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Transcript of Lec 3 Fatigue Failure 031004_for_students_2
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Chapter 6 Fatigue Failure
Theories
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Fatigue Failure Occurs when stresses are changing
throughout the life of a part.
_______________________ starts with a
crack that propagates until a catastrophic
failure occurs.
This usually begins at a manufacturing defector stress concentration that is subjected to
tensile stresses for part of its load cycle.
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Fatigue-Failure Models Stress-Life - cyclic stresses are kept
below fatigue strength or endurance
limit. Most widely used.
Strain-Life - complicated not often used.
_________________ - sometimes
used, gaining favor especially in the
aircraft and aerospace industry.
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Fatigue Stresses
-10000
-50000
5000
10000
15000
20000
25000
30000
0 2 4 6 8 10
Load Cycles
Ap
pliedStress
-psi
a
a
a
m
m
Fully Reversed Repeated Fluctuating
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Fully Reversed Failure Criteria Most data comes from R. R. Moore
rotating-beam test.
Highly polished specimen of 0.3 inches
in diameter is subjected to pure bending
stresses that are alternated by rotating
the specimen.
Rotation is at 1725 rpm.
Takes 1/2 day to reach 106 cycles.
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S-N Curve for Steel with Sut = 100 ksi
10000
100000
1.0E+3 10.0E+3 100.0E+3 1.0E+6 10.0E+6 100.0E+6
Cycles to Failure - N
Fatigue
Strength
-Sf
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Endurance Limit and Fatigue
Strength Endurance Limit of a Material (Se) -
stress below which fatigue failure does
not occur regardless of the number of
stress cycles.
____________________Strength of a
Material (Sf) -stress below which fatiguefailure does not occur for a specified
number of stress cycles.
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Typical S-N Curve for Non-Ferrous Metals
10000
100000
1.00E+03 1.00E+04 1.00E+05 1.00E+06 1.00E+07 1.00E+08 1.00E+09
Cycles to Failure
Fatigue
Strength
-psi
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Estimating Se or Sf For ____________:
Se= 0.5Sut for Sut200 ksi (1400 MPa)
For ______________:
Se= 0.4Sut for Sut60 ksi (400 MPa)
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Estimating Se or Sf contd For __________________:
Sf@5E8= 0.4Sut for Sut330 ksi (330 MPa)
For _____________________:
Se= 0.4Sut for Sut40 ksi (280 MPa)
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Correction Factors to Endurance
Limit and Fatigue Strength Se = CloadCsize CsurfCtempCreliab Se
Sf= CloadCsize CsurfCtempCreliab Sf
Se -corrected endurance limit for a part
Sf-corrected fatigue strength for a part
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Correction Factors to Endurance
Limit and Fatigue Strength Cload - load factor see eq. 6.7a pg 348
Csize - size factor see eqs. 6.7a,b,cpg 348-349
Csurf- surface factor see Figs. 6-26,6.27, and eq. 6.7e pg 349-352
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Correction Factors to Endurance
Limit and Fatigue Strength Ctemp - temperature factor see eq. 6.7f
pg 352-353
Creliab - reliability factor see Table 6.4
pg 353
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Stress Concentration Kf= 1+q(Kt+ 1)
Kt- geometric stress concentrationfactor
Kf-___________________________
q - notch sensitivity factor
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Fluctuating Stresses
Modified-Goodman Diagram
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Failure Lines for Fluctuating Stress
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Augmented Modified-Goodman
Diagram
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Stress ConcentrationApply Kfto the ______________
components of stress.
For __________ materials apply Kt to
the mean components of stress.
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Stress Concentration - contd If Kf|maxnom| < Sy then: Kfm = Kf
If Kf|maxnom| > Sy then:Kfm = (Sy - Kfanom)/ |mnom|
If Kf|maxnom - minnom| < 2Sy then: Kfm = 0
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Factor of Safety for Fluctuating Stress -
Case 1
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Factor of Safety for Fluctuating Stress -
Case 2
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Factor of Safety for Fluctuating Stress -
Case 3
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Factor of Safety for Fluctuating Stress -
Case 3
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Factor of Safety for Fluctuating Stress -
Case 4
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Factor of Safety for Fluctuating Stress -
Case 4
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Fluctuating Stresses
Multiaxial Stresses in Fatigue
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Fully Reversed Simple
Multiaxial Stresses
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Fluctuating Simple Multiaxial Stresses
Von Mises Method
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General Approach to High Cycle
Fatigue Design Generate Modified Goodman Diagram
Calculate alternating and mean components
of stress at areas of concern on the part.Include appropriate stress concentrationfactors.
Convert alternating and mean appliedstresses to alternating and mean Von Mises
Stresses. Plot these stresses on the Modified Goodman
Diagram and find the factor of safety.
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Example The figure pertains to the shaft of a disk
sander that is made from steel havingSu=900 MPa, and Sy=750 MPa. The most
severe loading occurs when an object is heldnear the periphery of the disk with sufficientforce to develop 12 N-m (which approachesthe stall torque of the motor).
Assume a coefficient of friction between theobject and the disk is 0.6.
What is the factor of safety with respect toeventual fatigue failure of the shaft?
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Example