Theoretical Strength of Glasses

The theoretical strength of a material is given by the force which must be applied to overcome the maximum restorative force predicted by Eq. 9.4. Once the interatomic separation distance exceeds the distance corresponding to the maximum restorative force, continued application of force will extend the bond distance until the bond is broken and a crack can propagate through the material. Orowan proposed that the stress necessary to break a bond is determined by the energy necessary to create two new surfaces due to the fracture. The Orowan stress, is given by the expression  

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The discrepancy between the theoretical strength of glasses and the values obtained in many practical applications exists because materials contain flaws that lower their strength. Operationally, a flaw is any structural feature in the part that raises the local stress at the feature above the applied stress in the part. The amphfication of stress, or the stress concentration factor, varies with the character of the flaw. For a cylindrical hole in a sheet of an isotropic material such as glass, the amplification is a factor of three at the edge of the hole. For cracks, which can be considered ellipsoids with a minimum radius of curvature of atomic dimensions, the stress concentration at the crack tip can be a factor of hundreds or thousands. Thus, with an applied stress of, say, 1000 psi, the stress at the crack tip can be raised to the theoretical value. 

Unfortunately, at present, theoretical estimates of 5ih do not exist for multicomponent compositions (such as E-glass) and are not reliable even for simple one-component glasses. For example, estimates of the theoretical strength of silica based on cohesive... 

Conunent on Griffith s choice of 1 nm for the length at fracture. Compare his estimate of the theoretical strength of his glass rods against the discussion on theoretical strength in Chapter 7. 

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