MAT-28

Taylor dislocation forest

τ = α G b √ρ. Forest hardening from dislocation density.

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StrengtheningTaylor 1934

Governing equation

\tau=\alpha G b\sqrt{\rho}

where

\alpha: Taylor α (—)
G: Shear modulus (GPa)
b: Burgers vector (nm)
\rho: Dislocation density (1/m²)
\tau: Flow stress (MPa)

Lecture brief

Historical brief

Hooke (1678), Hall–Petch grain size, Arrhenius activation and Paris fatigue-crack growth are the spine of materials selection. The sheets relate stress, microstructure and life. This sheet (MAT-28 — Taylor dislocation forest) is the form associated with Taylor 1934. Working symbols: $\alpha$ , $G$ , $b$ , $\rho$ $\rightarrow$ $\tau$ . Taylor related flow stress to the mean spacing 1/√ρ of a dislocation forest, times G b.

Purpose

Purpose: compute

\tau

from

\alpha

G

b

\rho

in Materials via

\tau=\alpha G b\sqrt{\rho}

τ = α G b √ρ. Forest hardening from dislocation density. Use it when a real materials question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\alpha = 0.300\,\mathrm{—}

G = 80.000\,\mathrm{GPa}

b = 0.255\,\mathrm{nm}

\rho = 1.000e+12\,\mathrm{1/m^{2}}

, the governing relation

\tau=\alpha G b\sqrt{\rho}

yields

\tau = 6.12\,\mathrm{MPa}

. A tangle of lines, a density ρ, a shear tick. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Taylor α \alpha0.3 —Shear modulus G80 GPaBurgers vector b0.255 nmDislocation density \rho1000000000000 1/m²

Outputs

Flow stress \tau6.12 MPa

Reading speed

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Narration of this film

A tangle of lines, a density ρ, a shear tick.

Taylor related flow stress to the mean spacing 1/√ρ of a dislocation forest, times G b.

Reading speed

Watch on YouTube