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Home/Engineering/Fatigue S-N Curve + Miner Rule

Fatigue S-N Curve + Miner Rule

Basquin S-N curve with optional endurance limit, three cyclic load blocks, and Palmgren-Miner cumulative damage D = Σ n_i/N_i.

S-N model

240 MPa
5.5

Load blocks

330 MPa
4.3
270 MPa
5.1
210 MPa
6

Measured values

Miner damage D0.356
Damage margin0.644
Nf at block A1.74e+5
Statusok

This is a linear cumulative-damage teaching model. Real fatigue depends on mean stress, notches, surface finish, residual stress, corrosion, load order, scatter, and inspection criteria.

Live graphs

About this model

Fatigue design often starts with an S-N curve: a stress amplitude S_a is associated with a cycle count N_f to crack initiation or failure. This simulator uses a Basquin-style relation N_f = N_e(S_a/S_e)^{-m} above an endurance-limit stress S_e, with an optional horizontal endurance plateau. Three load blocks contribute cumulative damage through the Palmgren-Miner rule D = Σ n_i/N_i. The page makes the bookkeeping visible on a log-log S-N plot and a damage bar. It is a teaching model only: real fatigue also depends on mean stress, stress concentration, size and surface finish, residual stress, corrosion, variable-amplitude sequence effects, scatter, and inspection criteria.

Who it's for: Machine design, mechanics of materials, reliability, and structural detail fatigue introductions.

Key terms

  • S-N curve
  • Basquin law
  • Endurance limit
  • Miner rule
  • Cumulative fatigue damage

How it works

Fatigue life sketch with a Basquin S-N curve, optional endurance limit, three cyclic load blocks, and Palmgren-Miner cumulative damage D = Σ n_i/N_i.

Key equations

N_f = N_e (S_a / S_e)^{-m} for S_a > S_e
Miner rule: D = Σ n_i / N_i; D ≥ 1 marks the linear damage failure threshold

Frequently asked questions

Does D = 1 always predict failure exactly?
No. Miner damage is a linear rule of thumb. It is useful for accounting, but real fatigue lives scatter widely and load order can matter.
Why do stresses below Se add no damage?
That is the ideal endurance-limit assumption used for some steels in benign conditions. Turning the endurance limit off continues the Basquin slope into high-cycle fatigue.