MAT-38

Orowan looping stress

τ = G b / λ. Bypass of impenetrable particles by dislocation loops.

Reading speed

StrengtheningOrowan 1948

Governing equation

\tau=\dfrac{G b}{\lambda}

where

G: Shear modulus (GPa)
b: Burgers vector (nm)
\lambda: Particle spacing (nm)
\tau: Orowan 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-38 — Orowan looping stress) is the form associated with Orowan 1948. Working symbols: $G$ , $b$ , $\lambda$ $\rightarrow$ $\tau$ . Orowan: a dislocation bows between particles spaced λ and leaves a loop. The critical stress is ~Gb/λ.

Purpose

Purpose: compute

\tau

from

G

b

\lambda

in Materials via

\tau=\dfrac{G b}{\lambda}

τ = G b / λ. Bypass of impenetrable particles by dislocation loops. Use it when a real materials question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

G = 80.000\,\mathrm{GPa}

b = 0.255\,\mathrm{nm}

\lambda = 80.000\,\mathrm{nm}

, the governing relation

\tau=\dfrac{G b}{\lambda}

yields

\tau = 255.00\,\mathrm{MPa}

. Two particles, a bowed line, a leftover loop. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Shear modulus G80 GPaBurgers vector b0.255 nmParticle spacing \lambda80 nm

Outputs

Orowan stress \tau255.00 MPa

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

Two particles, a bowed line, a leftover loop.

Orowan: a dislocation bows between particles spaced λ and leaves a loop. The critical stress is ~Gb/λ.

Reading speed

Watch on YouTube