the Griffith criterion
/ GRIF-ith /
Around 1920 A. A. Griffith was puzzled by a paradox: thin glass fibres could be enormously strong, yet a glass rod snaps easily. His answer, now the Griffith criterion, is the founding idea of fracture mechanics: a crack only grows if doing so releases more stored elastic energy than it costs to create the fresh new surfaces. Breaking is an energy bargain, and the crack grows the instant the bargain pays off.
Stretching a cracked plate stores elastic energy in it. If the crack extends a little, the material around the crack relaxes and releases some of that stored energy (the release grows with crack length and with stress squared). But opening new crack faces costs energy — you must pay the surface energy gamma_s to break the bonds. Griffith set release equal to cost and got the fracture stress: sigma_c = sqrt(2 E gamma_s / (pi a)), where E is Young's modulus, gamma_s the surface energy, and a the half-crack length. The crucial message: strength falls as 1/sqrt(a) — the bigger the flaw, the weaker the part, which is exactly why long cracks are lethal.
Griffith's formula works beautifully for truly brittle materials like glass, where the only energy cost is making new surface. In metals, though, a crack tip yields and drags a plastic zone along, which soaks up far more energy than the surface term — so Irwin and Orowan later added a plastic-work term, turning gamma_s into an effective work-of-fracture hundreds or thousands of times larger. That extension is why the same energy idea underlies the modern stress intensity factor and fracture toughness.
For window glass with E = 70 GPa and gamma_s about 1 J/m^2, a surface scratch just 0.01 mm deep (a = 5e-6 m) gives sigma_c = sqrt(2 times 70e9 times 1 / (pi times 5e-6)) = about 94 MPa — a fraction of glass's theoretical strength of thousands of MPa. A scratch you can barely see cuts the strength enormously.
Griffith's energy balance: a crack runs when released elastic energy outpaces the cost of new surface.
Pure Griffith (surface energy only) badly under-predicts the strength of metals, because it ignores the plastic work at the crack tip — usually the dominant energy cost. It is exact only for ideally brittle solids like glass and some ceramics.