Chapter 6. Fatigue Failure · 6-9 Endurance limit modifying factors 6-10 Stress concentration and notch sensitivity 6-11 to 13 Fluctuating stresses . 4 Introduction to Fatigue Failure
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1
Chapter 6. Fatigue Failure
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3
We will emphasize topics from the following sections:
6-1 to 6-3 Introduction to fatigue failure and failure theories
6-7 Stress- life method
6-8 S-N diagram
6-9 Endurance limit modifying factors
6-10 Stress concentration and notch sensitivity
6-11 to 13 Fluctuating stresses
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Introduction to Fatigue Failure
A – crack initiates at thread root
B – crack propagation (beach marks)
C – final fast fracture
Fatigue failure of a bolt subjected
to repeated unidirectional loads
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Methods for Predicting Fatigue Failure
1. Strain-Life Method– Analyzes localized plastic deformation
– Accurate for low-cycle fatigue problems
2. Fracture Mechanics Method– Predicts incremental crack growth rates
3. Stress-Life Method– Traditional method
– Based on stress levels only
– Easiest method to implement
We will consider only
the stress-life method
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Fatigue Testing
Uniaxial Fatigue Test Rotating Beam Test
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Fatigue Testing Procedure
− Perform test at many different stress levels
− Determine number of cycles to failure
− Plot number of cycles to failure vs. applied stress
− This plot (called the S-N diagram) can be used to estimate the number of cycles to failure for a given stress level
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Typical S-N Curve
Sut – failure at
first load cycle
– endurance limit
(can withstand unlimited
load cycles)
eS
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Endurance Limit
Endurance limit – the stress level below which
failure will not occur, regardless of how many
cycles (also known as the fatigue limit)
- endurance limit under ideal test conditions
- endurance limit under service conditionseS
eS
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Relation between Endurance Limit and
Tensile Strength
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Relation between Endurance Limit and
Tensile Strength (cont.)
ksi200ksi,100
ksi200,5.0
ut
utute
S
SSS
MPaSMPa
MPaSSS
ut
utute
1400,700
1400,5.0
in SI units
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Endurance Limit Modifying Factors
f
e
d
c
b
a
efedcbae
k
k
k
k
k
k
SkkkkkkS
- Surface condition modifying factor
- Size modification factor
- Load modification factor
- Temperature modification factor
- Reliability factor
- Miscellaneous effects modification factor
These are
called “Marin”
factors
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Surface Factor, ka
buta Sak
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Size Factor, kb
For bending and torsion
For axial loads
kb = 1
mm2545151.1
mm5179.224.1
in10291.0
in211.0879.0
157.0
107.0
157.0
107.0
dd
dd
dd
dd
kb
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Loading Factor, kc
torsion59.0
axial85.0
bending1
ck
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Temperature Factor, kd
RT
Td
S
Sk
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Reliability Factor, ke
Accounts for scatter in fatigue data and desired reliability
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Miscellaneous Effects Factor, kf
Corrosion
Electrolytic plating
Metal spraying
Cyclic frequency
Frettage corrosion
(corrosion at contact surfaces)
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Example 6-6
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Example 6-6 - Endurance Limit
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Example 6-6 - Fatigue Strength at 70,000 cycles
Section 6-8, for 103 < N < 106
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Example 6-6 - Fatigue Strength at 70,000 cycles
(cont.)
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Stress Concentration and Notch Sensitivity
Static loading (chapter 3) => Kt and Kts
Fatigue loading – some materials are less sensitive to stress
concentrations => reduced stress concentration
Fatigue stress concentration factors
ofs
of
K
K
max
max
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Notch Sensitivity
1
1
1
1
shear
ts
fs
t
f
K
Kq
K
Kq
where 0 ≤ q, qshear ≤ 1
Note:
q=0 => Kf = 1 (no sensitivity to notches)
q=1 => Kf = Kt (no reduction due to fatigue)
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Notch Sensitivity – Axial and Bending Loading
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Neuber Equation
(basis for Fig. 6-26 - steels)
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Notch Sensitivity – Torsion Loading
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Fatigue Stress Concentration Factors
)1(1
)1(1
1
1
1
1
shear
tsshearfs
tf
ts
fs
t
f
KqK
KqK
K
Kq
K
Kq
Solving for Kf and Kfs gives
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Example 6-7
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Example 6-7 (cont.)
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Characterization of Fluctuating Stress
rangestress
amplitudestress
0stressmean
r
a
m
Zero Mean Stress (ex. Rotating beam experiment)
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Characterization of Fluctuating Stress (cont.)
Non-zero mean stress (shafts under combined loading)
rangestress
stressminimum
stressmaximum
amplitudestress
stressmean
min
max
r
a
m
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Fluctuating Stress (cont.)
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Fatigue Failure Criteria for
Non-zero Mean Stress
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Yield Line (Langer Line)
Yielding occurs if
Factor of safety associated with yielding
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Goodman Failure Criteria
See text for other failure criteria (Gerber, ASME elliptic, etc.)
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Example 6-9 (cont.)
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