Cumulative Fatigue Damage (Miner's Rule)
A part rarely sees one stress level. Miner's rule adds up the share of life each block of cycles uses.
Example
You enter
- Ultimate strength Sut (psi) 100000
- Corrected endurance limit Se (psi) 50000
- Fatigue strength fraction f (blank for Shigley's fit) 0.9
- Block 1 reversed stress (psi) 70000
- Block 1 cycles 0.2
- Block 2 reversed stress (psi, optional) 55000
- Block 2 cycles 0.5
- Block 3 reversed stress (psi, optional) 40000
- Block 3 cycles 0.3
You get
- Total cycles to failure 83583
- Life at each block's stress 19173
- Life 2 cycles 326247
No published worked example is on file for this calculation. It is checked against a hand-worked derivation of its method and an independent reference test.
Details, formula, and sources
Scopen over the life N at that stress on the S-N line, and predicts failure when the shares reach 1. Up to three blocks; a block at or below the endurance limit does no damage. A 100 kpsi steel with a 50 kpsi endurance limit cycled 20% at 70 kpsi, 50% at 55 kpsi, and 30% at 40 kpsi lasts about 83,600 cycles, nearly all of the damage from the 70 kpsi share. Load order and scatter make this an estimate. Steel, reversed stress. A design aid; test data govern.
Formula or tableS-N line as fatigue-finite-life: a = (f Sut)^2/Se, b = -(1/3) log10(f Sut/Se), N_i = (sigma_i/a)^(1/b) for Se < sigma_i <= f Sut, no damage at or below Se; D = sum(n_i/N_i) per block; blocks to failure = 1/D; cycles to failure = (1/D) sum(n_i).
Source and editionThe Palmgren-Miner linear cumulative-damage rule (Shigley, Mischke and Budynas, Mechanical Engineering Design, Sec. 6-15), by name, on the Shigley finite-life S-N line.
Free accessStandard published fatigue relations; the strengths, f, and the stress blocks are the user's inputs.
What governsEstimate. AHJ and licensed professional govern.
API field namesultimate_strength_psi, endurance_limit_psi, fatigue_fraction, stress_1_psi, cycles_1, stress_2_psi, cycles_2, stress_3_psi, cycles_3, cycles_to_failure, life_1_cycles, life_2_cycles
- Damage rule D = sum(n_i/N_i), failure at D = 1Palmgren (1924), Miner (1945); Shigley Sec. 6-15
- Lives from the finite-life S-N line, computed by the fatigue-finite-life routineShigley Eqs. 6-13 to 6-16
- Below the endurance limit no damageShigley Sec. 6-15