{
  "schema": "scoped-material-product-qualification/v1",
  "title": "Independent evidence in material product qualification",
  "scope": "Declared educational methods within selected product bases; no actual material report, full product approval or universal service eligibility.",
  "quantity_definitions": {
    "S_m": "Specified minimum yield strength under the selected grade/design basis",
    "S_y": "Measured yield strength for the represented specimen and condition",
    "S_u": "Measured ultimate tensile strength for that specimen and condition",
    "yield_excess": "S_y minus S_m in the same stress unit",
    "yield_ratio": "S_y divided by S_u, dimensionless",
    "chemistry_inputs": "Numerical weight percentages; 1.20 denotes 1.20 wt%, not mass fraction 0.0120.",
    "PRE": "Composition index Cr+3.3Mo+16N, not corrosion rate",
    "PRE_W": "Distinct composition index Cr+3.3(Mo+0.5W)+16N; missing W is unknown",
    "impact_energy": "Absorbed Charpy energy in foot-pound-force; not bolting torque",
    "phase_results": "Illustrative region-average percentages; method/population and region scope must be established",
    "CE": "Numerical carbon-equivalent value on the stated weight-percent input convention, not measured carbon content."
  },
  "strength_example": {
    "basis": "Selected high-yield butt-welding fitting upper-bound example",
    "specified_minimum_ksi": 52,
    "maximum_excess_ksi": 20,
    "maximum_yield_ratio": 0.9,
    "other_requirements": "Minimum strength, elongation, representative condition/region and all other product qualifications remain required.",
    "cases": [
      {
        "case": "A",
        "measured_yield_ksi": 71,
        "measured_tensile_ksi": 78,
        "yield_excess_ksi": 19,
        "yield_ratio": 0.9102564102564102,
        "excess_check": true,
        "ratio_check": false,
        "result": "Fails ratio upper bound"
      },
      {
        "case": "B",
        "measured_yield_ksi": 75,
        "measured_tensile_ksi": 85,
        "yield_excess_ksi": 23,
        "yield_ratio": 0.8823529411764706,
        "excess_check": false,
        "ratio_check": true,
        "result": "Fails excess upper bound"
      }
    ]
  },
  "chemistry_examples": {
    "CE": {
      "formula_latex": "\\mathrm{CE}=C+\\frac{\\mathrm{Mn}}{6}+\\frac{\\mathrm{Cr}+\\mathrm{Mo}+\\mathrm{V}}{5}+\\frac{\\mathrm{Ni}+\\mathrm{Cu}}{15}",
      "selected_product": "High-yield wrought fitting basis",
      "local_limit": 0.42,
      "inputs_wt_percent": {
        "C": 0.1,
        "Mn": 1.2,
        "Cr": 0.1,
        "Mo": 0.05,
        "V": 0.03,
        "Ni": 0.2,
        "Cu": 0.1
      },
      "weighted_terms": [
        0.1,
        0.2,
        0.036,
        0.02
      ],
      "CE_result": 0.356,
      "CE_only_comparison": true,
      "unresolved": "Other elemental analysis, actual product properties and qualification are not supplied."
    },
    "PRE": {
      "formula": "PRE=Cr+3.3Mo+16N",
      "selected_basis": "Specified 22Cr duplex fitting/flange products",
      "minimum_index": 33,
      "nitrogen_range_wt_percent": [
        0.14,
        0.2
      ],
      "cases": [
        {
          "case": "P1",
          "inputs_wt_percent": {
            "Cr": 22,
            "Mo": 3.1,
            "N": 0.15
          },
          "PRE": 34.63,
          "index_check": true,
          "nitrogen_check": true,
          "result": "Meets these two composition screens only"
        },
        {
          "case": "P2",
          "inputs_wt_percent": {
            "Cr": 22,
            "Mo": 3.5,
            "N": 0.1
          },
          "PRE": 35.15,
          "index_check": true,
          "nitrogen_check": false,
          "result": "Fails independent nitrogen condition despite higher index"
        }
      ],
      "other_family": "Selected 25Cr products retain their own grade/basis and minimum PRE 40; the 22Cr nitrogen range is not generalized."
    },
    "PRE_W": {
      "formula": "PRE_W=Cr+3.3(Mo+0.5W)+16N",
      "inputs_wt_percent": {
        "Cr": 25,
        "Mo": 3,
        "N": 0.25,
        "W": 0.5
      },
      "PRE_W_result": 39.725,
      "PRE_without_W_result": 38.9,
      "difference": 0.825,
      "scope": "Model comparison only; no grade or product acceptance, no limit transferred between formulas."
    },
    "Pcm": "A separately stated 0.19 limit requires its own actual model and applicability. No formula is supplied or borrowed from CE."
  },
  "phase_example": {
    "basis": "Selected fitting/flange 30\u201365% each-tested-region average condition",
    "hypothetical_region_results_percent": [
      70,
      20
    ],
    "assumed_equal_weights": true,
    "pooled_mean_percent": 45,
    "each_region_check": [
      false,
      false
    ],
    "result": "Pooled45% cannot satisfy either failed region",
    "distinct_bases": [
      "Pipe product 35\u201355% in each region",
      "Separate welding-procedure 35\u201365 vol% condition",
      "Ferrite Number instrument scale is not microscopic volume fraction"
    ]
  },
  "impact_example": {
    "basis": "Selected SMYS 52 ksi high-yield fitting, wall \u22641.0 in, full-size specimens at \u221250\u00b0F",
    "minimum_mean_ft_lbf": 27,
    "minimum_individual_ft_lbf": 24,
    "cases": [
      {
        "energies_ft_lbf": [
          20,
          30,
          34
        ],
        "mean_ft_lbf": 28,
        "lowest_ft_lbf": 20,
        "mean_check": true,
        "individual_check": false,
        "result": "Fails individual minimum"
      },
      {
        "energies_ft_lbf": [
          24,
          28,
          29
        ],
        "mean_ft_lbf": 27,
        "lowest_ft_lbf": 24,
        "mean_check": true,
        "individual_check": true,
        "result": "Meets these two energy comparisons only"
      }
    ],
    "scope": "Other specimen orientation/region/size/shear/material qualification remains required; no missing or conflicting impact criterion filled."
  },
  "environmental_evidence": {
    "conditions": [
      "Represented product and final state",
      "Manufactured inner-surface exposure",
      "Water/gas condition and test temperature",
      "Selected SSC/SCC bend tests apply stress at 100% of measured actual yield strength at test temperature, with verified displacement.",
      "Defined specimen area, solution volume and duration",
      "Mechanism-specific crack, localized and general-loss observations"
    ],
    "local_volume_area_ratio": "30 mL/cm\u00b2 within selected environmental test method; not concentration or plant dose",
    "local_duration": "Minimum 720 h exposure; not predicted service life",
    "limitations": [
      "No actual composition or partial-pressure inputs supplied",
      "No beam formula substituted for required strain verification",
      "Duplicate production SSC versus triplicate prequalification SCC/pitting populations remain distinct"
    ],
    "applied_stress_loading": {
      "fraction_of_measured_actual_yield": 1.0,
      "quantity_basis": "Measured actual yield strength at the test temperature",
      "scope": "Selected SSC and SCC four-point bend qualification methods",
      "verification": "Displacement verified on suitably strain-gauged samples; no published beam formula substituted",
      "limit": "Not an installed piping allowable or a rule for every test"
    }
  },
  "diagram_mapping": {
    "svg": "c02-product-qualification.svg",
    "data": "c02-product-qualification.json",
    "authored_anchor": "c02-duplex-product-state"
  },
  "population_conditions": {
    "selected_product": "High-yield wrought-fitting matched-heat grouping where permitted",
    "conditions": [
      "Every reported element within \u00b110% of its mean across selected heats",
      "Same applicable finishing conditions",
      "Required additional-heat tests from most worked base-metal and weld regions"
    ],
    "limit": "Matching a weighted chemistry index alone does not establish the element-by-element grouping condition."
  },
  "local_post_treatment_product_conditions": {
    "area_reduction_limit_percent": 1.5,
    "cold_bending_for_straightening_limit_degrees": 2,
    "scope": "Selected duplex product procedure after final heat treatment; retain actual product and area/angle measurement basis. No general field-bending allowance or cold-work strength enhancement permission."
  }
}