Zerdly

Fatigue Life Estimator

This tool uses the Basquin high-cycle fatigue relation σa = σf'·(2N)^b, where σf' is the fatigue strength coefficient, b is the (negative) fatigue strength exponent and 2N is the number of load reversals.

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How to use this calculator

Enter Values

Enter your values and press Calculate to see results.

Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.

How to use this calculator

  1. Enter the stress amplitude σa (half the peak-to-peak stress range) in MPa, plus the material's fatigue strength coefficient σf' and fatigue strength exponent b (a small negative number, typically −0.05 to −0.12) from an S-N or strain-life datasheet.
  2. Optionally enter the mean stress σm and ultimate tensile strength σuts to apply a Goodman mean-stress correction — tensile mean stress shortens life.
  3. Read the estimated cycles to failure N and the life regime, then apply your own factor on life/stress and confirm against the governing fatigue standard.

How it works

This tool uses the Basquin high-cycle fatigue relation σa = σf'·(2N)^b, where σf' is the fatigue strength coefficient, b is the (negative) fatigue strength exponent and 2N is the number of load reversals. Rearranging gives N = 0.5·(σa/σf')^(1/b). Because b is negative and σa is below σf', the exponent 1/b is a large negative number and small increases in stress amplitude cut life dramatically.

When a tensile mean stress is present, the alternating amplitude is converted to an equivalent fully-reversed amplitude with the Goodman correction σar = σa/(1 − σm/σuts) before applying Basquin. The result is only as good as the S-N constants supplied and ignores notch sensitivity (Kf), surface finish, size, temperature, corrosion, residual stress and variable-amplitude loading — all of which real fatigue assessment (e.g. EN 1993-1-9, AS 4100, AISC) must account for.

Worked example

Steel component, σa = 300 MPa, σf' = 900 MPa, b = −0.085. A fully-reversed stress amplitude of 300 MPa on a steel with fatigue strength coefficient σf' = 900 MPa and fatigue strength exponent b = −0.085 (no mean stress). Basquin gives N = 0.5 · (300/900)^(1/−0.085) ≈ 205,192 cycles to failure — finite high-cycle life. Add a mean stress σm = 100 MPa with σuts = 1000 MPa and the Goodman correction raises the effective amplitude to σar = 333.33 MPa, dropping the estimate to about 59,407 cycles.

Common mistakes

  • Entering the full stress RANGE instead of the amplitude. σa is HALF the peak-to-peak range (σa = Δσ/2). Using the full range roughly halves the apparent amplitude error and badly skews the life.
  • Giving b as a positive number. The fatigue strength exponent b is always negative (typically −0.05 to −0.12); a positive value is rejected because it makes higher stress give longer life.
  • Treating the number as a design life. Basquin S-N is a mean-fit estimate with large scatter — apply a factor on life (often 10–20) or on stress, and use strain-life methods when N is below ~10³ cycles.

Frequently asked questions

What are σf' and b, and where do I get them?

σf' is the fatigue strength coefficient (roughly the stress intercept of the S-N line at one reversal) and b is the fatigue strength exponent (the slope, always negative). They come from a material's strain-life/S-N data — handbooks, mill certificates or test reports. For many steels σf' is of the order of the true fracture strength and b ≈ −0.08 to −0.10, but always use tested values for your alloy and condition.

When should I apply the mean-stress (Goodman) correction?

Apply it whenever the loading is not fully reversed — i.e. there is a non-zero mean stress. A tensile mean stress reduces fatigue life, so leaving it out is non-conservative. Enter σm and σuts and the tool converts to an equivalent fully-reversed amplitude before applying Basquin. Goodman is one of several corrections (Gerber, Soderberg, SWT); choose the one your standard specifies.

Is this valid for low-cycle fatigue?

Not really. The Basquin S-N power law is a high-cycle (elastic) model. Below about 10³ cycles plasticity dominates and you should use a strain-life approach such as Coffin–Manson. The tool flags this regime in the result so you know when the estimate is outside its intended range.

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