Fatigue for Engineers

Objective
• Overview nature/consequences of the fatigue failure mechanism • Determine number of cycles required to
– develop a fatigue crack – propagate a fatigue crack
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• Bend wire repeatedly until fracture
• Note:
– life (number of applied load cycles) depends on:
• applied stress amplitude • component “quality” (notches, scratches, etc.)
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Exercise
Estimate the fatigue lifetime needed for:
– Automobile axle – Railroad rail – Commercial aircraft components
• landing gear • lower wing skin
– Highway drawbridge mechanism – Space shuttle solid propellant rocket motor cases
Crack Length (a) Fracture
Stress
Crack a Time
Crack Nucleation Crack Growth
Elapsed Cycles N
• Fatigue life depends on initial quality, load, . . .
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Paper Clip Experiment
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Model Stress-life (S-N) Curve
Log ∆S/2
• Se = endurance limit
for steels – Se ~ 0.5 ultimate stress Sult – Se ~ 100 ksi if Sult 〈 200 ksi
∆S/2 = σf ’ (2N)b
• Control ∆ε • Measure
– “Reversals” (2Nf) to failure (1 cycle = 2 reversals) – Stable stress range ∆σ needed to maintain ∆ε
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∆ε
∆ε time
σ ∆σ
Note: “stable” ∆σ usually occurs by mid-life (2Nf /2)
– What is the required lifetime? – What are consequences of failure?
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Fatigue Crack Formation
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Fatigue Crack Formation
Objective
– Characterize resistance to fatigue crack formation – Predict number of cycles to “initiate” small* fatigue crack in component
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– limited by local plastic deformation – strain-life approach better for LCF (Low Cycle Fatigue)
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Strain-life (ε - N) Approach
Concept: Strain range ∆ε controls life ∆σ Experiment ε
Plastic
• • • • •
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Buckling Fracture Creep Corrosion Fatigue
Yield Permanent displacement
Displacement
Fatigue Failure Mechanism
• Caused by repeated (cyclic) loading • Involves crack foห้องสมุดไป่ตู้mation, growth, and final fracture
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Exercise
• Give an example of a High Cycle Fatigue (HCF) application.
– What is the required lifetime? – What are consequences of failure?
• Given an example of a Low Cycle Fatigue (LCF) application.
– heat emitted >> plastic deformation
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Characteristics of Fatigue
• “Brittle” fracture surface appearance • Cracks often form at free surface • Macro/micro “beach marks”/ “striations”
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Stress-life (S-N) Approach
Concept: Stress range controls fatigue life
S
S
∆S
∆S/2
S
time
Log cycles N
Note: • Life increases as load amplitude decreases
• Considerable scatter in data • “Run-outs” suggest “infinite life” possible • Life N usually total cycles to failure
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S-N Curve: Mean Stress
Mean stress effects life
stress ratio R = Smin / Smax Smean = 0.5(Smin + Smax) Sa = 0.5(Smax - Smin) = ∆S/2 S Smax ∆S = 2Sa Smin time
Mean stress models
Sa/Se + Sm /Sult = 1
∆S/2 = (σf ’ - Smean) (2N)b
Stress Amplitude
“Haigh” constant life diagram N = 103 N = 106
Mean Stress
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S-N Curve: Other Factors
• Discuss implications of fatigue on design and maintenance operations
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Structural Failure Modes
Force
• Excessive Deformation
– –
Elastic
Force
displacement
time
Cyclic Stress-Strain Curve
Relate stable cyclic stress and strain ranges
∆σ
∆ε
ε
∆ε
σ
σ
∆σ
∆ε time
time
ε
∆σ
Cyclic stress-strain curve ∆σ/2 ∆ε/2
“Hystersis” loop E = elastic modulus K’ = cyclic strength coefficient n’ = strain hardening exponent
Se Log reversals 2N
• σf ’ = fatigue strength coefficient • b = fatigue strength exponent
typically -0.12 < b < -0.05
Note: Measure life in terms of reversals 2N (1 cycle = 2 reversals)
• S-N curves are very sensitive to
– surface finish, coatings, notches – prior loading, residual stresses – specimen size effects, etc.
• Many empirical “knock-down” factors • S-N approach best suited for HCF (High Cycle Fatigue) applications