What does this equation mean?

Griffith’s criterion is an accounting statement. Extending a crack by a small increment releases stored elastic strain energy from the material that unloads around the new crack faces, and consumes energy in creating those faces. If the release exceeds the cost, extension is spontaneous and the crack runs. For a through-thickness crack of half-length a in a linear-elastic plate with modulus E and surface energy $\gamma_s$ , the critical remote stress is $\sigma_f = \sqrt{\frac{2E\gamma_s}{\pi a}}$. The structure of this expression matters more than its coefficients. Strength scales as the inverse square root of flaw size, so halving the largest flaw raises strength by roughly forty per cent, and doubling it costs about thirty per cent. Strength is not an intrinsic property at all in this picture; it is a joint property of the material and its worst defect. Griffith’s own experimental work was on glass, where the assumption of negligible plastic deformation is nearly exact and the theory therefore lands cleanly [ 1 , 2 ] .