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The energy balance approach
In essence Griffith proposed that the presence of a sharp crack or flaw in a body might be a sufficient stress concentrator that the theoretical strength could be reached in some small, localised area in that body. To get a first approximation of what the stress would need to be let us consider a semi-elliptic defect with a crack tip radius ? lying normal to the applied stress in a body:

According to a solution due to Inglis the stress at the ends of the crack is given By


If we put a few numerical values in, as before, we can see immediately that a defect length of even a few microns is sufficient to lower the fracture strength by two orders of magnitude. This approach therefore looks attractive but has serious limitations in that it assumes too much by taking a totally elastic solution (Inglis) to predict a stress which experience tells us is far from elastic.
Griffith overcame these objections by re-casting this approach in thermodynamic terms in order to get away from having to consider any of the crack tip processes.
Consider an infinite plate containing a central, through thickness crack of length 2a and subjected to a remotely applied uniform tensile stress of ?. We are in the habit of drawing this configuration as above despite having just stated that the plate is infinite in the x-y plane. What we really mean is that the boundaries of the plate are sufficiently far removed from the ends of the crack that the fracture process cannot be influenced by the boundaries.