Hall Petch Equation
LEAD Technologies Inc. V1.01
This equation indicates that the strength of a metal is equal to the frictional stress plus a factor (k) times the inverse of the square root of the grain size (D). Reducing the grain size will cause the material to become stronger. Grain size reduction is also a means to increase the toughness of a metal.
To learn more about this amazing equation and other methods to manipulate the mechanical properties of materials check out MTGN445 Mechanical Properties of Materials taught by Prof. Findley.