12.fatigue shigley
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MAE 316 – Strength of Mechanical Components
NC State University Department of Mechanical and Aerospace Engineering
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Up to now, we have designed structures for static loads.
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What if loading is not constant?
! Even if ! max ! Sy, failure could occur if enough cycles are
applied.
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! If ! min = - ! max, this is known as “fully-reversed” loading.
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The simplest design rule to prevent fatigue failure is
! This is a valid concept, but not quite so simple in reality.
! Se is determined experimentally.! Simple approximate Se formulas exist for steel, but must be
used carefully – better to have actual data.
! where Sut = ultimate strength and Se’ = unmodified, laboratory
determined value
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eapplied S 200 kpsi
' 700 MPa > 1400 MPa
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For real design we will modify Se’ to account for the surfacefinish, stress concentration, temperature, etc.
! These effects decrease the effective endurance limit.
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!
High-cycle fatigue life (N > 1000 cycles)! Typical S-N diagram for steel (see Fig 6-18 for f )
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R=:$C$': L+:&*"+>' M$B$# -./N6!
Modified endurance limit is defined as
! k a = surface finish factor = aS ut b
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R=:$C$': L+:&*"+>' M$B$# -./N6! k
b = size factor! Axial loading
! k b = 1
! Bending and torsion
!
k b = 0.879d -.107
(0.11 in" d " 2 in)! k b = 0.91d
-.157 (2 < d < 10 in)
! k b = 1.241d -.107 (2.79" d " 51 mm)
! k b = 1.51d -.157 (51 < d < 254 mm)
! d is the diameter of the round bar or the equivalent diameter
(de) of a non-rotating or non-circular bar (Table 6-3).
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R=:$C$': L+:&*"+>' M$B$# -./N6! k
c= loading factor
! 1 (bending)
! 0.85 (axial)
! 0.59 (torsion)
! k d = temperature factor
! If endurance limit (Se’) is known, or use
equation
! If Se’ is not known, use k d = 1 and temperature-corrected tensile
strength (Sut) (see Example 6-5 in textbook)
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R=:$C$': L+:&*"+>' M$B$# -./N6! k
e= reliability factor
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R=:$C$': L+:&*"+>' M$B$# -./N6! k
f= miscellaneous-effects factor
! Corrosion
! Electrolytic plating
! Metal Spraying
! Cyclic frequency
! Frettage corrosion
! If none of the above conditions apply, k f = 1
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! K f
= fatigue stress concentration factor
! K f = 1 + q(K t – 1)
! q = notch sensitivity
! K t = stress concentration factor
! K f can be used to reduce Se’ (multiply Se
’ by 1/K f ) or to modify the
nominal stress (! max = K f ! nom).
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