Strength and grain size

Equation 6.25 has the form of the Hall-Petch relation. Here, d represents the grain size. It says that the fracture stress should increase as the grain size decreases. In the case of briffle materials, if the initial flaw size is limifed by the grain size, the relation between the fracture strength and grain size is given by the Orowan relation. This relation is expressed by Equation 6.27. 

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