Effective Crack Length

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Effective crack length

The environment of the crack tip

In the case of macroscopically brittle fracture behaviour, plastic deformation often occurs due to stress concentration in front of the crack tip, i.e. the formation of a plastic zone. Assuming that the energy dissipated during crack growth in the region around the crack tip is proportional to the surface area (see also: fracture surface). The radius of the plastic zone is regarded as a fictitious extension of the crack. The consideration of this plastic zone, which is small in comparison to the component dimensions and the ligament (cross-section before the crack), lead Irwin in 1952 to a significant extension of the GRIFFITH crack model and is now referred to as the crack model according to IRWIN and Mc CLINTOCK.

LEFM with small-scale yielding

By taking the plastic zone into account when describing toughness, the transition from linear-elastic fracture mechanics (LEFM) to LEFM with small-scale yielding is formally completed. If the above conditions are fulfilled, the true crack length a (or initial crack length) and the radius of the plastic zone r_pl are combined to form an effective crack length a_eff.

$a_{eff}=a+r_{pl}$

(1)

The plastic zone is often visible on the fracture surface in the form of a fracture mirror as an expression of stable crack growth and can be detected using light or scanning electron microscopy (SEM). An example is shown in the Figure.

Figure:

Fracture survace of an ethylene/propylene random copolymer with 4 mol% ethylene (a) and schematic representation of the characteristic areas (b)

See also

• Initial crack length
• Plastic zone
• Notch
• Notching
• Fracture surface

References

• Blumenauer, H., Pusch, G.: Technische Bruchmechanik, Deutscher Verlag für Grundstoffindustrie, Leipzig Stuttgart (1993), (ISBN 3-342-00659-5; see AMK-Library under E 29-3)
• Grellmann, W., Seidler, S. (Eds.): Kunststoffprüfung. Carl Hanser Verlag, Munich (2024) 4th Edition, p. 244 (ISBN 978-3-446-44718-9; E-Book: ISBN 978-3-446-48105-3; see AMK-Library under A 23)