{
  "title": "Reading a tensile curve: geometry changes the reported stress",
  "kind": "Seeded synthetic measurement demonstration; no physical specimen or measured material performance",
  "seed": 20260924,
  "random_generator": "Python random.Random MT19937, Gaussian gauss method",
  "parameters": {
    "nominal_width_mm": 5.0,
    "nominal_thickness_mm": 0.5,
    "nominal_gauge_length_mm": 25.0,
    "assigned_initial_slope_MPa": 1200.0,
    "assigned_transition_strain": 0.025,
    "assigned_post_transition_slope_MPa": 40.0,
    "simulated_force_noise_SD_N": 0.05,
    "independent_dimension_relative_SD": 0.02
  },
  "formulas": {
    "engineering_stress": "sigma=F/A0 using original cross-sectional area",
    "engineering_strain": "epsilon=DeltaL/L0",
    "hypothetical_curve": "sigma=1200*epsilon up to 0.025; sigma=30+40*(epsilon-0.025) above",
    "geometry_error": "sigma_inferred/sigma_imposed-1=A_nominal/A_assumed_measured-1"
  },
  "row_counts": {
    "curve": 101,
    "geometry_draws": 10000
  },
  "summary": {
    "chosen_curve_endpoint_MPa": 33.0,
    "endpoint_force_N": 82.5,
    "geometry_error_empirical_p2_5": -0.05308386914150154,
    "geometry_error_empirical_median": -0.0002488240278548659,
    "geometry_error_empirical_p97_5": 0.05957020462544005,
    "geometry_error_sample_SD": 0.028649621773319645,
    "first_order_predicted_SD": 0.028284271247461905
  },
  "validation": {
    "independent_SI_stress_conversion_max_error_MPa": 7.105427357601002e-15,
    "extension_strain_identity": true,
    "transition_continuity": true,
    "geometry_inverse_area_identity_all_draws": true,
    "first_order_SD_agreement_within5percent": true
  },
  "limitations": [
    "All material-curve and noise parameters are assigned hypothetical inputs, not identified polymer properties.",
    "Engineering stress uses original area. No instantaneous-area true-stress model is present.",
    "33 MPa is the selected endpoint maximum, not ultimate tensile strength or fracture stress; no necking or failure is modelled.",
    "The 2.5 percent kink is an assigned slope change, not an experimentally measured yield point. Unloading and permanent deformation are not defined.",
    "Gaussian load noise and independent 2 percent dimensional errors are illustrative; real calibration, bias and correlation can differ.",
    "The geometry histogram is a propagated assumption distribution, not a confidence interval for a real material.",
    "A small Gaussian dimensional-error model can mathematically yield nonpositive dimensions; all 10,000 generated dimensions are explicitly checked positive.",
    "The model does not determine toughness to fracture, ductility at failure, fatigue, rate/temperature dependence, bending properties or design allowables."
  ],
  "sources": [
    {
      "title": "NIST, A Tensile-Testing Technique for Micrometer-Sized Free-Standing Thin Films",
      "url": "https://www.nist.gov/publications/tensile-testing-technique-micrometer-sized-free-standing-thin-films"
    },
    {
      "title": "NIST, Diffraction Stress Measurement Under Applied Load",
      "url": "https://www.nist.gov/programs-projects/ncal-diffraction-stress-measurement-under-applied-load"
    }
  ]
}