Hall-Petch Strength Calculator
Yield strength from grain size — why fine grain wins.
Refining steel from 50 µm to 5 µm grains adds ~230 MPa of yield — no alloying, no quenching. Grain boundaries block dislocations; more boundary, more blocking. Breaks down below ~20 nm.
Formula
Hall-Petch Strength Calculator is a free hall petch for design engineers, metallurgists and QA inspectors — instant, accurate and 100% client-side, with the governing formula and reference shown next to the result so the number can be defended, not just quoted.
About Hall-Petch Strength Calculator
Yield strength from grain size — why fine grain wins. The calculation implements σ_y = σ₀ + k_y/√d (Hall (1951), Petch (1953)). Refining steel from 50 µm to 5 µm grains adds ~230 MPa of yield — no alloying, no quenching. Grain boundaries block dislocations; more boundary, more blocking. Breaks down below ~20 nm.
How to use Hall-Petch Strength Calculator
- 1Enter Friction stress σ₀ in MPa (Mild steel ~70).
- 2Enter Hall-Petch coefficient k_y in MPa·√m (Steel ~0.74 · Al ~0.07 (weak effect)).
- 3Enter Grain diameter in µm.
- 4Read Yield strength instantly — no submit button needed.
Why use Hall-Petch Strength Calculator?
- ✓Implements the standard formula — σ_y = σ₀ + k_y/√d
- ✓Reference cited on-page: Hall (1951), Petch (1953)
- ✓Live worked example: the substitution recomputes from your numbers
- ✓Runs entirely in your browser — nothing uploaded, free forever
Frequently asked questions
What formula does the Hall-Petch Strength Calculator use?+
It computes σ_y = σ₀ + k_y/√d, per Hall (1951), Petch (1953). The formula is displayed under the result along with a worked example substituted with your own inputs.
What should I keep in mind when using this calculator?+
Refining steel from 50 µm to 5 µm grains adds ~230 MPa of yield — no alloying, no quenching. Grain boundaries block dislocations; more boundary, more blocking. Breaks down below ~20 nm.
Where do the material property defaults come from?+
Defaults are standard handbook values (ASM, manufacturer datasheets, the cited standard). Always substitute certified values from your material's test certificate for critical work.
Is the Hall-Petch Strength Calculator free to use?+
Yes — completely free, no sign-up, no limits. It runs client-side in your browser, so inputs stay private and results are instant even on slow connections.
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