12.Fatigue Shigley

8/18/2019 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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6/18

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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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' 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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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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14/18

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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12.Fatigue Shigley

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