In crystalline materials, grain boundaries act as barriers to dislocation movement, which is a primary mechanism of deformation. When the grain size is reduced, the number of grain boundaries increases, thereby impeding the movement of dislocations and resulting in higher material strength. This is encapsulated in the Hall-Petch equation:
σ_y = σ_0 + k * d^(-1/2)
Here, σ_y is the yield strength, σ_0 is the intrinsic material strength, k is a material-specific constant, and d is the average grain diameter.
