Basquin's Law¶
An empirical power-law segment relating cyclic stress to fatigue life under specified material, loading, and failure conditions.
Core Idea¶
Basquin's law is an empirical power-law segment relating a specified repeated-stress measure to fatigue life. In a modern fully reversed amplitude convention, \(\sigma_a=\sigma_f'(2N_f)^b\) with \(b<0\), where \(N_f\) is cycles to a defined failure endpoint and $2N_f$ is reversals. Taking logs makes stress versus life approximately linear over a calibrated range. Inverting correctly gives \(N_f=\tfrac12(\sigma_a/\sigma_f')^{1/b}\); the negative exponent means higher stress predicts shorter life in that range. The frozen seed's \(-1/b\) inversion was a sign error.[ref-41662d9d7764][ref-de79e49ec754]
Scope of Application¶
Basquin's 1910 paper analyzed endurance tests, including wrought-iron repeated bending, and found approximate straight segments on log stress–repetition plots. Lower-stress specimens that had not failed—including a 48.2-million-repetition runout—warn against extrapolating one line indefinitely. A later original composite study fits the equivalent form \(\sigma^mN=c\) to glass/polyester and glass/epoxy laminate data but shows that stress ratio, orientation and frequency alter the fit.[ref-90180fad4293][ref-f056694fa839]
The law is most useful for a bounded stress-life region where elastic strain dominates. Macroscopic cyclic plasticity calls for an additional Coffin–Manson strain-life term. Variable-amplitude damage accumulation is another separate model, not an implication of the Basquin line.
Clarity¶
State whether stress is amplitude, range or maximum, whether life counts cycles or reversals, and what failure endpoint is used. Basquin's original maximum-stress/repetition notation differs from the later \(\sigma_f'\) and $2N_f$ convention. Replacing $2N_f$ by \(N_f\) without adjusting the coefficient changes the intercept. Both intercept and slope can depend on material and loading conditions; they are not universal constants.[ref-90180fad4293][ref-41662d9d7764][^ref-f056694fa839]
Manages Complexity¶
One intercept and slope summarize a group of constant-amplitude fatigue results and make stress sensitivity visible. They do not remove test scatter, censored runouts, mean-stress effects or regime boundaries. Pooling unlike conditions may seem efficient but can produce a misleading common line; separate fits require more testing yet preserve the conditions on which predictions depend.[ref-90180fad4293][ref-f056694fa839]
Abstract Reasoning¶
For a fitted segment \(\sigma=C N^b\), \(\log\sigma=\log C+b\log N\); \(b<0\) is the log–log slope. Algebraic inversion yields \(N\propto\sigma^{1/b}\), not \(\sigma^{-1/b}\). If stress ratio, geometry or material state changes, the same slope and intercept need not transfer. If the data show a low-stress knee, a runout, or substantial cyclic plasticity, a single stress-life power segment may no longer support the intended prediction.[ref-90180fad4293][ref-41662d9d7764][^ref-f056694fa839]
Knowledge Transfer¶
The fitting skeleton maps from Basquin's wrought-iron bending tests to composite-laminate S–N data: specified cyclic stress, count to fatigue failure, calibrated negative power and a bounded regime. Neither the numerical exponent nor the failure mechanism transfers automatically. The broader idea of a power law is related, but Basquin's identity requires mechanical stress and fatigue life; live Gradual Deterioration and Allometry do not currently establish a strict parent edge.[ref-90180fad4293][ref-f056694fa839]
[^ref-90180fad4293]: O. H. Basquin, “The Exponential Law of Endurance Tests”, Proceedings ASTM 10 (1910), 625–630, scanned mirror/OCR, especially pp. 626–627; volume contents. [^ref-41662d9d7764]: D. J. Jones and P. Kurath, Cyclic Fatigue Damage Characteristics Observed for Simple Loadings Extended to Multiaxial Life Prediction, NASA CR 182126 (1988), §1.1.2. [^ref-de79e49ec754]: eFatigue, Fatigue Tests and Stress-Life (S–N) Approach, reversal/cycle convention; direct PDF access intermittent. [^ref-f056694fa839]: H. Ma et al., “Modeling the Effect of Stress Ratio, Loading Frequency and Fiber Orientation on the Fatigue Response of Composite Materials”, Polymers 14 (2022), §2 eqs. (1)–(3), Table 1 and §5.
Neighborhood in Abstraction Space¶
Basquin's Law sits in a sparse region of the domain-specific corpus (81st percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.
Family — Structural Mechanics & Materials (19 abstractions)
Nearest neighbors
- Material Ratcheting — 0.85
- Paris' Law — 0.83
- Permissible Stress Design — 0.83
- Plane Strain Compression Test — 0.81
- Aggregate Modulus — 0.81
Computed from structural-signature embeddings · 2026-10-08