Estimate fatigue life (cycles to failure) using Basquin relation. Input stress amplitude, material strength, and fatigue parameters. Visualize S‑N curve, endurance limit, and design safe life. Essential for mechanical design, aerospace, and automotive engineering.
Metal fatigue is a progressive, localized damage process caused by cyclic loading. Even if stresses are below the yield strength, repeated cycles can initiate cracks and lead to sudden failure. The S‑N curve (stress vs. number of cycles) characterizes a material’s fatigue behaviour. The Basquin relation describes the high‑cycle fatigue regime: σa = σf' (2N)b, where σf' is the fatigue strength coefficient and b the fatigue exponent (typically between -0.05 and -0.15).
Fatigue life N (cycles to failure) from Basquin:
N = ½ (Sa / σf')1/b
Fatigue research began in the 19th century with railway axle failures. August Wöhler (Germany) systematically tested railroad axles and introduced the S‑N diagram. Later, Basquin (1910) proposed the power‑law relationship. Today, fatigue analysis is mandatory in aerospace (FAA regulations), automotive (ISO 12107), pressure vessels (ASME BPVC), and bridge design. The concept of endurance limit (fatigue limit) is crucial for steels – below this stress, the material can withstand infinite cycles. For aluminum and titanium, a “fatigue strength” at a given number of cycles (e.g. 107) is used.
The calculator implements the Basquin equation for high‑cycle fatigue (N > 103 cycles). The fatigue strength coefficient σf' is often approximated as 0.9 × UTS for many steels, while b ranges from -0.05 to -0.12. For aluminum alloys, σf' ≈ 1.4×UTS? Actually common values: 2024‑T3 σf' ≈ 1100 MPa, UTS ≈ 480 MPa, so factor ~2.3. We use realistic presets based on MMPDS (formerly MIL‑HDBK‑5). The endurance limit Se is estimated as factor × UTS (0.5 for steels, 0.3–0.4 for non‑ferrous). If Sa < Se, the model predicts infinite life (theoretically >107 cycles), but we still show the Basquin life for reference (which may be extremely high).
Limitations: Mean stress effects (Goodman, Gerber) are not included; assumes fully reversed loading (R = -1). For other R ratios, use equivalent stress amplitude via a mean stress correction. Also does not cover low‑cycle fatigue (strain‑life approach).
Values compiled from MMPDS-01 and ASM Handbooks.
| Material | UTS (MPa) | σf' (MPa) | b | Endurance limit factor |
|---|---|---|---|---|
| Steel (low alloy, 700 MPa) | 700 | ~630 | -0.085 | 0.5 |
| Aluminum 2024-T3 | 480 | ~1100 | -0.12 | 0.3 |
| Titanium Ti-6Al-4V | 900 | ~1500 | -0.10 | 0.4 |
| Gray cast iron | 250 | ~350 | -0.09 | 0.35 |
An aerospace engineer evaluates a 2024-T3 aluminum bracket (UTS 480 MPa) subject to a repeated stress of 200 MPa. Using the calculator with preset “Aluminum”, σf' ≈ 1100 MPa, b = -0.12, endurance limit factor 0.3 → Se = 144 MPa. Since Sa = 200 > Se, finite life is predicted. The tool computes Nf ≈ 2.1×105 cycles. The engineer must either redesign (reduce stress) or plan inspections. The S‑N graph helps visualize the margin.
Engineers use several approaches: infinite‑life design (stress below endurance limit), safe‑life (predictable finite life with safety factor), and damage tolerance (crack growth analysis). This calculator supports the first two by providing life estimates and safety margins. For critical components, additional factors (load, size, surface finish) are applied to modify Se. The calculator’s factor can be adjusted to account for these (e.g., 0.4 instead of 0.5 for machined surfaces).