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Fatigue Failure Due to Variable Loading. Section V. 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

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talking points
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
variable loading
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.
what have we been ignoring
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?
reversed bending





Reversed Bending
  • As the shaft rotates the stress alternates between
    • Tension @ C
    • Compression @ D
  • Shaft rotates 180 degrees
    • Tension @ D
    • Compression @ C
reversed bending fatigue
Reversed Bending - Fatigue
  • Common indications of reverse bending fatigue
    • “Beach” Marks
    • Dark areas indicated in this figure are representative of abrupt or “fast” fracture



unidirection bending
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
what type of loading caused this failure
What type of loading caused this failure?

Fast fracture

Crack grew from

the center outward


how rate the lifetime of fatigue or cyclic loaded parts
Strain Life

Ideal for low cycle fatigue applications

1≤N≤103, 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


Large amounts of data

Widely used

Covered in this course

How rate the lifetime of fatigue or cyclic loaded parts?
endurance limit
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

N=1 - cycle represents a load application in one direction, removal, and then once again in the opposite direction


“Knee” of the S-N Curve

estimating fatigue life
Estimating Fatigue Life
  • Approximating fatigue
    • 103≤N≤106
  • 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…

determining the endurance limit
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.
much endurance data on record is for steels
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, highlypolished specimens that are free of surface defects.

Your text emphasizes this point by the inclusion of a prime mark above the endurance limit symbol.

endurance limit el modifying factors
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 - Marin’s Equation

Now we will discuss how to

effectively estimate these modification


surface factor k a
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
size factor k b
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.)

loading factor k c
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.
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


Manufacturing process

Residual stresses


All of which can have an adverse effect on the EL

Temperature, Reliability and Miscellaneous Factors
characterizing fluctuating stress
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
fatigue failure criterion
Fatigue Failure Criterion
  • Gerber
  • Modified Goodman
  • Soderberg