Griffith Crack: Fracture Energy Balance

Critical crack length, strain energy release rate, and stress intensity factor
a_c = EG_c/(πσ²)  |  K_I = σ√(πa)  |  K_Ic = √(EG_c)  |  G = K_I²/E

Material & Loading

a_c (mm)
K_I (MPa√m)
K_Ic (MPa√m)
Status
Griffith (1921): A crack of half-length a in an infinite plate under stress σ will propagate spontaneously when the strain energy released exceeds the energy to create new surfaces. Critical condition: σ√(πa) ≥ K_Ic = √(EG_c).

Stress intensity factor K_I: Characterizes the near-tip stress field: σ_ij ~ K_I/√(2πr) · f_ij(θ). Mode I (opening): K_I = σ√(πa). Fracture occurs when K_I ≥ K_Ic, the material's toughness. For steel K_Ic ≈ 50 MPa√m; glass ≈ 0.7 MPa√m.

Energy balance: Total energy U_T = U_elastic − U_strain = −σ²πa²/E + 4aγ. Maximum at a_c gives the critical crack — smaller cracks are stable, larger ones propagate catastrophically (Griffith criterion for brittle fracture).