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כיצד לחשב את Hall Petch

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Hall-Petch strengthening: yield strength = σ₀ + k·d^(-1/2), where d is grain diameter; primary strengthening mechanism.

מדריך שלב אחר שלב

  1. 1Input material constants σ₀ and k
  2. 2Vary grain size
  3. 3Calculate predicted yield strength

Worked Examples

קלט
Steel: σ₀ = 50 MPa, k = 0.8 MPa√mm
תוצאה
1mm grains → 50.8 MPa, 0.01mm → 80 MPa strength increase

Common Mistakes to Avoid

  • Using wrong units for grain size
  • Applying beyond material's valid range

Frequently Asked Questions

Is Hall-Petch always linear?

Approximately yes; breaks down at very small grain sizes (<100 nm).

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