GRIFFITH's Criteria

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GRIFFTH`s criteria

GFRIFFITH`s fracture criterion

The energy balance in the case of crack propagation in an infinitely extended plate with finite thickness was first discussed by Griffith [1]. According to GRIFFITH, crack propagation occurs when the elastic distortion energy W_e released by the elongation of the initial crack is equal to or greater than the surface energy W_o required to form the fracture surfaces, i.e.

$W_{e}\,\geq \,W_{o}$

(1)

The criterion for unstable crack propagation is

${\frac {dW_{e}}{da}}\,\geq \,{\frac {dW_{o}}{da}}$

(2)

Elastic distortion energy W_e is assumed,

$W_{e}\,=\,{\frac {\pi \sigma ^{2}a^{2}}{E}}$

(3)

with

a		Crack length
E		Elastic modulus

while the surface energy W_o is assumed for both fracture surfaces.

$W_{o}\,=\,4\,a\,\gamma _{o}$

(4)

with

$\gamma$o

Surface tension

amounts to.

The criterion of crack propagation then leads to

${\frac {2\,a\,\pi \,\sigma ^{2}}{E}}\,\geq \,4\,\gamma _{o}$

(5)

Energy balance of unstable crack propagation

Under the conditions of Eq. (5), an existing crack propagates in an unstable manner, i.e. without external energy input (Figure).

Figure:

Energy balance during unstable crack propagation [2] a) Surface energy b) Elastic distortion energy c) Total energy

The stress required for crack propagation is obtained as

$\sigma _{c}\,=\,{\sqrt {\frac {2E\gamma _{o}}{\pi a}}}$

(6)

while the corresponding critical crack length (Griffith length) is a_o

$a_{o}\,=\,{\frac {2E\gamma _{o}}{\pi \sigma ^{2}}}$

(7)

Experimental investigations have confirmed the usefulness of the relationship for critical stress and crack length in extremely brittle material behaviour [3].

The two basic hypotheses of the GRIFFITH criterion are [4]:

Hypothese 1:	The crack propagates in the direction of the crack.
Hypothese 2:	Crack growth occurs if Je ≥ 2 γo with Je – elastic component. The crack propagation is unstable if the following applies:
	${\frac {\delta K_{I}}{\delta a}}\,\geq \,0$

See also

• Crack model according to GRIFFITH
• Griffith, Alan Arnold
• Crack

References

[1]	Griffith, A. A.: The Phenomena of Rupture and Flow in Solids. Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, Vol. 221 (1921) pp. 163 – 198. JSTOR; DOI: https://www.jstor.org/stable/91192
[2]	Blumenauer, H.: Bruchmechanik – Grundlagen, Prüfmethoden, Anwendungsgebiete. Deutscher Verlag für Grundstoffindustrie, Leipzig (1973) pp. 37–38 (see AMK-Library under E 28)
[3]	Blumenauer, H.: Technische Bruchmechanik. Deutscher Verlag für Grundstoffindustrie, Leipzig (1987) 2nd Edition p. 22 (ISBN 3-342-00096-1; see AMK-Library under E 29-2)
[4]	Sähn, S., Göldner, H.: Bruch- und Beurteilungskriterien in der Festigkeitslehre. Fachbuchverlag, Leipzig Köln (1993) 2nd Edition, p. 139 (ISBN 3-343-00854-0; see AMK-Library under E 26)

Weblinks

• Wikipedia– The Free Encyclopedia: Griffith, Alan Arnold https://en.wikipedia.org/wiki/Alan_Arnold_Griffith
• 100 Jahre Bruchmechanik: Alan Arnold Griffith. DVM-Nachrichten N 71 • Frühjahr 2020 p. 9 Download als PDF