Hall–Petch relationship
estimates the yield strength change of polycrystalline materials based on grain size.
symbols, variables and units
σ_y,σ₀：Pa；d：m；k_y：Pa·m½。
applicable conditions and boundaries
Empirical relationship, material and grain range need to be calibrated; nanocrystals can deviate.
formula source code
The following is a copyable LaTeX expression.
\sigma_y=\sigma_0+k_y d^{-1/2}Reference and Extended Learning
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Hall Petchdie