Fatigue Failure Resulting from Variable Loading

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Chapter 7
Fatigue Failure Resulting from Variable
Loading
Dr. A. Aziz Bazoune King Fahd University of
Petroleum Minerals Mechanical Engineering
Department
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LECTURE 25
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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.

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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

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Any varying stress with a nonzero mean is
considered a fluctuating stress.
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• The steady, or static, stress is not the same as
  the midrange stress.
• The steady stress may have any value between smin
  and smin .
• 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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• 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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• Equations (7-39) use symbols sa and sm as the
  stress components at the location of scrutiny.
• In the absence of a notch, sa and sm are equal
  to the nominal stresses sao and smo induced by
  loads Fa and Fm , respectively.
• With a notch they are sa Kf sao and sm Kf
  smo , respectively.

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• 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.

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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.

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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.

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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
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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/Se enables a plot of
experimental results for a variety of steels.
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