The Dislocation Theory of Brittle Fracture

Although this is a discussion on brittle materials, such as ceramics (glass is a perfect, brittle material), several researchers have developed theories of fracture based on dislocation models. More specifically, the shear stress created by dislocation pile-ups at some obstacle, specifically grain boundaries in polycrystaUine materials, reaches a sufficient value for crack formation. The following illustrates Stroh s [52] basic concept of microcrack formation, ultimately leading to the occurrence of fracture in brittle materials. 

Similarly to Zener s model [9] of microcrack formation at a pile up of edge dislocations, Stroh [52] developed a theory of fracture based on the concept of cracks initiated by the stress concentration of a dislocation pile-up. For brittle materials in which crack growth is not damped-out by plastic flow, Stroh calculated that the conditions for crack initiation may be given by  

T is resolved shear stress acting on the pile-up, y is the surface energy of the cleavage plane and L is the distance of the pUe-up. Another expression for shear stress, Ts is given as  

Tj is the lattice-friction stress in the slip plane. In this case, the obstacle is grain boundary, d, which is taken into account by Stroh [52], as seen in Eq. (8.45a)  

Stress, Ts, is created by the internal pile-up of n dislocations, teff is an effective stress and Ty is the yield stress, y is the surface energy per unit area of the plane, as indicated earlier, and d/2 is the length of the dislocation pile-up. One illustration of Stroh s [52] concept is shown below  

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