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Hall-Petch strengthening: yield strength = σ₀ + k·d^(-1/2), where d is grain diameter; primary strengthening mechanism.
ステップバイステップガイド
- 1Input material constants σ₀ and k
- 2Vary grain size
- 3Calculate predicted yield strength
解いた例
入力
Steel: σ₀ = 50 MPa, k = 0.8 MPa√mm
結果
1mm grains → 50.8 MPa, 0.01mm → 80 MPa strength increase
避けるべきよくある間違い
- ✕Using wrong units for grain size
- ✕Applying beyond material's valid range
よくある質問
Is Hall-Petch always linear?
Approximately yes; breaks down at very small grain sizes (<100 nm).
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