Fatigue Life Composite⚠ unverified
Mechanical / Composites · Estimate the fatigue life of a composite using a simple power law
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| sigma_max | σmax | Pa | 1.0 | Maximum applied cyclic stress |
| sigma_u | σu | Pa | 1.0 | Ultimate (static) strength |
| m | m | — | 1.0 | Power-law fatigue exponent (dimensionless) |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | N | — | Estimated number of cycles to failure (dimensionless) |
The science & history
Understanding the Parameters
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Stress ratio $\sigma_u/\sigma_{max}$ — life depends on how far the cyclic stress sits below the static strength. At $\sigma_{max} = \sigma_u$, $N = 1$ (static failure); as $\sigma_{max}$ drops, $N$ grows as a power law.
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Fatigue exponent $m$ — governs the steepness of the S-N curve. Fiber-dominated CFRP has a very high $m$ (flat S-N, excellent fatigue life); matrix-dominated or off-axis loading gives a lower $m$ (steeper, poorer fatigue). It is the single most important fatigue parameter and is measured from tests.
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No endurance limit — unlike steel (Endurance Limit steel), most composites have no fatigue limit; the power law keeps decreasing, so "infinite life" design uses a high safety factor on stress rather than a threshold.
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Damage mechanism — composite fatigue is diffuse (matrix cracks multiply, then delaminations link, then fibers break) rather than a single crack, so stiffness degradation — not a crack length — is often the tracked damage metric.
Derivation (Approaching a Proof)
Composite S-N data are commonly fitted by a power law relating the normalised peak stress to life. Writing the stress ratio as $\sigma_{max}/\sigma_u$ and assuming a straight line on log(stress)–log(life) axes:
$$\frac{\sigma_{max}}{\sigma_u} = N^{-1/m} \;\Longrightarrow\; N = \left(\frac{\sigma_u}{\sigma_{max}}\right)^{m}.$$
The anchor $N = 1$ at $\sigma_{max} = \sigma_u$ (static failure) is built in, and the exponent $m$ sets the slope. This is the composite analog of the Basquin power law for metals (Fatigue Life cycles), but without an endurance-limit knee — reflecting the absence of a fatigue threshold in most composites. It is a phenomenological fit, not a mechanism-based model.
Dimensional check. $\sigma_u/\sigma_{max} = \text{Pa}/\text{Pa}$ = dimensionless; raised to the pure-number power $m$, $N$ is dimensionless — a cycle count, as required.
History and Development
Power-law S-N fits for composites emerged as fiber-reinforced polymers entered fatigue-critical service (aircraft, wind-turbine blades, pressure vessels). The key findings they encode — no endurance limit, distributed damage, and the outstanding fatigue resistance of well-aligned fiber-dominated laminates — shaped composite durability design. Detailed analysis uses residual-strength/stiffness degradation models and constant-life (Goodman-type) diagrams for mean-stress effects; this power law is the first-pass estimate.
Related Concepts: Fatigue Life cycles, S-N Curve, Longitudinal Strength, Endurance Limit steel, Fatigue From Vibration, Composite Laminate Theory
Notes: Phenomenological power law; $N=1$ at $\sigma_{max}=\sigma_u$. No endurance limit (unlike metals) — design with a stress safety factor. High $m$ = flat S-N = fatigue-resistant (fiber-dominated CFRP). Damage is diffuse (matrix cracks/delamination), tracked by stiffness loss. Composite analog of Basquin (Fatigue Life cycles).