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). 

The empirical HaU-Petch equation (HaU, 1951 Petch, 1953) is well known to express the grain-size dependence to the yield strength ... 

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

Using the HaU-Petch equation (6.25), the contribution to strengthening is Aucoarse = kjy/d... 

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... 

CTy = a-Q + kyCT Yield strength (as a fimction of average grain size)— HaU-Petch equation 230... 

---