Microcracks 2D — Stress-Intensity Map

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Applied stress σ (MPa) 200 σ_min for fatigue (MPa) 20

Cyclic loading (fatigue mode)

Crack & Material

Initial crack length a₀ (mm) 2.0 Fracture toughness Kc (MPa·√m) 50 Geometry factor Y 1.12 Cycles per frame 50

Live readout

Modestatic stress

Crack length a (mm)2.00

K (MPa·√m)—

K / Kc—

Cycles N0

Cycles to failure (est.)—

Statusstable

Stress-intensity factor: K = Y·σ·√(π·a). The crack propagates once K reaches the material's fracture toughness Kc. In fatigue mode the crack advances every cycle via the Paris law da/dN = C·(ΔK)^m using ΔK = Y·(σ−σ_min)·√(π·a), and grows until K_max ≥ Kc.