Fatigue S-N Curve / Life Estimator mechanism

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

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