Griffith Rift

The Griffith crack is a straight internal crack that is located in an infinitely extended disc . The Griffith crack represents the basic crack model in fracture mechanics and was named after Alan Arnold Griffith . Using this crack model, Griffith carried out fundamental theoretical analyzes of the crack and crack propagation. The Griffith crack is mainly used in theoretical considerations in linear-elastic fracture mechanics .

Load cases

Disc under tensile load

Griffith crack under tensile stress.

For a crack of length 2a in a disk under tensile stress (stress perpendicular to the crack plane) Griffith determined the rate of energy release ${\displaystyle \sigma _{\infty }}$

${\displaystyle G={\frac {2\pi \sigma _{\infty }^{2}a}{E'}}=4\gamma }$

With ${\displaystyle E'=\left\{{\begin{array}{ll}E&{\text{: ebener Spannungszustand (ESZ)}}\\\displaystyle {\frac {E}{(1-\nu )^{2}}}&{\text{: ebener Verzerrungszustand (EVZ).}}\end{array}}\right.}$

Where:

• ${\displaystyle E}$ the modulus of elasticity
• ${\displaystyle \nu }$ the Poisson's ratio
• ${\displaystyle \gamma }$ the specific surface energy

The stress intensity factor for crack opening mode I is calculated as follows

${\displaystyle K_{\mathrm {I} }=\sigma _{\infty }\cdot {\sqrt {\pi \cdot a}}}$.

Washer under shear stress

Griffith crack under shear stress.

The stress intensity factor for crack opening mode II under shear stress is calculated as follows ${\displaystyle \tau _{\infty }}$

${\displaystyle K_{\mathrm {II} }=\tau _{\infty }\cdot {\sqrt {\pi \cdot a}}}$.

meaning

Comparing the above K-factors for modes I and II with the general equation for the stress intensity factor for cracks in components

${\displaystyle \left\{{\begin{matrix}K_{\mathrm {I} }\\K_{\mathrm {II} }\end{matrix}}\right\}=\left\{{\begin{matrix}\sigma \\\tau \end{matrix}}\right\}\cdot {\sqrt {\pi \cdot a}}\cdot \left\{{\begin{matrix}Y_{\mathrm {I} }\\Y_{\mathrm {II} }\end{matrix}}\right\}}$,

this shows that the geometry factors for the Griffith crack are and . Thus, the stress intensity factors and for cracks in any components can be normalized to the stress intensity factors of the Griffith crack. ${\displaystyle Y_{\mathrm {I} }=1}$ ${\displaystyle Y_{\mathrm {II} }=1}$ ${\displaystyle K_{\mathrm {I} }}$ ${\displaystyle K_{\mathrm {II} }}$

See also

• Airy's stress function # The Griffith crack : Stress field around the crack in the linear, flat elastostatics.

literature

• TL Anderson: Fracture Mechanics; Fundamentals and Applications . CRC Press, Boca Raton 2004, ISBN 978-0849316562 .
• D. Gross, Th. Seelig: fracture mechanics with an introduction to micromechanics . 5th edition, Springer, Berlin 2011, ISBN 978-3-642-10196-0 .
• Kuna, M .: Numerical stress analysis of cracks - finite elements in fracture mechanics . 2nd edition, Vieweg + Teubner 2010, ISBN 978-3-8348-1006-9 .

Web links

• Crack, Fracture, and Fatigue (accessed September 13, 2018)
• Fundamentals of fracture mechanics (accessed on September 13, 2018)
• Paths and goals of the concepts in fracture mechanics (accessed on September 13, 2018)
• Plasticity and fracture mechanics (accessed on September 13, 2018)
• On the application of fracture mechanics concepts for modeling the crack-bridging effect of rovings (accessed on September 13, 2018)