OpenSpecEngineering

Estimates how many load cycles a part survives, or the stress or strain it can take for a target life. Use the High-Cycle (stress-life) regime above roughly 10³ cycles, where the part stays mostly elastic. Use the Low-Cycle (strain-life) regime below that, where each cycle yields the material. Pick a material to fill in its properties, or choose Custom.

High-cycle: the S-N line

S = a·N^b     a = (f·S_ut)²/S_e     b = −⅓·log₁₀(f·S_ut/S_e)

The line runs from f·S_ut at 10³ cycles to the endurance limit S_e at 10⁶ cycles [1]. S is the fully reversed stress amplitude, N the cycles to failure, S_ut the ultimate tensile strength and f the fraction of S_ut reached at 10³ cycles (about 0.9 for S_ut up to 500 MPa, falling to about 0.8 near 1,400 MPa [1]). You can enter S_e directly or correct the rotating-beam limit S_e′ with the Marin factors:

S_e = k_a·k_b·k_c·k_d·k_e·k_f·S_e′

k_a is the surface factor, fitted to S_ut for each finish. k_b = (d/7.62)^−0.107 for d up to 51 mm and 1.51·d^−0.157 up to 254 mm, with d in mm, and 1 for axial load. k_c is 1 for bending, 0.85 for axial and 0.59 for torsion. k_d (temperature, steel) and k_e (reliability) come from Tables 6-4 and 6-5 of [1]; k_f covers anything else. A material choice fills in S_e′ = 0.5·S_ut for steel, capped at 700 MPa.

Low-cycle: the strain-life curve

Δε/2 = (σ_f′/E)·(2N)^b + ε_f′·(2N)^c

Δε/2 is the total strain amplitude and 2N the number of reversals. σ_f′ and b are the fatigue strength coefficient and exponent, ε_f′ and c the ductility coefficient and exponent, and E the modulus [2]–[5].

Limits and common mistakes

• Both regimes assume fully reversed loading, with zero mean stress. A mean stress shortens the life, and the page does not correct for it.
• Aluminum and other nonferrous alloys have no true endurance limit. Their S_e is only a reference stress at 10⁶ cycles.
• For steel, a stress below S_e normally means infinite life, not the finite N past 10⁶ that the line gives.

Worked example

A machined steel shaft, 32 mm in diameter, has an ultimate strength of 690 MPa and sees a fully reversed bending stress of 220 MPa. Estimate its life at 90 % reliability.

1. Choose Material Custom and Fatigue Regime High-Cycle — Stress-Life (Basquin S-N).
2. Enter Ultimate Strength 690 MPa and Fraction Factor 0.86, read from the f chart in [1].
3. Choose Endurance Limit Source Derive endurance limit from Marin factors and enter S_e′ 345 MPa (0.5·S_ut).
4. Choose Surface Finish Machined or cold-drawn and Load Type Bending, and enter Characteristic Diameter 32 mm.
5. Choose Reliability 90%, keeping the other factors at their defaults.
6. Choose Solve For Cycles to failure, given stress, enter Stress Amplitude 220 MPa and press Solve. The Solution shows: Surface Factor (ka): 0.797777
   Size Factor (kb): 0.857666
   Load Factor (kc): 1
   Reliability Factor (ke): 0.897
   Corrected Endurance Limit (Se): 211.744 MPa
   Estimated Life (N): 773,833 cycles
   S-N coefficient (a): 1,662.97 MPa
   S-N exponent (b): −0.149179

Check: S_e = 0.7978 × 0.8577 × 0.897 × 345 = 211.7 MPa. The 220 MPa applied is only 4 % above it, so a life near 10⁶ cycles is what to expect.