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Lecture 18Fatigue

Mechanical Behavior of Materials Sec. 9.6-9.7 Jiangyu Li

University 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

MPaSMPakpsiSkpsi

MPakpsiSSS

ut

ut

utut

e1460,740212,107

)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

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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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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Example: ASME Elliptic

Table 7-11

1

2

3

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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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Safety Factor with Mean Stress

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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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Torsional Fatigue Strength

utsu SS 67.0

ytsy SS 577.0

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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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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

MPaJdTK a

fsaxy 3.162,

MPaJdTK m

fsmxy 212,

0xa

MPaa 2.28'

MPaZMK fxm 8.93

MPam 6.100'

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Assignment

Mechanical Behavior of Materials 9.30, 9.31,9.33 , 9.35