The force needed to pull apart the atomic bonds of a solid predicts a strength perhaps a hundred times greater than what real materials actually sustain. The gap exists because real solids are riddled with defects that concentrate stress and fail long before the bonds themselves reach their limit.
A crack or sharp notch in a loaded material does not share stress evenly; it multiplies the local stress enormously at its tip, in proportion to how long and sharp the crack is. This is why a small flaw can trigger failure at an overall load the bulk material could otherwise easily bear.
Griffith's insight treats cracking as a trade between the strain energy released as a crack extends and the surface energy needed to create new crack faces. A crack only runs catastrophically once it is long enough that the energy released exceeds the energy required, which explains why there is a critical crack size rather than a simple breaking stress.
A material's resistance to fracture depends on how much energy it absorbs before a crack can propagate, not on how high a stress it can momentarily carry. A material can be very strong yet brittle, shattering because it stores elastic energy that is released all at once rather than dissipating it as the crack tries to move.
Natural and engineered composites like wood and fibreglass gain toughness because weak interfaces between fibres and matrix divert or blunt advancing cracks rather than letting them run straight through. Deliberately introducing planes of weakness can make a whole structure stronger by forcing cracks to take longer, energy-consuming paths.
How far a material stretches under load (governed by its elastic modulus) is a distinct property from the load at which it breaks. A material can be stiff but weak or flexible but strong, so engineering choices must treat deflection and failure as separate design constraints.