Transcript LEC 25 CH-07 - KFUPM Open Courseware

ME 307 Machine Design I
Dr. A. Aziz Bazoune
King Fahd University of Petroleum & Minerals
Mechanical Engineering Department
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from Variable Loading
ME 307 Machine Design I
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from Variable Loading
CH-07
LEC 25
Slide 2
ME 307 Machine Design I
7-11 Characterizing Fluctuating Stresses
 Fluctuating stresses in machinery often take the form of sinusoidal
pattern because of the nature of the nature of some rotating machinery.
 Other patterns some quite irregular do occur.
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from Variable Loading
CH-07
LEC 25
Slide 3
ME 307 Machine Design I
7-11 Characterizing Fluctuating Stresses
 In periodic patterns exhibiting a single maximum and single minimum of
force, 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:
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from Variable Loading
CH-07
LEC 25
Slide 4
ME 307 Machine Design I
 Stress Range
 Mean (Midrange
Stress)
 Stress Amplitude
(Alternating Stress)
(R>0 )
(R =0)
 Stress Ratio
 Stress Amplitude
(R =-1)
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from Variable Loading
CH-07
LEC 25
Slide 5
ME 307 Machine Design I
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from Variable Loading
CH-07
LEC 25
Slide 6
ME 307 Machine Design I
Any varying stress with a nonzero mean
is considered a fluctuating stress.
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from Variable Loading
CH-07
LEC 25
Slide 7
ME 307 Machine Design I
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from Variable Loading
CH-07
LEC 25
Slide 8
ME 307 Machine Design I
 The steady, or static, stress is not the
same as the midrange stress.
 The steady stress may have any value
between σmin and σmin .
 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.
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from Variable Loading
CH-07
LEC 25
Slide 9
ME 307 Machine Design I
 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.
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from Variable Loading
CH-07
LEC 25
Slide 10
ME 307 Machine Design I
 Equations (7-39) use symbols σa and σm as the stress components at the
location of scrutiny.
 In the absence of a notch, σa and σm are equal to the nominal stresses σao
and σmo induced by loads Fa and Fm , respectively.
 With a notch they are σa = Kf σao and σm = Kf σmo , respectively.
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from Variable Loading
CH-07
LEC 25
Slide 11
ME 307 Machine Design I
 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 strainstrengthening.
 This is occurring at the location where fatigue crack nucleation and
growth are most likely.
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from Variable Loading
CH-07
LEC 25
Slide 12
ME 307 Machine Design I
Possible ways of quantifying the problem:
 Residual 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 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.
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from Variable Loading
CH-07
LEC 25
Slide 13
ME 307 Machine Design I
7-12 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.
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from Variable Loading
CH-07
LEC 25
Slide 14
ME 307 Machine Design I
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from Variable Loading
CH-07
LEC 25
Slide 15
ME 307 Machine Design I
Modified Goodman
Diagram
 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.
Figure 7-24
Modified Goodman diagram showing all the strengths
and the limiting values of all the stress components for
a particular midrange stress
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from Variable Loading
CH-07
LEC 25
Slide 16
ME 307 Machine Design I
Plot of Fatigue Failures for Midrange Stresses in both
Tensile and Compressive Regions.
Figure 7-25
Plot of fatigue failures
for midrange stresses
in both tensile and
compressive regions.
Normalizing the data
by using the ratio of
steady strength
components to tensile
strength Sm/Sut,
steady strength
component to
compressive strength
Sm/Suc, and strength
amplitude component
to endurance limit
Sa/S’e enables a plot
of experimental
results for a variety of
steels.
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from Variable Loading
CH-07
LEC 25
Slide 17
ME 307 Machine Design I
Master Fatigue Diagram.
Figure 7-26
Master fatigue
diagram for AISI
4340 steel with
Sut = 158
Sy = 147 kpsi.
The stress
component at A
are
σmin = 20,
σ max = 120,
σ m = 70,
σ o = 50
all in kpsi
Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from Variable Loading
CH-07
LEC 25
Slide 18