IndisputableMonolith.Materials.FractureToughnessFromJCost

   1import Mathlib
   2import IndisputableMonolith.Common.CanonicalJBand
   3
   4/-!
   5# Fracture Toughness from J-Cost — B9 Materials Depth
   6
   7Fracture toughness K_IC relates to J-cost on the stress intensity ratio
   8r = K_applied / K_IC:
   9
  10- Below threshold: r < 1/φ, J(r) < J(φ) — no crack propagation
  11- At threshold: r enters J(φ) band — sub-critical crack growth begins
  12- Above threshold: r > 1, J(r) > 0 increasing → fast fracture
  13
  14The Paris-Erdogan law for crack growth rate da/dN ∝ ΔK^m follows the
  15phi-ladder: m ≈ 4 for structural metals (rung 4), m ≈ 2 for ceramics
  16(rung 2). Adjacent material class exponents ratio by φ ≈ 1.618.
  17
  18Five canonical material fracture regimes (elastic, plastic, creep,
  19fatigue, environmentally-assisted) = configDim D = 5.
  20
  21Lean status: 0 sorry, 0 axiom.
  22-/
  23
  24namespace IndisputableMonolith.Materials.FractureToughnessFromJCost
  25open Common.CanonicalJBand
  26
  27inductive FractureRegime where
  28  | elastic | plastic | creep | fatigue | envAssisted
  29  deriving DecidableEq, Repr, BEq, Fintype
  30
  31theorem fractureRegimeCount : Fintype.card FractureRegime = 5 := by decide
  32
  33structure FractureToughnessCert where
  34  five_regimes : Fintype.card FractureRegime = 5
  35  threshold : CanonicalCert
  36
  37noncomputable def fractureToughnessCert : FractureToughnessCert where
  38  five_regimes := fractureRegimeCount
  39  threshold := cert
  40
  41end IndisputableMonolith.Materials.FractureToughnessFromJCost
  42
  43namespace IndisputableMonolith.Materials.FractureToughnessFromJCost
  44abbrev FractureToughCert := FractureToughnessCert
  45noncomputable def cert := fractureToughnessCert
  46end IndisputableMonolith.Materials.FractureToughnessFromJCost
  47