Basquin S-N Fatigue Life
High-cycle fatigue life from the Basquin power law — enter stress amplitude to get cycles, or cycles to get allowable stress.
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The engineering
Basquin's law is the straight line every high-cycle S-N curve draws on log-log axes: stress amplitude equals the fatigue strength coefficient σ'f times reversals-to-failure raised to a small negative exponent b. Feed it a stress amplitude from your loads analysis and it returns life; feed it a required life and it returns the allowable alternating stress. σ'f is roughly the true fracture stress (often near the monotonic tensile strength plus 50%), and b typically runs −0.05 to −0.12 for metals — pull both from MMPDS/MIL-HDBK-5 or coupon regression, not from guesswork.
Mind the exponent: because 1/b is on the order of −10, a 10% drop in stress amplitude buys roughly a 3× life increase — and a 10% underestimate of loads erases it just as fast. The law also assumes fully reversed loading (R = −1); with a mean stress present, correct σa first (Goodman, Gerber, or SWT) before entering it here. Below about 10³ cycles plastic strain dominates and Basquin alone is unconservative — that's Coffin-Manson territory.
Where this math comes from
August Wöhler spent the 1860s cycling full-size railway axles to failure at the Prussian state railways after a string of fatal derailments, producing the first stress-versus-life tables and the concept of an endurance limit. But it was O. H. Basquin, an engineering instructor at Northwestern, who noticed in a 1910 ASTM paper that Wöhler-type data fell on a straight line when plotted log-log — a two-parameter power law an engineer could regress and extrapolate.
The power law held up so well that it became the high-cycle half of the modern strain-life method: Coffin and Manson independently added the plastic-strain term in 1954 for thermal-cycle and low-cycle problems, and the combined curve is how aerospace fatigue allowables are reduced today. The coefficients this card wants live in MIL-HDBK-5 and its successor, MMPDS — the same tables Huntsville stress groups cite on every fatigue substantiation.
- 1867August WöhlerPublishes systematic rotating-bending fatigue data from railway-axle testing — the first S-N curves.
- 1910O. H. BasquinShows S-N data is linear on log-log axes and fits the power law this card evaluates.
- 1954L. F. Coffin & S. S. MansonIndependently add the plastic strain-life term, completing the strain-life equation.
- 1990J. A. Bannantine et al.Fundamentals of Metal Fatigue Analysis codifies the strain-life workflow used in industry.
- 2003FAA / BattelleMMPDS supersedes MIL-HDBK-5 as the source of statistically-based fatigue allowables.
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