EngiRef / Materials Engineering Formula

Fracture Toughness (Irwin, LEFM)

Fracture Toughness (Irwin, LEFM): Mode I stress intensity factor (Irwin's linear-elastic fracture mechanics relation). A Failure Theories formula in materials…

Failure Theories

Specification

Name
Fracture Toughness (Irwin, LEFM)
Discipline
materials
Category
Failure Theories
LaTeX
K_I = Y \sigma \sqrt{\pi a}
Description
Mode I stress intensity factor (Irwin's linear-elastic fracture mechanics relation)
Conditions
Y is geometry factor; a is crack length. Irwin's LEFM stress-intensity relation — Griffith's own criterion is the energy balance G = 2γs; the two agree for linear-elastic, plane-strain conditions with a small plastic zone.
Can solve for
Kᵢ, σ, a
Tags
fracture, toughness, crack, griffith, stress, intensity

Variables

Variables for Fracture Toughness (Irwin, LEFM)
SymbolNameUnitSi UnitImperial Unit
KᵢStress Intensity FactorMPa·√mMPa·√m
YGeometry Factor
σApplied StressPaPapsi
aCrack Lengthmmin