MAT-42

Griffith crack

Brittle fracture of a through-crack.

Reading speed

GoverningGriffith crack

Governing equation

\sigma_f=\sqrt{2E\gamma_s/(\pi a)}

$a \in \left[0.01, 4\right]$

where

E: E (GPa)
g: g (J/m²)
a: a (mm)
sf: Griffith crack (MPa)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

00:0 / 00:08

①

Governing law — red

\sigma_f=\sqrt{2E\gamma_s/(\pi a)}

$a \in \left[0.01, 4\right]$

$a = 0.01$ $sf = 211.1$

Along the curve

②

Domain of the variable — blue

a_{\min} = 0.01,\quad a_{\max} = 4

$a \in \left[0.01, 4\right]$

$a = 0.01$ $a = 0.01$

Along the curve

③

Response curve — green

\sigma_f=\sqrt{2E\gamma_s/(\pi a)}

$a \in \left[0.01, 4\right]$

$a = 0.01$ $sf = 211.1$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}sf}{\mathrm{d}a}

$a \in \left[0.01, 4\right]$

$a = 0.035$ $sf^{\prime} = -2491.7$

Along the curve

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-42 — Griffith crack) is the form associated with Griffith crack. Working symbols: $E$ , $g$ , $a$ $\rightarrow$ $sf$ . Brittle fracture of a through-crack. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

sf

from

E

g

a

in Materials via

\sigma_f=\sqrt{2E\gamma_s/(\pi a)}

Brittle fracture of a through-crack. Use it when a real materials question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

E = 70.000\,\mathrm{GPa}

g = 10.000\,\mathrm{J/m^{2}}

a = 0.200\,\mathrm{mm}

, the governing relation

\sigma_f=\sqrt{2E\gamma_s/(\pi a)}

yields

sf = 47.203\,\mathrm{MPa}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

E E70 GPag g10 J/m²a a0.2 mm

Outputs

Griffith crack sf47.203 MPa

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Brittle fracture of a through-crack. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube