HallPetchin
HallPetchin is a theoretical model in materials science that describes the relationship between grain size and the yield strength of a polycrystalline material. It proposes that as the grain size of a metal decreases, its yield strength increases. This phenomenon is attributed to the presence of grain boundaries, which act as obstacles to the movement of dislocations, the primary mechanism of plastic deformation in metals.
The Hall-Petch relationship is mathematically expressed as: σ_y = σ_0 + k_y * d^(-1/2)
where σ_y is the yield strength, σ_0 is the friction stress (related to the intrinsic resistance to
This model is widely applied in understanding and engineering the mechanical properties of metals and ceramics.