Fracture Toughness — Critical Stress / Crack Size
Solve linear-elastic fracture mechanics for critical stress, crack length, or the stress-intensity factor given K_IC.
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The engineering
Linear-elastic fracture mechanics says a sharp crack fails when the stress-intensity factor K reaches the material's plane-strain fracture toughness K_IC. Give this card either the working stress (to find the crack length that fails) or the crack length (to find the stress that fails), and the geometry factor Y ties the ideal center-crack solution to your real part.
Y = 1.0 is the infinite-plate center crack; Y ≈ 1.12 is the classic edge crack in tension — the default here — and thumbnail/corner cracks run lower. K_IC is only valid under plane strain, which E399 enforces through a specimen-size rule: thickness and crack length must both exceed 2.5·(K_IC/σ_ys)². Thinner sections show higher, thickness-dependent toughness (K_c) instead.
Where this math comes from
A. A. Griffith cracked the problem in 1920 while at the Royal Aircraft Establishment, explaining why real glass fails at a fraction of its theoretical strength: pre-existing flaws concentrate stress, and fracture is an energy trade between released strain energy and new surface. His energy balance was elegant but hard to apply to ductile metals.
George Irwin at the Naval Research Laboratory recast Griffith's energy argument into the stress-intensity factor K in the 1950s, adding a plastic-zone correction that made the theory usable for structural alloys — the framework behind every damage-tolerance analysis in aerospace. ASTM codified the plane-strain measurement as E399 in 1970, fixing specimen geometry, the validity size criterion, and the K_Q-to-K_IC qualification that engineers still follow.
- 1920A. A. GriffithEnergy-balance theory of brittle fracture from flaws in glass.
- 1957George R. IrwinIntroduces the stress-intensity factor K and the plastic-zone correction.
- 1961Paris, Gomez & AndersonLink K to fatigue crack growth (the Paris law), extending LEFM to cyclic life.
- 1970ASTM E399Standardizes the plane-strain K_IC test method and validity criteria.
See the full timeline of the math behind every calculator →
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