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sci.disocation-density-estimate Calculator
Calculates dislocation density from X-ray diffraction peak broadening or etch pit counts, and estimates yield strength via the Taylor hardening relation. Annealed metals have dislocation densities ~10¹⁰ m⁻²; heavily cold-worked metals reach 10¹⁵–10¹⁶ m⁻² — Taylor hardening: Δσ = αGb√ρ.
Inputs
Yield Strength Mpa
Stress at which permanent deformation begins. Design loads should stay below this — apply a safety factor of 1.5–3×.
Shear Modulus Gpa
Reference formula or conversion factor shown for context.
Burgers Vector Nm
Reference formula or conversion factor shown for context.
Results
dislocation density ρ (m⁻²)
The value at the specified point or condition.
ρ (cm⁻²)
Reference formula or conversion factor shown for context.
Taylor hardening: σy=MαGb√ρ
Sample size or count used in the calculation.
annealed metal
Sample size or count used in the calculation.
heavily cold-worked
Reference formula or conversion factor shown for context.
b for FCC metals (Cu)
Reference formula or conversion factor shown for context.