Fatigue Life Calculator (S–N Curve & Miner’s Rule)

How this fatigue life calculator works

This tool implements the classical stress–life (S–N) approach to high-cycle fatigue using the Basquin equation and optional Miner’s linear damage rule for variable amplitude loading. It is intended for preliminary design and education, not as a substitute for code-based design or full fatigue testing.

1. Basquin S–N curve model

For high-cycle fatigue under fully reversed loading (stress ratio R = −1), the stress amplitude σ_a and fatigue life N_f (reversals or cycles) are often related by Basquin’s law:

• σ_f^' – fatigue strength coefficient (MPa), roughly equal to the true fracture strength.
• b – fatigue strength exponent (negative), slope of the log S–N curve.
• N_f – number of cycles to failure.

From this equation the calculator can solve either:

• Cycles to failure for a given stress amplitude σ_a:

• Allowable stress amplitude for a target life N_f:

2. Mean stress correction (Goodman, Gerber, Soderberg)

Real components often see non-zero mean stress σ_m. To account for this, the calculator can convert the actual stress amplitude σ_a and mean stress σ_m into an equivalent fully reversed amplitude σ_a,eq using common correction models:

• Goodman (linear):

  σ_a,eq = σ_a / (1 − σ_m / σ_UTS)

• Gerber (parabolic):

  σ_a,eq = σ_a / (1 − (σ_m / σ_UTS)²)

• Soderberg (conservative, uses yield strength σ_y; here approximated with σ_UTS if σ_y is unknown):

  σ_a,eq = σ_a / (1 − σ_m / σ_y)

The calculator uses σ_a,eq in the Basquin equation instead of σ_a. If you don’t have mean stress data, leave the correction set to “None”.

3. Miner’s linear damage rule (variable amplitude)

For a loading history composed of blocks with different stress amplitudes σ_a,i and cycle counts n_i, the fatigue damage from each block is:

where N_f,i is the life at stress amplitude σ_a,i from Basquin’s law. The total damage is:

Failure is predicted when D reaches a critical value D_crit, usually taken as 1.0. The calculator reports the cumulative damage and whether failure is expected.

4. Typical values and units

• Use MPa consistently for all stresses (σ_a, σ_f^', σ_m, σ_UTS).
• For steels, σ_f^' is often in the range 800–1400 MPa; b is typically between −0.05 and −0.15.
• Cycles N_f are dimensionless; high-cycle fatigue usually means N > 10⁴–10⁵.

5. Limitations and engineering judgement

This simplified model does not include notch effects, multiaxial loading, residual stresses, corrosion, temperature, or detailed strain-life (ε–N) behavior. Always:

• Use material parameters from reliable fatigue test data or standards.
• Apply appropriate safety factors for design.
• Verify critical components with code-based methods and, where necessary, full fatigue testing.

FAQ: Fatigue life and S–N curves

What is fatigue life?

Fatigue life is the number of load cycles a material or component can withstand before crack initiation or failure under repeated or fluctuating stresses that are often well below the static strength.

What is an S–N curve?

An S–N curve (Wöhler curve) plots stress amplitude (S) versus number of cycles to failure (N) on a log scale. It summarizes fatigue test results and is the basis for the stress–life design approach.

When should I use the stress–life (S–N) method?

The S–N method is most appropriate for high-cycle fatigue where strains are mostly elastic (typically N > 10⁴–10⁵ cycles). For low-cycle fatigue with significant plasticity, a strain–life (ε–N, Coffin–Manson) approach is more accurate.

What is Miner’s rule?

Miner’s rule is a linear damage accumulation hypothesis. It assumes that each stress block consumes a fraction of the fatigue life proportional to n_i/N_f,i, and that failure occurs when the sum of these fractions reaches about 1. It is simple and widely used, but it does not capture load sequence effects.

Where do I get σ_f^' and b?

These parameters are obtained by curve-fitting fatigue test data for a specific material, surface finish, heat treatment, and environment. Many handbooks and standards provide recommended S–N curves and Basquin parameters for common engineering materials.