Equations · equation
Hall–Petch Relationship
Materials Science · 1951
- Equation
- σ_y = σ_0 + k_y·d^(−1/2)
- Field
- Materials Science
- Named After
- E. O. Hall and N. J. Petch
- Year
- 1951
Symbols
σ_y the yield stress · σ_0 the friction stress a dislocation feels in the lattice alone · k_y a constant of the material · d the mean grain diameter
Significance
Grain boundaries stop dislocations, so finer grain is stronger — by the inverse square root, so halving the grain size raises the boundary's share of the yield stress by 40 %. It is the one strengthening mechanism that raises toughness alongside strength instead of trading one for the other, which is why steel is normalised after forging, why niobium and vanadium earn their price in structural plate, and why an overheated part is a weak one. It reverses below about 20 nm, where the boundaries begin to slide instead of blocking.
Referenced by
equation
skill
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