Hall-Petch equation

A detailed discussion of the consequences of the Hall-Petch equation in terms of the nature of dislocations is outside the scope of this work. Readers are directed to the many excellent texts and monographs dealing with solids in general and dislocations in particular (e.g.. Ref. 11). 

In metals, GBs control mechanical properties when the grain size is small as seen from the Hall-Petch equation... 

Study of defects is important because many properties of the materials are affected by them. For example, there is one-to-one correlation between concentration of point defects and diffusion. As the concentration increases, diffusion also increases. There is also a correlation between grain size and mechanical strength. This relation is given by the Hall-Petch equation ... 

Hall-Petch equation— dependence of yield strength on grain size... 

This is the Hall-Fetch equation, containing the Hall-Petch constant fcnp. Its value is 3.5 N/mm / for copper, 12.6 N/mm / for titanium, and 22N/mm / for a low-alloy steel [55]. Figure 6.36 shows the dependence of the yield strength of a low-alloy steel on the grain size. 

The relationship in equation (4.1) has a familiar form, being the same as the Hall-Petch relationship for fracture stress or yield stress-grain size dependence. Through this connection the dominance of flow mechanisms in establishing hardness values is once again emphasized. 

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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