Source: https://guthlabs.ai/docs/instruments/fatigue-s-n-curve-life-estimator/mechanism/

instrument mechanism / verified-clean

# Fatigue S-N Curve / Life Estimator mechanism

The inspectable method record for Fatigue S-N Curve / Life Estimator, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Model scope

The core Basquin inversion and log-log interpolation methods are standard, but the instrument needs explicit definitions for cycles versus reversals, loading ratio and mean-stress treatment, correction-factor equations, valid interpolation range, and the governing source and applicability limits for the endurance-limit approximation. The honest estimate-only label is appropriate but does not resolve those technical ambiguities.

- Basquin's relation σa=σf'(2N)^b is standard when N denotes reversals to failure, with b<0; the stated output is cycles, so the implementation must solve N=0.5(σa/σf')^(1/b) and must not confuse reversals with cycles.

- Log-log interpolation is appropriate between tabulated S-N points only when both stress and life are positive and the interpolation convention is explicitly logarithmic in both axes.

- The rule Se≈0.5Su is only a rough textbook estimate for some steels under specified specimen, surface, loading, and life-range conditions. It is not a generally valid endurance-limit formula, and the stated Su<1400 MPa boundary is not universal across standards or steel grades.

- Surface, size, load, reliability, notch, residual-stress, and mean-stress effects are listed as inputs but no equations specify how they modify σa, Se, or the S-N curve.

- The specification does not define whether stress amplitude is nominal or local alternating stress, whether the S-N curve is for fully reversed loading (R=-1), or how nonzero mean stress is handled.

- No interpolation or extrapolation range, finite-life cutoff, fatigue-limit convention, or treatment of stresses below Se is specified.

## Units and conventions

- Stress amplitude, σf', Su, and Se must use one consistent stress unit within each calculation; MPa is used unless explicitly marked otherwise.

- N is cycles to failure, while 2N is reversals to failure in the Basquin equation.

- The worked examples assume fully reversed, constant-amplitude loading, no mean-stress correction, and all surface/size/load correction factors equal to 1.0 unless otherwise stated.

- The canonical table fragment uses a simplified steel S-N construction: 0.9Su at 10^3 cycles and 0.5Su at 10^6 cycles. This is a textbook idealization, not a universal material property table.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "method": "log_log_table_lookup",
    "material_class": "steel, idealized fully reversed S-N curve",
    "stress_amplitude_MPa": 900,
    "Su_MPa": 1000,
    "surface_factor": 1,
    "size_factor": 1,
    "load_factor": 1
  },
  "expected_outputs": {
    "N_cycles": 1000,
    "Se_MPa": 500
  },
  "reference_data": {
    "sn_table_rows": [
      {
        "N_cycles": 1000,
        "stress_amplitude_MPa": 900,
        "source_convention": "widely tabulated standard textbook value; canonical idealized steel S-N construction, Sf(10^3)=0.9Su"
      },
      {
        "N_cycles": 1000000,
        "stress_amplitude_MPa": 500,
        "source_convention": "widely tabulated standard textbook value; canonical idealized steel S-N construction, Se=0.5Su"
      }
    ],
    "endurance_factor": 0.5,
    "endurance_factor_source_convention": "widely tabulated standard textbook value for the stated approximation",
    "Su_MPa": 1000,
    "Su_source_convention": "widely tabulated standard textbook value used as the example material strength"
  },
  "working": "The input stress is exactly the first table row: σa=900 MPa at N=10^3 cycles. Therefore N=10^3=1000 cycles. Endurance estimate: Se=0.5Su=0.5×1000 MPa=500 MPa. No interpolation is performed."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The estimator encounters non-finite or undefined behavior at zero stress amplitude and at Basquin exponent b=0; it also has a major life error if stress range is confused with stress amplitude.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/fatigue-s-n-curve-life-estimator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/fatigue-s-n-curve-life-estimator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/fatigue-s-n-curve-life-estimator/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche7/tranche7-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`