lecture 18 fatigue mechanical behavior of materials sec. 9.6-9.7 jiangyu li
DESCRIPTION
Mechanics of Materials Lab. Lecture 18 Fatigue Mechanical Behavior of Materials Sec. 9.6-9.7 Jiangyu Li University of Washington. S-N Diagram. S-N Diagram. Endurance limit. Endurance Limit. For steel. Fatigue Failure Criteria. Effect of Mean Stress. Effect of Mean Stress. - PowerPoint PPT PresentationTRANSCRIPT
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1 Jiangyu Li, University of Washington
Lecture 18Fatigue
Mechanical Behavior of Materials Sec. 9.6-9.7 Jiangyu Li
University of Washington
Mechanics of Materials Lab
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2 Jiangyu Li, University of Washington
S-N Diagram
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3 Jiangyu Li, University of Washington
S-N Diagram
Endurance limit
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4 Jiangyu Li, University of Washington
Endurance Limit
MPaSMPakpsiSkpsi
MPakpsiSSS
ut
ut
utut
e1460,740212,107
)1460(212,504.0' For steel
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5 Jiangyu Li, University of Washington
Fatigue Failure Criteria
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6 Jiangyu Li, University of Washington
Effect of Mean Stress
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7 Jiangyu Li, University of Washington
Effect of Mean Stress
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8 Jiangyu Li, University of Washington
Fatigue Failure Criteria
1yt
m
yt
aSS
SS
1yt
m
e
aSS
SS
m
ar1)( 2
ut
m
e
aSS
SS
1ut
m
e
aSS
SS
1)()( 22 yt
m
e
aSS
SS
Multiply the stressBy safety factor n
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9 Jiangyu Li, University of Washington
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
rSS
SS
ut
m
e
a
kpsiK
kpsidF
aofma
moa
ao
38.8
,53.443
Changeover
Table 7-10
1
2
3
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10 Jiangyu Li, University of Washington
Example: ASME Elliptic
Table 7-11
1
2
3
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11 Jiangyu Li, University of Washington
Example
• AISI 4340 steel is subjected to cyclic load with a tensile mean stress of 200 MPA– What is the fatigue life for stress amplitude
of 450 MPA– Estimate the relationship between stress
amplitude and fatigue life for this mean stress
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12 Jiangyu Li, University of Washington
Safety Factor with Mean Stress
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13 Jiangyu Li, University of Washington
Example
• Man-Ten steel subject to stress amplitude of 180 Mpa and mean stress of 100PMa for 20000 cycles– What is the safety factor in life and
stress?
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14 Jiangyu Li, University of Washington
Torsional Fatigue Strength
utsu SS 67.0
ytsy SS 577.0
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15 Jiangyu Li, University of Washington
Combination of Loads
torsionaxialbening
kc59.085.01
• 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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16 Jiangyu Li, University of Washington
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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17 Jiangyu Li, University of Washington
Example
Tm=(20+160)/2=90Nm; Ta=(160-20)/2=70Nm
MPaJdTK a
fsaxy 3.162,
MPaJdTK m
fsmxy 212,
0xa
MPaa 2.28'
MPaZMK fxm 8.93
MPam 6.100'
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18 Jiangyu Li, University of Washington
Assignment
Mechanical Behavior of Materials 9.30, 9.31,9.33 , 9.35