1 fatigue failure due to variable loading section v
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1
Fatigue Failure Due to Variable Loading
Section V
2
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
Talking Points
3
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.
Variable Loading?
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
As the shaft rotates the stress alternates between Tension @ C Compression @ D
Shaft rotates 180 degrees Tension @ D Compression @ C
C
D
D
C
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 FORREVERSE BENDING
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
What type of loading caused this failure?
Fast fracture
Crack grew fromthe center outward
UNIAXIAL TENSILE LOADING
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
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
Se
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 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.
S f aN b
6
3
6
6
3
6
3
6
10
2
1010
10
10
10
10
6
10
1000
logloglog2
gives.... )( into ngSubstituti
log3
1log
3
1
gives.... equations two thesegSubtractin
)( 610loglog
)( 31000loglog
intercept theis and slope theis where
loglog
SS
SS
SC
b
S
fS
S
Sb
CbCbS
CbCbS
Cb
CNbS
e
ut
f
e
ut
S
fS
S
Sa
2
10
2
10
6
3
C log10(a)
Finally resulting in…
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
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.
S e 0.504Sut , ksi or MPa Sut 212 ksi (1460 MPa)
107 ksi Sut 212 ksi
740 MPa Sut 1460 MPa
Your text emphasizes this point by the inclusion of a prime mark above the endurance
limit symbol.
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.
Se kakbkckd kek f S eModified EL - Marin’s Equation
Now we will discuss how to effectively estimate these modification
factors.
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
ka aSutb
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
kb
0.879d 0.107 0.11 d 2 in.
0.91d 0157 2 < d 10 in.
1.24d 0.107 2.79 d 51 mm.
1.51d 0.157 51 < d 254 mm.
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 becomputed for non-circular geometry (see
Table 7-5.)
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.
kc 1 bending
0.85 axial
0.59 torsion
Se 0.50Su bending
0.45Su axial
0.29Su torsion
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
kd ST
SRT
where ST and SRT are the tensile strength
at the operating and room temperatures respectively.
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
a max min
2
m max min
2
Fatigue Failure Criterion Gerber
Modified Goodman
Soderberg
a
Se
m
Sy
1
n
a
Se
m
Sut
1
n
n a
Se
nm
Sut
2
1
Fatigue Failure Criterion Graphically
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