Coffin-Manson Low-Cycle Fatigue Life (Simplified)
Coffin-Manson Low-Cycle Fatigue Life (Simplified)
When cyclic loading is severe enough to cause noticeable plastic strain on each cycle — as in thermal cycling of a pressure vessel nozzle or repeated full-power engine startups — fatigue life is governed by strain range rather than stress amplitude, and the Coffin-Manson relation is the standard empirical model for this low-cycle regime. Low-cycle fatigue typically produces failure in a few hundred to a few tens of thousands of cycles, orders of magnitude fewer than high-cycle (Basquin-law) fatigue, which is why components subject to frequent large strain swings — rather than just high-frequency small vibrations — need this separate strain-based fatigue check.
The simplified Coffin-Manson relation gives cycles to failure as Nf = 0.5*(2*d_eps/ef)^(1/c), all dimensionless quantities. where d_eps is the applied plastic strain range, e_f is the fatigue ductility coefficient, and c_cm is the fatigue ductility exponent (a negative material constant).
Inputs
d_eps := 0.004=4e-03
e_f := 0.5=0.5
c_cm := -0.6=-0.6
Because low-cycle fatigue is strain-controlled, the ratio of applied strain amplitude to the material's ductility coefficient, raised to the 1/c power, plays the same governing role here that the stress ratio plays in Basquin's high-cycle law.
N_f := 0.5·(2·d_eps/e_f)^(1/c_cm)=492.16
Results
A predicted life in the low hundreds of cycles is typical for a strain range of this magnitude, consistent with components undergoing repeated significant thermal or mechanical strain excursions rather than small-amplitude vibration. Because the exponent 1/c is large in magnitude, small increases in the applied strain range shorten predicted life dramatically, which is why reducing peak strain (softer transitions, lower thermal gradients) is usually far more effective than material substitution alone for extending low-cycle fatigue life.
Assumptions & limitations
- Applies to the low-cycle, plastic-strain-dominated fatigue regime.
- Fully-reversed strain-controlled loading assumed.
- e_f and c are empirical material constants specific to the alloy and test conditions.
- Does not include the elastic (Basquin) strain contribution — a full strain-life model adds both terms.