Question

The Hall-Petch equation shows that increasing grain size in metallic materials: Select one: O a. Increases strength O b. Reduces ductility O c. Decreases strength O d. Increases fracture toughness

Answer 1

Answer is c i.e there will be the reduction of strength

As per hell petch equation yield stress is given as

$\sigma {_{y }}= \sigma {_{o }} + \frac{ky}{d^{0.5}}$

Here Ky is the strength coefficient and the $\sigma {_{o }}$ is the stress at which dislocation starts and d is the size of the grain. As the grain size increases. The term $Ky/d^{0.5}$ becomes smaller and thus yield stress decreases.

Note: the grain boundary is the obstruction to the movement of dislocation . As the grain size increases, there will be less obstructions for the dislocation to move in a crystal. less obstructions to dislocation movements translates to a reduced value of strength