Fatigue Failure Due to Variable Loading

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Fatigue Failure Due to Variable Loading
Section V
2
Talking Points

• Variable Loading?
• What have we been ignoring?
• How rate the lifetime of fatigue or cyclic loaded
  parts?
• Endurance Limit
• Estimating Fatigue Life
• Determining the Endurance Limit
• Characterizing Fluctuating Stress
• Fatigue Failure Criterion Graphically

3
Variable Loading?

• In many actual life applications, some machine
  members are subjected to stresses fluctuating
  between levels.
• Often, machine members are found to fail under
  the action of these repeated or fluctuated
  stresses.
• Most careful analysis reveals that the actual
  maximum stresses were below the ultimate strength
  of the material, and quite frequently even below
  the yield strength.
• The most distinguishing characteristic of these
  failures is that the stresses have been repeated
  a very large number of times.
• This type of failure is called fatigue failure.

4
What have we been ignoring?

• Suppose the countershaft is rotating
• Static
• Dynamic
• Is fatigue an issue?
• What type of stress condition do we now have if
  the shaft is rotating and the loads remain in a
  fixed direction?

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Reversed Bending

• As the shaft rotates the stress alternates
  between
• Tension _at_ C
• Compression _at_ D
• Shaft rotates 180 degrees
• Tension _at_ D
• Compression _at_ C

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Reversed Bending - Fatigue

• Common indications of reverse bending fatigue
• Beach Marks
• Dark areas indicated in this figure are
  representative of abrupt or fast fracture

STRESS PATTERNS FOR REVERSE BENDING
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Unidirection Bending
Common Fatigue Patterns

• What does each Beach mark represent?
• Crack slowly propagated and then stops
• Illustrates how the crack front propagates thru
  the cross-section
• Failure in a threaded rod or bolt due to
  unidirectional bending
• Rough area representing fast fracture

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What type of loading caused this failure?
Fast fracture
Crack grew from the center outward
UNIAXIAL TENSILE LOADING
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How rate the lifetime of fatigue or cyclic loaded
parts?

• Strain Life
• Ideal for low cycle fatigue applications
• 1N103, where N is the number of loading cycles
• Based on the plasticity at localized regions of
  the part
• Method is typically not practical for design use
  because it requires knowledge of strain
  concentration levels, pages 316 to 317

• Fracture Mechanics Approach
• Requires the assumption of a pre-existing crack
• Used to predict growth of the crack with respect
  to a specified level of stress intensity
• Pages 319 to 323
• Stress Life
• High fatigue life calculations
• 103N106
• Large amounts of data
• Widely used
• Covered in this course

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Endurance Limit

• Is a stress level in a material that can
  withstand an infinite number of loading cycles.
• In your text and throughout literature on the
  subject, the endurance limit is typically
  referenced by Se.
• To determine the endurance limit we use a S-N
  curve
• Always plotted on Log-Log Scale

S - Strength of the material N - Number of
cycles executed N1 - cycle represents a load
application in one direction, removal, and then
once again in the opposite direction
Se
Knee of the S-N Curve
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Estimating Fatigue Life

• Approximating fatigue
• 103N106
• Just as we saw the linear behavior of true
  stress-strain when plotted on log scale, the data
  tends to follow a piecewise linear function.
• We will use this same principal to develop a
  power-law for estimating points in the high cycle
  region on the S-N diagram.

Finally resulting in
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Determining the Endurance Limit

• A rotary device serves as an excellent means of
  acquiring such data in a timely manner.
• Several thousand cycles can be executed rather
  quickly
• Below is a sketch of a simple apparatus that can
  be used to determine the value of the endurance
  limit.

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Much Endurance Data on record is for steels

• Mischke, one of the authors of the text has
  actually done an extensive study in this area and
  has determined that the endurance limit of the
  material.
• Steels
• It is important to note that these estimates are
  for clean, highly polished specimens that are
  free of surface defects.

Your text emphasizes this point by the inclusion
of a prime mark above the endurance limit symbol.
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Endurance Limit (EL) Modifying Factors

• Factors that can reduce the EL
• Surface condition, (ka)
• Size factor, (kb)
• Load factor, (kc)
• Temperature, (kd)
• Reliability factor, (ke)
• Miscellaneous-effects factor, (kf)
• These factors are used to adjust the endurance
  limit obtained from rotating beam specimens.

Modified EL - Marins Equation
Now we will discuss how to effectively estimate
these modification factors.
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Surface Factor, ka

• Mischke performed a regression analysis to
  approximate the surface factor
• The surface factor, ka, takes the following form
  
• where Sut is the minimum tensile strength and a
  and b are found from the table

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Size Factor, kb

• Once again Mischke has provided a means for
  estimating the EL size modification factor
• The size factor arises because of the geometry of
  the specimen used to obtain the endurance limit
• Diameter 0.30 in.
• Extruded or drawn bar stock
• Grain elongation in the direction perpendicular
  to fatigue crack growth
• Likelihood of surface flaws is low

For larger parts are more likely to contain
flaws which can result in premature material
failure For axially loaded specimens the size
factor is one. Effective circular cross-section
may be computed for non-circular geometry
(see Table 7-5.)
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Loading Factor, kc

• Since the usual test used to obtain the EL is the
  reversed bending load, modification factors are
  needed.
• Some texts on this subject do not include this
  factor and require the user to implement an
  estimation in the EL instead.

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Temperature, Reliability and Miscellaneous Factors

• Temperature is relatively simple to compute and
  understand
• Reliability Factor
• Will not be covered in detail in this course
• Extensive, through coverage is given to this
  factor in the text
• Statistics background is required

• Miscellaneous effects
• Corrosion
• Manufacturing process
• Residual stresses
• Coatings
• All of which can have an adverse effect on the EL

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Characterizing Fluctuating Stress

• Fatigue loading is oftentimes caused by a
  variable loading source.
• To develop failure criterion for fluctuating
  stresses, which cause fatigue failures, we must
  characterize how the stress levels vary as time.
• Sinusoidal stress oscillating about a static
  stress
• Repeated Stress
• Completely reversed stress

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Fatigue Failure Criterion

• Gerber
• Modified Goodman
• Soderberg

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Fatigue Failure Criterion Graphically