Fatigue Stress Concentration⚠ unverified
Mechanical / Fatigue · Compute the fatigue stress-concentration factor Kf
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| Kf | Kf | — | 1.0 | Existing fatigue stress-concentration factor (dimensionless); unused in the current implementation |
| Kt | Kt | — | 1.0 | Theoretical (geometric) stress-concentration factor (dimensionless) |
| q | q | — | 1.0 | Notch sensitivity (dimensionless), between 0 and 1 |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | Kf | — | Fatigue stress-concentration factor Kf (dimensionless) |
The science & history
Understanding the Parameters
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Geometric factor $K_t$ — the elastic stress raiser from the feature's geometry alone, read from Peterson/Roark charts (e.g. a shoulder fillet $K_t \approx 1.5$–$2.5$). It sets the ceiling for $K_f$.
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Notch sensitivity $q$ — how much of $K_t$ carries into fatigue ($0 \le q \le 1$); a material-and-radius property from the Neuber/Peterson models. See Notch Sensitivity for its origin.
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Fatigue factor $K_f$ — bounded by $1 \le K_f \le K_t$. It multiplies the alternating stress (mean stress is treated separately in most methods) before comparison against the endurance limit.
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Where it enters — $K_f$ appears in Shaft Fatigue Factor, Bolt Fatigue Factor, and Weld Fatigue Factor as the amplifier on the alternating component; for high-strength steel with a sharp notch it can approach $K_t$ and dominate the design.
Derivation (Approaching a Proof)
$K_f$ is defined to interpolate linearly between the two physical limits of a notch's fatigue effect:
$$K_f = 1 + q\,(K_t - 1),$$
so that $q = 0 \Rightarrow K_f = 1$ (notch has no fatigue effect) and $q = 1 \Rightarrow K_f = K_t$ (full elastic peak acts in fatigue). Rearranged, $q = (K_f - 1)/(K_t - 1)$ is the definition of notch sensitivity. The physics lives in $q$, which the Neuber ($q = 1/(1+\sqrt{a/r})$) and Peterson ($q = 1/(1+a/r)$) models tie to the notch root radius $r$ and a material length constant $a$: sharper notches and softer materials give smaller $q$ and hence $K_f < K_t$.
Dimensional check. $K_f = 1 + q\,(K_t - 1)$ is dimensionless — every quantity is a pure ratio.
History and Development
The distinction between the theoretical concentration $K_t$ (Kirsch 1898; Neuber's notch theory) and the fatigue concentration $K_f$ was one of the key insights of 20th-century fatigue research: real parts tolerate sharp notches better than elastic theory warns. Neuber and Peterson supplied the notch-sensitivity models that make $K_f$ computable, and Shigley codified $K_f = 1 + q(K_t - 1)$ as the standard step between a stress-concentration chart and a fatigue safety factor.
Related Concepts: Notch Sensitivity, Fatigue Notch Factor, Stress Concentration, Shaft Fatigue Factor, Bolt Fatigue Factor, Weld Fatigue Factor
Notes: Duplicate of Notch Sensitivity; the Kf input is unused (placeholder). $1 \le K_f \le
K_t$. Multiplies the *alternating* stress. Get $K_t$ from charts, $q$ from Neuber/Peterson.