Every other calculator takes the grain size you measured and divides by its square root. For a quenched and tempered steel that understates the term by about 2.2×, because the barrier a dislocation meets in martensite is the packet — finer than the prior-austenite grain you measured. This one uses the effective size.
Grain size as measured — prior-austenite for transformed structures.
Defaults are the values METALLAI uses for that phase.
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Hall–Petch counts barriers to dislocation motion. In a single-phase ferrite that barrier is the grain boundary you etched and measured. In a transformed structure it is not: one prior-austenite grain contains several martensite packets, and it is the packet boundary — a high-angle boundary — that stops a dislocation.
| Structure | Effective barrier | deff | Floor | k used here |
|---|---|---|---|---|
| Ferrite / austenite | the grain boundary itself | d | 1 µm | 600 / 400 |
| Pearlite | colony boundary | 0.50 × d | 5 µm | 600 |
| Bainite | lath boundary | 0.30 × d | 3 µm | 600 |
| Martensite | packet / block boundary | 0.20 × d | 2 µm | 300 |
| Duplex | phase boundary | d | 1 µm | 500 |
Below roughly 20–30 nm the relation inverts: deformation switches from dislocation pile-up to grain-boundary sliding, and further refinement makes the material weaker. That is far below any normal engineering grain size, but it is why extrapolating the curve toward zero produces strengths no steel has ever reached. This calculator will not stop you going there — it will tell you when you have.
Lattice friction, solid solution, grain boundary, precipitation and dislocation strengthening — each as its own number, for your composition and your process route, with the uncertainty on the total.
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