Orowans Fracture Theory

Orowan considered Griffith s [22] theory. If no plastic deformation occurs, the radius of curvature at the tip of a crack must be equal to the atomic radius, a , representing the sharpest crack. By using the stress-concentration factor at the tip 

If it is assumed that the atomic radius is a , then the fracture stress at the crack tip becomes equal to the theoretical stress (as calculated in Chap. 3, Sect. 3.3.3, Eq. (3.18)) and is approximately  

A definite size effect exists in brittle materials, such as glass, and their strength depends on the volume of the material. This volume-dependence is simply explained by the fact that the probability of finding proper-sized cracks increases with volume. 

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The classic Griffith-Orowan theory describes the relationship between strength and toughness of brittle materials such as ceramics (Griffith, 1920 Orowan, 1949). In the simple basic equation of the theory, the stress to fracture <7f is related to Youngs elastic modulus E, the fracture energy y and the critical crack length c by... 

Becker was the first to suggest, in 1925, [2] that the deformation rate could be expressed by an Arrhenius-type equation. His concept was developed from the recognition of an identity between deformation and chemical reactions. The rate theory of thermally activated processes and, in general, the principles of deformation and fracture were established by Eyring [3], Orowan [4], and J. Frenkel [S]. In the latter part of the 20th century, these principles were further developed for polymers by Krausz and Eyring [6], Dorn [7], Zhurkov [8] and his collaborators [9], Kausch [10], and many others [11-14]. 

For line A the ratio Hb /hy 2 rather than unity, but the difference may be accounted for by the measurement of Hb at very low temperatures and possibly by the measurement of aB in flexure rather than in tension. (The latter may reduce the possibility of fracture at serious flaws in the surface.) It is encouraging that even an approximate relationship holds along the lines of the Ludwig-Davidenkov-Orowan hypothesis. Even more encouraging is the fact that line B has a slope Hb/hy 6, which is three times that of A, as expected on the basis of the plastic constraint theory. 

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