Calculation
σa = σD · (ND/N)^(1/k)
In a log-log S-N plot, the time-limited fatigue line follows a power law between the endurance limit and lower cycle counts.
Basquin-Gleichung (Wöhlerlinie); Dubbel Werkstofftechnik E 1.3.2, Bild 19 (Zeitfestigkeitsbereich, Grenzlastspielzahl 2–20·10⁶)
Time-limited fatigue strength via the Basquin equation
In a log-log S-N plot, the time-limited fatigue line follows a power law between the endurance limit and lower cycle counts.
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Result
Select a target and calculate.
Understand the inputs
- Allowable stress amplitude σa — Stress amplitude survivable at N cycles in the time-limited fatigue region.
- Endurance limit σD — Stress amplitude survivable from the knee-point cycle count ND onward (endurance region).
- Knee-point cycle count ND — Cycle count beyond which the S-N curve levels off into the endurance region; often 2 to 10 million for steel.
- Desired cycle count N — Cycle count in the time-limited region (N<ND) for which the allowable amplitude is sought.
- Slope exponent k — Reciprocal of the log-log slope of the time-limited fatigue line; material- and notch-dependent, often 3 to 15.
Example
σD=200 MPa, ND=2,000,000, N=100,000 and k=5 give σa=200·(20)^0.2≈364.1 MPa.
Assumptions and limits
Valid only in the time-limited region (N<ND) of an idealised log-log linear S-N curve; scatter, load spectra, mean-stress effects and the transition to low-cycle fatigue are excluded.
Understand Time-limited fatigue strength via the Basquin equation
This calculator determines one point on the time-limited fatigue line of an S-N diagram: the stress amplitude survivable at a given number of cycles, starting from the endurance limit.
What does this quantity describe?
In a log-log S-N diagram, time-limited fatigue strength runs as a straight line between low-cycle and endurance fatigue. The Basquin equation describes it as a power law: σa=σD·(ND/N)^(1/k), with knee-point cycle count ND marking the transition to the endurance region.
Formula and variables
σa = σD · (ND/N)^(1/k)
σa = σD · (ND/N)^(1/k)
| Symbol / input | Meaning |
|---|---|
| Allowable stress amplitude σa | Stress amplitude survivable at N cycles in the time-limited fatigue region. |
| Endurance limit σD | Stress amplitude survivable from the knee-point cycle count ND onward (endurance region). |
| Knee-point cycle count ND | Cycle count beyond which the S-N curve levels off into the endurance region; often 2 to 10 million for steel. |
| Desired cycle count N | Cycle count in the time-limited region (N<ND) for which the allowable amplitude is sought. |
| Slope exponent k | Reciprocal of the log-log slope of the time-limited fatigue line; material- and notch-dependent, often 3 to 15. |
Choose the inputs correctly
σD is the endurance limit (stress amplitude from ND cycles onward), ND the knee-point cycle count, N the desired cycle count in the time-limited region, and k the slope exponent of the time-limited line.
How to use the calculator
Take σD and ND from an S-N test, a component catalogue, or a standard such as DIN 743; derive k from the same test or from experience values for the material and notch case.
Worked example
σD=200 MPa, ND=2,000,000, N=100,000 and k=5 give σa=200·(20)^0.2≈364.1 MPa.
Understand the result and units
For N<ND, the allowable amplitude always exceeds σD; the smaller k, the more steeply the curve rises toward lower cycle counts.
σD and σa are stresses; ND, N and k are dimensionless.
Typical applications
Estimating allowable stress amplitude for a limited service life, e.g. for special load cases, test benches, or components with a defined rather than infinite design life.
Assumptions, limits and common mistakes
Valid only in the linear time-limited region (N<ND) of an idealised S-N curve; test-data scatter, load spectra instead of single-level loading, mean-stress effects and the transition to low-cycle fatigue (N<10⁴) are excluded.
Common mistake: Do not enter N>ND; above the knee-point cycle count the constant endurance limit σD applies, not the power law.
Frequently asked questions
What is “Time-limited fatigue strength via the Basquin equation” used for?
Estimating allowable stress amplitude for a limited service life, e.g. for special load cases, test benches, or components with a defined rather than infinite design life.
Where do the input values come from?
σD is the endurance limit (stress amplitude from ND cycles onward), ND the knee-point cycle count, N the desired cycle count in the time-limited region, and k the slope exponent of the time-limited line.
What does the result not cover?
Valid only in the linear time-limited region (N<ND) of an idealised S-N curve; test-data scatter, load spectra instead of single-level loading, mean-stress effects and the transition to low-cycle fatigue (N<10⁴) are excluded.