How to Calculate Grain Size
What is Grain Size?
Grain size affects mechanical properties: smaller grains = higher strength, higher hardness (Hall-Petch relationship).
Formula
Calculate strengthening effect using Hall-Petch: σ = σ₀ + k/√d
Step-by-Step Guide
- 1Input grain size (average diameter)
- 2Calculate strengthening effect using Hall-Petch: σ = σ₀ + k/√d
- 3Results show predicted yield strength
Worked Examples
Input
Grain size 1 μm vs. 100 μm
Result
1 μm ~ 50% stronger (Hall-Petch effect)
Common Mistakes to Avoid
- ✕Assuming smaller always better (sometimes reduces ductility)
- ✕Not accounting for material-specific k value
Frequently Asked Questions
How do you control grain size?
Cool rate (slower = larger grains), deformation (refines grains), annealing temperature.
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