CH-07 LEC 27 Slide 1

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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 27
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Fatigue Strength and Life
A- Completely Reversed Loading (R-1)
Ferrous Metals
Stress Ratio
Strength
Fatigue life
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Fatigue Life with Mean Stress Effect
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Example 7-13 (Textbook)
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(7-50)
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Fatigue Failure for Brittle Materials
The first quadrant fatigue failure criteria
follows a curve upward Smith-Dolan represented
by Or a design equation
(7-52)
(7-53)
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• For a radial load line of slope r, we substitute
  Sa/r for Sm and solve for Sa
• The fatigue diagram for a brittle material
  differs markedly from that of a ductile material
• Yielding is not involved since the material may
  not have a yield strength

(7-54)
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• The compressive ultimate strength exceeds the
  ultimate tensile strength severalfolds
• First-quadrant fatigue failure locus is
  concave-upward (Smith-Dolan)
• Brittle materials are more sensitive to midrange
  stress, being lowered
• Not enough work has been done on brittle fatigue
  to discover insightful generalities

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Torsional fatigue Strength Under Fluctuating
Stresses
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Combining Loading Modes

• Fatigue problems are classified under three
  categories
• Completely reversing simple loads
• It is handled with the S-N diagram, relating the
  alternating stress to a life. Only one type of
  loading is allowed here, and the midrange stress
  must be zero.
• Fluctuating simple loads
• It uses a criterion to relate midrange and
  alternating stresses (modified Goodman, Gerber,
  ASME-elliptic, or Soderberg). Again, only one
  type of loading is allowed at a time.
• Combinations of loading modes
• It uses combined bending, torsion, and axial
  loadings.

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Combining Loading Modes
Completely reversed single stress which is
handled with the S-N diagram, relating the
alternating stress to a life. Only one type of
loading is allowed here, and the midrange stress
must be zero. Fluctuating loads It uses a
criterion to relate midrange and alternating
stresses (modified Goodman, Gerber,
ASME-elliptic, or Soderberg). Again, only one
type of loading is allowed at a time.
Combination of different types of loading such
as combined bending, torsion, and axial.
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Combining Loading Modes
In Sec. 7-9, a load factor was used to obtain the
endurance limit, and hence the result is
dependent on whether the loading is axial,
bending, or torsion. But, how do we proceed when
the loading is a mixture of, say, axial, bending,
and torsional loads? This type of loading
introduces a few complications in that there may
now exist combined normal and shear stresses,
each with alternating and midrange values, and
several of the factors used in determining the
endurance limit depend on the type of loading.
There may also be multiple stress-concentration
factors, one for each mode of loading. The
problem of how to deal with combined stresses was
encountered when developing static failure
theories. The distortion energy failure theory
proved to be a satisfactory method of combining
the
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Combining Loading Modes

• multiple stresses on a stress element into a
  single equivalent von Mises stress. The same
  approach will be used here.
• The first step is to generate two stress
  elements, one for the alternating stresses and
  one for the midrange stresses.
• Apply the appropriate fatigue stress
  concentration factors to each of the stresses
  apply for the bending
  stresses, for the
• torsional stresses, and for the
  axial stresses.
• Next, calculate an equivalent von Mises stress
  for each of these two stress elements,
• Finally, select a fatigue failure criterion
  (modified Goodman, Gerber, ASME-elliptic, or
  Soderberg) to complete the fatigue analysis.

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Combining Loading Modes
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Combining Loading Modes
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Combining Loading Modes

• Case of Combined Axial, Bending and Torsion
  Loading
• (kc? Kf?).
• Assuming that all stress components are in time
  phase with each other.
• For the strength, use the fully corrected
  endurance limit for bending, Se.
• Apply the appropriate fatigue concentration
  factors to all stress components.
• Multiply any alternating axial stress components
  by 1/kc,ax
• Find the principal stresses.
• Find the von Miss alternating stress, ?a and
  mean stress ?m.
• Use any of the theories above to compute the
  safety factor.

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Combining Loading Modes

• ?a and mean stress ?m are alternating and mean
  VM stresses.
• Both the steady and alternating components are
  augmented by Kf and Kfs.
• If stress components are not in phase but have
  same frequency, the maxima can be found using
  phase angles and then summed.
• Otherwise assume that the stress components will
  reach an in-phase condition so their magnitudes
  are additive.

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Example 7-15 (Textbook)
Solution
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t 4 mm
s M/Znet
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