The theoretical brittle strength

When a single crystal is under tension, ideal brittle fracture occurs when the tensile stress reaches the value necessary to pull one block of molecules completely away from the adjacent block. 

Consider a specimen of area of cross-section ot under a tensile stress o and assume that the extension is stable until the brittle strength Og is reached. When fracture occurs the elastic energy in the nei bourhood of the fracture surface must provide the surface energy of the two fracture surfaces produced (surface energy is discussed in Chapter 7). In terms of chemical bonding, the elastic energy must be sufficient to break the bonds between the molecules across the fracture surface. 

Let ro be the intermolecular distance in the direction of tension and assume that fracture occurs at small strains so that, when o equals ob, r is closely equal to Tq, the equilibrium intermolecular distance. 

When a stress o produces a linear strain e in a Hookean solid of volume F, the strain energy in the solid is aeF/2, which is equal to o Vl2E, where E is Young s modulus of the material. If y is the specific surface free energy of the material (see Chapter 7), the total surface energy of the surfaces created by the fracture process is lay. 

A large fraction of this energy 2ay must be present at the moment of fracture between the molecules immediately adjacent to the fracture surface. Thus  

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