Strain Life Method (Low Cycle Fatigue)
Strain Life Method (Low Cycle Fatigue): Theoretical Foundations
What is the Strain-Life Method?
Professor, how is the strain-life method different from the S-N curve method?
The S-N curve method is stress-based for high-cycle fatigue ($N > 10^4$). The strain-life method is strain-based for low-cycle fatigue ($N < 10^4$). It is essential for problems with large plastic strain.
Coffin-Manson Equation
The first term is elastic strain (Basquin's equation), the second term is plastic strain (Coffin-Manson equation).
$\sigma_f'$: Fatigue strength coefficient, $b$: Fatigue strength exponent, $\varepsilon_f'$: Fatigue ductility coefficient, $c$: Fatigue ductility exponent.
It includes both elastic and plastic strain. In low-cycle (large strain) fatigue, the plastic term dominates.
The S-N method assumes stress is below yield. The strain-life method can directly handle plastic strain exceeding yield.
Summary
The Independent Discovery of Coffin-Manson
The Coffin-Manson law, which forms the basis of the strain-life method, was independently discovered in 1954 as part of nuclear-related research. Coffin studied thermal fatigue in turbine blades at Pratt & Whitney, while Manson studied steam turbines at NACK, a predecessor of NASA. That both arrived at the same equation Δεp/2=εf'(2Nf)^c is considered a curious coincidence in the history of science.
Computational Methods for Strain Life Method (Low Cycle Fatigue)
FEM for Strain-Life
1. Elastoplastic FEM Analysis — Track hysteresis loops under repeated loading.
2. Obtain stabilized strain range $\Delta\varepsilon$
3. Calculate life $N_f$ using Coffin-Manson equation
Fatigue software (nCode, fe-safe) automatically calculates life from FEM stress/strain results using Coffin-Manson.
Summary
Separation of Elastic and Plastic Strain Ranges
In the strain-life method, the total strain range Δε is separated into the Coffin-Manson equation (plastic component) and Basquin's law (elastic component) to evaluate life. The practical transition life 2Nt (the point where both components are equal) is typically around 2000 cycles for A7075 aluminum and about 4000 cycles for SS400 steel. In low-cycle fatigue (Nf<10^4), the plastic component becomes dominant.
Strain Life Method (Low Cycle Fatigue) in Practice
Strain-Life in Practice
Used for thermal fatigue in engine components, pressure cycles in pressure vessels, and low-cycle fatigue in earthquakes.
Practical Checklist
Low-Cycle Fatigue Assessment for Nuclear Power Plant Piping
Piping in nuclear power plants experiences large strain ranges during startup, shutdown, and earthquakes, making low-cycle fatigue a major design concern. ASME Code Sec.III NB-3200 uses material design fatigue curves (strain-life based) and stipulates that the allowable cumulative damage factor must be kept below 1.0. For Δε=0.5%, the allowable cycle count is about 100,000 cycles for 304SS.
Strain Life Method (Low Cycle Fatigue): Software & Solver Comparison
Tools
Differences in ε-N Method Material Constant Databases
The MATLAB Fatigue Toolbox compliant with SAE J1099 standard and nodeDB (formerly MatDB) contain literature values for the fatigue ductility coefficient εf of the same steel S45C that differ by about 8%. ANSYS nCode uses both ASME material DB and its own test DB, and its material selection UI mandates source disclosure, a point valued in reliability design.
Advanced Technologies
Advanced
Thermo-Mechanical Fatigue (TMF) and Strain-Life
Related Topics
Experience the theory firsthand with the interactive simulator for this field
All Simulators