MAT-27

Fracture toughness KIc

KIc = Y σ √(π a). Critical stress-intensity in mode I.

Reading speed

FractureIrwinASTM E399

Governing equation

K_{Ic}=Y\sigma\sqrt{\pi a}

$a \in \left[0.1, 40\right]$

where

Y: Geometry factor (—)
\sigma: Remote stress (MPa)
a: Crack length (mm)
K: Stress intensity (MPa√m)

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.

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①

Governing law — red

K_{Ic}=Y\sigma\sqrt{\pi a}

$a \in \left[0.1, 40\right]$

$a = 0.1$ $K = 2.382$

Along the curve

②

Domain of the variable — blue

a_{\min} = 0.1,\quad a_{\max} = 40

$a \in \left[0.1, 40\right]$

$a = 0.1$ $a = 0.1$

Along the curve

③

Response curve — green

K_{Ic}=Y\sigma\sqrt{\pi a}

$a \in \left[0.1, 40\right]$

$a = 0.1$ $K = 2.382$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}K}{\mathrm{d}a}

$a \in \left[0.1, 40\right]$

$a = 0.351$ $K^{\prime} = 6.898$

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-27 — Fracture toughness KIc) is the form associated with Irwin · ASTM E399. Working symbols: $Y$ , $\sigma$ , $a$ $\rightarrow$ $K$ . Irwin restated Griffith in terms of a stress-intensity factor K. Fracture when K reaches the material toughness KIc.

Purpose

Purpose: compute

K

from

Y

\sigma

a

in Materials via

K_{Ic}=Y\sigma\sqrt{\pi a}

KIc = Y σ √(π a). Critical stress-intensity in mode I. Use it when a real materials question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

Y = 1.120\,\mathrm{—}

\sigma = 120.000\,\mathrm{MPa}

a = 4.000\,\mathrm{mm}

, the governing relation

K_{Ic}=Y\sigma\sqrt{\pi a}

yields

K = 15.07\,\mathrm{MPa√m}

. A cracked plate, a K fan, a critical tick. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Geometry factor Y1.12 —Remote stress \sigma120 MPaCrack length a4 mm

Outputs

Stress intensity K15.07 MPa√m

Reading speed

Watch on YouTube

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Narration of this film

A cracked plate, a K fan, a critical tick.

Irwin restated Griffith in terms of a stress-intensity factor K. Fracture when K reaches the material toughness KIc.

Reading speed

Watch on YouTube