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Engineering
Grade college
Fatigue & S-N Curve Reference Cheat Sheet
A printable reference covering S-N curves, fatigue life, mean stress correction, endurance limit, stress concentration, and Miner’s rule for college engineering.
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Fatigue analysis predicts failure under repeated or fluctuating loading, often at stresses below the static yield strength. This cheat sheet covers S-N curve interpretation, stress amplitude, mean stress effects, endurance limits, and cumulative damage. College engineering students need these tools to estimate safe life, compare materials, and design parts that survive cyclic service.
Key Facts
- Stress range is Δσ = σmax - σmin, and stress amplitude is σa = Δσ/2.
- Mean stress is σm = (σmax + σmin)/2, and the stress ratio is R = σmin/σmax.
- For many metals in the finite-life region, Basquin's law is σa = A N^b, where A and b come from the S-N curve fit.
- A common log form of the S-N relation is log(σa) = log(A) + b log(N).
- Goodman mean stress correction is σa/Se + σm/Sut = 1 for the failure boundary under tensile mean stress.
- Gerber mean stress correction is σa/Se + (σm/Sut)^2 = 1 and is less conservative than Goodman for ductile metals.
- Soderberg mean stress correction is σa/Se + σm/Sy = 1 and is more conservative because it uses yield strength.
- Miner's rule for cumulative fatigue damage is D = Σ(ni/Ni), and failure is predicted when D is approximately 1.
Vocabulary
- S-N curve
- A graph showing the cyclic stress level S that causes failure after a number of cycles N.
- Fatigue life
- The number of loading cycles a material or component can withstand before fatigue failure.
- Endurance limit
- The stress amplitude below which some materials can survive a very large number of cycles without fatigue failure.
- Mean stress
- The average stress during a loading cycle, calculated as σm = (σmax + σmin)/2.
- Stress concentration factor
- A factor Kt that measures how much a notch, hole, fillet, or geometry change increases local elastic stress.
- Miner's rule
- A linear damage rule that estimates fatigue damage from variable loading using D = Σ(ni/Ni).
Common Mistakes to Avoid
- Using maximum stress instead of stress amplitude is wrong because most S-N curves are based on alternating stress or stress amplitude, not σmax.
- Ignoring mean stress is wrong because tensile mean stress usually reduces fatigue life, while compressive mean stress can improve it.
- Reading the S-N curve on linear axes is wrong when the curve uses log stress, log cycles, or both, because equal spacing does not represent equal changes.
- Applying an endurance limit to every material is wrong because many aluminum alloys and nonferrous metals do not have a true horizontal fatigue limit.
- Using Kt directly for all fatigue calculations can be wrong because fatigue notch sensitivity may require Kf instead of the theoretical stress concentration factor.
Practice Questions
- 1 A shaft cycles between σmax = 180 MPa and σmin = 20 MPa. Find Δσ, σa, σm, and R.
- 2 A component experiences 10,000 cycles at a stress level with Ni = 100,000 cycles and 50,000 cycles at a second stress level with Ni = 500,000 cycles. Use Miner’s rule to find D.
- 3 For a steel part with Se = 240 MPa, Sut = 600 MPa, and σm = 120 MPa, use the Goodman relation to estimate the allowable stress amplitude σa.
- 4 Explain why a polished specimen S-N curve may overpredict fatigue life for a real machined part with notches, surface roughness, and variable loading.