The Ludwig-Davidenkov-Orowan hypothesis

The influence of chemical and physical structure on the brittle-ductile transition can be analysed by considering how these factors affect the brittle stress curve and the yield stress curve, respectively. As will be appreciated, this approach b3Ttasses the relevance of fracture mechanics to brittle failure. If, however, we consider fracture initiation (as distinct from propagation of a crack) as governed by a 

As for metals the presence of a sharp notch can change the fracture of a pol3oner from ductile to brittle. For this reason a standard impact test for a pol3oner is the 

Charpy or Izod test, where a notched bar of pol3maer is struck by a pendulum and the energy dissipated in fracture is calculated. 

If Oy 3cty, the material is ductile in an unnotched tensile test but brittle when a sharp notch is introduced. 

If CTb 3cty5 the material is fully ductile, i.e. ductile in all tests, including those in notched specimens. 

Vincent and others [100-102] have shown that the brittle stress is not much affected by strain and temperature (e.g. by a factor of 2 in the temperature range — 180°C to + 20°C). 

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Many aspects of the brittle ductile transition in metals, including the effect of notching, which we will discuss separately, have been discussed in terms of the Ludwig-Davidenkov-Orowan hypothesis that brittle fracture occurs when the yield stress exceeds a critical value [95], as illustrated in Figure 12.29(a). It is assumed that brittle fracture and plastic flow are independent processes, giving separate characteristic curves for the brittle fracture stress and the yield stress 0 ... 

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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