1. Fatigue Failure Due to Variable Loading
Section V
Fatigue Failure Due to Variable Loading

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?

5. Reversed Bending As the shaft rotates the stress alternates betweenC D
Shaft rotates 180 degrees D C C D D C

6. 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

7. Common Fatigue Patterns
Unidirection Bending
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
Common Fatigue Patterns

8. What type of loading caused this failure?
Fast fracture
Crack grew from
the center outward
UNIAXIAL TENSILE LOADING

9. 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
10^3≤N≤106
Large amounts of data
Widely used
Covered in this course

10. 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 Se
“Knee” of the S-N Curve

11. 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…

12. 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.

13. 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.

14. 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
factors.

15. 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

16. 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.)

17. 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.

18. 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

19. 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

20. Fatigue Failure Criterion
Gerber
Modified Goodman
Soderberg

21. Fatigue Failure Criterion Graphically