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Home/Engineering/Fracture Mechanics: Griffith / K_IC

Fracture Mechanics: Griffith / K_IC

Linear-elastic fracture mechanics describes the near-tip stress field with a stress-intensity factor. For a mode-I crack under tensile stress, this simulator uses K_I = Y σ sqrt(πa), where a is crack half-length in meters and Y is a geometry correction. Comparing K_I with the material fracture toughness K_IC gives a simple Griffith/Irwin-style instability check: when K_I reaches K_IC, a crack can grow unstably. The simulator also solves the inverse questions: critical crack size a_c for the current stress and critical stress σ_c for the current crack. It is a teaching calculator, not a fitness-for-service assessment: finite-width corrections, crack-front shape, plastic-zone validity, residual stresses, fatigue crack growth, corrosion, inspection uncertainty, and code safety factors are not included.

Who it's for: Fracture mechanics, mechanics of materials, machine design, aerospace, civil, and materials engineering introductions.

Key terms

  • Fracture toughness
  • Stress intensity factor
  • Griffith criterion
  • Mode I crack
  • Critical crack size

This is a linear-elastic, mode-I fracture model. Real assessments also check crack shape, finite width, plastic zone size, fatigue crack growth, residual stress, inspection uncertainty, and code safety factors.

Live graphs

Crack and load

180 MPa
8 mm
1.12

Material toughness

45 MPa√m

KIC is a material property for plane-strain fracture toughness; small specimens, thin sheets, and ductile tearing need more detailed fracture mechanics.

Measured values

Stress intensity KI31.96MPa√m
Utilization KI/KIC0.71
Critical crack acrit15.9mm
Critical stress σcrit253.4MPa
Toughness margin1.41x
Statussafe

How it works

Linear-elastic fracture mechanics calculator: a crack under tensile stress has KI = Yσ√(πa). Compare KI with material toughness KIC and find the critical crack size or stress.

Key equations

K_I = Y σ sqrt(π a), with a in meters and K in MPa√m
Unstable crack growth when K_I ≥ K_IC; a_c = (K_IC / (Yσ))² / π

Frequently asked questions

Why is crack length converted from mm to meters?
K is reported in MPa√m, so the square-root length in K_I = Yσ√(πa) must be in meters when σ is in MPa. The UI uses mm because cracks are usually measured on that scale.
Does KI < KIC guarantee safety?
Only within the assumptions of linear-elastic fracture mechanics and the chosen geometry factor. Real designs add safety factors and check plastic zone size, crack growth, residual stress, loading spectrum, environment, and inspection reliability.