Linear Elastic Fracture Mechanics (LEFM) first assumes that the material is isotropic and linear elastic. Based on the assumption, the stress field near the crack tip is calculated using the theory of elasticity. When the stresses near the crack tip exceed the material fracture toughness, the crack will grow.
In Linear Elastic Fracture Mechanics, most formulas are derived for either plane stresses or plane straines, associated with the three basic modes of loadings on a cracked body: opening, sliding, and tearing. Click here for the illustrations of these modes.
Again, LEFM is valid only when the inelastic deformation is small compared to the size of the crack, what we called small-scale yielding. If large zones of plastic deformation develop before the crack grows, Elastic Plastic Fracture Mechanics (EPFM) must be used.