// multi-utility computation suite · offline · instant · precise
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sci.grain-size-hall-petch Calculator
Calculates the increase in yield strength with decreasing grain size using the Hall-Petch relation: σ_y = σ₀ + k/√d. Refining grain size from 100 µm to 1 µm can double steel yield strength — this is exploited in HSLA steels through controlled rolling and cooling.
Inputs
Yield Strength Fine Mpa
Stress at which permanent deformation begins. Design loads should stay below this — apply a safety factor of 1.5–3×.
Yield Strength Coarse Mpa
Stress at which permanent deformation begins. Design loads should stay below this — apply a safety factor of 1.5–3×.
Grain Size Fine Um
Reference formula or conversion factor shown for context.
Grain Size Coarse Um
Reference formula or conversion factor shown for context.
Results
Hall-Petch slope ky (MPa·m^0.5)
The gradient -- rise divided by run. In finance, rate of change per unit time.
friction stress σ₀ (MPa)
Internal force per unit area (Pa or MPa). Must stay below yield strength in service. Beyond yield: permanent deformation. Beyond tensile strength: fracture.
Hall-Petch: σy = σ₀ + ky/√d
Reference formula or conversion factor shown for context.
ky for low-carbon steel
Sample size or count used in the calculation.
grain refinement methods
The recommended calculation method or analytical approach for these conditions.