Marin Endurance Limit⚠ unverified
Mechanical / Fatigue · Compute the modified endurance limit using the Marin equation
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| Se_prime | Seprime | MPa | 1.0 | Rotating-beam endurance limit Se' |
| ka | ka | — | 1.0 | Surface finish modification factor (dimensionless) |
| kb | kb | — | 1.0 | Size modification factor (dimensionless) |
| kc | kc | — | 1.0 | Load modification factor (dimensionless) |
| kd | kd | — | 1.0 | Temperature modification factor (dimensionless) |
| ke | ke | — | 1.0 | Reliability modification factor (dimensionless) |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | Se | MPa | Modified endurance limit Se, in megapascals (MPa) |
The science & history
Understanding the Parameters
-
$S_e'$ — the starting value from Endurance Limit steel ($0.5\,S_{ut}$, capped at $700\ \text{MPa}$). All factors scale it multiplicatively.
-
Surface factor $k_a = a\,S_{ut}^{b}$ — the largest correction for most parts. Fatigue cracks start at the surface, so roughness matters: ground $k_a \approx 0.9$, machined $\approx 0.7$–$0.8$, hot-rolled $\approx 0.5$, as-forged $\approx 0.3$–$0.4$. Rougher and stronger steels are penalised more.
-
Size factor $k_b$ — the gradient effect (Size Factor); $1$ for axial, $<1$ and decreasing with diameter for bending/torsion.
-
Load factor $k_c$ — $1.0$ bending, $\approx 0.85$ axial, $\approx 0.59$ torsion. It rebases $S_e'$ (a bending value) to the actual loading mode.
-
Temperature $k_d$ (Temperature Factor) and reliability $k_e$ (Reliability Factor) — the environmental and statistical corrections.
-
The missing $k_f$ — Shigley's full product includes a sixth "miscellaneous-effects" factor $k_f$ (residual stress, corrosion, plating, fretting) that this five-factor form omits; apply it separately when relevant.
Derivation (Approaching a Proof)
The Marin equation is a multiplicative-correction model, not a derivation from mechanics. Its logic: the true endurance limit differs from $S_e'$ for several independent physical reasons, and to first order each scales endurance by its own factor. Assuming the effects are separable, the combined endurance limit is the product
$$S_e = S_e' \prod_i k_i = S_e'\,k_a k_b k_c k_d k_e\,(k_f).$$
Each $k_i$ is obtained empirically: $k_a$ by fitting surface-finish test data to $a\,S_{ut}^b$; $k_b$ from size-effect experiments (Size Factor); $k_c$ from bending-vs-axial-vs-torsion comparisons; $k_d$ from strength-vs-temperature ratios (Temperature Factor); $k_e$ from the endurance-limit scatter distribution (Reliability Factor). The multiplicative form is an engineering approximation — the factors are not perfectly independent — but it is accurate enough and transparent, which is why it endures.
Dimensional check. $S_e = S_e'\,k_a k_b k_c k_d k_e = \text{MPa}\times(\text{–})^5 = \text{MPa}$ — the factors are dimensionless, so $S_e$ inherits the stress units of $S_e'$.
History and Development
Joseph Marin proposed the modification-factor decomposition in the mid-20th century; Shigley's Mechanical Engineering Design popularised it as the backbone of the stress-life (infinite-life) method. It turned fatigue design from bespoke testing into a systematic hand calculation: estimate $S_e'$ from $S_{ut}$, look up or compute five (or six) factors, and get a defensible part endurance limit to use in a Goodman-type check. Its enduring value is pedagogical and practical clarity, even as fracture-mechanics (crack-growth) methods handle defect-tolerant design.
Related Concepts: Endurance Limit steel, Marin Modification Factors, Size Factor, Temperature Factor, Reliability Factor, Modified Goodman Factor, Fatigue Life cycles
Notes: Five-factor form here ($k_a k_b k_c k_d k_e$); Shigley's full product adds a sixth miscellaneous-effects factor $k_f$ (corrosion/residual stress/plating) — apply separately. $k_a$ (surface) usually dominates. Corrected $S_e$ feeds Goodman/Gerber/Soderberg/ASME-elliptic criteria.