Geometry Function

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Geometry function

The geometry function f (a/W)

The finite geometry of each component and test specimen, as well as the crack geometry, are taken into account in fracture mechanics material testing by introducing a geometry function f (a/W), whereby the stress intensity factor K introduced by Irwin can be written in the form

$K=\sigma _{N}\cdot \left(\pi a\right)^{\frac {1}{2}}\cdot f\left(a/W\right)$

The functions f (a/W) have been calculated for a large number of fracture mechanics test specimens. The figure shows the dimensions of test specimens used primarily for plastics. For an infinitely extended test specimen and the

limiting case of a crack with a notch radius ~ 0 is f (a/W) = 1.

At the beginning of unstable crack propagation, the stress intensity factor reaches a critical value K_Ic, which is referred to as fracture or crack toughness and has the dimension MPa mm^1/2. The three most commonly used test specimens are the SENB-specimen, the SENT-specimen, and the CT-specimen.

Selected test specimen shapes

The geometry functions f (a/W) have been calculated for a number of fracture mechanics test specimens. Table 1 shows the dimensions of test specimen shapes that are preferred for plastics in testing practice.

Table 1: Summary of frequently used test specimen shapes with their dimensions, the corresponding equations for calculating fracture toughness, and the geometric functions.

See also

• Fracture safety criterion
• CT-specimen
• Geometry criterion
• Plastic component
• SENB-specimen
• SENT-specimen

References

• Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser, Munich (2022); 3rd Edition, pp. 233/234 (ISBN 978-1-56990-806-8; E-Book: ISBN 978-1-56990-807-5; see AMK-Library under A 22)
• Anderson, T. L.: Fracture Mechanics. Fundamentals and Applications. 3rd Edition, CRC Press Boca, Raton (2005) (ISBN 978-0849342608; see AMK-Library under E 8-2); DOI: https://doi.org/10.1201/9781315370293
• Irwin, G. R.: Analysis of Stress and Strains Near the End of a Crack Traversing a Plate. J. Appl. Mech. 24 (1957) 361; https://doi.org/10.1115/1.4011547
• Tada, H., Paris, P. C., Irwin, G. R.: The Stress Analysis of Cracks Handbook. 3rd Edition, ASME Press, New York (2000) (ISBN 978-1-8605-8304-9); https://doi.org/10.1115/1.801535