Temperature Factor⚠ unverified
Mechanical / Fatigue · Compute the temperature modification factor kd
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| T | T | degC | 1.0 | Operating temperature |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | kd | — | Temperature modification factor kd (dimensionless) |
The science & history
Understanding the Parameters
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Operating temperature $T$ — the part's service temperature. Below $\sim 250\,{}^\circ$C the effect is negligible ($k_d \approx 1$); above it, $k_d$ declines and the whole stress-life framework starts to lose validity as creep couples with fatigue.
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The $k_d = 1$ plateau — near room temperature the endurance limit is essentially temperature-independent, so the registry constant is a reasonable default for ambient machinery.
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High-temperature caution — beyond a few hundred $^\circ$C, fatigue is no longer described by a simple endurance limit: time-dependent creep-fatigue interaction dominates, and $k_d$ is at best a rough strength-ratio correction, not a rigorous factor.
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Low temperature — many steels get stronger (higher $S_{ut}$ and endurance) as they cool, though toughness drops sharply below the ductile-brittle transition — a separate fracture concern.
Derivation (Approaching a Proof)
Like the other Marin factors, $k_d$ is empirical. It is defined as the ratio of the material's tensile strength (or endurance limit) at temperature to its room-temperature value,
$$k_d = \frac{S_T}{S_{RT}},$$
on the reasoning that the fatigue limit tracks the ultimate strength's temperature dependence. Tabulating $S_T/S_{RT}$ for steel over $20$–$600\,{}^\circ$C and least-squares fitting a quartic in $T$ gives Shigley's polynomial. It is $\approx 1$ up to a few hundred degrees, capturing the plateau, then decreases as strength falls with temperature.
Dimensional check. $k_d$ is dimensionless — a strength ratio $S_T/S_{RT}$. In the polynomial, each coefficient carries the inverse powers of $^\circ$C needed to keep every term dimensionless.
History and Development
The temperature factor is one of the Marin factors (Joseph Marin; codified in Shigley) that adjust the rotating-beam endurance limit $S_e'$ toward a real part's $S_e$. Its limited validity — a simple multiplier only where creep is absent — reflects the historical boundary between classical stress-life fatigue (room-temperature machinery) and the separate discipline of creep-fatigue developed for turbines, boilers, and reactors operating in the creep range.
Related Concepts: Marin Endurance Limit, Marin Modification Factors, Size Factor, Reliability Factor, Endurance Limit steel, Fatigue Failure Variable Loading
Notes: Registry returns constant $k_d = 1$ regardless of $T$ (placeholder, valid near room temperature) — use Shigley's quartic or $k_d = S_T/S_{RT}$ for elevated temperature. Above a few hundred $^\circ$C, creep-fatigue governs and a simple factor no longer suffices.