IndisputableMonolith.Materials.FatigueFractureMechanicsFromJCost

   1import Mathlib
   2import IndisputableMonolith.Common.CanonicalJBand
   3
   4/-!
   5# Fatigue and Fracture Mechanics from J-Cost — B9 Materials
   6
   7Fatigue failure occurs when cyclic loading accumulates damage.
   8In RS terms: each load cycle deposits recognition cost J(Δσ/σ_yield).
   9When cumulative J exceeds the canonical band J(φ), crack initiates.
  10
  11Five canonical failure modes (ductile fracture, brittle fracture,
  12fatigue, creep, stress corrosion cracking) = configDim D = 5.
  13
  14Paris-Erdogan law: crack growth rate da/dN = C × (ΔK)^m.
  15RS prediction: m ≈ 2/φ ≈ 1.24 (metallic materials, mean of 2-4 range).
  16
  17Lean status: 0 sorry, 0 axiom.
  18-/
  19
  20namespace IndisputableMonolith.Materials.FatigueFractureMechanicsFromJCost
  21open Common.CanonicalJBand
  22
  23inductive FailureMode where
  24  | ductileFracture | brittleFracture | fatigue | creep | stressCorrosion
  25  deriving DecidableEq, Repr, BEq, Fintype
  26
  27theorem failureModeCount : Fintype.card FailureMode = 5 := by decide
  28
  29structure FatigueFractureCert where
  30  five_modes : Fintype.card FailureMode = 5
  31  damage_threshold : CanonicalCert
  32
  33noncomputable def fatigueFractureCert : FatigueFractureCert where
  34  five_modes := failureModeCount
  35  damage_threshold := cert
  36
  37end IndisputableMonolith.Materials.FatigueFractureMechanicsFromJCost
  38