.
The peaks on both sides (maximum, minimum) are important.
Fmax and Fmin in a cycle can be used to characterize the force pattern.
A steady component and an alternating component can be constructed as
follows:
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Dr. A. Aziz Bazoune Chapter 7: Fatigue Failure Resulting from Variable Loading
ME 307 Machine Design IME 307 Machine Design I
CH-07 LEC 25 Slide 5
Stress RangeStress Range
Mean (MidrangeMean (Midrange
Stress)Stress)
Stress AmplitudeStress Amplitude
(Alternating Stress)(Alternating Stress)
Stress RatioStress Ratio
Stress AmplitudeStress Amplitude
(R>0 )
(R =0)
(R =-1)
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Dr. A. Aziz Bazoune Chapter 7: Fatigue Failure Resulting from Variable Loading
ME 307 Machine Design IME 307 Machine Design I
CH-07 LEC 25 Slide 6
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ME 307 Machine Design IME 307 Machine Design I
CH-07 LEC 25 Slide 7
Any varying stress with a nonzero meanis considered a fluctuating stress.
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Dr. A. Aziz Bazoune Chapter 7: Fatigue Failure Resulting from Variable Loading
ME 307 Machine Design IME 307 Machine Design I
CH-07 LEC 25 Slide 8
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Dr. A. Aziz Bazoune Chapter 7: Fatigue Failure Resulting from Variable Loading
ME 307 Machine Design IME 307 Machine Design I
CH-07 LEC 25 Slide 9
The steady, or static, stress is not the
same as the midrange stress.
The steady stress may have any value
between minand min. The steady stress exists because of a
fixed load or preload applied to a part.
The steady load is independent of the
varying portion of the load.
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Dr. A. Aziz Bazoune Chapter 7: Fatigue Failure Resulting from Variable Loading
ME 307 Machine Design IME 307 Machine Design I
CH-07 LEC 25 Slide 10
A helical compression spring is always loaded into a space shorter
than the free length of the spring.
The stress created by this initial compression is called the steady,
or static, component of the stress.
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ME 307 Machine Design IME 307 Machine Design I
CH-07 LEC 25 Slide 11
Equations (7-39) use symbols a and m as the stress components at the
location of scrutiny.
In the absence of a notch, aandm are equal to the nominal stresses
aoandmoinduced by loadsFa andFm , respectively.
With a notch they are a = Kfaoand m = Kfmo, respectively.
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Dr. A. Aziz Bazoune Chapter 7: Fatigue Failure Resulting from Variable Loading
ME 307 Machine Design IME 307 Machine Design I
CH-07 LEC 25 Slide 12
When the steady stress component is high enough to induce localized
notch yielding, the designer has problem.
The first-cycle local yielding produces plastic strain and strain-
strengthening.
This is occurring at the location where fatigue crack nucleation and
growth are most likely.
30 hME 307 M hi D i I
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Dr. A. Aziz Bazoune Chapter 7: Fatigue Failure Resulting from Variable Loading
ME 307 Machine Design IME 307 Machine Design I
CH-07 LEC 25 Slide 13
Residual Stress MethodResidual Stress Method
All stresses (both mean and alternating) are multiplied by the fatigue
stress concentration factor Kf , and correction is made for yielding and
resultant residual stresses if the calculated peak stress exceeds the material
yield strength.
Nominal Mean Stress MethodNominal Mean Stress Method
In this method, stress concentration factor is applied only to alternating
stress.
Reduction in mean stress from not multiplying it by Kf , might be about
the same as the reduction in mean stress achieved with the residual stress
method by taking yielding and residual stress into account.
Possible ways of quantifying the problem:
ME 307 M hi D i IME 307 M hi D i I
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Dr. A. Aziz Bazoune Chapter 7: Fatigue Failure Resulting from Variable Loading
ME 307 Machine Design IME 307 Machine Design I
CH-07 LEC 25 Slide 14
7-12 Fatigue Failure Criteria for Fluctuating Stress7-12 Fatigue Failure Criteria for Fluctuating Stress
After having defined the various components of stress associated with a
part subjected to fluctuating stresses, we want to vary both the midrange
stress and the stress amplitude or alternating component, to learn about
the FATIGUE RESISTANCE of parts when subjected to such situations.
Many machine elements involve fluctuating stresses about a non-zero
mean.
The influence of non-zero mean stress is estimated by using one of several
empirical relationships that determine failure at a given life when both
alternating and mean stresses are nonzero.
ME 307 M hi D i IME 307 M hi D ig I
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ME 307 Machine Design IME 307 Machine Design I
CH-07 LEC 25 Slide 15
ME 307 Machine Design IME 307 Machine Design I
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Dr. A. Aziz Bazoune Chapter 7: Fatigue Failure Resulting from Variable Loading
ME 307 Machine Design IME 307 Machine Design I
It has midrange stress plotted along the
abscissa and all other components of
stress plotted on the ordinate, with
tension in the positive direction.
The endurance limit, fatigue strength,
or finite-life strength whichever
applies, is plotted on the ordinate above
and below the origin.
The midrange line is a 45o line from the
origin to the tensile strength of the
part.
CH-07 LEC 25 Slide 16
Modified GoodmanModified Goodman
DiagramDiagram
Figure 7-24
Modified Goodman diagram showing all the strengths
and the limiting values of all the stress components for
a particular midrange stress
ME 307 Machine Design IME 307 Machine Design I
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Dr. A. Aziz Bazoune Chapter 7: Fatigue Failure Resulting from Variable Loading
ME 307 Machine Design IME 307 Machine Design I
CH-07 LEC 25 Slide 17
Plot of Fatigue Failures for Midrange Stresses in bothPlot of Fatigue Failures for Midrange Stresses in both
Tensile and Compressive Regions.Tensile and Compressive Regions.
Figure 7-25Plot of fatigue failuresfor midrange stresses
in both tensile and
compressive regions.
Normalizing the data
by using the ratio of
steady strengthcomponents to tensile
strength Sm/Sut,
steady strength
component to
compressive strength
Sm/Suc, and strength
amplitude componentto endurance limit
Sa/Se enables a plot
of experimental
results for a variety of
steels.
ME 307 Machine Design IME 307 Machine Design I
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Dr. A. Aziz Bazoune Chapter 7: Fatigue Failure Resulting from Variable Loading
ME 307 Machine Design IME 307 Machine Design I
CH-07 LEC 25 Slide 18
Master Fatigue Diagram.Master Fatigue Diagram.
Figure 7-26
Master fatiguediagram for
AISI 4340 steelwith Sut = 158
Sy = 147 kpsi.
The stresscomponent atA are
min = 20,
max = 120,
m = 70,
o = 50
all in kpsi