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Lecture 17Fatigue
Mechanical Behavior of Materials Sec. 9.6-9.7
Jiangyu LiUniversity of Washington
Mechanics of Materials Lab
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S-N Diagram
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S-N Diagram
Endurance limit
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Endurance Limit
MPaSMPa
kpsiSkpsi
MPakpsiSS
S
ut
ut
utut
e
1460,740
212,107
)1460(212,504.0' For steel
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Fatigue Failure Criteria
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Effect of Mean Stress
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Effect of Mean Stress
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Fatigue Failure Criteria
1yt
m
yt
a
SS
SS
1yt
m
e
a
SS
SS
m
ar1)( 2
ut
m
e
a
SS
SS
1ut
m
e
a
SS
SS
1)()( 22 yt
m
e
a
SS
SS
Multiply the stressBy safety factor n
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Example: Gerber Line
AISI 1050 cold-drawn bar, withstand a fluctuating axial load varying from 0 to16 kip. Kf=1.85; Find Sa and Sm and the safety factor using Gerber relation
Sut=100kpsi; Sy=84kpsi; Se’=0.504Sut kpsi
1
1)( 2
r
SS
SS
ut
m
e
a
kpsiK
kpsid
F
aofma
moa
ao
38.8
,53.443
Changeover
Table 7-10
1
2
3
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Example: ASME Elliptic
Table 7-11
1
2
3
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Torsional Fatigue Strength
utsu SS 67.0
ytsy SS 577.0
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Combination of Loads
torsion
axial
bening
kc59.0
85.0
1
• Use Se from bending;• Apply appropriate Kf for each mode;• Multiply axial stress component by 1/kc• Find the principle stresses• Find von Mises effective alternative stress• Use the fatigue failure criteria to determine safety factor
'a
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A rotating AISI 1018 cold-drawn steel tube (42x4 mm) has a 6mm diameter hole drilled transversely through it. The shaft is subjected to a torque Fluctuating from 20Nm to 160Nm, and a stead bending moment 150NmEstimate safety factor
Sut=440 Mpa, Syt=370MPa, Se’=0.504x440 =222 Mpa, Se=166MPa
Stress concentration factor Kt=2.366, from Table A-16, for bending, Kts=1.75 for torsion; from the Fig. 7-20, 7-21, notch sensitivity q is0.78 for bending, and 0.96 for torsion.
Thus Kf=2.07 for bending, and Kfs=1.72 for torsion
Example
899.0 buta aSk 833.024.1 107.0 dkb
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Example
Tm=(20+160)/2=90Nm; Ta=(160-20)/2=70Nm
MPaJdT
K afsaxy 3.162,
MPaJdT
K mfsmxy 212,
0xa
MPaa 2.28'
MPaZM
K fxm 8.93
MPam 6.100'
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Assignment
Mechanical Behavior of Materials
9.30, 9.33